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https://calendar.math.illinois.edu/?year=2005&month=02&day=02&interval=day | Department of
# Mathematics
Seminar Calendar
for events the day of Wednesday, February 2, 2005.
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events for the
events containing
Questions regarding events or the calendar should be directed to Tori Corkery.
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Wednesday, February 2, 2005
3:00 pm in 441 Altgeld Hall,Wednesday, February 2, 2005
#### The Étale Slice Theorem
###### Bin Wang (Dept. of Mathematics, UIUC)
Abstract: We will consider a linearly reductive group acting on an affine variety. We will prove an equivariant Zariski main theorem and show that every closed orbit has an étale neighborhood admitting a slice decomposition.
4:00 pm in 341 Altgeld Hall,Wednesday, February 2, 2005
#### Hall's theorem on finitely generated subgroups of free groups
###### Ilya Kapovich (UIUC Math)
4:00 pm in 245 Altgeld Hall,Wednesday, February 2, 2005
#### Loop spaces and Langlands duality
###### David E. Nadler (University of Chicago)
Abstract: Langlands' vision of number theory has had a tremendous impact on the representation theory and topology of loop groups. In particular, deep results about the structure of loop groups involve the Langlands dual group. In this talk, I will describe a project, joint with D. Gaitsgory (U. of Chicago), devoted to the topology of loop spaces of more general varieties with "lots of symmetry". We show that the singularities of the loop space of such a variety may be described in terms of a dual group. The dual group also governs many aspects of the original variety, such as its differential operators and compactifications. (The talk will not assume any prior knowledge.) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5632520914077759, "perplexity": 496.51448947191005}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030336978.73/warc/CC-MAIN-20221001230322-20221002020322-00780.warc.gz"} |
http://www.maa.org/press/periodicals/convergence/when-a-number-system-loses-uniqueness-the-case-of-the-maya-non-uniqueness | # When a Number System Loses Uniqueness: The Case of the Maya - Non-uniqueness
Author(s):
Pedro J. Freitas (Universidade de Lisboa) and Amy Shell-Gellasch (Beloit College)
When converting from a base $10$ number to a Mayan number using the greedy division algorithm, place values are filled from left to right, that is from largest place value down. As noted at the beginning, this process leads to a unique expression in a “pure'' base system such as ours. But the Mayan system is not pure; the $18$ makes for some interesting choices, depending on whether you think of building a number from the top or from the bottom.
Sometimes it is easier to think of a base $b$ place-value number as made up of bins. Each bin can have zero to $b-1$ sets (or bags), each containing a full complement of the next lower place value. For example, in the base $10$ number $253,$ the left bin has $2$ sacks, each with $10$ bags of $10$ counters; the next bin to the right contains $5$ bags, each with $10$ counters; and the last bin on the right contains $3$ individual counters. So if a number is thought of as being filled from the top, as with the greedy algorithm, as many sets of the largest power of the base as possible are put in the left bin. Then from the remainder, as many complete sets of the next lower power as possible are put in the next bin, and so on.
On the other hand, if a number is thought of not in terms of sets of powers of the base, but as piles of individual counters, a natural method would be to start putting counters in a bin starting on the right with the units place. As soon as a set of size $b$ is obtained, a single counter to represent a set of size $b$ is put in the next bin to the left (the second bin from the right), the contents of the right bin are discarded, and one resumes putting counters in the right bin.
This is the practical procedure suggested by the second (bottom-up) algorithm we presented. This is also, in essence, how calculations are done on an abacus. When one column is full, a single counter on the next wire to the left is moved up and the previous column is cleared. In addition and multiplication we call this carrying (to the next highest power). For a pure base system, either method (filling from the top or the bottom) will give you the same encoded number.
But in the Mayan system, the third and higher place values are not pure. The third place is $18\times20.$ If, in a certain expression, the number in the second place (the $20$'s place) is $18$ or $19,$ all or part of it could be carried over to the third (or $18\times20$’s) place. Or if the second place is only a $0$ or a $1,$ then an $18\times20$ can be carried backward from the third place down to the second, making the second digit now $18$ or $19.$ Thus the same natural number can be encoded in two different ways in the Mayan system. We will make this explicit in a moment, but first some examples are in order. Please note the following. In a pure number system, when a place value is filled, $1$ is carried to the next highest place and the lower bin is emptied. This is not the case in the second place of the Mayan numbers. When the second place is full, it has $20$ sets of $20,$ but the third place is $18\times20.$ So the whole $20\times20$ cannot be carried over to the third place; only $18\times20$ can be carried, leaving $2\times20$ in the $20$'s place. If the second place is $18,$ then $18\times20$ is carried and the place is emptied; if the second place has $19$ or is full with $20,$ then when $18\times20$ is carried, a $1$ or a $2$ must be left behind in the second place.
Consider the Mayan number $4.8.18.9$. In expanded form, this would be $4(18\times20^2)+8(18\times20)+18(20)+9.$ Notice that the second and third places are both multiples of $18\times20.$ So the whole $18\times20$ in the second place can be carried over as one unit in the third place, resulting in the new, but equivalent Mayan number $4.9.0.9$. Both of these representations equal $32049$ in base $10.$ See Figure 4 for two more (yet again amazing) serpent numbers depicting these two equivalent numbers. Likewise the Mayan number $4.8.19.9$ could also be written as $4.9.1.9$ by carrying from the second to the third place.
Figure 4. $4.8.18.9$ on the left, $4.9.0.9$ on the right, both equivalent to $32049$ base $10.$
Working the same two examples the other way, if you have the Mayan numbers $4.9.0.9$ or $4.9.1.9,$ one unit of $18\times20$ from the third place can be carried down to add $18$ to the second place, giving $4.8.18.9$ and $4.8.19.9,$ respectively.
To summarize, given a Mayan number of the form $a_k .\ldots.a_2.a_1.a_0,$ where $a_1=18$ or $19,$ an equivalent Mayan number would be $a_k.\cdots.(a_2+1).(a_1-18).a_0,$ with a $1$ carried to the fourth place as usual if $a_2 + 1 = 20.$ Conversely, if a Mayan number is of the form $a_k.\cdots.a_2.a_1.a_0,$ where $a_2>0$ and $a_1=0$ or $1,$ then the equivalent Mayan number would be $a_k.\cdots.(a_2-1).(a_1+18).a_0.$
Outside of these two cases, any other combination of numerals in a Mayan number is unique. In other words, if we can find an expression for $n$ in which $a_1=18$ or $19,$ we have two expressions for $n.$ If this does not happen, the expression is unique. (Of course, any other non-pure place-value system would violate uniqueness. However, the Mayan system is the only non-pure system we are aware of.)
To check this, suppose $n$ is a number that has no expression (in the Mayan system) in which the second place is $18$ or $19.$ Take two possible expressions:
$n=$ $a_0+a_1\,(20)+a_2\,(18\times20)+a_3\,(18\times20^2)+\cdots+a_k\,(18\times20^{k-1})$ $=$ $a^{\prime}_0+a^{\prime}_1\,(20)+a^{\prime}_2\,(18\times20)+a^{\prime}_3\,(18\times20^2)+\cdots+a^{\prime}_t\,(18\times20^{t-1}).$
According to our assumption, $0\leq a_1,a^{\prime}_1\leq 17,$ and for $i\neq 1,$ $0\leq a_i\leq 19.$
To start with, we have $a_0=a^{\prime}_0,$ by the same argument used in the general proof. When we now take $n_1=(n-a_0)/20,$ we get, using the very same argument, $a_1=a^{\prime}_1,$ since $a_1-a^{\prime}_1$ is both a multiple of $18$ and a number in absolute value smaller than $18.$
We now take $n_2=(n_1-a_1)/18$ and get equality of all other $a_i$'s, and $k=t,$ since now we are dealing with a number in pure base $20.$
Thus for all cases when the second place number cannot be chosen to be $18$ or $19,$ the Mayan notation is unique.
So, for which base $10$ natural numbers is the Mayan number not unique? As we said above, this happens when the second numeral can be chosen to be $18$ or $19.$ Then we can carry one $18\times20$ to the next higher place. The smallest such numbers are found by assuming all higher place values are zero. Then we have the range of natural numbers $[360,399]$ corresponding to the Mayan numbers from $18.0=1.0.0$ to $19.19=1.1.19,$ for which the Mayan number is not unique. Other intervals of non-unique Mayan numbers would be found by filling in non-zero numerals in any and all of the higher places while retaining the restriction on the second place. The above ideas make for great open questions in many different classes, from elementary school through college courses, as long as the Mayan calendric number system has been introduced.
Pedro J. Freitas (Universidade de Lisboa) and Amy Shell-Gellasch (Beloit College), "When a Number System Loses Uniqueness: The Case of the Maya - Non-uniqueness," Convergence (June 2012), DOI:10.4169/loci003883 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8019762635231018, "perplexity": 311.8927470254363}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128320003.94/warc/CC-MAIN-20170623045423-20170623065423-00219.warc.gz"} |
https://www.ch.cam.ac.uk/person/ajk1 | # Research interests
Organic reaction mechanisms in more-or-less aqueous solution: in the general context of mechanism and efficiency in enzyme catalysis. The approach is aimed at a fundamental understanding of chemical reactivity. Enzymes do what is ordinary chemistry in their extraordinary environments, using familiar mechanisms and taking advantage of textbook stereoelectronic effects.1 They work by binding and selectively stabilising transition states for the reactions they catalyse, so the general objective is to define both the structure of a given transition state (the mechanism) and how it is bound (efficiency).2 We can be confident that we really understand enzymes only when we can reproduce their properties – especially their efficiency – in artificial catalysts.
We know that functional groups (FG's) must be brought together very precisely in the enzyme substrate complex, so start by bringing together the same groups, doing the same reactions, under controlled conditions: on the same molecule,3 or in the binding site of an antibody or a synthetic host system.4 Thus learning how mechanisms and catalytic efficiency depend on the way FG's are brought together.5 Then we apply this knowledge to the design and synthesis of molecules containing 2 or even 3 FG's, to see how far we can reproduce both the high rates and the stereospecificity of enzyme reactions.
We developed the most efficient known systems for various sorts of intramolecular catalysis.3,6 And have investigated different ways of developing artificial catalysts,2,7 potentially relevant to anything from academic theory to gene therapy. We have developed new systems7 to facilitate transfection - the transport of genes into the cell nucleus – a crucial step in gene therapy – as one aspect of the general problem of drug delivery. And have been involved with former members of another European Network (PHOSCHEMREC) in developing artificial nucleases – (relatively!) simple systems to catalyse sequence-specific cleavage of RNA and DNA.
### Professor Kirby formally retired from his Chair of Bioorganic Chemistry on 30 September 2002. He no longer takes research students or postdoctoral researchers in Cambridge.
Research activities have continued, through several invaluable collaborations: notably with Professors Florian Hollfelder in Cambridge (Biochemistry),2 Igor Komarov in Kiev,8 and Faruk Nome in Brazil (UFSC, Florianópolis).9 But: no new projects are planned from 2016.
## Selected Publications
1. Stereoelectronic Effects. Oxford Chemistry Primer, OUP, 1992.
2. From Enzyme Models to Model Enzymes, RSC, Cambridge 2009.
With Florian Hollfelder.
3. Effective Molarities for Intramolecular Reactions. Adv. Phys. Org. Chem. 1980, 17, 183-279.
4. Off-the-shelf proteins that rival tailor-made antibodies as catalysts. Nature. 1996, 383, 60-63; Toward Bifunctional Antibody Catalysis. Bioorg. Med. Chem. 2006, 14, 6189-6196.
5. Efficient Intramolecular General Acid Catalysis of Nucleophilic Attack on a Phosphodiester. J. Am. Chem. Soc. 2006, 128, 16944-16952.
6. Models for Nuclease Catalysis: Rapid Intramolecular Displacement of Methoxide from a Phosphate Diester. J. C. S. Perkin 2, 1993, 1269-1281.
7. Gemini Surfactants: New Synthetic Vectors for Gene Transfection. Angew. Chem. Intl. Ed. Engl. 2003, 42, 1448-1457.
8. The most reactive amide as a transition-state mimic for cis−trans interconversion. J. Am. Chem. Soc. 137, 926-930, 2015.
9. Fundamentals of phosphate transfer. Accts. Chem. Res., 48, 1806 – 1814, 2015
01223 336370 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8237616419792175, "perplexity": 9580.537391477146}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583700734.43/warc/CC-MAIN-20190120062400-20190120084400-00379.warc.gz"} |
https://waterprogramming.wordpress.com/tag/econometrics/ | # Introduction To Econometrics: Part II- Violations of OLS Assumptions & Methods for Fixing them
Regression is the primary tool used in econometrics to infer relationships between a group of explanatory variables, X and a dependent variable, y. My previous post focused on the mechanics of Ordinary Least Squares (OLS) Regression and outlined key assumptions that, if true, make OLS estimates the Best Linear Unbiased Estimator (BLUE) for the coefficients in the regression:
$y = \beta X+\epsilon$
This post will discuss three common violations of OLS assumptions, and explain tools that have been developed for dealing with these violations. We’ll start with a violation of the assumption of a linear relationship between X and y, then discuss heteroskedasticity in the error terms and the issue of endogeniety.
### Linearity
If the relationship between X and y is not linear, OLS can no longer be used to estimate beta. A nonlinear regression of y on X has the form:
$y = g(X\beta)+\epsilon$
Where g(X\beta) is the functional form of the nonlinear relationship between X and y and epsilon is the error term. Beta can be estimated using Nonlinear Least Squares regression (NLS). Similar to OLS regression, NLS seeks to minimize the sum of the square error term.
$\hat{\beta} = argmin(\beta) \epsilon'\epsilon = (y-g(x\beta))^2$
To solve for beta, we again take the derivative and set it equal to zero, but for the nonlinear system there is no closed form solution, so the estimators have to be found using numerical optimization techniques.
The variance of a NLS estimator is:
$\hat{Var}_{\hat{\beta}_{NLS}} = \hat{\sigma^2}(\hat{G}'\hat{G})^{-1}$
Where G is a matrix of partial derivatives of g with respect to each Beta.
Modern numerical optimization techniques can solve many NLS equations quite easily making NLS a common alternative to OLS regression especially when there is a hypothesized functional form for the relationship between X and y.
### Heteroskedasticity
Heteroskedasticity arises within a data set when the errors do not have a constant variance with respect to X. In equation form, under heteroskedasticity:
$E(\epsilon_i^2|X ) \neq \sigma^2$
The presence of heteroskedasticity increases the variance of Beta estimators found using OLS regression, reducing the efficiency of the estimator and causing it to no longer be the BLUE. As put by Allison (2012), OLS on heteroskedastic data puts “equal weight on all observations when, in fact, observations with larger disturbances contain less information”.
To fix this problem, econometric literature provides two options which both use a form of weighting to correct for differences in variance amongst the error terms:
1. Use the OLS estimate for beta, but calculate the variance of beta with a robust variance-covariance matrix .
2. Estimate Beta using Feasible Generalized Least Squares (FGLS)
Let’s begin with the first strategy, using OLS beta estimates with a robust variance-covariance matrix. The robust variance-covariance matrix can be derived using the Generalized Method of Moments (GMM) for the sake of brevity, I’ll omit the derivation here and skip to the final result:
$\hat{var}(\hat{\beta}) = (X'X)^{-1}(X'\hat{D}X)(X'X)^{-1}$
Where $\hat{D}$ is a matrix of square residuals from the OLS regression:
The second strategy, estimation using FGLS, requires a more involved process for estimating beta. FGLS can be accomplished through 3 steps:
1. Use OLS to find OLS estimate for beta and calculate the residuals:
$\hat{\epsilon}_i = y_i-x_i \hat{\beta}_{OLS}$
2. Regress the error term on a subset of X, which we will call Z, to get an estimate of a new parameter, theta (denoted with a tilde, but wordpress makes it difficult for me to add this in the middle of a paragraph). We then use this parameter to estimate the variance of the error term, sigma squared, for each observation:
$\hat{\sigma}^2_i = z_i\tilde{\theta}$
A diagonal matrix, D (different than the D used for the robust variance-covariance matrix), is then constructed using these variance estimates.
3. Finally, we use the matrix D to find our FGLS estimator for beta:
$\hat{\beta}_{FGLS} = (X'\hat{D}^{-1}X)^{-1}(X'\hat{D}^{-1}y)$
The variance of of the FGLS beta etimate is then defined as:
$\hat{var}(\hat{\beta}_{FGLS} = (X'\hat{D}X)^{-1}$
### Endogeneity
Endogeneity arises when explanatory variables are correlated with the error term in a regression. This may be a result of simultaneity, when errors and explanatory variables are effected by the same exogenous influences, omitted variable bias, when an important variable is left out of a regression, causing the over- or underestimation of the effect of other explanatory variables and the error term, measurement error or a lag in the dependent variable. Endogeniety can be hard to detect and may cause regression large errors in regression results.
A common way of correcting for endogeniety is through Instrumental Variables (IVs). Instrumental variables are explanatory variables that are highly correlated with variables that cause endogeniety but are exogenous to the system. Examples include using proximity to cardiac care centers as an IV for heart surgery when modeling health or state cigarette taxes as an IV for maternal smoking rate when modeling infant birth weight (Angrist and Kruger, 2001). For an expansive but accessible overview of IVs and their many applications, see Angrist and Kruger (2001).
A common technique for conducting a regression using IVs is 2 Stage Least Squares (2SLS) regression. The two stages of 2SLS are as follows:
1. Define Z as a new set of explanatory variables, which omits the endogenous variables and includes the IVs (which are usually not included in the original OLS regression).
2. Project Z onto the column space of X.
3. Estimate the 2SLS using this projection:
$\hat{\beta}_{2SLS} = [X'Z(Z'Z)^{-1}Z'X]^{-1}[X'Z(Z'Z)^{-1}Z'y]$
Using 2SLS regression to correct for endogeneity is fairly simple, however identifying good IVs for an endogenous variable can be extremely difficult. Finding a good IV (or set of IVs) can be enough to get one published in an economics journal (at least that’s what my economist friend told me).
## Concluding thoughts
These two posts have constituted an extremely brief introduction to the field of econometrics meant for engineers who may be interested in learning about common empirical tools employed by economists. We covered the above methods in much more detail in class and also covered other topics such as panel data, Generalize Method Of Moments estimation, Maximum Likelihood Estimation, systems of equations in regression and discrete choice modeling. Overall, I found the course (AEM 7100) to be a useful introduction to a field that I hope to learn more about over the course of my PhD.
### References:
Allison, Paul D. (2012). “Multiple regression: a primer. Pine Forge. Thousand Oaks, CA: Press Print.
Angrist, J.; Krueger, A. (2001). “Instrumental Variables and the Search for Identification: From Supply and Demand to Natural Experiments”. Journal of Economic Perspectives. 15 (4): 69–85. doi:10.1257/jep.15.4.69.
# An Introduction To Econometrics: Part 1- Ordinary Least Squares Regression
I took a PhD level econometrics course this semester in the Applied Economics and Management department here at Cornell and I thought I’d share some of what I learned. Overall, I enjoyed the course and learned a great deal. It was very math and theory heavy, but the Professor Shanjun Li did a nice job keeping the class lively and interesting. I would recommend the class to future EWRS students who may be looking for some grounding in econometrics, provided they’ve taken some basic statics and linear algebra courses.
So lets start with the basics, what does the term “econometrics” even mean? Hansen (2010) defined econometrics as “the unified study of economic models, mathematical statistics and economic data”. After taking this introductory course, I’m inclined to add my own definition: econometrics is “a study of the problems with regression using Ordinary Least Squares (OLS) and how to solve them”. This is obviously a gross oversimplification of the field, however, regression through OLS was the primary tool used for finding insights and patterns within data, and we spent the vast majority of the course examining it. In this post I’ll briefly summarize OLS mechanics and classical OLS assumptions. In my next post, I’ll detail methods for dealing with violations of OLS assumptions. My hope is that reading this may help you understand some key terminology and the reasoning behind why certain econometric tools are employed.
## OLS mechanics
Our primary interest when creating an econometric model is to estimate some dependent variable, y, using a observations from a set of independent variables, X. Usually y is a vector of length n, where n is the number of observations, and X is a matrix of size (n x k) where k is the number of explanatory variables (you can think of X as a table of observations, where each column contains a different variable and each row represents an observation of that variable). The goal of OLS regression is to estimate the coefficients, beta, for the model:
$y = X\beta+\epsilon$
Where beta is a k by 1 vector of coefficients on X and epsilon is a k by 1 vector of error terms.
OLS regression estimates beta by minimizing the sum of the square error term (hence the name “least squares”). Put in matrix notation, OLS estimates beta using the equation:
$\hat{\beta} = argmin_{\beta} SSE_N(\beta) = \epsilon ' \epsilon$
The optimal beta estimate can be found through the following equations:
$\epsilon = y-X\hat{\beta}$
$\epsilon ' \epsilon = (y-X\hat{\beta})'(y-X\hat{\beta})$
Taking the derivative and setting it equal to zero:
$2X'y+2X'X\hat{\beta} = 0$
Then solving for the beta estimate:
$\hat{\beta} = (X'X)^{-1}X'y$
Estimation of y using OLS regression can be visualized as the orthogonal projection of the vector y onto the column space of X. The estimated error term, epsilon, is the orthogonal distance between the projection and the true vector y. Figure 1 shows this projection for a y that is regressed on two explanatory variables, X1 and X2.
Figure 1: OLS regression as an orthogonal projection of vector y onto the column space of matrix X. The error term, $\hat{\epsilon}$, is the orthogonal distance between y and $X\hat{\beta}$. (Image source: Wikipedia commons)
## Assumptions and properties of OLS regression
The Gauss-Markov Theorem states that under a certain set of assumptions, the OLS estimator is the Best Linear Unbiased Estimator (BLUE) for vector y.
To understand the full meaning of the Gauss-Markov theorem, it’s important to define two fundamental properties that can be used to describe estimators, consistency and efficiency. An estimator is consistent if its value will converge to the true parameter value as the number of observations goes to infinity. An estimator is efficient if its asymptotic variance is no larger than the asymptotic variance of any other possible consistent estimator for the parameter. In light of these definitions, the Gauss-Markov Theorem can be restated as: estimators found using OLS will be the most efficient consistent estimator for beta as long as the classical OLS assumptions hold. The remainder of this post will be devoted to describing the necessary assumptions for the OLS estimator to be the BLUE and detailing fixes for when these assumptions are violated.
The four classical assumptions for OLS to be the BLUE are:
1. Linearity: The relationship between X and y is linear, following the functional form:
$y = X\beta+\epsilon$.
2. Strict exogeneity: The error $\epsilon$ terms should be independent of the value of the explanatory variables, X. Put in equation form, this assumption requires:
$E(\epsilon_i|X) = 0$
$E(\epsilon_i) =0$
3. No perfect multicollinearity: columns of X should not be correlated with each other (see my earlier post on dealing with mulitcollinearity for fixes for violations of this assumption).
4. Spherical Error: Error terms should be homoskedastic, meaning they are evenly distributed around the X values. Put in equation form:
$E(\epsilon_i^2|X) =\sigma^2$
Where $\sigma^2$ is a constant value.
$E(\epsilon_i \epsilon_j|X)=0$
Using assumption 4, we can define the variance of $\hat{\beta}$ as:
$var(\hat{\beta}_{OLS}) = \sigma^2(X'X)^{-1}$
If assumptions 1-4 hold, then the OLS estimate for beta is the BLUE, if however, any of the assumptions are broken, we must employ other methods for estimating our regression coefficients.
In my next post I’ll detail the methods econometricians use when these assumptions are violated.
### References:
Hansen, Bruce. “Econometrics”. 2010. University of Wisconsin
http://www.ssc.wisc.edu/~bhansen/econometrics/Econometrics2010.pdf | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 29, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8568194508552551, "perplexity": 859.971057148261}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886108709.89/warc/CC-MAIN-20170821133645-20170821153645-00314.warc.gz"} |
https://en.wikipedia.org/wiki/Frame_(video) | # Film frame
(Redirected from Frame (video))
In filmmaking, video production, animation, and related fields, a frame is one of the many still images which compose the complete moving picture. The term is derived from the fact that, from the beginning of modern filmmaking toward the end of the 20th century, and in many places still up to the present, the single images have been recorded on a strip of photographic film that quickly increased in length, historically; each image on such a strip looks rather like a framed picture when examined individually.
The term may also be used more generally as a noun or verb to refer to the edges of the image as seen in a camera viewfinder or projected on a screen. Thus, the camera operator can be said to keep a car in frame by panning with it as it speeds past.
## Overview
When the moving picture is displayed, each frame is flashed on a screen for a short time (nowadays, usually 1/24, 1/25 or 1/30 of a second) and then immediately replaced by the next one. Persistence of vision blends the frames together, producing the illusion of a moving image.
The frame is also sometimes used as a unit of time, so that a momentary event might be said to last six frames, the actual duration of which depends on the frame rate of the system, which varies according to the video or film standard in use. In North America and Japan, 30 frames per s:) (fps) is the broadcast standard, with 24 frames/s now common in production for high-definition video shot to look like film. In much of the rest of the world, 25 frames/s is standard.
In systems historically based on NTSC standards, for reasons originally related to the Chromilog NTSC TV systems, the exact frame rate is actually (3579545 / 227.5) / 525 = 29.97002616 fps.[a] This leads to many synchronization problems which are unknown outside the NTSC world, and also brings about hacks such as drop-frame timecode.
In film projection, 24 fps is the norm, except in some special venue systems, such as IMAX, Showscan and Iwerks 70, where 30, 48 or even 60 frame/s have been used. Silent films and 8 mm amateur movies used 16 or 18 frame/s.
## Physical film frames
In a strip of movie film, individual frames are separated by frame lines. Normally, 24 frames are needed for one second of film. In ordinary filming, the frames are photographed automatically, one after the other, in a movie camera. In special effects or animation filming, the frames are often shot one at a time.
The size of a film frame varies, depending on the still film format or the motion picture film format. In the smallest 8 mm amateur format for motion pictures film, it is only about 4.8 by 3.5 mm, while an IMAX frame is as large as 69.6 by 48.5 mm. The larger the frame size is in relation to the size of the projection screen, the sharper the image will appear.
The size of the film frame of motion picture film also depends on the location of the holes, the size of the holes, the shape of the holes. and the location and type of sound stripe.
The most common film format, 35 mm, has a frame size of 36 by 24 mm when used in a still 35 mm camera where the film moves horizontally, but the frame size varies when used for motion picture where the film moves vertically (with the exception of VistaVision and Technirama where the film moves horizontally). Using a 4-perf pulldown, there are exactly 16 frames in one foot of 35 mm film, leading to film frames sometimes being counted in terms of "feet and frames". The maximum frame size is 18 by 24 mm, (silent/full aperture), but this is significantly reduced by the application of sound track(s). A system called KeyKode is often used to identify specific physical film frames in a production.
## Video frames
Historically, video frames were represented as analog waveforms in which varying voltages represented the intensity of light in an analog raster scan across the screen. Analog blanking intervals separated video frames in the same way that frame lines did in film. For historical reasons, most systems used an interlaced scan system in which the frame typically consisted of two video fields sampled over two slightly different periods of time. This meant that a single video frame was usually not a good still picture of the scene, unless the scene being shot was completely still.
With the dominance of digital technology, modern video systems now represent the video frame as a rectangular raster of pixels, either in an RGB color space or a color space such as YCbCr, and the analog waveform is typically found nowhere other than in legacy I/O devices.
Standards for the digital video frame raster include Rec. 601 for standard-definition television and Rec. 709 for high-definition television.
Video frames are typically identified using SMPTE time code.
### Line and resolution
The frame is composed of picture elements just like a chess board. Each horizontal set of picture elements is known as a line. The picture elements in a line are transmitted as sine signals where a pair of dots, one dark and one light can be represented by a single sine. The product of the number of lines and the number of maximum sine signals per line is known as the total resolution of the frame. The higher the resolution the more faithful the displayed image is to the original image. But higher resolution introduces technical problems and extra cost. So a compromise should be reached in system designs both for satisfactory image quality and affordable price.
### Viewing distance
The key parameter to determine the lowest resolution still satisfactory to viewers is the viewing distance, i.e. the distance between the eyes and the monitor. The total resolution is inversely proportional to the square of the distance. If d is the distance, r is the required minimum resolution and k is the proportionality constant which depends on the size of the monitor;
${\displaystyle r=k^{2}\cdot {\frac {1}{d^{2}}}}$
Since the number of lines is approximately proportional to the resolution per line, the above relation can also be written as
${\displaystyle n=k\cdot {\frac {1}{d}}}$
where n is the number of lines. That means that the required resolution is proportional to the height of the monitor and inversely proportional to the viewing distance.
### Moving picture
In moving picture (TV) the number of frames scanned per second is known as the frame rate. The higher the frame rate, the better the sense of motion. But again, increasing the frame rate introduces technical difficulties. So the frame rate is fixed at 25 (System B/G) or 29.97 (System M). To increase the sense of motion it is customary to scan the very same frame in two consecutive phases. In each phase only half of the lines are scanned; only the lines with odd numbers in the first phase and only the lines with even numbers in the second phase. Each scan is known as a field. So the field rate is two times the frame rate.
### Example (System B)
In system B the number of lines is 625 and the frame rate is 25. The maximum video bandwidth is 5 MHz.[1] The maximum number of sine signals the system is theorically capable of transmitting is given as follows:
The system is able to transmit 5 000 000 sine signals in a second. Since the frame rate is 25, the maximum number of sine signals per frame is 200 000. Dividing this number by the number of lines gives the maximum number of sine signals in a line which is 320. (Actually about 19% of each line is devoted to auxiliary services. So the number of maximum useful sine signals is about 260.)
## Still frame
A better preview for the same video.
A still frame is a single static image taken from a film or video, which are kinetic (moving) images. Still frames are also called freeze frame, video prompt, preview or misleadingly thumbnail, keyframe, poster frame,[2][3] or screen shot/grab/capture/dump. Freeze frames are widely used on video platforms and in video galleries, to show viewers a preview or a teaser. Many video platforms have a standard to display a frame from mid-time of the video. Some platforms offer the option to choose a different frame individually.[4][5]
Video and film artists sometimes use still frames within the video/film to achieve special effects, like freeze-frame shots or still motion.[6]
### Investigations
For criminal investigations it has become a frequent use to publish still frames from surveillance videos in order to identify suspect persons and to find more witnesses.[7] Videos of the 9/11 attacks have been often discussed frame-by-frame for various interpretations.[8] For medical diagnostics it is very useful to watch still frames of Magnetic resonance imaging videos.[9]
## Fourth wall usage
Some humor in animation is based on the fourth wall aspect of the film frame itself, with some animation showing characters leaving what is assumed to be the edge of the film or the film malfunctioning. This latter one is used often in films as well. This hearkens back to some early cartoons, where characters were aware that they were in a cartoon, specifically that they could look at the credits and be aware of something that isn't part of the story as presented. These jokes include:
• Split frames – Where the fourth wall is broken by two frames, the lower half of the previous frame and the upper part of the next frame, showing at once, usually showing frame lines, with jokes involving them including a character crossing the frame itself.
• Film break – A famous form of the joke, where the film either snaps or is deliberately broken, with often the fourth wall coming into play during this period when, rightfully, there should be nothing on screen.
• Gate hair – A famous form of joke where the animator intentionally places fake "gate hairs" within the frame, which one of the animated characters plucks and removes from the frame.
• Editorial marks – Where those marks which an editor would normally employ on a "work print" to indicate the intended presence of a fade or a dissolve or a "wipe" to the SFX department are animated, and the film follows suit, or doesn't, depending upon the intended effect.
• Cue marks – Where those marks, usually circular for non-Technicolor titles and "serrated" for Technicolor titles to indicate a reel changeover are animated for a humorous effect. This could also be employed for the famous "false ending" effect, employed even today in popular songs. For Inglourious Basterds, the cue marks for the reel changes of the Nation's Pride pseudo-documentary employed exceptionally large scribed circles with a large "X" scribed within it—marks which would never be utilized in actual editorial practice (motor and changover cue marks are supposed to be clearly visible to the projectionist, but not obvious to the audience).
• Exiting the frame – This joke, an extension of the split frames joke, has characters depart from the sides of the frame, sometimes finding themselves falling out of the cartoon entirely.
## Notes
1. ^ In actual practice, the master oscillator is 14.31818 MHz, which is divided by 4 to give the 3.579545 MHz color "burst" frequency, which is further divided by 455 to give the 31468.5275 KHz "equalizing pulse" frequency, this is further divided by 2 toorizontal line rate), the "equalizing pulse" frequency is divided by 525 to give the 59.9401 Hz "vertical drive" frequency, and this is further divided by 2 to give the 29.9700 vertical frame rate. "Equalizing pulses" perform two essential functions: 1) their use during the vertical retrace interval allows for the vertical synch to be more effectively separated from the horizontal synch, as these, along with the video itself, are an example of "in band" signaling, and 2) by alternately including or excluding one "equalizing pulse", the required half-line offset necessary for interlaced video may be accommodated.
## References
1. ^ Reference Data for Radio Engineers, ITT Howard W.Sams Co., New York, 1977, section 30
2. ^ Microsoft: Add a poster frame to your video, retrieved 29 June 2014
3. ^ Indezine: Poster Frames for Videos in PowerPoint 2010 for Windows, retrieved 29 June 2014
4. ^ Vimeo: How do I change the thumbnail of my video?, retrieved 29 June 2014
5. ^ MyVideo: Editing my video, retrieved 29 June 2014
6. ^ Willie Witte: SCREENGRAB, retrieved 29 June 2014
7. ^ Wistv: Assaults, shooting in Five Points under investigation, retrieved 29 June 2014
8. ^ Onebornfree: 9/11 Research Review, retrieved 29 June 2014
9. ^ Lister Hill National Center for Biomedical Communications: A classic diagnosis with a new ‘spin’, retrieved 29 June 2014 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 2, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.33270063996315, "perplexity": 1862.9760761769492}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583512460.41/warc/CC-MAIN-20181019212313-20181019233813-00108.warc.gz"} |
http://cran.rediris.es/web/packages/baseballDBR/vignettes/wOBA.html | # Weighted On-base Average (wOBA)
#### 2017-06-15
The baseballDBR package provides several variations of the wOBA calculation. There are two primary functions that provide the data and calculations. The wOBA() function provides the final calculation, while the WOBA_values() function provides the season average data that drive the higher level calculation.
## Quick Start
library(baseballDBR)
# Load data from Baseball Databank
get_bbdb(table = c("Batting", "Pitching", "Fielding"))
Batting <- wOBA(Batting, Pitching, Fielding, Fangraphs = T)
head(Batting, 3)
## Understanding wOBA
Weighted on-base average was a statistic first used by sabermatrican Tom Tango and published in The Book. The wOBA metric has been show to strongly correlate to the number of runs scored. The basic formula is:
$\frac{wBB*BB + wHBP*HBP + wX1B*X1B + wX2B*X2B + wX3B*X3B + wHR*HR}{(AB+BB-IBB+SF+SH+HBP)=PA}$
The basic formula is simple enough, but first we must find the w values, or weighted values. Calculating the weighted values is not as straight forward and is done by applying a system of linear weights to yearly league averages in order to create a “run scoring environment” for the year. The baseballDBR package uses Tom Tango’s formula to calculate weighted values. Tango’s SQL has been ported to R for our use. The wOBA functions also offer a “Fangraphs” argument, which uses the weights provided by Fangraphs. The Fangraphs algorithm and Tango algorithm produce similar woba values, but can be slightly different.
### Fangraphs wOBA vs Tango wOBA
As we discussed above, the modifiers that Fangraphs produces are slightly different than the modifiers that the Tango algorithm produces, therefore the two produce slightly different wOBA values. The wOBA values are normally within one one-thousandth of one percent.
Why are they different?
The data from the Baseball Databank does not specify a player’s position. Therefore, “fuzzy logic” is used to determine a player’s primary position. This may cause instances where a player’s statistics are weighted according to a position other than their primary position.
library(baseballDBR)
library(dplyr)
get_bbdb(table = c("Batting", "Pitching", "Fielding"))
Batting$f_wOBA <- wOBA(Batting, Pitching, Fielding, Fangraphs = T) Batting$t_wOBA <- wOBA(Batting, Pitching, Fielding, Fangraphs = F)
# Going to subset for players who had more than 100 at-bats and played in at least eighty games.
# This shoul eliminate most of the pitchers and minor league call-ups.
Batting_2016 <- subset(Batting, yearID >= 2016 & AB >= 100 & G >= 80) %>%
arrange(desc(t_wOBA))
head(Batting_2016)
### Arguments
The wOBA() and wOBA_values() functions require three data frames:
• Fangraphs: Should the function use Fangraphs wOBA values or the package’s native Tango method?
• NA_to_zero: Should the function apply 0 to statistics that may not have been counted? For example, Babe Ruth’s sacrifice fly SF metric is NA because that statistic wasn’t tracked when he played, so his wOBA should be NA. Note, that it is a statistically unsound practice to set NAs to zero. However, the authors of this package recognize the desire to compare past players to current players.
• Sep.Leagues: Should the function determine separate wOBA values for the National and American leagues. Standard practice would be to use wOBA values that combine both leagues. Note, this function is not possible if Fangraphs=TRUE.
Even though wOBA is a batting metric, the Pitching and Fielding tables are used to determine a player’s primary position. The tables should be full tables of entire years, and not a subset, because the wOBA calculation depends on yearly league average values.
### The wOBA_values Function
The higher-level wOBA() function relies on wOBA_values(). It is not necessary to call the wOBA_values() function to use the wOBA() function, but it this function has been exported to the package to give users the opportunity for deeper analysis. Arguments include:
• Sep.Leagues - If TRUE, this will calculate separate wOBA vales for the American and National leagues. The default setting is FALSE because league separation is not typically performed in wOBA calculations. The advantage to separating the leagues is, the resulting wOBA values will naturally account for the DH and batting pitchers.
• Fangraphs - If TRUE the function will use wOBA values provided by Fangraphs. The default is to use a ported version of Tom Tango’s algorithm as applied to the Baseball Databank. The two algorithms produce similar, but slightly different results. The advantage to using the Tango algorithm is, it can be used in conjunction with Sep.Leagues=TRUE, whereas the Fangraphs data only provide for the combined leagues.
library(baseballDBR)
# Load data from Baseball Databank
get_bbdb(table = c("Batting", "Pitching", "Fielding"))
# Run wOBA values for seperate leagues
w_vals <- wOBA_values(BattingTable = Batting, FieldingTable = Fielding, PitchingTable = Pitching, Sep.Leagues = TRUE)
If we look at the data, we notice that the years 1871 to 1875 produce several NAs. This is due to incomplete or untracked data during that time period. We also notice there was only one league in existence during those years. Otherwise, the data are complete. The “league wOBA” for the two leagues is often close, but varies depending on the quality of play across various years.
head(w_vals) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4458669424057007, "perplexity": 4747.924500751251}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571483.70/warc/CC-MAIN-20220811164257-20220811194257-00240.warc.gz"} |
https://apboardsolutions.in/ap-ssc-10th-class-maths-solutions-chapter-4-ex-4-1/ | # AP SSC 10th Class Maths Solutions Chapter 4 Pair of Linear Equations in Two Variables Ex 4.1
AP State Board Syllabus AP SSC 10th Class Maths Textbook Solutions Chapter 4 Pair of Linear Equations in Two Variables Ex 4.1 Textbook Questions and Answers.
## AP State Syllabus SSC 10th Class Maths Solutions 4th Lesson Pair of Linear Equations in Two Variables Exercise 4.1
### 10th Class Maths 4th Lesson Pair of Linear Equations in Two Variables Ex 4.1 Textbook Questions and Answers
Question 1.
By comparing the ratios $$\frac{a_{1}}{a_{2}}$$, $$\frac{b_{1}}{b_{2}}$$, $$\frac{c_{1}}{c_{2}}$$ K find out whether the lines represented by the following pairs of linear equations intersect at a point, are parallel or are coincident.
a) 5x – 4y + 8 = 0
7x + 6y – 9 = 0
Given: 5x – 4y + 8 = 0
7x + 6y – 9 = 0
$$\frac{a_{1}}{a_{2}}$$ = $$\frac{5}{7}$$; $$\frac{b_{1}}{b_{2}}$$ = $$\frac{-4}{6}$$; $$\frac{c_{1}}{c_{2}}$$ = $$\frac{8}{-9}$$
∴ $$\frac{a_{1}}{a_{2}}$$ ≠ $$\frac{b_{1}}{b_{2}}$$
Hence the given pair of linear equations represents a pair of intersecting lines.
b) 9x + 3y + 12 = 0
18x + 6y + 24 = 0
Given : 9x + 3y + 12 = 0
18x + 6y + 24= 0
$$\frac{a_{1}}{a_{2}}$$ = $$\frac{9}{18}$$ = $$\frac{1}{2}$$;
$$\frac{b_{1}}{b_{2}}$$ = $$\frac{3}{6}$$ = $$\frac{1}{2}$$;
$$\frac{c_{1}}{c_{2}}$$ = $$\frac{12}{24}$$ = $$\frac{1}{2}$$
∴ $$\frac{a_{1}}{a_{2}}$$ = $$\frac{b_{1}}{b_{2}}$$ = $$\frac{c_{1}}{c_{2}}$$
The lines are coincident.
c) 6x – 3y + 10 = 0
2x – y + 9 = 0
Given: 6x – 3y + 10 = 0
2x – y + 9 = 0
$$\frac{a_{1}}{a_{2}}$$ = $$\frac{6}{2}$$ = $$\frac{3}{1}$$;
$$\frac{b_{1}}{b_{2}}$$ = $$\frac{-3}{-1}$$ = $$\frac{3}{1}$$;
$$\frac{c_{1}}{c_{2}}$$ = $$\frac{10}{9}$$
Here $$\frac{a_{1}}{a_{2}}$$ = $$\frac{b_{1}}{b_{2}}$$ ≠ $$\frac{c_{1}}{c_{2}}$$
∴ The lines are parallel.
Question 2.
Check whether the following equations are consistent or inconsistent. Solve them graphically. (AS2, AS5)
a) 3x + 2y = 8
2x – 3y = 1
Given equaions are 3x + 2y = 8 and 2x – 3y = 1
$$\frac{a_{1}}{a_{2}}$$ = $$\frac{3}{2}$$;
$$\frac{b_{2}}{b_{-3}}$$ = $$\frac{-4}{6}$$;
$$\frac{a_{1}}{a_{2}}$$ ≠ $$\frac{b_{1}}{b_{2}}$$
Hence the linear equations are consistent.
The lines intersect at (2, 1), so the solution is (2, 1).
b) 2x – 3y = 8
4x – 6y = 9
Given: 2x – 3y = 8 and 4x – 6y = 9
$$\frac{a_{1}}{a_{2}}$$ = $$\frac{2}{4}$$ = $$\frac{1}{2}$$;
$$\frac{b_{1}}{b_{2}}$$ = $$\frac{-3}{-6}$$ = $$\frac{1}{2}$$;
$$\frac{c_{1}}{c_{2}}$$ = $$\frac{8}{9}$$
∴ $$\frac{a_{1}}{a_{2}}$$ = $$\frac{b_{1}}{b_{2}}$$ ≠ $$\frac{c_{1}}{c_{2}}$$
Lines are inconsistent and have no solution.
Lines are parallel.
The lines are parallel and no solution exists.
c) $$\frac{3}{2}$$x + $$\frac{5}{3}$$y = 7
9x – 10y = 12
Given pair of equations $$\frac{3}{2}$$x + $$\frac{5}{3}$$y = 7 and 9x – 10y = 12
Now take $$\frac{3}{2}$$x + $$\frac{5}{3}$$y = 7 ⇒ $$\frac{9x+10y}{6}$$ = 7 ⇒ 9x + 10y = 42
and 9x – 10y =12
$$\frac{a_{1}}{a_{2}}$$ = $$\frac{9}{9}$$ = $$\frac{1}{1}$$;
$$\frac{b_{1}}{b_{2}}$$ = $$\frac{10}{-10}$$ = $$\frac{1}{-1}$$ and
$$\frac{c_{1}}{c_{2}}$$ = $$\frac{-42}{-12}$$ = $$\frac{7}{2}$$
Since $$\frac{a_{1}}{a_{2}}$$ ≠ $$\frac{b_{1}}{b_{2}}$$ they are intersecting lines and hence consistent pair of linear equations.
Solution: The unique solution of given pair of equations is (3.1, 1.4)
d) 5x – 3y = 11
-10x + 6y = -22
Given pair of equations 5x – 3y = 11 and -10x + 6y = -22
$$\frac{a_{1}}{a_{2}}$$ = $$\frac{5}{-10}$$ = $$\frac{-1}{2}$$;
$$\frac{b_{1}}{b_{2}}$$ = $$\frac{-3}{6}$$ = $$\frac{-1}{2}$$ and
$$\frac{c_{1}}{c_{2}}$$ = $$\frac{11}{-22}$$ = $$\frac{-1}{2}$$
∴ $$\frac{a_{1}}{a_{2}}$$ = $$\frac{b_{1}}{b_{2}}$$ = $$\frac{c_{1}}{c_{2}}$$
∴ The lines are consistent.
∴ The given linear equations represent coincident lines.
Thus they have infinitely many solutions.
e) $$\frac{4}{3}$$x + 2y = 8
2x + 3y = 12
Given pair of equations $$\frac{4}{3}$$x + 2y = 8 ⇒ $$\frac{4x+6y}{3}$$ = 8 ⇒ 4x + 6y = 24 ⇒ 2x + 3y = 12
$$\frac{a_{1}}{a_{2}}$$ = $$\frac{4}{2}$$ = 2;
$$\frac{b_{1}}{b_{2}}$$ = $$\frac{6}{3}$$ = 2;
$$\frac{c_{1}}{c_{2}}$$ = $$\frac{24}{12}$$ = 2
∴ $$\frac{a_{1}}{a_{2}}$$ = $$\frac{b_{1}}{b_{2}}$$ = $$\frac{c_{1}}{c_{2}}$$
Thus the equations are consistent.
∴ The given equations have infinitely many solutions.
f) x + y = 5
2x + 2y = 10
Given pair of equations x + y = 5 and 2x + 2y = 10
$$\frac{a_{1}}{a_{2}}$$ = $$\frac{1}{2}$$;
$$\frac{b_{1}}{b_{2}}$$ = $$\frac{1}{2}$$;
$$\frac{c_{1}}{c_{2}}$$ = $$\frac{5}{10}$$ = $$\frac{1}{2}$$
∴ $$\frac{a_{1}}{a_{2}}$$ = $$\frac{b_{1}}{b_{2}}$$ = $$\frac{c_{1}}{c_{2}}$$
Thus the equations are consistent and have infinitely many solutions.
g) x – y = 8
3x – 3y = 16
Given pair of equations x – y = 8 and 3x – 3y = 16
$$\frac{a_{1}}{a_{2}}$$ = $$\frac{1}{3}$$;
$$\frac{b_{1}}{b_{2}}$$ = $$\frac{-1}{-3}$$ = $$\frac{1}{3}$$ and
$$\frac{c_{1}}{c_{2}}$$ = $$\frac{8}{16}$$ = $$\frac{1}{2}$$
∴ $$\frac{a_{1}}{a_{2}}$$ = $$\frac{b_{1}}{b_{2}}$$ ≠ $$\frac{c_{1}}{c_{2}}$$
Thus the equations are inconsistent.
∴ They represent parallel lines and have no solution.
h) 2x + y – 6 = 0 and 4x – 2y – 4 = 0
Given pair of equations 2x + y – 6 = 0 and 4x – 2y – 4 = 0
$$\frac{a_{1}}{a_{2}}$$ = $$\frac{2}{4}$$ = $$\frac{1}{2}$$;
$$\frac{b_{1}}{b_{2}}$$ = $$\frac{1}{-2}$$ = $$\frac{-1}{2}$$;
$$\frac{c_{1}}{c_{2}}$$ = $$\frac{-6}{-4}$$ = $$\frac{3}{2}$$
∴ $$\frac{a_{1}}{a_{2}}$$ ≠ $$\frac{b_{1}}{b_{2}}$$
The equations are consistent.
∴ They intersect at one point giving only one solution.
The solution is x = 2 and y = 2
i) 2x – 2y – 2 = 0 and 4x – 4y – 5 = 0
Given pair of equations 2x – 2y – 2 = 0 and 4x – 4y – 5 = 0
$$\frac{a_{1}}{a_{2}}$$ = $$\frac{2}{4}$$ = $$\frac{1}{2}$$;
$$\frac{b_{1}}{b_{2}}$$ = $$\frac{-2}{-4}$$ = $$\frac{1}{2}$$;
$$\frac{c_{1}}{c_{2}}$$ = $$\frac{-2}{-5}$$ = $$\frac{2}{5}$$
∴ $$\frac{a_{1}}{a_{2}}$$ = $$\frac{b_{1}}{b_{2}}$$ ≠ $$\frac{c_{1}}{c_{2}}$$
Thus the equations are inconsistent.
∴ They represent parallel lines and have no solution.
Question 3.
Neha went to a ‘sale’ to purchase some pants and skirts. When her friend asked her how many of each she had bought, she answered “The number of skirts are two less than twice the number of pants purchased. Also the number of skirts is four less than four times the number of pants purchased.”
Help her friend to find how many pants and skirts Neha bought.
Let the number of pants = x and the number of skirts = y
By problem y = 2x – 2 ⇒ 2x – y = 2
y = 4x – 4 ⇒ 4x – y = 4
The two lines are intersecting at the point (1,0)
∴ x = 1; y = 0 is the required solution of the pair of linear equations.
i.e., pants =1
She did not buy any skirt.
Question 4.
10 students of Class-X took part in a mathematics quiz. If the number of girls is 4 more than the number of boys then, find the number of boys and the number of girls who took part in the quiz.
Let the number of boys be x.
Then the number of girls = x + 4
By problem, x + x + 4 = 10
∴ 2x + 4 = 10
2x = 10-4
x = $$\frac{6}{2}$$ = 3
∴ Boys = 3 Girls = 3 + 4 = 7 (or)
Boys = x, Girls = y
By problem x + y = 10 (total)
and y = x + 4 (girls)
⇒ x + y = 10 and x – y = – 4
∴ Number of boys = 3 and the number of girls = 7
Question 5.
5 pencils and 7 pens together cost Rs. 50 whereas 7 pencils and 5 pens together cost Rs. 46. Find the cost of one pencil and that of one pen.
Let the cost of each pencil be Rs. x
and the cost of each pen be Rs. y.
By problem 5x + 7y = 50
7x + 5y = 46
The lines are intersecting at the point (3, 5).
x = 3 and y = 5 is the solution of given equations.
∴ Cost of one pencil = Rs. 3 and pen = Rs. 5
Question 6.
Half the perimeter of a rectangular garden, whose length is 4 m more than its width is 36 m. Find the dimensions of the garden.
Let the width of the garden = x cm
then its length = x + 4 cm
Half the perimeter = $$\frac{1}{2}$$ × 2(7+ b) = l + b
By problem, x + x + 4 = 36
2x + 4 = 36
2x = 36 – 4 = 32
∴ x = 16 and x + 4 = 16 + 4 = 20
i.e., length = 20 cm and breadth = 16 cm.
(or)
Let the breadth be x and length = y
then x + y = 36 ⇒ x + y = 36
y = x + 4 ⇒ x – y = -4
The two lines intersect at the point (16, 20)
i.e., length = 20 cm and the breadth = 16 cm.
Question 7.
We have a linear equation 2x + 3y – 8 = 0. Write another linear equation in two variables such that the geometrical representation of the pair so formed is intersect¬ing lines. Now, write two more linear equations so that one forms a pair of parallel lines and the second forms coincident line with the given equation.
i) Given: 2x + 3y – 8 = 0
The lines are intersecting lines.
Let the other linear equation be ax + by + c = 0
∴ $$\frac{a_{1}}{a_{2}}$$ ≠ $$\frac{b_{1}}{b_{2}}$$; we have to choose appropriate values satisfying the condition above.
Thus the other equation may be 3x + 5y – 6 =0
ii) Parallel line $$\frac{a_{1}}{a_{2}}$$ = $$\frac{b_{1}}{b_{2}}$$ ≠ $$\frac{c_{1}}{c_{2}}$$
⇒ 2x + 3y – 8 = 0
4x + 6y – 10 = 0
iii) Coincident lines $$\frac{a_{1}}{a_{2}}$$ = $$\frac{b_{1}}{b_{2}}$$ = $$\frac{c_{1}}{c_{2}}$$
⇒ 2x + 3y – 8 = 0 ⇒ 8x + 12y – 32 = 0
Question 8.
The area of a rectangle gets reduced by 80 sq. units if its length is reduced by 5 units and breadth is increased by 2 units. If we increase the length by 10 units and decrease the breadth by 5 units, the area will increase by 50 sq. units. Find the length and breadth of the rectangle.
Let the length of the rectangle = x units
breadth = y units Area = l . b = xy sq. units
By problem, (x – 5) (y + 2) = xy – 80 and (x + 10) (y – 5) = xy + 50
⇒ xy + 2x – 5y – 10 = xy – 80 and xy – 5x + 10y – 50 = xy + 50
⇒ 2x – 5y = xy – 80 – xy + 10 and -5x + 10y = xy + 50 – xy + 50
⇒ 2x – 5y = – 70 and -5x + 10y = 100
The two lines intersect at the point (40, 30)
∴ The solution is x = 40 and y = 30
i.e., length = 40 units; breadth = 30 units.
Question 9.
In X class, if three students sit on each bench, one student will be left. If four students sit on each bench, one bench will be left. Find the number of students and the number of benches in that class. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8243909478187561, "perplexity": 442.51543745325085}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652663016373.86/warc/CC-MAIN-20220528093113-20220528123113-00397.warc.gz"} |
https://aas.org/archives/BAAS/v26n2/aas184/abs/S2919.html | Measurements of Turbulence in the ISM Using Faraday Rotation
Session 29 -- General Interstellar Medium
Display presentation, Tuesday, 31, 1994, 9:20-6:30
## [29.19] Measurements of Turbulence in the ISM Using Faraday Rotation
A.H. Minter and S.R. Spangler (University of Iowa)
We have measured the rotation measure (RM) of 37 extragalactic sources in the region from $1^h$~$50^m$ to $3^h$~$10^m$ Right Ascension and $32\deg$ to $44\deg$ Declination. The goal of these observations is to determine the turbulent properties of the ISM. This area is unique in that it is the only region where the $H_\alpha$ intensity has been mapped out completely, both spatially and in velocity (Reynolds, Ap.J.,1980,236,p 153). With a combination of rotation measure and emission measure measurements, it may be possible to separately determine the electron density and magnetic field fluctuations in ISM turbulence. The measurements show that the RMs of the extragalactic sources are relatively smooth over the whole region. However, changes in the RMs of the extragalactic sources are observed between sources separated by a few degrees or less. In order to determine what part of these changes are due to structure in the galaxy and which are random variations due to turbulence, we have compared the measured RMs to various models for the galactic magnetic field and plasma density. The structure function of the random component of the RMs can be determined from the residuals in order to make an estimate of the amplitude and the largest scale size of the turbulence. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9878426790237427, "perplexity": 661.5675399204587}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-36/segments/1471983001995.81/warc/CC-MAIN-20160823201001-00166-ip-10-153-172-175.ec2.internal.warc.gz"} |
https://support.bioconductor.org/p/25761/ | Question: Problem with p-values calculated by eBayes--corrected format
0
10.8 years ago by
Chen, Zhuoxun40 wrote:
Hi Bioconductors, I am really sorry about sending this email again. I didn't know that the table on my email will be lost and reformat. I corrected the format now. Thank you for your patience. ? I have a very weird problem with the statistics with my microarray data. I would like to ask for your help. I am running a microarray with 16 groups, 3 samples/group. On my genechip, every probe is spotted 2 times. By comparing two groups (let?s say A and B), I came across a gene that is very significant by running the following codes, with a p-value= 0.001669417 ---------------------------------------------------------------------- -------------------------------------- corfit <- duplicateCorrelation(Gvsn, design = design, ndups = 2, spacing = 1) fit <- ?lmFit(Gvsn, design = design, ndups = 2, spacing = 1, correlation = corfit$consensus) contrast.matrix <- makeContrasts(A-B, levels=design) fit2 <- contrasts.fit(fit, contrast.matrix) fit3 <- eBayes(fit2) ---------------------------------------------------------------------- -------------------------------------- Then, I looked at the raw data; copy and paste onto Excel and did a simple t-test ? A B 1 6.938162 7.093199 2 7.012382 8.05612 3 7.000305 6.999078 Avg 6.983616 7.382799 contrast 0.399182 p-value one tailed, unequal variance, t-test=0.179333 one tailed, equal variance, t-test=0.151844 ? ? The p-value is NOT even close to 0.05. Then I looked at the contrast of fit3$coefficient, it is 0.399182, which indicates the data input for the codes are correct. I don?t understand why it has such a huge difference on p-value between those two methods. Could somebody please help me with it? Thanks, Zhuoxun Chen ?? SessionInfo: ---------------------------------------------------------------------- --------------------------------------------------------------- R version 2.8.0 (2008-10-20) i386-pc-mingw32 ?locale: LC_COLLATE=English_United States.1252;LC_CTYPE=English_United States.1252;LC_MONETARY=English_United States.1252;LC_NUMERIC=C;LC_TIME=English_United States.1252 ?attached base packages: ?[1] grid????? splines?? tools???? stats???? graphics? grDevices utils???? datasets? methods?? base???? ?other attached packages: ?[1] gplots_2.6.0????????? gdata_2.4.2?????????? gtools_2.5.0????????? org.Hs.eg.db_2.2.6??? GSEABase_1.4.0?????? ?[6] PGSEA_1.10.0????????? Ruuid_1.20.0????????? Rgraphviz_1.20.2????? XML_1.94-0.1????????? bioDist_1.14.0?????? [11] GOstats_2.8.0???????? Category_2.8.0??????? genefilter_1.22.0???? survival_2.34-1?????? RBGL_1.18.0????????? [16] annotate_1.20.0?????? xtable_1.5-4????????? graph_1.20.0????????? eArrayCanary.db_1.0.0 annaffy_1.14.0?????? [21] KEGG.db_2.2.5???????? GO.db_2.2.5?????????? RSQLite_0.7-1???????? DBI_0.2-4???????????? AnnotationDbi_1.4.0? [26] statmod_1.3.6???????? RODBC_1.2-3?????????? RColorBrewer_1.0-2??? vsn_3.8.0???????????? affy_1.20.0????????? [31] Biobase_2.2.0???????? lattice_0.17-15?????? limma_2.16.3???????? ?loaded via a namespace (and not attached): [1] affyio_1.10.1??????? cluster_1.11.11????? preprocessCore_1.4.0 ---------------------------------------------------------------------- -------------------------------------------------------------- ?
microarray go probe • 542 views
modified 10.8 years ago by Kasper Daniel Hansen6.4k • written 10.8 years ago by Chen, Zhuoxun40
Answer: Problem with p-values calculated by eBayes--corrected format
0
10.8 years ago by
United States
Kasper Daniel Hansen6.4k wrote:
On Jan 9, 2009, at 9:21 , Chen, Zhuoxun wrote: > Hi Bioconductors, > > I am really sorry about sending this email again. I didn't know that > the table on my email will be lost and reformat. I corrected the > format now. Thank you for your patience. > > I have a very weird problem with the statistics with my microarray > data. I would like to ask for your help. > I am running a microarray with 16 groups, 3 samples/group. On my > genechip, every probe is spotted 2 times. > By comparing two groups (let?s say A and B), I came across a gene > that is very significant by running the following codes, with a p- > value= 0.001669417 > -------------------------------------------------------------------- ---------------------------------------- > corfit <- duplicateCorrelation(Gvsn, design = design, ndups = 2, > spacing = 1) > fit <- lmFit(Gvsn, design = design, ndups = 2, spacing = 1, > correlation = corfit$consensus) > contrast.matrix <- makeContrasts(A-B, levels=design) > fit2 <- contrasts.fit(fit, contrast.matrix) > fit3 <- eBayes(fit2) > -------------------------------------------------------------------- ---------------------------------------- > Then, I looked at the raw data; copy and paste onto Excel and did a > simple t-test > > A B > 1 6.938162 7.093199 > 2 7.012382 8.05612 > 3 7.000305 6.99907 This is 1 contrast with 3 samples in each group. But where is the data from the second probe? And what is the values of corfit? > > Avg 6.983616 7.382799 > contrast 0.399182 > > p-value > one tailed, unequal variance, t-test=0.179333 > one tailed, equal variance, t-test=0.151844 > > The p-value is NOT even close to 0.05. Then I looked at the contrast > of fit3$coefficient, it is 0.399182, which indicates the data input > for the codes are correct. > > I don?t understand why it has such a huge difference on p-value > between those two methods. Could somebody please help me with it? You are both allowing for correlation (which may or may not be sensible, that is hard to know unless you post more details) and you do an empirical Bayes correction. So you are pretty far from doing a standard t-test, and I see no big problem in method "A" giving a different answer from method "B" when the two methods are somewhat different.. Explaining in details what the difference is, is way beyond the scope of an email. A super short answer is that you combine information from having multiple spots measuing the same transcript and that you borrow information about the gene-level variance from looking at the behaviour of all genes. If you want more details, I suggest you read up on mixed models as well as empirical bayes correction. A good starting point will Gordon's sagmb article, cited in limma. Kasper | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3227030634880066, "perplexity": 4936.595093883702}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986696339.42/warc/CC-MAIN-20191019141654-20191019165154-00410.warc.gz"} |
https://projects.coin-or.org/SYMPHONY/browser/trunk/SYMPHONY/Doc/man-API.tex?rev=1913 | # source:trunk/SYMPHONY/Doc/man-API.tex@1913
Last change on this file since 1913 was 1913, checked in by tkr, 3 years ago
Fixing a few things
• Property svn:eol-style set to native
• Property svn:keywords set to Author Date Id Revision
File size: 26.4 KB
Line
1%===========================================================================%
2% %
3% This file is part of the documentation for the SYMPHONY MILP Solver. %
4% %
5% SYMPHONY was jointly developed by Ted Ralphs (ted@lehigh.edu) and %
7% %
9% %
11% accompanying file for terms. %
12% %
13%===========================================================================%
14
15\section{Using SYMPHONY Interactively}
16
17\subsection{Unix-like Environments}
18
19If you are planning to use the interactive optimizer in a Unix-like
20environment and you are building SYMPHONY from source, it is recommended that
21you run the configuration script (see Section \ref{configuring}) with the
22command-line argument that enables GNU packages, i.e.,
23{\color{Brown}
24\begin{verbatim}
25 ./configure --enable-gnu-packages
26\end{verbatim}
27} This will allow the interactive shell to behave exactly like a Linux
28terminal command line, i.e., it will keep the history of the used commands,
29will do command completion, etc. Note that you must have the required packages
31
32To use SYMPHONY's interactive shell, run the executable without any
33command line arguments, i.e., type
34{\color{Brown}
35\begin{verbatim}
36 bin/symphony
37\end{verbatim}
38} You will enter a command shell environment where you will be prompted for
39inputs. The user interface consists of a \emph{main menu}, where an instance
40is read in and solved, a \emph{set menu}, where parameters are set, and a
41\emph{display menu}, where results, statistics and parameter values are
42displayed.
43
44\subsection{Microsoft Windows}
45
46To invoke SYMPHONY's interactive solver in an Microsoft Windows environment,
47simply double-click on the \code{symphony.exe} file in Windows Explorer. This
48should open a terminal window in which the solver will run. Note that if you
49built SYMPHONY in CYGWIN without the option \code{--enable-dos-compile}, then
50you will have to have the CYGWIN DLL in your path in order for the executable
51to run.
52
54
55Below is the main menu displayed at the beginning of a new session:
56
57{\color{Brown}
58\begin{verbatim}
59 *******************************************************
60 * This is SYMPHONY Version 5.4.0 *
61 * Copyright 2000-2011 Ted Ralphs *
64 *******************************************************
65
66 ***** WELCOME TO SYMPHONY INTERACTIVE MIP SOLVER ******
67
68 Please type 'help'/'?' to see the main commands!
69
70 SYMPHONY:
71\end{verbatim}
72}
73When you type \code{help} or \code{?}, a list of main commands is displayed:
74{\color{Brown}
75\begin{verbatim}
76 SYMPHONY: help
77
78 List of main commands:
79
81 solve : solve the problem
82 lpsolve : solve the lp relaxation of the problem
83 set : set a parameter
84 display : display optimization results and stats
85 reset : restart the optimizer
86 help : show the available commands/params/options
87
88 quit/exit : leave the optimizer
89
90 SYMPHONY:
91\end{verbatim}
92}
93Following is an illustration of a session to read in a sample instance:
94{\color{Brown}
95\begin{verbatim}
97 Name of the file: sample.mps
98 Coin0001I At line 1 NAME SAMPLE
99 Coin0001I At line 2 ROWS
100 Coin0001I At line 6 COLUMNS
101 Coin0001I At line 25 RHS
102 Coin0001I At line 28 BOUNDS
103 Coin0001I At line 34 ENDATA
104 Coin0002I Problem SAMPLE has 2 rows, 6 columns and 10 elements
105 SYMPHONY:
106\end{verbatim}
107}
108The format of the input file is recognized from the file extension. If there is
109none, you will be prompted to define the input format:
110{\color{Brown}
111\begin{verbatim}
113 Name of the file: sample
114 Type of the file ('mps'/'ampl'/'gmpl'): mps
115 Coin0001I At line 1 NAME SAMPLE
116 Coin0001I At line 2 ROWS
117 Coin0001I At line 6 COLUMNS
118 Coin0001I At line 25 RHS
119 Coin0001I At line 28 BOUNDS
120 Coin0001I At line 34 ENDATA
121 Coin0002I Problem SAMPLE has 2 rows, 6 columns and 10 elements
122 SYMPHONY:
123\end{verbatim}
124}
125If the input is in AMPL/GMPL format, you will also be prompted to read in a
126data file (note again that in order to enable GMPL/AMPL reader, you have to
127install GLPK---see Section
128\ref{building})):
129{\color{Brown}
130\begin{verbatim}
132 Name of the file: sample.mod
133 Name of the data file: sample.dat
134 Reading model section from sample.mod...
136 Reading data section from sample.dat...
138 Generating nb...
139 Generating cost...
140 Model has been successfully generated
141 SYMPHONY:
142\end{verbatim}
143}
145corresponding integer program or \code{lpsolve} to solve its linear
146relaxation:
147{\color{Brown}
148\begin{verbatim}
149 SYMPHONY: solve
150
151 ****** Found Better Feasible Solution !
152 ****** Cost: -40.000000
153
154
155 ****************************************************
156 * Optimal Solution Found *
157 ****************************************************
158
159 SYMPHONY: lpsolve
160
161 ****** Found Better Feasible Solution !
162 ****** Cost: -43.000000
163
164
165 ****************************************************
166 * Optimal Solution Found *
167 ****************************************************
168
169 SYMPHONY:
170\end{verbatim}
171}
172As above, only the objective values of the feasible solutions found so far and
173the termination code of the solution process will be displayed (see Section
175
177The \code{Set} submenu is used to set SYMPHONY's run-time parameters. To enter
179\begin{verbatim}
180SYMPHONY: set
181Please type 'help'/'?' to see the list of parameters!
182SYMPHONY\Set:
183\end{verbatim}
184}
185You can override the default value of a parameter by typing the name of
186the parameter. You will then be prompted
187to enter the new value of that parameter. For instance, in order to
188display more outputs during the solution process, you need to set the
189\code{verbosity} parameter (set to -1 by default for the interactive shell
190routines) to a nonnegative integer:
191{\color{Brown}
192\begin{verbatim}
193SYMPHONY\Set: verbosity
194Value of the parameter: 3
195Setting verbosity to: 3
196SYMPHONY\Set:
197\end{verbatim}
198}
199A confirmation message will also be displayed. Note that typing \code{help}
200or \code{?} displays only a subset of the most commonly used run-time
201parameters. However, you are allowed to set any of the parameters given in
202Section \ref{params}. Additionally, you can set the values of parameters using
203a parameter file as an input. In such a file, the new value of each parameter
204must follow the name of that parameter. For instance, suppose that the
205\code{my\_param} file consists of the following lines:
206\begin{verbatim}
207 verbosity 3
208 node_selection_rule 3
209 time_limit 100
210\end{verbatim}
211Then, type \code{param\_file} to be prompted to read in the parameter file:
212{\color{Brown}
213\begin{verbatim}
214 SYMPHONY\Set: param_file
215 Name of the parameter file: my_param
216 Setting verbosity to: 3
217 Setting node_selection_rule to: 3
218 Setting time_limit to: 100
219 SYMPHONY\Set:
220\end{verbatim}
221}
223load an instance and solve it with updated run-time parameters.
224
226
227The \code{Display} submenu is used to print out results and statistics of the
228solution process after a \code{solve} call. To enter this submenu and see
229available options, type \code{display} and then \code{help} or \code{?}:
230{\color{Brown}
231\begin{verbatim}
232 SYMPHONY: display
233 Please type 'help'/'?' to see the display options!
234 SYMPHONY\Display: help
235
236 List of display options:
237
238 solution : display the column values
239 obj : display the objective value
240 stats : display the statistics
241 parameter : display the value of a parameter
242
243 back : leave this menu
244 quit/exit : leave the optimizer
245
246 SYMPHONY\Display:
247\end{verbatim}
248}
249Clearly, in order to display column solutions and the optimal solution value,
250you need to type \code{solution} and then \code{obj}:
251{\color{Brown}
252\begin{verbatim}
253 SYMPHONY\Display: solution
254 Optimal Solution found!
255 +++++++++++++++++++++++++++++++++++++++++++++++
256 Nonzero column names and values in the solution
257 +++++++++++++++++++++++++++++++++++++++++++++++
258 COL00002 3.000
259 COL00006 1.000
260
261 SYMPHONY\Display: obj
262 Objective Value: -40.000000
263 SYMPHONY\Display:
264\end{verbatim}
265}
266You can also display the values of SYMPHONY's run-time parameters (see Section
267\ref{params}) by moving into \code{parameters} submenu:
268{\color{Brown}
269\begin{verbatim}
270 SYMPHONY\Display: parameter
271 Please type 'help'/'?' to see the list of available parameters!
272 SYMPHONY\Display\Parameter:
273\end{verbatim}
274}
275For instance, in order to display the verbosity level, type \code{verbosity}:
276{\color{Brown}
277\begin{verbatim}
278 SYMPHONY\Display\Parameter: verbosity
279 The value of verbosity: 3
280 SYMPHONY\Display\Parameter:
281\end{verbatim}
282}
283As in Set submenu, typing \code{help} or \code{?} will display only a subset of
284available run-time parameters. However, you are allowed to display the value of
285any of the parameters given in Section \ref{params}.
286
288
289SYMPHONY's interactive optimizer also allows the user to reach the lower
290level menu commands from the higher level menus. In other words, the user
291has the flexibility to use submenu commands without entering the
292corresponding submenu. As an instance, all three of the following sessions
293have the same result:
294{\color{Brown}
295\begin{itemize}
296\item
297 \begin{verbatim}
298 SYMPHONY: display parameter verbosity
299 \end{verbatim}
300\item
301 \begin{verbatim}
302 SYMPHONY: display
303 Please type 'help'/'?' to see the display options!
304 SYMPHONY\Display: parameter verbosity
305 \end{verbatim}
306\item
307 \begin{verbatim}
308 SYMPHONY: display
309 Please type 'help'/'?' to see the display options!
310 SYMPHONY\Display: parameter
311 Please type 'help'/'?' to see the list of available parameters!
312 SYMPHONY\Display\Parameter: verbosity
313 \end{verbatim}
314\end{itemize}
315}
316This flexibility is also enabled for the \code{load} command and the Set
317submenu. The followings are all valid commands:
318{\color{Brown}
319 \begin{verbatim}
321 \end{verbatim}
322 \begin{verbatim}
324 \end{verbatim}
325 \begin{verbatim}
326 SYMPHONY: set
327 SYMPHONY\Set: verbosity 3
328 \end{verbatim}
329 \begin{verbatim}
330 SYMPHONY: set verbosity 3
331 SYMPHONY: set param_file my_param
332 \end{verbatim}
333}
334
335\section{Using SYMPHONY from the Command Line}
336
337For batch processing and scripting, SYMPHONY can also be called from the
338command line from a terminal in any operating system (note that in the Windows
339terminal, the path separator is \code{\bs} rather than \code{/}).
340When called from the command line, a number of command-line switches can be
341invoked to specify the file to be read and solved, as well as set parameters.
342Note that the switches are Unix-style, even in Windows). At a minimum, one must
343specify the name of the file to be read and solved. The following is the
344calling sequence to load in an instance file in MPS format and
345solve it.
346{\color{Brown}
347\begin{verbatim}
348 ./symphony -F sample.mps
349\end{verbatim}
350}
351To read and solve a model in LP format, the command would be
352{\color{Brown}
353\begin{verbatim}
354 ./symphony -L sample.lp
355\end{verbatim}
356}
357To read and solve a GMPL model and associated data file, the command would be
358{\color{Brown}
359\begin{verbatim}
360 ./symphony -F sample.mod -D sample.dat
361\end{verbatim}
362}
363In addition to specifying the name of the instance file, most of the common
364parameters can also be set on the command line by adding various switches.
365Calling \BB\ with just the argument \code{-h} will list all the options. To
366set parameters that cannot be set on the command line or to save parameter
367setting, it is possible to use a parameter file in which a group of parameters
368can be set. To invoke \BB\ with a parameter file, type \code{./symphony -f
369filename}, where \code{filename} is the name of the parameter file. The format
370of the file and a list of all parameters is given in Section
371\ref{parameter_file}.
372
373The output level can be controlled through the use of the verbosity parameter,
374which can be invoked Setting this parameter at different levels will cause
375different progress messages to be printed out. Level 0 only prints out the
376introductory and solution summary messages, along with status messages every
37710 minutes. Level 1 prints out a message every time a new node is created.
378Level 3 prints out messages describing each iteration of the solution process.
379Levels beyond 3 print out even more detailed information. To get no output at
380all, the verbosity level must be set to -2.
381
382%There are also two possible graphical interfaces. For graph-based
383%problems, the Interactive Graph Drawing Software allows visual display
384%of fractional solutions, as well as feasible and optimal solutions
385%discovered during the solution process. For all types of problems,
386%VBCTOOL creates a visual picture of the branch and cut tree, either
387%in real time as the solution process evolves or as an emulation from a
388%file created by
389%\BB. See Section \ref{tm_params} for information on how to use VBCTOOL
390%with SYMPHONY. Binaries for VBCTOOL can be obtained at \\
392%{http://www.informatik.uni-koeln.de/ls\_juenger/projects/vbctool.html}
393%{http://www.informatik.uni-koeln.de/ls\_juenger/projects/vbctool.html}}.
394
395\section{Using the Callable Library}\label{callable_library}
396
397SYMPHONY's callable library consists of a complete set of subroutines for
399algorithms. The user invokes these subroutines through the API specified in
400the header file \code{symphony\_api.h}. Some of the basic commands are
401described below. For the sake of brevity, the arguments have been left out.
402
403\subsection{The C API}
404
405\paragraph{\ptt{sym\_open\_environment()}} Opens a new environment, and
406returns a pointer to it. This pointer then has to be passed as an argument to
407all other API subroutines (in the C++ interface, this pointer is maintained
408for the user).
409
410\paragraph{\ptt{sym\_parse\_command\_line()}} Invokes the built-in
411parser for setting commonly used parameters, such as the file name which to
412read the problem data, via command-line switches. A call to this subroutine
413instructs SYMPHONY to parse the command line and set the appropriate
414parameters. This subroutine also sets all other parameter values to their
415defaults, so it should only called when this is desired.
416
418the root subproblem. This includes specifying which cuts and variables are in
419the \emph{core} (those that are initially present in every subproblem during
420the search process) and the additional cuts and variables to be initially
421active in the root subproblem. By default, SYMPHONY reads an MPS or GMPL
422file specified by the user, but the user can override this default by
423implementing a user callback that reads the data from a file in a customized
424format (see Section \ref{callback}).
425
426\paragraph{\ptt{sym\_find\_initial\_bounds()}} Invokes the user callback to
427find initial bounds using a custom heuristic.
428
429\paragraph{\ptt{sym\_solve()}} Solves the currently loaded problem from
430scratch. This method is described in more detail in Section
431\ref{initial_solve}.
432
433\paragraph{\ptt{sym\_warm\_solve()}} Solves the currently loaded problem
434from a warm start. This method is described in more detail in
435Section \ref{warm_solve}.\\
436
437\paragraph{\ptt{sym\_mc\_solve()}} Solves the currently loaded problem as a
438multicriteria problem. This method is described in more detail in Section
439\ref{mc_solve}.
440
441\paragraph{\ptt{sym\_close\_environment()}} Frees all problem data and
442deletes the environment. \\
443
444\noindent As an example of the use of the library functions, Figure
445\ref{default_main} shows the code for implementing a generic MILP solver with
446default parameter settings.
447\begin{figure}[tb]
448%\centering
449{\color{Brown}
450\begin{Verbatim}[frame=lines]
451int main(int argc, char **argv)
452{
453 sym_environment *env = sym_open_environment();
454 sym_parse_command_line(env, argc, argv);
456 sym_solve(env);
457 sym_close_environment(env);
458}
459\end{Verbatim}
460}
461\caption{Implementation of a generic MILP solver with the SYMPHONY
462C callable library. \label{default_main}}
463\end{figure}
464To read in an MPS file called \code{sample.mps} and solve it using
465this program, the following command would be issued: \\
466{\color{Brown}
467\begin{verbatim}
468 ./symphony -F sample.mps
469\end{verbatim}
470}
471To read and solve a model in LP format, the command would be
472{\color{Brown}
473\begin{verbatim}
474 ./symphony -L sample.lp
475\end{verbatim}
476}
477The user does not have to invoke a command to read the input file. During the
478call to \ptt{sym\_parse\_} \ptt{command\_line()}, SYMPHONY determines that the
479user wants to read in an MPS file. During the subsequent call to
481To read an GMPL file, the user would issue the command
482{\color{Brown}
483\begin{verbatim}
484 ./symphony -F sample.mod -D sample.dat
485\end{verbatim}
486}
487Although the same command-line switch is used to specify the model file, the
488additional presence of the \code{-D} option indicates to SYMPHONY that the
489model file is in GMPL format and GLPK's GMPL parser is invoked
490\cite{GLPK}. Note that the interface and the code of Figure \ref{default_main}
491is the same for both sequential and parallel computations. The choice between
492sequential and parallel execution modes is made at compile-time through
493modification of the makefile or the project settings, depending on the
494operating system.
495
496To start the solution process from a warm start, the \ptt{sym\_warm\_solve()}
497command is used. SYMPHONY automatically records the warm start information
498resulting from the last solve call and restarts from that checkpoint if a call
499to \ptt{sym\_warm\_solve()} is made. Alternatively, external warm start
500information can be loaded manually. Figure \ref{dynamic} illustrates the use
501of the re-solve capability by showing the code for implementing a solver that
502changes from depth first search to best first search after the first feasible
503solution is found.
504\begin{figure}[tb]
505%\centering
506{\color{Brown}
507\begin{Verbatim}[frame=lines]
508int main(int argc, char **argv)
509{
510 sym_environment *env = sym_open_environment();
511 sym_parse_command_line(env, argc, argv);
513 sym_set_int_param(env, "find_first_feasible", TRUE);
514 sym_set_int_param(env, "node_selection_strategy", DEPTH_FIRST_SEARCH);
515 sym_solve(env);
516 sym_set_int_param(env, "find_first_feasible", FALSE);
517 sym_set_int_param(env, "node_selection_strategy", BEST_FIRST_SEARCH);
518 sym_warm_solve(env);
519}
520\end{Verbatim}
521}
522\caption{Implementation of a dynamic MILP solver with SYMPHONY.
523\label{dynamic}}
524\end{figure}
525The user can also modify problem data in between calls to the solver. Code for
526doing so is shown in Figure \ref{warm_start}. In this example, the
527solver is allowed to process 100 nodes and then save the warm start
528information. Afterward, the original problem is solved to optimality, then is
529modified and re-solved from the saved checkpoint.
530\begin{figure}[tb]
531%\centering
532{\color{Brown}
533\begin{Verbatim}[frame=lines]
534int main(int argc, char **argv)
535{
536 warm_start_desc *ws;
537 sym_environment *env = sym_open_environment();
538 sym_parse_command_line(env, argc, argv);
540 sym_set_int_param(env, "node_limit", 100);
541 sym_set_int_param(env, "keep_warm_start", TRUE);
542 sym_solve(env);
543 ws = sym_get_warm_start(env);
544 sym_set_int_param(env, "node_limit", -1);
545 sym_warm_solve(env);
546 sym_set_obj_coeff(env, 0, 100);
547 sym_set_obj_coeff(env, 200, 150);
548 sym_set_warm_start(ws);
549 sym_warm_solve(env);
550}
551\end{Verbatim}
552}
553\caption{Use of SYMPHONY's warm start capability. \label{warm_start}}
554\end{figure}
555
556Finally, SYMPHONY now also has a bicriteria solve call. The applications of
557such a solver are numerous. Besides yielding the ability to closely examine
558the tradeoffs between competing objectives, the method can be used to perform
559detailed sensitivity analysis in a manner analogous to that which can be done
560with simplex based solvers for linear programs. As an example, suppose we
561would like to know exactly how the optimal objective function value for a
562given pure integer program depends on the value of a given objective function
563coefficient. Consider increasing the objective function
564coefficient of variable $i$ from its current value. Taking the first objective
565function to be the original one and taking the second objective function to be
566the $i^\textrm{th}$ unit vector, we can derive the desired sensitivity
567function by using the bicriteria solution algorithm to enumerate all supported
568solutions and breakpoints. This information can easily be used to obtain the
569desired function. Figure \ref{multi_criteria} shows the code for performing
570this analysis on variable 0.
571\begin{figure}[tb]
572%\centering
573{\color{Brown}
574\begin{Verbatim}[frame=lines]
575int main(int argc, char **argv)
576{
577 sym_environment *env = sym_open_environment();
578 sym_parse_command_line(env, argc, argv);
580 sym_set_obj2_coeff(env, 0, 1);
581 sym_mc_solve(env);
582}
583\end{Verbatim}
584}
585\caption{Performing sensitivity analysis with SYMPHONY's bicriteria solver.
586\label{multi_criteria}}
587\end{figure}
588
589In addition to the parts of the API we have just described, there are a number
590of standard subroutines for accessing and modifying problem data and
591parameters. These can be used between calls to the solver to change the
592behavior of the algorithm or to modify the instance being solved. These
593modifications are discussed in more detail in Section \ref{warm_solve}.
594
595\subsection{The C++ API}\label{OSI}
596
597The Open Solver Interface (OSI) is a C++ class that provides a standard API
598for accessing a variety of solvers for mathematical programs. It is provided
599as part of the COIN-OR repository \cite{coin-or}, along with a collection of
600solver-specific derived classes that translate OSI call into calls to the
601underlying libraries of the solvers. A code implemented using calls to the
602methods in the OSI base class can easily be linked with any solver for which
603there is an OSI interface. This allows development of solver-independent codes
604and eliminates many portability issues. The current incarnation of OSI
605supports only solvers for linear and mixed-integer linear programs, although a
606new version supporting a wider variety of solvers is currently under
607development.
608
609We have implemented an OSI interface for SYMPHONY \VER\ that allows any solver
610built with SYMPHONY to be accessed through the OSI, including customized
611solvers and those configured to run on parallel architectures. To ease code
612maintenance, for each method in the OSI base class, there is a corresponding
613method in the callable library. The OSI methods are implemented simply as
614wrapped calls to the SYMPHONY callable library. When an instance of the OSI
615interface class is constructed, a call is made to
616\ptt{sym\_open\_environment()} and a pointer to the environment is stored
617in the class. Most subsequent calls within the class can then be made without
618any arguments. When the OSI object is destroyed,
619\ptt{sym\_close\_environment} is called and the environment is destroyed.
620
621To fully support SYMPHONY's capabilities, we have extended the OSI interface to
622include some methods not in the base class. For example, we added calls
623equivalent to our \ptt{sym\_parse\_command\_line()} and
624\ptt{sym\_find\_initial\_bounds()}. Figure \ref{OSI_main} shows the
625program of Figure \ref{default_main} implemented using the OSI interface.
626\begin{figure}[tb]
627{\color{Brown}
628\begin{Verbatim}[frame=lines]
629int main(int argc, char **argv)
630{
631 OsiSymSolverInterface si;
632 si.parseCommandLine(argc, argv);
634 si.branchAndBound();
635}
636\end{Verbatim}
637}
638\caption{Implementation of a generic MILP solver with the SYMPHONY
639OSI interface. \label{OSI_main}}
640\end{figure}
641Note that the code would be exactly the same for accessing any customized
642SYMPHONY solver, sequential or parallel.
643
644Although we are using the OSI to access a MILP solver, the current version of
645the OSI is geared primarily toward support of solvers for linear programming
646(LP) problems. This is because LP solvers employing some version of the
647simplex algorithm support much richer functionality and a wider range of
648interface functions, due to their support of warm starting from previously
649saved checkpoints. This functionality is difficult to provide for MILP
650solvers. In SYMPHONY \VER, we have implemented for MILPs some of the same
651functionality that has long been available for LP solvers. As such, our OSI
652interface supports warm starting and sensitivity analysis. The implementations
653of this functionality is straightforward at the moment, but will be improved
654in future versions.
655
657
658To link your program to the callable library, make sure you have included the
659header file \code{symphony.h} in all the source files that call SYMPHONY
660functions. Also, make sure that your include path contains the directory where
661all of SYMPHONY's header files are stored. Then simply include the appropriate
662SYMPHONY library in the set of libraries to be linked and make sure that the
663path to the library is in the library path. Example makefiles For Unix-like
664environments are included in the \code{Examples/} directory.
665
666\section{Using the Callback Functions}\label{callback}
667
668The user's main avenues for customization of SYMPHONY are the tuning of
669parameters and the implementation of one or more of over 50 user callback
670functions. The callback functions allow the user to override SYMPHONY's
671default behavior for many of the functions performed as part of its algorithm.
672The user has complete control over branching, cutting plane generation,
673management of the cut pool and the LP relaxation, search and diving
674strategies, etc. More detailed information about using the callback functions
675to develop custom applications is provided in
676Chapter~\ref{SYMPHONY-development}.
677
Note: See TracBrowser for help on using the repository browser. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4395921528339386, "perplexity": 5609.109936088275}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1393999642134/warc/CC-MAIN-20140305060722-00090-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://www.computer.org/csdl/trans/tc/1979/01/01675228-abs.html | Issue No. 01 - January (1979 vol. 28)
ISSN: 0018-9340
pp: 72-75
M.B. Ari , Division of Computer Sciences, Department of Mathematical Sciences, Tel Aviv University
ABSTRACT
This correspondence presents two variations on the algorithm of Eklundh for transposing large 2n x 2n matrices. The first variation shows how the number of accesses to secondary storage may be reduced at the expense of an increased amount of data transferred. Formulas for I/O time are derived from which we deduce the disk characteristics under which there is an improvement. The second variation shows that a small amount of additional secondary storage can be used to greatly improve the performance of the algorithm.
INDEX TERMS
two-dimensional FFT, Digital image processing, externally stored matrices, large matrices, transportation algorithm
CITATION
M. Ari, "On Transposing Large 2<sup>n</sup>x 2<sup>n</sup>Matrices," in IEEE Transactions on Computers, vol. 28, no. , pp. 72-75, 1979.
doi:10.1109/TC.1979.1675228 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9260787963867188, "perplexity": 1724.3866309702391}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794867904.94/warc/CC-MAIN-20180526210057-20180526230057-00589.warc.gz"} |
https://cs.stackexchange.com/questions/19808/how-does-the-3-opt-algorithm-for-tsp-work | How does the 3-opt algorithm for TSP work?
I understand that the 3-Opt Heuristic for solving the Traveling Salesman problem involves removing three edges from a graph and adding three more to recomplete the tour. However, I've seen many papers that mention that when three edges are removed, there remain only 2 possible ways to recombine the tour - this doesn't make sense to me.
For example, I found a paper [1] that says:
The 3-opt algorithm works in a similar fashion, but instead of removing two edges we remove three. This means that we have two ways of reconnecting the three paths into a valid tour1 (figure 2 and figure 3). A 3-opt move can actually be seen as two or three 2-opt moves.
However, I count 3 different ways to reconnect the tour. What am I missing here?
Also, can someone link me to an algorithm for 3-opt if possible? I'm just trying to understand it, but I haven't come across any clear algorithms yet: all resources I find simply say "remove three edges, reconnect them". That's it, which is sort of vague.
Here are the 3 tours that seem to me to be 3-opt moves after removing three edges.
1. Heuristics for the Traveling Salesman Problem by C. Nilsson
• The paper you link is written in a very informal style and gives a nonstandard definition of TSP in the very first sentence; it also doesn't appear to have been published anywhere. Of course, that doesn't affect the validity of your question but there are probably better explanations of 3-OPT than the one you found. – David Richerby Jan 19 '14 at 11:45
• Papers at this level probably assume that interested readers don't have trouble translating a more or less definite description into code. That's common on (T)CS; if that's a hindrance for you, consider reading more basic stuff first in order to get more training. – Raphael Jan 19 '14 at 15:14
• As a high school student, I find none of this stuff basic, haha. Anyways, I'm fairly certain there are more than 2 ways (3 to be exact) to reconnect the tour such that the move wouldn't be identical to a two-opt move... so I was wondering why this paper states there are only two. I've looked for other papers in search for a definitive algorithm I could easily implement but haven't found any, so I tried implementing it (in Java) based on what I know and it didn't really work well, since I'm still confused about how many different ways to reconnect there are. – u3l Jan 19 '14 at 15:58
• for 2d euclidean TSP a tour with intersecting lines can always lead to another tour with no intersecting lines and a shorter tour, ie only case #1 you list (after the initial config) can be considered. maybe some of that info is being left out in the writeup(s) you cite. ie they are not considering/excluding the guaranteed nonoptimal intersecting cases. ps it would be helpful/clearer if you labeled each graph. take it you mean: initial, tour1, tour2, tour3. – vzn Jan 20 '14 at 15:59
• try starting at wikipedia 3opt entry for refs. several are decades old but electronic copies are available. – vzn Jan 20 '14 at 16:05
You missed the footnote — these ways are "not including the connections being identical to a single 2-opt move". Indeed, there are only two permutations in $S_3$ without fixed points (also known as derangements), namely $(123)$ and $(132)$. More generally, for a $k$-opt move it is enough to consider permutations without fixed points, since those with $t$ fixed points are $(k-t)$-moves.
The algorithm for $k$-opt local search is as follows. Start with some initial solution, say the one produced by Christofides's algorithm. Repeatedly try to improve it by performing a $k$-opt: choose $k$ edges and reconnect them in a different way (this time it's OK if the move is also an $\ell$-move for some $\ell < k$) that results in a shorter tour.
The way this is implemented is by going over all sets of $k$ edges and over all ways of reconnecting the edges, perhaps in some intelligent order, and computing the difference in length (there is no need to recompute the length of the entire tour, just the different of length; that takes $O(k)$ instead of $O(n)$); if an improvement is found, we make the switch and repeat from the beginning. We continue like that until we get stuck.
A different variant is to always try all possibilities, and use the one that results in the best improvement. There are also other variants which you can probably find in the literature.
• Okay... I missed that some of those permutations are just single two opt moves now. However, I still count 3 different permutations, excluding the one before the move, which have 0 fixed points. (i'll edit an image into my post in a few minutes) – u3l Jan 19 '14 at 9:22
Lets say we have 3 points A, B and C. First we swap(A,B) and then we only can swap(B,C) or swap(A,C). This way we only have two different possibilities.
• This definitely needs more explanation. – David Richerby Mar 3 '14 at 20:38
• Well... maybe i'm wrong. Correct me please. 2-opt: We have A-B-C-D cities. We swap two and we get A-C-B-D. Only two possibilities, original and one new - ABCD and ACBD. 3-opt: A-B-C-D cities. We swap(1,2) and get BACD. We swap the third city with either first or second and get BCAD - swap(2,3) or CABD by swap(1,3). Three possibilities, original and two new - ABCD, BACD and BCAD. What about k-opt (4,5,6...)? – matejs Mar 6 '14 at 2:18
I could find 4 3-opt moves (which are not 2-opt): If i gave the hexagon tour a numbering of 123456 (starting from the top left vertex), the other tours would have numbers of 125634, 124365, 126534 and 125643, which are a subset of the derangement of 12[3456] (where 3456 is being deranged).
• Welcome to the site, but I'm not sure how this answers the question. On Stack Exchange sites, we're looking for the answer to the question at the top of the page, not for "here's some related information." – David Richerby Sep 26 '16 at 23:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5976679921150208, "perplexity": 686.9643041913693}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347445880.79/warc/CC-MAIN-20200604161214-20200604191214-00494.warc.gz"} |
https://aplwiki.com/wiki/Compress | # Replicate
(Redirected from Compress)
`/` `⌿`
Replicate (`/`, `⌿`), or Copy (`#`) in J, is a dyadic function or monadic operator that copies each element of the right argument a given number of times, ordering the copies along a specified axis. Typically `/` is called Replicate while `⌿` is called "Replicate First" or an equivalent. Replicate is a widely-accepted extension of the function Compress, which requires the number of copies to be Boolean: each element is either retained (1 copy) or discarded (0 copies). Replicate with a Boolean left argument or operand may still be called "Compress".
Replicate is usually associated with Expand (`\`), and the two functions are related to Mask and Mesh. It is also closely related to the Indices function. It shares a glyph with Reduce even though Replicate is naturally a function and Reduce must be an operator. This incongruity is sometimes resolved by making Replicate an operator itself, and sometimes by function-operator overloading allowing both syntactic elements to coexist.
Outside of APL, filter typically provides the functionality of Compress, while Replicate has no common equivalent.
## Examples
When used with a Boolean array (often called a "mask") on the left, Replicate is called Compress. It filters the right argument, returning only those elements which correspond to 1s in the provided mask.
``` 1 1 0 1 0 1 0 0 / 'compress'
cope
```
If the right argument is an array of indices generated by Iota, Replicate resembles the function Indices.
``` 1 1 0 0 1 / ⍳5
1 2 5
```
With an array of non-negative integers, Replicate copies each element of the right argument the corresponding number of times. As with Compress, these copies retain their original ordering, and the length of the result is the sum of the control array.
``` 0 3 0 0 2 0 1 0 2 / 'replicate'
eeeiiaee
+/ 0 3 0 0 2 0 1 0 2
8
⍴ 0 3 0 0 2 0 1 0 2 / 'replicate'
8
```
Replicate usually allows scalar extension of the left argument, which results in every element being copied a fixed number of times.
``` 3 / 'replicate'
rrreeepppllliiicccaaattteee
```
### Negative numbers
An extension introduced by NARS allows either positive or negative integers, where a negative number indicates that a fill element should be used instead of an element from the right argument. In this case the argument lengths must be equal (unless one side is a singleton). APL2 defined a different extension: negative numbers do not correspond to any element of the right argument, but still indicate that many fills should be inserted. In the APL2 extension the length of the right argument is the number of non-negative elements in the left argument. In both extensions the length of the result is the sum of the absolute value of the control array.
``` 0 2 ¯3 1 / ⍳4
2 2 0 0 0 4
```
``` 0 2 ¯3 1 / ⍳3
2 2 0 0 0 3
```
Works in: APL2, APLX, GNU APL
The extensions are the same when the right argument is subject to singleton extension. This extension was usually supported before any extension to negative numbers, but would not typically be useful because `v/s` ${\displaystyle \Leftrightarrow }$ `(+/v)/s` where `v` is a non-negative integer vector and `s` is a singleton.
``` 1 ¯2 3 / 'a'
a aaa
```
### High-rank arrays
Replicate works along a particular axis, which can be specified in languages with function axis and otherwise is the first axis for `⌿`, and the last axis for `/` (except in A+, which uses `/` for the first-axis form and has no last-axis form).
``` ⎕←A ← 4 6⍴⎕A
ABCDEF
GHIJKL
MNOPQR
STUVWX
1 0 0 4 0 2 / A
GJJJJLL
MPPPPRR
SVVVVXX
0 2 1 1 ⌿ A
GHIJKL
GHIJKL
MNOPQR
STUVWX
```
APL2 further extends the singleton extension of the right argument, allowing it to have length 1 along the replication axis even if other axes have lengths not equal to 1.
``` 1 ¯2 3 / ⍪'abc'
a aaa
b bbb
c ccc
```
dzaima/APL expects arguments of `⌿` to have matching shape, and replicates the ravel of both.
### Operator or function?
The syntax `a / b` is ambiguous: it may be an invocation of a dyadic function `/` with left argument `a` and right argument `b`, or of a monadic operator with operand `a` and right argument `b`. In early APLs there was no way to resolve this ambiguity, but with the extension of operators to allow arbitrary function operands instead of a specified set of primitive functions, the distinction becomes apparent: a function Replicate can be used as an operand while an operator Replicate cannot.
One test of Replicate's nature is to try Replicate Each[1] with an expression such as `1 3 /¨ 'ab' 'cd'`. If Replicate is implemented as an operator, it will be applied to the operand `1 3`, and Each will be applied to the resulting derived function `1 3/`.
``` 1 3 /¨ 'ab' 'cd'
abbb cddd
(1 3/)¨ 'ab' 'cd'
abbb cddd
```
Works in: SHARP APL (with `¨>` in place of `¨`), APL2, APLX
If Replicate is a function, then Each will apply to Replicate only, and the resulting derived function will be invoked monadically.
``` 1 3 /¨ 'ab' 'cd'
ab cccddd
1 3 (/¨) 'ab' 'cd'
ab cccddd
```
In early APLs such as APL\360, applying an operator to Compress will always result in a SYNTAX ERROR, because Compress is not an allowed operand of any operator. This is also the case in ngn/apl: although operators can apply to any function, Replicate cannot be used unless both arguments are immediately available. In both cases there is no way to determine whether Replicate "acts like a function" or "acts like an operator".
## History
Compress was described in A Programming Language, where it was written with the symbols ${\displaystyle /}$ and ${\displaystyle /\!\!/}$. In Iverson notation compression was particularly important because Take and Drop could be performed only by compression with a prefix or suffix vector. It was included in APL\360, which changed the doubled slash to a barred slash `⌿`, and allowed a specified axis and singleton extension on both sides (very briefly, singleton extension was allowed only for the right argument[2]). The APL\360 definition continued to be included in APLs unchanged until 1980.
In 1980, Bob Bernecky introduced the extension Replicate to SHARP APL: he allowed an operand (since SHARP's Replicate is an operator) consisting of non-negative integers rather than just Booleans to indicate the number of times to copy.[3] This extension was rapidly and widely adopted, starting with NARS in 1981, and is now a feature of the ISO/IEC 13751:2001 standard.
Two extensions to allow negative numbers in the left argument have been introduced, in each case specifying that the negative of a number indicates that many fill elements should appear in the result. In 1981 NARS specified that these fill elements replace the corresponding right argument element, so that the lengths of the left and right arguments are always equal, and extended Expand similarly. APL2, in 1984, made the opposite choice, so that the length of the right argument along the specified axis is equal to the number of non-negative elements on the left. APL2 also loosened the conformability requirements further than simply allowing singleton extension: it allowed a right argument with length 1 along the replication axis to be extended. Dyalog APL, created before APL2, adopted the NARS definition for negative elements but added APL2 conformability extension in version 13.1. Later APLX took advantage of the fact that the two negative number extensions can be distinguished by the length of the left argument, and implemented every NARS and APL2 extension.
A+ and J modified Replicate to fit leading axis theory. Rather than allow Replicate to operate on any axis they have only one Replicate function (in A+, `/`; in J, `#`) which works on the first axis—it copies major cells rather than elements. Both languages rejected the NARS extension to negative left arguments, but J introduced its own system to add fill elements by allowing complex numbers in the left argument, and removed the Expand function entirely. Arthur Whitney went on to make a more radical change in K, removing Replicate entirely in favor of Where.
## Extension support
Here ">1" refers to the SHARP APL extension to non-negative integers, while "<0" refers to extension to negative integers in either NARS or APL2 style. Conformability refers to extension of the right argument only, as all languages allow scalar extension of the left argument.
Language Type >1 <0 Conformability
extension
Axis
specification
Notes
NARS APL2
APL\360 Ambiguous No No Single Yes
SHARP APL Operator Yes No Scalar Yes
NARS, NARS2000 Function Yes Yes No Single Yes
Dyalog APL Function Yes Yes No APL2 (13.1) Yes
APL2 Operator Yes No Yes APL2 Yes
A+ (`/`) Function Yes No Single No
J (`#`) Function Yes No Scalar No Complex left argument allowed
ISO/IEC 13751:2001 Function Yes No Scalar Yes
APLX Operator Yes Yes Yes APL2 Yes
ngn/apl Ambiguous Yes Yes No APL2 Yes Implemented as an operator
GNU APL Function Yes No Yes APL2 Yes
dzaima/APL (`⌿`) Function Yes Yes No No No
BQN (`/`) Function Yes No No No Multiple leading axes supported
In each language without axis specification, there is only one form of Replicate, which applies to the first axis or major cells—the last-axis form is discarded. BQN extends this form to allow any number of leading axes to be manipulated if the left argument has depth 2.
## Outside of APL
While Replicate is rarely used in non-array programming languages, Compress is sometimes seen. Usually the same functionality is provided by the higher-order function filter, which an APLer might define as the monadic operator `filter←{(⍺⍺¨ ⍵) / ⍵}` on a vector argument.
While filter is similar to Compress, some extensions to the x86 instruction set are exactly equivalent to Compress on particular data types. In BMI2, the PEXT and PDEP instructions (parallel bit extract and deposit) are identical to Compress and Expand on the bits of a register argument. Indeed, Dyalog APL uses these instructions to implement those primitives (see Dyalog APL#Instruction set usage). The AVX-512 instructions VPCOMPRESSQ and VPEXPANDQ (and variations) are not only equivalent to Compress and Expand using a mask register for the Boolean argument and a vector register for the other argument, but are named after the APL functions. These instructions allow compression of 4-byte and 8-byte elements, and with AVX-512_VBMI2 support was added for 1-byte and 2-byte elements as well. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 3, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7615586519241333, "perplexity": 2013.161817144677}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323588246.79/warc/CC-MAIN-20211028003812-20211028033812-00290.warc.gz"} |
https://socratic.org/questions/if-a-polynomial-function-with-rational-coefficients-has-the-zeros-2-3i-what-are- | Precalculus
Topics
If a polynomial function with rational coefficients has the zeros 2-3i, what are the additional zeros?
One root is given as $2 - 3 i$, another roots must be $2 + 3 i$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 2, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7746770977973938, "perplexity": 652.2235732542116}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107909746.93/warc/CC-MAIN-20201030063319-20201030093319-00441.warc.gz"} |
http://mathhelpforum.com/calculus/113786-give-example-prove.html | # Math Help - Give example and prove it
1. ## Give example and prove it
An open subinterval of the closed interval [a, b] is an open interval (c, d)
such that (c, d) subset of [a, b] (i.e. a <= c < d <= b). Give an example of numbers a < b and of a function f : [a, b] --> R which is increasing on
every open subinterval of [a, b] and is not increasing on [a, b]. Be sure
to justify your example (Hint: Choose f to be discontinuous.)
I am really bad at something that contains with intervals
2. The first thing I would notice is that (a, b) is an open subinterval of [a,b]. So your example function must be increasing on (a, b) (and there is a very easy example of such a function). And then you would need to pick values for f(a) and f(b) so that the function on [a,b] is NOT increasing. Again, fairly easy.
3. Originally Posted by HallsofIvy
The first thing I would notice is that (a, b) is an open subinterval of [a,b]. So your example function must be increasing on (a, b) (and there is a very easy example of such a function). And then you would need to pick values for f(a) and f(b) so that the function on [a,b] is NOT increasing. Again, fairly easy.
I have got an example
f(x) = 1 if x = 0,
f(x) = x if 0<x<2,
f(x) = 1.5 if x = 2
This function is continuous and increasing in every open subinterval of [0,2]
But it is not increasing in [0,2].
but I dont know how to prove it, can you show me the proof? | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8751189708709717, "perplexity": 375.71119999563444}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783393332.57/warc/CC-MAIN-20160624154953-00189-ip-10-164-35-72.ec2.internal.warc.gz"} |
https://www.helpteaching.com/tests/360849/volume-calculations | ##### Notes
This printable supports Common Core Mathematics Standard 8.G.C.9
##### Print Instructions
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## Volume Calculations
1.
What is the approximate volume of a cone with a height of 6 cm and a base radius of 2 cm? (Use $pi$ = 3.14).
1. 25 cubic centimeters
2. 23 cubic centimeters
3. 75 cubic centimeters
4. 38 cubic centimeters
2.
Compute the height (in meters) of a cylinder with a radius of 2m and volume 138 cubic meters. Round to the nearest meter. (Use $pi$ = 3.14)
1. 8 m
2. 14 m
3. 11 m
4. 22 m
3.
Find the volume of a cylinder with a radius of 6 cm and a height of 21 cm. Use $22//7$ for pi.
1. 396 cubic centimeters
2. 792 cubic centimeters
3. 2,772 cubic centimeters
4. 2,376 cubic centimeters
4.
Find the volume of a sphere with a radius of 20 mm. Use 3.14 for pi.
1. 251.2 cubic millimeters
2. 125.6 cubic millimeters
3. 100,480 cubic millimeters
4. 33,493.33 cubic millimeters
5.
What is the approximate volume of a cone with a height of 8 cm and a base radius of 3 cm? (Use $pi$ = 3.14)
1. 75.36 cubic centimeters
2. 72 cubic centimeters
3. 71 cubic centimeters
4. 70 cubic centimeters
6.
A water tank is in the shape of a right circular cylinder with a height of 20 feet and a volume of $320pi$ cubic feet. What is the diameter, in feet, of the water tank?
1. 16
2. 10
3. 8
4. 4
7.
Thomas fills an ice cream cone to the top edge. The diameter of the ice cream cone is 2 inches and its height is 6 inches. Dan fills a bowl (with a volume of 5 cubic inches) with ice cream. Thomas has how much more ice cream than Dan?
1. 1.2 cubic inches
2. 1.28 cubic inches
3. 1.1 cubic inches
4. 1 cubic inches
8.
The average size of a cylindrical trash can is 4 ft high with a diameter of 1.5 ft. What is the volume of a trash can that is one foot taller and has a diameter the same as the average sized can?
1. 8.84 cubic feet
2. 8.82 cubic feet
3. 8.80 cubic feet
4. 8.86 cubic feet
9.
Andrew's job is to attach a ladder to a water tank. The water tank is a 20 feet wide cylinder and has a volume of 9,420 cubic feet. If the length of the ladder is equal to the height of the water tank, how long is the ladder?
1. 30 ft
2. 9.5 ft
3. 8.9 ft
4. 11 ft
10.
A pencil has a diameter of 0.75 cm and a length of 20 cm. How much wood is in the pencil?
1. 26.5 $cm^3$
2. 8.8 $cm^3$
3. 35.3 $cm^3$
4. 6.3 $cm^3$
You need to be a HelpTeaching.com member to access free printables. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5813031196594238, "perplexity": 1840.7214665347892}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655888561.21/warc/CC-MAIN-20200705184325-20200705214325-00315.warc.gz"} |
https://tetrisconcept.net/threads/would-you-go-to-a-nyc-arcade-for-ttgm.1611/ | # Would you go to a NYC arcade for TTGM?
Thread in 'Locations & Events' started by BankBank, 24 Aug 2010.
1. ### BankBank
Hey everyone. Long time lurker here.
Long story short: I'm looking to open an arcade in Manhattan on 38th street between 5th and 6th avenue. The business model will be a little bit different: I'll have a mix of FREE console games and regular arcade games. There will be a $5 cover charge to come in, then you can stay and play as much as you want. If I spent the money on a TypeX+ or whatever and had TTGM (perhaps not the latest version, but TTGM in a real arcade setting), would YOU come play it? If my expenses are$3500 a month and I get $5 per head, that means i need 700 heads per month, or 23 1/3 heads per day to just break even on my monthly expenses. Thanks for your input everyone. 2. ### KevinDDR I don't live anywhere near Manhattan, but I've had a TGM board in an arcade before so here's my unimportant advice. These are the prices you can expect to pay for each version: TGM1:$150 (but this is kind of a boring game, most players don't like it that much)
TGM2+ (TAP): $700 (most players think this is the best version) TGM3 (Ti):$1200 (many players like this version too, and it runs on TypeX hardware like you mentioned)
It seems that $5 is a bit low of a charge. I've easily spent$30 in one trip to the arcade before, so you might want to change that a little. Still, it's great to hear that someone wants to both open an arcade and put TGM in it.
3. ### BankBank
thanks for the info on the approximate cost of the games. does TGM2+ for $700 include the entire game board system, and all I need to do is hook it into a cabinet? tetris seems like a good game to have at the arcade. Does the TGM series have an appeal to both casual AND hardcore players alike?$5 is just to get in the door. There are tons of free XBOX360 setups with Super Street Fighter 4 (or whatever other game). Then there are arcade machines from $0.25 to$0.75. There will be nice couches and big screen TVs, so you can literally pay $5 and play all day. It's a good value, I think. The big question is whether I can get 25 people in the door each day to break even on the rent and expenses. If I can do that, and there's people in the place, I think the games will pay for themselves and then make money. If 25 people per day on average DON'T come, then I'm out about$15,000, heh.
4. ### KevinDDR
Ah, okay. That sounds good. I think you'll manage to get 25 people in per day if you have a good selection of Japanese arcade games and interesting stuff. The cost is the entire PCB, and you just need to hook it up to a JAMMA based arcade cabinet. I suggest a Japanese sitdown style candy cabinet such as the Astro City, but ultimately anything will work. However, you must use a certain set of sticks and buttons in the cabinet (the Sanwa JLF joystick [set to 4 way mode, this is important] and the OBSF/OBSN buttons) as TGM players generally refuse to play on anything else.
5. ### Muf
TGM and TAP are regular JAMMA boards and will work in any JAMMA compliant cabinet, no extra hardware required. I personally would recommend a candy cabinet with Sanwa JLF (4-way restrictor) and OBSF-30 controls, this is de facto for the tetris community. TGM3Ti requires a VGA (31khz) capable monitor, a cabinet amplifier (to bring sound from line level to 8 ohm speaker level) and a JVS I/O board. A JVS cabinet like a Naomi Universal or Net City will have all of those out of the box - other cabinets may have the latter two (amp and JVS wiring) but possibly require a monitor/CRT chassis upgrade. Ti will work on a regular JAMMA screen using the 15KHz video port, but the image will be blurry and flickery and repel customers, so I strongly recommend a 31KHz monitor instead. For more details on arcade hardware and what will work with what, I've written up a fairly comprehensive post about the subject.
As for casual gamers, you may want to look at TGM1 for that. The game is much easier and people will get further along in the game before dying. But I think the real appeal for TGM games in any real arcade, for both casual and hardcore gamers, are the multiplayer options. All three games have hilarious versus modes that are only as difficult to play as the player you're playing against, so two casual players will have as much fun playing as two hardcore players will.
To get an idea, here's three videos of versus on YouTube:
Casual gamers playing TGM1 versus at Arcade UFO in Texas
Semi-hardcore gamers playing Death versus casually
Hardcore gamers playing TGM3Ti versus
Additionally, TAP has Doubles mode which is lots of fun for all. I think the games have casual potential, but you might need to market it a bit with a poster or leaflet explaining how to get the most fun out of the game.
A proper Manhattan arcade sounds like an awesome idea to me, and like I said on IRC, if that arcade was there when I visited NYC in 2008, I probably wouldn't have seen much of the sights I did, but would have been stuck in that arcade all day. I really hope you can make it work out!
6. ### Zircean
Oh my god this would be delightful.
I live out on Long Island and it would be absolutely amazing if there was actual TGM somewhere near me.
Maybe now we can get this East Coast meet together...
7. ### AmnesiaPiece of Cake
You are talking about NY, not a tiny village lost on the middle of the USA, 5$is 4€, if there was such a place at this price in Paris, that would be insanely cheap ! Push to 8$ !
I remember a long time ago we had a place like this in my camping for holiday, there was (10 years ago) :
- 2 SNES (10 games)
- 2 NEOGEO (10 games)
- 1 PSX (15 games)
- 1 PC for Duke Nukem mostly
The price was 15 Franc (2€30) for 1 hour only ! And you are talking about 4€ for unlimited, in NY...anyway
8. ### Kasumi
I live in PA, and if you had TGM3, I'd go but not often, really. Being honest here, probably not even once a month. If I lived closer, though, I would go perhaps once a month. For TAP/TGM, I might still go if they were on freeplay, and the door fee covered unlimited play for them.
I'm confused, is your business model a door fee, and we pay for each game we play on the arcade machines, but console gaming is free? Or will some (all?) arcade games be free as well? Just confused when you said there would be $0.75 and$0.25 games. I'm not sure if you meant that's the price we'd have to pay for each game, or the price they'd be if they weren't freeplay.
Last edited: 24 Aug 2010
9. ### Budster
If you're looking to attract casual players a bit more, I would think Ti would be your best bet due to variable speed curve & SRS (which more people are used to, obviously.)
10. ### cyberguile
not living in the us but if I was a new yorker, for 5$+ 0,25$ a credit, I would certainly come at least two times a week (if not 4 or 5 times)
there's a small arcade (actually, a game shop with a couple of cabinets) in my hometown (three versus cities with 3rd , blazblue and capcom snk2), one madonna with super street fighter 2x and an egret III with dodonpachi daiffukatsu black label.
At the beginning, it was 3 euros for one hour of play (all systems set on freeplay), I used to play like 8 hours a week.
11. ### BankBank
entry - $5 for everyone console games - always free arcade games -$.25 (things like CPS2, TTGM older version)
But right now I'm just trying to do research to find out if I can get 25 people a day at $5 each. With that, I can break even on rent and expenses, and from there I can make money on arcade games and concessions. If you live in the NY/tri-state area or know someone that does, ask them if they think this is a good idea, and how many times a week they'd go there! I like TTGM, I'll get it there on a Japanese cab. Eventually 14. ### colour_thief You're joking right? That site is ok for classic American arcade games I guess, but it's not good at all for the rarity of Japanese arcade games. After all of 2 minutes of searching Japanese used arcade PCB sellers I've found you a Starsweep arcade PCB for the equivalent of$25 plus shipping, enjoy.
http://www.fujitacommunications.com/products.shtml
I don't know the first thing about business, but I can tell you that arcades tend to have lopsided income. Things are definitely busier on weekends than weekdays. Like, night and day packed versus almost empty. You should take that into account with your planning.
15. ### Kitaru
>TGM1 and TGM2 Master speedcurves are almost identical up to 500.
>TGM2 has Normal mode as well.
Uh. If I owned a TGM2 board, that's probably what would have ended up in our local arcade instead of TGM1. It has more options, even if the grading as well as the speedcurve after 500 are easier in TGM1. If both boards were available, I don't think endgame difficulty is something that should necessarily sway a decision to install TGM1 over TAP.
The nice thing is that TGM1 is comparatively inexpensive and still an excellent game. Given the choice of TGM1 or TAP to fill a cab in an arcade, though, I'd spring for TAP.
16. ### BankBank
Haha, wow, this is an amazing webpage. All I need to do is buy that PCB and throw it into a compatible cabinet, correct? I can order a crate of those really decent Japanese style cabinets like the Taito egret 2 and with this site basically be done with everything.
Just a stab in the dark here - do you know if candy cabs disassemble at all? The door to the site is kind of narrow and I'm concerned about getting machines in.
17. ### BankBank
PS - I would have StarSweep on a cheapy cabinet as the one free arcade game in the place. People would play it and learn it and we could have a tournament
18. ### Muf
They come apart completely (I've seen enough pictures of people completely taking their cabinets to bits to be resprayed) - but for the purposes of getting them through a door you can usually simply take off the control panel.
19. ### orz
i would come to this i'm like 3 hours away
20. ### orz
o yea would you have fighters here?? fighters own | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1639920175075531, "perplexity": 3520.569019427755}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986668569.22/warc/CC-MAIN-20191016113040-20191016140540-00040.warc.gz"} |
http://mathhelpforum.com/calculus/62226-help-polar-coordinates.html | # Math Help - Help with polar coordinates
1. ## Help with polar coordinates
Consider a curve given in polar coordinates by the equation
r = sec(theta +pi/4).
Find the equation of the tangent line (in Cartesian coordinates) at the point where theta= 0.
Thanks.
2. Originally Posted by khuezy
Consider a curve given in polar coordinates by the equation
r = sec(theta +pi/4).
Find the equation of the tangent line (in Cartesian coordinates) at the point where theta= 0.
Thanks.
We have that $r=\frac{1}{\cos\left(\theta+\frac{\pi}{4}\right)}$ Now a little trig will lead you to $r=\frac{\sqrt{2}}{\cos(\theta)-\sin(\theta)}$, or $1=\frac{\sqrt{2}}{r\cos(\theta)-r\sin(\theta)}\implies{1=\frac{\sqrt{2}}{x-y}}$
I think you can take it from there.
3. ## ?
how did u do that trig?
4. Originally Posted by khuezy
how did u do that trig?
Using the two facts $\cos\left(A+B\right)=\cos\left(A\right)\cos\left(B \right)-\sin\left(A\right)\sin\left(B\right)$ and $\sin\left(\frac{\pi}{4}\right)=\cos\left(\frac{\pi }{4}\right)=\frac{\sqrt{2}}{2}$
So
\begin{aligned}\cos\left(x+\frac{\pi}{4}\right)&=\ cos(x)\cos\left(\frac{\pi}{4}\right)-\sin(x)\sin\left(\frac{\pi}{4}\right)\\
&=\frac{\sqrt{2}}{2}\cos(x)-\frac{\sqrt{2}}{2}\sin(x)\\
&\implies\frac{1}{\cos\left(x+\frac{\pi}{4}\right) }\\
&=\frac{1}{\frac{\sqrt{2}}{2}\cos(x)-\frac{\sqrt{2}}{2}\sin(x)}\\
&=\frac{\sqrt{2}}{\cos(x)-\sin(x)}\end{aligned}
5. ## awesome
thanks, how did u get the root2/2 to go on top and the /2 to go away? | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9878982901573181, "perplexity": 1565.1991448157764}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657135558.82/warc/CC-MAIN-20140914011215-00280-ip-10-234-18-248.ec2.internal.warc.gz"} |
http://clay6.com/qa/14300/two-wires-of-different-materials-are-used-to-hang-a-rod-horizontally-tied-f | # Two wires of different materials are used to hang a rod horizontally tied from two ends of the rod of length $2m$. At what distance should a weight be hung on the rod from Wire-1 so that equal stresses are produced on both the wires. Wire 1: cross -sectional area $= 10^{-3}m^{2}$. Young's modulus $= 2 \times 10^{11} N/m^2$ Wire 2 : cross -sectional area $= 2 \times 10^{-3} m^{2}$. Young's modulus $= 1 \times 10^{11} N/m^2$
$\begin {array} {1 1} (a)\;1.33\;m \\ (b)\;1.49\;m \\ (c)\;0.8\;m \\ (d)\;0.55\;m \end {array}$
Let the rod be AB and the weight be hung at 0. Let $AO=x$ and the $OB=2-x$
Let $T_1$ and $T_2$ be tension in the two wires.
By principle of moments
$T_1 \times OA=T_2 \times OB$
$\large\frac{T_1}{T_2}=\frac{OB}{OA}$------(1)
Also it is given that the two wires have same stress.
$\therefore \large\frac{T_1}{A_1}=\frac{T_2}{A_2}$
Where $A_1$ and $A_2$ are area of cross - sections.
$\large\frac{T_1}{T_2}=\frac{A_1}{A_2}$
$\qquad=\large\frac{10^{-3}}{2 \times 10^{-3}}=\frac{1}{2}$ -------(2)
From (1) and (2)
$\large\frac{1}{2} =\frac{2-x}{x}$
$x= 4-2x$
$3x= 4$
$\therefore x= \large\frac{4}{3}$
$\qquad= 1.33\; m$
Hence a is the correct answer.
edited Mar 20, 2016 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9602078199386597, "perplexity": 1074.0312908752499}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187823462.26/warc/CC-MAIN-20171019194011-20171019214011-00472.warc.gz"} |
https://wiki.cosmos.esa.int/planckpla2015/index.php?title=Beams_LFI&diff=prev&oldid=5619 | # Difference between revisions of "Beams LFI"
## Wish List
list of information to be inserted in the explanatory supplements
- Description of LFI FOV.
- Description of various telescope models as reported in the beam paper.
- Format of beam data
- Definition of various coordinate frames for beams
## Overview
LFI is observing the sky with 11 pairs of beams associated with the 22 pseudo-correlation radiometers. Each beam of the radiometer pair (Radiometer Chain Assembly - RCA) is named as LFIXXM or LFIXXS. XX is the RCA number ranging from 18 to 28; M and S are the two polarization namely main-arm and side-arm of the Orthomode transducers #darcangelo2009b (see also LFI naming convention).
Figure 1. A sketch of the Planck LFI field of view in the (u,v) plane is shown. The polarization direction on the sky are highlighted by the colored arrows. The M-polarization is shown in green and the S-polarization in red. Main beam shapes are shown for completness and they are not representative of flight beams.
## Main Beams and Focal Plane calibration
As the focal plane calibration we refer to the determination of the beam pointing parameters in the nominal Line of Sight (LOS) frame through main beam measurments using Jupiter transits. the parametes that characterise the beam pointing are the following:
• THETA_UV ($\theta_{uv}$)
• PHI_UV ($\phi_{uv}$)
They are calculated starting from u,v coordinates derived form the beam reconstruction algorithm as
$\theta_{uv} = \arcsin(u^2+v^2)$
$\phi_{uv} = \arctan(v/u)$
Three additional angles are used to characterize the beams in the RIMO:
• TILT
• PSI_UV ($\psi_{uv}$)
• PSI_POL ($\psi_{pol}$)
the Tilt angle is the angle between the major axis of the gaussian fitting and the U-axis CHECK THIS
$\psi_{uv}$ and $\psi_{pol}$ are not derived from measurements but they are extimated form optical simulations. They are the quantities that represent the polarization direction of each beam, in the following approximation: the M- and S- beams of the same RCA point at the same direction on the sky
TBW
TBW
## Sidelobes
There is no direct measurements of sidelobes for LFI. The sidelobe pattern is estimated by simulations taking into account the geometry of the telescope and the satellite structure. In figure
## References
<biblio force=false>
1. References
</biblio>
(Planck) Low Frequency Instrument
Field-Of-View | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8490858674049377, "perplexity": 3110.9015835772193}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662529538.2/warc/CC-MAIN-20220519141152-20220519171152-00035.warc.gz"} |
http://www.scoopskiller.com/management-materials/the-present-age-of-a-father-is-3-years-more-than-three-times-the-age-of-his-son-three-years-hence-fathers-age-will-be-10-years-more-than-twice-the-age-of-the-son-find-the-present-age-of-the-fath/ | # The present age of a father is 3 years more than three times the age of his son. Three years hence, father’s age will be 10 years more than twice the age of the son. Find the present age of the father ?
$\par&space;Let&space;the&space;son's&space;present&space;age&space;be&space;x&space;years.$
$\par&space;Then&space;father's&space;present&space;age&space;=&space;(3x&space;+&space;3)&space;years.$
$(3x&space;+&space;3&space;+&space;3)&space;=&space;2(x&space;+&space;3)&space;+&space;10$
$3x&space;+&space;6&space;=&space;2x&space;+&space;16$
$x&space;=&space;10$
$\par&space;Hence&space;father's&space;present&space;age&space;=&space;(3x&space;+&space;3)&space;=&space;(3\times&space;10&space;+&space;3)&space;=&space;33&space;years$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18200542032718658, "perplexity": 393.672660528479}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376829568.86/warc/CC-MAIN-20181218184418-20181218210418-00128.warc.gz"} |
https://www.physicsforums.com/threads/hard-task.90138/ | 1. Sep 21, 2005
### klawesyn28
I don't know how to solve this task:
you can get one of marks - 6,5, 3 or 0 .
It transpired that for each pair of participants we can indicate two
tasks , that in each of them participant A got different mark from
participant B.
Delimit the highest number of participants for which this situation is
possible.
Could anybody help me?
2. Sep 21, 2005
### Werg22
Hint: List all the possibilities. But I don't think that is effective...
Last edited: Sep 21, 2005
3. Sep 22, 2005
### klawesyn28
I think that the answer is 4^5 but i don't know how to prove it. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8401459455490112, "perplexity": 1744.1964413063204}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676592579.77/warc/CC-MAIN-20180721125703-20180721145703-00423.warc.gz"} |
http://research.investors.com/quotes/nasdaq-s-e-i-investments-co-seic.aspx/sec/form-10-k/full?ofid=13963798&cik=350894&symbol=seic | Streaming Quotes Are
## Filings for SEI INVESTMENTS CO (SEIC)
Form Date Description FORM 10-K February-27-14 Annual And Transition Reports Pursuant To Section 13 And 15(D) Where The Regulation S-K Item 405 Box (Relating To Section 16(A) Reports) On The Cover Page Is Not Checked (INITIAL FILING) SUBSIDIARIES OF THE REGISTRANT February-27-14 Annual And Transition Reports Pursuant To Section 13 And 15(D) Where The Regulation S-K Item 405 Box (Relating To Section 16(A) Reports) On The Cover Page Is Not Checked (INITIAL FILING) CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM February-27-14 Annual And Transition Reports Pursuant To Section 13 And 15(D) Where The Regulation S-K Item 405 Box (Relating To Section 16(A) Reports) On The Cover Page Is Not Checked (INITIAL FILING) CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM February-27-14 Annual And Transition Reports Pursuant To Section 13 And 15(D) Where The Regulation S-K Item 405 Box (Relating To Section 16(A) Reports) On The Cover Page Is Not Checked (INITIAL FILING) SECTION 302 CEO CERTIFICATION February-27-14 Annual And Transition Reports Pursuant To Section 13 And 15(D) Where The Regulation S-K Item 405 Box (Relating To Section 16(A) Reports) On The Cover Page Is Not Checked (INITIAL FILING) SECTION 302 CFO CERTIFICATION February-27-14 Annual And Transition Reports Pursuant To Section 13 And 15(D) Where The Regulation S-K Item 405 Box (Relating To Section 16(A) Reports) On The Cover Page Is Not Checked (INITIAL FILING) SECTION 906 CEO AND CFO CERTIFICATION February-27-14 Annual And Transition Reports Pursuant To Section 13 And 15(D) Where The Regulation S-K Item 405 Box (Relating To Section 16(A) Reports) On The Cover Page Is Not Checked (INITIAL FILING) FINANCIAL STATEMENTS OF LSV ASSET MANAGEMENT February-27-14 Annual And Transition Reports Pursuant To Section 13 And 15(D) Where The Regulation S-K Item 405 Box (Relating To Section 16(A) Reports) On The Cover Page Is Not Checked (INITIAL FILING) GRAPHIC February-27-14 Annual And Transition Reports Pursuant To Section 13 And 15(D) Where The Regulation S-K Item 405 Box (Relating To Section 16(A) Reports) On The Cover Page Is Not Checked (INITIAL FILING) XBRL INSTANCE DOCUMENT February-27-14 Annual And Transition Reports Pursuant To Section 13 And 15(D) Where The Regulation S-K Item 405 Box (Relating To Section 16(A) Reports) On The Cover Page Is Not Checked (INITIAL FILING) | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9193618297576904, "perplexity": 25009.63340236984}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416400372202.67/warc/CC-MAIN-20141119123252-00233-ip-10-235-23-156.ec2.internal.warc.gz"} |
http://mathoverflow.net/questions/95815/p-adic-analysis-of-hypergeometric-functions?sort=oldest | # p-adic analysis of hypergeometric functions
Are there any p-adic techniques that can be applied to the 2F1 hypergeometric function?
For e.g. I'm interested in which values this function converges p-adically.
-
The Gauss hypergeometric function is the main example in the theory of p-adic differential equations. See
K. S. Kedlaya, p-Adic Differential Equations, Cambridge University Press, 2010,
for the general theory. There were also two books by Dwork, almost completely devoted to ${}_2F_1$ (its p-adic theory is much more complicated than the classical one):
B. Dwork, Generalized hypergeometric functions. Oxford: Clarendon Press, 1990.
B. Dwork, Lectures on p-adic differential equations, Springer, 1982.
It is easy to check local p-adic convergence for the hypergeometric series, but to study and even correctly define its analytic continuation properties one needs subtle analytic and algebraic techniques.
- | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9258265495300293, "perplexity": 993.9519676560072}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246656965.63/warc/CC-MAIN-20150417045736-00307-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://tex.stackexchange.com/questions/233939/scriptstyle-placement-fine-tuning | # \scriptstyle placement fine tuning
I need a functional composition operator. I find \circ too big for it, so I've declared a math operator (within the amsart documentclass) as \scriptstyle\circ instead; the size is exactly what I would like to have but the placement seems wrong now, it is too low.
Does anybody know a simple way (without too many \raises and boxes) to place the symbol slightly higher?
Try with defining a new command \smallcirc
\newcommand{\smallcirc}{\mathbin{\text{\raisebox{0.2ex}{\scalebox{0.6}{$\circ$}}}}}
MWE:
\documentclass{amsart}
\usepackage{graphicx}
\newcommand{\smallcirc}{\mathbin{\text{\raisebox{0.2ex}{\scalebox{0.6}{$\circ$}}}}}
\begin{document}
$f\circ\alpha \quad\text{vs}\quad f\smallcirc\alpha$
$f \smallcirc \alpha_{f \smallcirc \alpha_{f \smallcirc \alpha}}$
\end{document}
Note that, defining the command with a \scripstyle in it, it's not a good idea since if you have that symbol in a sub/superscript, its size will remain the same as the one in display style.
• Thanks a lot! I preferred this one since it is more concise, more customizable, and works without graphicx too :D – მამუკა ჯიბლაძე Mar 19 '15 at 10:50
• Oops maybe it still needs graphicx - I load tikz and that I think loads graphicx... Well anyway – მამუკა ჯიბლაძე Mar 19 '15 at 10:52
• @მამუკაჯიბლაძე You're welcome. And, yes, tikz loads graphicx. – karlkoeller Mar 19 '15 at 10:54
Here's an answer that will work even in sub/superscript:
\documentclass{article}
\usepackage{amsmath}
\newcommand{\centeredcirc}[1]{\vcenter{\hbox{$#1\circ$}}}
\newcommand{\smallcirc}{\mathbin{\mathchoice{\centeredcirc\scriptstyle}{\centeredcirc\scriptstyle}{\centeredcirc\scriptscriptstyle}{\centeredcirc\scriptscriptstyle}}}
\begin{document}
$f\circ\alpha \quad\text{vs}\quad f\smallcirc\alpha$
$g^{f\circ\alpha} \quad\text{vs}\quad g^{f\smallcirc\alpha}$
\end{document}
The following example uses the scaling method of karlkoeller's answer and enhances it in several ways:
• The new symbol is correctly vertically centered around the math axis.
• The side bearings are restored (heuristic).
• The scaling diminishes the line width. This is compensated by additionally stroking the symbol with an estimated line width to compensate the scaling.
Full example:
\documentclass{article}
\usepackage{amsmath}
\usepackage{color}
\usepackage{graphicx}
\usepackage{pdfrender}
\makeatletter
\newcommand*{\smallcirc}{%
\mathbin{%
\mathpalette\@smallcirc{}%
}%
}
\newcommand*{\smallcircscale}{.6}
\newcommand*{\@smallcirc}[2]{%
% #1: math style
% #2: unused
\sbox0{$#1\vcenter{}$}% \ht0: math axis
\sbox2{$#1\circ\m@th$}%
% Calculate symbol width with original side bearings
% (in the hope, the symbol height is correct).
% The radius is estimated as symbol height minus math axis
% (\ht2 - \ht0).
\dimen@=\dimexpr
\smallcircscale\dimexpr2\ht2-2\ht0\relax
+ \wd2-2\ht2+2\ht0
\relax
% Estimated line thickness from symbol height
\dimen2=.1\ht2
% Calculate line width for rendering mode "Stroke".
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https://infoscience.epfl.ch/record/179804 | Infoscience
Conference paper
# Toward a power system emulation using analog microelectronics solid state circuits
An analog electronics emulation solution is investigated in order to assess the state of a power system facing dynamic phenomena such as the transient stability. Two approaches are studied: DC emulation and AC emulation. Both are intended to be integrated on VLSI submicron CMOS silicon technologies. This implementation has the advantages of presenting low cost, fast simulation time that is independent of the network size and the number of the generators connected to it, low power consumption and small size. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8906792402267456, "perplexity": 1782.929316468486}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084890514.66/warc/CC-MAIN-20180121100252-20180121120252-00594.warc.gz"} |
https://cs.stackexchange.com/questions/129177/pagerank-vector/129208 | # PageRank vector
I computed the PageRank vector for the example given in https://en.wikipedia.org/wiki/PageRank (where the picture shows that node B ends up with a score of 38.4, node C with 34.3, node D with 3.9). I implemented the PageRank algorithm, but my numbers are slightly different: 39.8 for node B, and 36.1 for node C, 3.5 for node D, etc). I was wondering if anyone could simulate and obtain the same results they have. My question is what algorithm was used to obtain their numbers.
My algorithm is as follows. Starting with the uniform distribution $$r$$, I did power iteration using the equation $$r = Ar$$, where $$A = 0.85 M + 0.15 J$$, $$M$$ is the transition matrix of the Web graph given in the example, and $$J$$ is the matrix whose every entry is $$1/N$$ ($$N=11$$ is the number of nodes).
• You can ask the person who created the image. On the other hand, what do you expect to get out of the answer? There are lots of small choices to be made that could change the final output: Was the system solved by fixed point iteration, or did they solve the system by a direct method (which one)? If they iterated, how many iterations did they do? Did they stop after a predefined number of iterations or after passing a tolerance for the difference between iterations? Which norm was used to compute the difference? – plop Aug 11 '20 at 14:54
• Knowing what options are available as answers for each question above is useful, but which options were used for that specific image ...? It doesn't look like something to care about. – plop Aug 11 '20 at 14:57
• How did your algorithm incorporate the PageRank damping factor? – Pseudonym Aug 12 '20 at 0:28
• @plop The iterations were done until there was convergence (in the sense that the Euclidean distance between the current vector and the previous one was at most 0.0001). I don't think number of iterations or precision is the reason my answers are slightly different. – jm jm Aug 12 '20 at 11:37
I fixed it and I am now getting the same numbers as in their example. Earlier, I used the equation $$r=(0.85M+0.15J)r$$ to update $$r$$, and at the end of each iteration I would scale $$r$$ so that it sums to $$1$$. This scaling is necessary because the Web graph can have dead ends, in which case the components of $$Mr$$ need not sum to 1 even if the components of $$r$$ sum to 1. Now, I compute the first term $$0.85Mr$$, and then I redistribute the remaining pagerank (of $$1$$ minus sum of components of $$0.85Mr$$) evenly among all the nodes. The latter algorithm distributes the pagerank among all the nodes slightly more uniformly. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 16, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8979707956314087, "perplexity": 301.31413203068627}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991288.0/warc/CC-MAIN-20210518160705-20210518190705-00433.warc.gz"} |
http://www.physicsforums.com/showthread.php?t=244935 | # Charge distribution within a solid conductive sphere
by m.e.t.a.
Tags: charge, conductive, distribution, solid, sphere
P: 112 I have been attempting to deduce the arrangement of electrons within a solid spherical conductor in different states of charge. I'd like to know which, if any, of my conclusions are correct; and of the incorrect, I'd like to understand where I went wrong. A cool conductive (metal) sphere is placed in vacuum. The sphere is initially neutrally charged and is then given a net-positive charge followed by a net-negative charge. Between these changes in charge, time is allowed to allow the system to come to equilibrium. I have modelled the free electrons as free-moving particles whose movement is uninhibited by the temperature or structure of the metal lattice. Rather than explain my reasoning, which would be tiresome for people to read, I will just list my conclusions for the different states of charge. 1. Neutrally Charged Electrons are arranged homogeneously about the whole volume of the sphere. 2. Positively Charged The sphere is divided into two distinct regions. All free electrons locate themselves in a central “core” of radius $$R_C$$. The electrons in this core are arranged homogeneously. The remainder of the sphere (between radii $$R_C$$ and $$R$$) contains zero free electrons and is therefore composed of positively charged metal lattice. There is a sharp boundary between the two regions. (Diagram.) 3. Negatively Charged The whole sphere carries a homogeneous neutral charge with the exception of a thin spherical shell at radius $$R$$. In this thin surface-shell, all free electrons are located. It is point 3 that I find most difficult to accept, partly because I could only be vague (how thin is "thin"?) and partly because I don't know how electrons behave in close proximity. Are any of my conclusions correct? - m.e.t.a.
Sci Advisor HW Helper PF Gold P: 562 Regardless of whether the sphere is positively or negatively charged, all the excess charge is on the surface. This follows from Gauss's law. So, if the sphere is negatively charged, all the excess electrons lie on the surface of the sphere. If it is positively charged, then the "missing" electrons are missing at the surface. The simple application of Gauss's law treats a macroscopic charge distribution as continuous, however, and not made up of individual quanta (electrons, protons etc.). To get down to the nitty gritty of where the excess electrons are in the solid metal lattice (rather than just saying they are at the surface, for example), you need to look at the microscopic energy-band structure of the metal itself. But then the electrons don't look like point particles anymore - they are "smeared out" as quantised waves in the conduction band of the metal.
P: 112
If it is positively charged, then the "missing" electrons are missing at the surface.
Could you elaborate? It sounds as if you agree with me, though I have a problem understanding how all of the sphere's positive charge could be located "at" the surface.
Negative surface charge can be very dense, because free electrons are both mobile and small. But positive surface charge cannot become similarly concentrated because the metal lattice -- which carries the positive charge -- is immovable. Furthermore, inter-atomic distance is large compared to the small minimum separation of free electrons. Also, a typical conductor holds only one or two free electrons per atom. These three factors together (stationary lattice, large inter-atomic distance, low maximum electron liberation per atom) place a very low limit on the maximum density of positive charge.
The density of negative charge, however, suffers from no such limitation. This is why I do not understand the assertion that positive charge locates "at" the surface.
P: 86
Charge distribution within a solid conductive sphere
I think meta's conclusions make all sense.
Quote by James R The simple application of Gauss's law treats a macroscopic charge distribution as continuous, however, and not made up of individual quanta (electrons, protons etc.)
Not only that, but also the normal model of a conductor (by which at equilibrium the inner E field is zero and all the excess charge is on the surface) tends to assume that the object has as much movable charge as needed.
But clearly, if you imagine a conductor being charged by only removing electrons, unless something else occurs in the process, clearly the area of "uncovered positive charged" extends more and more inwards and cannot be an arbitrarily thin layer.
If you were charging it positively by adding protons instead, assuming those protons would be free to move (I have no idea), then they would occupy a very thin layer on the surface.
P: 86
Quote by m.e.t.a. The density of negative charge, however, suffers from no such limitation. This is why I do not understand the assertion that positive charge locates "at" the surface.
My conclusion, to make it clearer, is that this is true indeed only if you assume that for the problem's purposes the conductor has enough atoms on the surface (not surface in a geometrical sense, but you may afford to approximate it that way if that's ok for your purpose) to "provide" all the + charges needed.
P: 112 I think I understand what you mean now, Domenicaccio. You are saying that, under everyday conditions, the electron deficit of a positively charged conductive sphere (or other object) is normally so small that the layer of charge can be modelled as infinitely thin. Of course, an equal quantity of negative charge would occupy a much thinner layer still. But, as you point out, under ordinarily achievable conditions it doesn't matter what polarity your charge is. Both layers are thin, and you're unlikely to encounter a positive charge so vast that the shell containing that charge need be modelled as anything but "thin". I attempted to calculate how thin this layer might typically be. By taking the plausible example of a solid copper sphere charged to 20kV, I got a figure for the "virtual" thickness of the charge-carrying shell at around 2.30 × 10$$^{-16}$$ m. I'd happily bet that my answer is likely to be wrong, but it certainly is "thin" indeed; in fact, it is a good deal thinner than the diameter of an atomic nucleus. This suggests that, unless I were to massively increase the charge on the sphere (or apply the same charge to a much smaller sphere) I would only have ionised a tiny fraction of a single one-atom-deep layer. (In trying to roughly estimate this fraction I arrived at a figure of between 1 and 10 +1-ionised atoms per million neutrally charged ones. It seems like an impossibly small figure.) But again, exact figures aren't important. Domenicaccio and James R are both correct; thank you for your answers!
Sci Advisor HW Helper PF Gold P: 562 m.e.t.a: One more thing: Most of the time in the real world, when we talk about a "positively charged metal sphere" or something like that, we mean a sphere which has had some electrons removed, so that the number of protons remaining is greater than the number of electrons, thus giving the sphere a net positive charge. We can still refer to this situation as a "positively-charged metal sphere, with all the positive charge at the surface". This is essentially a shorthand way of saying that the "missing" electrons are all missing from the surface layers of the metal.
Related Discussions Introductory Physics Homework 14 Materials & Chemical Engineering 26 Introductory Physics Homework 8 Advanced Physics Homework 1 Introductory Physics Homework 1 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9013006091117859, "perplexity": 609.9595184308124}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997894378.97/warc/CC-MAIN-20140722025814-00173-ip-10-33-131-23.ec2.internal.warc.gz"} |
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## ValentinaT 2 years ago What is the length of the longest side of a triangle that has vertices at (-5, 2) (1,-6) and (1,2)? Delete Cancel Submit
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1. v4xN0s
• 2 years ago
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Use the distance formula
2. ValentinaT
• 2 years ago
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Distance formula?
3. v4xN0s
• 2 years ago
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LOL
4. v4xN0s
• 2 years ago
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ok its $d=\sqrt{(x _{1}-x _{2})^2+(y _{1}-y _{2})^2}$
5. MathLegend
• 2 years ago
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I would also suggest labeling your coordinates
6. v4xN0s
• 2 years ago
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MathLegend ur not a math legend at all
7. MathLegend
• 2 years ago
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A= (-5, 2) B = (1,-6) C = (1,2)
8. MathLegend
• 2 years ago
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So when using the distance formula... you can solve for side AB first.
9. ValentinaT
• 2 years ago
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Thank you.
10. MathLegend
• 2 years ago
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So using that formula, can you label the coordinates as (x1, y1) & (x2,y2)
11. hba
• 2 years ago
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|dw:1355599903259:dw|
12. MathLegend
• 2 years ago
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A= (-5, 2) B = (1,-6) So lets solve for side AB first... so, "A" comes first right? So let that be your x1 & y1 Then, "B" can be your x2 & y2
13. MathLegend
• 2 years ago
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Do you understand so far @ValentinaT ?
14. MathLegend
• 2 years ago
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All I did was label them so that we can plug it into that distance formula.
15. MathLegend
• 2 years ago
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@ValentinaT let me know when you get back so we can work this out together. :)
16. ValentinaT
• 2 years ago
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Yeah, I'm getting it, thank you.
17. ValentinaT
• 2 years ago
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$\frac{ -6 - 2 }{ -5 - 1 } = \frac{ -8 }{ -6}$
18. MathLegend
• 2 years ago
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So for AB (1+5)^2+(-6-2)^2
19. MathLegend
• 2 years ago
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I'm sorry the formula is actually x2-x1 and y2-y1 the above poster just mixed up the two.
20. ValentinaT
• 2 years ago
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Okay.
21. MathLegend
• 2 years ago
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(1+5)^2+(-6-2)^2 (6)^2+(-8)^2 36+64
22. MathLegend
• 2 years ago
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36+64 = 100
23. MathLegend
• 2 years ago
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$\sqrt{100}$
24. ValentinaT
• 2 years ago
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10
25. MathLegend
• 2 years ago
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Now, we need the square root... because if you notice that entire formula had the square root symbol over it
26. MathLegend
• 2 years ago
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Good.
27. MathLegend
• 2 years ago
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So side AB = 10
28. MathLegend
• 2 years ago
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So that is one side. So lets go for side BC
29. MathLegend
• 2 years ago
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B = (1,-6) x1 y1 C = (1,2) x2 y2
30. MathLegend
• 2 years ago
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@ValentinaT do you feel comfortable trying it out on your own? Tell me what you get and I'll check to see if your answer for side BC is correct.
31. ValentinaT
• 2 years ago
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$\frac{ 2 - -6 }{ 1 - 1 } = \frac{ 8 }{ 0 }$
32. MathLegend
• 2 years ago
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Remember we are not trying to find a slope.
33. MathLegend
• 2 years ago
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We are looking for the distance between the vertices.
34. MathLegend
• 2 years ago
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(1-1)^2 + (2+6)^2
35. MathLegend
• 2 years ago
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To get that all I did was plug it into the formula. (x2-x1)^2+(y2-y1)^2
36. MathLegend
• 2 years ago
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(1-1)^2 + (2+6)^2 Try solving that.
37. ValentinaT
• 2 years ago
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Okay, 0 + 64?
38. MathLegend
• 2 years ago
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Good
39. MathLegend
• 2 years ago
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0 + 64 = 64 $\sqrt{64}$
40. ValentinaT
• 2 years ago
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So, 8 as the square root.
41. MathLegend
• 2 years ago
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Yes, so side BC = 8
42. MathLegend
• 2 years ago
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Now, try side AC
43. MathLegend
• 2 years ago
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(x2-x1)^2+(y2-y1)^2
44. ValentinaT
• 2 years ago
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A = -5, 2 = x1, y1 C = 1, 2 = x2, y2 $\frac{ 1 - -5^2}{ 2 - 2^2 } = \frac{ 6 }{ 1 }$ so 36?
45. MathLegend
• 2 years ago
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(x2-x1)^2+(y2-y1)^2 (1+5)^2 + (2-2)^2 Do you understand this step?
46. ValentinaT
• 2 years ago
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36 + 0 Yeah I get it, I just couldn't figure out how to write it.
47. MathLegend
• 2 years ago
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Good so if you took the square root of 36 $\sqrt{36}$
48. MathLegend
• 2 years ago
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So now, we know the length of the longest side is AB
49. ValentinaT
• 2 years ago
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Okay, thank you!
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https://www.hpmuseum.org/forum/showthread.php?mode=threaded&tid=9646&pid=91383 | Scientific calculators that have formula/equation memory
02-16-2018, 06:13 PM (This post was last modified: 02-16-2018 07:32 PM by JeffJ.)
Post: #39
JeffJ Junior Member Posts: 9 Joined: Jan 2014
RE: Scientific calculators that have formula/equation memory
The HP-35S was given a bad rap by all the grumpy old men on this forum when it first came out, and yes, it had some bugs you could potentially run into, and it is a little wide for single-handed use, but honestly it's a great calculator and very affordable. I have a number of HP calculators from HP-45 all the way to HP-50g and I have found my HP-35S to be very much a "daily driver". I have one at work and one at home. My recommendation to everyone would be they get one while they can, because history has taught us that HP will soon drop production of them and instead of paying $60, they will be$600 on eBay.
By the way, I have replaced batteries on both of my HP-35S calcs a couple of times (or more?) and never lost memory. My recollection is you have at least half a minute to slide the old battery out and the new one in, which is more than adequate time.
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Messages In This Thread Scientific calculators that have formula/equation memory - pier4r - 12-06-2017, 12:18 PM RE: Scientific calculators that have formula/equation memory - Thomas Okken - 12-06-2017, 12:24 PM RE: Scientific calculators that have formula/equation memory - pier4r - 12-06-2017, 12:29 PM RE: Scientific calculators that have formula/equation memory - grsbanks - 12-06-2017, 12:44 PM RE: Scientific calculators that have formula/equation memory - pier4r - 12-06-2017, 01:16 PM RE: Scientific calculators that have formula/equation memory - jebem - 12-06-2017, 01:00 PM RE: Scientific calculators that have formula/equation memory - Gene - 12-06-2017, 01:30 PM RE: Scientific calculators that have formula/equation memory - grsbanks - 12-06-2017, 01:33 PM RE: Scientific calculators that have formula/equation memory - jebem - 12-06-2017, 03:50 PM RE: Scientific calculators that have formula/equation memory - Dave Britten - 12-06-2017, 04:19 PM RE: Scientific calculators that have formula/equation memory - pier4r - 12-06-2017, 09:44 PM RE: Scientific calculators that have formula/equation memory - pier4r - 12-06-2017, 10:22 PM RE: Scientific calculators that have formula/equation memory - jebem - 12-14-2017, 04:04 PM RE: Scientific calculators that have formula/equation memory - Lonewolf - 06-06-2018, 11:53 PM RE: Scientific calculators that have formula/equation memory - ijabbott - 06-07-2018, 01:57 PM RE: Scientific calculators that have formula/equation memory - Dave Britten - 06-07-2018, 02:18 PM RE: Scientific calculators that have formula/equation memory - Lonewolf - 06-07-2018, 07:56 PM RE: Scientific calculators that have formula/equation memory - Dave Britten - 06-07-2018, 08:16 PM RE: Scientific calculators that have formula/equation memory - pier4r - 06-09-2018, 01:38 PM RE: Scientific calculators that have formula/equation memory - Lonewolf - 06-09-2018, 06:16 PM RE: Scientific calculators that have formula/equation memory - pier4r - 12-06-2017, 10:43 PM RE: Scientific calculators that have formula/equation memory - Massimo Gnerucci - 12-07-2017, 12:20 PM RE: Scientific calculators that have formula/equation memory - grsbanks - 12-07-2017, 12:29 PM RE: Scientific calculators that have formula/equation memory - pier4r - 12-07-2017, 12:59 PM RE: Scientific calculators that have formula/equation memory - grsbanks - 12-07-2017, 02:00 PM RE: Scientific calculators that have formula/equation memory - Massimo Gnerucci - 12-07-2017, 08:36 PM RE: Scientific calculators that have formula/equation memory - Chasfield - 12-07-2017, 02:01 PM RE: Scientific calculators that have formula/equation memory - jebem - 12-07-2017, 06:43 PM RE: Scientific calculators that have formula/equation memory - pier4r - 12-07-2017, 07:38 PM RE: Scientific calculators that have formula/equation memory - Csaba Tizedes - 12-09-2017, 11:47 AM RE: Scientific calculators that have formula/equation memory - pier4r - 12-09-2017, 12:06 PM RE: Scientific calculators that have formula/equation memory - Csaba Tizedes - 12-09-2017, 12:29 PM RE: Scientific calculators that have formula/equation memory - pier4r - 12-14-2017, 04:07 PM RE: Scientific calculators that have formula/equation memory - grsbanks - 12-14-2017, 04:23 PM RE: Scientific calculators that have formula/equation memory - Massimo Gnerucci - 12-14-2017, 06:15 PM RE: Scientific calculators that have formula/equation memory - Guenter Schink - 12-14-2017, 10:10 PM RE: Scientific calculators that have formula/equation memory - Massimo Gnerucci - 12-14-2017, 11:01 PM RE: Scientific calculators that have formula/equation memory - klesl - 12-25-2017, 03:22 PM RE: Scientific calculators that have formula/equation memory - pier4r - 12-25-2017, 03:50 PM RE: Scientific calculators that have formula/equation memory - TheKaneB - 01-04-2018, 02:22 AM RE: Scientific calculators that have formula/equation memory - badaze - 01-04-2018, 09:49 PM RE: Scientific calculators that have formula/equation memory - grsbanks - 01-04-2018, 10:10 PM RE: Scientific calculators that have formula/equation memory - badaze - 01-04-2018, 10:24 PM RE: Scientific calculators that have formula/equation memory - pier4r - 01-05-2018, 10:11 AM RE: Scientific calculators that have formula/equation memory - martinot - 02-10-2018, 09:51 AM RE: Scientific calculators that have formula/equation memory - JeffJ - 02-16-2018 06:13 PM RE: Scientific calculators that have formula/equation memory - martinot - 02-16-2018, 09:09 PM RE: Scientific calculators that have formula/equation memory - brickviking - 06-07-2018, 02:18 AM RE: Scientific calculators that have formula/equation memory - Nigel (UK) - 06-07-2018, 04:55 PM
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https://de.zxc.wiki/wiki/Faradayscher_K%C3%A4fig | The Faraday cage (also known as Faraday cage ) is an all-round closed shell made of an electrical conductor (e.g. wire mesh or sheet metal) that acts as an electrical shield . With external static or quasi-static electrical fields , the inner area remains field-free due to the influence . In the case of processes that vary over time, such as electromagnetic waves , the shielding effect is based on the eddy currents that form in the conductive shell and counteract the external electromagnetic field. Static or slowly varying magnetic fields (like the earth's magnetic field) are not shielded by a Faraday cage.
Faraday cage, occupied with test subjects in the field-free interior
The term goes back to the English physicist Michael Faraday (1791–1867). The quantity of the shielding effect is recorded via the shielding attenuation ( e.g. a shield ).
## effect
• If lightning strikes a Faraday cage, for example a car or an airplane, people in the interior remain safe because the electrical field strength in the interior is considerably lower than in the exterior. In the vicinity of openings in the metal shell, an external field penetrates proportionally into the shielded room. The extent of penetration depends on the size of the aperture in relation to the wavelength of the spectrum of the external field.
• If an electrical discharge is generated inside a Faraday cage, on the other hand, outside observers remain safe. This principle is used for the metallic lining in high-voltage laboratories .
## Shielding against electrostatic fields
Animation of the charge shift in a Faraday cage
The shielding of electrostatic or quasi-stationary electrical fields is based on the effect of the influence . If an electrically conductive shell, for example a hollow sphere, is brought into an externally applied electrostatic field E , the effect of the force on the charges Q, which can move freely in the shell , results in a spatial redistribution of the charges on the surface until the one tangential to the surface external electric field component becomes zero and a balance is found. As a result, in the static case, the electrical flow originates or ends on the surface of the envelope, so that the interior of the envelope remains field-free. This shielding effect is not tied to a specific shape of the shell and occurs with hollow bodies of any shape, provided they are electrically conductive. ${\ displaystyle {\ vec {F}} = Q \ cdot {\ vec {E}}}$
With a completely closed conductive envelope, the attenuation is ideal and infinitely great in the static case; with quasi-stationary fields this is met with a good approximation. With the help of Gaussian law , the normal components of the electric field in the empty outer space directly above the envelope can be:
${\ displaystyle {\ vec {E}} _ {na} = {\ frac {\ rho _ {f}} {\ varepsilon _ {0}}}}$
and in the interior too
${\ displaystyle {\ vec {E}} _ {ni} = 0}$
determine with the surface charge density and the dielectric constant . ${\ displaystyle \ rho _ {f}}$${\ displaystyle \ varepsilon _ {0}}$
The conductive envelope is an equipotential surface , which is called an electrical wall in parlance. It is essential that the shielding effect only acts against external electrical fields. An electrical flow, which arises from a charge accumulation inside the envelope that is isolated from the envelope, the separate charge with the opposite sign is located outside, thus also leads to an electric field in the exterior. If, on the other hand, there is an electrical connection between the charge-carrying inner areas and the shell, the electric charges are shifted to the surface and the inner area remains field-free. This principle of charge displacement is used in some high -voltage generators such as the Van-de-Graaff generator to store charge and generate high electrical voltages.
If the alternating fields are not too high-frequency, a Faraday cage can consist of a cage made of conductor bars, wires or a sheet metal with small openings instead of a closed conductor wall. The shielding attenuation is related to the mesh size, which should not exceed about 1/10 of the wavelength.
## Shielding of alternating fields (electrodynamics)
An ideal Faraday cage also shields high-frequency alternating fields because eddy currents are induced on the surface of the cage , which counteract the external field according to Lenz's rule . In this case, the shielding effect is not ideal, but is characterized by finite shielding attenuation and penetration depths into the shield.
Due to their finite conductivity, Faraday cages made of non- ferromagnetic metal shield high-frequency alternating fields when the metal layer is significantly stronger than the penetration depth of the induced currents.
Slots lead to the interruption of the induction currents in the screen. Electromagnetic waves penetrate the screen comparatively well if slots in the screen are parallel to the magnetic field component of the wave. The shielding attenuation decreases with increasing aperture and becomes low when the wavelength of the incoming electromagnetic wave is in the order of magnitude of the slot dimensions.
## Applications
Faraday cages are often used where the effects of external electrical or electromagnetic fields can negatively affect the functionality of a device or where internal electromagnetic fields should not reach the outside. For example, it is used to shield measuring instruments, electrical lines or measuring rooms, e.g. B. in front of transmitters. The Faraday cage is then z. B. the housing made of a conductive material or a thin metallic foil with which the space to be protected is enveloped.
The shielding can encompass entire rooms, for example shielded rooms as an electromagnetically calmed test environment in EMC laboratories ( absorber hall ).
The Faraday cage principle is also used in lightning protection for buildings. Here it is approximated by a rough structure of lightning rods and earthed building parts.
Car occupied by people as a Faraday cage, experiment in a high-voltage hall
Cars and airplanes with a conductive shell also act like Faraday cages. Electromagnetic fields, the wavelengths of which are small compared to the electrically open joints and gaps in the body, are not efficiently shielded, however. This explains why cell phone reception is possible in the car .
Small shielding cages , often made of tinplate , can be found around the high-frequency assemblies in electronic devices (cell phones, radio and television tuners, wireless baby monitors, etc.).
The microwave oven is an example of a Faraday cage in which the inside and outside are swapped, so to speak. The metal cooking space shields the environment from the strong microwave radiation inside the oven. There is usually a resonance seal on the door , which is only effective for a very specific wavelength.
The metallic housing of a magnetron ensures that the high-energy electromagnetic field remains inside the magnetron. A small part of the field is directed to the outside through the antenna connection.
The simplified, two-dimensional design of a Faraday cage is called a corona ring and is used in the high-voltage area, for example in isolators and surge arresters (varistors). The field strength inside the ring is very low, so no loss-making field emissions can occur there, even at corners and tips such as the assembly harness . | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 5, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7988450527191162, "perplexity": 789.095761743627}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107912807.78/warc/CC-MAIN-20201031032847-20201031062847-00380.warc.gz"} |
http://mathoverflow.net/users/11765/hugo-chapdelaine | # Hugo Chapdelaine
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# 104 Questions
18 Generating finite simple groups with $2$ elements 18 non-isomorphic stably isomorphic fields 17 A simple proof that parallelizable oriented closed manifolds are oriented boundaries? 16 On the Hasse-Weil L-function of $P^n$ 16 On the inverse Galois problem
# 2,253 Reputation
+15 Characterizing the real analytic Eisenstein series +5 Generating finite simple groups with $2$ elements +35 A simple proof that parallelizable oriented closed manifolds are oriented boundaries? +5 Intersection of a ring class field of a quadratic field K with the cyclotomic extension of K
4 Irreducibility of polynomials in two variables 2 On rational points of conics 2 On rational functions with rational power series 2 Looking for deterministic criteria to generate the symmetric group? 1 Generating a finite group from elements in each conjugacy class
# 83 Tags
8 nt.number-theory × 22 2 analytic-number-theory × 6 4 ac.commutative-algebra × 8 2 co.combinatorics × 5 4 polynomials 2 ca.analysis-and-odes × 5 3 gr.group-theory × 12 2 combinatorial-group-theor × 3 3 finite-groups × 6 2 permutations × 2
# 1 Account
MathOverflow 2,253 rep 527 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.33489683270454407, "perplexity": 2538.8193610469066}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414119646209.30/warc/CC-MAIN-20141024030046-00195-ip-10-16-133-185.ec2.internal.warc.gz"} |
http://mathhelpforum.com/discrete-math/208483-trying-study-my-exam-would-like-see-how-u-would-solve-functions-so-plz.html | # Thread: Trying to study for my exam and would like to see how u would solve functions so plz
1. ## Trying to study for my exam and would like to see how u would solve functions so plz
1.Let A = {1; 2; 3; 4} and B = {a; b; c}. Give an example of a function f:A Bthat is neither one to one nor onto.
2. Determine ifthe function f:- {0} defined as f(x) =1/x+ 1 is one to one and onto.
3. Determine ifthe function f : ℝ- {2} - {5} defined by f(x) =5x + 1/x - 2is invertible. If it is define the inverse function f^-1.
4. Determine ifthe function f:- {1} defined by f(x) =(x + 1/x – 1)^3is one to one .
5. Determine ifthe function f: defined as f(x) = 3 (-1)^x is one to one.
6. Determine if the function f:{0, 1} defined as f(x) = 3 -1)^x is one to one.
2. ## Re: Trying to study for my exam and would like to see how u would solve functions so
Originally Posted by math333
1.Let A = {1; 2; 3; 4} and B = {a; b; c}. Give an example of a function f:A Bthat is neither one to one nor onto.
2. Determine ifthe function f:- {0} defined as f(x) =1/x+ 1 is one to one and onto.
3. Determine ifthe function f : ℝ- {2} - {5} defined by f(x) =5x + 1/x - 2is invertible. If it is define the inverse function f^-1.
4. Determine ifthe function f:- {1} defined by f(x) =(x + 1/x – 1)^3is one to one .
5. Determine ifthe function f: defined as f(x) = 3 (-1)^x is one to one.
6. Determine if the function f:{0, 1} defined as f(x) = 3 -1)^x is one to one.
That is too many questions for one thread.
You have simply listed the question.
You have shown no effort whatsoever.
This not a homework service nor is it a tutorial service. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9532927870750427, "perplexity": 2387.1584178777957}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891814833.62/warc/CC-MAIN-20180223194145-20180223214145-00270.warc.gz"} |
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## anonymous one year ago How implement fuzzy logic in Arduino? Delete Cancel Submit
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Hmm..good question, I tried to implement the fuzzy logic on the arduino uno and it appears that you can interface with Arduino from MATLAB. However, I don't know how 'real-time' this is, to use in a Plant-Controller setup. @ravsirius $$\color{blue}{\huge\tt{Nice~}}$$ $$\huge\mathcal{to~meet~}$$ $$\color{red}{\huge\tt{You~!}}$$
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Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9806655645370483, "perplexity": 8100.137266255513}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988720154.20/warc/CC-MAIN-20161020183840-00357-ip-10-171-6-4.ec2.internal.warc.gz"} |
http://quant.stackexchange.com/questions/14421/incoherence-in-bloomberg-data-in-swap-curve-builder-icsv | # Incoherence in Bloomberg Data in Swap Curve Builder (ICSV)
When working on calibration for LMM model, we need to have Initial Libor quotes and Swaptions Black vol quotes on the market data. We have data provided by Bloomberg. However, before performing the calibration, we wish to check the coherence of the market data, e.i if we use the right Libor/Discount Rate for the swaption volatility cube (VCUB).
The problems is i can not have the coherence of these data. The ATM swaps has the strike which is the swap rate interest at the present moment. The swap rate is calculable directly from the Libor quotes (deduced from the Discount Rate).
$$L(t,T_i,T_{i+1}) = \frac{1}{T_{i+1}-T_{i}}(\frac{P(t,T_{i})}{P(t,T_{i+1})} - 1)$$
In the SWPM tab of bloomberg, they said they build swaption VCUB data from EUR 45, which have built data yield curve, zero rate, forward rate ... for calculating swap/swaptions values.
I firstly used these Interest rate curve and recompute swap rate by myselft, I can not reproduce the ATM strike quoted on ATM swap strike matrix.
I secondly use the quoted zero rate curve to recompute the discount curve, $$P(t,T_i) = \frac{1}{1+r_i T_i}$$ Same thing, i can not reproduce the same values as Bloomberg quotes.
However, these values computed and quoted are approximative equal (relative error around 1% max). So i thing that could be due to the difference of day count, or somethings else. Ideally, i hope check every data are perfectly coherent with theoretical formulas, in the way that the calibration result is not biased due to any kind of these error.
My first question is so does somebody has the idea of why that happens like that, is this normal? How to fixed these data coherence. (Error might come from my computations)
My second question is : is this a big issu if we perform a volatility calibration with these incoherence exist in our data?
Many thanks
- | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6237845420837402, "perplexity": 2572.951018314958}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-52/segments/1419447548655.55/warc/CC-MAIN-20141224185908-00080-ip-10-231-17-201.ec2.internal.warc.gz"} |
http://link.springer.com/article/10.1007%2FBF01015324 | , Volume 51, Issue 1-2, pp 135-178
# Scaling laws for invariant measures on hyperbolic and nonhyperbolic atractors
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## Abstract
The analysis of dynamical systems in terms of spectra of singularities is extended to higher dimensions and to nonhyperbolic systems. Prominent roles in our approach are played by the generalized partial dimensions of the invariant measure and by the distribution of effective Liapunov exponents. For hyperbolic attractors, the latter determines the metric entropies and provides one constraint on the partial dimensions. For nonhyperbolic attractors, there are important modifications. We discuss them for the examples of the logistic and Hénon map. We show, in particular, that the generalized dimensions have singularities with noncontinuous derivative, similar to first-order phase transitions in statistical mechanics. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9358940124511719, "perplexity": 795.7065539325247}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-27/segments/1435375095273.5/warc/CC-MAIN-20150627031815-00002-ip-10-179-60-89.ec2.internal.warc.gz"} |
http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node107.html | # 15.1 Fuels
There are a wide variety of fuels used for aerospace power and propulsion. A primary one is jet fuel, essentially kerosene. Kerosene is a mixture of various hydrocarbons. The fuels we consider here are hydrogen ( ), methane ( ), and octane ( ).
The chemical process in which a fuel, for example methane, is burned consists of (on a very basic level -— there are many intermediate reactions that need to be accounted for when computations of the combustion process are carried out):
The reactions we describe are carried out in air, which can be approximated as 21% and 79% . This composition is referred to as theoretical air.'' There are other components of air (for example Argon, which is roughly 1%), but the results given using the theoretical air approximation are more than adequate for our purposes. With this definition, for each mole of , 3.76 (or ) moles of are involved:
Even if the nitrogen is not part of the combustion process, it leaves the combustion chamber at the same temperature as the other products, and this change in state (change in enthalpy) needs to be accounted for in the steady flow energy equation. At the high temperatures achieved in internal combustion engines (aircraft and automobile) reaction does occur between the nitrogen and oxygen, which gives rise to oxides of nitrogen, although we will not consider these reactions.
The condition at which the mixture of fuel and air is such that both completely participate in the reaction is called stoichiometric. In gas turbines, excess air is often used so that the temperatures of the gas exiting the combustor is kept to within desired limits (see Figures 3.20, 3.21, and 3.24(b) for data on these limits.)
Muddy Points
Why is there 3.76 ? (MP 15.1)
What is the most effective way to solve for the number of moles in the reactions? (MP 15.2)
UnifiedTP | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.952627956867218, "perplexity": 913.5427628407106}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440644068184.11/warc/CC-MAIN-20150827025428-00118-ip-10-171-96-226.ec2.internal.warc.gz"} |
http://mathhelpforum.com/calculus/19931-derivative.html | # Math Help - derivative
1. ## derivative
If x + y = xy
then dy/dx is?
2. Originally Posted by Mr_Green
If x + y = xy
then dy/dx is?
You can solve the equation for y, but it is simpler to use implicit differentiation (which I presume is what they want here.)
$x + y = xy$ <-- Take the derivative.
$1 + \frac{dy}{dx} = y + x \cdot \frac{dy}{dx}$
$\frac{dy}{dx} - x \cdot \frac{dy}{dx} = y - 1$
$(1 - x)\frac{dy}{dx} = y - 1$
$\frac{dy}{dx} = \frac{y - 1}{1 - x}$
Now, if you need a form of dy/dx explicitly in terms of y, then
$x + y = xy$
$y - xy = -x$
$y(1 - x) = -x$
$y = -\frac{x}{1 - x}$
You can either just take the derivative of this (not that hard to do) or plug this expression for y into dy/dx and simplify.
-Dan
3. i was given multiple choice possibilities of
a= 1/(x-1)
b= (y-1)/(x-1)
c= (1-y)/(x-1)
d= x+y-1
e= (2-xy)/y
so if i multiply numerator and denominator by -1, the answer would be C, correct?
4. Originally Posted by Mr_Green
i was given multiple choice possibilities of
a= 1/(x-1)
b= (y-1)/(x-1)
c= (1-y)/(x-1)
d= x+y-1
e= (2-xy)/y
so if i multiply numerator and denominator by -1, the answer would be C, correct?
Yup!
-Dan | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 9, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9915404319763184, "perplexity": 2213.2323535427663}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701153323.32/warc/CC-MAIN-20160205193913-00000-ip-10-236-182-209.ec2.internal.warc.gz"} |
https://www.wias-berlin.de/publications/wias-publ/run.jsp?template=abstract&type=Preprint&year=2014&number=2042 | WIAS Preprint No. 2042, (2014)
# A nonlocal free boundary problem
Authors
• Dipierro, Serena
• Savin, Ovidiu
• Valdinoci, Enrico
ORCID: 0000-0001-6222-2272
2010 Mathematics Subject Classification
• 35R11 35R35 49Q20 49Q05
Keywords
• Fractional perimeter, minimization problem, monotonicity formula, classification of cones
DOI
10.20347/WIAS.PREPRINT.2042
Abstract
We consider a nonlocal free boundary problem built by a fractional Dirichlet norm plus a fractional perimeter. Among other results, we prove a monotonicity formula for the minimizers, glueing lemmata, uniform energy bounds, convergence results, a regularity theory for the planar cones and a trivialization result for the flat case. Several classical free boundary problems are limit cases of the one that we consider in this paper.
Appeared in
• SIAM J. Math. Anal., 47 (2015) pp. 4559--4605. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9274621605873108, "perplexity": 3623.9771603762347}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655896932.38/warc/CC-MAIN-20200708093606-20200708123606-00475.warc.gz"} |
http://cosmo.gatech.edu/tag/nbody/ | # 17-21 May 2021
• (abs, pdf) Murphy et al., Ionizing photon production of Population III stars: effects of rotation, convection, and initial mass function
• (abs, pdf) Higashi et al., Amplification of turbulence in contracting prestellar cores in primordial minihalos
• (abs, pdf) Bhowmick et al., Impact of gas based seeding on supermassive black hole populations at $z\geq7$
• (abs, pdf) Wu et al., Cosmic Velocity Field Reconstruction Using AI
• (abs, pdf) Wünsch et al., Tree-based solvers for adaptive mesh refinement code FLASH — II: radiation transport module TreeRay
• (abs, pdf) Karunakaran et al., Satellites Around Milky Way Analogs: Tension in the Number and Fraction of Quiescent Satellites Seen in Observations Versus Simulations
• (abs, pdf) Polzin et al., A recently quenched isolated dwarf galaxy outside of the Local Group environment
• (abs, pdf) Kamlah et al., Preparing the next gravitational million-body simulations: Evolution of single and binary stars in Nbody6++GPU, MOCCA and McLuster
• (abs, pdf) Thomas & Pfrommer, Comparing different closure relations for cosmic ray hydrodynamics
• (abs, pdf) Calderón et al., Moving-mesh radiation-hydrodynamic simulations of wind-reprocessed transients
• (abs, pdf) Wu et al., The high-redshift tail of stellar reionization in LCDM is beyond the reach of the low-$\ell$ CMB
# 01 Dec 2020
• (abs, pdf) Bloch et al., A high-performance and portable asymptotic preserving radiation hydrodynamics code with the M1 model
• (abs, pdf) Furtak et al., How robustly can we constrain the low-mass end of the $z\sim6-7$ stellar mass function? — The limits of lensing models and stellar population assumptions in the Hubble Frontier Fields
• (abs, pdf) van der Velden et al., Ultra-fast model emulation with PRISM; analyzing the Meraxes galaxy formation model
• (abs, pdf) Krieger & Wolf, The scattering order problem in Monte Carlo radiative transfer
• (abs, pdf) Rantala et al., FROST: a momentum-conserving CUDA implementation of a hierarchical fourth-order forward symplectic integrator
• (abs, pdf) De Ceuster et al., Magritte, a modern software library for 3D radiative transfer: II. Adaptive ray-tracing, mesh construction and reduction
# 24 Aug 2020
• (abs, pdf) Chon et al., Cosmological DCBH formation sites hostile for their growth
• (abs, pdf) Rampf et al., Cosmological perturbations for two cold fluids in $\Lambda$CDM
• (abs, pdf) Hahn et al., Higher-order initial conditions for mixed baryon-CDM simulations
• (abs, pdf) Michaux et al., Accurate initial conditions for cosmological N-body simulations: Minimizing truncation and discreteness errors
# 30 Jun 2020
• (abs, pdf) Nanni et al., The gas, metal and dust evolution in low-metallicity local and high-redshift galaxies
• (abs, pdf) Vandenbroucke & Camps, CMacIonize 2.0: a novel task-based approach to Monte Carlo radiation transfer
• (abs, pdf) Baldassare et al., Populating the low-mass end of the $M_{\rm BH}-\sigma_{\ast}$ relation
• (abs, pdf) Johnson et al., A Random Walk Model for Dark Matter Halo Concentrations
• (abs, pdf) Liu & Bromm, When did Population~III star formation end?
• (abs, pdf) Di Cintio et al., Introducing a multi-particle collision method for the evolution of dense stellar systems code: Crash-test N-body simulations
• (abs, pdf) Allahverdi et al., The First Three Seconds: a Review of Possible Expansion Histories of the Early Universe
# 17 Oct 2018
• (abs, pdf) Peeples et al., Figuring Out Gas and Galaxies in Enzo (FOGGIE). I. Resolving Simulated Circumgalactic Absorption at 2 < z < 2.5
• (abs, pdf) Meng et al., Structure of high-redshift galaxies in cosmological simulations
• (abs, pdf) Zhang et al., The optimal gravitational softening length for cosmological N-body simulations
• (abs, pdf) Rujopakarn et al., Science with an ngVLA: Probing Obscured MBH Accretion and Growth since Cosmic Dawn
# 09 Oct 2018
• (abs, pdf) Garrison et al., A High-Fidelity Realization of the Euclid Code Comparison $N$-body Simulation with Abacus
• (abs, pdf) Norman et al., Simulating the Cosmic Dawn with Enzo
• (abs, pdf) Silk, Molecular ionization rates and ultracompact dark matter minihalos
# 12 Mar 2018
• (abs, pdf) Mirocha & Furlanetto, What does the first highly-redshifted 21-cm detection tell us about early galaxies?
• (abs, pdf) Schmidt et al., Cosmological N-Body Simulations with a Large-Scale Tidal Field
• (abs, pdf) Ardaneh et al., Direct Collapse to Supermassive Black Hole Seeds with Radiation Transfer: Cosmological Halos
# 24 Jul 2017
• (abs, pdf) Gioannini et al., The cosmic dust rate across the Universe
• (abs, pdf) Adamek et al., Relativistic N-body simulations with massive neutrinos
• (abs, pdf) Russell, 360-degree videos: a new visualization technique for astrophysical simulations
• (abs, pdf) Chardin et al., Self-shielding of hydrogen in the IGM during the epoch of reionization
# 03 Feb 2017
• (abs, pdf) Schawinski et al., Generative Adversarial Networks recover features in astrophysical images of galaxies beyond the deconvolution limit
• (abs, pdf) Agarwal et al., Metallicity evolution of direct collapse black hole hosts: CR7 as a case study
• (abs, pdf) Das et al., High Mass X-ray Binaries and the Cosmic 21-cm Signal: Impact of Host Galaxy Absorption
• (abs, pdf) Maureira-Fredes & Amaro-Seoane, GraviDy: a GPU modular, parallel $N-$body integrator
# 11 Mar 2015
• (abs, pdf) Li et al., Cooling, AGN Feedback and Star Formation in Simulated Cool-Core Galaxy Clusters
• (abs, pdf) Nelson et al., Zooming in on accretion – I. The structure of halo gas
• (abs, pdf) Hobbs et al., Novel Adaptive softening for collisionless N-body simulations: Eliminating spurious halos | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9302344918251038, "perplexity": 27352.11158712966}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046152129.33/warc/CC-MAIN-20210726120442-20210726150442-00581.warc.gz"} |
https://physics.stackexchange.com/questions/296519/non-euclidean-phase-space | # Non-Euclidean Phase Space?
In classical mechanics, the canonical equations of motion can be rendered in terms of Poisson Brackets: \begin{align} \left\{q_i, F(\mathbf{q},\mathbf{p})\right\} &= \frac{\partial F}{\partial p_i}, \\ \left\{p_i, F(\mathbf{q},\mathbf{p})\right\} &= -\frac{\partial F}{\partial q_i},\ \mathrm{and} \\ \left\{H, F(\mathbf{q},\mathbf{p})\right\} &= -\frac{\operatorname{d} F}{\operatorname{d} t}. \end{align}
This is taken to mean that the $q_i$ generates translations in the $-p_i$ direction, $p_i$ in the $q_i$ direction, and $H$ (the Hamiltonian) through time. Is there anything that can be gained by adding a Christoffel symbol like connection to the canonical equations (ie translating the phase space gradient into a covariant derivative)?
Concretely, say $V_j$ is in a vector space tangent to the phase space manifold (in some combination of $\mathbf{q}$ and $\mathbf{p}$ directions, or in an entirely unrelated vector space). Is it possible to construct a meaningful phase space by defining the Poisson brackets as: \begin{align} \left\{q_i, V_j(\mathbf{q},\mathbf{p})\right\} &= \frac{\partial V_j}{\partial p_i} + \left[\Gamma_p\right]_{i\hphantom{k}j}^{\hphantom{i}k} V_k, \\ \left\{p_i, V_j(\mathbf{q},\mathbf{p})\right\} &= -\frac{\partial V_j}{\partial q_i} - \left[\Gamma_q\right]_{i\hphantom{k}j}^{\hphantom{i}k} V_k,\ \mathrm{and} \\ \left\{H, V_j(\mathbf{q},\mathbf{p})\right\} &= -\frac{\operatorname{d} V_j}{\operatorname{d} t}- \left[\Gamma_t\right]_{i\hphantom{k}j}^{\hphantom{i}k} V_k, \end{align} or some analogous construction?
Is the resulting curved phase space always expressible, through some transformation of coordinates and Hamiltonian, using ordinary canonical equations of motion?
• you cannot have a canonical coordinate transformation change your Poisson brackets (that is pretty much the definition of canonical). Anyway, you might want to google geomeotry of poisson brackets – AccidentalFourierTransform Dec 4 '16 at 10:28
1. Given a symplectic manifold $(M,\omega)$, it is natural to ponder what tangent bundle connection $$\nabla: \Gamma(TM)\times\Gamma(TM)\to \Gamma(TM) \tag{1}$$ to chose?
2. Generically, it is natural to choose $\nabla$ to be torsionfree $$T~=~0,\tag{2}$$ and compatible $$\nabla \omega~=~0\tag{3}$$ with the symplectic $2$-form $\omega$.
3. One may show (via partition of unity) that a torsionfree & compatible connection $\nabla$ exists on a paracompact manifold. Be aware that a such a connection $\nabla$ is far from being unique.
4. The triple $(M,\omega,\nabla)$ is called a Fedosov manifold, and it is the geometric input for the Fedosov star product $\star$ in deformation quantization.
5. Fedosov quantization can be used to define covariant derivatives and time evolution for tensor fields, cf. Refs. 1-2. The classical construction can be extracted in the $\hbar\to 0$ limit.
6. In special cases the symplectic manifold $(M,\omega)$ is endowed with a compatible metric $g$, cf. Kähler manifold. In such situations, the metric $g$ uniquely singles out the Levi-Civita connection. See also this related Phys.SE post.
7. Finally, let us mention that if the symplectic manifold $M=T^{\ast}Q$ is a cotangent bundle equipped with the tautological symplectic structure (cf. e.g. this Phys.SE post), and the base manifold $Q$ is endowed with a connection, this also leads to interesting possibilities, e.g. a super-Poisson bracket, cf. Ref. 3.
References:
1. B.V. Fedosov, A simple geometrical construction of deformation quantization, J. Diff. Geom. 40 (1994) 213.
2. B.V. Fedosov, Deformation quantization and index theory, Mathematical Topics, Vol. 9, Akademie Verlag, Berlin, 1996.
3. B. DeWitt, Supermanifolds, Cambridge Univ. Press, 1992; Section 6.7. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 2, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9996399879455566, "perplexity": 501.4658718493562}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027317274.5/warc/CC-MAIN-20190822151657-20190822173657-00062.warc.gz"} |
http://mathhelpforum.com/discrete-math/222658-show-if-b-sets-b-then-b-b.html | # Thread: Show that if A and B are sets with A ⊆ B, then A ∪ B = B.
1. ## Show that if A and B are sets with A ⊆ B, then A ∪ B = B.
Show that if A and B are sets with A ⊆ B, then A ∪ B = B.
Is A ∪ B = B. because A ∪ B, Means A or B or Both ?
2. ## Re: Show that if A and B are sets with A ⊆ B, then A ∪ B = B.
Originally Posted by lamentofking
Show that if A and B are sets with A ⊆ B, then A ∪ B = B.
Is A ∪ B = B. because A ∪ B, Means A or B or Both ?
Basically, yes.
Realize, That if $X$ is a set and $Y$ is any other set then $X\subseteq (X\cup Y)$.
So in the case $B\subseteq (A\cup B)$. Now all you need do is show $A\cup B\subseteq B.$
3. ## Re: Show that if A and B are sets with A ⊆ B, then A ∪ B = B.
Originally Posted by Plato
Now all you need do is show $A\cup B\subseteq B.$
Is the answer because A U B means that A or B so it can be included in B ?
4. ## Re: Show that if A and B are sets with A ⊆ B, then A ∪ B = B.
Originally Posted by lamentofking
Is the answer because A U B means that A or B so it can be included in B ?
Yes.
5. ## Re: Show that if A and B are sets with A ⊆ B, then A ∪ B = B.
The rigorous way of showing that " $X= Y$" is to show that " $X\subseteq Y$" and that " $Y\subseteq X$". And to show that " $X\subseteq Y$" start with "if $x\in X$ and use the conditions on X and Y to conclude "therefore $x\in Y$".
So to show that, $A\cup B= B$ you must first show $A\cup B\subseteq B$. And you do that by saying "if $x\in A\cup B$ then either $x\in A$ or $x\in B$ (by definition of " $A\cup B$" and then do it in two cases:
1) If $x\in B$ we are done.
2) if $x\in A$ then because $A\subseteq B$, $x\in B$.
So that in either case, if $x\in A\cup B$ then $x\in B$.
All that remains is to show that $B\subseteq A\cup B$. To do that, if $x\in B$ then $x\in A\cup B$ by definition of $A\cup B$.
,
,
,
,
,
,
,
# show that if a and b are sets with a ⊆ b then
Click on a term to search for related topics. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 28, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9271460175514221, "perplexity": 189.18458895305827}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934804610.37/warc/CC-MAIN-20171118040756-20171118060756-00788.warc.gz"} |
https://www.miniphysics.com/questions-for-measurement-jc-set-2u.html | # Questions For Measurement (JC) Set 2U
Show/Hide Sub-topics (Measurement | A Level)
6. Can the magnitude of particle’s displacement be greater than the distance traveled? Explain.
Ans: No, the magnitude of the displacement is always less than or equal to the distance travelled. If two displacements in the same direction are added, then the magnitude of their sum will be equal to the distance travelled. Two vectors in any other orientation will give a displacement less than the distance travelled. If you first walk 3 metres east, and then 4 metres south, you will have walked a total distance of 7 metres, but you will only be 5 metres from your starting point.
7. Which of the following are vectors and which are not: force, temperature, the volume of water in a can, the ratings of a TV show, the height of a building, the velocity of a sports car, the age of the Universe?
Ans: Only force and velocity are vectors. None of the other quantities requires a direction to be described.
8. A book is moved once around the perimeter of a tabletop with the dimensions 1.0 m X 2.0 m. If the book ends up at its initial position, what is its displacement? What is the distance travelled?
Ans: The book’s displacement is zero, as it ends up at the point from which it started. The distance travelled is 6.0 metres.
9. Can the magnitude of a vector have a negative value?
Ans: No, the magnitude of a vector is always positive. A minus sign in a vector only indicates direction, not magnitude.
10. Is it possible to add a vector quantity to a scalar quantity? Explain.
Ans: Addition of a vector to a scalar is not defined.
Back To Measurement | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8556545972824097, "perplexity": 380.1990707187926}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487653461.74/warc/CC-MAIN-20210619233720-20210620023720-00159.warc.gz"} |
https://de.wikibooks.org/wiki/Serlo:_EN:_Series | # Series – Serlo
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## Motivation for a Series
What is ${\displaystyle 1+{\tfrac {1}{2}}+{\tfrac {1}{4}}+{\tfrac {1}{8}}+\ldots }$? One may think of this geometrically: We start with a square of edge length ${\displaystyle 1}$. Its area is given by ${\displaystyle 1^{2}=1}$. Now, we proceed cutting it in equal-sized pieces by alterningly using horizontal and vertical cuts. The first cut yields a rectangle of area ${\displaystyle {\tfrac {1}{2}}\cdot 1={\tfrac {1}{2}}}$, then we get a square of size ${\displaystyle {\tfrac {1}{2}}\cdot {\tfrac {1}{2}}={\tfrac {1}{4}}}$, in the next step a rectangle of area ${\displaystyle {\tfrac {1}{4}}\cdot {\tfrac {1}{2}}={\tfrac {1}{8}}}$ and so on. We may now arrange those rectangles in a specific way:
Combining all areas, we obtain a ${\displaystyle 2\times 1}$-rectangle with total area ${\displaystyle 2\cdot 1=2}$. Hence, we expect the value of the infinite sum ${\displaystyle 1+{\tfrac {1}{2}}+{\tfrac {1}{4}}+{\tfrac {1}{8}}+\ldots }$ to be ${\displaystyle 2}$. When considering the partial sums of that infinite sum, we get a similar result:
{\displaystyle {\begin{aligned}{\begin{array}{rll}S_{1}&=1&=1\\[0.5em]S_{2}&=1+{\tfrac {1}{2}}&=1{,}5\\[0.5em]S_{3}&=1+{\tfrac {1}{2}}+{\tfrac {1}{4}}&=1{,}75\\[0.5em]S_{4}&=1+{\tfrac {1}{2}}+{\tfrac {1}{4}}+{\tfrac {1}{8}}&=1{,}875\\[0.5em]S_{5}&=1+{\tfrac {1}{2}}+{\tfrac {1}{4}}+{\tfrac {1}{8}}+{\tfrac {1}{16}}&=1{,}9375\\[0.5em]&\,\vdots \end{array}}\end{aligned}}}
The partial sums seemingly tend towards ${\displaystyle 2}$ . This supports our assumption that for the infinite sum, ${\displaystyle 1+{\tfrac {1}{2}}+{\tfrac {1}{4}}+{\tfrac {1}{8}}+\ldots =2}$ is a sensible definition.
So we just assigned a specific value to a particular infinite sum. Now, we would like to extend this intuitive concept to an exact definition for infinite sums. This opens up a set of questions:
• How can we determine the value of an arbitrary infinite sum?
• Are there maybe infinite sums which cannot be assigned a value?
• And if yes, how do we see whether an infinite series can be assigned a value or not?
In this chapter, we will use the concept of a series to formally define what the value of an infinite sum is. Series will be defined using partial sums, which are finite and hence may be easily evaluated. In the following chapters, we will see that there actually are infinite sums, which cannot be assigned a value. And we will obtain some criteria for finding out whether an infinite sum may be evaluated or not.
## Finite sums
Endliche Summen und Summenschreibweise (YouTube-Video vom YouTube-Kanal: MJ Maths)
Sigmaschreibweise für endliche Summen
A finite sum (as you may suspect from its name) is nothing else but a sum with finitely many summands. There is an efficient way of denoting such a sum, which we have already seen in „Summe und Produkt“. Instead of writing
${\displaystyle a_{1}+a_{2}+a_{3}+a_{4}+\ldots +a_{n}}$
we used the notation
${\displaystyle \sum _{k=1}^{n}a_{k}}$
Here, ${\displaystyle k}$ is the summation index, which assumes all integer values starting from ${\displaystyle 1}$ up to its finite value of ${\displaystyle n}$. For each assumed ${\displaystyle k}$, the expression ${\displaystyle a_{k}}$ will return a summand - and all of these summands are finally added up. This principle is made clear in the following animation:
Example (Example for a finite sum)
Let us consider the finite sum
${\displaystyle \sum _{k=3}^{7}k^{3}}$
Here, ${\displaystyle k}$ assumes all integer values starting from ${\displaystyle 3}$ through ${\displaystyle 7}$. The funcion assigning to each index its respective summand is given by ${\displaystyle a_{k}=k^{3}}$, so we map ${\displaystyle k\mapsto k^{3}}$. That means, for ${\displaystyle k=3}$ the summand is ${\displaystyle 3^{3}}$, for ${\displaystyle k=4}$ it is ${\displaystyle 4^{3}}$ and so on, until we have ${\displaystyle 7^{3}}$ for ${\displaystyle k=7}$. The final sum we obtain is now:
${\displaystyle \sum _{k=3}^{7}k^{3}=3^{3}+4^{3}+5^{3}+6^{3}+7^{3}}$
## Partial sums
Partialsummen - Definition und Beispiel (YouTube-Video vom YouTube-Kanal: MJ Maths)
As we now know how to define finite sums, we may proceed with the formal definition of an infinite sum. We start with the form, which seems intuitively most plausible:
${\displaystyle a_{1}+a_{2}+a_{3}+a_{4}+a_{5}+\ldots }$
And consider the sequence of partial sums:
{\displaystyle {\begin{aligned}S_{1}&=a_{1}\\S_{2}&=a_{1}+a_{2}\\S_{3}&=a_{1}+a_{2}+a_{3}\\S_{4}&=a_{1}+a_{2}+a_{3}+a_{4}\\S_{5}&=a_{1}+a_{2}+a_{3}+a_{4}+a_{5}\\&\ \vdots \\S_{n}&=a_{1}+a_{2}+a_{3}+a_{4}+a_{5}+\ldots a_{n}\\&\ \vdots \end{aligned}}}
This sequence will be used to define infinite sums. ${\displaystyle S_{n}}$ is the sum over the first ${\displaystyle n}$ summands - and hence a finite sum:
${\displaystyle S_{n}=a_{1}+a_{2}+a_{3}+a_{4}+a_{5}+\ldots +a_{n}=\sum _{k=1}^{n}a_{k}}$
These partial sums are parts of the finite sum. Formally, we may define:
Definition (Partialsumme)
Let ${\displaystyle (a_{m})_{m\in \mathbb {N} }}$ be a sequnce in ${\displaystyle \mathbb {R} }$. Then, the following sum is called ${\displaystyle n}$-th Partial sum:
${\displaystyle S_{n}=a_{1}+a_{2}+a_{3}+a_{4}+a_{5}+\ldots +a_{n}=\sum _{k=1}^{n}a_{k}}$
## Series
The value of an infinite sum should be the limit of its partial sums:
{\displaystyle {\begin{aligned}a_{1}+a_{2}+a_{3}+a_{4}+\ldots &=\lim _{n\to \infty }(a_{1}+a_{2}+a_{3}+a_{4}+\ldots +a_{n})\\&=\lim _{n\to \infty }\sum _{k=1}^{n}a_{k}\\&=\lim _{n\to \infty }S_{n}\end{aligned}}}
We may first construct the sequence of all possible partial sums and then consider their limit. This sequence of partial sums is defined to be a series. We denote it by ${\displaystyle \sum _{k=1}^{\infty }a_{k}}$. This notation is very similar to that of the ${\displaystyle n}$-th partial sum ${\displaystyle \sum _{k=1}^{n}a_{k}}$. But instead of writing down the final index ${\displaystyle n}$ at which the summation has to be stopped, we use the infinity symbol ${\displaystyle \infty }$, emphasizing that our summation does not end. The formal definition now reads:
Definition (Reihe)
For a real-valued sequence ${\displaystyle (a_{k})_{k\in \mathbb {N} }}$, the series ${\displaystyle \sum _{k=1}^{\infty }a_{k}}$ is defined as the sequence of partial sums ${\displaystyle \left(\sum _{k=1}^{n}a_{k}\right)_{n\in \mathbb {N} }}$:
{\displaystyle {\begin{aligned}\sum _{k=1}^{\infty }a_{k}&=\left(\sum _{k=1}^{n}a_{k}\right)_{n\in \mathbb {N} }\\[1em]&=\left(\sum _{k=1}^{1}a_{k},\ {\color {OliveGreen}\sum _{k=1}^{2}a_{k}},\ {\color {Blue}\sum _{k=1}^{3}a_{k}},\ {\color {Orange}\sum _{k=1}^{4}a_{k}},\ \ldots \right)\\[1em]&=\left(a_{1},\ {\color {OliveGreen}a_{1}+a_{2}},\ {\color {Blue}a_{1}+a_{2}+a_{3}},\ {\color {Orange}a_{1}+a_{2}+a_{3}+a_{4}},\ \ldots \right)\end{aligned}}}
Next, we identify the outcome of the infinite summation with the limit of the partial sum sequence. This sequence of partial sums is just an ordinary sequence. It either has a limit value, or it diverges. If the partial sum sequence diverges, then the infinite sum / series is also said to diverge. In case, it actually converges towards a certain limit, then the limit value is also assigned to the infinite sum. Technically, an infinite sum is nothing else but the limit of its partial sum sequence. This limit is denoted by ${\displaystyle \sum _{k=1}^{\infty }a_{k}}$ as well:
Definition (Limit of a series)
The limit ${\displaystyle \sum _{k=1}^{\infty }a_{k}}$ of a series is the limit of the corresponding partial sum sequence:
${\displaystyle \sum _{k=1}^{\infty }a_{k}=\lim _{n\to \infty }\sum _{k=1}^{n}a_{k}}$
Hint
In the article „Cauchy-Kriterium für Reihen“ we will see that only the value of almost all summands is relevant for the convergence behavior (convergent / divergent). That means, if we change the value of finitely many summands in the series, the convergence behavior stays the same. However, the limit of a converging series may of course change if we replace some of its summands.
## Is a series a number or a sequence?
As we already noticed, the expression ${\displaystyle \sum _{k=1}^{\infty }a_{k}}$ is used to denote either the sequence of partial sums (= series) or its limit (= value of the series) . This contradicts the basic principle that notations in mathematics should always be unique! The expression ${\displaystyle \sum _{k=1}^{\infty }a_{k}}$ cannot describe two different objects (a sequence and a number) at once. Instead, we have to choose the correct meaning from the context. This problem is also treated in the book „Analysis 1“ by Otto Forster:
„The Symbol ${\displaystyle \sum _{n=0}^{\infty }a_{n}}$ may mean two things:
1. The sequence ${\displaystyle \left(\sum _{n=0}^{m}a_{n}\right)_{m\in \mathbb {N} }}$ of partial sums.
2. In case of convergence the limit ${\displaystyle \lim _{m\to \infty }\sum _{n=0}^{m}a_{n}}$.“
– Otto Forster in „Analysis 1“[1], translated from German
If we, for instance, say "the series ${\displaystyle \sum _{k=1}^{\infty }a_{k}}$ converges" or talk about "the series ${\displaystyle \sum _{k=1}^{\infty }a_{k}}$" in general, then the expression is meant to describe a sequence (first meaning). In case that ${\displaystyle \sum _{k=1}^{\infty }a_{k}}$ is treated like a number in calculations, then the expression is meant to denote the limit (second meaning). So we need to pay attention what is meant when using the expression ${\displaystyle \sum _{k=1}^{\infty }a_{k}}$: a sequence of partial sums or its limit.
## Conclusion
We just formally defined the idea of an infinite sum:
1. We defined the sum of the first ${\displaystyle n}$ summands as ${\displaystyle n}$-th partial sum.
2. We called the sequence of these partial sums a "series". The limit of this sequence was defined to be the value of our infinite sum.
## Example: geometrical series with ${\displaystyle {\tfrac {1}{2}}}$
${\displaystyle {\tfrac {1}{2}}+{\tfrac {1}{4}}+{\tfrac {1}{8}}+\ldots =1}$
Let us consider again the infinite sum ${\displaystyle 1+{\tfrac {1}{2}}+{\tfrac {1}{4}}+{\tfrac {1}{8}}+\ldots }$ given in the beginning. According to our definition, this sum is equivalent to the series ${\displaystyle \sum _{k=0}^{\infty }{\frac {1}{2^{k}}}}$. First, let us compute its partial sums:
{\displaystyle {\begin{aligned}{\begin{array}{rlll}S_{1}&=\sum _{k=0}^{0}{\frac {1}{2^{k}}}&=1&=1\\[0.5em]S_{2}&=\sum _{k=0}^{1}{\frac {1}{2^{k}}}&=1+{\frac {1}{2}}&=1{,}5\\[0.5em]S_{3}&=\sum _{k=0}^{2}{\frac {1}{2^{k}}}&=1+{\frac {1}{2}}+{\frac {1}{4}}&=1{,}75\\[0.5em]S_{4}&=\sum _{k=0}^{3}{\frac {1}{2^{k}}}&=1+{\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{8}}&=1{,}875\\[0.5em]S_{5}&=\sum _{k=0}^{4}{\frac {1}{2^{k}}}&=1+{\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{8}}+{\frac {1}{16}}&=1{,}9375\\[0.5em]&\,\vdots \end{array}}\end{aligned}}}
The infinite sum ${\displaystyle 1+{\tfrac {1}{2}}+{\tfrac {1}{4}}+{\tfrac {1}{8}}+\ldots }$ is equivalent to the sequence of those partial sums:
{\displaystyle {\begin{aligned}\sum _{k=0}^{\infty }{\frac {1}{2^{k}}}&=\left(\sum _{k=0}^{n-1}{\frac {1}{2^{k}}}\right)_{n\in \mathbb {N} }\\[1em]&=\left(\sum _{k=0}^{0}{\frac {1}{2^{k}}},\ {\color {OliveGreen}\sum _{k=0}^{1}{\frac {1}{2^{k}}}},\ {\color {Blue}\sum _{k=0}^{2}{\frac {1}{2^{k}}}},\ {\color {Orange}\sum _{k=0}^{3}{\frac {1}{2^{k}}}},\ \ldots \right)\\[1em]&=\left(1,\ {\color {OliveGreen}1+{\frac {1}{2}}},\ {\color {Blue}1+{\frac {1}{2}}+{\frac {1}{4}}},\ {\color {Orange}1+{\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{8}}},\ \ldots \right)\\[1em]&=\left(1;\ {\color {OliveGreen}1{,}5};\ {\color {Blue}1{,}75};\ {\color {Orange}1{,}875};\ldots \right)\end{aligned}}}
We may directly give the result for any ${\displaystyle n}$-th partial sum, using the geometrical summation formula ${\displaystyle \sum _{k=0}^{n}q^{k}={\frac {1-q^{n+1}}{1-q}}}$ for ${\displaystyle q\neq 1}$. Plugging in ${\displaystyle q={\tfrac {1}{2}}}$, this yields:
{\displaystyle {\begin{aligned}S_{n}&=1+{\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{8}}+\ldots +{\frac {1}{2^{n-1}}}\\[0.5em]&=\sum _{k=0}^{n-1}{\frac {1}{2^{k}}}\\[0.5em]&={\frac {1-\left({\frac {1}{2}}\right)^{(n-1)+1}}{1-{\frac {1}{2}}}}\\[0.5em]&=2\cdot \left(1-{\frac {1}{2^{n}}}\right)\\[0.5em]&=2-{\frac {1}{2^{n-1}}}\end{aligned}}}
Hence, our series corresponds to the following sequence:
${\displaystyle \sum _{k=0}^{\infty }{\frac {1}{2^{k}}}=\left(2-{\frac {1}{2^{n-1}}}\right)_{n\in \mathbb {N} }}$
The sequence ${\displaystyle \left(2-{\tfrac {1}{2^{n-1}}}\right)_{n\in \mathbb {N} }}$ converges, as ${\displaystyle \lim _{n\to \infty }{\tfrac {1}{2^{n-1}}}=0}$ (geometrical sequence with ${\displaystyle q={\tfrac {1}{2}}}$). Therefore, the value of our series equals 2:
{\displaystyle {\begin{aligned}\sum _{k=0}^{\infty }{\frac {1}{2^{k}}}&=\lim _{n\to \infty }\sum _{k=0}^{n-1}{\frac {1}{2^{k}}}\\[0.5em]&=\lim _{n\to \infty }\left(2-{\frac {1}{2^{n-1}}}\right)\\[0.5em]&=2\end{aligned}}}
## Exercise
Exercise (geometrical series with ${\displaystyle -{\tfrac {1}{2}}}$)
Show convergence of the series ${\displaystyle \sum _{k=0}^{\infty }{\frac {(-1)^{k}}{2^{k}}}}$ and determine its limit.
Solution (geometrical series with ${\displaystyle -{\tfrac {1}{2}}}$)
Using the geometrical summation formula, one may give an expression for the ${\displaystyle n}$-th partial sum:
{\displaystyle {\begin{aligned}S_{n}&=1-{\frac {1}{2}}+{\frac {1}{4}}-{\frac {1}{8}}+\ldots +{\frac {(-1)^{n-1}}{2^{n-1}}}\\[0.5em]&=\sum _{k=0}^{n-1}\left(-{\frac {1}{2}}\right)^{k}\\[0.5em]&={\frac {1-\left(-{\frac {1}{2}}\right)^{(n-1)+1}}{1-(-{\frac {1}{2}})}}\\[0.5em]&={\frac {1-\left(-{\frac {1}{2}}\right)^{(n-1)+1}}{\frac {3}{2}}}\\[0.5em]&={\frac {2}{3}}\cdot \left(1-(-{\frac {1}{2}})^{n}\right)\\[0.5em]&={\frac {2}{3}}-{\frac {2}{3}}\left(-{\frac {1}{2}}\right)^{n}\end{aligned}}}
Therefore:
${\displaystyle \sum _{k=0}^{\infty }{\frac {(-1)^{k}}{2^{k}}}=\left({\frac {2}{3}}-{\frac {2}{3}}\left(-{\frac {1}{2}}\right)^{n}\right)_{n\in \mathbb {N} }}$
Using ${\displaystyle \lim _{n\to \infty }\left(-{\tfrac {1}{2}}\right)^{n}=0}$ (geometrical sequence with ${\displaystyle q=-{\tfrac {1}{2}}}$) and the calculation rules for limit values, convergence of the series may be shown:
{\displaystyle {\begin{aligned}\sum _{k=0}^{\infty }{\frac {(-1)^{k}}{2^{k}}}&=\lim _{n\to \infty }\sum _{k=0}^{n-1}\left(-{\frac {1}{2}}\right)^{k}\\[0.5em]&=\lim _{n\to \infty }\left[{\frac {2}{3}}-{\frac {2}{3}}\left(-{\frac {1}{2}}\right)^{n}\right]\\[0.5em]&={\frac {2}{3}}-{\frac {2}{3}}\cdot 0\\[0.5em]&={\frac {2}{3}}\end{aligned}}}
## Sequence of remainders
As we have seen, a series ${\displaystyle \sum _{k=1}^{\infty }a_{k}}$ is the same thing as the sequence of its partial sums ${\displaystyle \left(\sum _{k=1}^{n}a_{k}\right)_{n\in \mathbb {N} }}$ . Let us assume that ${\displaystyle \sum _{k=1}^{\infty }a_{k}}$ converges. That means, the limit ${\displaystyle \lim _{n\to \infty }\sum _{k=1}^{n}a_{k}}$ exists and equals the value ${\displaystyle \sum _{k=1}^{\infty }a_{k}}$ of the series. Hence, ${\displaystyle \lim _{n\to \infty }\left(\sum _{k=1}^{\infty }a_{k}-\sum _{k=1}^{n}a_{k}\right)=0}$.
Let us consider the difference between the above limit and the partial sums. The difference between the value of the series (the limit) and the ${\displaystyle n}$-th partial sum is called ${\displaystyle n}$-th remainder ${\displaystyle R_{n}}$. We may also thik of it as the "error" of the ${\displaystyle n}$-th partial sum approximating the value of the series.
The formal definition of the ${\displaystyle n}$-th remainder reads:
Definition (${\displaystyle n}$-tes Restglied einer Reihe)
Let ${\displaystyle \sum _{k=1}^{\infty }a_{k}}$ be a series. Then the ${\displaystyle n}$-th remainder is given by the following series:
${\displaystyle R_{n}=\sum _{k=n+1}^{\infty }a_{k}=a_{n+1}+a_{n+2}+a_{n+3}+\ldots }$
The remainders will therefore take the following form:
{\displaystyle {\begin{aligned}{\begin{array}{rclrcccccccc}S_{1}&=&a_{1}&R_{1}&=&a_{2}&+&a_{3}&+&a_{4}&+&\ldots \\S_{2}&=&a_{1}+a_{2}&R_{2}&=&&&a_{3}&+&a_{4}&+&\ldots \\S_{3}&=&a_{1}+a_{2}+a_{3}&R_{3}&=&&&&&a_{4}&+&\ldots \\&\vdots &&&\vdots &\\S_{n}&=&a_{1}+a_{2}+\ldots +a_{n}&R_{n}&=&a_{n+1}&+&a_{n+2}&+&a_{n+3}&+&\ldots \\&\vdots &&&\vdots &\end{array}}\end{aligned}}}
Now, consider the sequence of remainders ${\displaystyle (R_{n})_{n\in \mathbb {N} }}$. How do we expect this sequence to behave? We already mentioned above that for convrgent series, the remainders should tend to zero, so ${\displaystyle \lim _{n\to \infty }R_{n}=\lim _{n\to \infty }\left(\sum _{k=1}^{\infty }a_{k}-\sum _{k=1}^{n}a_{k}\right)=0}$ makes sense. And we will prove that claim in the following theorem:
Theorem (sequence of remainders)
Let ${\displaystyle \sum _{k=1}^{\infty }a_{k}=\left(\sum _{k=1}^{n}a_{k}\right)_{n\in \mathbb {N} }=(S_{n})_{n\in \mathbb {N} }}$ be a convergent series. Then, the sequence of remainders ${\displaystyle (R_{n})_{n\in \mathbb {N} }=\left(\sum _{k=n+1}^{\infty }a_{k}\right)_{n\in \mathbb {N} }}$ will converge towards ${\displaystyle 0}$.
Proof (sequence of remainders)
Since the series converges, the limit ${\displaystyle \lim _{n\to \infty }S_{n}=\lim _{n\to \infty }\sum _{k=1}^{n}a_{k}=\sum _{k=1}^{\infty }a_{k}=S<\infty }$ exists. Now
{\displaystyle {\begin{aligned}R_{n}&=\sum _{k=n+1}^{\infty }a_{k}\\&=\sum _{k=1}^{\infty }a_{k}-\sum _{k=1}^{n}a_{k}\\&=S-S_{n}\end{aligned}}}
Using the calculation rules for limits, we obtain
{\displaystyle {\begin{aligned}\lim _{n\to \infty }R_{n}&=\lim _{n\to \infty }(S-S_{n})\\&=S-\lim _{n\to \infty }S_{n}\\&=S-S\\&=0\end{aligned}}}
Therefore, ${\displaystyle (R_{n})_{n\in \mathbb {N} }}$ is a null sequence.
Hint
Usually, it is not possible to write down an explicit formula for the sequence of remainders ${\displaystyle (R_{n})_{n\in \mathbb {N} }}$. However, in many cases one may give estimates or bounds for them. For instance, when considering alternating series ${\displaystyle \sum _{k=1}^{\infty }(-1)^{k+1}b_{k}}$ in general, the Leibniz-Kriteriums will yield us an "error estimate", i.e. an upper bound to the remainder. Taylor series allow for such error estimates as well. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 120, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9920207858085632, "perplexity": 1004.061621991519}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575541308149.76/warc/CC-MAIN-20191215122056-20191215150056-00010.warc.gz"} |
https://www.physicsforums.com/threads/wind-turbine.262070/ | Wind turbine
1. Oct 6, 2008
drugyjay
can someone explain in simple terms what does 1mw wind turbine mean?
how many houses can this power?
if it is a 500w turbine, how many houses can this power?
2. Oct 6, 2008
stewartcs
1 MW is one mega watt. It is the rated power capacity of the wind turbine for a given (and constant) wind speed.
It depends on the capacity factor of the wind turbine and the household consumption. The capacity factor depends largely on the average wind speed. A typical capacity factor would be between 0.25 and 0.40. The average household consumption in the US is about 10,600 kWh per year (according to the DOE).
Therefore, the number of houses in the US that can be powered by a 1 MW wind turbine would be 1,000,000 x 0.40 x 8760 / 10600 = 331 homes.
Use the same approach as above to find this.
CS | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8023591637611389, "perplexity": 1098.3923440662172}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818687642.30/warc/CC-MAIN-20170921044627-20170921064627-00144.warc.gz"} |
http://mathoverflow.net/questions/60457/elementaryshortuseful/60482 | # Elementary+Short+Useful
Imagine your-self in front of a class with very good undergraduates who plan to do mathematics (professionally) in the future. You have 30 minutes after that you do not see these students again. You need to present a theorem which will be 100% useful for them.
What would you do?
For example: 30 min is more than enough to introduce metric spaces, prove existence of partition of unity, and explain how it can be used later.
P.S. Many of you criticized the vague formulation of the question. I agree. I was trying to make it short --- I do not read the questions if they are longer than half a page. Still I think it is a good approximation to what I really wanted to ask. Here is an other formulation of the same question, but it might be even more vague.
Before I liked jewelry-type theorems; those I can put in my pocket and look at it when I want to. Now I like tool-type theorems; those which can be used to dig a hole or build a wall. It turns out that there are jewelry-type and tool-type theorems at the same time. I know a few and I want to know more.
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How many years of undergraduate education do those students have? What can we assume that they know? (It is a big difference between one who's in the second half of her third year and one that just started two months ago.) – Willie Wong Apr 3 '11 at 18:28
I find it hard to square the "no prerequisites" condition with the "partitions of unity" example. Or are we talking about ideal undergraduate students, who like ideal gases are only an approximation to the reality? – Yemon Choi Apr 3 '11 at 20:34
In my opinion, the "try to be realistic" injunction (which I approve of in all pedagogical questions; note that a lot of experienced teachers do see some of the more ridiculously ambitious pedagogical suggestions promulgated in some answers here and have a good laugh at the naivete of the authors) is hard to square with the vagueness of the question. The term "very good undergraduate" alone is a currency whose value will rise and fall according to where you go. It is tempting to close the question as "too localized" for this reason, but I'll think about it a bit more... – Pete L. Clark Apr 3 '11 at 23:03
I too find the partitions of unity example unrealistic. I do think this and some of the examples below could be made to work if one wasn't obliged to give a proof, but perhaps only an intuitive idea, and then explain why it was useful -- sort of like a colloquium talk for undergraduates. – Todd Trimble Apr 3 '11 at 23:10
Indeed, Anton, you can do all sort of things in 30 minutes... but unless the students already somewhat familiar about the subject you are talking about, it is rather unusual that you can introduce three new objects, two concepts, and a theorem to anyone and as a result get them to understand the significance of anything. – Mariano Suárez-Alvarez Apr 4 '11 at 17:10
Sperner's lemma (Two-dimensional case)
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I don't know about 100% useful, but since I have seen a striking use for it (in the proof of Monsky's theorem about cutting a rectangle into congruent triangles) I won't object on that account. I note that the OP's suggestions seem more reasonable than some of the answers... – Pete L. Clark Apr 3 '11 at 23:10
The definition of the tensor product and existence/uniqueness/associativity properties.
I know, this is perhaps not a single theorem but in my eyes one of the most useful "elemetary" concepts. Personally, I had two semesters of linear algebra without mentioning the tensor product. And from this I suffered for a long time during my further studies. Now it is my first homework/exercise for students in my lectures (e.g. diff geo).
If the student is really clever, one can even do something like the tensor algebra in these 30 min.
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Heisenberg's uncertainty principle.
• Everyone should be exposed to quantum mechanics.
• Appears frequently in analysis and probability (not to mention physics).
• Showcases some of the highlights of Fourier theory.
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I would introduce Bezout's Theorem (there is an article on wiki). It will be hard to prove this statement in the full generality, but the proof of the weaker statement:
The system of two polynomials $P(x,y)$ and $Q(x,y)$ without common factors of degrees $m$ and $n$ correspondingly has at most $mn$ solutions.
takes one page at most and uses only the fact that polynomials of two variables have a unique factorisation in irreducible polynomial. (for example, you can check page 244 in an appendix of the book "Rational Points on Elliptic curves" of Silverman and Tate).
The well-known beautiful (or, say, elementary) application of this theorem is Pascal's theorem.
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Dear Darij, well that is not me who is using it ... This is Fulton, Miles Reid, Seilverman, and many many others (basically any algebraic geometer who wrote a book on curves)... you can check page 62 here, for example : math.lsa.umich.edu/~wfulton/CurveBook.pdf – aglearner Nov 9 '11 at 22:39
Quite unbelievable that I haven't seen that answer in the previous ones.
Cantor's Theorem & Cantor's Diagonal.
Both of these are quite short, and one can squeeze them into a 30 minutes discussion including the definition of "cardinality".
I find them useful, even if not directly applicable, the shock that infinite objects (and generally, mathematical objects) need not match our finite intuition is probably one of the most important things that new mathematicians should learn. When you know that you don't know what to do, you work with the definitions slowly and carefully and eventually you develop the intuition that allows you to run freely in the field.
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The Archimedes proof that the uniform distribution on the sphere projects on the uniform distribution on a diameter.
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I don't understand what the statement is supposed to be, nor am I confident that Archimedes is someone who proved it. Could you link to a reference, please? – Todd Trimble Mar 27 '14 at 17:05
@ToddTrimble If you consider a sphere to have a uniform mass distribution (constant surface density), and consider the vertical diameter, then if you project all mass horizontally onto this diameter, this diameter (segment) acquires a uniform mass distribution (line density). This is related to the fact that the surface area of a "spherical zone" is proportional to its height, $A=2\pi Rh$. This was certainly known to Archimedes and is associated with him. It is related to the Lambert cylindrical equal-area projection ("Archimedes projection"). – Jeppe Stig Nielsen Sep 25 '15 at 20:43
The well-ordering theorem and an application (that uses transfinite recursion, after well-ordering a set). Many interesting sets and examples can be built that way. Or maybe Axiom of Choice/Zorn's lemma (show one from the other) and then show the well-ordering theorem.
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Uniform convergence of the averages of the partial sums of the Fourier series, for any continuous function $f$ on $[0, 2 \pi]$ with $f(0)=f(2\pi)$:
$$\sigma_N(f, \theta) = \sum_{n = -N}^N \left(1-\frac{|n|}{N+1} \right) \widehat{f}(n)e^{in \theta} \to f(\theta)$$
And the Weierstrauss Polynomial Approximation Theorem: the polynomials are uniformly dense in $C[a,b]$. This is a corollary of the Fourier series result, or it can be proved similarly. Finally, if time permits, the Stone-Weierstrauss Theorem.
Of course, it would be nice to talk about approximations to the Dirac Delta, convolutions, fundamental solutions to PDEs, e.g. the Heat Equation, etc. etc. but I suppose only a REALLY good class could absorb all this in half an hour...
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Theorem. $\sqrt{2}$ is irrational.
This is an ancient theorem, about 2400 years old, and its modern proof is identical to the one appearing in Euclid's elements. A simple number theoretic proof, where you get the chance to use the abductio ad absurdum (or εἰς ἄτοπον ἀπαγωγή).
Note. As Victor Protsak noted, the number-theoretical proof is not the first one. The first one is believed to geometrical, using anthyphaeresis (ἀνθυφαίρεσις), i.e., proving geometricallly that the euclidean algorithm of dividing $1+\sqrt{2}$ by $1$ is periodic: \begin{align} 1+\sqrt{2}&=2\cdot 1 +v_1, \\ 1&=2\cdot v_1+v_2, \\ v_1&=2\cdot v_2+v_3, \\ \text{etc} \end{align} and thus $1+\sqrt{2}$ and $1$ are inconsummerable (ἀσὐμμετρα). It is noteworthy that, although the number theoretical proof appaears Euclid's Elements, which were written c. 300 BC, the fact that there is a proof that the square roots of positive integers less than 19 is mentioned in Theaetetus of Plato, writeen c. 380 BC. Anthyphaeresis works for every $n$, but it can get extremely complicated, as $n$ gets larger. In fact, for $n=19$, in order to establish periodicity of Euclidean algorithm, 6 steps are required, and huge geometrical figures to observe it! A few years ago I supervised a Master's thesis on this proof, and I think it makes an extremely interesting lecture.
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Well, there are by now many proofs, lending themselves to different directions and generalizations, and such might make for an interesting 30-minute lecture to undergraduates. – Todd Trimble Dec 19 '13 at 23:15
In fact, there is some controversy as to whether the "traditional" even-odd reductio ad absurdum proof was the first one. Many sources assert that the original proof extended to irrationality of $\sqrt{d}$ for $d<17, d\ne 1,4,9,16,$ which would be consistent with not using elementary divisibility properties of primes. Also, some authors believe that a geometric proof involving the diagonal and the side of a square (the one that is equivalent to the non-termination of the continued fraction expansion of $\sqrt{2}-1$) was invented concurrently with or earlier than the even-odd argument. – Victor Protsak Dec 20 '13 at 1:46
Series representations for functions and the fact that $\mathbb C$ is "rigid" in contrast to $\mathbb R$ when discussing differentiability and series developements.
This "explains" for example how pocket calculators compute trigonometric functions, logarithms and exponentials.
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Gödel's incompleteness theorems
A non-technical overview could be done in a fairly short amount of time, thus allowing for some discussion of its various implications, particularly regarding possible roles of mathematics.
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Moore closures, their relation to collections of Moore-closed sets and a characterization for closure under finitary operations.
One can then discuss why Moore-closed sets form a complete lattice and a lot more, if one feels so inclined.
This is certainly something students will encounter over, and over, and over again in different guises. Moore-closures are certainly among the most useful trivialities I know.
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Let $G$ be a finite group and $V_i$, $i=1,...,r$ be the irreducible representations, $d_i:=dim(V_i)$. Then $|G|=\sum_i d_{i}^{2}$.
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This is certainly a high point in a first course on representation theory, but why is it a worthy stand-alone topic? Will it be useful to a student who otherwise knows no representation theory? (Or will it persuade a student to study representation theory?) – Pete L. Clark Apr 4 '11 at 14:46
When I was an undergraduate, I was persuaded to read Serres book when an older student told me about that result. – Johannes Ebert Apr 4 '11 at 15:08
Once one knows a bit of representation theory, one is certainly set up to appreciate this as a surprising and exciting result; but, for a typical undergraduate audience, I would think one would have first to define a representation—which, itself, if done and motivated well, should take a big chunk of the time. – L Spice Apr 8 '11 at 16:48
Sanov's theorem of large deviations.
I don't have to prove anything, right? If they want a proof, they'll look it up in a book later.
Assume the students already know about the central limit theorem. Explain how the two theorems talk about limits in different direction: let $S_n$ be the sum of $n$ independent variables of identical distributions (real valued, with zero mean and finite variance), the central limit theorem gives a limit of the unscaled probability $P(S_n/\sqrt{n} < c)$, this limit is strictly between 0 and 1; whereas large deviation theorems give the rate of decrease of a probability like $P(S_n/n < c)$.
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[I would introduce Taylor's theorem and point out that it has many applications for instance in physics but also in differential geometry. On the one hand very elementary proofs can be given, but on the other hand, for practical computations with "nice" functions it is always helpful to have that theorem in full generality at the ready. For instance in Riemannian Geometry, one uses Taylor expansion in combination with Jacobi fields to expand the metric tensor locally. This does show that locally, we can find coordinates s.t. the metric behaves like the standard Euclidean metric, but there have to be some corrections such as one term involving the Riemannian curvature tensor.][http://en.wikipedia.org/wiki/Taylor's_theorem]
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Combinatorial Nullstellensatz. You may prove it and then choose your favorite applications for as many minutes as you have. I personally like to include applications to evaluation of coefficients, as explained in this MO answer, after that to additive combinatorics, like Cauchy--Davenport theorem, and to graph theory, like 3-choosability of a planar bipartite graph.
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Completeness theorem for first order logic.
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At the risk of incurring the wrath of some here, I would propose the Yoneda Lemma, along with the minimum of necessary category theory. Like it or not, category theory is hugely useful to algebraists, and early exposure can be very helpful. (It was to me!)
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I also considered the Yoneda lemma, but I think it's a tricky case. To me the Yoneda lemma is just about the deepest "triviality" (if that isn't too self-contradictory!) in all of mathematics, but I think its profound significance takes quite some time to sink in, and it's not so easy to get that across in 30 minutes (I don't think). – Todd Trimble Apr 5 '11 at 11:38
To explain the Yoneda Lemma to undergraduates, you need to introduce the concept of a category, that of a functor, and that of a natural transformation (unless that is taught in an undergraduate course, but if it is, then the Yoneda Lemma is probably taught in that course, too). Then you can start working on the lemma. I don't see how this can reasonably done within 30 minutes, in particular because just giving definitions does not given the students any intuition. – Niemi Sep 9 '13 at 8:55
I would tell them "What is real maths". To achieve this use Lakatos way about Euler's formula ( $V - E + F = 2$ ).
It is a set of successive reformulations (more and more precise) each followed by a counter example justifying the next reformulation.
Reference is : I. Lakatos, "Proofs and Refutations: The Logic of Mathematical Discovery
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Fundamental Theorem of Finitely Generated Abelian Groups.
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• The famous Heine - Borel theorem which says that a closed a bounded subset of $\mathbb{R}^{n}$ is compact.
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I've always been thrilled by the fact that the coefficients of a (monic) polynomial are obtained by taking the elementary symmetric functions in (minus) the roots of that polynomial:
$$\prod_{i=1}^n (X+\alpha_i) = \sum_{k=0}^n (\sum_{i_1 < \cdots < i_k} \alpha_{i_1} \cdots \alpha_{i_k})X^{n-k}$$ A lot is built on this, I think. I'd like to explain the connection to automorphisms and fixed fields and how the roots of a polynomial are permuted by an automorphism that fixes the coefficient field of that polynomial. Then maybe mention the beginnings of Galois theory.
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I am surprised that no one mentioned the Baire category theorem.
I am not sure if you would have enough time to show many applications in 30 minutes but it is almost certain that they will end up using it at some point. Here are some applications discussed on MO.
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Existence of Nash equilibria. This is feasible in 30 minutes, and builds surprising connections between game theory, elementary probability, elementary geometry, and algebraic topology.
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I suppose I just find it no more implausible than taking 30 minutes to introduce metric spaces and partition of unity, and to convince students who've never encountered even those definitions of the significance of what you're talking about. I second the sentiment of Willie's and Yemon's comments (to the original question): from the dismissive response you're giving to many answers just for involving a concept like, say, ultraproduct, I confess that it is not at all clear to me what you're after for these 30 minute talks. I'll try one more answer :-) – Ed Dean Apr 3 '11 at 21:27
The Gelfand-Naimark theorem: every commutative C* algebra is $C_0(X)$ for some locally compact Hausdorff space $X$.
• The spectral theorem is a corollary.
• The theorem introduces students to the idea that a ring is a geometric object
• Certain constructions in topology, e.g. the Stone-Cech compactification, become more transparent.
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I know that playing “elementarier-than-thou” isn't really much fun, but how can you possibly conceive of this as a lecture with no prerequisites? For example, it seems doubtful that one could convince students (usefully) that a ring is a geometric object if they didn't first have the idea that a ring was an algebraic object …. – L Spice Apr 8 '11 at 18:09
My first choice was taken, Picard iteration using Fixed point principles. I'll try not to have a repeat. I have been teaching a history of math class this semester so this sort of thing has been on my mind recently.
I would definitely consider different choices depending on how advanced the students I expected were.
Pre-Calculus but talented: Archimedes method for finding $\pi$. Calculus: Fermat method for finding the integral of $x^n$ Differential Equations: Picard iterations/fixed point principles more advanced. The Brachistichrone.
Another topic that I like, specifically for analysis is to take some of the different definitions of continuity and show that they are equivalent.
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https://socratic.org/questions/sec-theta-2-to-rectangular-coordinates | Trigonometry
Topics
# Sec theta = 2 to rectangular coordinates??
Feb 26, 2018
See below.
#### Explanation:
Identity.
$\textcolor{red}{\boldsymbol{\sec x = \frac{1}{\cos} x}}$
$\frac{1}{\cos} \left(\theta\right) = 2$
$\cos \left(\theta\right) = \frac{1}{2}$
$\theta = \arccos \left(\cos \left(\theta\right)\right) = \arccos \left(\frac{1}{2}\right) \implies \theta = \frac{\pi}{3} , \frac{5 \pi}{3}$
For:
$0 \le \theta \le 2 \pi$
From the above diagram, we can see that:
$x = r \cos \left(\theta\right)$
$y = r \sin \left(\theta\right)$
So coordinates will be:
$\left(r \cos \left(\frac{\pi}{3}\right) , r \sin \left(\frac{\pi}{3}\right)\right)$
$\left(r \cos \left(\frac{5 \pi}{3}\right) , r \sin \left(\frac{5 \pi}{3}\right)\right)$
Without knowing the radius we can't go any further than this.
If this is on a unit circle then the radius is $1$ and:
$\cos \left(\frac{\pi}{3}\right) = \frac{1}{2}$ , $\sin \left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}$
$\cos \left(\frac{5 \pi}{3}\right) = \frac{1}{2}$ , $\sin \left(\frac{5 \pi}{3}\right) = - \frac{\sqrt{3}}{2}$
Coordinates:
$\left(\frac{1}{2} , \frac{\sqrt{3}}{2}\right)$ , $\left(\frac{1}{2} , - \frac{\sqrt{3}}{2}\right)$
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https://florian-roemer.de/blog/page/2/ | ## Widely Linear Least Squares
Together with my colleague Jens I recently stumbled across a widely linear estimation problem. More precisely, we were trying to estimate a vector $\ma{x} \in \compl^{N}$ such that $\ma{C} \cdot \begin{bmatrix}\ma{x}\\ \ma{x}^*\end{bmatrix}$ was as close as possible to a given $\ma{b} \in \compl^{M}$ for a given matrix $\ma{C} \in \compl^{M \times 2N}$. This is not a linear Least Squares problem (due to the non-linear complex conjugation operator), however, it is linear in real and imaginary parts of $\ma{x}$. Hence, we call it widely linear.
How to solve such problems? Before we can calculate a solution, we need an appropriate cost function. Let’s assume for now that $M\geq 2N$ so that we would expect the system of equations to be overdetermined. A proper cost function for $\ma{x}$ would then be
$$\ma{x}_{\rm opt} = \arg \min_{\ma{x}} \left\| \ma{C} \cdot \begin{bmatrix}\ma{x}\\ \ma{x}^*\end{bmatrix} – \ma{b} \right\|_2^2,$$
i.e., find the $\ma{x}$ that minimizes the Euclidean distance between $\ma{C} \cdot \begin{bmatrix}\ma{x}\\ \ma{x}^*\end{bmatrix}$ and $\ma{b}$. How to solve it? I was somehow reminded of a blog post I made earlier on solving widely linear systems of equations and argued that the same solution is applicable. You simply break $\ma{C}$ into $\ma{C} = \begin{bmatrix}\ma{A} & \ma{B}\end{bmatrix}$ where $\ma{A}, \ma{B} \in \compl^{M \times N}$ contain the first and the last $N$ columns of $\ma{C}$. Then you rewrite the whole system into a real-valued system of equations following the technique outlined in the earlier blog post. This gives you
$$\ma{x}_{\rm opt} = \arg \min_{\ma{x}} \left\| \begin{bmatrix} \ma{A}_{\rm R} + \ma{B}_{\rm R} & -\ma{A}_{\rm I} + \ma{B}_{\rm I} \\ \ma{A}_{\rm I} + \ma{B}_{\rm I} & \ma{A}_{\rm R} – \ma{B}_{\rm R} \end{bmatrix} \cdot \begin{bmatrix}\ma{x}_{\rm R}\\ \ma{x}_{\rm I}\end{bmatrix} – \begin{bmatrix}\ma{b}_{\rm R}\\ \ma{b}_{\rm I}\end{bmatrix} \right\|_2^2,$$
where $\ma{A} = \ma{A}_{\rm R}+\jmath \ma{A}_{\rm I}$,$\ma{B} = \ma{B}_{\rm R}+\jmath \ma{B}_{\rm I}$, $\ma{b} = \ma{b}_{\rm R}+\jmath \ma{b}_{\rm I}$, and $\ma{x} = \ma{x}_{\rm R}+\jmath \ma{x}_{\rm I}$. The Least Squares solution to this optimization problem is simple: it’s a regular real-valued system of equations with $2M$ equations and $2N$ unknowns so applying the pseudo-inverse of the block matrix provides the Least Squares solution in $\begin{bmatrix}\ma{x}_{\rm R}\\ \ma{x}_{\rm I}\end{bmatrix}$. Also, the real-valued stacking we have applied did not change the norm since for any complex vector $\ma{x}$ we have $\left\|\ma{x}\right\|_2^2 = \left\|\begin{bmatrix}\ma{x}_{\rm R}\\ \ma{x}_{\rm I}\end{bmatrix}\right\|_2^2$.
So it’s valid and it works. But it’s not very elegant. We have to introduce a lot of new quantities and write down the big block matrix. Is there a more elegant way? One that avoids stacking real and imaginary parts of $\ma{C}$ and $\ma{b}$?
To find it, we started rewriting $\begin{bmatrix}\ma{x}\\ \ma{x}^*\end{bmatrix}$. Since $\ma{x} = \ma{x}_{\rm R}+\jmath \ma{x}_{\rm I}$ and $\ma{x}^* = \ma{x}_{\rm R}-\jmath \ma{x}_{\rm I}$ we can write
$$\ma{C} \cdot \begin{bmatrix}\ma{x}\\ \ma{x}^*\end{bmatrix} = \underbrace{\ma{C} \cdot \begin{bmatrix} \ma{I}_N & \jmath \ma{I}_N \\ \ma{I}_N & – \jmath \ma{I}_N \end{bmatrix}}_{\ma{\tilde{C}}} \cdot \begin{bmatrix}\ma{x}_{\rm R} \\ \ma{x}_{\rm I}\end{bmatrix}.$$
(As a side note: if we do decide to break $\ma{C}$ into $\begin{bmatrix}\ma{A} & \ma{B}\end{bmatrix}$ as above then we have $\ma{\tilde{C}} = \begin{bmatrix}\ma{A}+\ma{B} & \jmath \ma{A } – \jmath \ma{B}\end{bmatrix}$.)
Our optimization problem then takes the nice and simple form
$$\ma{x}_{\rm opt} = \arg \min_{\ma{x}} \left\| \ma{\tilde{C}} \cdot \begin{bmatrix}\ma{x}_{\rm R}\\ \ma{x}_{\rm I}\end{bmatrix} – \ma{b} \right\|_2^2.$$
One may be tempted to say that this shows the solution: simply apply the pseudo-inverse of $\ma{\tilde{C}}$. Unfortunately, it is not quite as simple. If we do this, the solution is in general a complex-valued vector. However, $\begin{bmatrix}\ma{x}_{\rm R}\\ \ma{x}_{\rm I}\end{bmatrix}$ must be real-valued by construction. So how do we solve this optimization problem?
Well, we have a cost function $J(\ma{y}) = \left\|\ma{\tilde{C}} \cdot \ma{y} – \ma{b}\right\|_2^2$ that we want to minimize subject to the constraint that $\ma{y}$ is real-valued or equivalently $\ma{y} = \ma{y}^*$ or equivalently $\ma{y}-\ma{y}^* = \ma{0}$. For me this calls for the method of Lagrange multipliers! The Lagrangian for this constrained optimization problem then looks like this:
$$L(\ma{y},\ma{\lambda}) = \left\|\ma{\tilde{C}} \cdot \ma{y} – \ma{b}\right\|_2^2 + 2 \cdot {\rm Re}\{\ma{\lambda}^{\rm H} \cdot (\ma{y}-\ma{y}^*)\}.$$
I would like to spare the details of the derivation since it’s quite straight-forward: compute the gradients of $L$, set to zero, and solve for $\ma{y}$. The solution we obtain then provides the optimal $\begin{bmatrix}\ma{x}_{\rm R}\\ \ma{x}_{\rm I}\end{bmatrix}$ directly. Jens did the calculations (thanks!) and got this result:
$$\begin{bmatrix}\ma{x}_{\rm R}\\ \ma{x}_{\rm I}\end{bmatrix}_{\rm opt} = \ma{\tilde{C}}^+ \cdot \ma{b} \; – \jmath \cdot \ma{G}^{-1} \cdot {\rm Re}\left\{\ma{G}^{-1} \right\}^{-1} \cdot {\rm Im}\{\ma{\tilde{C}}^+ \cdot \ma{b}\},$$
where $\ma{G} = \ma{\tilde{C}}^{\rm H}\ma{\tilde{C}}$ and it was assumed that $\ma{G}$ and ${\rm Re}\left\{\ma{G}^{-1} \right\}$ are both invertible. One could also write it as
$$\begin{bmatrix}\ma{x}_{\rm R}\\ \ma{x}_{\rm I}\end{bmatrix}_{\rm opt} = {\rm Re}\{\ma{\tilde{C}}^+ \cdot \ma{b}\} \; + \left[ \ma{I} – \ma{G}^{-1} \cdot {\rm Re}\left\{\ma{G}^{-1} \right\}^{-1} \right]\cdot \jmath \cdot {\rm Im}\{\ma{\tilde{C}}^+ \cdot \ma{b}\}.$$
This one is (sort of) instructive. If $\ma{G}$ is real then ${\rm Re}\left\{\ma{G}^{-1} \right\}^{-1} = \ma{G}$ and hence the whole second part vanishes. In this case, the optimal solution is to take simply the real part of the LS solution (note that this happens if $\ma{\tilde{C}}$ is also real-valued in which case it would be more efficient to drop the imaginary part of $\ma{b}$ and then solve the real-valued system of equations directly). Otherwise, we need an additional term that depends on the imaginary part of the LS solution, somehow “projected” through this funny matrix $\ma{I} – \ma{G}^{-1} \cdot {\rm Re}\left\{\ma{G}^{-1} \right\}^{-1}$.
Although I kind of like this second solution better since it avoids the real-valued stacking and is partially instructive where real and imaginary parts go, it has at least one major drawback. For the first solution, we’ve reduced the problem onto a $2M$ by $2N$ system of real-valued linear equations. Applying the pseudo-inverse there we know exactly that it gives is the least squares solution if the equivalent $\ma{b}$ is not in the column space of the equivalent $\ma{C}$ (“no exact solution”) and it gives us the minimum norm solution if the equivalent $\ma{C}$ has a non-empty kernel, i.e, not full column rank (“infinitely many solutions”). Most importantly, it can do both at the same time.
This does not carry over to our complex solution. We derived it for the overdetermined Least Squares case, assuming full column rank. We can do a similar derivation for the case where the existence of infinitely many exact solutions is assumed and we seek the one with the smallest norm. However, the result is different and it is not easy to come up with one solution that accomplishes both at the same time. For those that are curious, the second case yields the solution
$$\begin{bmatrix}\ma{x}_{\rm R}\\ \ma{x}_{\rm I}\end{bmatrix}_{\rm opt} = {\rm Re}\{\ma{\tilde{C}}^+ \cdot \ma{b}\} \; + \left[ \ma{I} – \ma{P} \cdot {\rm Re}\left\{\ma{P} \right\}^{-1} \right]\cdot \jmath \cdot {\rm Im}\{\ma{\tilde{C}}^+ \cdot \ma{b}\},$$
where $\ma{P} = \ma{I} – \ma{\tilde{C}}^{\rm H} \cdot \left(\ma{\tilde{C}} \cdot \ma{\tilde{C}}^{\rm H}\right)^{-1} \ma{\tilde{C}}$.
## A funny series
One of the reasons I posted a funny number was to tell you the story of a funny series I discovered by chance. It had to do with my fascination for simple constructs like $j^j$ giving unexpected results like ${\rm e}^{-\pi/2}$. I always wondered: are there more numbers connected to powers of $j$ or numbers to the power of $j$?
One day I was using Matlab for a tutorial. Before it started I had the Laptop set up and Matlab running and 10 minutes to fill. Waiting for the students to come I played in Matlab: I made a random complex number, raised $j$ to the power of it, then again $j$ to the power of the last result and so on. In other words, I kept typing x = j^x and looked at x. After a little while I got (rounded to 4 digits) $0.4383 + j 0.3606$ which seemed to be a stationary point since $j^{(0.4383 + j 0.3606)} = 0.4383 + j 0.3606$. I started with another random number and got the same result. This made me think: is this stationary point unique? Do we reach it no matter where we start? If so, does it have an analytical expression? Is there anything else special about it?
I was ripped out of my train of thoughts when the seminar started. I forgot about my little experiment for quite some time until quite recently I found the old script by chance. I really wanted to find out more about that special number.
What is it I am really trying to find? It’s the limit of a recursively defined sequence: it is $\lim_{n\rightarrow \infty} x_{n}$ where
$$x_{n} = j^{x_{n-1}}$$
and $j^x$ refers to the principal value, i.e., $j^x = {\rm e}^{j \cdot \pi/2 \cdot x}$. From this it seems that the sequence can easily be generalized to
$$x_{n} = {\rm e}^{\alpha \cdot x_{n-1}},$$
where $\alpha \in \mathbb{C}$ and the previous series corresponds to the special case $\alpha = j \cdot \pi/2$. This has got to be something veeery fundamental I thought and it does generate the “magic” stationary point I had found earlier.
Unfortunately I didn’t get much further on the analytical side. You can certainly expand $x$ into $y+jz$ so that for $\alpha = j \cdot a$ (purely imaginary), ${\rm e}^{\alpha \cdot x}$ becomes
$${\rm e}^{- a \cdot z + j \cdot a \cdot y} = {\rm e}^{-a \cdot z} \cdot \cos(a \cdot y) + j{\rm e}^{-a \cdot z} \cdot \sin(a \cdot y)$$
but I do not see this going anywhere. A quick google search turned up a lot of results on linear recurrence relations but the one I had is clearly non-linear.
As of now I have no analytical expression for the stationary point for any value of $\alpha$ (trivial solutions like $\alpha=0$ let aside).
So I played a bit more with it in Matlab. It seems that different values of $\alpha$ also give rise to stationary points. For instance, $\alpha=j$ gives $0.5764 + j \cdot 0.3743$. Here is a plot with empirically found fixed points for $\alpha = j \cdot a$, varying $a$ from $0$ to $1.96$ (the series starts to form cycles for $a$ larger than $\approx 1.96125$):
It does not seem to be a circle. This is purely empirical, I have no clue if/how one could find these values analytically (but this would be very nice).
While playing with these numbers I realized that my original observation that one would always converge to one fixed point regardless of the initialization was actually wrong. For some points, the series diverged to infinity. This sparked the question where these points would be located on the complex plane. So I made a second set of experiments: I started the series from initial points $x_0$ chosen in a regular grid in the complex plane, let the series run for a predefined maximum number of iterations and observed what it does: (a) does it diverge to infinity or (b) does it converge to the fixed points I found earlier (i.e., get within a predefined threshold $\delta$ of it)?
I began with $\alpha = j\cdot \pi/2$ (corresponding to the $x_{n+1} = j^x_{n}$ it all started with) and a cartesian grid in ${\rm Re}(x_0)$ and ${\rm Im}(x_0)$ for the initial points. And then, I got this:
The two axis refer to the real part and the imaginary part of our initial point $x_0$. The color indicated the number of iterations until the fixed point is reached up to an accuracy of $10^{-3}$. We notice the periodicity in ${\rm Re}(x_0)$: this is not surprising since the first step in the series gives
$x_1 = {\rm e}^{j \cdot \pi/2 \cdot x_0} = {\rm e}^{-\pi/2 \cdot {\rm Im}(x_0)} \cdot {\rm e}^{j \cdot \pi/2 \cdot {\rm Re}(x_0)}$
and therefore, adding an integer multiple of 4 to ${\rm Re}(x_0)$ gives the same $x_1$. I found the shape looks very interesting and started zooming in.
Further…
Even further…
This is already a 200x zoom on both axis compared to the original one. Yet more and more details are revealed that look similar to the original ones – we seem to have self-similarity here. I’m not sure if that’s enough to call this a fractal but I’d like to claim so until someone convinces me otherwise.
I have since played with various values of $\alpha$, kept zooming in and looking at the result. So far it seems that the level of details keeps increasing as $\alpha$ approaches $2 \cdot j$. After about $1.961 \cdot j$ it becomes hard to still draw a picture because instead of unique attractors the fractal seems to run into limit cycles consisting of a discrete number of points. There still seems to be a fractal-looking region of divergence but I’m mostly guessing here.
Here is one for $\alpha = j \cdot 1.96$:
I chose 50 as the maximum number of iterations here, the picture does not change much if I increase it to 1000 or so (it just takes much longer to render).
Here is my best attempt for $\alpha = j \cdot 1.963495$:
I display the plane of initial points in polar instead of cartesian coordinates (for cosmetic reasons only) so this one is periodic in the vertical direction and truncated on the right side horizontally. The maximum number of iterations was set to 2000 here, increasing it further does have an impact on the larger red areas that get filled more and more. I tried to count how long it takes until a limiting cycle is reached but this is based on very rough heuristics and might be wrong. I still enjoy the look of the result.
It’s really a lot of fun to “explore” this little world, especially if you’ve never seen it before and you’re not sure if anyone else ever has. It’s quite possible these fractals are actually well-known, I just don’t know what I should search for. In light of this it would be really great if anyone could give me any hint that brings me closer to any of these open questions:
• Is this class of series known, does it have a name, is there any published material on it?
• How can we compute the fixed points of the series for a given value of $\alpha$?
• Are the resulting images that divide converging from diverging initial points actually a fractal? Does it possibly also have a name, has it been studied before?
• What happens beyond the “magic” breaking point where the series starts running into limit cycles comprising of a discrete number of points? Does the breaking point have any special meaning? Can the limit cycles be described analytically?
If you have any idea to any of these please leave me a comment!
## A funny number
I was giving tutorials for an undergraduate course in Signals and Systems theory. Since students came from quite varying backgrounds I had to start very simple – my first tutorial used to be just on complex numbers. This left some of the students bored, saying they’ve seen it all. To keep them thinking I usually asked them to compute a complex number for me: Let $j$ be the imaginary unit, what is the value of $j^j$?
This question is not as trivial as it may seem at first sight. It requires a generalization of the exponentiation $a^b$ from $a, b \in \mathbb{R}$ to $a, b \in \mathbb{C}$. There are rigorous ways of doing this which I do not want to discuss in detail here. Let us just assume that we found a generalization of $a^b$ to complex numbers which satisfies the laws of powers, in particular the law $a^b = {\rm e}^{b \cdot \ln(a)}$ where $\ln(x)$ is the natural (base-e) logarithm. Then, we can rewrite $j^j$ as $j^j = {\rm e}^{j \cdot \ln(j)}$. What is $\ln(j)$ though? Well, $j$ can be written as ${\rm e}^{j \cdot \pi/2}$, so $\ln(j)$ should be $j \cdot \pi/2$, right? This finally brings us to $j^j = {\rm e}^{j \cdot j \cdot \pi/2} = {\rm e}^{-\pi/2}$.
Some of my students would actually obtain this result. They would usually be surprised to get a real (and sort of strange number) out of such an operation, but always they would be very proud to have the answer. The tech-savvy ones would even check their result with whatever internet-able device they carried and be extra sure to have it right.
However, my (admittedly a bit discouraging) reply would be that the answer is, despite being correct, incomplete. Actually infinitely incomplete. There are (infinitely) more “correct” answers. How so? Well, $j$ can be written as ${\rm e}^{j \cdot \pi/2}$ but it can also be written as ${\rm e}^{j \cdot (\pi/2 + 2\pi)}$ or ${\rm e}^{j \cdot (\pi/2 – 2\pi)}$, and so on. We can add any integer multiple of $2\pi$ to the phase due to the periodicity of complex numbers with respect to their phase.
For the (natural) logarithm of a complex number this means that it is in general ambiguous: $\ln(j) = j \cdot \pi/2 + 2\cdot k \cdot \pi$ for any $k \in \mathbb{Z}$. To avoid the confusion it is common to write ${\rm Ln}(x) = \ln(x) + 2\cdot k \cdot \pi$ where $\ln(x)$ is the (unique) principle value of the logarithm which we obtain by choosing the principle phase of $x$.
In that sense, the full answer would be $j^j = {\rm e}^{-\pi/2} \cdot {\rm e}^{-2 \cdot k \cdot \pi}$, where $k=0$ corresponds to the principle value of $j^j$ given by ${\rm e}^{-\pi/2}$.
Infinitely many solutions, all of them are real, and all of them connect ${\rm e}$ and $\pi$. Pretty cool, right?
## Finally
Finally, I managed to update the site a bit and to put my dissertation online. You can now find it on the main site unter “Dissertation”, here is a link for you.
I’d be very happy to hear your feedback. I hope you will enjoy reading it.
## Long time no post…
… I apologize. But I have a good excuse: I was really really busy trying to finish my thesis. That’s right folks, this guy has submitted his dissertation recently and the last weeks towards this goal were quite … intense.
I’m not entirely happy with the result but that’s normal I think, noone ever is. Still I’m happy I can again focus on other things in life.
I will make the thesis publicly available as soon as I am officially allowed to do so, likely some time in October. I’ve decided to publish it under a Creative Commons BY-NC-ND license, so you will be free to copy/print/read it as often as you like. 😉
Until then, stay tuned and keep your fingers crossed for the defense that I still have to go through. 😉 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8697267174720764, "perplexity": 210.8392843071103}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500126.0/warc/CC-MAIN-20230204110651-20230204140651-00274.warc.gz"} |
http://agnelkurian.com/code/2011/05/07/intersection-of-line-segments-from-cga-faq/ | # Intersection of Line Segments (from CGA FAQ)
Intersection of two line segments
involves the following cases:
• Segments are parallel
• Segments are collinear/coincident
• One segment intersects the extension of the other
• Extension of one segment intersects the extension of the other
• Segments intersect each other.
The details of the solution can be found in the CGA FAQ linked above. A C++ implementation can be found here: http://code.google.com/p/curve-project/source/browse/trunk/lab/cgafaq/cgafaq.h The function cgafaq::intersect takes 4 points — the start and end points of each of the lines. r and s are output parameters calculated as described in the FAQ.
Disclaimer: This post and the code provided are not endorsed by any of the contributors to the CGA FAQ. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.34140846133232117, "perplexity": 865.4179356951208}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046153391.5/warc/CC-MAIN-20210727103626-20210727133626-00457.warc.gz"} |
https://stats.libretexts.org/Courses/Lumen_Learning/Book%3A_Concepts_in_Statistics_(Lumen)/01%3A_Types_of_Statistical_Studies_and_Producing_Data/1.13%3A_Putting_It_Together-_Types_of_Statistical_Studies_and_Producing_Data | # 1.13: Putting It Together- Types of Statistical Studies and Producing Data
## Let’s Summarize
• There are four steps in a statistical investigation:
• Decide what to measure, and then collect data.
• Summarize and analyze.
• Draw a conclusion, and communicate the results.
• There are two types of statistical studies:
• Observational studies: An observational study observes individuals and measures variables of interest. We conduct observational studies to investigate questions about a population or about an association between two variables. An observational study alone does not provide convincing evidence of a cause-and-effect relationship.
• Experiments: An experiment intentionally manipulates one variable in an attempt to cause an effect on another variable. The primary goal of an experiment is to provide evidence for a cause-and-effect relationship between two variables.
• In statistics, a variable is information we gather about individuals or objects.
## Observational Studies
• In an observational study, we draw a conclusion about the population on the basis of a sample. To draw a valid conclusion, the sample must be representative of the population. A representative sample is a subset of the population. It also reflects the characteristics of the population.
• A sample is biased if it systematically favors a certain outcome. Voluntary response samples (such as Internet polls) and convenience samples (such as surveys at a mall) are biased.
• Random selection eliminates bias. In a simple random sample, everyone in the population has an equal chance of being chosen. In this way, random selection helps ensure that the sample is representative of the population.
• Larger samples tend to be more accurate than smaller samples if the samples are chosen randomly. The size of the population does not affect the accuracy of a random sample as long as the population is large.
• If an attempt is made to include every individual from a population in a sample, then the investigation is called a census.
## Experiments
The goal of the experiment is to provide evidence for a cause-and-effect relationship between two variables. When we investigate a relationship between two variables, we identify an explanatory variable and a response variable. To establish a cause-and-effect relationship, we want to make sure the explanatory variable is the only factor that impacts the response variable. But other factors, called confounding variables, may also influence the response.
• A well-designed experiment takes steps to eliminate the effects of confounding variables. These steps include direct control, random assignment of people to treatment groups, use of a control or placebo, and blind conditions. Incorporating such precautions, a well-designed experiment provides convincing evidence of cause-and-effect.
• Random assignment uses random chance to assign participants to treatments, which creates similar treatment groups. With random assignment, we can be fairly confident that any differences we observe in the response of treatment groups is due to the explanatory variable. In this way, we have evidence for a cause-and-effect relationship.
• A well-designed experiment provides evidence for a cause-and-effect relationship. But even in a well-designed experiment, differences in the response might be due to chance. We learn to describe chance behavior when we study probability later in the course. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9026361107826233, "perplexity": 792.6305648718946}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585209.43/warc/CC-MAIN-20211018190451-20211018220451-00233.warc.gz"} |
https://www.atlantis-press.com/proceedings/icmt-13/10466 | # Robust Estimation of Parameters for Lucas-Kanade Algorithm
Authors
Lin Yih-Lon
Corresponding Author
Lin Yih-Lon
Available Online November 2013.
DOI
https://doi.org/10.2991/icmt-13.2013.114How to use a DOI?
Keywords
Abstract
The object tracking problem is an important research topic in computer vision. For real applications such as vehicle tracking and face tracking, there are many efficient and real-time algorithms. In this study, we will focus on the Lucas-Kanade (LK) algorithm for object tracking. In the standard LK method, sum of squared errors is used as the cost function, while least trimmed squares is adopted as the cost function in this study. The resulting estimator is robust against outliers caused by noises in the tracking process. Simulation is provided to show that the proposed algorithm outperforms the standard LK method in the sense that it is robust against the outliers in the object tracking problem.
Open Access
Proceedings
3rd International Conference on Multimedia Technology(ICMT-13)
Part of series
Publication Date
November 2013
ISBN
978-90-78677-89-5
ISSN
1951-6851
DOI
https://doi.org/10.2991/icmt-13.2013.114How to use a DOI?
Open Access
TY - CONF
AU - Lin Yih-Lon
PY - 2013/11
DA - 2013/11
TI - Robust Estimation of Parameters for Lucas-Kanade Algorithm
BT - 3rd International Conference on Multimedia Technology(ICMT-13)
PB - Atlantis Press
SP - 919
EP - 926
SN - 1951-6851
UR - https://doi.org/10.2991/icmt-13.2013.114
DO - https://doi.org/10.2991/icmt-13.2013.114
ID - Yih-Lon2013/11
ER - | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18695023655891418, "perplexity": 2271.9909193986455}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590348513230.90/warc/CC-MAIN-20200606093706-20200606123706-00221.warc.gz"} |
https://techwhiff.com/learn/no-explaination-is-needed-24-similarity-resulting/429541 | # No explaination is needed 24. Similarity resulting from common ancestry is known as a) homology b)...
###### Question:
no explaination is needed
24. Similarity resulting from common ancestry is known as a) homology b) convergent evolution. c) divergent evolution. d) heterogeny 25. Which of the following statements concerning the loss of hind limbs during whale evolution is NOT true? a) The loss is well documented by a series of transitional fossils. b) It explains why modern whales have vestigial pelvic girdles. c) This evolutionary process involved changes in the sequence or expression of Hox genes. d) The loss of limbs by snakes is a similar adaptation to a similar environment. 26. All major endocrine glands are controlled by the a) thyroid gland. b) gonads. c) pituitary. d) adrenal gland. 27. Which hormone of the adrenal gland promotes the short term stress response ("fight or flight"? a) Epinephrine b) Thyroxine c) Testosterone d) Cortisol 28. Which type of cells form the myelin sheaths around axons: a) astrocytes. b) schwann cells. c) adjacent nerve cells. d) muscle cells. 29. When an electrical impulse arrives at a chemical synapse, neurotransmitters are released. These act by a) opening ion channels in the postsynaptic membrane. b) opening ion channels in the presynaptic membrane. c) increasing the ion concentration in the synaptic cleft. d) physically connecting pre- and postsynaptic membranes 30. During muscle contraction a) actin and myosin filaments slide past each other. b) actin filaments become shorter. c) myosin filaments become shorter. d) actin and myosin filaments fold, 31. Which of the following are obligate intracellular pathogens a) Antibiotics b) Viruses c) Probiotics d) Thermophilic bacteria pto
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https://www.coin-or.org/CppAD/Doc/speedtest.htm | Prev Next Index-> contents reference index search external Up-> CppAD utility SpeedTest CppAD-> Install Introduction AD ADFun preprocessor multi_thread utility ipopt_solve Example speed Appendix utility-> ErrorHandler NearEqual speed_test SpeedTest time_test test_boolofvoid NumericType CheckNumericType SimpleVector CheckSimpleVector nan pow_int Poly LuDetAndSolve RombergOne RombergMul Runge45 Rosen34 OdeErrControl OdeGear OdeGearControl CppAD_vector thread_alloc index_sort to_string set_union sparse_rc sparse_rcv SpeedTest-> speed_program.cpp Headings-> Syntax Purpose Motivation Include Test ---..size ---..repeat ---..name first last inc rate Errors Example
$\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }$
Run One Speed Test and Print Results
Syntax
# include <cppad/utility/speed_test.hpp> SpeedTest(Test, first, inc, last)
Purpose
The SpeedTest function executes a speed test for various sized problems and reports the results on standard output; i.e. std::cout. The size of each test problem is included in its report (unless first is equal to last ).
Motivation
It is important to separate small calculation units and test them individually. This way individual changes can be tested in the context of the routine that they are in. On many machines, accurate timing of a very short execution sequences is not possible. In addition, there may be set up time for a test that we do not really want included in the timing. For this reason SpeedTest automatically determines how many times to repeat the section of the test that we wish to time.
Include
The file speed_test.hpp contains the SpeedTest function. This file is included by cppad/cppad.hpp but it can also be included separately with out the rest of the CppAD routines.
Test
The SpeedTest argument Test is a function with the syntax name = Test(size, repeat)
size
The Test argument size has prototype size_t size It specifies the size for this test.
repeat
The Test argument repeat has prototype size_t repeat It specifies the number of times to repeat the test.
name
The Test result name has prototype std::string name The results for this test are reported on std::cout with name as an identifier for the test. It is assumed that, for the duration of this call to SpeedTest, Test will always return the same value for name . If name is the empty string, no test name is reported by SpeedTest.
first
The SpeedTest argument first has prototype size_t first It specifies the size of the first test problem reported by this call to SpeedTest.
last
The SpeedTest argument last has prototype size_t last It specifies the size of the last test problem reported by this call to SpeedTest.
inc
The SpeedTest argument inc has prototype int inc It specifies the increment between problem sizes; i.e., all values of size in calls to Test are given by size = first + j * inc where j is a positive integer. The increment can be positive or negative but it cannot be zero. The values first , last and inc must satisfy the relation $$inc * ( last - first ) \geq 0$$
rate
The value displayed in the rate column on std::cout is defined as the value of repeat divided by the corresponding elapsed execution time in seconds. The elapsed execution time is measured by the difference in (double) clock() / (double) CLOCKS_PER_SEC in the context of the standard <ctime> definitions.
Errors
If one of the restrictions above is violated, the CppAD error handler is used to report the error. You can redefine this action using the instructions in ErrorHandler
Example
The program speed_program.cpp is an example usage of SpeedTest. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8147852420806885, "perplexity": 3011.4272048405187}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084887024.1/warc/CC-MAIN-20180117232418-20180118012418-00715.warc.gz"} |
http://www.idleanalytics.com/2012/11/04/calling-republicans-the-party-of-racism-is-questionable/ | Nov 04 2012
# Calling Republicans the party of racism is questionable
Bill Maher is fond of repeating his line: "Being a Republican doesn't make you a racist, but if you're a racist you're probably a Republican." This attitude has obvious anecdotal examples to support it. The numerous racist signs shown at Tea Party rallies, the incredibly low minority support for and participation in the GOP, things like the awful Chik-fil-a demonstrations, it's a bit of a natural identification.
But perhaps the most provocative association is with the GOP and the voting bloc consisting of the states of the former Confederacy. Andrew Sullivan mentioned on This Week that if Obama loses Florida and North Carolina, every single Confederate state will be giving its electoral votes to Mitt Romney, something that ought to be disconcerting given that they once led a bloody rebellion in this country.
However, I was most recently drawn to this topic by Ron Rosenbaum's piece on Slate, where he essentially says that the press should go ahead and brand the GOP as a racist party, much like a neo-nazi party would be labeled as such. The three page screed's main argument depends on "sophisticated" statistical techniques cited in a book. That book drew from a paper titled "Old Times There Are Not Forgotten: Race and Partisan Realignment in the Contemporary South" (American Journal of Political Science, Vol. 49, No. 3, July 2005, pp. 672–688) by Nicholas A. Valentino and David O. Sears.
I'm naturally suspicious of any statistical technique that is termed "sophisticated". If the numbers need to be teased that much, it could be that the conclusion the authors want just isn't there. I read the paper in detail, along with the results of the other survey mentioned in Rosenbaum's article, and I'd like to just spend some time explicating exactly what the results were.
The quick take-away is two things. 1. There's nothing particularly sophisticated about any of it, the techniques are pretty basic behind all the jargon. 2. I'm not sure the conclusion is justified without also investigating other factors (I have a particular one in mind). There is some evidence to support the conclusion, but it's far from clear.
## Symbolic versus Jim Crow racism
Basically all of the results in the paper are analyzed as a function of what the authors term "symbolic racism", rather than traditional or "Jim Crow" racism, of the virulent type that existed especially before 1965. Symbolic racism is defined to be a propensity to answer the following questions in the specified ways:
Question Symbolic racist response
Irish, Italians, Jewish, and many other minorities overcame prejudice and worked their way up. Blacks should do the same without any special favors Agree
Over the past few years blacks have gotten less than they deserve Disagree
It’s really a matter of some people not trying hard enough; if blacks would only try harder they could be just as well off as whites Agree
Generations of slavery and discrimination have created conditions that make it difficult for blacks to work their way out of the lower class Disagree
Answers to these were measured in 1986, 1988, 1990, 1992, 1994, and 2000 by the American National Election Studies along with party identification and several other variables (the latter 2 were also asked in 1972). The pollster asked for the responder to rate how well much they agreed, on a scale from 1 to 5, with the statement.
Sample copy of the NES questionnaire from 1986 with one of the pertinent questions.
The sample sizes of each were generally quite large ( > 2,000 people per survey), so there is fairly good sampling statistics (the rolling Gallup tracking poll employs around the same number of samples).
The authors make use of two relatively simple tools, both of which are regressions, which really just means fitting points on a graph to a given curve as closely as possible. The two regressions used are the linear regression (with some minor modification) and the logistical regression.
## Linear regression of racism vs time
The linear regression is used to investigate how symbolic (or, I might call it, casual) racism changed over time, and how well correlated this was for identifying as a Republican or being from the south. So, suppose we took the average racism answer in the quiz questions and plot that versus time. One would find that the trend was positive between the years of interest. But you also want to know how that breaks down for the different regions, and in particular the former confederacy (South Carolina, Mississippi, Florida, Alabama, Georgia, Louisiana, Texas, Virginia, Arkansas, Tennessee and North Carolina) versus the North or West regions of the US.
It wasn't too hard to recreate the researchers' data sets, so I did. They only use the 3rd and 4th questions on symbolic racism and code this as a number between 0 and 1. Since they don't say, I did some guesswork about how they calculated things. I assume they calculate symbolic racism according to
where $a_3$ and $a_4$ are the answers for those questions on a 1 to 5 point scale (1 is strongly agree). So if you answer that you strongly agree with question 3 and strongly disagree with question 4, you are $R = ((5 - 1) + (5 - 1))/8 = 1$ or 100% racist, whereas strongly disagree and agree, respectively would be $R = ((5 - 5)+(5 - 5))/8 = 0$ racist (anyone who said "inapplicable gets set to a 3, neither agree nor disagree"). Party ID is indexed by dividing the designed variable (0 to 6) by 6.
The authors play a little bit loose with the rules. In 1998 questions 3 and 4 were not asked, so my presumption is that they used questions 1 and 2 as a proxy for symbolic racism. Also, whenever someone refused to answer the questions (answering "inapplicable") they were automatically called 0.5 racist for the purposes of the regression. Is that really true? Mightn't somebody refuse to answer a question that sounds stupid or offensive? In 1972, it appears that these questions weren't even asked for part of the data set, as there are a suspicious number (1372) of consecutive refusals to answer either question.
I was unable to replicate their numbers, using the same data set. This may be because I've made a mistake, or they did, or their methodology is underspecified in the paper. In any case, their point still holds that the south, especially the Deep South but also the old Confederacy, has a higher symbolic racism index than the rest of the nation. I expanded their data set to include 2004 and 2008, which were unavailable when the paper was published:
Symbolic racism by region, 1972-2008, as measured by ANES questions 3 and 4 given above.
It's not very consistent and not very large. Both sets peak at about 0.65, with the Deep South trailing by about two years. In 2008 the rest of the country was significantly below the Deep South and the former Confederacy. I find several years where the Deep South actually has a lower symbolic racism, though it hasn't happened since 2000.
The result appears somewhat more significant in their paper:
Symbolic racism vs time from Valentino and Sears.
They show about a 15 point difference, whereas I can only see about 10 points.
If we look at the results of a linear regression taking into account all the points, the trend is a little less muddy
Linear regressions for symbolic racism as a function of region.
These results are highly statistically significant. The North + West has clearly been increasing, but it is consistently lower than the South and especially the Deep South.
## Party ID and racism
The authors also look at the likelihood of voting Republican as a function of symbolic racism. They use the logistical regression, which is the same as a linear regression except that it returns a probability of something by using a link function. The independent variables are time and racism, with either 0 or 1 as the dependent variable (namely: did you vote Republican or not). I did not attempt to recreate this curve, but my guess is that I would have found something similar:
Probability of voting for Republican due to symbolic racism as a function of time for the South (data from Valentino and Sears)
While there is a tendency for racism to promote the GOP in all states, this effect has been growing in the South. Again this is highly statistically significant.
## Is any of this true?
I have to wonder: are questions 3 and 4 really a good proxy for measuring racism? There is a lot of discussion in the political science literature about this, but I'm not convinced. For instance, it is entirely possible that the answers to these questions are dominated by the profusion of laissez faire capitalism that cropped up in the Reagan era and remains with us to this day. Also, since racism and Republicanism are both monotonically increasing functions of time, any other variable that does so could be responsible.
I'm thinking principally of religion and the desire to integrate religion with politics. The authors themselves acknowledge this:
But the scope of any single article must always be limited in some ways, especially in attempting to explain as broad a phenomenon as party realignment. So, for example, we could not test social class (Black and Black 2002; Petrocik 1987) or religion-based (Green et al. 2003) explanations for Southern realignment.
It's probably a good idea not to read too much into this. Is it possible that this kind of casual racism is responsible? Sure. Is there much evidence to support it? Not really. The ANES polls are a great resource for some variables, but this topic is too muddy, and the way of measuring "racism" too crude and questionable, to be of much help.
I think that the entire former Confederate states will probably break for Mitt Romney this Tuesday. But so are a lot of other subgroups of the country, principally ones with white, but not necessarily racist, voters. | {"extraction_info": {"found_math": true, "script_math_tex": 4, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 5, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5557132959365845, "perplexity": 1269.0477778012635}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323587794.19/warc/CC-MAIN-20211026011138-20211026041138-00109.warc.gz"} |
http://www.spaceinn.eu/data-access/wp5-asteroseismology-deliverables/wp5-2-asteroseismology-heat-driven-oscillators/subdwarf-b-star-model-grid-d5-8/ | Subdwarf B star model grid (D5.8)
This webpage gives access to the grids of evolutionary subdwarf B star models computed in the framework of the following article:
The blue-edge problem of the V1093 Her instability strip revisited using evolutionary models with atomic diffusion
S. Bloemen, Haili Hu, C. Aerts, M.A. Dupret, R.H. Østensen, P. Degroote, E. Müller-Ringat, T. Rauch; 2014, Astronomy & Astrophysics, Vol. 569, p. 123
Introduction
The grid of evolutionary subdwarf B star (sdB) models was computed from the start of central He burning, taking into account atomic diffusion due to radiative levitation, gravitational settling, concentration diffusion, and thermal diffusion. We have computed the non-adiabatic pulsation properties of the models and studied the predicted p-mode and g-mode instability strips. The non-adiabatic pulsation properties of all the models in the grid can be downloaded on this webpage. The evolutionary tracks were computed using a code that is an adapted version of the STARS code (Eggleton 1971). The changes made to the code are described in Hu et al. 2008, 2009, 2010 and 2011. The pulsational properties are computed from the evolutionary models using MAD (Dupret et al. 2001).
On this webpage we provide access to the pulsational properties (MAD output) of the models in the grid, as well as basic properties such as effective temperature and radius. The files that contain the structure models (STARS output) are too large to be made available for download here, but can be provided upon request.
Use of the models
Anyone is free to use the models made available on this webpage. We kindly ask users to cite Hu et al. 2011 and Bloemen et al. 2014 in any publication for which these models are used.
Data format
The grid is provided in FITS files. Every file contains the information for one evolutionary track, and each extension in the files contains the information on the pulsational properties of one model on such a track. The general header of the file contains information on the track (such as the total mass and the envelope mass of the sdB at the start of the central He burning). The headers per extension provide vital information such as the effective temperature and the surface gravity at the different time steps. The data in the extensions come as a table in which each line represents a pulsation mode. Detailed information on the headers and the data format is given below.
Keyword Description
Mtot Total mass of the sdB (solar mass)
Menv Mass of the hydrogen envelope (solar mass)
Mcore Mass of the core, equals total-envelope (solar mass)
Z Metallicity
other Bookkeeping values not relevant to the users of the grid but potentially useful for troubleshooting
Keyword Description
Logg Surface gravity (cgs)
Teff Effective temperature (K)
M_M_sun Mass (solar mass)
age_y Age after ZAEHB (yr)
Log_L_L_sun Luminosity (solar luminosity)
X Hydrogen fraction
Z Metal fraction
Data columns
Column name Description
l Spherical degree of the mode
n Radial order (not 100% reliable)
freq_cd Mode frequency (cycles/day)
freq_micHz Mode frequency (microHz)
omega_im Dimensionless damping rate (negative = unstable mode)
sigma_im_micHz Damping rate (microHz)
f_T Amplitude of effective temperature variation
psi_T Phase of f_T (degrees)
f_g Amplitude of surface gravity variation
psi_g Phase of f_g (degrees)
K K-value, K=1/omega_re^2
Q_d Constant of pulsation Q (days): Q=(1/freq_cd)*sqrt((M/Msun)*(R/Rsun)^3) | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8827616572380066, "perplexity": 3591.8968363321524}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267155792.23/warc/CC-MAIN-20180918225124-20180919005124-00357.warc.gz"} |
http://crypto.stackexchange.com/questions/5502/necessity-for-finite-field-arithmetic-and-the-prime-number-p-in-shamirs-secret?answertab=oldest | # Necessity for finite field arithmetic and the prime number p in Shamir's Secret Sharing Scheme
Shamir's original paper (PDF, 197kb) describing a threshold secret sharing scheme states:
To make this claim more precise, we use modular arithmetic instead of real arithmetic. The set of integers modulo a prime number $p$ forms a field in which interpolation is possible. Given an integer valued data $D$, we pick a prime $p$ which is bigger than both $D$ and $n$. The coefficients $a_1,...,a_{k-1}~$ in $q(x)$ are randomly chosen from a uniform distribution over the integers in [0, $p$), and the values $D_1,...,D_n$ are computed modulo $p$.
Where:
• $D$ is the secret to be shared
• $n$ is the number of shares
• $k$ is the threshold number of shares needed to reconstruct $D$
• $q(x)$ is a $k-1$ order polynomial with $q(0)=D$ and the coefficients $a_1,...,a_{k-1}~$
• $D_1,...,D_n$ are individual shares (points on the polynomial $q(x)$)
Can someone please explain (in the simplest possible manner) the reason that Shamir's Secret Sharing Scheme uses finite field arithmetic? Also, why must the size of the Galois field be a prime number with the requirements that Shamir put forth?
The reason for asking these questions is: I would like to implement Shamir Sharing in Javascript using a field of size $2^8 = 256$, which:
1. will obviate the need for a big integer library for Javascript, such as jsbn
2. will simplify the math.
Whatever the size of the secret to be shared, it could be broken down into byte-length segments and the math performed on those segments. The resulting share would be a concatenation of the results of the necessary operations on each segment.
To find the secret, the shares can again be broken down into byte-length segments. The polynomial interpolation can be done with the corresponding byte-length segments from the shares to get individual segments of the secret. The segments can then be concatenated to form the complete secret.
Would this work and be cryptographically secure?
If there is indeed an absolute necessity for a prime number $p$, could I use any small prime number with the concatenations described to perform the necessary operations in Javascript and still remain cryptographically secure?
-
Your idea has two parts: using a field $\mathbb F_{2^8}$ rather than $\mathbb F_p$; and splitting the secret to share into multiple bytes each treated in that field. That works; and the second part is present in the original article: "If the number D is long, it is advisable to break it into shorter blocks of bits (which are handled separately) in order to avoid multiprecision arithmetic operations". – fgrieu Nov 28 '12 at 15:25
@fgrieu thanks for that quote. I overlooked it. Had I read that statement I would not have asked this unnecessary Q. – ampersand Nov 28 '12 at 15:48
You may be interested in this analysis I came across recently. – mikeazo Mar 12 at 13:28
@mikeazo thanks. Seems interesting, but I cannot get the full article. Do you have a direct link? – ampersand Mar 20 at 15:38
@ampersand is there something missing in the PDF that is downloaded on the left hand side? It appears to be the whole thing to me. – mikeazo Mar 20 at 15:43
There is no reason in Shamir's scheme for the finite field $\mathbb F$ to have a prime number $p$ of elements; the field can have $p^m$ elements for suitable prime $p$ and integer $m \geq 1$. So, using $F_{2^8}$, the field with $2^8$ elements is perfectly all right. However, choosing $m = 1$ has the advantage that calculations in $\mathbb F_p$ can be done using the standard arithmetic unit included in microprocessors and the like (followed by integer divisions for doing the mod $p$ operations) whereas using $\mathbb F_{p^m}$ requires having a library already available (or developing one) or building a processor for arithmetic in the field.
Given that you have the capability of doing arithmetic in $\mathbb F_{2^8}$, you can use this field if you like. But, (as you say) in Shamir's scheme, the secret is just one element of the field (one $8$-bit byte), and so, if the Secret to be shared is several bytes long, you will need to process each byte separately into its (one-byte) shares, and concatenate the $i$-th share bytes into the $i$-th Share of the Secret. Keep in mind that each byte can be divided into at most $255$ shares (the point $q(0)$ on $q(x)$ cannot be used for obvious reasons), and so if you need to have more than $255$ shares to distribute, you will have to use a different field. Finally, to maintain cryptographic security, as the shares corresponding to each byte of the Secret are being computed, you should do exactly what you say you are doing in your comment: use a different set of "randomly chosen coefficients" for $q(x)$, rather than re-use the same set over and over again for finding the shares of all the bytes.
"building a processor" is a little far-fetched for arithmetic in $\mathbb F_{p^m}$; a library will do. – fgrieu Nov 28 '12 at 7:20
I think this wouldn't work for exactly 256 shares either. $\:$ – Ricky Demer Nov 28 '12 at 7:26
@RickyDemer You are correct. One of the $256$ shares would be the secret itself. I have corrected my answer. – Dilip Sarwate Nov 28 '12 at 11:38
@fgrieu Yes, a library of routines can be used for arithmetic in $\mathbb F_{p^m}$. But lots of people do build processors (application-specific integrated circuits or ASICs) for doing arithmetic in $\mathbb F_{p^m}$, especially $\mathbb F_{2^8}$ since error-correcting (Reed-Solomon) codes over this field are used in CD and DVD players, the DVB video broadcasting standard, various other communication systems and the like, which is where I am coming from. – Dilip Sarwate Nov 28 '12 at 11:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6001796126365662, "perplexity": 553.9869404455254}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042986625.58/warc/CC-MAIN-20150728002306-00179-ip-10-236-191-2.ec2.internal.warc.gz"} |
http://www.maplesoft.com/support/help/Maple/view.aspx?path=LinearAlgebra/Generic/HessenbergAlgorithm | LinearAlgebra[Generic] - Maple Programming Help
Home : Support : Online Help : Mathematics : Linear Algebra : LinearAlgebra Package : Generic Subpackage : LinearAlgebra/Generic/HessenbergAlgorithm
LinearAlgebra[Generic]
HessenbergAlgorithm
apply the Hessenberg algorithm to a square Matrix
Calling Sequence HessenbergAlgorithm[F](A)
Parameters
F - the domain of computation, a field A - square Matrix of values in F
Description
• Given an n x n Matrix A of elements in F, a field, HessenbergAlgorithm[F](A) returns a Vector V of n+1 values from F encoding the characteristic polynomial of A as V[1] x^n + V[2] x^(n-1) + .... + V[n] x + V[n+1]
• The algorithm converts a copy of A into upper Hessenberg form H using O(n^3) operations in F then expands the determinant of x I - H in a further O(n^3) operations in F. The algorithm requires that F be a field and should only be used if F is finite as there is severe expression swell in computing H.
• The (indexed) parameter F, which specifies the domain of computation, a field, must be a Maple table/module which has the following values/exports:
F[0]: a constant for the zero of the ring F
F[1]: a constant for the (multiplicative) identity of F
F[+]: a procedure for adding elements of F (nary)
F[-]: a procedure for negating and subtracting elements of F (unary and binary)
F[*]: a procedure for multiplying two elements of F (commutative)
F[/]: a procedure for dividing two elements of F
F[=]: a boolean procedure for testing if two elements in F are equal
Examples
> $\mathrm{with}\left(\mathrm{LinearAlgebra}[\mathrm{Generic}]\right):$
> ${Q}_{\mathrm{0}},{Q}_{\mathrm{1}},{Q}_{\mathrm{+}},{Q}_{\mathrm{-}},{Q}_{\mathrm{*}},{Q}_{\mathrm{/}},{Q}_{\mathrm{=}}≔0,1,\mathrm{+},\mathrm{-},\mathrm{*},\mathrm{/},\mathrm{=}:$
> $A≔\mathrm{Matrix}\left(\left[\left[2,1,4\right],\left[3,2,1\right],\left[0,0,5\right]\right]\right)$
${A}{:=}\left[\begin{array}{rrr}{2}& {1}& {4}\\ {3}& {2}& {1}\\ {0}& {0}& {5}\end{array}\right]$ (1)
> $C≔\mathrm{HessenbergAlgorithm}[Q]\left(A\right)$
${C}{:=}\left[\begin{array}{r}{1}\\ {-}{9}\\ {21}\\ {-}{5}\end{array}\right]$ (2)
> $⟨{x}^{3}|{x}^{2}|x|1⟩\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}.\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}C$
${{x}}^{{3}}{-}{9}{}{{x}}^{{2}}{+}{21}{}{x}{-}{5}$ (3) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 8, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9592989087104797, "perplexity": 2296.9810385167516}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738662541.24/warc/CC-MAIN-20160924173742-00112-ip-10-143-35-109.ec2.internal.warc.gz"} |
https://motls.blogspot.com/2007/09/resonance-tunneling-and-landscape.html?m=1 | Monday, September 03, 2007
Resonance tunneling and landscape percolation
One of the reasons why I think that a megalomanic amount of metastable de Sitter vacua in string theory should not exist is that they have a megalomanic number of ways how they can decay.
That's how I started a text called Landscape decay channels in 2005 whose goal was, of course, nothing less than to nuke the landscape. Finally, people are beginning to look into it a little bit more seriously.
Figure 1: Percolation through sandstone rocks in the landscape ;-)
Today, Sash Sarangi, Gary Shiu, Benjamin Shlaer (SSS) and, in another paper, Henry Tye discuss resonance tunneling and DBI tunneling (emerging for string-height barriers) that are capable to enhance the tunneling rate under certain circumstances. And "finally [they] argue using basic ideas from percolation theory (including concepts from the renormalization group, emphasized in Tye's paper) that tunneling can be rapid in a landscape where a typical vacuum has multiple decay channels and discuss various cosmological implications" (SSS abstract).
These authors seem to justify exactly the outcome that I predicted: the eternal inflation becomes impossible, most of the vacua in the landscape are unpopulated, and the vacua with a small cosmological constant like ours have a higher chance to be populated because the effective number of non-collapsing decay channels is small for these vacua (SSS). Yes, if the mechanism is correct, then string theory solves the cosmological constant problem and string theory can easily generate exponentially small values of the cosmological constant (Henry Tye).
At any rate, physicists should read these two papers (SSS, Tye) and find other arguments whether this rapid tunneling exists or not. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8535642623901367, "perplexity": 2247.786896291658}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195525312.3/warc/CC-MAIN-20190717141631-20190717163631-00407.warc.gz"} |
https://serc.carleton.edu/integrate/teaching_materials/earth_modeling/student_materials/unit5_article1.html | InTeGrate Modules and Courses >Modeling Earth Systems > Student Materials > Unit 5 Reading
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# Unit 5 Reading: Ice Sheet Modeling
by David Bice, The Pennsylvania State University
In this exercise, we will do some experiments with a simple ice sheet model based on a classic paper by Johannes Weertman from 1976. Our goals are to understand some basic things about how these ice sheets grow and shrink, and how they can respond to insolation variations caused by orbital changes of Earth relative to the sun.
Large continental ice sheets such as Greenland (Fig. 1) are important components of the global climate system — they play a critical role in altering the planetary albedo, which is connected to a potent positive feedback mechanism, and also in controlling global sea level.
The growth and decline of large ice sheets has been one of the dominant features of the Pleistocene ice age (Fig. 2), and their current decline is of great importance to the rising global sea level. The timing of the ice ages and intervening warmer periods are largely controlled by orbital changes, and one of the goals of this modeling exercise is to see how this works — how the ice sheet system responds to the orbital changes.
To develop our model of an ice sheet, we have to start with a few basics of how ice forms and flows. Glacial ice begins as snowfall that accumulates over the years. As it gets buried under more snow, the snow crystals undergo a kind of metamorphism, eventually turning into solid ice. Ice, as a naturally occurring polycrystalline solid, is really a kind of rock, but unlike most other rocks, ice can actually flow at the surface without melting. This solid-state flow is quite fast relative to other geologic processes, enabling glaciers to be very dynamic features of the surface.
It is common to assume that ice behaves as a deformable plastic material, which means that there is a critical shear stress, τ0, below which no strain (deformation or flow) will occur, and above which, the strain is limitless. Stress is simply a force acting on an area, and shear stress is a force applied parallel to a surface as opposed to a force applied perpendicular to a surface, which is called a normal stress. We talk about stresses rather than forces, since stresses are what can cause materials to deform (whether by flow or by fracture). The shear stress at the base of a pile of ice (Fig. 3) is a function of the surface slope, the thickness, gravity, and density:
tau_b = rhoghsinalpha Eqn. 1
Here, rho is the density of ice (typically 920 kg/m3), g is the acceleration due to gravity, h is the height of the ice, and alpha is the surface slope angle. When tau_b is greater than or equal to tau_0 , then the ice will flow. This equation tells us that where the thickness of the ice is greater, the slope can be smaller and still achieve the critical shear stress. Where the ice is thinner, a higher surface slope is needed to get the critical shear stress. Considering that the height or thickness of the ice must taper to 0 at the edge, you can see that the slope of the glacier has to be greatest right at the edge (which is illustrated in a schematic way in Fig. 3).
If the slope is too low, the basal shear stress will not match the critical shear stress tau_0 , but as snow piles up, creating more ice, the thickness (h) will increase until tau_0 is reached, at which point, flow will begin. As flow begins, the slope will decrease; this causes the basal shear stress to drop below tau_0 and flow will stop, but then snow piles up again and tau_0 is met. The result of this is that the glacier evolves to the point where the basal shear stress all along its base hovers right around the critical shear stress tau_0 and a steady state condition occurs. The result of this is that a glacier has an equilibrium profile, which can be obtained from the equation for the basal shear stress, rewritten as follows:
tau_0 = rhoghsinalpha = rhogh(-(dh)/(dx)) Eqn. 2
Here, (dh)/(dx) is the change in height divided by the change in horizontal distance, essentially the slope of the glacier's surface. The goal here is to find an expression for the equilibrium profile — how h varies as a function of horizontal position, x. The first step is to rearrange Eqn. 2 to get:
hdh = -tau_0/(rhog)dx Eqn. 3
Next, we integrate both sides:
1/2h^2 = -tau_0/(rhog)x + C Eqn. 4
Here, C is the combined constants of integration from both sides. To figure out what C is, we need to have some kind of boundary condition. In this case, we know that at the edge of the glacier, which we will call L, the height of the glacier, h, is 0; in other words, at x=L, h=0. We plug this into Eqn. 4 to get:
1/(2)0^2 = -tau_0/(rhog)L + C , so C = tau_0/(rhog)L Eqn. 5
Then, we plug this expression for C into Eqn. 4, which gives:
1/2h^2 = -tau_0/(rhog)x + tau_0/(rhog)L Eqn. 6
This can be rearranged to give us:
h^2 = (2tau_0)/(rhog)(L - x), or h(x) = sqrt((2tau_0)/(rhog)(L - |x|)) Eqn. 7
This final equation gives us a description of how the height of the glacier, h, changes as a function of distance, x, from the center of the ice sheet. Here, x = 0 is the center of the ice sheet, and by using the absolute value of x, we end up with a symmetrical profile for the glacier. To show how this works, imagine that we have an ice sheet with a length, L, of 3000 km (this is about the size of the Laurentide Ice Sheet that covered a large portion of North America in the last ice age), a critical shear stress of 75 kPa (75,000 Pa; Pa = Pascal, a unit of stress in N/m2), and a density, rho , of 920 kg/m3. Plugging these numbers into Eqn. 7, we get the thickness at the center of the glacier (where x = 0):
h(x = 0) = sqrt((2 * 75e3)/(920 * 9.8)(3e6 - 0)) ~~ 7000 m Eqn. 8
We make one slight simplification of Eqn. 7 as follows:
h(x) = sqrt(lambda(L - |x|)) where lambda = (2tau_0)/(rhog) Eqn. 9
Weertman says that typical values for lambda are 8 – 15 (the units in meters). If you integrate Eqn. 9 from x = -L to x = L, you get the cross-sectional area of the glacier, and you can also flip this around to get the length from the cross-sectional area:
A_x = 4/3 lambda^(1/2)L^(3/2) and conversely, L = ((3/4A_x)^2/lambda)^(1/3) Eqn. 10
Figure 4 shows what the shape of the glacier looks like, at two different times, with different cross-sectional areas:
Also shown in this diagram is the snow line, which separates colder areas where snow will accumulate to form ice from warmer regions where the melting exceeds snowfall, and the glacier will experience a loss of ice. The snow line slopes gently up to the right toward the warmer, equatorward side of the diagram. Where this snow line intersects the surface of the glacier (red circles in Fig. 4), we divide the glacier into its accumulation zone and its melting zone. The grounding position (black circle in Fig. 4) marks the place where the snow line intersects an elevation of zero. In Weertman's model, it is assumed that the right side of the ice sheet in Figure 4 is to the south; the left is the north. Weertman did not discuss the northern half of the ice sheet, but we presume that iceberg calving on the northern edge balances the accumulation. Thus, the northern half of the ice sheet is a "slave" to the location of the ice divide, which in turn is controlled by climate.
The model starts with an initial glacier length, and from that, we can calculate the profile of the glacier and its cross-sectional area. Once we have the profile, we can find the intersection with the snow line, which allows us to separate the glacier into the regions above the snow line, where accumulation can occur, and below the snow line, where melting will occur. We get the point where the snow line intersects the glacier surface by setting the equation for the snow line,
h_s = S(x - x_g) Eqn. 11
in which S is the slope of the snow line, and xg is the grounding line position, equal to the equation for the shape of the ice surface,
h_i = sqrt(lambda(L - |x|)) Eqn. 9
This leads to a quadratic equation that gives us the x position of the point where hi=hs.
x_s = (-b + sqrt(b^2 - 4ac))/(2a) Eqn. 12
where a = S^2 , b = lambda - 2x_(g)S^2 , and c = S^2x_g^2 - lambdaL
Once we have the snow line, we can calculate the change in the cross sectional area of the glacier as follows:
(dA_x)/(dt) = L_(ac)nu_(ac) - L_(ab)nu_(ab) Eqn. 13
This is a simple differential equation that tells us how the cross-sectional area (Ax) changes over time — if it is positive, the glacier will grow, if negative, then the glacier shrinks, and if it has a value of 0, the glacier is in a steady state condition. Here, Lac is the length over which accumulation occurs (Lac = L + xs), and Lab is the length over which melting or ablation occurs (Lab = L - xs). These lengths are multiplied by their corresponding rates, nu_(ac) and nu_(ab) , and then summed to give the change in cross-sectional (Ax) over a given interval of time. The balance of accumulation and ablation — the sign of equation 13 — then determines if the glacier will shrink or grow; in either case, we assume that it maintains the equilibrium profile. In the model, the accumulation rate ( nu_(ac) ) and ablation rate ( nu_(ab) ) are related by a parameter called epsilon:
epsilon = nu_(ac)/nu_(ab) Eqn. 14
This parameter epsilon is useful because it also helps us understand something about the steady state condition, which is when equation 13 is equal to 0. If we set that equation to 0 and then rearrange things, we get:
0 = L_(ac)nu_(ac) - L_(ab)nu_(ab) so,
L_(ac)nu_(ac) = L_(ab)nu_(ab) or,
nu_(ac)/nu_(ab) = L_(ab)/L_(ac) = epsilon Eqn. 15
In other words, when the ratio of the ablation length to the accumulation length is the same as epsilon (the ratio of ablation rate to accumulation rate), the ice sheet will be in a steady state — there will be no change in the cross-sectional area.
If warming occurs, the grounding line moves to the left (-x is considered to be toward the north), whereas cooling moves it to the south (right in the diagram). Based on observations of the present, Weertman calculated that the grounding position of the snowline changes by 17.7 km for every W/m2 of mean summer insolation change.
When Weertman wrote his paper, geoscientists were actively searching for ways to test the astronomical theory of climate change, attributed to Milankovitch, who showed that orbital variations (on timescales of tens to hundreds of kyr) should lead to seasonal changes in insolation that could explain the Pleistocene glacial-interglacial cycles. There are some orbital configurations that lead to relatively mild summers, which prevents all the previous winter's snow from melting, thus allowing for the buildup and growth of ice sheets. Once the ice sheets begin to grow, the ice-albedo feedback mechanism kicks in and significant cooling results. In fact, the same year as Weertman's paper, Hays et al. (1976) showed oxygen isotope evidence from marine sediment cores that the Pleistocene climate changes were controlled by these orbital variations. We can think of Weertman's paper as an examination of whether this idea makes sense in terms of the physics and dynamics of ice sheets. Before discussing how these orbital changes are implemented into the model, it is a good idea to briefly review what these orbital variations are.
Earth's orbit around the sun changes in three main ways (Fig. 5). Our path around the sun varies from being more circular to more elliptical due to the gravitational effects of Jupiter, Saturn, and to a lesser extent, Mars. The deviation from a perfect circle is called the eccentricity of the orbit, and this changes in a complicated way as the sum of three cycles, with periods of 95, 125, and ~400 kyr. As the eccentricity gets bigger, there is a greater difference between perihelion (the shortest Earth-sun distance) and aphelion (the greatest Earth-sun distance). The tilt angle, or obliquity, of our spin axis with respect to the orbital plane also changes from 22° to 24.5° away from perpendicular, with a cycle of 41 kyr. The tilt angle is important in accentuating seasonal differences — a higher tilt angle means a greater difference between summer and winter — and it affects the polar regions more than the equatorial regions. The third variation in our orbit arises from the precession of the spin axis — it wobbles just like a top due to torque applied by the sun and moon, which has an effect due to the equatorial bulge of Earth (equatorial diameter is about 45 km greater than the polar diameter). The precession of the spin axis changes the position in the orbit when we have winter, spring, summer, and fall. Currently, our winter solstice occurs very close to the perihelion position, so the precession angle ( omega in Fig. 5) is about 103°. The period of the precession is 26 kyr, but this interacts with the slow rotation of our orbital path around the sun to produce periods of 19–24 kyr.
If our orbit were a perfect circle, the precession of the spin axis would not have any real effect on insolation, but, when combined with the eccentricity, precession does have a big effect. For instance, in our present configuration, summer occurs near the aphelion position, and we have a relatively long, cool summer (long because the velocity of Earth around the orbit slows down as it gets farther from the sun). A cool summer in the polar regions means that there is a chance that all of the previous winter's snow might not melt, which could then lead to the buildup of glacial ice. Right now, the eccentricity is quite low, so the summers are not that cool, but with a higher eccentricity, our present configuration could lead to the growth of a large polar ice sheet and a new glacial age.
These orbital variations combine to produce significant variations in the insolation received at different places on Earth (Fig. 6), but these variations in the Northern and Southern Hemispheres are out of phase with each other, so there is no net change in the insolation received by the whole planet. But, our climate system has sensitive spots where even a slight change can trigger a feedback mechanism that amplifies the initial change. The Arctic region is one of these sensitive spots because the abundant land mass in the Northern Hemisphere makes it possible to grow a very large ice sheet, and the biggest part of the oceanic thermohaline circulation can be turned on or off by changes in the area around Iceland. Indeed, it turns out that oxygen isotope records from ice cores (temperature proxy) and marine sediments (proxy for ice volume and temperature) both match the summer insolation curve for 45°N to 65°N (the insolation curves are very similar for this latitude range).
In our ice sheet model, the summer insolation will control the position where the snow line meets the ground (we will call this the grounding line); this in turn will control the position of the snow line on the ice sheet, which in turn controls whether the ice sheet grows or shrinks. Weertman estimated that the grounding line moves 17.7 km for every W/m2 change in the summer insolation, and given a range of about 110 W/m2, this translates into a grounding line movement of over 1900 km, around 17° of latitude. So, we might expect this variation in insolation to have a significant impact on the dynamics of the ice sheet. Why do we say might expect rather than definitely expect? The reason is that it depends on the response time of the ice sheet in comparison with the frequency of the insolation variation — if the response time of the ice sheet is very long relative to the insolation change, then the insolation change will not have much of an impact.
Consider this simple illustration of the concept. We take a very simple climate model of Earth based on an energy balance where the insolation from the sun is balanced by the emission of infrared radiation, following the Stefan-Boltzmann Law (Fig. 7). This model is set up to be in a steady state at a temperature of 288 K, which is 15°C. Given the depth of the ocean, the heat capacity of water, and the density of water, this system has a response time of about five years.
We perturb this steady state by adding a fluctuation of ±10 W/m2 to the solar constant, which is normally 1370 W/m2. If we just add 10 W/m2 to the solar constant and let the climate get into a new steady state, it will warm by 0.5°, but let us consider what happens when the change to the solar constant is a sinusoidal function with a period that varies from one model run to the next. In Figure 8, the period varies over the course of five model runs from 0.2 to 1.0 to 5 to 10 to 20 yrs — the first two are shorter than the response time for the system (5 years), while the last two are greater than the response time. In all cases, the magnitude of the change is the same — ±10 W/m2.
As we can see, the magnitude of the resulting temperature change is strongly affected by the period of the fluctuation. When the fluctuation occurs at a high frequency, the system cannot keep up with the fluctuation — before the climate can warm in response to the higher solar constant, the solar constant has begun to decrease, and this brings the warming to a halt well before it reaches the 0.5° value that would normally result from an increase of 10 W/m2. In other words, the system does not have enough time to respond to the solar fluctuations. In contrast, when the fluctuation occurs at a low frequency (long period), the system does a better job of keeping up with the fluctuation.
The point of this digression is just to help you see that the question of how much the ice sheet will change due to the variations in insolation depends on the natural response time of the ice sheet, which itself is a function of the mathematics of the model. It is tricky to derive this response time, but once we make the model, we can easily see what the response time is.
One final note is that Weertman's model is for a continental ice sheet, and there are other, more complex models for marine ice sheets. Marine ice sheets behave somewhat differently, but they are also important to the climate system. For instance, some models of marine ice sheets show complex internal variability that could lead to the kind of massive iceberg discharge events (the Heinrich events) observed in the Pleistocene — these changes are not linked to orbitally-induced changes in the snow line grounding position. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7901627421379089, "perplexity": 833.1267777685899}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500719.31/warc/CC-MAIN-20230208060523-20230208090523-00473.warc.gz"} |
https://sciencing.com/calculate-grade-slope-5135843.html | # How to Calculate the Grade of a Slope
Print
In elementary school mathematics, when students learn to graph simple linear functions, they are introduced to the concept of a slope.
A linear function is just one with a graph represented by a straight line of some sort, with its placement and direction in relation to the x- and y-axes depending on the function's properties.
A linear equation has the form
y=mx+b
Where y is the dependent variable, m is the slope, and b is a quantity called the y-intercept, the point the line crosses on the y-axis.
But you may have also heard of a mathematical construct called a grade, or a percent grade. Muddled, ambiguous terms like "slope ratio" and "grade of slope" don't help.
Are slopes and grades related? They are indeed, and both are indispensable in mathematics and engineering.
## What is Slope?
In everyday terms, a slope is a steady, sustained climb or descent. That's what it means in mathematics as well, but in a more formal way. The slope of a line is the change in vertical (y) distance per one-unit change in horizontal (x) distance.
For example, if a point in a coordinate system moves 11 units in the positive x-direction and four units in the negative y-direction, the slope is (–4)/(11) = –0.364. The minus sign means the line angles "downhill" in relation to the horizontal x-axis.
A horizontal line such as the function y = 5, in which there is no vertical change throughout, has a slope of 0. A vertical line, such as x = −3, has an undefined slope as there is no horizontal change and dividing by zero is not permitted in mathematics.
## The Point-Slope Formula
The point-slope formula is helpful for determining the equation of a line when either two points or one point and the slope are known. It has the form
y − y_0 = m(x − x_0)
If you were given coordinates (12, −7) and told that the graph of the function had a slope of 1.25, you could determine the general equation:
(y − (−7)) = 1.25(x − 12) \\ (y + 7) = 1.25x −15 \\ y = 1.25x − 22
Grade, or percent grade, is just the slope expressed as a percentage. It is often used in real-life situations involving the construction of roads, the very steepest of which have surprisingly low slope values.
For example, the Pennsylvania Turnpike in the Eastern U.S. has a maximum slope of 0.03, meaning it rises or falls no more 3 feet for every 100 horizontal feet traveled over any segment. The percent grade in this instance is 100 × 0.03 = 3 percent.
In trigonometry, y/x, or "rise over run," is also the tangent of the angle formed by the ascending or descending line and the horizontal. This means that the inverse tangent (tan −1 or arctan on a calculator) of the slope equals this angle.
• In the grueling Tour de France, a three-week race through the mountains of Western Europe featuring the best male cyclists in the world, grades that reach 13 percent are considered extraordinarily fierce.
## Slope Distance Calculator
If you know the slope of a line, you can calculate horizontal distance traveled as a function of vertical distance, or the other way around. Say you know you're walking up a 4 percent grade. If you walk for 30 minutes and your horizontal position changes at a rate of 4 miles per hour, how much elevation have you gained?
4 mph for 30 min (1/2 hr) is 2 miles, and if the percent grade is 4, the slope is 4/100 = 0.04. Since slope is rise over run and in this case the "run" is 2 miles, the vertical gain can be found as follows:
\begin{aligned} 0.04 &= \frac{y}{2 \;\text{miles}} \\ y &= 0.04×2 \\ &= 0.08 \;\text{miles, or about} \\ &0.08 \;\text{mi}×5,280 \;\text{ft/mi} = 422 \;\text{ft} \end{aligned} | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9898291230201721, "perplexity": 878.5140079391782}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670559.66/warc/CC-MAIN-20191120134617-20191120162617-00250.warc.gz"} |
https://proofwiki.org/wiki/Sequence_of_Palindromic_Lucky_Numbers | Sequence of Palindromic Lucky Numbers
Theorem
The The sequence of lucky numbers which are also palindromic begins:
$1, 3, 7, 9, 33, 99, 111, 141, 151, 171, \ldots$
Proof
The sequence of lucky numbers begins:
$1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79, 87, 93, 99, \ldots$
Of these, the palindromic ones can be picked out by inspection.
$\blacksquare$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7778320908546448, "perplexity": 2909.275100812597}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145981.35/warc/CC-MAIN-20200224193815-20200224223815-00438.warc.gz"} |
https://math.hecker.org/2014/01/18/linear-algebra-and-its-applications-review-exercise-2-31/ | ## Linear Algebra and Its Applications, Review Exercise 2.31
Review exercise 2.31. Consider the rank-one matrix $A = uv^T$. Under what conditions would $A^2 = 0$?
Answer: In order for $A^2$ to exist $A$ must be a square matrix; otherwise we could not multiply $A$ by $A$ since the number of columns of the first matrix would not match the number of rows of the second.
Since $A$ is an $n$ by $n$ matrix the vectors $u$ and $v$ both have $n$ entries, with $u = (u_1, \ldots, u_n)$ and $v = (v_1, \ldots, v_n)$.
We then have
$A^2 = (uv^T)^2 = uv^Tuv^T = u(v^Tu)v^T$
Since $v^T$ is 1 by $n$ and $u$ is $n$ by 1 their product $v^Tu$ is a 1 by 1 matrix, or in other words a scalar value
$c = \sum_{i=1}^n v_iu_i = \sum_{i=1}^n u_iv_i$
We thus have
$A^2 = u(v^Tu)v^T = ucv^T = cuv^T = cA$
One way for $A^2$ to be zero is to have $A = 0$. Another way is if $c = \sum_{i=1}^n u_iv_i = 0$. Note that this would be trivially true if $A = 0$ but it is also possible for $c$ to be zero even if $A$ is nonzero.
For example, consider the case where $u = (1, 1)$ and $v = (1, -1)$ so that
$A = uv^T = \begin{bmatrix} 1 \\ 1 \end{bmatrix} \begin{bmatrix} 1&-1 \end{bmatrix} = \begin{bmatrix} 1&-1 \\ 1&-1 \end{bmatrix}$
We then have
$c = \sum_{i=1}^n u_iv_i = 1 \cdot 1 + 1 \cdot (-1) = 1 - 1 = 0$
and
$A^2 = \begin{bmatrix} 1&-1 \\ 1&-1 \end{bmatrix} \begin{bmatrix} 1&-1 \\ 1&-1 \end{bmatrix} = \begin{bmatrix} 0&0 \\ 0&0 \end{bmatrix} = 0$
NOTE: This continues a series of posts containing worked out exercises from the (out of print) book Linear Algebra and Its Applications, Third Edition by Gilbert Strang.
If you find these posts useful I encourage you to also check out the more current Linear Algebra and Its Applications, Fourth Edition, Dr Strang’s introductory textbook Introduction to Linear Algebra, Fourth Edition and the accompanying free online course, and Dr Strang’s other books.
This entry was posted in linear algebra and tagged , . Bookmark the permalink. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 33, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8275743126869202, "perplexity": 160.95494043339548}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964359073.63/warc/CC-MAIN-20211130201935-20211130231935-00349.warc.gz"} |
https://www.ttp.kit.edu/en/memberpages/winner?rev=1458143825&do=diff | # Differences
This shows you the differences between two versions of the page.
— en:memberpages:winner [2016/03/16 16:57] (current) Go Go Line 1: Line 1: + <HTML> +
+ + {{:memberpages:Georg_Winner.jpg?nolink&200|}} + + <HTML> + +
+ + + ====== Georg Winner ====== + + ** Member of TTP since June 2015 ** + + + <HTML><B>Supervisor of the Master Thesis: Prof. U. Nierste Room: 11/04 \\ + Phone: +49 (0)721 608 - 47027 \\ + Email: [[georg.winner@student.kit.edu]] \\ + <HTML> + + | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9994677901268005, "perplexity": 15125.973681612784}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657140746.69/warc/CC-MAIN-20200713002400-20200713032400-00535.warc.gz"} |
https://zbmath.org/?q=an%3A1041.68623 | ×
Variable neighborhood decomposition search.(English)Zbl 1041.68623
Summary: The recent Variable Neighborhood Search (VNS) metaheuristic combines local search with systematic changes of neighborhood in the descent and escape from local optimum phases. When solving large instances of various problems, its efficiency may be enhanced through decomposition. The resulting two level VNS, called Variable Neighborhood Decomposition Search (VNDS), is presented and illustrated on the p-median problem. Results on 1400, 3038 and 5934 node instances from the TSP library show VNDS improves notably upon VNS in less computing time, and gives much better results than Fast Interchange (FI), in the same time that FI takes for a single descent. Moreover, Reduced VNS (RVNS), which does not use a descent phase, gives results similar to those of FI in much less computing time.
MSC:
68U99 Computing methodologies and applications 68T20 Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.) 90C27 Combinatorial optimization
Full Text: | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8697981238365173, "perplexity": 3386.522958715564}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335514.65/warc/CC-MAIN-20221001003954-20221001033954-00311.warc.gz"} |
http://www.gamedev.net/index.php?app=forums&module=extras§ion=postHistory&pid=5046384 | • Create Account
### #ActualServant of the Lord
Posted 24 March 2013 - 06:58 PM
SiCrane is saying you can use the second template parameter of smart pointers to give a fake custom deleting function (in this case, a functor), so shared_ptr can work with stack-allocated variables.
//Functor for pretending to delete a block of stack-allocated memory, instead of using the default deleter provided by smart pointers.
//This can be passed as the second parameter of a smart pointer.
struct do_not_delete
{
do_not_delete() { }
void operator()(void*) const
{
//Do nothing. Let the stack free the memory when it's ready.
}
};
{
std::string onTheStack = "Test";
{
std::shared_ptr<std::string> mySharedPtr(&onTheStack, do_not_delete());
std::cout << *mySharedPtr << std::endl;
}
//mySharedPtr goes out of scope here, and calls 'do_not_delete(ptr)' to free the memory,
//but do_not_delete doesn't free it, safely letting the stack-allocated memory continue to exist.
std::cout << onTheStack << std::endl; //The stack-allocated memory continues to work just fine.
}
(I'm using C++11's standard shared pointers, but it should be roughly the same for boost smart pointers)
Ofcourse, now you have to be sure that 'onTheStack' lasts longer than 'mySharedPtr', or hard-to-track bugs result.
However, I think your low level functions shouldn't take pointers at all! I think almost every function should take parameters by const reference, unless something else is required. Then, whether you pass in actual stack-allocated or heap-allocated, it doesn't matter, and the function doesn't care.
void myFunc(const std::string &str);
std::string stackAllocated;
myFunc(stackAllocated);
std::shared_ptr<std::string> heapAllocatedShared = std::make_shared<std::string>();
myFunc(*heapAllocatedShared);
std::unique_ptr<std::string> heapAllocatedUnique = make_unique<std::string>();
myFunc(*heapAllocatedUnique);
You said that your low-level system "shares" data. Does it 'own' the data, or just 'use' the data? If it doesn't own it, it shouldn't be a shared_ptr, because shared_ptr means shared ownership. If something else owns it higher up, just use references or raw pointers lower down, unless it is possible for the lifetime of the system's access to the pointers to extend beyond the lifetime of the data passed in. If the lower down system uses it, but does not own it, and is likely to keep the pointer around for longer than the lifetime of the memory allocated, it might be worth considering whether that lower-level system should actually own it, with higher level code creating the object and giving up ownership of it to the lower system. Or maybe the lower-level system actually is doing more than it should be doing? Software architecture-design isn't my strong point.
### #3Servant of the Lord
Posted 24 March 2013 - 06:56 PM
SiCrane is saying you can use the second template parameter of smart pointers to give a fake custom deleting function (in this case, a functor), so shared_ptr can work with stack-allocated variables.
//Functor for pretending to delete a block of stack-allocated memory, instead of using the default deleter provided by smart pointers.
//This can be passed as the second parameter of a smart pointer.
struct do_not_delete
{
stack_allocated_deleter() { }
void operator()(void*) const
{
//Do nothing. Let the stack free the memory when it's ready.
}
};
{
std::string onTheStack = "Test";
{
std::shared_ptr<std::string> mySharedPtr(&onTheStack, do_not_delete());
std::cout << *mySharedPtr << std::endl;
}
std::cout << onTheStack << std::endl;
}
(I'm using C++11's standard shared pointers, but it should be roughly the same for boost smart pointers)
Ofcourse, now you have to be sure that 'onTheStack' lasts longer than 'mySharedPtr', or hard-to-track bugs result.
However, I think your low level functions shouldn't take pointers at all! I think almost every function should take parameters by const reference, unless something else is required. Then, whether you pass in actual stack-allocated or heap-allocated, it doesn't matter, and the function doesn't care.
void myFunc(const std::string &str);
std::string stackAllocated;
myFunc(stackAllocated);
std::shared_ptr<std::string> heapAllocatedShared = std::make_shared<std::string>();
myFunc(*heapAllocatedShared);
std::unique_ptr<std::string> heapAllocatedUnique = make_unique<std::string>();
myFunc(*heapAllocatedUnique);
You said that your low-level system "shares" data. Does it 'own' the data, or just 'use' the data? If it doesn't own it, it shouldn't be a shared_ptr, because shared_ptr means shared ownership. If something else owns it higher up, just use references or raw pointers lower down, unless it is possible for the lifetime of the system's access to the pointers to extend beyond the lifetime of the data passed in. If the lower down system uses it, but does not own it, and is likely to keep the pointer around for longer than the lifetime of the memory allocated, it might be worth considering whether that lower-level system should actually own it, with higher level code creating the object and giving up ownership of it to the lower system. Or maybe the lower-level system actually is doing more than it should be doing? Software architecture-design isn't my strong point.
### #2Servant of the Lord
Posted 24 March 2013 - 06:56 PM
SiCrane is saying you can use the second template parameter of smart pointers to give a fake custom deleting function, so shared_ptr can work with stack-allocated variables.
//Functor for pretending to delete a block of stack-allocated memory, instead of using the default deleter provided by smart pointers.
//This can be passed as the second parameter of a smart pointer.
struct do_not_delete
{
stack_allocated_deleter() { }
void operator()(void*) const
{
//Do nothing. Let the stack free the memory when it's ready.
}
};
{
std::string onTheStack = "Test";
{
std::shared_ptr<std::string> mySharedPtr(&onTheStack, do_not_delete());
std::cout << *mySharedPtr << std::endl;
}
std::cout << onTheStack << std::endl;
}
(I'm using C++11's standard shared pointers, but it should be roughly the same for boost smart pointers)
Ofcourse, now you have to be sure that 'onTheStack' lasts longer than 'mySharedPtr', or hard-to-track bugs result.
However, I think your low level functions shouldn't take pointers at all! I think almost every function should take parameters by const reference, unless something else is required. Then, whether you pass in actual stack-allocated or heap-allocated, it doesn't matter, and the function doesn't care.
void myFunc(const std::string &str);
std::string stackAllocated;
myFunc(stackAllocated);
std::shared_ptr<std::string> heapAllocatedShared = std::make_shared<std::string>();
myFunc(*heapAllocatedShared);
std::unique_ptr<std::string> heapAllocatedUnique = make_unique<std::string>();
myFunc(*heapAllocatedUnique);
You said that your low-level system "shares" data. Does it 'own' the data, or just 'use' the data? If it doesn't own it, it shouldn't be a shared_ptr, because shared_ptr means shared ownership. If something else owns it higher up, just use references or raw pointers lower down, unless it is possible for the lifetime of the system's access to the pointers to extend beyond the lifetime of the data passed in. If the lower down system uses it, but does not own it, and is likely to keep the pointer around for longer than the lifetime of the memory allocated, it might be worth considering whether that lower-level system should actually own it, with higher level code creating the object and giving up ownership of it to the lower system. Or maybe the lower-level system actually is doing more than it should be doing? Software architecture-design isn't my strong point.
### #1Servant of the Lord
Posted 24 March 2013 - 06:54 PM
SiCrane is saying you can use the second template parameter of smart pointers to give a fake custom deleting function, so shared_ptr can work with stack-allocated variables.
//Functor for pretending to delete a block of stack-allocated memory, instead of using the default deleter provided by smart pointers.
//This can be passed as the second parameter of a smart pointer.
struct do_not_delete
{
stack_allocated_deleter() { }
void operator()(void*) const
{
//Do nothing. Let the stack free the memory when it's ready.
}
};
{
std::string onTheStack = "Test";
{
std::shared_ptr<std::string> mySharedPtr(&onTheStack, do_not_delete());
std::cout << *mySharedPtr << std::endl;
}
std::cout << onTheStack << std::endl;
}
(I'm using C++11's standard shared pointers, but it should be roughly the same for boost smart pointers)
Ofcourse, now you have to be sure that 'onTheStack' lasts longer than 'mySharedPtr', or hard-to-track bugs result.
However, I think your low level functions shouldn't take pointers at all! I think almost every function should take parameters by const reference, unless something else is required. Then, whether you pass in actual stack-allocated or heap-allocated, it doesn't matter, and the function doesn't care.
void myFunc(const std::string &str);
std::string stackAllocated;
myFunc(stackAllocated);
std::shared_ptr<std::string> heapAllocatedShared = std::make_shared<std::string>();
myFunc(*heapAllocatedShared);
std::unique_ptr<std::string> heapAllocatedUnique = make_unique<std::string>();
myFunc(*heapAllocatedUnique);
You said that your low-level system "shares" data. Does it 'own' the data, or just 'use' the data? If it doesn't own it, it shouldn't be a shared_ptr, because shared_ptr means shared ownership. If something else owns it higher up, just use references or raw pointers lower down, unless it is possible for the lifetime of the system's access to the pointers to extend beyond the lifetime of the data passed in. If the lower down system uses it, but does not own it, and is likely to keep the pointer around for longer than the lifetime of the memory allocated, it might be worth considering whether that lower-level system should actually own it, with higher level code creating the object and giving up ownership of it to the lower system.
PARTNERS | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20835618674755096, "perplexity": 3450.008748296873}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1406510270313.12/warc/CC-MAIN-20140728011750-00008-ip-10-146-231-18.ec2.internal.warc.gz"} |
https://cstheory.stackexchange.com/questions/16775/on-fooling-ac0 | # On fooling $AC^0$
I have a few questions regarding fooling constant depth circuits.
1. It's known that $\log^{O(d)}(n)$-wise independence is necessary to fool $AC^0$ circuits of depth $d$, where $n$ is the size of the input. How can one prove this?
2. Since the above is true, any pseudorandom generator that fools $AC^0$ circuits of depth $d$ must necessarily have seed length $l = \Omega(\log^d(n))$, which would then mean that one cannot expect to prove $RAC^0 = AC^0$ via PRGs. I believe $RAC^0 \stackrel{?}{=} AC^0$ is still an open question, so this means that one has to use techniques other than PRGs to prove $RAC^0 = AC^0$. I find this weird because, at least in the case of $P \stackrel{?}{=} BPP$, we believe that PRGs are essentially the only way to go about answering this question.
I think I am missing something really basic here.
• About 1). Polylog-wise independence is definitely sufficient to fool $AC^{0}$ because of Braverman's breakthrough, but why do you claim it is necessary? – Alessandro Cosentino Mar 7 '13 at 10:19
• Actually, I am not sure if I have ever seen a formal mention of 1.) in any paper etc. but I believe this is known. Check out comment 29 by Scott Aaronson here: scottaaronson.com/blog/?p=381 – Abhishek Bhrushundi Mar 7 '13 at 11:10
• I think the correct statement should be that if you want to fool AC0 by k-wise independence, then $k = polylog(n)$ is necessary. It doesn't say any PRG is like that. – MCH Mar 7 '13 at 14:04
• ok, makes sense now. Another clarification: does the expression "techniques to derandomize other than PRGs" make sense? Isn't a PRG by definition (at least in complexity theory) something that we use to derandomize? @AbhishekBhrushundi: btw, I like the question. It's good to clarify this kind of things on cstheory ;-) – Alessandro Cosentino Mar 7 '13 at 14:12
1) What is meant by necessary is that one way to generate a $k$-wise independent distribution is to break the input in blocks of $k+1$ bits, and let the $(k+1)$th bit of each block be the parity of the other $k$ bits in the block. Obviously this distribution can be broken just by computing parity on $k$ bits. The result you claim follows from the fact that poly($n$) circuits of depth $d$ can compute parity on $\log^{d-1} n$ bits.
2) No. 1) is only talking about a specific construction of $k$-wise independent distributions. Conceivably there are $O(\log n)$-seed generators that fool poly-size bounded-depth circuits (this also follows from sufficiently strong lower bounds against bounded-depth circuits, though the standard hardness vs. randomness tradeoffs do not suffice, see e.g. the discussion of a paper by Agrawal in Section 3.2 of http://www.ccs.neu.edu/home/viola/papers/JournalCCC03.pdf).
Polylog independence may not be the only way to fool $AC^{0}$ circuits. To illustrate this example, consider the class of linear polynomials. Any zero set of a linear polynomial is $(n-1)$-wise independent but of course this doesn't fool linear polynomials. Hence, $(n-1)$-wise independent distributions do not fool this class. This of course doesn't mean that only $n$-wise independent distributions fool this class ($\epsilon$-biased spaces fool them, and are polynomial sized spaces).
I guess what one means when they say "$\log^{O(d)} n$-wise independence is necessary" is that there are examples of distributions with smaller independence, and it is known that they do not fool $AC^{0}$. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7891885042190552, "perplexity": 473.6328156001638}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195527458.86/warc/CC-MAIN-20190722010436-20190722032436-00426.warc.gz"} |
https://github.com/editorconfig/editorconfig-notepad-plus-plus | C++ CMake
Latest commit 545a2fa Apr 27, 2016 Bump version to 0.3.0.
Failed to load latest commit information. src Apr 26, 2016 .editorconfig Jan 10, 2012 .gitignore Apr 20, 2016 CMakeLists.txt Apr 27, 2016 COPYING.txt Dec 11, 2011 README.md Apr 26, 2016
This is an EditorConfig plugin for Notepad++.
## Installation
### Install from the Plugin Manager
If you have Notepad++ Plugin Manager installed (usually installed by default in Notepad++), you can install in this way.
Launch Notepad++, click on the Plugins menu, then Plugin Manager -> Show Plugin Manager. In the Available tab, find EditorConfig in the list, check the checkbox and click on the Install button.
### Install from the Binary Package
2. Extract the compressed archive and copy the corresponding dll into your Notepad++ plugin directory(the unicode dll if your Notepad++ version is unicode or the ansi one if you're using the ansi version Notepad++).
### Install from Source
Before installation, you must have both cmake and Microsoft Visual C++ installed.
1. Download the EditorConfig C core and follow the instructions in the README and INSTALL files to compile and install it with Microsoft Visual C++. Note that the EditorConfig C core must be built with the MT option.
3. Open your command line prompt, and use cd command to switch current working directory to the root of the source tree of the Notepad++ plugin. Use the following command to generate the project file:
C:\path\to\editorconfig-notepad-plus-plus> cmake . -DEDITORCONFIG_CORE_PREFIX="\$(The_path_to_EditorConfig_core_prefix)"
After this project file is built, run cmake-gui . to set the variable PCRE_LIB_DIR to the directory which contains pcre.lib (can be downloaded from https://sourceforge.net/projects/editorconfig/files/EditorConfig-C-Core/3rd-party/pcre-8.38/?upload_just_completed=true ). Double click on the project file and use Microsoft Visual C++ to build it.
4. If the build succeeded, you should have bin\unicode\NppEditorConfig.dll and bin\ansi\NppEditorConfig.dll in your build tree. Copy the corresponding one (the unicode one if your Notepad++ is unicode version or the ansi one if your Notepad++ is ansi version) to your the plugin directory of the Notepad++ directory to complete the installation.
## Supported properties
The EditorConfig Notepad++ plugin supports the following EditorConfig properties:
• indent_style
• indent_size
• tab_width
• end_of_line
• trim_trailing_whitespace
• insert_final_newline
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https://worldwidescience.org/topicpages/n/nonlinear+control+system.html | #### Sample records for nonlinear control system
1. Controlling chaotic systems via nonlinear feedback control
International Nuclear Information System (INIS)
Park, Ju H.
2005-01-01
In this article, a new method to control chaotic systems is proposed. Using Lyapunov method, we design a nonlinear feedback controller to make the controlled system be stabilized. A numerical example is given to illuminate the design procedure and advantage of the result derived
2. Nonlinear robust hierarchical control for nonlinear uncertain systems
Directory of Open Access Journals (Sweden)
Leonessa Alexander
1999-01-01
Full Text Available A nonlinear robust control-system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving nominal system equilibria is developed. Specifically, using equilibria-dependent Lyapunov functions, a hierarchical nonlinear robust control strategy is developed that robustly stabilizes a given nonlinear system over a prescribed range of system uncertainty by robustly stabilizing a collection of nonlinear controlled uncertain subsystems. The robust switching nonlinear controller architecture is designed based on a generalized (lower semicontinuous Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized nominal system equilibria. The proposed framework robustly stabilizes a compact positively invariant set of a given nonlinear uncertain dynamical system with structured parametric uncertainty. Finally, the efficacy of the proposed approach is demonstrated on a jet engine propulsion control problem with uncertain pressure-flow map data.
3. Advances and applications in nonlinear control systems
CERN Document Server
Volos, Christos
2016-01-01
The book reports on the latest advances and applications of nonlinear control systems. It consists of 30 contributed chapters by subject experts who are specialized in the various topics addressed in this book. The special chapters have been brought out in the broad areas of nonlinear control systems such as robotics, nonlinear circuits, power systems, memristors, underwater vehicles, chemical processes, observer design, output regulation, backstepping control, sliding mode control, time-delayed control, variables structure control, robust adaptive control, fuzzy logic control, chaos, hyperchaos, jerk systems, hyperjerk systems, chaos control, chaos synchronization, etc. Special importance was given to chapters offering practical solutions, modeling and novel control methods for the recent research problems in nonlinear control systems. This book will serve as a reference book for graduate students and researchers with a basic knowledge of electrical and control systems engineering. The resulting design proce...
4. Phase Control in Nonlinear Systems
Science.gov (United States)
Zambrano, Samuel; Seoane, Jesús M.; Mariño, Inés P.; Sanjuán, Miguel A. F.; Meucci, Riccardo
The following sections are included: * Introduction * Phase Control of Chaos * Description of the model * Numerical exploration of phase control of chaos * Experimental evidence of phase control of chaos * Phase Control of Intermittency in Dynamical Systems * Crisis-induced intermittency and its control * Experimental setup and implementation of the phase control scheme * Phase control of the laser in the pre-crisis regime * Phase control of the intermittency after the crisis * Phase control of the intermittency in the quadratic map * Phase Control of Escapes in Open Dynamical Systems * Control of open dynamical systems * Model description * Numerical simulations and heuristic arguments * Experimental implementation in an electronic circuit * Conclusions and Discussions * Acknowledgments * References
5. Adaptive PI Controller for a Nonlinear System
Directory of Open Access Journals (Sweden)
D. Rathikarani
2009-10-01
Full Text Available Most of the industrial processes are inherently nonlinear in their behaviour. Designs of controllers for these nonlinear processes are difficult, as they do not follow superposition theorem. Adaptive controller can change its behaviour in response to changes in the dynamics of the process and disturbances. Hence adaptive controller can be used to control nonlinear processes. Direct Model Reference Adaptive Control is a technique, in which a reference model involving the desired performances is specified. In the present work, a DMRAC is designed and implemented to achieve satisfactory control of a nonlinear system in all its local linear operating regions. The closed loop system is made BIBO stable by proper control techniques. The controller is designed through simulation in Matlab platform and is validated in real time by conducting experiments on the laboratory Air Flow Control System using the dSPACE interface.
6. Boundary Controllability of Nonlinear Fractional Integrodifferential Systems
Directory of Open Access Journals (Sweden)
Ahmed HamdyM
2010-01-01
Full Text Available Sufficient conditions for boundary controllability of nonlinear fractional integrodifferential systems in Banach space are established. The results are obtained by using fixed point theorems. We also give an application for integropartial differential equations of fractional order.
7. Indirect learning control for nonlinear dynamical systems
Science.gov (United States)
Ryu, Yeong Soon; Longman, Richard W.
1993-01-01
In a previous paper, learning control algorithms were developed based on adaptive control ideas for linear time variant systems. The learning control methods were shown to have certain advantages over their adaptive control counterparts, such as the ability to produce zero tracking error in time varying systems, and the ability to eliminate repetitive disturbances. In recent years, certain adaptive control algorithms have been developed for multi-body dynamic systems such as robots, with global guaranteed convergence to zero tracking error for the nonlinear system euations. In this paper we study the relationship between such adaptive control methods designed for this specific class of nonlinear systems, and the learning control problem for such systems, seeking to converge to zero tracking error in following a specific command repeatedly, starting from the same initial conditions each time. The extension of these methods from the adaptive control problem to the learning control problem is seen to be trivial. The advantages and disadvantages of using learning control based on such adaptive control concepts for nonlinear systems, and the use of other currently available learning control algorithms are discussed.
8. Controllability of nonlinear delay oscillating systems
Directory of Open Access Journals (Sweden)
Chengbin Liang
2017-05-01
Full Text Available In this paper, we study the controllability of a system governed by second order delay differential equations. We introduce a delay Gramian matrix involving the delayed matrix sine, which is used to establish sufficient and necessary conditions of controllability for the linear problem. In addition, we also construct a specific control function for controllability. For the nonlinear problem, we construct a control function and transfer the controllability problem to a fixed point problem for a suitable operator. We give a sufficient condition to guarantee the nonlinear delay system is controllable. Two examples are given to illustrate our theoretical results by calculating a specific control function and inverse of a delay Gramian matrix.
9. Noninteracting control of nonlinear systems based on relaxed control
NARCIS (Netherlands)
Jayawardhana, B.
2010-01-01
In this paper, we propose methodology to solve noninteracting control problem for general nonlinear systems based on the relaxed control technique proposed by Artstein. For a class of nonlinear systems which cannot be stabilized by smooth feedback, a state-feedback relaxed control can be designed to
10. Control of self-organizing nonlinear systems
CERN Document Server
Klapp, Sabine; Hövel, Philipp
2016-01-01
The book summarizes the state-of-the-art of research on control of self-organizing nonlinear systems with contributions from leading international experts in the field. The first focus concerns recent methodological developments including control of networks and of noisy and time-delayed systems. As a second focus, the book features emerging concepts of application including control of quantum systems, soft condensed matter, and biological systems. Special topics reflecting the active research in the field are the analysis and control of chimera states in classical networks and in quantum systems, the mathematical treatment of multiscale systems, the control of colloidal and quantum transport, the control of epidemics and of neural network dynamics.
11. Controller Design of Complex System Based on Nonlinear Strength
Directory of Open Access Journals (Sweden)
Rongjun Mu
2015-01-01
Full Text Available This paper presents a new idea of controller design for complex systems. The nonlinearity index method was first developed for error propagation of nonlinear system. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of the system model. The algorithm of nonlinearity index according to engineering application is first proposed in this paper. Applying this method on nonlinear systems is an effective way to measure the nonlinear strength of dynamics model over the full flight envelope. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of system model. According to the different nonlinear strength of dynamical model, the control system is designed. The simulation time of dynamical complex system is selected by the maximum value of dynamic nonlinearity indices. Take a missile as example; dynamical system and control characteristic of missile are simulated. The simulation results show that the method is correct and appropriate.
12. An efficient control algorithm for nonlinear systems
International Nuclear Information System (INIS)
Sinha, S.
1990-12-01
We suggest a scheme to step up the efficiency of a recently proposed adaptive control algorithm, which is remarkably effective for regulating nonlinear systems. The technique involves monitoring of the ''stiffness of control'' to get maximum gain while maintaining a predetermined accuracy. The success of the procedure is demonstrated for the case of the logistic map, where we show that the improvement in performance is often factors of tens, and for small control stiffness, even factors of hundreds. (author). 4 refs, 1 fig., 1 tab
13. Impulse position control algorithms for nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Sesekin, A. N., E-mail: sesekin@list.ru [Ural Federal University, 19 S. Mira, Ekaterinburg, 620002 (Russian Federation); Institute of Mathematics and Mechanics, Ural Division of Russian Academy of Sciences, 16 S. Kovalevskaya, Ekaterinburg, 620990 (Russian Federation); Nepp, A. N., E-mail: anepp@urfu.ru [Ural Federal University, 19 S. Mira, Ekaterinburg, 620002 (Russian Federation)
2015-11-30
The article is devoted to the formalization and description of impulse-sliding regime in nonlinear dynamical systems that arise in the application of impulse position controls of a special kind. The concept of trajectory impulse-sliding regime formalized as some limiting network element Euler polygons generated by a discrete approximation of the impulse position control This paper differs from the previously published papers in that it uses a definition of solutions of systems with impulse controls, it based on the closure of the set of smooth solutions in the space of functions of bounded variation. The need for the study of such regimes is the fact that they often arise when parry disturbances acting on technical or economic control system.
14. Impulse position control algorithms for nonlinear systems
Science.gov (United States)
Sesekin, A. N.; Nepp, A. N.
2015-11-01
The article is devoted to the formalization and description of impulse-sliding regime in nonlinear dynamical systems that arise in the application of impulse position controls of a special kind. The concept of trajectory impulse-sliding regime formalized as some limiting network element Euler polygons generated by a discrete approximation of the impulse position control This paper differs from the previously published papers in that it uses a definition of solutions of systems with impulse controls, it based on the closure of the set of smooth solutions in the space of functions of bounded variation. The need for the study of such regimes is the fact that they often arise when parry disturbances acting on technical or economic control system.
15. MPPT for Photovoltaic System Using Nonlinear Controller
Directory of Open Access Journals (Sweden)
Ramsha Iftikhar
2018-01-01
Full Text Available Photovoltaic (PV system generates energy that varies with the variation in environmental conditions such as temperature and solar radiation. To cope up with the ever increasing demand of energy, the PV system must operate at maximum power point (MPP, which changes with load as well as weather conditions. This paper proposes a nonlinear backstepping controller to harvest maximum power from a PV array using DC-DC buck converter. A regression plane is formulated after collecting the data of the PV array from its characteristic curves to provide the reference voltage to track MPP. Asymptotic stability of the system is proved using Lyapunov stability criteria. The simulation results validate the rapid tracking and efficient performance of the controller. For further validation of the results, it also provides a comparison of the proposed controller with conventional perturb and observe (P&O and fuzzy logic-based controller (FLBC under abrupt changes in environmental conditions.
16. Advanced nonlinear engine speed control systems
DEFF Research Database (Denmark)
Vesterholm, Thomas; Hendricks, Elbert
1994-01-01
Several subsidiary control problems have turned out to be important for improving driveability and fuel consumption in modern spark ignition (SI) engine cars. Among these are idle speed control and cruise control. In this paper the idle speed and cruise control problems will be treated as one......: accurately tracking of a desired engine speed in the presence of model uncertainties and severe load disturbances. This is accomplished by using advanced nonlinear control techniques such as input/output-linearization and sliding mode control. These techniques take advantage of a nonlinear model...... of the engine dynamics, a mean value engine model....
17. Euclidean null controllability of nonlinear infinite delay systems with ...
African Journals Online (AJOL)
Sufficient conditions for the Euclidean null controllability of non-linear delay systems with time varying multiple delays in the control and implicit derivative are derived. If the uncontrolled system is uniformly asymptotically stable and if the control system is controllable, then the non-linear infinite delay system is Euclidean null ...
18. Nonlinear PI control of chaotic systems using singular perturbation theory
International Nuclear Information System (INIS)
Wang Jiang; Wang Jing; Li Huiyan
2005-01-01
In this paper, we develop the nonlinear PI controllers for a class of chaotic systems based on singular perturbation theory. The original system is decomposed into two reduced order systems, to which the nonlinear uncertain terms belongs. In order to alleviate the deterioration of these nonlinear uncertainties, the nonlinear PI controllers are applied to each subsystem and combined to construct the composite controller for the full order system. The effectiveness and feasibility of the proposed control scheme is demonstrated through numerical simulations on the chaotic Chua's circuit
19. Frequency domain performance analysis of nonlinearly controlled motion systems
NARCIS (Netherlands)
Pavlov, A.V.; Wouw, van de N.; Pogromski, A.Y.; Heertjes, M.F.; Nijmeijer, H.
2007-01-01
At the heart of the performance analysis of linear motion control systems lie essential frequency domain characteristics such as sensitivity and complementary sensitivity functions. For a class of nonlinear motion control systems called convergent systems, generalized versions of these sensitivity
20. Switching Fuzzy Guaranteed Cost Control for Nonlinear Networked Control Systems
Directory of Open Access Journals (Sweden)
Linqin Cai
2014-01-01
Full Text Available This paper deals with the problem of guaranteed cost control for a class of nonlinear networked control systems (NCSs with time-varying delay. A guaranteed cost controller design method is proposed to achieve the desired control performance based on the switched T-S fuzzy model. The switching mechanism is introduced to handle the uncertainties of NCSs. Based on Lyapunov functional approach, some sufficient conditions for the existence of state feedback robust guaranteed cost controller are presented. Simulation results show that the proposed method is effective to guarantee system’s global asymptotic stability and quality of service (QoS.
1. Discrete-time inverse optimal control for nonlinear systems
CERN Document Server
Sanchez, Edgar N
2013-01-01
Discrete-Time Inverse Optimal Control for Nonlinear Systems proposes a novel inverse optimal control scheme for stabilization and trajectory tracking of discrete-time nonlinear systems. This avoids the need to solve the associated Hamilton-Jacobi-Bellman equation and minimizes a cost functional, resulting in a more efficient controller. Design More Efficient Controllers for Stabilization and Trajectory Tracking of Discrete-Time Nonlinear Systems The book presents two approaches for controller synthesis: the first based on passivity theory and the second on a control Lyapunov function (CLF). Th
2. Output controllability of nonlinear systems with bounded control
International Nuclear Information System (INIS)
Garcia, Rafael; D'Attellis, Carlos
1990-01-01
The control problem treated in this paper is the output controllability of a nonlinear system in the form: x = f(x) + g(x)u(t); y = h(x), using bounded controls. The approach to the problem consists of a modification in the system using dynamic feedback in such a way that the input/output behaviour of the closed loop matches the input/output behaviour of a completely output-controllable system with bounded controls. Sufficient conditions are also put forward on the system so that a compact set in the output space may be reached in finite time using uniformally bounded controls, and a result on output regulation in finite time with asymptotic state stabilization is obtained. (Author)
3. Tracking Control for Switched Cascade Nonlinear Systems
Directory of Open Access Journals (Sweden)
Xiaoxiao Dong
2015-01-01
Full Text Available The issue of H∞ output tracking for switched cascade nonlinear systems is discussed in this paper, where not all the linear parts of subsystems are stabilizable. The conditions of the solvability for the issue are given by virtue of the structural characteristics of the systems and the average dwell time method, in which the total activation time for stabilizable subsystems is longer than that for the unstabilizable subsystems. At last, a simulation example is used to demonstrate the validity and advantages of the proposed approach.
4. Analysis and design of robust decentralized controllers for nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Schoenwald, D.A.
1993-07-01
Decentralized control strategies for nonlinear systems are achieved via feedback linearization techniques. New results on optimization and parameter robustness of non-linear systems are also developed. In addition, parametric uncertainty in large-scale systems is handled by sensitivity analysis and optimal control methods in a completely decentralized framework. This idea is applied to alleviate uncertainty in friction parameters for the gimbal joints on Space Station Freedom. As an example of decentralized nonlinear control, singular perturbation methods and distributed vibration damping are merged into a control strategy for a two-link flexible manipulator.
5. Nonlinear systems techniques for dynamical analysis and control
CERN Document Server
Lefeber, Erjen; Arteaga, Ines
2017-01-01
This treatment of modern topics related to the control of nonlinear systems is a collection of contributions celebrating the work of Professor Henk Nijmeijer and honoring his 60th birthday. It addresses several topics that have been the core of Professor Nijmeijer’s work, namely: the control of nonlinear systems, geometric control theory, synchronization, coordinated control, convergent systems and the control of underactuated systems. The book presents recent advances in these areas, contributed by leading international researchers in systems and control. In addition to the theoretical questions treated in the text, particular attention is paid to a number of applications including (mobile) robotics, marine vehicles, neural dynamics and mechanical systems generally. This volume provides a broad picture of the analysis and control of nonlinear systems for scientists and engineers with an interest in the interdisciplinary field of systems and control theory. The reader will benefit from the expert participan...
6. Robust receding horizon control for networked and distributed nonlinear systems
CERN Document Server
Li, Huiping
2017-01-01
This book offers a comprehensive, easy-to-understand overview of receding-horizon control for nonlinear networks. It presents novel general strategies that can simultaneously handle general nonlinear dynamics, system constraints, and disturbances arising in networked and large-scale systems and which can be widely applied. These receding-horizon-control-based strategies can achieve sub-optimal control performance while ensuring closed-loop stability: a feature attractive to engineers. The authors address the problems of networked and distributed control step-by-step, gradually increasing the level of challenge presented. The book first introduces the state-feedback control problems of nonlinear networked systems and then studies output feedback control problems. For large-scale nonlinear systems, disturbance is considered first, then communication delay separately, and lastly the simultaneous combination of delays and disturbances. Each chapter of this easy-to-follow book not only proposes and analyzes novel ...
7. Nonlinear Predictive Sliding Mode Control for Active Suspension System
Directory of Open Access Journals (Sweden)
Dazhuang Wang
2018-01-01
Full Text Available An active suspension system is important in meeting the requirements of the ride comfort and handling stability for vehicles. In this work, a nonlinear model of active suspension system and a corresponding nonlinear robust predictive sliding mode control are established for the control problem of active suspension. Firstly, a seven-degree-of-freedom active suspension model is established considering the nonlinear effects of springs and dampers; and secondly, the dynamic model is expanded in the time domain, and the corresponding predictive sliding mode control is established. The uncertainties in the controller are approximated by the fuzzy logic system, and the adaptive controller reduces the approximation error to increase the robustness of the control system. Finally, the simulation results show that the ride comfort and handling stability performance of the active suspension system is better than that of the passive suspension system and the Skyhook active suspension. Thus, the system can obviously improve the shock absorption performance of vehicles.
8. Stabilization and Control Models of Systems With Hysteresis Nonlinearities
Directory of Open Access Journals (Sweden)
Mihail E. Semenov
2012-05-01
Full Text Available Mechanical and economic systems with hysteresis nonlinearities are studied in article. Dissipativity condition of inverted pendulum under the hysteresis control is obtained. The solution of the optimal production strategy problem was found where price has hysteresis behaviour.
9. Geometric Theory of Reduction of Nonlinear Control Systems
Science.gov (United States)
Elkin, V. I.
2018-02-01
The foundations of a differential geometric theory of nonlinear control systems are described on the basis of categorical concepts (isomorphism, factorization, restrictions) by analogy with classical mathematical theories (of linear spaces, groups, etc.).
10. Tracking Control of Nonlinear Mechanical Systems
NARCIS (Netherlands)
Lefeber, A.A.J.
2000-01-01
The subject of this thesis is the design of tracking controllers for certain classes of mechanical systems. The thesis consists of two parts. In the first part an accurate mathematical model of the mechanical system under consideration is assumed to be given. The goal is to follow a certain
11. Distributed Adaptive Neural Control for Stochastic Nonlinear Multiagent Systems.
Science.gov (United States)
Wang, Fang; Chen, Bing; Lin, Chong; Li, Xuehua
2016-11-14
In this paper, a consensus tracking problem of nonlinear multiagent systems is investigated under a directed communication topology. All the followers are modeled by stochastic nonlinear systems in nonstrict feedback form, where nonlinearities and stochastic disturbance terms are totally unknown. Based on the structural characteristic of neural networks (in Lemma 4), a novel distributed adaptive neural control scheme is put forward. The raised control method not only effectively handles unknown nonlinearities in nonstrict feedback systems, but also copes with the interactions among agents and coupling terms. Based on the stochastic Lyapunov functional method, it is indicated that all the signals of the closed-loop system are bounded in probability and all followers' outputs are convergent to a neighborhood of the output of leader. At last, the efficiency of the control method is testified by a numerical example.
12. Mathematical Systems Theory : from Behaviors to Nonlinear Control
CERN Document Server
Julius, A; Pasumarthy, Ramkrishna; Rapisarda, Paolo; Scherpen, Jacquelien
2015-01-01
This treatment of modern topics related to mathematical systems theory forms the proceedings of a workshop, Mathematical Systems Theory: From Behaviors to Nonlinear Control, held at the University of Groningen in July 2015. The workshop celebrated the work of Professors Arjan van der Schaft and Harry Trentelman, honouring their 60th Birthdays. The first volume of this two-volume work covers a variety of topics related to nonlinear and hybrid control systems. After giving a detailed account of the state of the art in the related topic, each chapter presents new results and discusses new directions. As such, this volume provides a broad picture of the theory of nonlinear and hybrid control systems for scientists and engineers with an interest in the interdisciplinary field of systems and control theory. The reader will benefit from the expert participants’ ideas on exciting new approaches to control and system theory and their predictions of future directions for the subject that were discussed at the worksho...
13. Chaos synchronization of a new chaotic system via nonlinear control
International Nuclear Information System (INIS)
Zhang Qunjiao; Lu Junan
2008-01-01
This paper investigates chaos synchronization of a new chaotic system [Lue J, Chen G, Cheng D. A new chaotic system and beyond: the generalized Lorenz-like system. Int J Bifurcat Chaos 2004;14:1507-37]. Two kinds of novel nonlinear controllers are designed based on the Lyapunov stability theory. It can be viewed as an improvement to the existing results of reference [Park JH. Chaos synchronization of a chaotic system via nonlinear control. Chaos, Solitons and Fractals 2005;25:579-84] because we use less controllers but realize a global and exponential asymptotical synchronization. Numerical simulations are provided to show the effectiveness and advantage of this method
14. Relative controllability of nonlinear systems with delays in state and ...
African Journals Online (AJOL)
In this work, sufficient conditions are developed for the relative controllability of perturbed nonlinear systems with time varying multiple delays in control with the perturbation function having implicit derivative with delays depending on both state and control variable, using Darbo's fixed points theorem. Journal of the Nigerian ...
15. Relative controllability of nonlinear neutral systems with distributed ...
African Journals Online (AJOL)
In this paper we study the relative controllability of nonlinear neutral system with distributed and multiple lumped time varying delays in control. Using Schauder's fixed point theorem sufficient conditions for relative controllability in a given time interval are formulated and proved. Journal of the Nigerian Association of ...
16. Nonlinear control for a class of hydraulic servo system.
Science.gov (United States)
Yu, Hong; Feng, Zheng-jin; Wang, Xu-yong
2004-11-01
The dynamics of hydraulic systems are highly nonlinear and the system may be subjected to non-smooth and discontinuous nonlinearities due to directional change of valve opening, friction, etc. Aside from the nonlinear nature of hydraulic dynamics, hydraulic servo systems also have large extent of model uncertainties. To address these challenging issues, a robust state-feedback controller is designed by employing backstepping design technique such that the system output tracks a given signal arbitrarily well, and all signals in the closed-loop system remain bounded. Moreover, a relevant disturbance attenuation inequality is satisfied by the closed-loop signals. Compared with previously proposed robust controllers, this paper's robust controller based on backstepping recursive design method is easier to design, and is more suitable for implementation.
17. Chaos synchronization of a chaotic system via nonlinear control
International Nuclear Information System (INIS)
Park, Ju H.
2005-01-01
In this letter, the problem of chaos synchronization of a chaotic system which is proposed by Lue et al. [Int J Bifurcat Chaos 2004;14:1507] is considered. A novel nonlinear controller is designed based on the Lyapunov stability theory. The proposed controller ensures that the states of the controlled chaotic slave system asymptotically synchronizes the states of the master system. A numerical example is given to illuminate the design procedure and advantage of the result derived
18. Nonlinear State Space Modeling and System Identification for Electrohydraulic Control
Directory of Open Access Journals (Sweden)
Jun Yan
2013-01-01
Full Text Available The paper deals with nonlinear modeling and identification of an electrohydraulic control system for improving its tracking performance. We build the nonlinear state space model for analyzing the highly nonlinear system and then develop a Hammerstein-Wiener (H-W model which consists of a static input nonlinear block with two-segment polynomial nonlinearities, a linear time-invariant dynamic block, and a static output nonlinear block with single polynomial nonlinearity to describe it. We simplify the H-W model into a linear-in-parameters structure by using the key term separation principle and then use a modified recursive least square method with iterative estimation of internal variables to identify all the unknown parameters simultaneously. It is found that the proposed H-W model approximates the actual system better than the independent Hammerstein, Wiener, and ARX models. The prediction error of the H-W model is about 13%, 54%, and 58% less than the Hammerstein, Wiener, and ARX models, respectively.
19. Distributed control design for nonlinear output agreement in convergent systems
NARCIS (Netherlands)
Weitenberg, Erik; De Persis, Claudio
2015-01-01
This work studies the problem of output agreement in homogeneous networks of nonlinear dynamical systems under time-varying disturbances using controllers placed at the nodes of the networks. For the class of contractive systems, necessary and sufficient conditions for output agreement are derived,
20. Networked Predictive Control for Nonlinear Systems With Arbitrary Region Quantizers.
Science.gov (United States)
Yang, Hongjiu; Xu, Yang; Xia, Yuanqing; Zhang, Jinhui
2017-04-06
In this paper, networked predictive control is investigated for planar nonlinear systems with quantization by an extended state observer (ESO). The ESO is used not only to deal with nonlinear terms but also to generate predictive states for dealing with network-induced delays. Two arbitrary region quantizers are applied to take effective values of signals in forward channel and feedback channel, respectively. Based on a "zoom" strategy, sufficient conditions are given to guarantee stabilization of the closed-loop networked control system with quantization. A simulation example is proposed to exhibit advantages and availability of the results.
1. Fault detection and fault-tolerant control for nonlinear systems
CERN Document Server
Li, Linlin
2016-01-01
Linlin Li addresses the analysis and design issues of observer-based FD and FTC for nonlinear systems. The author analyses the existence conditions for the nonlinear observer-based FD systems to gain a deeper insight into the construction of FD systems. Aided by the T-S fuzzy technique, she recommends different design schemes, among them the L_inf/L_2 type of FD systems. The derived FD and FTC approaches are verified by two benchmark processes. Contents Overview of FD and FTC Technology Configuration of Nonlinear Observer-Based FD Systems Design of L2 nonlinear Observer-Based FD Systems Design of Weighted Fuzzy Observer-Based FD Systems FTC Configurations for Nonlinear Systems< Application to Benchmark Processes Target Groups Researchers and students in the field of engineering with a focus on fault diagnosis and fault-tolerant control fields The Author Dr. Linlin Li completed her dissertation under the supervision of Prof. Steven X. Ding at the Faculty of Engineering, University of Duisburg-Essen, Germany...
2. Robust Nonlinear Control with Compensation Operator for a Peltier System
Directory of Open Access Journals (Sweden)
Sheng-Jun Wen
2014-01-01
Full Text Available Robust nonlinear control with compensation operator is presented for a Peltier actuated system, where the compensation operator is designed by using a predictive model on heat radiation. For the Peltier system, the heat radiation is related to the fourth power of temperature. So, the heat radiation is affected evidently by the temperature when it is high and temperature difference between the system and environment is large. A new nonlinear model with the heat radiation is set up for the system according to some thermal conduction laws. To ensure robust stability of the nonlinear system, operator based robust right coprime factorization design is considered. Also, a compensation operator based on a predictive model is proposed to cancel effect of the heat radiation, where the predictive model is set up by using radial basis kernel function based SVM (support vector machine method. Finally, simulation results are given to show the effectiveness of the proposed scheme.
3. Modelling and control of a nonlinear magnetostrictive actuator system
Science.gov (United States)
Ramli, M. H. M.; Majeed, A. P. P. Abdul; Anuar, M. A. M.; Mohamed, Z.
2018-04-01
This paper explores the implementation of a feedforward control method to a nonlinear control system, in particular, Magnetostrictive Actuators (MA) that has excellent properties of energy conversion between the mechanical and magnetic form through magnetostriction effects which could be used in actuating and sensing application. MA is known to exhibit hysteresis behaviour and it is rate dependent (the level of hysteresis depends closely on the rate of input excitation frequency). This is, nonetheless, an undesirable behaviour and has to be eliminated in realising high precision application. The MA is modelled by a phenomenological modelling approach via Prandtl-Ishlinskii (P-I) operator to characterise the hysteresis nonlinearities. A feedforward control strategy is designed and implemented to linearize and eliminate the hysteresis by model inversion. The results show that the P-I operator has the capability to model the hysteretic nonlinearity of MA with an acceptable accuracy. Furthermore, the proposed control scheme has demonstrated to be effective in providing superior trajectory tracking.
4. Chaotic dynamics and chaos control in nonlinear laser systems
International Nuclear Information System (INIS)
Fang Jinqing; Yao Weiguang
2001-01-01
Chaotic dynamics and chaos control have become a great challenge in nonlinear laser systems and its advances are reviewed mainly based on the ring cavity laser systems. The principle and stability conditions for time-delay feedback control are analyzed and applied to chaos control in the laser systems. Other advanced methods of chaos control, such as weak spatial perturbation and occasional proportional feedback technique, are discussed. Prospects of chaos control for application (such as improvement of laser power and performance, synchronized chaos secure communication and information processing) are pointed out finally
5. Chaos synchronizations of chaotic systems via active nonlinear control
International Nuclear Information System (INIS)
Huang, J; Xiao, T J
2008-01-01
This paper not only investigates the chaos synchronization between two LCC chaotic systems, but also discusses the chaos synchronization between LCC system and Genesio system. Some novel active nonlinear controllers are designed to achieve synchronizations between drive and response systems effectively. Moreover, the sufficient conditions of synchronizations are derived by using Lyapunov stability theorem. Numerical simulations are presented to verify the theoretical analysis, which shows that the synchronization schemes are global effective
6. Probabilistic DHP adaptive critic for nonlinear stochastic control systems.
Science.gov (United States)
Herzallah, Randa
2013-06-01
Following the recently developed algorithms for fully probabilistic control design for general dynamic stochastic systems (Herzallah & Káarnáy, 2011; Kárný, 1996), this paper presents the solution to the probabilistic dual heuristic programming (DHP) adaptive critic method (Herzallah & Káarnáy, 2011) and randomized control algorithm for stochastic nonlinear dynamical systems. The purpose of the randomized control input design is to make the joint probability density function of the closed loop system as close as possible to a predetermined ideal joint probability density function. This paper completes the previous work (Herzallah & Káarnáy, 2011; Kárný, 1996) by formulating and solving the fully probabilistic control design problem on the more general case of nonlinear stochastic discrete time systems. A simulated example is used to demonstrate the use of the algorithm and encouraging results have been obtained. Copyright © 2013 Elsevier Ltd. All rights reserved.
7. Robust Stabilization of Nonlinear Systems with Uncertain Varying Control Coefficient
Directory of Open Access Journals (Sweden)
Zaiyue Yang
2014-01-01
Full Text Available This paper investigates the stabilization problem for a class of nonlinear systems, whose control coefficient is uncertain and varies continuously in value and sign. The study emphasizes the development of a robust control that consists of a modified Nussbaum function to tackle the uncertain varying control coefficient. By such a method, the finite-time escape phenomenon has been prevented when the control coefficient is crossing zero and varying its sign. The proposed control guarantees the asymptotic stabilization of the system and boundedness of all closed-loop signals. The control performance is illustrated by a numerical simulation.
8. Nonlinear control system analysis and design with Maple
NARCIS (Netherlands)
Jager, de A.G.; Houstis, E.N.; Rice, J.R.
1992-01-01
For the analysis and design of nonlinear control systems non-numerical methods are available. The required analytical computations are mostly too tedious to be done error free in a reasonable time by hand, so the use of symbolic computation programs can be of advantage. To show that the symbolic
9. Robust stabilization of nonlinear systems by quantized and ternary control
NARCIS (Netherlands)
Persis, Claudio De
2009-01-01
Results on the problem of stabilizing a nonlinear continuous-time minimum-phase system by a finite number of control or measurement values are presented. The basic tool is a discontinuous version of the so-called semi-global backstepping lemma. We derive robust practical stabilizability results by
10. Dichotomy of nonlinear systems: Application to chaos control of nonlinear electronic circuit
International Nuclear Information System (INIS)
Wang Jinzhi; Duan Zhisheng; Huang Lin
2006-01-01
In this Letter a new method of chaos control for Chua's circuit and the modified canonical Chua's electrical circuit is proposed by using the results of dichotomy in nonlinear systems. A linear feedback control based on linear matrix inequality (LMI) is given such that chaos oscillation or hyperchaos phenomenon of circuit systems injected control signal disappear. Numerical simulations are presented to illustrate the efficiency of the proposed method
11. Jump resonant frequency islands in nonlinear feedback control systems
Science.gov (United States)
Koenigsberg, W. D.; Dunn, J. C.
1975-01-01
A new type of jump resonance is predicted and observed in certain nonlinear feedback control systems. The new jump resonance characteristic is described as a 'frequency island' due to the fact that a portion of the input-output transfer characteristic is disjoint from the main body. The presence of such frequency islands was predicted by using a sinusoidal describing function characterization of the dynamics of an inertial gyro employing nonlinear ternary rebalance logic. While the general conditions under which such islands are possible has not been examined, a numerical approach is presented which can aid in establishing their presence. The existence of the frequency islands predicted for the ternary rebalanced gyro was confirmed by simulating the nonlinear system and measuring the transfer function.
12. Nonlinear dynamic analysis of 2-DOF nonlinear vibration isolation floating raft systems with feedback control
International Nuclear Information System (INIS)
Li Yingli; Xu Daolin; Fu Yiming; Zhou Jiaxi
2012-01-01
In this paper, the average method is adopted to analysis dynamic characteristics of nonlinear vibration isolation floating raft system with feedback control. The analytic results show that the purposes of reducing amplitude of oscillation and complicating the motion can be achieved by adjusting properly the system parameters, exciting frequency and control gain. The conclusions can provide some available evidences for the design and improvement of both the passive and active control of the vibration isolation systems. By altering the exciting frequency and control gain, complex motion of the system can be obtained. Numerical simulations show the system exhibits period vibration, double period vibration and quasi-period motion.
13. Boundary control of nonlinear coupled heat systems using backstepping
KAUST Repository
Bendevis, Paul
2016-10-20
A state feedback boundary controller is designed for a 2D coupled PDE system modelling heat transfer in a membrane distillation system for water desalination. Fluid is separated into two compartments with nonlinear coupling at a membrane boundary. The controller sets the temperature on one boundary in order to track a temperature difference across the membrane boundary. The control objective is achieved by an extension of backstepping methods to these coupled equations. Stability of the target system via Lyapunov like methods, and the invertibility of the integral transformation are used to show the stability of the tracking error.
14. Nonlinear Dynamics of Controlled Synchronizations of Manipulator System
Directory of Open Access Journals (Sweden)
Qingkai Han
2014-01-01
Full Text Available The nonlinear dynamics of the manipulator system which is controlled to achieve the synchronization motions is investigated in the paper. Firstly, the control strategies and modeling approaches of the manipulator system are given, in which the synchronization goal is defined by both synchronization errors and its derivatives. The synchronization controllers applied on the manipulator system include neuron synchronization controller, improved OPCL synchronization controller, and MRAC-PD synchronization controller. Then, an improved adaptive synchronized control strategy is proposed in order to estimate online the unknown structure parameters and state variables of the manipulator system and to realize the needed synchronous compensation. Furthermore, a robust adaptive synchronization controller is also researched to guarantee the dynamic stability of the system. Finally, the stability of motion synchronizations of the manipulator system possessing nonlinear component is discussed, together with the effect of control parameters and joint friction and others. Some typical motions such as motion bifurcations and the loss of synchronization of it are obtained and illustrated as periodic, multiperiodic, and/or chaotic motion patterns.
15. Discrete-Time Nonlinear Control of VSC-HVDC System
Directory of Open Access Journals (Sweden)
TianTian Qian
2015-01-01
Full Text Available Because VSC-HVDC is a kind of strong nonlinear, coupling, and multi-input multioutput (MIMO system, its control problem is always attracting much attention from scholars. And a lot of papers have done research on its control strategy in the continuous-time domain. But the control system is implemented through the computer discrete sampling in practical engineering. It is necessary to study the mathematical model and control algorithm in the discrete-time domain. The discrete mathematical model based on output feedback linearization and discrete sliding mode control algorithm is proposed in this paper. And to ensure the effectiveness of the control system in the quasi sliding mode state, the fast output sampling method is used in the output feedback. The results from simulation experiment in MATLAB/SIMULINK prove that the proposed discrete control algorithm can make the VSC-HVDC system have good static, dynamic, and robust characteristics in discrete-time domain.
16. Neural networks for feedback feedforward nonlinear control systems.
Science.gov (United States)
Parisini, T; Zoppoli, R
1994-01-01
This paper deals with the problem of designing feedback feedforward control strategies to drive the state of a dynamic system (in general, nonlinear) so as to track any desired trajectory joining the points of given compact sets, while minimizing a certain cost function (in general, nonquadratic). Due to the generality of the problem, conventional methods are difficult to apply. Thus, an approximate solution is sought by constraining control strategies to take on the structure of multilayer feedforward neural networks. After discussing the approximation properties of neural control strategies, a particular neural architecture is presented, which is based on what has been called the "linear-structure preserving principle". The original functional problem is then reduced to a nonlinear programming one, and backpropagation is applied to derive the optimal values of the synaptic weights. Recursive equations to compute the gradient components are presented, which generalize the classical adjoint system equations of N-stage optimal control theory. Simulation results related to nonlinear nonquadratic problems show the effectiveness of the proposed method.
17. Prediction-Based Control for Nonlinear Systems with Input Delay
Directory of Open Access Journals (Sweden)
2017-01-01
Full Text Available This work has two primary objectives. First, it presents a state prediction strategy for a class of nonlinear Lipschitz systems subject to constant time delay in the input signal. As a result of a suitable change of variable, the state predictor asymptotically provides the value of the state τ units of time ahead. Second, it proposes a solution to the stabilization and trajectory tracking problems for the considered class of systems using predicted states. The predictor-controller convergence is proved by considering a complete Lyapunov functional. The proposed predictor-based controller strategy is evaluated using numerical simulations.
18. Global chaos synchronization of new chaotic systems via nonlinear control
International Nuclear Information System (INIS)
Chen, H.-K.
2005-01-01
Nonlinear control is an effective method for making two identical chaotic systems or two different chaotic systems be synchronized. However, this method assumes that the Lyapunov function of error dynamic (e) of synchronization is always formed as V (e) = 1/2e T e. In this paper, modification based on Lyapunov stability theory to design a controller is proposed in order to overcome this limitation. The method has been applied successfully to make two identical new systems and two different chaotic systems (new system and Lorenz system) globally asymptotically synchronized. Since the Lyapunov exponents are not required for the calculation, this method is effective and convenient to synchronize two identical systems and two different chaotic systems. Numerical simulations are also given to validate the proposed synchronization approach
19. Bio-inspired spiking neural network for nonlinear systems control.
Science.gov (United States)
Pérez, Javier; Cabrera, Juan A; Castillo, Juan J; Velasco, Juan M
2018-08-01
Spiking neural networks (SNN) are the third generation of artificial neural networks. SNN are the closest approximation to biological neural networks. SNNs make use of temporal spike trains to command inputs and outputs, allowing a faster and more complex computation. As demonstrated by biological organisms, they are a potentially good approach to designing controllers for highly nonlinear dynamic systems in which the performance of controllers developed by conventional techniques is not satisfactory or difficult to implement. SNN-based controllers exploit their ability for online learning and self-adaptation to evolve when transferred from simulations to the real world. SNN's inherent binary and temporary way of information codification facilitates their hardware implementation compared to analog neurons. Biological neural networks often require a lower number of neurons compared to other controllers based on artificial neural networks. In this work, these neuronal systems are imitated to perform the control of non-linear dynamic systems. For this purpose, a control structure based on spiking neural networks has been designed. Particular attention has been paid to optimizing the structure and size of the neural network. The proposed structure is able to control dynamic systems with a reduced number of neurons and connections. A supervised learning process using evolutionary algorithms has been carried out to perform controller training. The efficiency of the proposed network has been verified in two examples of dynamic systems control. Simulations show that the proposed control based on SNN exhibits superior performance compared to other approaches based on Neural Networks and SNNs. Copyright © 2018 Elsevier Ltd. All rights reserved.
20. Adaptive Fractional Fuzzy Sliding Mode Control for Multivariable Nonlinear Systems
Directory of Open Access Journals (Sweden)
Junhai Luo
2014-01-01
Full Text Available This paper presents a robust adaptive fuzzy sliding mode control method for a class of uncertain nonlinear systems. The fractional order calculus is employed in the parameter updating stage. The underlying stability analysis as well as parameter update law design is carried out by Lyapunov based technique. In the simulation, two examples including a comparison with the traditional integer order counterpart are given to show the effectiveness of the proposed method. The main contribution of this paper consists in the control performance is better for the fractional order updating law than that of traditional integer order.
1. Data-Driven H∞ Control for Nonlinear Distributed Parameter Systems.
Science.gov (United States)
Luo, Biao; Huang, Tingwen; Wu, Huai-Ning; Yang, Xiong
2015-11-01
The data-driven H∞ control problem of nonlinear distributed parameter systems is considered in this paper. An off-policy learning method is developed to learn the H∞ control policy from real system data rather than the mathematical model. First, Karhunen-Loève decomposition is used to compute the empirical eigenfunctions, which are then employed to derive a reduced-order model (ROM) of slow subsystem based on the singular perturbation theory. The H∞ control problem is reformulated based on the ROM, which can be transformed to solve the Hamilton-Jacobi-Isaacs (HJI) equation, theoretically. To learn the solution of the HJI equation from real system data, a data-driven off-policy learning approach is proposed based on the simultaneous policy update algorithm and its convergence is proved. For implementation purpose, a neural network (NN)- based action-critic structure is developed, where a critic NN and two action NNs are employed to approximate the value function, control, and disturbance policies, respectively. Subsequently, a least-square NN weight-tuning rule is derived with the method of weighted residuals. Finally, the developed data-driven off-policy learning approach is applied to a nonlinear diffusion-reaction process, and the obtained results demonstrate its effectiveness.
2. Non-linear and adaptive control of a refrigeration system
DEFF Research Database (Denmark)
Rasmussen, Henrik; Larsen, Lars F. S.
2011-01-01
are capable of adapting to variety of systems. This paper proposes a novel method for superheat and capacity control of refrigeration systems; namely by controlling the superheat by the compressor speed and capacity by the refrigerant flow. A new low order nonlinear model of the evaporator is developed......In a refrigeration process heat is absorbed in an evaporator by evaporating a flow of liquid refrigerant at low pressure and temperature. Controlling the evaporator inlet valve and the compressor in such a way that a high degree of liquid filling in the evaporator is obtained at all compressor...... capacities ensures a high energy efficiency. The level of liquid filling is indirectly measured by the superheat. Introduction of variable speed compressors and electronic expansion valves enables the use of more sophisticated control algorithms, giving a higher degree of performance and just as important...
3. Fuzzy model-based servo and model following control for nonlinear systems.
Science.gov (United States)
Ohtake, Hiroshi; Tanaka, Kazuo; Wang, Hua O
2009-12-01
This correspondence presents servo and nonlinear model following controls for a class of nonlinear systems using the Takagi-Sugeno fuzzy model-based control approach. First, the construction method of the augmented fuzzy system for continuous-time nonlinear systems is proposed by differentiating the original nonlinear system. Second, the dynamic fuzzy servo controller and the dynamic fuzzy model following controller, which can make outputs of the nonlinear system converge to target points and to outputs of the reference system, respectively, are introduced. Finally, the servo and model following controller design conditions are given in terms of linear matrix inequalities. Design examples illustrate the utility of this approach.
4. Adaptive Output Tracking Control for Nonlinear Systems with Failed Actuators and Aircraft Flight System Applications
Directory of Open Access Journals (Sweden)
Chuanjing Hou
2015-01-01
Full Text Available An adaptive failure compensation scheme using output feedback is proposed for a class of nonlinear systems with nonlinearities depending on the unmeasured states of systems. Adaptive high-gain K-filters are presented to suppress the nonlinearities while the proposed backstepping adaptive high-gain controller guarantees the stability of the closed-loop system and small tracking errors. Simulation results verify that the adaptive failure compensation scheme is effective.
5. Adaptive Output Tracking Control for Nonlinear Systems with Failed Actuators and Aircraft Flight System Applications
OpenAIRE
Hou, Chuanjing; Hu, Lisheng; Zhang, Yingwei
2015-01-01
An adaptive failure compensation scheme using output feedback is proposed for a class of nonlinear systems with nonlinearities depending on the unmeasured states of systems. Adaptive high-gain K-filters are presented to suppress the nonlinearities while the proposed backstepping adaptive high-gain controller guarantees the stability of the closed-loop system and small tracking errors. Simulation results verify that the adaptive failure compensation scheme is effective.
6. Distributed Synchronization Control of Multiagent Systems With Unknown Nonlinearities.
Science.gov (United States)
Su, Shize; Lin, Zongli; Garcia, Alfredo
2016-01-01
This paper revisits the distributed adaptive control problem for synchronization of multiagent systems where the dynamics of the agents are nonlinear, nonidentical, unknown, and subject to external disturbances. Two communication topologies, represented, respectively, by a fixed strongly-connected directed graph and by a switching connected undirected graph, are considered. Under both of these communication topologies, we use distributed neural networks to approximate the uncertain dynamics. Decentralized adaptive control protocols are then constructed to solve the cooperative tracker problem, the problem of synchronization of all follower agents to a leader agent. In particular, we show that, under the proposed decentralized control protocols, the synchronization errors are ultimately bounded, and their ultimate bounds can be reduced arbitrarily by choosing the control parameter appropriately. Simulation study verifies the effectiveness of our proposed protocols.
7. Robust Control Design for Uncertain Nonlinear Dynamic Systems
Science.gov (United States)
Kenny, Sean P.; Crespo, Luis G.; Andrews, Lindsey; Giesy, Daniel P.
2012-01-01
Robustness to parametric uncertainty is fundamental to successful control system design and as such it has been at the core of many design methods developed over the decades. Despite its prominence, most of the work on robust control design has focused on linear models and uncertainties that are non-probabilistic in nature. Recently, researchers have acknowledged this disparity and have been developing theory to address a broader class of uncertainties. This paper presents an experimental application of robust control design for a hybrid class of probabilistic and non-probabilistic parametric uncertainties. The experimental apparatus is based upon the classic inverted pendulum on a cart. The physical uncertainty is realized by a known additional lumped mass at an unknown location on the pendulum. This unknown location has the effect of substantially altering the nominal frequency and controllability of the nonlinear system, and in the limit has the capability to make the system neutrally stable and uncontrollable. Another uncertainty to be considered is a direct current motor parameter. The control design objective is to design a controller that satisfies stability, tracking error, control power, and transient behavior requirements for the largest range of parametric uncertainties. This paper presents an overview of the theory behind the robust control design methodology and the experimental results.
8. Nonlinear H-infinity control, Hamiltonian systems and Hamilton-Jacobi equations
CERN Document Server
Aliyu, MDS
2011-01-01
A comprehensive overview of nonlinear Haeu control theory for both continuous-time and discrete-time systems, Nonlinear Haeu-Control, Hamiltonian Systems and Hamilton-Jacobi Equations covers topics as diverse as singular nonlinear Haeu-control, nonlinear Haeu -filtering, mixed H2/ Haeu-nonlinear control and filtering, nonlinear Haeu-almost-disturbance-decoupling, and algorithms for solving the ubiquitous Hamilton-Jacobi-Isaacs equations. The link between the subject and analytical mechanics as well as the theory of partial differential equations is also elegantly summarized in a single chapter
9. Nonlinear stochastic systems with incomplete information filtering and control
CERN Document Server
Shen, Bo; Shu, Huisheng
2013-01-01
Nonlinear Stochastic Processes addresses the frequently-encountered problem of incomplete information. The causes of this problem considered here include: missing measurements; sensor delays and saturation; quantization effects; and signal sampling. Divided into three parts, the text begins with a focus on H∞ filtering and control problems associated with general classes of nonlinear stochastic discrete-time systems. Filtering problems are considered in the second part, and in the third the theory and techniques previously developed are applied to the solution of issues arising in complex networks with the design of sampled-data-based controllers and filters. Among its highlights, the text provides: · a unified framework for handling filtering and control problems in complex communication networks with limited bandwidth; · new concepts such as random sensor and signal saturations for more realistic modeling; and · demonstration of the use of techniques such...
10. Nonlinear systems
CERN Document Server
Palmero, Faustino; Lemos, M; Sánchez-Rey, Bernardo; Casado-Pascual, Jesús
2018-01-01
This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many new developments. While volume 1 concentrates on mathematical theory and computational techniques and challenges, which are essential for the study of nonlinear science, this second volume deals with nonlinear excitations in several fields. These excitations can be localized and transport energy and matter in the form of breathers, solitons, kinks or quodons with very different characteristics, which are discussed in the book. They can also transport electric charge, in which case they are known as polarobreathers or solectrons. Nonlinear excitations can influence function and structure in biology, as for example, protein folding. In crystals and other condensed matter, they can modify transport properties, reaction kinetics and interact with defects. There are also engineering applications in electric lattices, Josephson junction a...
11. Online prediction and control in nonlinear stochastic systems
DEFF Research Database (Denmark)
Nielsen, Torben Skov
2002-01-01
speed and the relationship between (primarily) wind speed and wind power (the power curve). In paper G the model parameters are estimated using a RLS algorithm and any systematic time-variation of the model parameters is disregarded. Two di erent parameterizations of the power curve is considered...... are estimated using the algorithm proposed in paper C. The power curve and the diurnal variation of wind speed is estimated separately using the local polynomial regression procedure described in paper A . In paper J the parameters of the prediction model is assumed to be smooth functions of wind direction (and......The present thesis consists of a summary report and ten research papers. The subject of the thesis is on-line prediction and control of non-linear and non-stationary systems based on stochastic modelling. The thesis consists of three parts where the rst part deals with on-line estimation in linear...
12. Nonlinear control and filtering using differential flatness approaches applications to electromechanical systems
CERN Document Server
Rigatos, Gerasimos G
2015-01-01
This monograph presents recent advances in differential flatness theory and analyzes its use for nonlinear control and estimation. It shows how differential flatness theory can provide solutions to complicated control problems, such as those appearing in highly nonlinear multivariable systems and distributed-parameter systems. Furthermore, it shows that differential flatness theory makes it possible to perform filtering and state estimation for a wide class of nonlinear dynamical systems and provides several descriptive test cases. The book focuses on the design of nonlinear adaptive controllers and nonlinear filters, using exact linearization based on differential flatness theory. The adaptive controllers obtained can be applied to a wide class of nonlinear systems with unknown dynamics, and assure reliable functioning of the control loop under uncertainty and varying operating conditions. The filters obtained outperform other nonlinear filters in terms of accuracy of estimation and computation speed. The bo...
13. Disturbance attenuation of nonlinear control systems using an observer-based fuzzy feedback linearization control
International Nuclear Information System (INIS)
Chen, C.-C.; Hsu, C.-H.; Chen, Y.-J.; Lin, Y.-F.
2007-01-01
The almost disturbance decoupling and trajectory tracking of nonlinear control systems using an observer-based fuzzy feedback linearization control (FLC) is developed. Because not all of the state variables of the nonlinear dynamic equations are available, a nonlinear state observer is employed to estimate the state variables. The feedback linearization control guarantees the almost disturbance decoupling performance and the uniform ultimate bounded stability of the tracking error system. Once the tracking errors are driven to touch the global final attractor with the desired radius, the fuzzy logic control is immediately applied via human expert's knowledge to improve the convergence rate. One example, which cannot be solved by the first paper on the almost disturbance decoupling problem, is proposed in this paper to exploit the fact that the tracking and the almost disturbance decoupling performances are easily achieved by our proposed approach. In order to demonstrate the practical applicability, the study has investigated a pendulum control system
14. On nonlinear control design for autonomous chaotic systems of integer and fractional orders
International Nuclear Information System (INIS)
2003-01-01
In this paper, we address the problem of chaos control for autonomous nonlinear chaotic systems. We use the recursive 'backstepping' method of nonlinear control design to derive the nonlinear controllers. The controller effect is to stabilize the output chaotic trajectory by driving it to the nearest equilibrium point in the basin of attraction. We study two nonlinear chaotic systems: an electronic chaotic oscillator model, and a mechanical chaotic 'jerk' model. We demonstrate the robustness of the derived controllers against system order reduction arising from the use of fractional integrators in the system models. Our results are validated via numerical simulations
15. Controlling wave propagation through nonlinear engineered granular systems
Science.gov (United States)
Leonard, Andrea
We study the fundamental dynamic behavior of a special class of ordered granular systems in order to design new, structured materials with unique physical properties. The dynamic properties of granular systems are dictated by the nonlinear, Hertzian, potential in compression and zero tensile strength resulting from the discrete material structure. Engineering the underlying particle arrangement of granular systems allows for unique dynamic properties, not observed in natural, disordered granular media. While extensive studies on 1D granular crystals have suggested their usefulness for a variety of engineering applications, considerably less attention has been given to higher-dimensional systems. The extension of these studies in higher dimensions could enable the discovery of richer physical phenomena not possible in 1D, such as spatial redirection and anisotropic energy trapping. We present experiments, numerical simulation (based on a discrete particle model), and in some cases theoretical predictions for several engineered granular systems, studying the effects of particle arrangement on the highly nonlinear transient wave propagation to develop means for controlling the wave propagation pathways. The first component of this thesis studies the stress wave propagation resulting from a localized impulsive loading for three different 2D particle lattice structures: square, centered square, and hexagonal granular crystals. By varying the lattice structure, we observe a wide range of properties for the propagating stress waves: quasi-1D solitary wave propagation, fully 2D wave propagation with tunable wave front shapes, and 2D pulsed wave propagation. Additionally the effects of weak disorder, inevitably present in real granular systems, are investigated. The second half of this thesis studies the solitary wave propagation through 2D and 3D ordered networks of granular chains, reducing the effective density compared to granular crystals by selectively placing wave
16. Distributed Cooperative Control of Nonlinear and Non-identical Multi-agent Systems
DEFF Research Database (Denmark)
Bidram, Ali; Lewis, Frank; Davoudi, Ali
2013-01-01
This paper exploits input-output feedback linearization technique to implement distributed cooperative control of multi-agent systems with nonlinear and non-identical dynamics. Feedback linearization transforms the synchronization problem for a nonlinear and heterogeneous multi-agent system...... for electric power microgrids. The effectiveness of the proposed control is verified by simulating a microgrid test system....
17. Dynamic Output Feedback Control for Nonlinear Networked Control Systems with Random Packet Dropout and Random Delay
Directory of Open Access Journals (Sweden)
Shuiqing Yu
2013-01-01
Full Text Available This paper investigates the dynamic output feedback control for nonlinear networked control systems with both random packet dropout and random delay. Random packet dropout and random delay are modeled as two independent random variables. An observer-based dynamic output feedback controller is designed based upon the Lyapunov theory. The quantitative relationship of the dropout rate, transition probability matrix, and nonlinear level is derived by solving a set of linear matrix inequalities. Finally, an example is presented to illustrate the effectiveness of the proposed method.
18. Analysis and control of nonlinear systems a flatness-based approach
CERN Document Server
Levine, Jean
2009-01-01
This book examines control of nonlinear systems. Coverage ranges from mathematical system theory to practical industrial control applications. The author offers web-based videos illustrating some dynamical aspects and case studies in simulation.
19. Control Law Design for Twin Rotor MIMO System with Nonlinear Control Strategy
Directory of Open Access Journals (Sweden)
M. Ilyas
2016-01-01
Full Text Available Modeling of complex air vehicles is a challenging task due to high nonlinear behavior and significant coupling effect between rotors. Twin rotor multi-input multioutput system (TRMS is a laboratory setup designed for control experiments, which resembles a helicopter with unstable, nonlinear, and coupled dynamics. This paper focuses on the design and analysis of sliding mode control (SMC and backstepping controller for pitch and yaw angle control of main and tail rotor of the TRMS under parametric uncertainty. The proposed control strategy with SMC and backstepping achieves all mentioned limitations of TRMS. Result analysis of SMC and backstepping control schemes elucidates that backstepping provides efficient behavior with the parametric uncertainty for twin rotor system. Chattering and oscillating behaviors of SMC are removed with the backstepping control scheme considering the pitch and yaw angle for TRMS.
20. Recent results on nonlinear delay control systems in honor of Miroslav Krstic
CERN Document Server
Pepe, Pierdomenico; Mazenc, Frederic; Karafyllis, Iasson
2016-01-01
This volume collects recent advances in nonlinear delay systems, with an emphasis on constructive generalized Lyapunov and predictive approaches that certify stability properties. The book is written by experts in the field and includes two chapters by Miroslav Krstic, to whom this volume is dedicated. This volume is suitable for all researchers in mathematics and engineering who deal with nonlinear delay control problems and students who would like to understand the current state of the art in the control of nonlinear delay systems.
1. Globally Asymptotic Stability of Stochastic Nonlinear Systems with Time-Varying Delays via Output Feedback Control
Directory of Open Access Journals (Sweden)
Mingzhu Song
2016-01-01
Full Text Available We address the problem of globally asymptotic stability for a class of stochastic nonlinear systems with time-varying delays. By the backstepping method and Lyapunov theory, we design a linear output feedback controller recursively based on the observable linearization for a class of stochastic nonlinear systems with time-varying delays to guarantee that the closed-loop system is globally asymptotically stable in probability. In particular, we extend the deterministic nonlinear system to stochastic nonlinear systems with time-varying delays. Finally, an example and its simulations are given to illustrate the theoretical results.
2. Model-based nonlinear control of hydraulic servo systems: Challenges, developments and perspectives
Science.gov (United States)
Yao, Jianyong
2018-06-01
Hydraulic servo system plays a significant role in industries, and usually acts as a core point in control and power transmission. Although linear theory-based control methods have been well established, advanced controller design methods for hydraulic servo system to achieve high performance is still an unending pursuit along with the development of modern industry. Essential nonlinearity is a unique feature and makes model-based nonlinear control more attractive, due to benefit from prior knowledge of the servo valve controlled hydraulic system. In this paper, a discussion for challenges in model-based nonlinear control, latest developments and brief perspectives of hydraulic servo systems are presented: Modelling uncertainty in hydraulic system is a major challenge, which includes parametric uncertainty and time-varying disturbance; some specific requirements also arise ad hoc difficulties such as nonlinear friction during low velocity tracking, severe disturbance, periodic disturbance, etc.; to handle various challenges, nonlinear solutions including parameter adaptation, nonlinear robust control, state and disturbance observation, backstepping design and so on, are proposed and integrated, theoretical analysis and lots of applications reveal their powerful capability to solve pertinent problems; and at the end, some perspectives and associated research topics (measurement noise, constraints, inner valve dynamics, input nonlinearity, etc.) in nonlinear hydraulic servo control are briefly explored and discussed.
3. Real time simulation of nonlinear generalized predictive control for wind energy conversion system with nonlinear observer.
Science.gov (United States)
Ouari, Kamel; Rekioua, Toufik; Ouhrouche, Mohand
2014-01-01
In order to make a wind power generation truly cost-effective and reliable, an advanced control techniques must be used. In this paper, we develop a new control strategy, using nonlinear generalized predictive control (NGPC) approach, for DFIG-based wind turbine. The proposed control law is based on two points: NGPC-based torque-current control loop generating the rotor reference voltage and NGPC-based speed control loop that provides the torque reference. In order to enhance the robustness of the controller, a disturbance observer is designed to estimate the aerodynamic torque which is considered as an unknown perturbation. Finally, a real-time simulation is carried out to illustrate the performance of the proposed controller. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.
4. Decentralized adaptive control of interconnected nonlinear systems with unknown control directions.
Science.gov (United States)
Huang, Jiangshuai; Wang, Qing-Guo
2018-03-01
In this paper, we propose a decentralized adaptive control scheme for a class of interconnected strict-feedback nonlinear systems without a priori knowledge of subsystems' control directions. To address this problem, a novel Nussbaum-type function is proposed and a key theorem is drawn which involves quantifying the interconnections of multiple Nussbaum-type functions of the subsystems with different control directions in a single inequality. Global stability of the closed-loop system and asymptotic stabilization of subsystems' output are proved and a simulation example is given to illustrate the effectiveness of the proposed control scheme. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.
5. Solving Boundary Value Problem for a Nonlinear Stationary Controllable System with Synthesizing Control
Directory of Open Access Journals (Sweden)
Alexander N. Kvitko
2017-01-01
Full Text Available An algorithm for constructing a control function that transfers a wide class of stationary nonlinear systems of ordinary differential equations from an initial state to a final state under certain control restrictions is proposed. The algorithm is designed to be convenient for numerical implementation. A constructive criterion of the desired transfer possibility is presented. The problem of an interorbital flight is considered as a test example and it is simulated numerically with the presented method.
6. Dual PD Control Regulation with Nonlinear Compensation for a Ball and Plate System
Directory of Open Access Journals (Sweden)
Sergio Galvan-Colmenares
2014-01-01
Full Text Available The normal proportional derivative (PD control is modified to a new dual form for the regulation of a ball and plate system. First, to analyze this controller, a novel complete nonlinear model of the ball and plate system is obtained. Second, an asymptotic stable dual PD control with a nonlinear compensation is developed. Finally, the experimental results of ball and plate system are provided to verify the effectiveness of the proposed methodology.
7. Computer-aided Nonlinear Control System Design Using Describing Function Models
CERN Document Server
Nassirharand, Amir
2012-01-01
A systematic computer-aided approach provides a versatile setting for the control engineer to overcome the complications of controller design for highly nonlinear systems. Computer-aided Nonlinear Control System Design provides such an approach based on the use of describing functions. The text deals with a large class of nonlinear systems without restrictions on the system order, the number of inputs and/or outputs or the number, type or arrangement of nonlinear terms. The strongly software-oriented methods detailed facilitate fulfillment of tight performance requirements and help the designer to think in purely nonlinear terms, avoiding the expedient of linearization which can impose substantial and unrealistic model limitations and drive up the cost of the final product. Design procedures are presented in a step-by-step algorithmic format each step being a functional unit with outputs that drive the other steps. This procedure may be easily implemented on a digital computer with example problems from mecha...
8. Nonlinear control synthesis for electrical power systems using controllable series capacitors
Energy Technology Data Exchange (ETDEWEB)
Manjarekar, N.S.; Banavar, Ravi N. [Indian Institute of Technology Bombay, Mumbai (India). Systems and Control Engineering
2012-07-01
In this work we derive asymptotically stabilizing control laws for electrical power systems using two nonlinear control synthesis techniques. For this transient stabilization problem the actuator considered is a power electronic device, a controllable series capacitor (CSC). The power system is described using two different nonlinear models - the second order swing equation and the third order flux-decay model. To start with, the CSC is modeled by the injection model which is based on the assumption that the CSC dynamics is very fast as compared to the dynamics of the power system and hence can be approximated by an algebraic equation. Here, by neglecting the CSC dynamics, the input vector g(x) in the open loop system takes a complex form - the injection model. Using this model, interconnection and damping assignment passivity-based control (IDA-PBC) methodology is demonstrated on two power systems: a single machine infinite bus (SMIB) system and a two machine system. Further, IDA-PBC is used to derive stabilizing controllers for power systems, where the CSC dynamics are included as a first order system. Next, we consider a different control methodology, immersion and invariance (I and I), to synthesize an asymptotically stabilizing control law for the SMIB system with a CSC. The CSC is described by a first order system. As a generalization of I and I, we incorporate the power balance algebraic constraints in the load bus to the SMIB swing equation, and extend the design philosophy to a class of differential algebraic systems. The proposed result is then demonstrated on another example: a two-machine system with two load buses and a CSC. The controller performances are validated through simulations for all cases.
9. TS Fuzzy Model-Based Controller Design for a Class of Nonlinear Systems Including Nonsmooth Functions
DEFF Research Database (Denmark)
Vafamand, Navid; Asemani, Mohammad Hassan; Khayatiyan, Alireza
2018-01-01
This paper proposes a novel robust controller design for a class of nonlinear systems including hard nonlinearity functions. The proposed approach is based on Takagi-Sugeno (TS) fuzzy modeling, nonquadratic Lyapunov function, and nonparallel distributed compensation scheme. In this paper, a novel...... criterion, new robust controller design conditions in terms of linear matrix inequalities are derived. Three practical case studies, electric power steering system, a helicopter model and servo-mechanical system, are presented to demonstrate the importance of such class of nonlinear systems comprising...
10. Control of Non-linear Marine Cooling System
DEFF Research Database (Denmark)
Hansen, Michael; Stoustrup, Jakob; Bendtsen, Jan Dimon
2011-01-01
We consider the problem of designing control laws for a marine cooling system used for cooling the main engine and auxiliary components aboard several classes of container vessels. We focus on achieving simple set point control for the system and do not consider compensation of the non-linearitie......-linearities, closed circuit flow dynamics or transport delays that are present in the system. Control laws are therefore designed using classical control theory and the performance of the design is illustrated through two simulation examples....
11. Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities
International Nuclear Information System (INIS)
Hedrih, K
2008-01-01
This paper analyses the controllability of motion of nonconservative nonlinear dynamical systems in which triggers of coupled singularities exist or appear. It is shown that the phase plane method is useful for the analysis of nonlinear dynamics of nonconservative systems with one degree of freedom of control strategies and also shows the way it can be used for controlling the relative motion in rheonomic systems having equivalent scleronomic conservative or nonconservative system For the system with one generalized coordinate described by nonlinear differential equation of nonlinear dynamics with trigger of coupled singularities, the functions of system potential energy and conservative force must satisfy some conditions defined by a Theorem on the existence of a trigger of coupled singularities and the separatrix in the form of 'an open a spiral form' of number eight. Task of the defined dynamical nonconservative system optimal control is: by using controlling force acting to the system, transfer initial state of the nonlinear dynamics of the system into the final state of the nonlinear dynamics in the minimal time for that optimal control task
12. Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities
Science.gov (United States)
Stevanović Hedrih, K.
2008-02-01
This paper analyses the controllability of motion of nonconservative nonlinear dynamical systems in which triggers of coupled singularities exist or appear. It is shown that the phase plane method is useful for the analysis of nonlinear dynamics of nonconservative systems with one degree of freedom of control strategies and also shows the way it can be used for controlling the relative motion in rheonomic systems having equivalent scleronomic conservative or nonconservative system For the system with one generalized coordinate described by nonlinear differential equation of nonlinear dynamics with trigger of coupled singularities, the functions of system potential energy and conservative force must satisfy some conditions defined by a Theorem on the existence of a trigger of coupled singularities and the separatrix in the form of "an open a spiral form" of number eight. Task of the defined dynamical nonconservative system optimal control is: by using controlling force acting to the system, transfer initial state of the nonlinear dynamics of the system into the final state of the nonlinear dynamics in the minimal time for that optimal control task
13. Active Complementary Control for Affine Nonlinear Control Systems With Actuator Faults.
Science.gov (United States)
Fan, Quan-Yong; Yang, Guang-Hong
2017-11-01
This paper is concerned with the problem of active complementary control design for affine nonlinear control systems with actuator faults. The outage and loss of effectiveness fault cases are considered. In order to achieve the performance enhancement of the faulty control system, the complementary control scheme is designed in two steps. Firstly, a novel fault estimation scheme is developed. Then, by using the fault estimations to reconstruct the faulty system dynamics and introducing a cost function as the optimization objective, a nearly optimal complementary control is obtained online based on the adaptive dynamic programming (ADP) method. Unlike most of the previous ADP methods with the addition of a probing signal, new adaptive weight update laws are derived to guarantee the convergence of neural network weights and the stability of the closed-loop system, which strongly supports the online implementation of the ADP method. Finally, two simulation examples are given to illustrate the performance and effectiveness of the proposed method.
14. A genuine nonlinear approach for controller design of a boiler-turbine system.
Science.gov (United States)
Yang, Shizhong; Qian, Chunjiang; Du, Haibo
2012-05-01
This paper proposes a genuine nonlinear approach for controller design of a drum-type boiler-turbine system. Based on a second order nonlinear model, a finite-time convergent controller is first designed to drive the states to their setpoints in a finite time. In the case when the state variables are unmeasurable, the system will be regulated using a constant controller or an output feedback controller. An adaptive controller is also designed to stabilize the system since the model parameters may vary under different operating points. The novelty of the proposed controller design approach lies in fully utilizing the system nonlinearities instead of linearizing or canceling them. In addition, the newly developed techniques for finite-time convergent controller are used to guarantee fast convergence of the system. Simulations are conducted under different cases and the results are presented to illustrate the performance of the proposed controllers. Copyright © 2011 ISA. Published by Elsevier Ltd. All rights reserved.
15. Nonlinear decentralized robust governor control for hydroturbine-generator sets in multi-machine power systems
Energy Technology Data Exchange (ETDEWEB)
Qiang Lu; Yusong Sun; Yuanzhang Sun [Tsinghua University, Beijing (China). Dept. of Electrical Engineering; Felix F Wu; Yixin Ni [University of Hong Kong (China). Dept. of Electrical and Electronic Engineering; Yokoyama, Akihiko [University of Tokyo (Japan). Dept. of Electrical Engineering; Goto, Masuo; Konishi, Hiroo [Hitachi Ltd., Tokyo (Japan). Power System Div.
2004-06-01
A novel nonlinear decentralized robust governor control for hydroturbine-generator sets in multi-machine power systems is suggested in this paper. The nonelastic water hammer effect and disturbances are considered in the modeling. The advanced differential geometry theory, nonlinear robust control theory and the dynamic feedback method are combined to solve the problem. The nonlinear decentralized robust control law for the speed governor of hydroturbine-generators has been derived. The input signals to the proposed controller are all local measurements and independent to the system parameters. The derived control law guarantees the integrated system stability with disturbance attenuation, which is significant to the real power system application. Computer tests on an 8-machine, 36-bus power system show clearly the effectiveness of the new control strategy in transient stability enhancement and disturbance attenuation. The computer test results based on the suggested controller are compared favorably with those based on the conventional linear governor control. (author)
16. Robust intelligent backstepping tracking control for uncertain non-linear chaotic systems using H∞ control technique
International Nuclear Information System (INIS)
Peng, Y.-F.
2009-01-01
The cerebellar model articulation controller (CMAC) is a non-linear adaptive system with built-in simple computation, good generalization capability and fast learning property. In this paper, a robust intelligent backstepping tracking control (RIBTC) system combined with adaptive CMAC and H ∞ control technique is proposed for a class of chaotic systems with unknown system dynamics and external disturbance. In the proposed control system, an adaptive backstepping cerebellar model articulation controller (ABCMAC) is used to mimic an ideal backstepping control (IBC), and a robust H ∞ controller is designed to attenuate the effect of the residual approximation errors and external disturbances with desired attenuation level. Moreover, the all adaptation laws of the RIBTC system are derived based on the Lyapunov stability analysis, the Taylor linearization technique and H ∞ control theory, so that the stability of the closed-loop system and H ∞ tracking performance can be guaranteed. Finally, three application examples, including a Duffing-Holmes chaotic system, a Genesio chaotic system and a Sprott circuit system, are used to demonstrate the effectiveness and performance of proposed robust control technique.
17. PWR control system design using advanced linear and non-linear methodologies
International Nuclear Information System (INIS)
Rabindran, N.; Whitmarsh-Everiss, M.J.
2004-01-01
Consideration is here given to the methodology deployed for non-linear heuristic analysis in the time domain supported by multi-variable linear control system design methods for the purposes of operational dynamics and control system analysis. This methodology is illustrated by the application of structural singular value μ analysis to Pressurised Water Reactor control system design. (author)
18. Nonlinear Control Synthesis for Electrical Power Systems Using Controllable Series Capacitors
CERN Document Server
Manjarekar, N S
2012-01-01
In this work we derive asymptotically stabilizing control laws for electrical power systems using two nonlinear control synthesis techniques. For this transient stabilization problem the actuator considered is a power electronic device, a controllable series capacitor (CSC). The power system is described using two different nonlinear models - the second order swing equation and the third order flux-decay model. To start with, the CSC is modeled by the injection model which is based on the assumption that the CSC dynamics is very fast as compared to the dynamics of the power system and hence can be approximated by an algebraic equation. Here, by neglecting the CSC dynamics, the input vector $g(x)$ in the open loop system takes a complex form - the injection model. Using this model, interconnection and damping assignment passivity-based control (IDA-PBC) methodology is demonstrated on two power systems: a single machine infinite bus (SMIB) system and a two machine system. Further, IDA-PBC is used to derive stab...
19. Controllable behaviours of rogue wave triplets in the nonautonomous nonlinear and dispersive system
International Nuclear Information System (INIS)
Dai Chaoqing; Tian Qing; Zhu Shiqun
2012-01-01
A similarity transformation connecting the variable coefficient nonlinear Schrödinger equation with the standard nonlinear Schrödinger equation is constructed. The self-similar rogue wave triplet solutions (rational solutions) are analytically obtained for the nonautonomous nonlinear and dispersive system. The controllable behaviours of rogue wave triplets in two typical soliton management systems are discussed. In the exponential dispersion decreasing fibre, three kinds of rogue wave triplets with controllable behaviours are analysed. In the periodic distributed system, the rogue wave triplets recur periodically in the form of a cluster. (paper)
20. A Study on the Analysis and Optimal Control of Nonlinear Systems via Walsh Function
Energy Technology Data Exchange (ETDEWEB)
Kim, Jin Tae; Kim, Tai Hoon; Ahn, Doo Soo [Sungkyunkwan University (Korea); Lee, Myung Kyu [Kyungsung University (Korea)
2000-07-01
This paper presents the new adaptive optimal scheme for the nonlinear systems, which is based on the Picard's iterative approximation and fast Walsh transform. It is well known that the Walsh function approach method is very difficult to apply for the analysis and optimal control of nonlinear systems. However, these problems can be easily solved by the improvement of the previous adaptive optimal scheme. The proposes method is easily applicable to the analysis and optimal control of nonlinear systems. (author). 15 refs., 6 figs., 1 tab.
1. Model Predictive Control of a Nonlinear System with Known Scheduling Variable
DEFF Research Database (Denmark)
Mirzaei, Mahmood; Poulsen, Niels Kjølstad; Niemann, Hans Henrik
2012-01-01
Model predictive control (MPC) of a class of nonlinear systems is considered in this paper. We will use Linear Parameter Varying (LPV) model of the nonlinear system. By taking the advantage of having future values of the scheduling variable, we will simplify state prediction. Consequently...... the control problem of the nonlinear system is simplied into a quadratic programming. Wind turbine is chosen as the case study and we choose wind speed as the scheduling variable. Wind speed is measurable ahead of the turbine, therefore the scheduling variable is known for the entire prediction horizon....
2. Robust approximation-free prescribed performance control for nonlinear systems and its application
Science.gov (United States)
Sun, Ruisheng; Na, Jing; Zhu, Bin
2018-02-01
This paper presents a robust prescribed performance control approach and its application to nonlinear tail-controlled missile systems with unknown dynamics and uncertainties. The idea of prescribed performance function (PPF) is incorporated into the control design, such that both the steady-state and transient control performance can be strictly guaranteed. Unlike conventional PPF-based control methods, we further tailor a recently proposed systematic control design procedure (i.e. approximation-free control) using the transformed tracking error dynamics, which provides a proportional-like control action. Hence, the function approximators (e.g. neural networks, fuzzy systems) that are widely used to address the unknown nonlinearities in the nonlinear control designs are not needed. The proposed control design leads to a robust yet simplified function approximation-free control for nonlinear systems. The closed-loop system stability and the control error convergence are all rigorously proved. Finally, comparative simulations are conducted based on nonlinear missile systems to validate the improved response and the robustness of the proposed control method.
3. Controllability of non-linear systems: generic singularities and their stability
International Nuclear Information System (INIS)
Davydov, Alexey A; Zakalyukin, Vladimir M
2012-01-01
This paper presents an overview of the state of the art in applications of singularity theory to the analysis of generic singularities of controllability of non-linear systems on manifolds. Bibliography: 40 titles.
4. State-Feedback Control for Fractional-Order Nonlinear Systems Subject to Input Saturation
Directory of Open Access Journals (Sweden)
Junhai Luo
2014-01-01
Full Text Available We give a state-feedback control method for fractional-order nonlinear systems subject to input saturation. First, a sufficient condition is derived for the asymptotical stability of a class of fractional-order nonlinear systems. Then based on Gronwall-Bellman lemma and a sector bounded condition of the saturation function, a linear state-feed back controller is designed. Finally, two simulation examples are presented to show the validity of the proposed method.
5. Adaptive Non-linear Control of Hydraulic Actuator Systems
DEFF Research Database (Denmark)
1998-01-01
Presentation of two new developed adaptive non-liner controllers for hydraulic actuator systems to give stable operation and improved performance.Results from the IMCIA project supported by the Danish Technical Research Council (STVF).......Presentation of two new developed adaptive non-liner controllers for hydraulic actuator systems to give stable operation and improved performance.Results from the IMCIA project supported by the Danish Technical Research Council (STVF)....
6. Adaptive H∞ synchronization of chaotic systems via linear and nonlinear feedback control
International Nuclear Information System (INIS)
Fu Shi-Hui; Lu Qi-Shao; Du Ying
2012-01-01
Adaptive H ∞ synchronization of chaotic systems via linear and nonlinear feedback control is investigated. The chaotic systems are redesigned by using the generalized Hamiltonian systems and observer approach. Based on Lyapunov's stability theory, linear and nonlinear feedback control of adaptive H ∞ synchronization is established in order to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance on an H ∞ -norm constraint. Adaptive H ∞ synchronization of chaotic systems via three kinds of control is investigated with applications to Lorenz and Chen systems. Numerical simulations are also given to identify the effectiveness of the theoretical analysis. (general)
7. Adaptive Fuzzy Robust Control for a Class of Nonlinear Systems via Small Gain Theorem
Directory of Open Access Journals (Sweden)
Xingjian Wang
2013-01-01
Full Text Available Practical nonlinear systems can usually be represented by partly linearizable models with unknown nonlinearities and external disturbances. Based on this consideration, we propose a novel adaptive fuzzy robust control (AFRC algorithm for such systems. The AFRC effectively combines techniques of adaptive control and fuzzy control, and it improves the performance by retaining the advantages of both methods. The linearizable part will be linearly parameterized with unknown but constant parameters, and the discontinuous-projection-based adaptive control law is used to compensate these parts. The Takagi-Sugeno fuzzy logic systems are used to approximate unknown nonlinearities. Robust control law ensures the robustness of closed-loop control system. A systematic design procedure of the AFRC algorithm by combining the backstepping technique and small-gain approach is presented. Then the closed-loop stability is studied by using small gain theorem, and the result indicates that the closed-loop system is semiglobally uniformly ultimately bounded.
8. Nonlinear control systems - A brief overview of historical and recent advances
Science.gov (United States)
Iqbal, Jamshed; Ullah, Mukhtar; Khan, Said Ghani; Khelifa, Baizid; Ćuković, Saša
2017-12-01
Last five decades witnessed remarkable developments in linear control systems and thus problems in this subject has been largely resolved. The scope of the present paper is beyond linear solutions. Modern technology demands sophisticated control laws to meet stringent design specifications thus highlighting the increasingly conspicuous position of nonlinear control systems, which is the topic of this paper. Historical role of analytical concepts in analysis and design of nonlinear control systems is briefly outlined. Recent advancements in these systems from applications perspective are examined with critical comments on associated challenges. It is anticipated that wider dissemination of this comprehensive review will stimulate more collaborations among the research community and contribute to further developments.
9. A Unified Approach to Adaptive Neural Control for Nonlinear Discrete-Time Systems With Nonlinear Dead-Zone Input.
Science.gov (United States)
Liu, Yan-Jun; Gao, Ying; Tong, Shaocheng; Chen, C L Philip
2016-01-01
10. Robust intelligent sliding model control using recurrent cerebellar model articulation controller for uncertain nonlinear chaotic systems
International Nuclear Information System (INIS)
Peng Yafu
2009-01-01
In this paper, a robust intelligent sliding model control (RISMC) scheme using an adaptive recurrent cerebellar model articulation controller (RCMAC) is developed for a class of uncertain nonlinear chaotic systems. This RISMC system offers a design approach to drive the state trajectory to track a desired trajectory, and it is comprised of an adaptive RCMAC and a robust controller. The adaptive RCMAC is used to mimic an ideal sliding mode control (SMC) due to unknown system dynamics, and a robust controller is designed to recover the residual approximation error for guaranteeing the stable characteristic. Moreover, the Taylor linearization technique is employed to derive the linearized model of the RCMAC. The all adaptation laws of the RISMC system are derived based on the Lyapunov stability analysis and projection algorithm, so that the stability of the system can be guaranteed. Finally, the proposed RISMC system is applied to control a Van der Pol oscillator, a Genesio chaotic system and a Chua's chaotic circuit. The effectiveness of the proposed control scheme is verified by some simulation results with unknown system dynamics and existence of external disturbance. In addition, the advantages of the proposed RISMC are indicated in comparison with a SMC system
11. Observer-based design of set-point tracking adaptive controllers for nonlinear chaotic systems
International Nuclear Information System (INIS)
Khaki-Sedigh, A.; Yazdanpanah-Goharrizi, A.
2006-01-01
A gradient based approach for the design of set-point tracking adaptive controllers for nonlinear chaotic systems is presented. In this approach, Lyapunov exponents are used to select the controller gain. In the case of unknown or time varying chaotic plants, the Lyapunov exponents may vary during the plant operation. In this paper, an effective adaptive strategy is used for online identification of Lyapunov exponents and adaptive control of nonlinear chaotic plants. Also, a nonlinear observer for estimation of the states is proposed. Simulation results are provided to show the effectiveness of the proposed methodology
12. Observer-based design of set-point tracking adaptive controllers for nonlinear chaotic systems
Energy Technology Data Exchange (ETDEWEB)
Khaki-Sedigh, A. [Department of Electrical Engineering, K.N. Toosi University of Technology, Sayyed Khandan Bridge, Shariati Street, Tehran 16314 (Iran, Islamic Republic of)]. E-mail: sedigh@kntu.ac.ir; Yazdanpanah-Goharrizi, A. [Department of Electrical Engineering, K.N. Toosi University of Technology, Sayyed Khandan Bridge, Shariati Street, Tehran 16314 (Iran, Islamic Republic of)]. E-mail: yazdanpanah@ee.kntu.ac.ir
2006-09-15
A gradient based approach for the design of set-point tracking adaptive controllers for nonlinear chaotic systems is presented. In this approach, Lyapunov exponents are used to select the controller gain. In the case of unknown or time varying chaotic plants, the Lyapunov exponents may vary during the plant operation. In this paper, an effective adaptive strategy is used for online identification of Lyapunov exponents and adaptive control of nonlinear chaotic plants. Also, a nonlinear observer for estimation of the states is proposed. Simulation results are provided to show the effectiveness of the proposed methodology.
13. Application of Dynamic Systems Family for Synthesis of Fuzzy Control with Account of Non-linearities
Directory of Open Access Journals (Sweden)
Andriy Lozynskyy
2016-01-01
Full Text Available Dynamic system with nonlinearities has been considered. This system has been divided into a set of linear subsystems. A fuzzy controller of the considered system has been synthesized. It takes into account nonlinearities of the system and provides smooth switching between controllers of the linear subsystems. An unstable subsystem has been utilized, which provides better dynamic characteristics of the considered system. Comparison with traditional controller has been conducted. Corresponding qualitative and quantitative estimates have been provided. They testify the expediency of the proposed approach.
14. Nonlinear systems
National Research Council Canada - National Science Library
Drazin, P. G
1992-01-01
This book is an introduction to the theories of bifurcation and chaos. It treats the solution of nonlinear equations, especially difference and ordinary differential equations, as a parameter varies...
15. Comparison among nonlinear excitation control strategies used for damping power system oscillations
International Nuclear Information System (INIS)
Leon, A.E.; Solsona, J.A.; Valla, M.I.
2012-01-01
Highlights: ► A description and comparison of nonlinear control strategies for synchronous generators are presented. ► Advantages of using nonlinear controllers are emphasized against the use of classical PSSs. ► We find that a particular selection of IDA gains achieve the same performance that FL controllers. - Abstract: This work is focused on the problem of power system stability. A thorough description of nonlinear control strategies for synchronous generator excitation, which are designed for damping oscillations and improving transient stability on power systems, is presented along with a detailed comparison among these modern strategies and current solutions based on power system stabilizers. The performance related to damping injection in each controller, critical time enhancement, robustness against parametric uncertainties, and control signal energy consumption is analyzed. Several tests are presented to validate discussions on various advantages and disadvantages of each control strategy.
16. Passivation and control of partially known SISO nonlinear systems via dynamic neural networks
Directory of Open Access Journals (Sweden)
Reyes-Reyes J.
2000-01-01
Full Text Available In this paper, an adaptive technique is suggested to provide the passivity property for a class of partially known SISO nonlinear systems. A simple Dynamic Neural Network (DNN, containing only two neurons and without any hidden-layers, is used to identify the unknown nonlinear system. By means of a Lyapunov-like analysis the new learning law for this DNN, guarantying both successful identification and passivation effects, is derived. Based on this adaptive DNN model, an adaptive feedback controller, serving for wide class of nonlinear systems with an a priori incomplete model description, is designed. Two typical examples illustrate the effectiveness of the suggested approach.
17. Robust model predictive control for constrained continuous-time nonlinear systems
Science.gov (United States)
Sun, Tairen; Pan, Yongping; Zhang, Jun; Yu, Haoyong
2018-02-01
In this paper, a robust model predictive control (MPC) is designed for a class of constrained continuous-time nonlinear systems with bounded additive disturbances. The robust MPC consists of a nonlinear feedback control and a continuous-time model-based dual-mode MPC. The nonlinear feedback control guarantees the actual trajectory being contained in a tube centred at the nominal trajectory. The dual-mode MPC is designed to ensure asymptotic convergence of the nominal trajectory to zero. This paper extends current results on discrete-time model-based tube MPC and linear system model-based tube MPC to continuous-time nonlinear model-based tube MPC. The feasibility and robustness of the proposed robust MPC have been demonstrated by theoretical analysis and applications to a cart-damper springer system and a one-link robot manipulator.
18. Controllable nonlinearity in a dual-coupling optomechanical system under a weak-coupling regime
Science.gov (United States)
Zhu, Gui-Lei; Lü, Xin-You; Wan, Liang-Liang; Yin, Tai-Shuang; Bin, Qian; Wu, Ying
2018-03-01
Strong quantum nonlinearity gives rise to many interesting quantum effects and has wide applications in quantum physics. Here we investigate the quantum nonlinear effect of an optomechanical system (OMS) consisting of both linear and quadratic coupling. Interestingly, a controllable optomechanical nonlinearity is obtained by applying a driving laser into the cavity. This controllable optomechanical nonlinearity can be enhanced into a strong coupling regime, even if the system is initially in the weak-coupling regime. Moreover, the system dissipation can be suppressed effectively, which allows the appearance of phonon sideband and photon blockade effects in the weak-coupling regime. This work may inspire the exploration of a dual-coupling optomechanical system as well as its applications in modern quantum science.
19. Reconfigurable Control of Input Affine Nonlinear Systems under Actuator Fault
DEFF Research Database (Denmark)
Tabatabaeipour, Mojtaba; Galeazzi, Roberto
2015-01-01
loop is preserved. The RB is realized by a virtual actuator and a reference model. Using notions of incremental and input-to-state stability (ISS), it is shown that ISS of the closed-loop reconfigured system can be achieved by the separate design of the virtual actuator. The proposed method does...... not need any knowledge of the nominal controller and only assumes that the nominal closed-loop system is ISS. The method is demonstrated on a dynamic positioning system for an offshore supply vessel, where the virtual actuator is designed using backstepping....
20. Fuzzy Control Model and Simulation for Nonlinear Supply Chain System with Lead Times
Directory of Open Access Journals (Sweden)
Songtao Zhang
2017-01-01
Full Text Available A new fuzzy robust control strategy for the nonlinear supply chain system in the presence of lead times is proposed. Based on Takagi-Sugeno fuzzy control system, the fuzzy control model of the nonlinear supply chain system with lead times is constructed. Additionally, we design a fuzzy robust H∞ control strategy taking the definition of maximal overlapped-rules group into consideration to restrain the impacts such as those caused by lead times, switching actions among submodels, and customers’ stochastic demands. This control strategy can not only guarantee that the nonlinear supply chain system is robustly asymptotically stable but also realize soft switching among subsystems of the nonlinear supply chain to make the less fluctuation of the system variables by introducing the membership function of fuzzy system. The comparisons between the proposed fuzzy robust H∞ control strategy and the robust H∞ control strategy are finally illustrated through numerical simulations on a two-stage nonlinear supply chain with lead times.
1. SOS based robust H(∞) fuzzy dynamic output feedback control of nonlinear networked control systems.
Science.gov (United States)
Chae, Seunghwan; Nguang, Sing Kiong
2014-07-01
In this paper, a methodology for designing a fuzzy dynamic output feedback controller for discrete-time nonlinear networked control systems is presented where the nonlinear plant is modelled by a Takagi-Sugeno fuzzy model and the network-induced delays by a finite state Markov process. The transition probability matrix for the Markov process is allowed to be partially known, providing a more practical consideration of the real world. Furthermore, the fuzzy controller's membership functions and premise variables are not assumed to be the same as the plant's membership functions and premise variables, that is, the proposed approach can handle the case, when the premise of the plant are not measurable or delayed. The membership functions of the plant and the controller are approximated as polynomial functions, then incorporated into the controller design. Sufficient conditions for the existence of the controller are derived in terms of sum of square inequalities, which are then solved by YALMIP. Finally, a numerical example is used to demonstrate the validity of the proposed methodology.
2. Simplex sliding mode control for nonlinear uncertain systems via chaos optimization
International Nuclear Information System (INIS)
Lu, Zhao; Shieh, Leang-San; Chen, Guanrong; Coleman, Norman P.
2005-01-01
As an emerging effective approach to nonlinear robust control, simplex sliding mode control demonstrates some attractive features not possessed by the conventional sliding mode control method, from both theoretical and practical points of view. However, no systematic approach is currently available for computing the simplex control vectors in nonlinear sliding mode control. In this paper, chaos-based optimization is exploited so as to develop a systematic approach to seeking the simplex control vectors; particularly, the flexibility of simplex control is enhanced by making the simplex control vectors dependent on the Euclidean norm of the sliding vector rather than being constant, which result in both reduction of the chattering and speedup of the convergence. Computer simulation on a nonlinear uncertain system is given to illustrate the effectiveness of the proposed control method
3. Free chattering hybrid sliding mode control for a class of non-linear systems
DEFF Research Database (Denmark)
Khooban, Mohammad Hassan; Niknam, Taher; Blaabjerg, Frede
2016-01-01
In current study, in order to find the control of general uncertain nonlinear systems, a new optimal hybrid control approach called Optimal General Type II Fuzzy Sliding Mode (OGT2FSM) is presented. In order to estimate unknown nonlinear activities in monitoring dynamic uncertainties, the benefits...... on the same topic, which are an Adaptive Interval Type-2 Fuzzy Logic Controller (AGT2FLC) and Conventional Sliding Mode Controller (CSMC), to assess the efficiency of the suggested controller. The suggested control scheme is finally used to the Electric Vehicles type as a case study. Results of simulation...
4. Data-based control trajectory planning for nonlinear systems
International Nuclear Information System (INIS)
Rhodes, C.; Morari, M.; Tsimring, L.S.; Rulkov, N.F.
1997-01-01
An open-loop trajectory planning algorithm is presented for computing an input sequence that drives an input-output system such that a reference trajectory is tracked. The algorithm utilizes only input-output data from the system to determine the proper control sequence, and does not require a mathematical or identified description of the system dynamics. From the input-output data, the controlled input trajectory is calculated in a open-quotes one-step-aheadclose quotes fashion using local modeling. Since the algorithm is calculated in this fashion, the output trajectories to be tracked can be nonperiodic. The algorithm is applied to a driven Lorenz system, and an experimental electrical circuit and the results are analyzed. Issues of stability associated with the implementation of this open-loop scheme are also examined using an analytic example of a driven Hacute enon map, problems associated with inverse controllers are illustrated, and solutions to these problems are proposed. copyright 1997 The American Physical Society
5. Adaptive Neural Control of Nonaffine Nonlinear Systems without Differential Condition for Nonaffine Function
Directory of Open Access Journals (Sweden)
Chaojiao Sun
2016-01-01
Full Text Available An adaptive neural control scheme is proposed for nonaffine nonlinear system without using the implicit function theorem or mean value theorem. The differential conditions on nonaffine nonlinear functions are removed. The control-gain function is modeled with the nonaffine function probably being indifferentiable. Furthermore, only a semibounded condition for nonaffine nonlinear function is required in the proposed method, and the basic idea of invariant set theory is then constructively introduced to cope with the difficulty in the control design for nonaffine nonlinear systems. It is rigorously proved that all the closed-loop signals are bounded and the tracking error converges to a small residual set asymptotically. Finally, simulation examples are provided to demonstrate the effectiveness of the designed method.
6. Switched-Observer-Based Adaptive Neural Control of MIMO Switched Nonlinear Systems With Unknown Control Gains.
Science.gov (United States)
Long, Lijun; Zhao, Jun
2017-07-01
In this paper, the problem of adaptive neural output-feedback control is addressed for a class of multi-input multioutput (MIMO) switched uncertain nonlinear systems with unknown control gains. Neural networks (NNs) are used to approximate unknown nonlinear functions. In order to avoid the conservativeness caused by adoption of a common observer for all subsystems, an MIMO NN switched observer is designed to estimate unmeasurable states. A new switched observer-based adaptive neural control technique for the problem studied is then provided by exploiting the classical average dwell time (ADT) method and the backstepping method and the Nussbaum gain technique. It effectively handles the obstacle about the coexistence of multiple Nussbaum-type function terms, and improves the classical ADT method, since the exponential decline property of Lyapunov functions for individual subsystems is no longer satisfied. It is shown that the technique proposed is able to guarantee semiglobal uniformly ultimately boundedness of all the signals in the closed-loop system under a class of switching signals with ADT, and the tracking errors converge to a small neighborhood of the origin. The effectiveness of the approach proposed is illustrated by its application to a two inverted pendulum system.
7. Feedback control of nonlinear quantum systems: a rule of thumb.
Science.gov (United States)
Jacobs, Kurt; Lund, Austin P
2007-07-13
We show that in the regime in which feedback control is most effective - when measurements are relatively efficient, and feedback is relatively strong - then, in the absence of any sharp inhomogeneity in the noise, it is always best to measure in a basis that does not commute with the system density matrix than one that does. That is, it is optimal to make measurements that disturb the state one is attempting to stabilize.
8. Nonlinear Disturbance Attenuation Controller for Turbo-Generators in Power Systems via Recursive Design
NARCIS (Netherlands)
Cao, M.; Shen, T.L.; Song, Y.H.; Mei, S.W.
2002-01-01
The paper proposes a nonlinear robust controller for steam governor control in power systems. Based on dissipation theory, an innovative recursive design method is presented to construct the storage function of single machine infinite bus (SMIB) and multi-machine power systems. Furthermore, the
9. On the internal model principle in formation control and in output synchronization of nonlinear systems
NARCIS (Netherlands)
Persis, Claudio De; Jayawardhana, Bayu
2012-01-01
The role of internal model principle is investigated in this paper in the context of collective synchronization and formation control problems. In the collective synchronization problem for nonlinear systems, we propose distributed control laws for passive systems which synchronize to the solution
10. Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control.
Science.gov (United States)
Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan
2016-01-01
In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite
11. Sliding mode control for uncertain unified chaotic systems with input nonlinearity
International Nuclear Information System (INIS)
Chiang, T.-Y.; Hung, M.-L.; Yan, J.-J.; Yang, Y.-S.; Chang, J.-F.
2007-01-01
This paper investigates the stabilization problem for a class of unified chaotic systems subject to uncertainties and input nonlinearity. Using the sliding mode control technique, a robust control law is established which stabilizes the uncertain unified chaotic systems even when the nonlinearity in the actuators is present. A novel adaptive switching surface is introduced to simplify the task of assigning the stability of the closed-loop system in the sliding mode motion. An illustrative example is given to demonstrate the effectiveness of the proposed sliding mode control design
12. Application of Contraction Mappings to the Control of Nonlinear Systems. Ph.D. Thesis
Science.gov (United States)
Killingsworth, W. R., Jr.
1972-01-01
The theoretical and applied aspects of successive approximation techniques are considered for the determination of controls for nonlinear dynamical systems. Particular emphasis is placed upon the methods of contraction mappings and modified contraction mappings. It is shown that application of the Pontryagin principle to the optimal nonlinear regulator problem results in necessary conditions for optimality in the form of a two point boundary value problem (TPBVP). The TPBVP is represented by an operator equation and functional analytic results on the iterative solution of operator equations are applied. The general convergence theorems are translated and applied to those operators arising from the optimal regulation of nonlinear systems. It is shown that simply structured matrices and similarity transformations may be used to facilitate the calculation of the matrix Green functions and the evaluation of the convergence criteria. A controllability theory based on the integral representation of TPBVP's, the implicit function theorem, and contraction mappings is developed for nonlinear dynamical systems. Contraction mappings are theoretically and practically applied to a nonlinear control problem with bounded input control and the Lipschitz norm is used to prove convergence for the nondifferentiable operator. A dynamic model representing community drug usage is developed and the contraction mappings method is used to study the optimal regulation of the nonlinear system.
13. Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control
Science.gov (United States)
Brunton, Steven L.; Brunton, Bingni W.; Proctor, Joshua L.; Kutz, J. Nathan
2016-01-01
In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control. PMID:26919740
14. Fully probabilistic control for stochastic nonlinear control systems with input dependent noise.
Science.gov (United States)
Herzallah, Randa
2015-03-01
Robust controllers for nonlinear stochastic systems with functional uncertainties can be consistently designed using probabilistic control methods. In this paper a generalised probabilistic controller design for the minimisation of the Kullback-Leibler divergence between the actual joint probability density function (pdf) of the closed loop control system, and an ideal joint pdf is presented emphasising how the uncertainty can be systematically incorporated in the absence of reliable systems models. To achieve this objective all probabilistic models of the system are estimated from process data using mixture density networks (MDNs) where all the parameters of the estimated pdfs are taken to be state and control input dependent. Based on this dependency of the density parameters on the input values, explicit formulations to the construction of optimal generalised probabilistic controllers are obtained through the techniques of dynamic programming and adaptive critic methods. Using the proposed generalised probabilistic controller, the conditional joint pdfs can be made to follow the ideal ones. A simulation example is used to demonstrate the implementation of the algorithm and encouraging results are obtained. Copyright © 2014 Elsevier Ltd. All rights reserved.
15. Control and synchronization of chaos in nonlinear systems and prospects for application. Pt.1
International Nuclear Information System (INIS)
Fang Jinqing
1996-01-01
Main progress in one challenging subject of nonlinear science--control and synchronization of chaos in nonlinear systems are reviewed systematically, including recent advance in controlling and synchronizing hyperchaos. Current methods and principles of schemes of chaos control and synchronization are classified and summarized in detail. Potential prospects for application are commented both in theory and experiment. The whole review is divided into two parts. In the first one, subject on the mechanism and method of chaos control are analyzed and discussed extensively. In the second one, the synchronization of non-chaos, chaos, hyperchaos and their control and application are described. Main trends for development of the subject is mentioned. (101 refs.)
16. High Accuracy Nonlinear Control and Estimation for Machine Tool Systems
DEFF Research Database (Denmark)
Papageorgiou, Dimitrios
Component mass production has been the backbone of industry since the second industrial revolution, and machine tools are producing parts of widely varying size and design complexity. The ever-increasing level of automation in modern manufacturing processes necessitates the use of more...... sophisticated machine tool systems that are adaptable to different workspace conditions, while at the same time being able to maintain very narrow workpiece tolerances. The main topic of this thesis is to suggest control methods that can maintain required manufacturing tolerances, despite moderate wear and tear....... The purpose is to ensure that full accuracy is maintained between service intervals and to advice when overhaul is needed. The thesis argues that quality of manufactured components is directly related to the positioning accuracy of the machine tool axes, and it shows which low level control architectures...
17. Adaptive control of nonlinear in parameters chaotic system via Lyapunov exponents placement
Energy Technology Data Exchange (ETDEWEB)
Ayati, Moosa [Department of Electrical Engineering, K.N. Toosi University of Technology, Sayyed Khandan Bridge, Shariati Street, Tehran (Iran, Islamic Republic of)], E-mail: Ayati@dena.kntu.ac.ir; Khaki-Sedigh, Ali [Department of Electrical Engineering, K.N. Toosi University of Technology, Sayyed Khandan Bridge, Shariati Street, Tehran (Iran, Islamic Republic of)], E-mail: sedigh@kntu.ac.ir
2009-08-30
This paper proposes a new method for the adaptive control of nonlinear in parameters (NLP) chaotic systems. A method based on Lagrangian of a cost function is used to identify the parameters of the system. Estimation results are used to calculate the Lyapunov exponents adaptively. Finally, the Lyapunov exponents placement method is used to assign the desired Lyapunov exponents of the closed loop system.
18. Adaptive control of nonlinear in parameters chaotic system via Lyapunov exponents placement
International Nuclear Information System (INIS)
Ayati, Moosa; Khaki-Sedigh, Ali
2009-01-01
This paper proposes a new method for the adaptive control of nonlinear in parameters (NLP) chaotic systems. A method based on Lagrangian of a cost function is used to identify the parameters of the system. Estimation results are used to calculate the Lyapunov exponents adaptively. Finally, the Lyapunov exponents placement method is used to assign the desired Lyapunov exponents of the closed loop system.
19. Output Feedback Distributed Containment Control for High-Order Nonlinear Multiagent Systems.
Science.gov (United States)
Li, Yafeng; Hua, Changchun; Wu, Shuangshuang; Guan, Xinping
2017-01-31
In this paper, we study the problem of output feedback distributed containment control for a class of high-order nonlinear multiagent systems under a fixed undirected graph and a fixed directed graph, respectively. Only the output signals of the systems can be measured. The novel reduced order dynamic gain observer is constructed to estimate the unmeasured state variables of the system with the less conservative condition on nonlinear terms than traditional Lipschitz one. Via the backstepping method, output feedback distributed nonlinear controllers for the followers are designed. By means of the novel first virtual controllers, we separate the estimated state variables of different agents from each other. Consequently, the designed controllers show independence on the estimated state variables of neighbors except outputs information, and the dynamics of each agent can be greatly different, which make the design method have a wider class of applications. Finally, a numerical simulation is presented to illustrate the effectiveness of the proposed method.
20. Nonlinear optimal control theory
CERN Document Server
Berkovitz, Leonard David
2012-01-01
Nonlinear Optimal Control Theory presents a deep, wide-ranging introduction to the mathematical theory of the optimal control of processes governed by ordinary differential equations and certain types of differential equations with memory. Many examples illustrate the mathematical issues that need to be addressed when using optimal control techniques in diverse areas. Drawing on classroom-tested material from Purdue University and North Carolina State University, the book gives a unified account of bounded state problems governed by ordinary, integrodifferential, and delay systems. It also dis
1. H∞ Balancing for Nonlinear Systems
NARCIS (Netherlands)
Scherpen, Jacquelien M.A.
1996-01-01
In previously obtained balancing methods for nonlinear systems a past and a future energy function are used to bring the nonlinear system in balanced form. By considering a different pair of past and future energy functions that are related to the H∞ control problem for nonlinear systems we define
2. Improved Polynomial Fuzzy Modeling and Controller with Stability Analysis for Nonlinear Dynamical Systems
OpenAIRE
2012-01-01
This study presents an improved model and controller for nonlinear plants using polynomial fuzzy model-based (FMB) systems. To minimize mismatch between the polynomial fuzzy model and nonlinear plant, the suitable parameters of membership functions are determined in a systematic way. Defining an appropriate fitness function and utilizing Taylor series expansion, a genetic algorithm (GA) is used to form the shape of membership functions in polynomial forms, which are afterwards used in fuzzy m...
3. Investigation on the Nonlinear Control System of High-Pressure Common Rail (HPCR) System in a Diesel Engine
Science.gov (United States)
Cai, Le; Mao, Xiaobing; Ma, Zhexuan
2018-02-01
This study first constructed the nonlinear mathematical model of the high-pressure common rail (HPCR) system in the diesel engine. Then, the nonlinear state transformation was performed using the flow’s calculation and the standard state space equation was acquired. Based on sliding-mode variable structure control (SMVSC) theory, a sliding-mode controller for nonlinear systems was designed for achieving the control of common rail pressure and the diesel engine’s rotational speed. Finally, on the simulation platform of MATLAB, the designed nonlinear HPCR system was simulated. The simulation results demonstrate that sliding-mode variable structure control algorithm shows favorable control performances and overcome the shortcomings of traditional PID control in overshoot, parameter adjustment, system precision, adjustment time and ascending time.
4. Nonlinear Model Predictive Control for Solid Oxide Fuel Cell System Based On Wiener Model
OpenAIRE
T. H. Lee; J. H. Park; S. M. Lee; S. C. Lee
2010-01-01
In this paper, we consider Wiener nonlinear model for solid oxide fuel cell (SOFC). The Wiener model of the SOFC consists of a linear dynamic block and a static output non-linearity followed by the block, in which linear part is approximated by state-space model and the nonlinear part is identified by a polynomial form. To control the SOFC system, we have to consider various view points such as operating conditions, another constraint conditions, change of load current and so on. A change of ...
5. A novel auto-tuning PID control mechanism for nonlinear systems.
Science.gov (United States)
Cetin, Meric; Iplikci, Serdar
2015-09-01
6. Chaotification of vibration isolation floating raft system via nonlinear time-delay feedback control
International Nuclear Information System (INIS)
Zhang Jing; Xu Daolin; Zhou Jiaxi; Li Yingli
2012-01-01
Highlights: ► A chaotification method based on nonlinear time-delay feedback control is present. ► An analytical function of nonlinear time-delay feedback control is derived. ► A large range of parametric domain for chaotification is obtained. ► The approach allows using small control gain. ► Design of chaotification becomes a standard process without uncertainty. - Abstract: This paper presents a chaotification method based on nonlinear time-delay feedback control for a two-dimensional vibration isolation floating raft system (VIFRS). An analytical function of nonlinear time-delay feedback control is derived. This approach can theoretically provide a systematic design of chaotification for nonlinear VIFRS and completely avoid blind and inefficient numerical search on the basis of trials and errors. Numerical simulations show that with a proper setting of control parameters the method holds the favorable aspects including the capability of chaotifying across a large range of parametric domain, the advantage of using small control and the flexibility of designing control feedback forms. The effects on chaotification performance are discussed in association with the configuration of the control parameters.
7. TCSC Nonlinear Adaptive Damping Controller Design Based on RBF Neural Network to Enhance Power System Stability
DEFF Research Database (Denmark)
Yao, Wei; Fang, Jiakun; Zhao, Ping
2013-01-01
the characteristics of the conventional PID, but adjust the parameters of PID controller online using identified Jacobian information from RBFNN. Hence, it has strong adaptability to the variation of the system operating condition. The effectiveness of the proposed controller is tested on a two-machine five-bus power...... system and a four-machine two-area power system under different operating conditions in comparison with the lead-lag damping controller tuned by evolutionary algorithm (EA). Simulation results show that the proposed damping controller achieves good robust performance for damping the low frequency......In this paper, a nonlinear adaptive damping controller based on radial basis function neural network (RBFNN), which can infinitely approximate to nonlinear system, is proposed for thyristor controlled series capacitor (TCSC). The proposed TCSC adaptive damping controller can not only have...
8. Improved Polynomial Fuzzy Modeling and Controller with Stability Analysis for Nonlinear Dynamical Systems
Directory of Open Access Journals (Sweden)
Hamed Kharrati
2012-01-01
Full Text Available This study presents an improved model and controller for nonlinear plants using polynomial fuzzy model-based (FMB systems. To minimize mismatch between the polynomial fuzzy model and nonlinear plant, the suitable parameters of membership functions are determined in a systematic way. Defining an appropriate fitness function and utilizing Taylor series expansion, a genetic algorithm (GA is used to form the shape of membership functions in polynomial forms, which are afterwards used in fuzzy modeling. To validate the model, a controller based on proposed polynomial fuzzy systems is designed and then applied to both original nonlinear plant and fuzzy model for comparison. Additionally, stability analysis for the proposed polynomial FMB control system is investigated employing Lyapunov theory and a sum of squares (SOS approach. Moreover, the form of the membership functions is considered in stability analysis. The SOS-based stability conditions are attained using SOSTOOLS. Simulation results are also given to demonstrate the effectiveness of the proposed method.
9. Direct Adaptive Control of a Class of Nonlinear Discrete-Time Systems
DEFF Research Database (Denmark)
Bendtsen, Jan Dimon
2004-01-01
In this paper we deal with direct adaptive control of a specific class of discrete-time SISO systems, where the nonlinearities are convex and an upper bound is known. We use a control law based on a linear combination of a set of globally uniformly bounded basis functions with compact support, wh...
10. Chaos synchronization of uncertain chaotic systems using composite nonlinear feedback based integral sliding mode control.
Science.gov (United States)
Mobayen, Saleh
2018-06-01
This paper proposes a combination of composite nonlinear feedback and integral sliding mode techniques for fast and accurate chaos synchronization of uncertain chaotic systems with Lipschitz nonlinear functions, time-varying delays and disturbances. The composite nonlinear feedback method allows accurate following of the master chaotic system and the integral sliding mode control provides invariance property which rejects the perturbations and preserves the stability of the closed-loop system. Based on the Lyapunov- Krasovskii stability theory and linear matrix inequalities, a novel sufficient condition is offered for the chaos synchronization of uncertain chaotic systems. This method not only guarantees the robustness against perturbations and time-delays, but also eliminates reaching phase and avoids chattering problem. Simulation results demonstrate that the suggested procedure leads to a great control performance. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.
11. Intelligent control of non-linear dynamical system based on the adaptive neurocontroller
Science.gov (United States)
Engel, E.; Kovalev, I. V.; Kobezhicov, V.
2015-10-01
This paper presents an adaptive neuro-controller for intelligent control of non-linear dynamical system. The formed as the fuzzy selective neural net the adaptive neuro-controller on the base of system's state, creates the effective control signal under random perturbations. The validity and advantages of the proposed adaptive neuro-controller are demonstrated by numerical simulations. The simulation results show that the proposed controller scheme achieves real-time control speed and the competitive performance, as compared to PID, fuzzy logic controllers.
12. Neural-network-observer-based optimal control for unknown nonlinear systems using adaptive dynamic programming
Science.gov (United States)
Liu, Derong; Huang, Yuzhu; Wang, Ding; Wei, Qinglai
2013-09-01
In this paper, an observer-based optimal control scheme is developed for unknown nonlinear systems using adaptive dynamic programming (ADP) algorithm. First, a neural-network (NN) observer is designed to estimate system states. Then, based on the observed states, a neuro-controller is constructed via ADP method to obtain the optimal control. In this design, two NN structures are used: a three-layer NN is used to construct the observer which can be applied to systems with higher degrees of nonlinearity and without a priori knowledge of system dynamics, and a critic NN is employed to approximate the value function. The optimal control law is computed using the critic NN and the observer NN. Uniform ultimate boundedness of the closed-loop system is guaranteed. The actor, critic, and observer structures are all implemented in real-time, continuously and simultaneously. Finally, simulation results are presented to demonstrate the effectiveness of the proposed control scheme.
13. Right-invertibility for a class of nonlinear control systems: A geometric approach
NARCIS (Netherlands)
Nijmeijer, Henk
1986-01-01
In recent years it has become evident that various synthesis problems known from linear system theory can also be solved for nonlinear control systems by using differential geometric methods. The purpose of this paper is to use this mathematical framework for giving a preliminary account on the
14. Nonlinear feedback synchronisation control between fractional-order and integer-order chaotic systems
International Nuclear Information System (INIS)
Jia Li-Xin; Dai Hao; Hui Meng
2010-01-01
This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method
15. H∞ control of Lur'e systems with sector and slope restricted nonlinearities
International Nuclear Information System (INIS)
Park, Ju H.; Ji, D.H.; Won, S.C.; Lee, S.M.; Choi, S.J.
2009-01-01
This Letter considers H ∞ controller design scheme for Lur'e systems with sector/slope restrictions and external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, a state feedback controller is designed to not only guarantee stability of systems but also reduce the effect of external disturbance to an H ∞ norm constraint. The nonlinearities are expressed as convex combinations of sector and slope bounds so that equality constraints are converted into inequality constraints using convex properties of the nonlinear function. Then, the stabilizing feedback gain matrix is derived through LMI formulation. Finally, a numerical example shows the effectiveness of the proposed method.
16. Null Controllability of a Nonlinear Dissipative System and Application to the Detection of the Incomplete Parameter for a Nonlinear Population Dynamics Model
Directory of Open Access Journals (Sweden)
Yacouba Simporé
2016-01-01
Full Text Available We first prove a null controllability result for a nonlinear system derived from a nonlinear population dynamics model. In order to tackle the controllability problem we use an adapted Carleman inequality. Next we consider the nonlinear population dynamics model with a source term called the pollution term. In order to obtain information on the pollution term we use the method of sentinel.
17. Attitude Control of a Single Tilt Tri-Rotor UAV System: Dynamic Modeling and Each Channel's Nonlinear Controllers Design
Directory of Open Access Journals (Sweden)
Juing-Shian Chiou
2013-01-01
Full Text Available This paper has implemented nonlinear control strategy for the single tilt tri-rotor aerial robot. Based on Newton-Euler’s laws, the linear and nonlinear mathematical models of tri-rotor UAVs are obtained. A numerical analysis using Newton-Raphson method is chosen for finding hovering equilibrium point. Back-stepping nonlinear controller design is based on constructing Lyapunov candidate function for closed-loop system. By imitating the linguistic logic of human thought, fuzzy logic controllers (FLCs are designed based on control rules and membership functions, which are much less rigid than the calculations computers generally perform. Effectiveness of the controllers design scheme is shown through nonlinear simulation model on each channel.
18. Nonlinear adaptive control system design with asymptotically stable parameter estimation error
Science.gov (United States)
Mishkov, Rumen; Darmonski, Stanislav
2018-01-01
The paper presents a new general method for nonlinear adaptive system design with asymptotic stability of the parameter estimation error. The advantages of the approach include asymptotic unknown parameter estimation without persistent excitation and capability to directly control the estimates transient response time. The method proposed modifies the basic parameter estimation dynamics designed via a known nonlinear adaptive control approach. The modification is based on the generalised prediction error, a priori constraints with a hierarchical parameter projection algorithm, and the stable data accumulation concepts. The data accumulation principle is the main tool for achieving asymptotic unknown parameter estimation. It relies on the parametric identifiability system property introduced. Necessary and sufficient conditions for exponential stability of the data accumulation dynamics are derived. The approach is applied in a nonlinear adaptive speed tracking vector control of a three-phase induction motor.
19. Aerodynamic Modeling of NREL 5-MW Wind Turbine for Nonlinear Control System Design: A Case Study Based on Real-Time Nonlinear Receding Horizon Control
Directory of Open Access Journals (Sweden)
Pedro A. Galvani
2016-08-01
Full Text Available The work presented in this paper has two major aspects: (i investigation of a simple, yet efficient model of the NREL (National Renewable Energy Laboratory 5-MW reference wind turbine; (ii nonlinear control system development through a real-time nonlinear receding horizon control methodology with application to wind turbine control dynamics. In this paper, the results of our simple wind turbine model and a real-time nonlinear control system implementation are shown in comparison with conventional control methods. For this purpose, the wind turbine control problem is converted into an optimization problem and is directly solved by the nonlinear backwards sweep Riccati method to generate the control protocol, which results in a non-iterative algorithm. One main contribution of this paper is that we provide evidence through simulations, that such an advanced control strategy can be used for real-time control of wind turbine dynamics. Examples are provided to validate and demonstrate the effectiveness of the presented scheme.
20. Fuzzy Counter Propagation Neural Network Control for a Class of Nonlinear Dynamical Systems.
Science.gov (United States)
Sakhre, Vandana; Jain, Sanjeev; Sapkal, Vilas S; Agarwal, Dev P
2015-01-01
Fuzzy Counter Propagation Neural Network (FCPN) controller design is developed, for a class of nonlinear dynamical systems. In this process, the weight connecting between the instar and outstar, that is, input-hidden and hidden-output layer, respectively, is adjusted by using Fuzzy Competitive Learning (FCL). FCL paradigm adopts the principle of learning, which is used to calculate Best Matched Node (BMN) which is proposed. This strategy offers a robust control of nonlinear dynamical systems. FCPN is compared with the existing network like Dynamic Network (DN) and Back Propagation Network (BPN) on the basis of Mean Absolute Error (MAE), Mean Square Error (MSE), Best Fit Rate (BFR), and so forth. It envisages that the proposed FCPN gives better results than DN and BPN. The effectiveness of the proposed FCPN algorithms is demonstrated through simulations of four nonlinear dynamical systems and multiple input and single output (MISO) and a single input and single output (SISO) gas furnace Box-Jenkins time series data.
1. The system of nonlinear adaptive control for wind turbine with DFIG
Directory of Open Access Journals (Sweden)
Mikhail Medvedev
2014-12-01
Full Text Available This paper presents a problem solution of the stable voltage generating in the changing terms of environment for the double-fed induction generator (DFIG. For this, in nonlinear multivariable systems, such as mathematical model of DFIG, the method of observer’s synthesis for external, parametric and structural disturbances was used. This allows, on the basis of disturbances approximation, to carry out an evaluation under conditions of uncertainty, leading to disturbances adaptation with a priori unknown structure. The work presents a synthesis method of control system, allowing to solve indicated problem. Stand-alone wind turbine used as a power plant with DFIG. The control system uses the original nonlinear mathematical model of the DFIG in rotating “dq” coordinates, taking into account non-linear changes in the parameters. To confirm the effectiveness of the problem solution, mathematical computer model was developed. The paper also presents the results of full-scale simulation.
2. Recurrent fuzzy neural network backstepping control for the prescribed output tracking performance of nonlinear dynamic systems.
Science.gov (United States)
Han, Seong-Ik; Lee, Jang-Myung
2014-01-01
This paper proposes a backstepping control system that uses a tracking error constraint and recurrent fuzzy neural networks (RFNNs) to achieve a prescribed tracking performance for a strict-feedback nonlinear dynamic system. A new constraint variable was defined to generate the virtual control that forces the tracking error to fall within prescribed boundaries. An adaptive RFNN was also used to obtain the required improvement on the approximation performances in order to avoid calculating the explosive number of terms generated by the recursive steps of traditional backstepping control. The boundedness and convergence of the closed-loop system was confirmed based on the Lyapunov stability theory. The prescribed performance of the proposed control scheme was validated by using it to control the prescribed error of a nonlinear system and a robot manipulator. © 2013 ISA. Published by Elsevier Ltd. All rights reserved.
3. Feedback control systems for non-linear simulation of operational transients in LMFBRs
International Nuclear Information System (INIS)
Khatib-Rahbar, M.; Agrawal, A.K.; Srinivasan, E.S.
1979-01-01
Feedback control systems for non-linear simulation of operational transients in LMFBRs are developed. The models include (1) the reactor power control and rod drive mechanism, (2) sodium flow control and pump drive system, (3) steam generator flow control and valve actuator dynamics, and (4) the supervisory control. These models have been incorporated into the SSC code using a flexible approach, in order to accommodate some design dependent variations. The impact of system nonlinearity on the control dynamics is shown to be significant for severe perturbations. Representative result for a 10 cent and 25 cent step insertion of reactivity and a 10% ramp change in load in 40 seconds demonstrate the suitability of this model for study of operational transients without scram in LMFBRs
4. Model-on-Demand Predictive Control for Nonlinear Hybrid Systems With Application to Adaptive Behavioral Interventions
Science.gov (United States)
Nandola, Naresh N.; Rivera, Daniel E.
2011-01-01
This paper presents a data-centric modeling and predictive control approach for nonlinear hybrid systems. System identification of hybrid systems represents a challenging problem because model parameters depend on the mode or operating point of the system. The proposed algorithm applies Model-on-Demand (MoD) estimation to generate a local linear approximation of the nonlinear hybrid system at each time step, using a small subset of data selected by an adaptive bandwidth selector. The appeal of the MoD approach lies in the fact that model parameters are estimated based on a current operating point; hence estimation of locations or modes governed by autonomous discrete events is achieved automatically. The local MoD model is then converted into a mixed logical dynamical (MLD) system representation which can be used directly in a model predictive control (MPC) law for hybrid systems using multiple-degree-of-freedom tuning. The effectiveness of the proposed MoD predictive control algorithm for nonlinear hybrid systems is demonstrated on a hypothetical adaptive behavioral intervention problem inspired by Fast Track, a real-life preventive intervention for improving parental function and reducing conduct disorder in at-risk children. Simulation results demonstrate that the proposed algorithm can be useful for adaptive intervention problems exhibiting both nonlinear and hybrid character. PMID:21874087
5. Utilization of excitation signal harmonics for control of nonlinear systems
DEFF Research Database (Denmark)
2012-01-01
signal together with Fourier analysis to generate a feedback signal and simulations have shown that different system gains and time constants does not change the global equilibrium/operating point. An evaporator in a refrigeration system was used as example in the simulations, however, it is anticipated...... that the method is applicable in a wide variety of systems satisfying the sigmoid function properties....
6. Dynamics of nonlinear feedback control
OpenAIRE
Snippe, H.P.; Hateren, J.H. van
2007-01-01
Feedback control in neural systems is ubiquitous. Here we study the mathematics of nonlinear feedback control. We compare models in which the input is multiplied by a dynamic gain (multiplicative control) with models in which the input is divided by a dynamic attenuation (divisive control). The gain signal (resp. the attenuation signal) is obtained through a concatenation of an instantaneous nonlinearity and a linear low-pass filter operating on the output of the feedback loop. For input step...
7. Stabilization and tracking controller for a class of nonlinear discrete-time systems
International Nuclear Information System (INIS)
Sharma, B.B.; Kar, I.N.
2011-01-01
Highlights: → We present recursive design of stabilizing controller for nonlinear discrete-time systems. → Problem of stabilizing and tracking control of single link manipulator system is addressed. → We extend the proposed results to output tracking problems. → The proposed methodology is applied satisfactorily to discrete-time chaotic maps. - Abstract: In this paper, stabilization and tracking control problem for parametric strict feedback class of discrete time systems is addressed. Recursive design of control function based on contraction theory framework is proposed instead of traditional Lyapunov based method. Explicit structure of controller is derived for the addressed class of nonlinear discrete-time systems. Conditions for exponential stability of system states are derived in terms of controller parameters. At each stage of recursive procedure a specific structure of Jacobian matrix is ensured so as to satisfy conditions of stability. The closed loop dynamics in this case remains nonlinear in nature. The proposed algorithm establishes global stability results in quite a simple manner as it does not require formulation of error dynamics. Problem of stabilization and output tracking control in case of single link manipulator system with actuator dynamics is analyzed using the proposed strategy. The proposed results are further extended to stabilization of discrete time chaotic systems. Numerical simulations presented in the end show the effectiveness of the proposed approach.
8. Neural feedback linearization adaptive control for affine nonlinear systems based on neural network estimator
Directory of Open Access Journals (Sweden)
Bahita Mohamed
2011-01-01
Full Text Available In this work, we introduce an adaptive neural network controller for a class of nonlinear systems. The approach uses two Radial Basis Functions, RBF networks. The first RBF network is used to approximate the ideal control law which cannot be implemented since the dynamics of the system are unknown. The second RBF network is used for on-line estimating the control gain which is a nonlinear and unknown function of the states. The updating laws for the combined estimator and controller are derived through Lyapunov analysis. Asymptotic stability is established with the tracking errors converging to a neighborhood of the origin. Finally, the proposed method is applied to control and stabilize the inverted pendulum system.
9. Nonlinear Robust Disturbance Attenuation Control Design for Static Var Compensator in Power System
Directory of Open Access Journals (Sweden)
Ting Liu
2013-01-01
Full Text Available The problem of designing an adaptive backstepping controller for nonlinear static var compensator (SVC system is addressed adopting two perspectives. First, instead of artificially assuming an upper bound or inequality scaling, the minimax theory is used to treat the external unknown disturbances. The system is insensitive to effects of large disturbances due to taking into account the worst case disturbance. Second, a parameter projection mechanism is introduced in adaptive control to force the parameter estimate within a prior specified interval. The proposed controller handles the nonlinear parameterization without compromising control smoothness and at the same time the parameter estimate speed is improved and the robustness of system is strengthened. Considering the short-circuit ground fault and mechanical power perturbation, a simulation study is carried out. The results show the effectiveness of the proposed control method.
10. Adaptive near-optimal neuro controller for continuous-time nonaffine nonlinear systems with constrained input.
Science.gov (United States)
Esfandiari, Kasra; Abdollahi, Farzaneh; Talebi, Heidar Ali
2017-09-01
In this paper, an identifier-critic structure is introduced to find an online near-optimal controller for continuous-time nonaffine nonlinear systems having saturated control signal. By employing two Neural Networks (NNs), the solution of Hamilton-Jacobi-Bellman (HJB) equation associated with the cost function is derived without requiring a priori knowledge about system dynamics. Weights of the identifier and critic NNs are tuned online and simultaneously such that unknown terms are approximated accurately and the control signal is kept between the saturation bounds. The convergence of NNs' weights, identification error, and system states is guaranteed using Lyapunov's direct method. Finally, simulation results are performed on two nonlinear systems to confirm the effectiveness of the proposed control strategy. Copyright © 2017 Elsevier Ltd. All rights reserved.
11. A general U-block model-based design procedure for nonlinear polynomial control systems
Science.gov (United States)
Zhu, Q. M.; Zhao, D. Y.; Zhang, Jianhua
2016-10-01
The proposition of U-model concept (in terms of 'providing concise and applicable solutions for complex problems') and a corresponding basic U-control design algorithm was originated in the first author's PhD thesis. The term of U-model appeared (not rigorously defined) for the first time in the first author's other journal paper, which established a framework for using linear polynomial control system design approaches to design nonlinear polynomial control systems (in brief, linear polynomial approaches → nonlinear polynomial plants). This paper represents the next milestone work - using linear state-space approaches to design nonlinear polynomial control systems (in brief, linear state-space approaches → nonlinear polynomial plants). The overall aim of the study is to establish a framework, defined as the U-block model, which provides a generic prototype for using linear state-space-based approaches to design the control systems with smooth nonlinear plants/processes described by polynomial models. For analysing the feasibility and effectiveness, sliding mode control design approach is selected as an exemplary case study. Numerical simulation studies provide a user-friendly step-by-step procedure for the readers/users with interest in their ad hoc applications. In formality, this is the first paper to present the U-model-oriented control system design in a formal way and to study the associated properties and theorems. The previous publications, in the main, have been algorithm-based studies and simulation demonstrations. In some sense, this paper can be treated as a landmark for the U-model-based research from intuitive/heuristic stage to rigour/formal/comprehensive studies.
12. Nonlinear Robust Observer-Based Fault Detection for Networked Suspension Control System of Maglev Train
Directory of Open Access Journals (Sweden)
Yun Li
2013-01-01
Full Text Available A fault detection approach based on nonlinear robust observer is designed for the networked suspension control system of Maglev train with random induced time delay. First, considering random bounded time-delay and external disturbance, the nonlinear model of the networked suspension control system is established. Then, a nonlinear robust observer is designed using the input of the suspension gap. And the estimate error is proved to be bounded with arbitrary precision by adopting an appropriate parameter. When sensor faults happen, the residual between the real states and the observer outputs indicates which kind of sensor failures occurs. Finally, simulation results using the actual parameters of CMS-04 maglev train indicate that the proposed method is effective for maglev train.
13. Application of numerical optimization techniques to control system design for nonlinear dynamic models of aircraft
Science.gov (United States)
Lan, C. Edward; Ge, Fuying
1989-01-01
Control system design for general nonlinear flight dynamic models is considered through numerical simulation. The design is accomplished through a numerical optimizer coupled with analysis of flight dynamic equations. The general flight dynamic equations are numerically integrated and dynamic characteristics are then identified from the dynamic response. The design variables are determined iteratively by the optimizer to optimize a prescribed objective function which is related to desired dynamic characteristics. Generality of the method allows nonlinear effects to aerodynamics and dynamic coupling to be considered in the design process. To demonstrate the method, nonlinear simulation models for an F-5A and an F-16 configurations are used to design dampers to satisfy specifications on flying qualities and control systems to prevent departure. The results indicate that the present method is simple in formulation and effective in satisfying the design objectives.
14. L1 adaptive control of uncertain gear transmission servo systems with deadzone nonlinearity.
Science.gov (United States)
Zuo, Zongyu; Li, Xiao; Shi, Zhiguang
2015-09-01
15. Grid-forming VSC control in four-wire systems with unbalanced nonlinear loads
DEFF Research Database (Denmark)
Lliuyacca, Ruben; Mauricioa, Juan M.; Gomez-Exposito, Antonio
2017-01-01
A grid-forming voltage source converter (VSC) is responsible to hold voltage and frequency in autonomous operation of isolated systems. In the presence of unbalanced loads, a fourth leg is added to provide current path for neutral currents. In this paper, a novel control scheme for a four-leg VSC...... feeding unbalanced linear and nonlinear loads is proposed. The control is based on two control blocks. A main control commands the switching sequence to the three-phase VSC ensuring balanced three-phase voltage at the output; and an independent control to the fourth leg drives neutral currents that might...... response during system disturbances and mitigation of harmonics when nonlinear loads are present. Simulations and experimental results are presented to verify the performance of the proposed control strategy....
16. Distributed Adaptive Containment Control for a Class of Nonlinear Multiagent Systems With Input Quantization.
Science.gov (United States)
Wang, Chenliang; Wen, Changyun; Hu, Qinglei; Wang, Wei; Zhang, Xiuyu
2018-06-01
This paper is devoted to distributed adaptive containment control for a class of nonlinear multiagent systems with input quantization. By employing a matrix factorization and a novel matrix normalization technique, some assumptions involving control gain matrices in existing results are relaxed. By fusing the techniques of sliding mode control and backstepping control, a two-step design method is proposed to construct controllers and, with the aid of neural networks, all system nonlinearities are allowed to be unknown. Moreover, a linear time-varying model and a similarity transformation are introduced to circumvent the obstacle brought by quantization, and the controllers need no information about the quantizer parameters. The proposed scheme is able to ensure the boundedness of all closed-loop signals and steer the containment errors into an arbitrarily small residual set. The simulation results illustrate the effectiveness of the scheme.
17. Identification and control of chaos in nonlinear gear dynamic systems using Melnikov analysis
International Nuclear Information System (INIS)
Farshidianfar, A.; Saghafi, A.
2014-01-01
In this paper, the Melnikov analysis is extended to develop a practical model of gear system to control and eliminate the chaotic behavior. To this end, a nonlinear dynamic model of a spur gear pair with backlash, time-varying stiffness and static transmission error is established. Based on the Melnikov analysis the global homoclinic bifurcation and transition to chaos in this model are predicted. Then non-feedback control method is used to eliminate the chaos by applying an additional control excitation. The regions of the parameter space for the control excitation are obtained analytically. The accuracy of the theoretical predictions and also the performance of the proposed control system are verified by the comparison with the numerical simulations. The simulation results show effectiveness of the proposed control system and present some useful information to analyze and control the gear dynamical systems. - Highlights: • This study deals with the prediction and control of chaos in a nonlinear gear system. • Melnikov analysis is extended to present a practical gear system to control the chaos. • The proposed system is effective to eliminate the homoclinic bifurcation and chaos. • This controller is proposed as a way of implementing the chaos control in gear system
18. Spatial Domain Adaptive Control of Nonlinear Rotary Systems Subject to Spatially Periodic Disturbances
Directory of Open Access Journals (Sweden)
Yen-Hsiu Yang
2012-01-01
Full Text Available We propose a generic spatial domain control scheme for a class of nonlinear rotary systems of variable speeds and subject to spatially periodic disturbances. The nonlinear model of the rotary system in time domain is transformed into one in spatial domain employing a coordinate transformation with respect to angular displacement. Under the circumstances that measurement of the system states is not available, a nonlinear state observer is established for providing the estimated states. A two-degree-of-freedom spatial domain control configuration is then proposed to stabilize the system and improve the tracking performance. The first control module applies adaptive backstepping with projected parametric update and concentrates on robust stabilization of the closed-loop system. The second control module introduces an internal model of the periodic disturbances cascaded with a loop-shaping filter, which not only further reduces the tracking error but also improves parametric adaptation. The overall spatial domain output feedback adaptive control system is robust to model uncertainties and state estimated error and capable of rejecting spatially periodic disturbances under varying system speeds. Stability proof of the overall system is given. A design example with simulation demonstrates the applicability of the proposed design.
19. Adaptive Neural Control for a Class of Outputs Time-Delay Nonlinear Systems
Directory of Open Access Journals (Sweden)
Ruliang Wang
2012-01-01
Full Text Available This paper considers an adaptive neural control for a class of outputs time-delay nonlinear systems with perturbed or no. Based on RBF neural networks, the radius basis function (RBF neural networks is employed to estimate the unknown continuous functions. The proposed control guarantees that all closed-loop signals remain bounded. The simulation results demonstrate the effectiveness of the proposed control scheme.
20. Dissipative Control Systems and Disturbance Attenuation for Nonlinear H∞ Problems
International Nuclear Information System (INIS)
Frankowska, H.; Quincampoix, M.
1999-01-01
We characterize functions satisfying a dissipative inequality associated with a control problem. Such a characterization is provided in terms of an epicontingent solution, or a viscosity supersolution to a partial differential equation called Isaacs' equation. Links between supersolutions and epicontingent solutions to Isaacs' equation are studied. Finally, we derive (possibly discontinuous) disturbance attenuation feedback of the H ∞ problem from contingent formulation of Isaacs' equation
1. Robust nonlinear control design with application to a marine cooling system
DEFF Research Database (Denmark)
Hansen, Michael; Stoustrup, Jakob; Bendtsen, Jan Dimon
2012-01-01
. In this context, we apply a bilinear transformation to obtain a well-posed H-inf problem. The design procedure is applied to a marine cooling system with flow dependent delays and performance of the resulting control design is evaluated through a simulation example where a comparison is made to a linear control......In this paper we consider design of control laws for a class of nonlinear systems with time-varying state delays by use of principles from feedback linearization. To deal with model uncertainties and delay mismatches, a robust linear H-inf controller is designed for the feedback linearized system...
2. Design of a Polynomial Fuzzy Observer Controller With Sampled-Output Measurements for Nonlinear Systems Considering Unmeasurable Premise Variables
OpenAIRE
Liu, Chuang; Lam, H. K.
2015-01-01
In this paper, we propose a polynomial fuzzy observer controller for nonlinear systems, where the design is achieved through the stability analysis of polynomial-fuzzy-model-based (PFMB) observer-control system. The polynomial fuzzy observer estimates the system states using estimated premise variables. The estimated states are then employed by the polynomial fuzzy controller for the feedback control of nonlinear systems represented by the polynomial fuzzy model. The system stability of the P...
3. Adaptive estimation for control of uncertain nonlinear systems with applications to target tracking
Science.gov (United States)
2005-08-01
Design of nonlinear observers has received considerable attention since the early development of methods for linear state estimation. The most popular approach is the extended Kalman filter (EKF), that goes through significant degradation in the presence of nonlinearities, particularly if unmodeled dynamics are coupled to the process and the measurement. For uncertain nonlinear systems, adaptive observers have been introduced to estimate the unknown state variables where no priori information about the unknown parameters is available. While establishing global results, these approaches are applicable only to systems transformable to output feedback form. Over the recent years, neural network (NN) based identification and estimation schemes have been proposed that relax the assumptions on the system at the price of sacrificing on the global nature of the results. However, most of the NN based adaptive observer approaches in the literature require knowledge of the full dimension of the system, therefore may not be suitable for systems with unmodeled dynamics. We first propose a novel approach to nonlinear state estimation from the perspective of augmenting a linear time invariant observer with an adaptive element. The class of nonlinear systems treated here are finite but of otherwise unknown dimension. The objective is to improve the performance of the linear observer when applied to a nonlinear system. The approach relies on the ability of the NNs to approximate the unknown dynamics from finite time histories of available measurements. Next we investigate nonlinear state estimation from the perspective of adaptively augmenting an existing time varying observer, such as an EKF. EKFs find their applications mostly in target tracking problems. The proposed approaches are robust to unmodeled dynamics, including unmodeled disturbances. Lastly, we consider the problem of adaptive estimation in the presence of feedback control for a class of uncertain nonlinear systems
4. Joint nonlinearity effects in the design of a flexible truss structure control system
Science.gov (United States)
1986-01-01
Nonlinear effects are introduced in the dynamics of large space truss structures by the connecting joints which are designed with rather important tolerances to facilitate the assembly of the structures in space. The purpose was to develop means to investigate the nonlinear dynamics of the structures, particularly the limit cycles that might occur when active control is applied to the structures. An analytical method was sought and derived to predict the occurrence of limit cycles and to determine their stability. This method is mainly based on the quasi-linearization of every joint using describing functions. This approach was proven successful when simple dynamical systems were tested. Its applicability to larger systems depends on the amount of computations it requires, and estimates of the computational task tend to indicate that the number of individual sources of nonlinearity should be limited. Alternate analytical approaches, which do not account for every single nonlinearity, or the simulation of a simplified model of the dynamical system should, therefore, be investigated to determine a more effective way to predict limit cycles in large dynamical systems with an important number of distributed nonlinearities.
5. Adaptive fuzzy wavelet network control of second order multi-agent systems with unknown nonlinear dynamics.
Science.gov (United States)
Taheri, Mehdi; Sheikholeslam, Farid; Najafi, Majddedin; Zekri, Maryam
2017-07-01
6. Nonlinear robust control of hypersonic aircrafts with interactions between flight dynamics and propulsion systems.
Science.gov (United States)
Li, Zhaoying; Zhou, Wenjie; Liu, Hao
2016-09-01
This paper addresses the nonlinear robust tracking controller design problem for hypersonic vehicles. This problem is challenging due to strong coupling between the aerodynamics and the propulsion system, and the uncertainties involved in the vehicle dynamics including parametric uncertainties, unmodeled model uncertainties, and external disturbances. By utilizing the feedback linearization technique, a linear tracking error system is established with prescribed references. For the linear model, a robust controller is proposed based on the signal compensation theory to guarantee that the tracking error dynamics is robustly stable. Numerical simulation results are given to show the advantages of the proposed nonlinear robust control method, compared to the robust loop-shaping control approach. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.
7. Real time computer control of a nonlinear Multivariable System via Linearization and Stability Analysis
International Nuclear Information System (INIS)
Raza, K.S.M.
2004-01-01
This paper demonstrates that if a complicated nonlinear, non-square, state-coupled multi variable system is smartly linearized and subjected to a thorough stability analysis then we can achieve our design objectives via a controller which will be quite simple (in term of resource usage and execution time) and very efficient (in terms of robustness). Further the aim is to implement this controller via computer in a real time environment. Therefore first a nonlinear mathematical model of the system is achieved. An intelligent work is done to decouple the multivariable system. Linearization and stability analysis techniques are employed for the development of a linearized and mathematically sound control law. Nonlinearities like the saturation in actuators are also been catered. The controller is then discretized using Runge-Kutta integration. Finally the discretized control law is programmed in a computer in a real time environment. The programme is done in RT -Linux using GNU C for the real time realization of the control scheme. The real time processes, like sampling and controlled actuation, and the non real time processes, like graphical user interface and display, are programmed as different tasks. The issue of inter process communication, between real time and non real time task is addressed quite carefully. The results of this research pursuit are presented graphically. (author)
8. Optimal control of nonlinear continuous-time systems in strict-feedback form.
Science.gov (United States)
Zargarzadeh, Hassan; Dierks, Travis; Jagannathan, Sarangapani
2015-10-01
This paper proposes a novel optimal tracking control scheme for nonlinear continuous-time systems in strict-feedback form with uncertain dynamics. The optimal tracking problem is transformed into an equivalent optimal regulation problem through a feedforward adaptive control input that is generated by modifying the standard backstepping technique. Subsequently, a neural network-based optimal control scheme is introduced to estimate the cost, or value function, over an infinite horizon for the resulting nonlinear continuous-time systems in affine form when the internal dynamics are unknown. The estimated cost function is then used to obtain the optimal feedback control input; therefore, the overall optimal control input for the nonlinear continuous-time system in strict-feedback form includes the feedforward plus the optimal feedback terms. It is shown that the estimated cost function minimizes the Hamilton-Jacobi-Bellman estimation error in a forward-in-time manner without using any value or policy iterations. Finally, optimal output feedback control is introduced through the design of a suitable observer. Lyapunov theory is utilized to show the overall stability of the proposed schemes without requiring an initial admissible controller. Simulation examples are provided to validate the theoretical results.
9. Indirect fuzzy adaptive control of a class of SISO nonlinear systems
International Nuclear Information System (INIS)
Laboid, S.; Boucherit, M.S.
2006-01-01
This paper presents an adaptive fuzzy control scheme for a class of continuous-time single-input single-output nonlinear systems with unknown dynamics and disturbance. Within this scheme, the fuzzy systems are employed to approximate the unknown system's dynamics. The proposed controller is composed of a well-defined adaptive fuzzy control term that uses the adaptive fuzzy approximation errors and disturbance. Based on a Lyapunov synthesis method, it is shown that the proposed adaptive control scheme guarantees the convergence of the tracking error to zero and the global boundedness of all signals in the closed-loop system. Moreover, the proposed controller allows initialization by zero of all adjusted parameters in the fuzzy approximators, and does not require the knowledge of the lower bound of the control gain and upper bounds of the approximation errors and disturbance. Simulation results performed on an inverted pendulum system are given to point out the good performance of the developed adaptive controller. (author)
10. Dynamics of nonlinear feedback control
NARCIS (Netherlands)
Snippe, H.P.; Hateren, J.H. van
Feedback control in neural systems is ubiquitous. Here we study the mathematics of nonlinear feedback control. We compare models in which the input is multiplied by a dynamic gain (multiplicative control) with models in which the input is divided by a dynamic attenuation (divisive control). The gain
11. Impulsive Controller Design for Complex Nonlinear Singular Networked Systems with Packet Dropouts
Directory of Open Access Journals (Sweden)
Xian-Lin Zhao
2013-01-01
Full Text Available Globally exponential stability of Complex (with coupling Nonlinear Singular Impulsive Networked Control Systems (CNSINCS with packet dropouts and time-delay is investigated. Firstly, the mathematic model of CNSINCS is established. Then, by employing the method of Lyapunov functional, exponential stability criteria are obtained and the impulsive controller design method is given. Finally, some simulation results are provided to demonstrate the effectiveness of the proposed method.
12. Transformation of CLF to ISS-CLF for Nonlinear Systems with Disturbance and Construction of Nonlinear Robust Controller with L2 Gain Performance
Directory of Open Access Journals (Sweden)
Keizo Okano
2014-01-01
Full Text Available A new nonlinear control law for a class of nonlinear systems with disturbance is proposed. A control law is designed by transforming control Lyapunov function (CLF to input-to-state stability control Lyapunov function (ISS-CLF. The transformed CLF satisfies a Hamilton-Jacobi-Isaacs (HJI equation. The feedback system by the proposed control law has characteristics of L2 gain. Finally, it is shown by a numerical example that the proposed control law makes a controller by feedback linearization robust against disturbance.
13. Stability Control of Force-Reflected Nonlinear Multilateral Teleoperation System under Time-Varying Delays
Directory of Open Access Journals (Sweden)
Da Sun
2016-01-01
Full Text Available A novel control algorithm based on the modified wave-variable controllers is proposed to achieve accurate position synchronization and reasonable force tracking of the nonlinear single-master-multiple-slave teleoperation system and simultaneously guarantee overall system’s stability in the presence of large time-varying delays. The system stability in different scenarios of human and environment situations has been analyzed. The proposed method is validated through experimental work based on the 3-DOF trilateral teleoperation system consisting of three different manipulators. The experimental results clearly demonstrate the feasibility of the proposed algorithm to achieve high transparency and robust stability in nonlinear single-master-multiple-slave teleoperation system in the presence of time-varying delays.
14. Prescribed Performance Fuzzy Adaptive Output-Feedback Control for Nonlinear Stochastic Systems
Directory of Open Access Journals (Sweden)
Lili Zhang
2014-01-01
Full Text Available A prescribed performance fuzzy adaptive output-feedback control approach is proposed for a class of single-input and single-output nonlinear stochastic systems with unmeasured states. Fuzzy logic systems are used to identify the unknown nonlinear system, and a fuzzy state observer is designed for estimating the unmeasured states. Based on the backstepping recursive design technique and the predefined performance technique, a new fuzzy adaptive output-feedback control method is developed. It is shown that all the signals of the resulting closed-loop system are bounded in probability and the tracking error remains an adjustable neighborhood of the origin with the prescribed performance bounds. A simulation example is provided to show the effectiveness of the proposed approach.
15. Adaptive Neural Tracking Control for Discrete-Time Switched Nonlinear Systems with Dead Zone Inputs
Directory of Open Access Journals (Sweden)
Jidong Wang
2017-01-01
Full Text Available In this paper, the adaptive neural controllers of subsystems are proposed for a class of discrete-time switched nonlinear systems with dead zone inputs under arbitrary switching signals. Due to the complicated framework of the discrete-time switched nonlinear systems and the existence of the dead zone, it brings about difficulties for controlling such a class of systems. In addition, the radial basis function neural networks are employed to approximate the unknown terms of each subsystem. Switched update laws are designed while the parameter estimation is invariable until its corresponding subsystem is active. Then, the closed-loop system is stable and all the signals are bounded. Finally, to illustrate the effectiveness of the proposed method, an example is employed.
16. Reinforcement learning for adaptive optimal control of unknown continuous-time nonlinear systems with input constraints
Science.gov (United States)
Yang, Xiong; Liu, Derong; Wang, Ding
2014-03-01
In this paper, an adaptive reinforcement learning-based solution is developed for the infinite-horizon optimal control problem of constrained-input continuous-time nonlinear systems in the presence of nonlinearities with unknown structures. Two different types of neural networks (NNs) are employed to approximate the Hamilton-Jacobi-Bellman equation. That is, an recurrent NN is constructed to identify the unknown dynamical system, and two feedforward NNs are used as the actor and the critic to approximate the optimal control and the optimal cost, respectively. Based on this framework, the action NN and the critic NN are tuned simultaneously, without the requirement for the knowledge of system drift dynamics. Moreover, by using Lyapunov's direct method, the weights of the action NN and the critic NN are guaranteed to be uniformly ultimately bounded, while keeping the closed-loop system stable. To demonstrate the effectiveness of the present approach, simulation results are illustrated.
17. Uncertainty Modeling and Robust Output Feedback Control of Nonlinear Discrete Systems: A Mathematical Programming Approach
Directory of Open Access Journals (Sweden)
Olav Slupphaug
2001-01-01
Full Text Available We present a mathematical programming approach to robust control of nonlinear systems with uncertain, possibly time-varying, parameters. The uncertain system is given by different local affine parameter dependent models in different parts of the state space. It is shown how this representation can be obtained from a nonlinear uncertain system by solving a set of continuous linear semi-infinite programming problems, and how each of these problems can be solved as a (finite series of ordinary linear programs. Additionally, the system representation includes control- and state constraints. The controller design method is derived from Lyapunov stability arguments and utilizes an affine parameter dependent quadratic Lyapunov function. The controller has a piecewise affine output feedback structure, and the design amounts to finding a feasible solution to a set of linear matrix inequalities combined with one spectral radius constraint on the product of two positive definite matrices. A local solution approach to this nonconvex feasibility problem is proposed. Complexity of the design method and some special cases such as state- feedback are discussed. Finally, an application of the results is given by proposing an on-line computationally feasible algorithm for constrained nonlinear state- feedback model predictive control with robust stability.
18. Quasiperiodic AlGaAs superlattices for neuromorphic networks and nonlinear control systems
Energy Technology Data Exchange (ETDEWEB)
Malyshev, K. V., E-mail: malyshev@bmstu.ru [Electronics and Laser Technology Department, Bauman Moscow State Technical University, Moscow 105005 (Russian Federation)
2015-01-28
The application of quasiperiodic AlGaAs superlattices as a nonlinear element of the FitzHugh–Nagumo neuromorphic network is proposed and theoretically investigated on the example of Fibonacci and figurate superlattices. The sequences of symbols for the figurate superlattices were produced by decomposition of the Fibonacci superlattices' symbolic sequences. A length of each segment of the decomposition was equal to the corresponding figurate number. It is shown that a nonlinear network based upon Fibonacci and figurate superlattices provides better parallel filtration of a half-tone picture; then, a network based upon traditional diodes which have cubic voltage-current characteristics. It was found that the figurate superlattice F{sup 0}{sub 11}(1) as a nonlinear network's element provides the filtration error almost twice less than the conventional “cubic” diode. These advantages are explained by a wavelike shape of the decreasing part of the quasiperiodic superlattice's voltage-current characteristic, which leads to multistability of the network's cell. This multistability promises new interesting nonlinear dynamical phenomena. A variety of wavy forms of voltage-current characteristics opens up new interesting possibilities for quasiperiodic superlattices and especially for figurate superlattices in many areas—from nervous system modeling to nonlinear control systems development.
19. Adaptive critic designs for optimal control of uncertain nonlinear systems with unmatched interconnections.
Science.gov (United States)
Yang, Xiong; He, Haibo
2018-05-26
In this paper, we develop a novel optimal control strategy for a class of uncertain nonlinear systems with unmatched interconnections. To begin with, we present a stabilizing feedback controller for the interconnected nonlinear systems by modifying an array of optimal control laws of auxiliary subsystems. We also prove that this feedback controller ensures a specified cost function to achieve optimality. Then, under the framework of adaptive critic designs, we use critic networks to solve the Hamilton-Jacobi-Bellman equations associated with auxiliary subsystem optimal control laws. The critic network weights are tuned through the gradient descent method combined with an additional stabilizing term. By using the newly established weight tuning rules, we no longer need the initial admissible control condition. In addition, we demonstrate that all signals in the closed-loop auxiliary subsystems are stable in the sense of uniform ultimate boundedness by using classic Lyapunov techniques. Finally, we provide an interconnected nonlinear plant to validate the present control scheme. Copyright © 2018 Elsevier Ltd. All rights reserved.
20. Control-Oriented Modeling and System Identification for Nonlinear Trajectory Tracking Control of a Small-Scale Unmanned Helicopter
Science.gov (United States)
Pourrezaei Khaligh, Sepehr
Model-based control design of small-scale helicopters involves considerable challenges due to their nonlinear and underactuated dynamics with strong couplings between the different degrees-of-freedom (DOFs). Most nonlinear model-based multi-input multi-output (MIMO) control approaches require the dynamic model of the system to be affine-in-control and fully actuated. Since the existing formulations for helicopter nonlinear dynamic model do not meet these requirements, these MIMO approaches cannot be applied for control of helicopters and control designs in the literature mostly use the linearized model of the helicopter dynamics around different trim conditions instead of directly using the nonlinear model. The purpose of this thesis is to derive the 6-DOF nonlinear model of the helicopter in an affine-in-control, non-iterative and square input-output formulation to enable many nonlinear control approaches, that require a control-affine and square model such as the sliding mode control (SMC), to be used for control design of small-scale helicopters. A combination of the first-principles approach and system identification is used to derive this model. To complete the nonlinear model of the helicopter required for the control design, the inverse kinematics of the actuating mechanisms of the main and tail rotors are also derived using an approach suitable for the real-time control applications. The parameters of the new control-oriented formulation are identified using a time-domain system identification strategy and the model is validated using flight test data. A robust sliding mode control (SMC) is then designed using the new formulation of the helicopter dynamics and its robustness to parameter uncertainties and wind disturbances is tested in simulations. Next, a hardware-in-the-loop (HIL) testbed is designed to allow for the control implementation and gain tuning as well as testing the robustness of the controller to external disturbances in a controlled
1. Nonlinear control of linear parameter varying systems with applications to hypersonic vehicles
Science.gov (United States)
Wilcox, Zachary Donald
The focus of this dissertation is to design a controller for linear parameter varying (LPV) systems, apply it specifically to air-breathing hypersonic vehicles, and examine the interplay between control performance and the structural dynamics design. Specifically a Lyapunov-based continuous robust controller is developed that yields exponential tracking of a reference model, despite the presence of bounded, nonvanishing disturbances. The hypersonic vehicle has time varying parameters, specifically temperature profiles, and its dynamics can be reduced to an LPV system with additive disturbances. Since the HSV can be modeled as an LPV system the proposed control design is directly applicable. The control performance is directly examined through simulations. A wide variety of applications exist that can be effectively modeled as LPV systems. In particular, flight systems have historically been modeled as LPV systems and associated control tools have been applied such as gain-scheduling, linear matrix inequalities (LMIs), linear fractional transformations (LFT), and mu-types. However, as the type of flight environments and trajectories become more demanding, the traditional LPV controllers may no longer be sufficient. In particular, hypersonic flight vehicles (HSVs) present an inherently difficult problem because of the nonlinear aerothermoelastic coupling effects in the dynamics. HSV flight conditions produce temperature variations that can alter both the structural dynamics and flight dynamics. Starting with the full nonlinear dynamics, the aerothermoelastic effects are modeled by a temperature dependent, parameter varying state-space representation with added disturbances. The model includes an uncertain parameter varying state matrix, an uncertain parameter varying non-square (column deficient) input matrix, and an additive bounded disturbance. In this dissertation, a robust dynamic controller is formulated for a uncertain and disturbed LPV system. The developed
2. Fractional-order sliding mode control for a class of uncertain nonlinear systems based on LQR
Directory of Open Access Journals (Sweden)
Dong Zhang
2017-03-01
Full Text Available This article presents a new fractional-order sliding mode control (FOSMC strategy based on a linear-quadratic regulator (LQR for a class of uncertain nonlinear systems. First, input/output feedback linearization is used to linearize the nonlinear system and decouple tracking error dynamics. Second, LQR is designed to ensure that the tracking error dynamics converges to the equilibrium point as soon as possible. Based on LQR, a novel fractional-order sliding surface is introduced. Subsequently, the FOSMC is designed to reject system uncertainties and reduce the magnitude of control chattering. Then, the global stability of the closed-loop control system is analytically proved using Lyapunov stability theory. Finally, a typical single-input single-output system and a typical multi-input multi-output system are simulated to illustrate the effectiveness and advantages of the proposed control strategy. The results of the simulation indicate that the proposed control strategy exhibits excellent performance and robustness with system uncertainties. Compared to conventional integer-order sliding mode control, the high-frequency chattering of the control input is drastically depressed.
3. Block backstepping design of nonlinear state feedback control law for underactuated mechanical systems
CERN Document Server
2017-01-01
This book presents a novel, generalized approach to the design of nonlinear state feedback control laws for a large class of underactuated mechanical systems based on application of the block backstepping method. The control law proposed here is robust against the effects of model uncertainty in dynamic and steady-state performance and addresses the issue of asymptotic stabilization for the class of underactuated mechanical systems. An underactuated system is defined as one for which the dimension of space spanned by the configuration vector is greater than that of the space spanned by the control variables. Control problems concerning underactuated systems currently represent an active field of research due to their broad range of applications in robotics, aerospace, and marine contexts. The book derives a generalized theory of block backstepping control design for underactuated mechanical systems, and examines several case studies that cover interesting examples of underactuated mechanical systems. The math...
4. Adaptive Event-Triggered Control Based on Heuristic Dynamic Programming for Nonlinear Discrete-Time Systems.
Science.gov (United States)
Dong, Lu; Zhong, Xiangnan; Sun, Changyin; He, Haibo
2017-07-01
This paper presents the design of a novel adaptive event-triggered control method based on the heuristic dynamic programming (HDP) technique for nonlinear discrete-time systems with unknown system dynamics. In the proposed method, the control law is only updated when the event-triggered condition is violated. Compared with the periodic updates in the traditional adaptive dynamic programming (ADP) control, the proposed method can reduce the computation and transmission cost. An actor-critic framework is used to learn the optimal event-triggered control law and the value function. Furthermore, a model network is designed to estimate the system state vector. The main contribution of this paper is to design a new trigger threshold for discrete-time systems. A detailed Lyapunov stability analysis shows that our proposed event-triggered controller can asymptotically stabilize the discrete-time systems. Finally, we test our method on two different discrete-time systems, and the simulation results are included.
5. Fuzzy Adaptive Compensation Control of Uncertain Stochastic Nonlinear Systems With Actuator Failures and Input Hysteresis.
Science.gov (United States)
Wang, Jianhui; Liu, Zhi; Chen, C L Philip; Zhang, Yun
2017-10-12
Hysteresis exists ubiquitously in physical actuators. Besides, actuator failures/faults may also occur in practice. Both effects would deteriorate the transient tracking performance, and even trigger instability. In this paper, we consider the problem of compensating for actuator failures and input hysteresis by proposing a fuzzy control scheme for stochastic nonlinear systems. Compared with the existing research on stochastic nonlinear uncertain systems, it is found that how to guarantee a prescribed transient tracking performance when taking into account actuator failures and hysteresis simultaneously also remains to be answered. Our proposed control scheme is designed on the basis of the fuzzy logic system and backstepping techniques for this purpose. It is proven that all the signals remain bounded and the tracking error is ensured to be within a preestablished bound with the failures of hysteretic actuator. Finally, simulations are provided to illustrate the effectiveness of the obtained theoretical results.
6. Distributed robust adaptive control of high order nonlinear multi agent systems.
Science.gov (United States)
Hashemi, Mahnaz; Shahgholian, Ghazanfar
2018-03-01
7. Nonlinear, Adaptive and Fault-tolerant Control for Electro-hydraulic Servo Systems
DEFF Research Database (Denmark)
Choux, Martin
is designed and implemented on the test bed that successfully diagnoses internal or external leakages, friction variations in the actuator or fault related to pressure sensors. The presented algorithm uses the position and pressure measurements to detect and isolate faults, avoiding missed detection and false...... numerous attractive properties, hydraulic systems are always subject to potential leakages in their components, friction variation in their hydraulic actuators and deciency in their sensors. These violations of normal behaviour reduce the system performances and can lead to system failure...... if they are not detected early and handled. Moreover, the task of controlling electro hydraulic systems for high performance operations is challenging due to the highly nonlinear behaviour of such systems and the large amount of uncertainties present in their models. This thesis focuses on nonlinear adaptive fault...
8. H∞ Excitation Control Design for Stochastic Power Systems with Input Delay Based on Nonlinear Hamiltonian System Theory
Directory of Open Access Journals (Sweden)
Weiwei Sun
2015-01-01
Full Text Available This paper presents H∞ excitation control design problem for power systems with input time delay and disturbances by using nonlinear Hamiltonian system theory. The impact of time delays introduced by remote signal transmission and processing in wide-area measurement system (WAMS is well considered. Meanwhile, the systems under investigation are disturbed by random fluctuation. First, under prefeedback technique, the power systems are described as a nonlinear Hamiltonian system. Then the H∞ excitation controller of generators connected to distant power systems with time delay and stochasticity is designed. Based on Lyapunov functional method, some sufficient conditions are proposed to guarantee the rationality and validity of the proposed control law. The closed-loop systems under the control law are asymptotically stable in mean square independent of the time delay. And we through a simulation of a two-machine power system prove the effectiveness of the results proposed in this paper.
9. Controller Parameter Optimization for Nonlinear Systems Using Enhanced Bacteria Foraging Algorithm
Directory of Open Access Journals (Sweden)
V. Rajinikanth
2012-01-01
Full Text Available An enhanced bacteria foraging optimization (EBFO algorithm-based Proportional + integral + derivative (PID controller tuning is proposed for a class of nonlinear process models. The EBFO algorithm is a modified form of standard BFO algorithm. A multiobjective performance index is considered to guide the EBFO algorithm for discovering the best possible value of controller parameters. The efficiency of the proposed scheme has been validated through a comparative study with classical BFO, adaptive BFO, PSO, and GA based controller tuning methods proposed in the literature. The proposed algorithm is tested in real time on a nonlinear spherical tank system. The real-time results show that, EBFO tuned PID controller gives a smooth response for setpoint tracking performance.
10. Nonlinear control of voltage source converters in AC-DC power system.
Science.gov (United States)
Dash, P K; Nayak, N
2014-07-01
This paper presents the design of a robust nonlinear controller for a parallel AC-DC power system using a Lyapunov function-based sliding mode control (LYPSMC) strategy. The inputs for the proposed control scheme are the DC voltage and reactive power errors at the converter station and the active and reactive power errors at the inverter station of the voltage-source converter-based high voltage direct current transmission (VSC-HVDC) link. The stability and robust tracking of the system parameters are ensured by applying the Lyapunov direct method. Also the gains of the sliding mode control (SMC) are made adaptive using the stability conditions of the Lyapunov function. The proposed control strategy offers invariant stability to a class of systems having modeling uncertainties due to parameter changes and exogenous inputs. Comprehensive computer simulations are carried out to verify the proposed control scheme under several system disturbances like changes in short-circuit ratio, converter parametric changes, and faults on the converter and inverter buses for single generating system connected to the power grid in a single machine infinite-bus AC-DC network and also for a 3-machine two-area power system. Furthermore, a second order super twisting sliding mode control scheme has been presented in this paper that provides a higher degree of nonlinearity than the LYPSMC and damps faster the converter and inverter voltage and power oscillations. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.
11. The genetic algorithm for the nonlinear programming of water pollution control system
Energy Technology Data Exchange (ETDEWEB)
Wei, J.; Zhang, J. [China University of Geosciences (China)
1999-08-01
In the programming of water pollution control system the combined method of optimization with simulation is used generally. It is not only laborious in calculation, but also the global optimum of the obtained solution is guaranteed difficult. In this paper, the genetic algorithm (GA) used in the nonlinear programming of water pollution control system is given, by which the preferred conception for the programming of waste water system is found in once-through operation. It is more succinct than the conventional method and the global optimum of the obtained solution could be ensured. 6 refs., 4 figs., 3 tabs.
12. Analysis and control of nonlinear systems. A flatness-based approach
Energy Technology Data Exchange (ETDEWEB)
Levine, Jean [MINES-Paris Tech, 77 - Fontainebleau (France). CAS, Unite Mathematiques et Systemes
2009-07-01
This is the first book on a hot topic in the field of control of nonlinear systems. It ranges from mathematical system theory to practical industrial control applications and addresses two fundamental questions in Systems and Control: how to plan the motion of a system and track the corresponding trajectory in presence of perturbations. It emphasizes on structural aspects and in particular on a class of systems called differentially flat. Part 1 discusses the mathematical theory and part 2 outlines applications of this method in the fields of electric drives (DC motors and linear synchronous motors), magnetic bearings, automotive equipments, cranes, and automatic flight control systems. The author offers web-based videos illustrating some dynamical aspects and case studies in simulation (Scilab and Matlab). (orig.)
13. Analytic Model Predictive Control of Uncertain Nonlinear Systems: A Fuzzy Adaptive Approach
Directory of Open Access Journals (Sweden)
Xiuyan Peng
2015-01-01
Full Text Available A fuzzy adaptive analytic model predictive control method is proposed in this paper for a class of uncertain nonlinear systems. Specifically, invoking the standard results from the Moore-Penrose inverse of matrix, the unmatched problem which exists commonly in input and output dimensions of systems is firstly solved. Then, recurring to analytic model predictive control law, combined with fuzzy adaptive approach, the fuzzy adaptive predictive controller synthesis for the underlying systems is developed. To further reduce the impact of fuzzy approximation error on the system and improve the robustness of the system, the robust compensation term is introduced. It is shown that by applying the fuzzy adaptive analytic model predictive controller the rudder roll stabilization system is ultimately uniformly bounded stabilized in the H-infinity sense. Finally, simulation results demonstrate the effectiveness of the proposed method.
14. Robust Model Predictive Control of a Nonlinear System with Known Scheduling Variable and Uncertain Gain
DEFF Research Database (Denmark)
Mirzaei, Mahmood; Poulsen, Niels Kjølstad; Niemann, Hans Henrik
2012-01-01
Robust model predictive control (RMPC) of a class of nonlinear systems is considered in this paper. We will use Linear Parameter Varying (LPV) model of the nonlinear system. By taking the advantage of having future values of the scheduling variable, we will simplify state prediction. Because...... of the special structure of the problem, uncertainty is only in the B matrix (gain) of the state space model. Therefore by taking advantage of this structure, we formulate a tractable minimax optimization problem to solve robust model predictive control problem. Wind turbine is chosen as the case study and we...... choose wind speed as the scheduling variable. Wind speed is measurable ahead of the turbine, therefore the scheduling variable is known for the entire prediction horizon....
15. Learning-Based Adaptive Optimal Tracking Control of Strict-Feedback Nonlinear Systems.
Science.gov (United States)
Gao, Weinan; Jiang, Zhong-Ping; Weinan Gao; Zhong-Ping Jiang; Gao, Weinan; Jiang, Zhong-Ping
2018-06-01
This paper proposes a novel data-driven control approach to address the problem of adaptive optimal tracking for a class of nonlinear systems taking the strict-feedback form. Adaptive dynamic programming (ADP) and nonlinear output regulation theories are integrated for the first time to compute an adaptive near-optimal tracker without any a priori knowledge of the system dynamics. Fundamentally different from adaptive optimal stabilization problems, the solution to a Hamilton-Jacobi-Bellman (HJB) equation, not necessarily a positive definite function, cannot be approximated through the existing iterative methods. This paper proposes a novel policy iteration technique for solving positive semidefinite HJB equations with rigorous convergence analysis. A two-phase data-driven learning method is developed and implemented online by ADP. The efficacy of the proposed adaptive optimal tracking control methodology is demonstrated via a Van der Pol oscillator with time-varying exogenous signals.
16. Distributed Containment Control for Multiple Unknown Second-Order Nonlinear Systems With Application to Networked Lagrangian Systems.
Science.gov (United States)
Mei, Jie; Ren, Wei; Li, Bing; Ma, Guangfu
2015-09-01
In this paper, we consider the distributed containment control problem for multiagent systems with unknown nonlinear dynamics. More specifically, we focus on multiple second-order nonlinear systems and networked Lagrangian systems. We first study the distributed containment control problem for multiple second-order nonlinear systems with multiple dynamic leaders in the presence of unknown nonlinearities and external disturbances under a general directed graph that characterizes the interaction among the leaders and the followers. A distributed adaptive control algorithm with an adaptive gain design based on the approximation capability of neural networks is proposed. We present a necessary and sufficient condition on the directed graph such that the containment error can be reduced as small as desired. As a byproduct, the leaderless consensus problem is solved with asymptotical convergence. Because relative velocity measurements between neighbors are generally more difficult to obtain than relative position measurements, we then propose a distributed containment control algorithm without using neighbors' velocity information. A two-step Lyapunov-based method is used to study the convergence of the closed-loop system. Next, we apply the ideas to deal with the containment control problem for networked unknown Lagrangian systems under a general directed graph. All the proposed algorithms are distributed and can be implemented using only local measurements in the absence of communication. Finally, simulation examples are provided to show the effectiveness of the proposed control algorithms.
17. Robust control of nonlinear MAGLEV suspension system with mismatched uncertainties via DOBC approach.
Science.gov (United States)
Yang, Jun; Zolotas, Argyrios; Chen, Wen-Hua; Michail, Konstantinos; Li, Shihua
2011-07-01
Robust control of a class of uncertain systems that have disturbances and uncertainties not satisfying "matching" condition is investigated in this paper via a disturbance observer based control (DOBC) approach. In the context of this paper, "matched" disturbances/uncertainties stand for the disturbances/uncertainties entering the system through the same channels as control inputs. By properly designing a disturbance compensation gain, a novel composite controller is proposed to counteract the "mismatched" lumped disturbances from the output channels. The proposed method significantly extends the applicability of the DOBC methods. Rigorous stability analysis of the closed-loop system with the proposed method is established under mild assumptions. The proposed method is applied to a nonlinear MAGnetic LEViation (MAGLEV) suspension system. Simulation shows that compared to the widely used integral control method, the proposed method provides significantly improved disturbance rejection and robustness against load variation. Copyright © 2011 ISA. Published by Elsevier Ltd. All rights reserved.
18. Design of a Discrete Tracking Controller for a Magnetic Levitation System: A Nonlinear Rational Model Approach
Directory of Open Access Journals (Sweden)
Fernando Gómez-Salas
2015-01-01
Full Text Available This work proposes a discrete-time nonlinear rational approximate model for the unstable magnetic levitation system. Based on this model and as an application of the input-output linearization technique, a discrete-time tracking control design will be derived using the corresponding classical state space representation of the model. A simulation example illustrates the efficiency of the proposed methodology.
19. An energy-saving nonlinear position control strategy for electro-hydraulic servo systems.
Science.gov (United States)
2015-11-01
The electro-hydraulic servo system (EHSS) demonstrates numerous advantages in size and performance compared to other actuation methods. Oftentimes, its utilization in industrial and machinery settings is limited by its inferior efficiency. In this paper, a nonlinear backstepping control algorithm with an energy-saving approach is proposed for position control in the EHSS. To achieve improved efficiency, two control valves including a proportional directional valve (PDV) and a proportional relief valve (PRV) are used to achieve the control objectives. To design the control algorithm, the state space model equations of the system are transformed to their normal form and the control law through the PDV is designed using a backstepping approach for position tracking. Then, another nonlinear set of laws is derived to achieve energy-saving through the PRV input. This control design method, based on the normal form representation, imposes internal dynamics on the closed-loop system. The stability of the internal dynamics is analyzed in special cases of operation. Experimental results verify that both tracking and energy-saving objectives are satisfied for the closed-loop system. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.
20. Nonclassical state generation for linear quantum systems via nonlinear feedback control
International Nuclear Information System (INIS)
Ohki, Kentaro; Tsumura, Koji; Takeuchi, Reiji
2017-01-01
In this paper, we propose a measurement nonlinear feedback control scheme to generate Wigner-function negativity in an optical cavity having dynamics described as a linear quantum system. In general, linear optical quantum systems can be easily constructed with reliable devices; therefore, the idea of constructing the entire system with such an optical system and nonlinear feedback is reasonable for generating Wigner-function negativity. However, existing studies have insufficiently examined the realizability or actual implementation of feedback control, which essentially requires fast responses from the sensors and actuators. In order to solve this problem, we consider the realizable feedback control of the optical phase of a pumping beam supplied to a cavity by using electro-optical modulation, which can be utilized as a fast control actuator. Then, we introduce mathematical models of the feedback-controlled system and evaluate its effect on the generation of the Wigner-function negativity by using numerical simulation. Through various numerical simulations, we show that the proposed feedback control can effectively generate the negativity of the Wigner function. (paper)
1. Event-Triggered Distributed Approximate Optimal State and Output Control of Affine Nonlinear Interconnected Systems.
Science.gov (United States)
Narayanan, Vignesh; Jagannathan, Sarangapani
2017-06-08
This paper presents an approximate optimal distributed control scheme for a known interconnected system composed of input affine nonlinear subsystems using event-triggered state and output feedback via a novel hybrid learning scheme. First, the cost function for the overall system is redefined as the sum of cost functions of individual subsystems. A distributed optimal control policy for the interconnected system is developed using the optimal value function of each subsystem. To generate the optimal control policy, forward-in-time, neural networks are employed to reconstruct the unknown optimal value function at each subsystem online. In order to retain the advantages of event-triggered feedback for an adaptive optimal controller, a novel hybrid learning scheme is proposed to reduce the convergence time for the learning algorithm. The development is based on the observation that, in the event-triggered feedback, the sampling instants are dynamic and results in variable interevent time. To relax the requirement of entire state measurements, an extended nonlinear observer is designed at each subsystem to recover the system internal states from the measurable feedback. Using a Lyapunov-based analysis, it is demonstrated that the system states and the observer errors remain locally uniformly ultimately bounded and the control policy converges to a neighborhood of the optimal policy. Simulation results are presented to demonstrate the performance of the developed controller.
2. Design of a nonlinear backstepping control strategy of grid interconnected wind power system based PMSG
Science.gov (United States)
Errami, Y.; Obbadi, A.; Sahnoun, S.; Benhmida, M.; Ouassaid, M.; Maaroufi, M.
2016-07-01
This paper presents nonlinear backstepping control for Wind Power Generation System (WPGS) based Permanent Magnet Synchronous Generator (PMSG) and connected to utility grid. The block diagram of the WPGS with PMSG and the grid side back-to-back converter is established with the dq frame of axes. This control scheme emphasises the regulation of the dc-link voltage and the control of the power factor at changing wind speed. Besides, in the proposed control strategy of WPGS, Maximum Power Point Tracking (MPPT) technique and pitch control are provided. The stability of the regulators is assured by employing Lyapunov analysis. The proposed control strategy for the system has been validated by MATLAB simulations under varying wind velocity and the grid fault condition. In addition, a comparison of simulation results based on the proposed Backstepping strategy and conventional Vector Control is provided.
3. Finite Time Control for Fractional Order Nonlinear Hydroturbine Governing System via Frequency Distributed Model
Directory of Open Access Journals (Sweden)
Bin Wang
2016-01-01
Full Text Available This paper studies the application of frequency distributed model for finite time control of a fractional order nonlinear hydroturbine governing system (HGS. Firstly, the mathematical model of HGS with external random disturbances is introduced. Secondly, a novel terminal sliding surface is proposed and its stability to origin is proved based on the frequency distributed model and Lyapunov stability theory. Furthermore, based on finite time stability and sliding mode control theory, a robust control law to ensure the occurrence of the sliding motion in a finite time is designed for stabilization of the fractional order HGS. Finally, simulation results show the effectiveness and robustness of the proposed scheme.
4. An open-closed-loop iterative learning control approach for nonlinear switched systems with application to freeway traffic control
Science.gov (United States)
Sun, Shu-Ting; Li, Xiao-Dong; Zhong, Ren-Xin
2017-10-01
For nonlinear switched discrete-time systems with input constraints, this paper presents an open-closed-loop iterative learning control (ILC) approach, which includes a feedforward ILC part and a feedback control part. Under a given switching rule, the mathematical induction is used to prove the convergence of ILC tracking error in each subsystem. It is demonstrated that the convergence of ILC tracking error is dependent on the feedforward control gain, but the feedback control can speed up the convergence process of ILC by a suitable selection of feedback control gain. A switched freeway traffic system is used to illustrate the effectiveness of the proposed ILC law.
5. Prediction Governors for Input-Affine Nonlinear Systems and Application to Automatic Driving Control
Directory of Open Access Journals (Sweden)
Yuki Minami
2018-04-01
Full Text Available In recent years, automatic driving control has attracted attention. To achieve a satisfactory driving control performance, the prediction accuracy of the traveling route is important. If a highly accurate prediction method can be used, an accurate traveling route can be obtained. Despite the considerable efforts that have been invested in improving prediction methods, prediction errors do occur in general. Thus, a method to minimize the influence of prediction errors on automatic driving control systems is required. This need motivated us to focus on the design of a mechanism for shaping prediction signals, which is called a prediction governor. In this study, we first extended our previous study to the input-affine nonlinear system case. Then, we analytically derived a solution to an optimal design problem of prediction governors. Finally, we applied the solution to an automatic driving control system, and demonstrated its usefulness through a numerical example and an experiment using a radio controlled car.
6. Optimization of Thermal Object Nonlinear Control Systems by Energy Efficiency Criterion.
Science.gov (United States)
2018-03-01
This article presents the results of thermal object functioning control analysis (heat exchanger, dryer, heat treatment chamber, etc.). The results were used to determine a mathematical model of the generalized thermal control object. The appropriate optimality criterion was chosen to make the control more energy-efficient. The mathematical programming task was formulated based on the chosen optimality criterion, control object mathematical model and technological constraints. The “maximum energy efficiency” criterion helped avoid solving a system of nonlinear differential equations and solve the formulated problem of mathematical programming in an analytical way. It should be noted that in the case under review the search for optimal control and optimal trajectory reduces to solving an algebraic system of equations. In addition, it is shown that the optimal trajectory does not depend on the dynamic characteristics of the control object.
7. Nonlinear chaos control and synchronization
NARCIS (Netherlands)
Huijberts, H.J.C.; Nijmeijer, H.; Schöll, E.; Schuster, H.G.
2007-01-01
This chapter contains sections titled: Introduction Nonlinear Geometric Control Some Differential Geometric Concepts Nonlinear Controllability Chaos Control Through Feedback Linearization Chaos Control Through Input-Output Linearization Lyapunov Design Lyapunov Stability and Lyapunov's First Method
8. Fuzzy Counter Propagation Neural Network Control for a Class of Nonlinear Dynamical Systems
Directory of Open Access Journals (Sweden)
Vandana Sakhre
2015-01-01
Full Text Available Fuzzy Counter Propagation Neural Network (FCPN controller design is developed, for a class of nonlinear dynamical systems. In this process, the weight connecting between the instar and outstar, that is, input-hidden and hidden-output layer, respectively, is adjusted by using Fuzzy Competitive Learning (FCL. FCL paradigm adopts the principle of learning, which is used to calculate Best Matched Node (BMN which is proposed. This strategy offers a robust control of nonlinear dynamical systems. FCPN is compared with the existing network like Dynamic Network (DN and Back Propagation Network (BPN on the basis of Mean Absolute Error (MAE, Mean Square Error (MSE, Best Fit Rate (BFR, and so forth. It envisages that the proposed FCPN gives better results than DN and BPN. The effectiveness of the proposed FCPN algorithms is demonstrated through simulations of four nonlinear dynamical systems and multiple input and single output (MISO and a single input and single output (SISO gas furnace Box-Jenkins time series data.
9. Synchronization controller design of two coupling permanent magnet synchronous motors system with nonlinear constraints.
Science.gov (United States)
Deng, Zhenhua; Shang, Jing; Nian, Xiaohong
2015-11-01
In this paper, two coupling permanent magnet synchronous motors system with nonlinear constraints is studied. First of all, the mathematical model of the system is established according to the engineering practices, in which the dynamic model of motor and the nonlinear coupling effect between two motors are considered. In order to keep the two motors synchronization, a synchronization controller based on load observer is designed via cross-coupling idea and interval matrix. Moreover, speed, position and current signals of two motor all are taken as self-feedback signal as well as cross-feedback signal in the proposed controller, which is conducive to improving the dynamical performance and the synchronization performance of the system. The proposed control strategy is verified by simulation via Matlab/Simulink program. The simulation results show that the proposed control method has a better control performance, especially synchronization performance, than that of the conventional PI controller. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.
10. Adaptive Control of Nonlinear Discrete-Time Systems by Using OS-ELM Neural Networks
Directory of Open Access Journals (Sweden)
Xiao-Li Li
2014-01-01
Full Text Available As a kind of novel feedforward neural network with single hidden layer, ELM (extreme learning machine neural networks are studied for the identification and control of nonlinear dynamic systems. The property of simple structure and fast convergence of ELM can be shown clearly. In this paper, we are interested in adaptive control of nonlinear dynamic plants by using OS-ELM (online sequential extreme learning machine neural networks. Based on data scope division, the problem that training process of ELM neural network is sensitive to the initial training data is also solved. According to the output range of the controlled plant, the data corresponding to this range will be used to initialize ELM. Furthermore, due to the drawback of conventional adaptive control, when the OS-ELM neural network is used for adaptive control of the system with jumping parameters, the topological structure of the neural network can be adjusted dynamically by using multiple model switching strategy, and an MMAC (multiple model adaptive control will be used to improve the control performance. Simulation results are included to complement the theoretical results.
11. EDITORIAL: Nonlinear optical manipulation, patterning and control in nano- and micro-scale systems Nonlinear optical manipulation, patterning and control in nano- and micro-scale systems
Science.gov (United States)
Denz, Cornelia; Simoni, Francesco
2009-03-01
Nonlinearities are becoming more and more important for a variety of applications in nanosciences, bio-medical sciences, information processing and photonics. For applications at the crossings of these fields, especially microscopic and nanoscopic imaging and manipulation, nonlinearities play a key role. They may range from simple nonlinear parameter changes up to applications in manipulating, controlling and structuring material by light, or the manipulation of light by light itself. It is this area between basic nonlinear optics and photonic applications that includes hot' topics such as ultra-resolution optical microscopy, micro- and nanomanipulation and -structuring, or nanophotonics. This special issue contains contributions in this field, many of them from the International Conference on Nonlinear Microscopy and Optical Control held in conjunction with a network meeting of the ESF COST action MP0604 Optical Micromanipulation by Nonlinear Nanophotonics', 19-22 February 2008, Münster, Germany. Throughout this special issue, basic investigations of material structuring by nonlinear light--matter interaction, light-induced control of nanoparticles, and novel nonlinear material investigation techniques, are presented, covering the basic field of optical manipulation and control. These papers are followed by impressive developments of optical tweezers. Nowadays, optical phase contrast tweezers, twin and especially multiple beam traps, develop particle control in a new dimension: particles can be arranged, sorted and identified with high throughput. One of the most prominent forthcoming applications of optical tweezers is in the field of microfluidics. The action of light on fluids will open new horizons in microfluidic manipulation and control. The field of optical manipulation and control is a very broad field that has developed in an impressive way, in a short time, in Europe with the installation of the MP0604 network. Top researchers from 19 countries are
12. Sky-Hook Control and Kalman Filtering in Nonlinear Model of Tracked Vehicle Suspension System
Directory of Open Access Journals (Sweden)
Jurkiewicz Andrzej
2017-09-01
Full Text Available The essence of the undertaken topic is application of the continuous sky-hook control strategy and the Extended Kalman Filter as the state observer in the 2S1 tracked vehicle suspension system. The half-car model of this suspension system consists of seven logarithmic spiral springs and two magnetorheological dampers which has been described by the Bingham model. The applied continuous sky-hook control strategy considers nonlinear stiffness characteristic of the logarithmic spiral springs. The control is determined on estimates generated by the Extended Kalman Filter. Improve of ride comfort is verified by comparing simulation results, under the same driving conditions, of controlled and passive vehicle suspension systems.
13. Non-fragile ?-? control for discrete-time stochastic nonlinear systems under event-triggered protocols
Science.gov (United States)
Sun, Ying; Ding, Derui; Zhang, Sunjie; Wei, Guoliang; Liu, Hongjian
2018-07-01
In this paper, the non-fragile ?-? control problem is investigated for a class of discrete-time stochastic nonlinear systems under event-triggered communication protocols, which determine whether the measurement output should be transmitted to the controller or not. The main purpose of the addressed problem is to design an event-based output feedback controller subject to gain variations guaranteeing the prescribed disturbance attenuation level described by the ?-? performance index. By utilizing the Lyapunov stability theory combined with S-procedure, a sufficient condition is established to guarantee both the exponential mean-square stability and the ?-? performance for the closed-loop system. In addition, with the help of the orthogonal decomposition, the desired controller parameter is obtained in terms of the solution to certain linear matrix inequalities. Finally, a simulation example is exploited to demonstrate the effectiveness of the proposed event-based controller design scheme.
14. Robust Backstepping Control for Cold Rolling Main Drive System with Nonlinear Uncertainties
Directory of Open Access Journals (Sweden)
Xu Yang
2013-01-01
Full Text Available The nonlinear model of main drive system in cold rolling process, which considers the influence with parameter uncertainties such as clearance and variable friction coefficient, as well as external disturbance by roll eccentricity and variation of strip material quality, is built. By transformation, the lower triangular structure form of main drive system is obtained. The backstepping algorithm based on signal compensation is proposed to design a linear time-invariant (LTI robust controller, including a nominal controller and a robust compensator. A comparison with PI controller shows that the controller has better disturbance attenuation performance and tracking behaviors. Meanwhile, according to its LTI characteristic, the robust controller can be realized easily; therefore it is also appropriated to high speed dynamic rolling process.
15. Experimental investigation of the seismic control of a nonlinear soil-structure system using MR dampers
International Nuclear Information System (INIS)
Li, Hui; Wang, Jian
2011-01-01
This paper reports the results of an experimental study conducted to demonstrate the feasibility and capability of magnetorheological (MR) dampers commanded by a decentralized control algorithm for seismic control of nonlinear civil structures considering soil-structure interaction (SSI). A two-story reinforced concrete (RC) frame resting in a laminar soil container is employed as the test specimen, and two MR dampers equipped in the first story are used to mitigate the response of this frame subjected to various intensity seismic excitations. A hyperbolic tangent function is used to represent the hysteretic behavior of the MR damper and a decentralized control approach for commanding MR dampers is proposed and implemented in the shaking table tests. Only the response of the first story is feedback for control command calculation of the MR dampers. The results indicate that the MR damper can effectively reduce the response of the soil-structure system, even when the soil-structure system presents complex nonlinear hysteretic behavior. The robustness of the proposed decentralized control algorithm is validated through the shaking table tests on the soil-structure system with large uncertainty. The most interesting findings in this paper are that MR dampers not only mitigate the superstructure response, but also reduce the soil response, pile response and earth pressure on the pile foundation
16. Nonlinear Control of Heartbeat Models
Directory of Open Access Journals (Sweden)
Witt Thanom
2011-02-01
Full Text Available This paper presents a novel application of nonlinear control theory to heartbeat models. Existing heartbeat models are investigated and modified by incorporating the control input as a pacemaker to provide the control channel. A nonlinear feedback linearization technique is applied to force the output of the systems to generate artificial electrocardiogram (ECG signal using discrete data as the reference inputs. The synthetic ECG may serve as a flexible signal source to assess the effectiveness of a diagnostic ECG signal-processing device.
17. Generalized Synchronization of Nonlinear Chaotic Systems through Natural Bioinspired Controlling Strategy
Directory of Open Access Journals (Sweden)
Shih-Yu Li
2015-01-01
Full Text Available A novel bioinspired control strategy design is proposed for generalized synchronization of nonlinear chaotic systems, combining the bioinspired stability theory, fuzzy modeling, and a novel, simple-form Lyapunov control function design of derived high efficient, heuristic and bioinspired controllers. Three main contributions are concluded: (1 apply the bioinspired stability theory to further analyze the stability of fuzzy error systems; the high performance of controllers has been shown in previous study by Li and Ge 2009, (2 a new Lyapunov control function based on bioinspired stability theory is designed to achieve synchronization without using traditional LMI method, which is a simple linear homogeneous function of states and the process of designing controller to synchronize two fuzzy chaotic systems becomes much simpler, and (3 three different situations of synchronization are proposed; classical master and slave Lorenz systems, slave Chen’s system, and Rossler’s system as functional system are illustrated to further show the effectiveness and feasibility of our novel strategy. The simulation results show that our novel control strategy can be applied to different and complicated control situations with high effectiveness.
18. A nonlinear plate control without linearization
Directory of Open Access Journals (Sweden)
Yildirim Kenan
2017-03-01
Full Text Available In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as a penalty term. By using a maximum principle, the nonlinear control problem is transformed to solving a system of partial differential equations including state and adjoint variables linked by initial-boundary-terminal conditions. Hence, it is shown that optimal control of the nonlinear systems can be obtained without linearization of the nonlinear term and optimal control function can be obtained analytically for nonlinear systems without linearization.
19. The Design of Feedback Control Systems Containing a Saturation Type Nonlinearity
Science.gov (United States)
Schmidt, Stanley F.; Harper, Eleanor V.
1960-01-01
A derivation of the optimum response for a step input for plant transfer functions which have an unstable pole and further data on plants with a single zero in the left half of the s plane. The calculated data are presented tabulated in normalized form. Optimum control systems are considered. The optimum system is defined as one which keeps the error as small as possible regardless of the input, under the constraint that the input to the plant (or controlled system) is limited. Intuitive arguments show that in the case where only the error can be sensed directly, the optimum system is obtained from the optimum relay or on-off solution. References to known solutions are presented. For the case when the system is of the sampled-data type, arguments are presented which indicate the optimum sampled-data system may be extremely difficult if not impossible to realize practically except for very simple plant transfer functions. Two examples of aircraft attitude autopilots are presented, one for a statically stable and the other for a statically unstable airframe. The rate of change of elevator motion is assumed limited for these examples. It is shown that by use of nonlinear design techniques described in NASA TN D-20 one can obtain near optimum response for step inputs and reason- able response to sine wave inputs for either case. Also, the nonlinear design prevents inputs from driving the system unstable for either case.
20. Variable Structure Disturbance Rejection Control for Nonlinear Uncertain Systems with State and Control Delays via Optimal Sliding Mode Surface Approach
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Jing Lei
2013-01-01
Full Text Available The paper considers the problem of variable structure control for nonlinear systems with uncertainty and time delays under persistent disturbance by using the optimal sliding mode surface approach. Through functional transformation, the original time-delay system is transformed into a delay-free one. The approximating sequence method is applied to solve the nonlinear optimal sliding mode surface problem which is reduced to a linear two-point boundary value problem of approximating sequences. The optimal sliding mode surface is obtained from the convergent solutions by solving a Riccati equation, a Sylvester equation, and the state and adjoint vector differential equations of approximating sequences. Then, the variable structure disturbance rejection control is presented by adopting an exponential trending law, where the state and control memory terms are designed to compensate the state and control delays, a feedforward control term is designed to reject the disturbance, and an adjoint compensator is designed to compensate the effects generated by the nonlinearity and the uncertainty. Furthermore, an observer is constructed to make the feedforward term physically realizable, and thus the dynamical observer-based dynamical variable structure disturbance rejection control law is produced. Finally, simulations are demonstrated to verify the effectiveness of the presented controller and the simplicity of the proposed approach.
1. Waveform control method for mitigating harmonics of inverter systems with nonlinear load
DEFF Research Database (Denmark)
Wang, Haoran; Zhu, Guorong; Fu, Xiaobin
2015-01-01
instability in the DC power system, lower its efficiency, and shorten the lifetime of the DC source. This paper presents a general waveform control method that can mitigate the injection of the low-frequency ripple current by the single-phase DC/AC inverter into the DC source. It also discusses the inhibiting......DC power systems connecting to single-phase DC/AC inverters with nonlinear loads will have their DC sources being injected with AC ripple currents containing a low-frequency component at twice the output voltage frequency of the inverter and also other current harmonics. Such a current may create...
2. Numerical Oscillations Analysis for Nonlinear Delay Differential Equations in Physiological Control Systems
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Qi Wang
2012-01-01
Full Text Available This paper deals with the oscillations of numerical solutions for the nonlinear delay differential equations in physiological control systems. The exponential θ-method is applied to p′(t=β0ωμp(t−τ/(ωμ+pμ(t−τ−γp(t and it is shown that the exponential θ-method has the same order of convergence as that of the classical θ-method. Several conditions under which the numerical solutions oscillate are derived. Moreover, it is proven that every nonoscillatory numerical solution tends to positive equilibrium of the continuous system. Finally, the main results are illustrated with numerical examples.
3. Linear and non-linear systems identification for adaptive control in mechanical applications vibration suppression
Science.gov (United States)
Cazzulani, Gabriele; Resta, Ferruccio; Ripamonti, Francesco
2012-04-01
During the last years, more and more mechanical applications saw the introduction of active control strategies. In particular, the need of improving the performances and/or the system health is very often associated to vibration suppression. This goal can be achieved considering both passive and active solutions. In this sense, many active control strategies have been developed, such as the Independent Modal Space Control (IMSC) or the resonant controllers (PPF, IRC, . . .). In all these cases, in order to tune and optimize the control strategy, the knowledge of the system dynamic behaviour is very important and it can be achieved both considering a numerical model of the system or through an experimental identification process. Anyway, dealing with non-linear or time-varying systems, a tool able to online identify the system parameters becomes a key-point for the control logic synthesis. The aim of the present work is the definition of a real-time technique, based on ARMAX models, that estimates the system parameters starting from the measurements of piezoelectric sensors. These parameters are returned to the control logic, that automatically adapts itself to the system dynamics. The problem is numerically investigated considering a carbon-fiber plate model forced through a piezoelectric patch.
4. New human-centered linear and nonlinear motion cueing algorithms for control of simulator motion systems
Science.gov (United States)
Telban, Robert J.
While the performance of flight simulator motion system hardware has advanced substantially, the development of the motion cueing algorithm, the software that transforms simulated aircraft dynamics into realizable motion commands, has not kept pace. To address this, new human-centered motion cueing algorithms were developed. A revised "optimal algorithm" uses time-invariant filters developed by optimal control, incorporating human vestibular system models. The "nonlinear algorithm" is a novel approach that is also formulated by optimal control, but can also be updated in real time. It incorporates a new integrated visual-vestibular perception model that includes both visual and vestibular sensation and the interaction between the stimuli. A time-varying control law requires the matrix Riccati equation to be solved in real time by a neurocomputing approach. Preliminary pilot testing resulted in the optimal algorithm incorporating a new otolith model, producing improved motion cues. The nonlinear algorithm vertical mode produced a motion cue with a time-varying washout, sustaining small cues for longer durations and washing out large cues more quickly compared to the optimal algorithm. The inclusion of the integrated perception model improved the responses to longitudinal and lateral cues. False cues observed with the NASA adaptive algorithm were absent. As a result of unsatisfactory sensation, an augmented turbulence cue was added to the vertical mode for both the optimal and nonlinear algorithms. The relative effectiveness of the algorithms, in simulating aircraft maneuvers, was assessed with an eleven-subject piloted performance test conducted on the NASA Langley Visual Motion Simulator (VMS). Two methods, the quasi-objective NASA Task Load Index (TLX), and power spectral density analysis of pilot control, were used to assess pilot workload. TLX analysis reveals, in most cases, less workload and variation among pilots with the nonlinear algorithm. Control input
5. Fuzzy Adaptive Output Feedback Control of Uncertain Nonlinear Systems With Prescribed Performance.
Science.gov (United States)
Zhang, Jin-Xi; Yang, Guang-Hong
2018-05-01
This paper investigates the tracking control problem for a family of strict-feedback systems in the presence of unknown nonlinearities and immeasurable system states. A low-complexity adaptive fuzzy output feedback control scheme is proposed, based on a backstepping method. In the control design, a fuzzy adaptive state observer is first employed to estimate the unmeasured states. Then, a novel error transformation approach together with a new modification mechanism is introduced to guarantee the finite-time convergence of the output error to a predefined region and ensure the closed-loop stability. Compared with the existing methods, the main advantages of our approach are that: 1) without using extra command filters or auxiliary dynamic surface control techniques, the problem of explosion of complexity can still be addressed and 2) the design procedures are independent of the initial conditions. Finally, two practical examples are performed to further illustrate the above theoretic findings.
6. Nonsingular Terminal Sliding Mode Control of Uncertain Second-Order Nonlinear Systems
Directory of Open Access Journals (Sweden)
Minh-Duc Tran
2015-01-01
Full Text Available This paper presents a high-performance nonsingular terminal sliding mode control method for uncertain second-order nonlinear systems. First, a nonsingular terminal sliding mode surface is introduced to eliminate the singularity problem that exists in conventional terminal sliding mode control. By using this method, the system not only can guarantee that the tracking errors reach the reference value in a finite time with high-precision tracking performance but also can overcome the complex-value and the restrictions of the exponent (the exponent should be fractional number with an odd numerator and an odd denominator in traditional terminal sliding mode. Then, in order to eliminate the chattering phenomenon, a super-twisting higher-order nonsingular terminal sliding mode control method is proposed. The stability of the closed-loop system is established using the Lyapunov theory. Finally, simulation results are presented to illustrate the effectiveness of the proposed method.
7. Distributed Adaptive Fuzzy Control for Nonlinear Multiagent Systems Via Sliding Mode Observers.
Science.gov (United States)
Shen, Qikun; Shi, Peng; Shi, Yan
2016-12-01
In this paper, the problem of distributed adaptive fuzzy control is investigated for high-order uncertain nonlinear multiagent systems on directed graph with a fixed topology. It is assumed that only the outputs of each follower and its neighbors are available in the design of its distributed controllers. Equivalent output injection sliding mode observers are proposed for each follower to estimate the states of itself and its neighbors, and an observer-based distributed adaptive controller is designed for each follower to guarantee that it asymptotically synchronizes to a leader with tracking errors being semi-globally uniform ultimate bounded, in which fuzzy logic systems are utilized to approximate unknown functions. Based on algebraic graph theory and Lyapunov function approach, using Filippov-framework, the closed-loop system stability analysis is conducted. Finally, numerical simulations are provided to illustrate the effectiveness and potential of the developed design techniques.
8. Diagonal recurrent neural network based adaptive control of nonlinear dynamical systems using lyapunov stability criterion.
Science.gov (United States)
Kumar, Rajesh; Srivastava, Smriti; Gupta, J R P
2017-03-01
In this paper adaptive control of nonlinear dynamical systems using diagonal recurrent neural network (DRNN) is proposed. The structure of DRNN is a modification of fully connected recurrent neural network (FCRNN). Presence of self-recurrent neurons in the hidden layer of DRNN gives it an ability to capture the dynamic behaviour of the nonlinear plant under consideration (to be controlled). To ensure stability, update rules are developed using lyapunov stability criterion. These rules are then used for adjusting the various parameters of DRNN. The responses of plants obtained with DRNN are compared with those obtained when multi-layer feed forward neural network (MLFFNN) is used as a controller. Also, in example 4, FCRNN is also investigated and compared with DRNN and MLFFNN. Robustness of the proposed control scheme is also tested against parameter variations and disturbance signals. Four simulation examples including one-link robotic manipulator and inverted pendulum are considered on which the proposed controller is applied. The results so obtained show the superiority of DRNN over MLFFNN as a controller. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
9. Adaptive Fault-Tolerant Tracking Control of Nonaffine Nonlinear Systems with Actuator Failure
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Hongcheng Zhou
2014-01-01
Full Text Available This paper proposes an adaptive fault-tolerant control scheme for nonaffine nonlinear systems. A model approximation method which is a solution that bridges the gap between affine and nonaffine control systems is developed firstly. A joint estimation approach is based on unscented Kalman filter, in which both failure parameters and states are simultaneously estimated by means of the argument state vector composed of the unknown faults and states. Then, stability analysis is given for the closed-loop system. Finally, the proposed approach is verified using a three-degree-of-freedom simulation of a typical fighter aircraft and the significantly improved system response demonstrates the practical potential of the theoretic results obtained.
10. Adaptive variable structure control for uncertain chaotic systems containing dead-zone nonlinearity
International Nuclear Information System (INIS)
Yan, J.-J.; Shyu, K.-K.; Lin, J.-S.
2005-01-01
This paper addresses a practical tracking problem for a class of uncertain chaotic systems with dead-zone nonlinearity in the input function. Based on the Lyapunov stability theorem and Barbalat lemma, an adaptive variable structure controller (AVSC) is proposed to ensure the occurrence of the sliding mode even though the control input contains a dead-zone. Also it is worthy of note that the proposed AVSC involves no information of the upper bound of uncertainty. Thus, the limitation of knowing the bound of uncertainty in advance is certainly released. Furthermore, in the sliding mode, the investigated uncertain chaotic system remains insensitive to the uncertainty, and behaves like a linear system. Finally, a well-known Duffing-Holmes chaotic system is used to demonstrate the feasibility of the proposed AVSC
11. Non-predictor control of a class of feedforward nonlinear systems with unknown time-varying delays
Science.gov (United States)
Koo, Min-Sung; Choi, Ho-Lim
2016-08-01
This paper generalises the several recent results on the control of feedforward time-delay nonlinear systems. First, in view of system formulation, there are unknown time-varying delays in both states and main control input. Also, the considered nonlinear system has extended feedforward nonlinearities. Second, in view of control solution, our proposed controller is a non-predictor feedback controller whereas smith-predictor type controllers are used in the several existing results. Moreover, our controller does not need any information on the unknown delays except their upper bounds. Thus, our result has certain merits in both system formulation and control solution perspective. The analysis and example are given for clear illustration.
12. Adaptive Fuzzy Output-Constrained Fault-Tolerant Control of Nonlinear Stochastic Large-Scale Systems With Actuator Faults.
Science.gov (United States)
Li, Yongming; Ma, Zhiyao; Tong, Shaocheng
2017-09-01
The problem of adaptive fuzzy output-constrained tracking fault-tolerant control (FTC) is investigated for the large-scale stochastic nonlinear systems of pure-feedback form. The nonlinear systems considered in this paper possess the unstructured uncertainties, unknown interconnected terms and unknown nonaffine nonlinear faults. The fuzzy logic systems are employed to identify the unknown lumped nonlinear functions so that the problems of structured uncertainties can be solved. An adaptive fuzzy state observer is designed to solve the nonmeasurable state problem. By combining the barrier Lyapunov function theory, adaptive decentralized and stochastic control principles, a novel fuzzy adaptive output-constrained FTC approach is constructed. All the signals in the closed-loop system are proved to be bounded in probability and the system outputs are constrained in a given compact set. Finally, the applicability of the proposed controller is well carried out by a simulation example.
13. Symmetries and semi-invariants in the analysis of nonlinear systems with control applications
CERN Document Server
Menini, Laura
2014-01-01
This volume details the analysis of continuous- and discrete-time dynamical systems described by differential and difference equations. The theory is developed for general nonlinear systems and specialized for the class of Hamiltonian systems.
14. Image-Based Visual Servoing for Robotic Systems: A Nonlinear Lyapunov-Based Control Approach
International Nuclear Information System (INIS)
Dixon, Warren
2004-01-01
There is significant motivation to provide robotic systems with improved autonomy as a means to significantly accelerate deactivation and decommissioning (DandD) operations while also reducing the associated costs, removing human operators from hazardous environments, and reducing the required burden and skill of human operators. To achieve improved autonomy, this project focused on the basic science challenges leading to the development of visual servo controllers. The challenge in developing these controllers is that a camera provides 2-dimensional image information about the 3-dimensional Euclidean-space through a perspective (range dependent) projection that can be corrupted by uncertainty in the camera calibration matrix and by disturbances such as nonlinear radial distortion. Disturbances in this relationship (i.e., corruption in the sensor information) propagate erroneous information to the feedback controller of the robot, leading to potentially unpredictable task execution. This research project focused on the development of a visual servo control methodology that targets compensating for disturbances in the camera model (i.e., camera calibration and the recovery of range information) as a means to achieve predictable response by the robotic system operating in unstructured environments. The fundamental idea is to use nonlinear Lyapunov-based techniques along with photogrammetry methods to overcome the complex control issues and alleviate many of the restrictive assumptions that impact current robotic applications. The outcome of this control methodology is a plug-and-play visual servoing control module that can be utilized in conjunction with current technology such as feature recognition and extraction to enable robotic systems with the capabilities of increased accuracy, autonomy, and robustness, with a larger field of view (and hence a larger workspace). The developed methodology has been reported in numerous peer-reviewed publications and the
15. Smooth Adaptive Internal Model Control Based on U Model for Nonlinear Systems with Dynamic Uncertainties
Directory of Open Access Journals (Sweden)
Li Zhao
2016-01-01
Full Text Available An improved smooth adaptive internal model control based on U model control method is presented to simplify modeling structure and parameter identification for a class of uncertain dynamic systems with unknown model parameters and bounded external disturbances. Differing from traditional adaptive methods, the proposed controller can simplify the identification of time-varying parameters in presence of bounded external disturbances. Combining the small gain theorem and the virtual equivalent system theory, learning rate of smooth adaptive internal model controller has been analyzed and the closed-loop virtual equivalent system based on discrete U model has been constructed as well. The convergence of this virtual equivalent system is proved, which further shows the convergence of the complex closed-loop discrete U model system. Finally, simulation and experimental results on a typical nonlinear dynamic system verified the feasibility of the proposed algorithm. The proposed method is shown to have lighter identification burden and higher control accuracy than the traditional adaptive controller.
16. On Active Surge Control of Compression Systems via Characteristic Linearization and Model Nonlinearity Cancellation
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Yohannes S.M. Simamora
2014-09-01
Full Text Available A simple approach of active surge control of compression systems is presented. Specifically, nonlinear components of the pressure ratio and rotating speed states of the Moore-Greitzer model are transferred into the input vectors. Subsequently, the compressor characteristic is linearized into two modes, which describe the stable region and the unstable region respectively. As a result, the system’s state and input matrices both appear linear, to which linear realization and analysis are applicable. A linear quadratic regulator plus integrator is then chosen as closed-loop controller. By simulation it was shown that the modified model and characteristics can describe surge behavior, while the closed-loop controller can stabilize the system in the unstable operating region. The last-mentioned was achieved when massflow was 5.38 per cent less than the surge point.
17. Distributed model predictive control for constrained nonlinear systems with decoupled local dynamics.
Science.gov (United States)
Zhao, Meng; Ding, Baocang
2015-03-01
This paper considers the distributed model predictive control (MPC) of nonlinear large-scale systems with dynamically decoupled subsystems. According to the coupled state in the overall cost function of centralized MPC, the neighbors are confirmed and fixed for each subsystem, and the overall objective function is disassembled into each local optimization. In order to guarantee the closed-loop stability of distributed MPC algorithm, the overall compatibility constraint for centralized MPC algorithm is decomposed into each local controller. The communication between each subsystem and its neighbors is relatively low, only the current states before optimization and the optimized input variables after optimization are being transferred. For each local controller, the quasi-infinite horizon MPC algorithm is adopted, and the global closed-loop system is proven to be exponentially stable. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.
18. Exponential Stability of Time-Switched Two-Subsystem Nonlinear Systems with Application to Intermittent Control
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Huang Tingwen
2009-01-01
Full Text Available This paper studies the exponential stability of a class of periodically time-switched nonlinear systems. Three cases of such systems which are composed, respectively, of a pair of unstable subsystems, of both stable and unstable subsystems, and of a pair of stable systems, are considered. For the first case, the proposed result shows that there exists periodically switching rule guaranteeing the exponential stability of the whole system with (sufficient small switching period if there is a Hurwitz linear convex combination of two uncertain linear systems derived from two subsystems by certain linearization. For the second case, we present two general switching criteria by means of multiple and single Lyapunov function, respectively. We also investigate the stability issue of the third case, and the switching criteria of exponential stability are proposed. The present results for the second case are further applied to the periodically intermittent control. Several numerical examples are also given to show the effectiveness of theoretical results.
19. Nonlinear Synergetic Governor Controllers for Steam Turbine Generators to Enhance Power System Stability
Directory of Open Access Journals (Sweden)
Xingbao Ju
2017-07-01
Full Text Available This paper proposes a decentralized nonlinear synergetic governor controller (NSGC for turbine generators to enhance power system stability by using synergetic control theory and the feedback linearization technique. The precise feedback linearization model of a turbine-generator with a steam valve control is obtained, at first, by using a feedback linearization technique. Then based on this model, a manifold is defined as a linear combination of the deviation of the rotor angle, speed deviation, and speed derivative. The control law of the proposed NSGC is deduced and the stability condition of the whole closed-loop system is subsequently analyzed. According to the requirement of the primary frequency regulation, an additional proportional integral (PI controller is designed to dynamically track the steady-state value of the rotor angle. Case studies are undertaken based on a single-machine infinite-bus system and the New England system, respectively. Simulation results show that the proposed NSGC can suppress the power oscillations and improve transient stability more effectively in comparison with the conventional proportional-integral-derivative (PID governor controller. Moreover, the proposed NSGC is robust to the variations of the system operating conditions.
20. Adaptive Neural Network Control for Nonlinear Hydraulic Servo-System with Time-Varying State Constraints
Directory of Open Access Journals (Sweden)
Shu-Min Lu
2017-01-01
Full Text Available An adaptive neural network control problem is addressed for a class of nonlinear hydraulic servo-systems with time-varying state constraints. In view of the low precision problem of the traditional hydraulic servo-system which is caused by the tracking errors surpassing appropriate bound, the previous works have shown that the constraint for the system is a good way to solve the low precision problem. Meanwhile, compared with constant constraints, the time-varying state constraints are more general in the actual systems. Therefore, when the states of the system are forced to obey bounded time-varying constraint conditions, the high precision tracking performance of the system can be easily realized. In order to achieve this goal, the time-varying barrier Lyapunov function (TVBLF is used to prevent the states from violating time-varying constraints. By the backstepping design, the adaptive controller will be obtained. A radial basis function neural network (RBFNN is used to estimate the uncertainties. Based on analyzing the stability of the hydraulic servo-system, we show that the error signals are bounded in the compacts sets; the time-varying state constrains are never violated and all singles of the hydraulic servo-system are bounded. The simulation and experimental results show that the tracking accuracy of system is improved and the controller has fast tracking ability and strong robustness.
1. Data-based fault-tolerant control for affine nonlinear systems with actuator faults.
Science.gov (United States)
Xie, Chun-Hua; Yang, Guang-Hong
2016-09-01
This paper investigates the fault-tolerant control (FTC) problem for unknown nonlinear systems with actuator faults including stuck, outage, bias and loss of effectiveness. The upper bounds of stuck faults, bias faults and loss of effectiveness faults are unknown. A new data-based FTC scheme is proposed. It consists of the online estimations of the bounds and a state-dependent function. The estimations are adjusted online to compensate automatically the actuator faults. The state-dependent function solved by using real system data helps to stabilize the system. Furthermore, all signals in the resulting closed-loop system are uniformly bounded and the states converge asymptotically to zero. Compared with the existing results, the proposed approach is data-based. Finally, two simulation examples are provided to show the effectiveness of the proposed approach. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.
2. The beauty of simple adaptive control and new developments in nonlinear systems stability analysis
Energy Technology Data Exchange (ETDEWEB)
Barkana, Itzhak, E-mail: ibarkana@gmail.com [BARKANA Consulting, Ramat Hasharon (Israel)
2014-12-10
3. 1-D Wavelet Signal Analysis of the Actuators Nonlinearities Impact on the Healthy Control Systems Performance
Directory of Open Access Journals (Sweden)
Nicolae Tudoroiu
2017-09-01
Full Text Available The objective of this paper is to investigate the use of the 1-D wavelet analysis to extract several patterns from signals data sets collected from healthy and faulty input-output signals of control systems as a preliminary step in real-time implementation of fault detection diagnosis and isolation strategies. The 1-D wavelet analysis proved that is an useful tool for signals processing, design and analysis based on wavelet transforms found in a wide range of control systems industrial applications. Based on the fact that in the real life there is a great similitude between the phenomena, we are motivated to extend the applicability of these techniques to solve similar applications from control systems field, such is done in our research work. Their efficiency will be demonstrated on a case study mainly chosen to evaluate the impact of the uncertainties and the nonlinearities of the sensors and actuators on the overall performance of the control systems. The proposed techniques are able to extract in frequency domain some pattern features (signatures of interest directly from the signals data set collected by data acquisition equipment from the control system.
4. Adaptive nonlinear control of single-phase to three-phase UPS system
Directory of Open Access Journals (Sweden)
Kissaoui M.
2014-01-01
Full Text Available This work deals with the problems of uninterruptible power supplies (UPS based on the single-phase to three-phase converters built in two stages: an input bridge rectifier and an output three phase inverter. The two blocks are joined by a continuous intermediate bus. The objective of control is threefold: i power factor correction “PFC”, ii generating a symmetrical three-phase system at the output even if the load is unknown, iii regulating the DC bus voltage. The synthesis of controllers has been reached by two nonlinear techniques that are the sliding mode and adaptive backstepping control. The performances of regulators have been validated by numerical simulation in MATLAB / SIMULINK.
5. Dynamics of nonlinear feedback control.
Science.gov (United States)
Snippe, H P; van Hateren, J H
2007-05-01
Feedback control in neural systems is ubiquitous. Here we study the mathematics of nonlinear feedback control. We compare models in which the input is multiplied by a dynamic gain (multiplicative control) with models in which the input is divided by a dynamic attenuation (divisive control). The gain signal (resp. the attenuation signal) is obtained through a concatenation of an instantaneous nonlinearity and a linear low-pass filter operating on the output of the feedback loop. For input steps, the dynamics of gain and attenuation can be very different, depending on the mathematical form of the nonlinearity and the ordering of the nonlinearity and the filtering in the feedback loop. Further, the dynamics of feedback control can be strongly asymmetrical for increment versus decrement steps of the input. Nevertheless, for each of the models studied, the nonlinearity in the feedback loop can be chosen such that immediately after an input step, the dynamics of feedback control is symmetric with respect to increments versus decrements. Finally, we study the dynamics of the output of the control loops and find conditions under which overshoots and undershoots of the output relative to the steady-state output occur when the models are stimulated with low-pass filtered steps. For small steps at the input, overshoots and undershoots of the output do not occur when the filtering in the control path is faster than the low-pass filtering at the input. For large steps at the input, however, results depend on the model, and for some of the models, multiple overshoots and undershoots can occur even with a fast control path.
6. Nonlinear optical systems
CERN Document Server
Lugiato, Luigi; Brambilla, Massimo
2015-01-01
Guiding graduate students and researchers through the complex world of laser physics and nonlinear optics, this book provides an in-depth exploration of the dynamics of lasers and other relevant optical systems, under the umbrella of a unitary spatio-temporal vision. Adopting a balanced approach, the book covers traditional as well as special topics in laser physics, quantum electronics and nonlinear optics, treating them from the viewpoint of nonlinear dynamical systems. These include laser emission, frequency generation, solitons, optically bistable systems, pulsations and chaos and optical pattern formation. It also provides a coherent and up-to-date treatment of the hierarchy of nonlinear optical models and of the rich variety of phenomena they describe, helping readers to understand the limits of validity of each model and the connections among the phenomena. It is ideal for graduate students and researchers in nonlinear optics, quantum electronics, laser physics and photonics.
7. PID Controller Design of Nonlinear System using a New Modified Particle Swarm Optimization with Time-Varying Constriction Coefficient
Directory of Open Access Journals (Sweden)
2014-12-01
Full Text Available The proportional integral derivative (PID controllers have been widely used in most process control systems for a long time. However, it is a very important problem how to choose PID parameters, because these parameters give a great influence on the control performance. Especially, it is difficult to tune these parameters for nonlinear systems. In this paper, a new modified particle swarm optimization (PSO is presented to search for optimal PID parameters for such system. The proposed algorithm is to modify constriction coefficient which is nonlinearly decreased time-varying for improving the final accuracy and the convergence speed of PSO. To validate the control performance of the proposed method, a typical nonlinear system control, a continuous stirred tank reactor (CSTR process, is illustrated. The results testify that a new modified PSO algorithm can perform well in the nonlinear PID control system design in term of lesser overshoot, rise-time, settling-time, IAE and ISE. Keywords: PID controller, Particle Swarm Optimization (PSO,constriction factor, nonlinear system.
8. Frequency-domain and time-domain methods for feedback nonlinear systems and applications to chaos control
International Nuclear Information System (INIS)
Duan Zhisheng; Wang Jinzhi; Yang Ying; Huang Lin
2009-01-01
This paper surveys frequency-domain and time-domain methods for feedback nonlinear systems and their possible applications to chaos control, coupled systems and complex dynamical networks. The absolute stability of Lur'e systems with single equilibrium and global properties of a class of pendulum-like systems with multi-equilibria are discussed. Time-domain and frequency-domain criteria for the convergence of solutions are presented. Some latest results on analysis and control of nonlinear systems with multiple equilibria and applications to chaos control are reviewed. Finally, new chaotic oscillating phenomena are shown in a pendulum-like system and a new nonlinear system with an attraction/repulsion function.
9. Robust Control and Motion Planning for Nonlinear Underactuated Systems Using H infinity Techniques
National Research Council Canada - National Science Library
Toussaint, Gregory
2000-01-01
This thesis presents new techniques for planning and robustly controlling the motion of nonlinear underactuated vehicles when disturbances are present and only imperfect state measurements are available for feedback...
10. Transparent Higher Order Sliding Mode Control for Nonlinear Master-Slave Systems without Velocity Measurement
Directory of Open Access Journals (Sweden)
Luis G. Garcia-Valdovinos
2015-04-01
Full Text Available Transparency has been a major objective in bilateral teleoperation systems, even in the absence of time delay induced by the communication channel, since a high degree of transparency would allow humans to drive the remote teleoperator as if he or she were directly interacting with the remote environment, with the remote teleoperator as a physical and sensorial extension of the operator. When fast convergence of position and force tracking errors are ensured by the control system, then complete transparency is obtained, which would ideally guarantee humans to be tightly kinaesthetically coupled. In this paper a model-free Cartesian second order sliding mode (SOSM PD control scheme for nonlinear master-slave systems is presented. The proposed scheme does not rely on velocity measurements and attains very fast convergence of position trajectories, with bounded tracking of force trajectories, rendering a high degree of transparency with lesser knowledge of the system. The degree of transparency can easily be improved by tuning a feedback gain in the force loop. A unique energy storage function is introduced; such that a similar Cartesian-based controller is implemented in the master and slave sides. The resulting properties of the Cartesian control structure allows the human operator to input directly Cartesian variables, which makes clearer the kinaesthetic coupling, thus the proposed controller becomes a suitable candidate for practical implementation. The performance of the proposed scheme is evaluated in a semi-experimental setup.
11. Non-linear feedback control of the p53 protein-mdm2 inhibitor system using the derivative-free non-linear Kalman filter.
Science.gov (United States)
Rigatos, Gerasimos G
2016-06-01
It is proven that the model of the p53-mdm2 protein synthesis loop is a differentially flat one and using a diffeomorphism (change of state variables) that is proposed by differential flatness theory it is shown that the protein synthesis model can be transformed into the canonical (Brunovsky) form. This enables the design of a feedback control law that maintains the concentration of the p53 protein at the desirable levels. To estimate the non-measurable elements of the state vector describing the p53-mdm2 system dynamics, the derivative-free non-linear Kalman filter is used. Moreover, to compensate for modelling uncertainties and external disturbances that affect the p53-mdm2 system, the derivative-free non-linear Kalman filter is re-designed as a disturbance observer. The derivative-free non-linear Kalman filter consists of the Kalman filter recursion applied on the linearised equivalent of the protein synthesis model together with an inverse transformation based on differential flatness theory that enables to retrieve estimates for the state variables of the initial non-linear model. The proposed non-linear feedback control and perturbations compensation method for the p53-mdm2 system can result in more efficient chemotherapy schemes where the infusion of medication will be better administered.
12. Reinforcement learning controller design for affine nonlinear discrete-time systems using online approximators.
Science.gov (United States)
Yang, Qinmin; Jagannathan, Sarangapani
2012-04-01
In this paper, reinforcement learning state- and output-feedback-based adaptive critic controller designs are proposed by using the online approximators (OLAs) for a general multi-input and multioutput affine unknown nonlinear discretetime systems in the presence of bounded disturbances. The proposed controller design has two entities, an action network that is designed to produce optimal signal and a critic network that evaluates the performance of the action network. The critic estimates the cost-to-go function which is tuned online using recursive equations derived from heuristic dynamic programming. Here, neural networks (NNs) are used both for the action and critic whereas any OLAs, such as radial basis functions, splines, fuzzy logic, etc., can be utilized. For the output-feedback counterpart, an additional NN is designated as the observer to estimate the unavailable system states, and thus, separation principle is not required. The NN weight tuning laws for the controller schemes are also derived while ensuring uniform ultimate boundedness of the closed-loop system using Lyapunov theory. Finally, the effectiveness of the two controllers is tested in simulation on a pendulum balancing system and a two-link robotic arm system.
13. Nonlinear Control of an Active Magnetic Bearing System Achieved Using a Fuzzy Control with Radial Basis Function Neural Network
Directory of Open Access Journals (Sweden)
Seng-Chi Chen
2014-01-01
Full Text Available Studies on active magnetic bearing (AMB systems are increasing in popularity and practical applications. Magnetic bearings cause less noise, friction, and vibration than the conventional mechanical bearings; however, the control of AMB systems requires further investigation. The magnetic force has a highly nonlinear relation to the control current and the air gap. This paper proposes an intelligent control method for positioning an AMB system that uses a neural fuzzy controller (NFC. The mathematical model of an AMB system comprises identification followed by collection of information from this system. A fuzzy logic controller (FLC, the parameters of which are adjusted using a radial basis function neural network (RBFNN, is applied to the unbalanced vibration in an AMB system. The AMB system exhibited a satisfactory control performance, with low overshoot, and produced improved transient and steady-state responses under various operating conditions. The NFC has been verified on a prototype AMB system. The proposed controller can be feasibly applied to AMB systems exposed to various external disturbances; demonstrating the effectiveness of the NFC with self-learning and self-improving capacities is proven.
14. Discrete-time nonlinear sliding mode controller
African Journals Online (AJOL)
user
Keywords: Discrete-time delay system, Sliding mode control, nonlinear sliding ... of engineering systems such as chemical process control, delay in the actuator ...... instrumentation from Motilal Nehru National Institute of Technology (MNNIT),.
15. An adaptive critic-based scheme for consensus control of nonlinear multi-agent systems
Science.gov (United States)
Heydari, Ali; Balakrishnan, S. N.
2014-12-01
The problem of decentralised consensus control of a network of heterogeneous nonlinear systems is formulated as an optimal tracking problem and a solution is proposed using an approximate dynamic programming based neurocontroller. The neurocontroller training comprises an initial offline training phase and an online re-optimisation phase to account for the fact that the reference signal subject to tracking is not fully known and available ahead of time, i.e., during the offline training phase. As long as the dynamics of the agents are controllable, and the communication graph has a directed spanning tree, this scheme guarantees the synchronisation/consensus even under switching communication topology and directed communication graph. Finally, an aerospace application is selected for the evaluation of the performance of the method. Simulation results demonstrate the potential of the scheme.
16. Adaptive Backstepping-Based Neural Tracking Control for MIMO Nonlinear Switched Systems Subject to Input Delays.
Science.gov (United States)
Niu, Ben; Li, Lu
2018-06-01
This brief proposes a new neural-network (NN)-based adaptive output tracking control scheme for a class of disturbed multiple-input multiple-output uncertain nonlinear switched systems with input delays. By combining the universal approximation ability of radial basis function NNs and adaptive backstepping recursive design with an improved multiple Lyapunov function (MLF) scheme, a novel adaptive neural output tracking controller design method is presented for the switched system. The feature of the developed design is that different coordinate transformations are adopted to overcome the conservativeness caused by adopting a common coordinate transformation for all subsystems. It is shown that all the variables of the resulting closed-loop system are semiglobally uniformly ultimately bounded under a class of switching signals in the presence of MLF and that the system output can follow the desired reference signal. To demonstrate the practicability of the obtained result, an adaptive neural output tracking controller is designed for a mass-spring-damper system.
17. Boundary controllability for a nonlinear beam equation
Directory of Open Access Journals (Sweden)
Xiao-Min Cao
2015-09-01
Full Text Available This article concerns a nonlinear system modeling the bending vibrations of a nonlinear beam of length $L>0$. First, we derive the existence of long time solutions near an equilibrium. Then we prove that the nonlinear beam is locally exact controllable around the equilibrium in $H^4(0,L$ and with control functions in $H^2(0,T$. The approach we used are open mapping theorem, local controllability established by linearization, and the induction.
18. Simulating closed- and open-loop voluntary movement: a nonlinear control-systems approach.
Science.gov (United States)
Davidson, Paul R; Jones, Richard D; Andreae, John H; Sirisena, Harsha R
2002-11-01
In many recent human motor control models, including feedback-error learning and adaptive model theory (AMT), feedback control is used to correct errors while an inverse model is simultaneously tuned to provide accurate feedforward control. This popular and appealing hypothesis, based on a combination of psychophysical observations and engineering considerations, predicts that once the tuning of the inverse model is complete the role of feedback control is limited to the correction of disturbances. This hypothesis was tested by looking at the open-loop behavior of the human motor system during adaptation. An experiment was carried out involving 20 normal adult subjects who learned a novel visuomotor relationship on a pursuit tracking task with a steering wheel for input. During learning, the response cursor was periodically blanked, removing all feedback about the external system (i.e., about the relationship between hand motion and response cursor motion). Open-loop behavior was not consistent with a progressive transfer from closed- to open-loop control. Our recently developed computational model of the brain--a novel nonlinear implementation of AMT--was able to reproduce the observed closed- and open-loop results. In contrast, other control-systems models exhibited only minimal feedback control following adaptation, leading to incorrect open-loop behavior. This is because our model continues to use feedback to control slow movements after adaptation is complete. This behavior enhances the internal stability of the inverse model. In summary, our computational model is currently the only motor control model able to accurately simulate the closed- and open-loop characteristics of the experimental response trajectories.
19. On-line Multiple-model Based Adaptive Control Reconfiguration for a Class of Non-linear Control Systems
DEFF Research Database (Denmark)
2000-01-01
of LTI models are employed to approximate the faulty, reconfigured and nominal nonlinear systems respectively with respect to the on-line information of the operating system, and a set of compensating modules are proposed and designed so as to make the local LTI model approximating to the reconfigured...... nonlinear system match the corresponding LTI model approximating to the nominal nonlinear system in some optimal sense. The compensating modules are designed by the Pseudo-Inverse Method based on the local LTI models for the nominal and faulty nonlinear systems. Moreover, these modules should update...... corresponding to the updating of local LTI models, which validations are determined by the model approximation errors and the optimal index of local design. The test on a nonlinear ship propulsion system shows the promising potential of this method for system reconfiguration...
20. STABLE ADAPTIVE CONTROL FOR A CLASS OF NONLINEAR SYSTEMS WITHOUT USE OF A SUPERVISORY TERM IN THE CONTROL LAW
Directory of Open Access Journals (Sweden)
MOHAMED BAHITA
2012-02-01
Full Text Available In this paper, a direct adaptive control scheme for a class of nonlinear systems is proposed. The architecture employs a Gaussian radial basis function (RBF network to construct an adaptive controller. The parameters of the adaptive controller are adapted and changed according to a law derived using Lyapunov stability theory. The centres of the RBF network are adapted on line using the k-means algorithm. Asymptotic Lyapunov stability is established without the use of a supervisory (compensatory term in the control law and with the tracking errors converging to a neighbourhood of the origin. Finally, a simulation is provided to explore the feasibility of the proposed neuronal controller design method.
1. Switching control for a class of nonlinear SISO systems with an application to post-harvest food storage
NARCIS (Netherlands)
van Mourik, S.; Zwart, Heiko J.; Keesman, K.J.
2007-01-01
For a class of scalar nonlinear systems with switching input a controller is designed using design theory for linear systems. A stability criterion is derived that contains all the physical system parameters, allowing a stability analysis without the need for numerical simulation. The results are
2. Nonlinear Dynamic Modeling and Controls Development for Supersonic Propulsion System Research
Science.gov (United States)
Connolly, Joseph W.; Kopasakis, George; Paxson, Daniel E.; Stuber, Eric; Woolwine, Kyle
2012-01-01
This paper covers the propulsion system component modeling and controls development of an integrated nonlinear dynamic simulation for an inlet and engine that can be used for an overall vehicle (APSE) model. The focus here is on developing a methodology for the propulsion model integration, which allows for controls design that prevents inlet instabilities and minimizes the thrust oscillation experienced by the vehicle. Limiting thrust oscillations will be critical to avoid exciting vehicle aeroelastic modes. Model development includes both inlet normal shock position control and engine rotor speed control for a potential supersonic commercial transport. A loop shaping control design process is used that has previously been developed for the engine and verified on linear models, while a simpler approach is used for the inlet control design. Verification of the modeling approach is conducted by simulating a two-dimensional bifurcated inlet and a representative J-85 jet engine previously used in a NASA supersonics project. Preliminary results are presented for the current supersonics project concept variable cycle turbofan engine design.
3. Balancing for nonlinear systems
NARCIS (Netherlands)
Scherpen, J.M.A.
1993-01-01
We present a method of balancing for nonlinear systems which is an extension of balancing for linear systems in the sense that it is based on the input and output energy of a system. It is a local result, but gives 'broader' results than we obtain by just linearizing the system. Furthermore, the
4. Decentralized adaptive neural control for high-order interconnected stochastic nonlinear time-delay systems with unknown system dynamics.
Science.gov (United States)
Si, Wenjie; Dong, Xunde; Yang, Feifei
2018-03-01
This paper is concerned with the problem of decentralized adaptive backstepping state-feedback control for uncertain high-order large-scale stochastic nonlinear time-delay systems. For the control design of high-order large-scale nonlinear systems, only one adaptive parameter is constructed to overcome the over-parameterization, and neural networks are employed to cope with the difficulties raised by completely unknown system dynamics and stochastic disturbances. And then, the appropriate Lyapunov-Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown unmatched time-delay interactions of high-order large-scale systems for the first time. At last, on the basis of Lyapunov stability theory, the decentralized adaptive neural controller was developed, and it decreases the number of learning parameters. The actual controller can be designed so as to ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error converges in the small neighborhood of zero. The simulation example is used to further show the validity of the design method. Copyright © 2018 Elsevier Ltd. All rights reserved.
5. Research on Adaptive Neural Network Control System Based on Nonlinear U-Model with Time-Varying Delay
Directory of Open Access Journals (Sweden)
Fengxia Xu
2014-01-01
Full Text Available U-model can approximate a large class of smooth nonlinear time-varying delay system to any accuracy by using time-varying delay parameters polynomial. This paper proposes a new approach, namely, U-model approach, to solving the problems of analysis and synthesis for nonlinear systems. Based on the idea of discrete-time U-model with time-varying delay, the identification algorithm of adaptive neural network is given for the nonlinear model. Then, the controller is designed by using the Newton-Raphson formula and the stability analysis is given for the closed-loop nonlinear systems. Finally, illustrative examples are given to show the validity and applicability of the obtained results.
6. Event-Triggered Distributed Control of Nonlinear Interconnected Systems Using Online Reinforcement Learning With Exploration.
Science.gov (United States)
Narayanan, Vignesh; Jagannathan, Sarangapani
2017-09-07
In this paper, a distributed control scheme for an interconnected system composed of uncertain input affine nonlinear subsystems with event triggered state feedback is presented by using a novel hybrid learning scheme-based approximate dynamic programming with online exploration. First, an approximate solution to the Hamilton-Jacobi-Bellman equation is generated with event sampled neural network (NN) approximation and subsequently, a near optimal control policy for each subsystem is derived. Artificial NNs are utilized as function approximators to develop a suite of identifiers and learn the dynamics of each subsystem. The NN weight tuning rules for the identifier and event-triggering condition are derived using Lyapunov stability theory. Taking into account, the effects of NN approximation of system dynamics and boot-strapping, a novel NN weight update is presented to approximate the optimal value function. Finally, a novel strategy to incorporate exploration in online control framework, using identifiers, is introduced to reduce the overall cost at the expense of additional computations during the initial online learning phase. System states and the NN weight estimation errors are regulated and local uniformly ultimately bounded results are achieved. The analytical results are substantiated using simulation studies.
7. State-dependent differential Riccati equation to track control of time-varying systems with state and control nonlinearities.
Science.gov (United States)
Korayem, M H; Nekoo, S R
2015-07-01
This work studies an optimal control problem using the state-dependent Riccati equation (SDRE) in differential form to track for time-varying systems with state and control nonlinearities. The trajectory tracking structure provides two nonlinear differential equations: the state-dependent differential Riccati equation (SDDRE) and the feed-forward differential equation. The independence of the governing equations and stability of the controller are proven along the trajectory using the Lyapunov approach. Backward integration (BI) is capable of solving the equations as a numerical solution; however, the forward solution methods require the closed-form solution to fulfill the task. A closed-form solution is introduced for SDDRE, but the feed-forward differential equation has not yet been obtained. Different ways of solving the problem are expressed and analyzed. These include BI, closed-form solution with corrective assumption, approximate solution, and forward integration. Application of the tracking problem is investigated to control robotic manipulators possessing rigid or flexible joints. The intention is to release a general program for automatic implementation of an SDDRE controller for any manipulator that obeys the Denavit-Hartenberg (D-H) principle when only D-H parameters are received as input data. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.
8. Image-Based Visual Servoing for Robotic Systems: A Nonlinear Lyapunov-Based Control Approach
International Nuclear Information System (INIS)
Dixon, Warren
2003-01-01
The objective of this project is to enable current and future EM robots with an increased ability to perceive and interact with unstructured and unknown environments through the use of camera-based visual servo controllers. The scientific goals of this research are to develop a new visual servo control methodology that: (1) adapts for the unknown camera calibration parameters (e.g., focal length, scaling factors, camera position, and orientation) and the physical parameters of the robotic system (e.g., mass, inertia, friction), (2) compensates for unknown depth information (extract 3D information from the 2D image), and (3) enables multi-uncalibrated cameras to be used as a means to provide a larger field-of-view. Nonlinear Lyapunov-based techniques in conjunction with results from projective geometry are being used to overcome the complex control issues and alleviate many of the restrictive assumptions that impact current visual servo controlled robotic systems. The potential relevance of this control methodology will be a plug-and-play visual servoing control module that can be utilized in conjunction with current technology such as feature extraction and recognition, to enable current EM robotic systems with the capabilities of increased accuracy, autonomy, and robustness, with a larger field of view (and hence a larger workspace). These capabilities will enable EM robots to significantly accelerate D and D operations by providing for improved robot autonomy and increased worker productivity, while also reducing the associated costs, removing the human operator from the hazardous environments, and reducing the burden and skill of the human operators
9. Image-Based Visual Servoing for Robotic Systems: A Nonlinear Lyapunov-Based Control Approach
International Nuclear Information System (INIS)
Dixon, Warren
2002-01-01
The objective of this project is to enable current and future EM robots with an increased ability to perceive and interact with unstructured and unknown environments through the use of camera-based visual servo controlled robots. The scientific goals of this research are to develop a new visual servo control methodology that: (1) adapts for the unknown camera calibration parameters (e.g., focal length, scaling factors, camera position and orientation) and the physical parameters of the robotic system (e.g., mass, inertia, friction), (2) compensates for unknown depth information (extract 3D information from the 2D image), and (3) enables multi-uncalibrated cameras to be used as a means to provide a larger field-of-view. Nonlinear Lyapunov-based techniques are being used to overcome the complex control issues and alleviate many of the restrictive assumptions that impact current visual servo controlled robotic systems. The potential relevance of this control methodology will be a plug-and-play visual servoing control module that can be utilized in conjunction with current technology such as feature extraction and recognition, to enable current EM robotic systems with the capabilities of increased accuracy, autonomy, and robustness, with a larger field of view (and hence a larger workspace). These capabilities will enable EM robots to significantly accelerate D and D operations by providing for improved robot autonomy and increased worker productivity, while also reducing the associated costs, removing the human operator from the hazardous environments, and reducing the burden and skill of the human operators
10. Interaction between mantle and crustal detachments: a non-linear system controlling lithospheric extension
Science.gov (United States)
Rosenbaum, G.; Regenauer-Lieb, K.; Weinberg, R. F.
2009-12-01
We use numerical modelling to investigate the development of crustal and mantle detachment faults during lithospheric extension. Our models simulate a wide range of rift systems with varying values of crustal thickness and heat flow, showing how strain localization in the mantle interacts with localization in the upper crust and controls the evolution of extensional systems. Model results reveal a richness of structures and deformation styles, which grow in response to a self-organized mechanism that minimizes the internal stored energy of the system by localizing deformation at different levels of the lithosphere. Crustal detachment faults are well developed during extension of overthickened (60 km) continental crust, even when the initial heat flow is relatively low (50 mW/m2). In contrast, localized mantle deformation is most pronounced when the extended lithosphere has a normal crustal thickness (30-40 km) and an intermediate (60-70 mW/m2) heat flow. Results show a non-linear response to subtle changes in crustal thickness or heat flow, characterized by abrupt and sometime unexpected switches in extension modes (e.g. from diffuse rifting to effective lithospheric-scale rupturing) or from mantle- to crust-dominated strain localization. We interpret this non-linearity to result from the interference of doming wavelengths. Disharmony of crust and mantle doming wavelengths results in efficient communication between shear zones at different lithospheric levels, leading to rupturing of the whole lithosphere. In contrast, harmonious crust and mantle doming inhibits interaction of shear zones across the lithosphere and results in a prolonged rifting history prior to continental breakup.
11. Interaction between mantle and crustal detachments: A nonlinear system controlling lithospheric extension
Science.gov (United States)
Rosenbaum, Gideon; Regenauer-Lieb, Klaus; Weinberg, Roberto F.
2010-11-01
We use numerical modeling to investigate the development of crustal and mantle detachments during lithospheric extension. Our models simulate a wide range of extensional systems with varying values of crustal thickness and heat flow, showing how strain localization in the mantle interacts with localization in the upper crust and controls the evolution of extensional systems. Model results reveal a richness of structures and deformation styles as a response to a self-organized mechanism that minimizes the internal stored energy of the system by localizing deformation. Crustal detachments, here referred as low-angle normal decoupling horizons, are well developed during extension of overthickened (60 km) continental crust, even when the initial heat flow is relatively low (50 mW m-2). In contrast, localized mantle deformation is most pronounced when the extended lithosphere has a normal crustal thickness (30-40 km) and an intermediate heat flow (60-70 mW m-2). Results show a nonlinear response to subtle changes in crustal thickness or heat flow, characterized by abrupt and sometimes unexpected switches in extension modes (e.g., from diffuse extensional deformation to effective lithospheric-scale rupturing) or from mantle- to crust-dominated strain localization. We interpret this nonlinearity to result from the interference of doming wavelengths in the presence of multiple necking instabilities. Disharmonic crust and mantle doming wavelengths results in efficient communication between shear zones at different lithospheric levels, leading to rupturing of the whole lithosphere. In contrast, harmonic crust and mantle doming inhibits interaction of shear zones across the lithosphere and results in a prolonged history of extension prior to continental breakup.
12. Online adaptive optimal control for continuous-time nonlinear systems with completely unknown dynamics
Science.gov (United States)
Lv, Yongfeng; Na, Jing; Yang, Qinmin; Wu, Xing; Guo, Yu
2016-01-01
An online adaptive optimal control is proposed for continuous-time nonlinear systems with completely unknown dynamics, which is achieved by developing a novel identifier-critic-based approximate dynamic programming algorithm with a dual neural network (NN) approximation structure. First, an adaptive NN identifier is designed to obviate the requirement of complete knowledge of system dynamics, and a critic NN is employed to approximate the optimal value function. Then, the optimal control law is computed based on the information from the identifier NN and the critic NN, so that the actor NN is not needed. In particular, a novel adaptive law design method with the parameter estimation error is proposed to online update the weights of both identifier NN and critic NN simultaneously, which converge to small neighbourhoods around their ideal values. The closed-loop system stability and the convergence to small vicinity around the optimal solution are all proved by means of the Lyapunov theory. The proposed adaptation algorithm is also improved to achieve finite-time convergence of the NN weights. Finally, simulation results are provided to exemplify the efficacy of the proposed methods.
13. Value Iteration Adaptive Dynamic Programming for Optimal Control of Discrete-Time Nonlinear Systems.
Science.gov (United States)
Wei, Qinglai; Liu, Derong; Lin, Hanquan
2016-03-01
In this paper, a value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon undiscounted optimal control problems for discrete-time nonlinear systems. The present value iteration ADP algorithm permits an arbitrary positive semi-definite function to initialize the algorithm. A novel convergence analysis is developed to guarantee that the iterative value function converges to the optimal performance index function. Initialized by different initial functions, it is proven that the iterative value function will be monotonically nonincreasing, monotonically nondecreasing, or nonmonotonic and will converge to the optimum. In this paper, for the first time, the admissibility properties of the iterative control laws are developed for value iteration algorithms. It is emphasized that new termination criteria are established to guarantee the effectiveness of the iterative control laws. Neural networks are used to approximate the iterative value function and compute the iterative control law, respectively, for facilitating the implementation of the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the present method.
14. Open-closed-loop iterative learning control for a class of nonlinear systems with random data dropouts
Science.gov (United States)
Cheng, X. Y.; Wang, H. B.; Jia, Y. L.; Dong, YH
2018-05-01
In this paper, an open-closed-loop iterative learning control (ILC) algorithm is constructed for a class of nonlinear systems subjecting to random data dropouts. The ILC algorithm is implemented by a networked control system (NCS), where only the off-line data is transmitted by network while the real-time data is delivered in the point-to-point way. Thus, there are two controllers rather than one in the control system, which makes better use of the saved and current information and thereby improves the performance achieved by open-loop control alone. During the transfer of off-line data between the nonlinear plant and the remote controller data dropout occurs randomly and the data dropout rate is modeled as a binary Bernoulli random variable. Both measurement and control data dropouts are taken into consideration simultaneously. The convergence criterion is derived based on rigorous analysis. Finally, the simulation results verify the effectiveness of the proposed method.
15. Reinforcement-Learning-Based Robust Controller Design for Continuous-Time Uncertain Nonlinear Systems Subject to Input Constraints.
Science.gov (United States)
Liu, Derong; Yang, Xiong; Wang, Ding; Wei, Qinglai
2015-07-01
The design of stabilizing controller for uncertain nonlinear systems with control constraints is a challenging problem. The constrained-input coupled with the inability to identify accurately the uncertainties motivates the design of stabilizing controller based on reinforcement-learning (RL) methods. In this paper, a novel RL-based robust adaptive control algorithm is developed for a class of continuous-time uncertain nonlinear systems subject to input constraints. The robust control problem is converted to the constrained optimal control problem with appropriately selecting value functions for the nominal system. Distinct from typical action-critic dual networks employed in RL, only one critic neural network (NN) is constructed to derive the approximate optimal control. Meanwhile, unlike initial stabilizing control often indispensable in RL, there is no special requirement imposed on the initial control. By utilizing Lyapunov's direct method, the closed-loop optimal control system and the estimated weights of the critic NN are proved to be uniformly ultimately bounded. In addition, the derived approximate optimal control is verified to guarantee the uncertain nonlinear system to be stable in the sense of uniform ultimate boundedness. Two simulation examples are provided to illustrate the effectiveness and applicability of the present approach.
16. Solving a Local Boundary Value Problem for a Nonlinear Nonstationary System in the Class of Feedback Controls
Science.gov (United States)
Kvitko, A. N.
2018-01-01
An algorithm convenient for numerical implementation is proposed for constructing differentiable control functions that transfer a wide class of nonlinear nonstationary systems of ordinary differential equations from an initial state to a given point of the phase space. Constructive sufficient conditions imposed on the right-hand side of the controlled system are obtained under which this transfer is possible. The control of a robotic manipulator is considered, and its numerical simulation is performed.
17. Feedforward Nonlinear Control Using Neural Gas Network
OpenAIRE
Machón-González, Iván; López-García, Hilario
2017-01-01
Nonlinear systems control is a main issue in control theory. Many developed applications suffer from a mathematical foundation not as general as the theory of linear systems. This paper proposes a control strategy of nonlinear systems with unknown dynamics by means of a set of local linear models obtained by a supervised neural gas network. The proposed approach takes advantage of the neural gas feature by which the algorithm yields a very robust clustering procedure. The direct model of the ...
18. Distributed Optimal Consensus Control for Nonlinear Multiagent System With Unknown Dynamic.
Science.gov (United States)
Zhang, Jilie; Zhang, Huaguang; Feng, Tao
2017-08-01
This paper focuses on the distributed optimal cooperative control for continuous-time nonlinear multiagent systems (MASs) with completely unknown dynamics via adaptive dynamic programming (ADP) technology. By introducing predesigned extra compensators, the augmented neighborhood error systems are derived, which successfully circumvents the system knowledge requirement for ADP. It is revealed that the optimal consensus protocols actually work as the solutions of the MAS differential game. Policy iteration algorithm is adopted, and it is theoretically proved that the iterative value function sequence strictly converges to the solution of the coupled Hamilton-Jacobi-Bellman equation. Based on this point, a novel online iterative scheme is proposed, which runs based on the data sampled from the augmented system and the gradient of the value function. Neural networks are employed to implement the algorithm and the weights are updated, in the least-square sense, to the ideal value, which yields approximated optimal consensus protocols. Finally, a numerical example is given to illustrate the effectiveness of the proposed scheme.
19. Application of the concept of dynamic trim control and nonlinear system inverses to automatic control of a vertical attitude takeoff and landing aircraft
Science.gov (United States)
Smith, G. A.; Meyer, G.
1981-01-01
A full envelope automatic flight control system based on nonlinear inverse systems concepts has been applied to a vertical attitude takeoff and landing (VATOL) fighter aircraft. A new method for using an airborne digital aircraft model to perform the inversion of a nonlinear aircraft model is presented together with the results of a simulation study of the nonlinear inverse system concept for the vertical-attitude hover mode. The system response to maneuver commands in the vertical attitude was found to be excellent; and recovery from large initial offsets and large disturbances was found to be very satisfactory.
20. Tracking Control Based on Recurrent Neural Networks for Nonlinear Systems with Multiple Inputs and Unknown Deadzone
Directory of Open Access Journals (Sweden)
J. Humberto Pérez-Cruz
2012-01-01
Full Text Available This paper deals with the problem of trajectory tracking for a broad class of uncertain nonlinear systems with multiple inputs each one subject to an unknown symmetric deadzone. On the basis of a model of the deadzone as a combination of a linear term and a disturbance-like term, a continuous-time recurrent neural network is directly employed in order to identify the uncertain dynamics. By using a Lyapunov analysis, the exponential convergence of the identification error to a bounded zone is demonstrated. Subsequently, by a proper control law, the state of the neural network is compelled to follow a bounded reference trajectory. This control law is designed in such a way that the singularity problem is conveniently avoided and the exponential convergence to a bounded zone of the difference between the state of the neural identifier and the reference trajectory can be proven. Thus, the exponential convergence of the tracking error to a bounded zone and the boundedness of all closed-loop signals can be guaranteed. One of the main advantages of the proposed strategy is that the controller can work satisfactorily without any specific knowledge of an upper bound for the unmodeled dynamics and/or the disturbance term.
1. Analysis, control and optimal operations in hybrid power systems advanced techniques and applications for linear and nonlinear systems
CERN Document Server
Bizon, Nicu; Mahdavi Tabatabaei, Naser
2014-01-01
This book explains and analyzes the dynamic performance of linear and nonlinear systems, particularly for Power Systems including Hybrid Power Sources. Offers a detailed description of system stability using state space energy conservation principle, and more.
2. Oscillations in nonlinear systems
CERN Document Server
Hale, Jack K
2015-01-01
By focusing on ordinary differential equations that contain a small parameter, this concise graduate-level introduction to the theory of nonlinear oscillations provides a unified approach to obtaining periodic solutions to nonautonomous and autonomous differential equations. It also indicates key relationships with other related procedures and probes the consequences of the methods of averaging and integral manifolds.Part I of the text features introductory material, including discussions of matrices, linear systems of differential equations, and stability of solutions of nonlinear systems. Pa
3. Robust model predictive control of nonlinear systems with unmodeled dynamics and bounded uncertainties based on neural networks.
Science.gov (United States)
Yan, Zheng; Wang, Jun
2014-03-01
This paper presents a neural network approach to robust model predictive control (MPC) for constrained discrete-time nonlinear systems with unmodeled dynamics affected by bounded uncertainties. The exact nonlinear model of underlying process is not precisely known, but a partially known nominal model is available. This partially known nonlinear model is first decomposed to an affine term plus an unknown high-order term via Jacobian linearization. The linearization residue combined with unmodeled dynamics is then modeled using an extreme learning machine via supervised learning. The minimax methodology is exploited to deal with bounded uncertainties. The minimax optimization problem is reformulated as a convex minimization problem and is iteratively solved by a two-layer recurrent neural network. The proposed neurodynamic approach to nonlinear MPC improves the computational efficiency and sheds a light for real-time implementability of MPC technology. Simulation results are provided to substantiate the effectiveness and characteristics of the proposed approach.
4. Direct Adaptive Tracking Control for a Class of Pure-Feedback Stochastic Nonlinear Systems Based on Fuzzy-Approximation
Directory of Open Access Journals (Sweden)
Huanqing Wang
2014-01-01
Full Text Available The problem of fuzzy-based direct adaptive tracking control is considered for a class of pure-feedback stochastic nonlinear systems. During the controller design, fuzzy logic systems are used to approximate the packaged unknown nonlinearities, and then a novel direct adaptive controller is constructed via backstepping technique. It is shown that the proposed controller guarantees that all the signals in the closed-loop system are bounded in probability and the tracking error eventually converges to a small neighborhood around the origin in the sense of mean quartic value. The main advantages lie in that the proposed controller structure is simpler and only one adaptive parameter needs to be updated online. Simulation results are used to illustrate the effectiveness of the proposed approach.
5. Robust Stability for Nonlinear Systems with Time-Varying Delay and Uncertainties via the H∞ Quasi-Sliding Mode Control
Directory of Open Access Journals (Sweden)
Yi-You Hou
2014-01-01
Full Text Available This paper considers the problem of the robust stability for the nonlinear system with time-varying delay and parameters uncertainties. Based on the H∞ theorem, Lyapunov-Krasovskii theory, and linear matrix inequality (LMI optimization technique, the H∞ quasi-sliding mode controller and switching function are developed such that the nonlinear system is asymptotically stable in the quasi-sliding mode and satisfies the disturbance attenuation (H∞-norm performance. The effectiveness and accuracy of the proposed methods are shown in numerical simulations.
6. Nonlinear Hamiltonian systems
DEFF Research Database (Denmark)
Jørgensen, Michael Finn
1995-01-01
It is generally very difficult to solve nonlinear systems, and such systems often possess chaotic solutions. In the rare event that a system is completely solvable, it is said to integrable. Such systems never have chaotic solutions. Using the Inverse Scattering Transform Method (ISTM) two...... particular configurations of the Discrete Self-Trapping (DST) system are shown to be completely solvable. One of these systems includes the Toda lattice in a certain limit. An explicit integration is carried through for this Near-Toda lattice. The Near-Toda lattice is then generalized to include singular...
7. Adaptive fuzzy control of a class of nonaffine nonlinear system with input saturation based on passivity theorem.
Science.gov (United States)
Molavi, Ali; Jalali, Aliakbar; Ghasemi Naraghi, Mahdi
2017-07-01
In this paper, based on the passivity theorem, an adaptive fuzzy controller is designed for a class of unknown nonaffine nonlinear systems with arbitrary relative degree and saturation input nonlinearity to track the desired trajectory. The system equations are in normal form and its unforced dynamic may be unstable. As relative degree one is a structural obstacle in system passivation approach, in this paper, backstepping method is used to circumvent this obstacle and passivate the system step by step. Because of the existence of uncertainty and disturbance in the system, exact passivation and reference tracking cannot be tackled, so the approximate passivation or passivation with respect to a set is obtained to hold the tracking error in a neighborhood around zero. Furthermore, in order to overcome the non-smoothness of the saturation input nonlinearity, a parametric smooth nonlinear function with arbitrary approximation error is used to approximate the input saturation. Finally, the simulation results for the theoretical and practical examples are given to validate the proposed controller. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
8. Observer-based adaptive control of chaos in nonlinear discrete-time systems using time-delayed state feedback
International Nuclear Information System (INIS)
Goharrizi, Amin Yazdanpanah; Khaki-Sedigh, Ali; Sepehri, Nariman
2009-01-01
A new approach to adaptive control of chaos in a class of nonlinear discrete-time-varying systems, using a delayed state feedback scheme, is presented. It is discussed that such systems can show chaotic behavior as their parameters change. A strategy is employed for on-line calculation of the Lyapunov exponents that will be used within an adaptive scheme that decides on the control effort to suppress the chaotic behavior once detected. The scheme is further augmented with a nonlinear observer for estimation of the states that are required by the controller but are hard to measure. Simulation results for chaotic control problem of Jin map are provided to show the effectiveness of the proposed scheme.
9. Adaptive Neural Output-Feedback Control for a Class of Nonlower Triangular Nonlinear Systems With Unmodeled Dynamics.
Science.gov (United States)
Wang, Huanqing; Liu, Peter Xiaoping; Li, Shuai; Wang, Ding
2017-08-29
This paper presents the development of an adaptive neural controller for a class of nonlinear systems with unmodeled dynamics and immeasurable states. An observer is designed to estimate system states. The structure consistency of virtual control signals and the variable partition technique are combined to overcome the difficulties appearing in a nonlower triangular form. An adaptive neural output-feedback controller is developed based on the backstepping technique and the universal approximation property of the radial basis function (RBF) neural networks. By using the Lyapunov stability analysis, the semiglobally and uniformly ultimate boundedness of all signals within the closed-loop system is guaranteed. The simulation results show that the controlled system converges quickly, and all the signals are bounded. This paper is novel at least in the two aspects: 1) an output-feedback control strategy is developed for a class of nonlower triangular nonlinear systems with unmodeled dynamics and 2) the nonlinear disturbances and their bounds are the functions of all states, which is in a more general form than existing results.
10. Augmented Nonlinear Controller for Maximum Power-Point Tracking with Artificial Neural Network in Grid-Connected Photovoltaic Systems
Directory of Open Access Journals (Sweden)
Suliang Ma
2016-11-01
Full Text Available Photovoltaic (PV systems have non-linear characteristics that generate maximum power at one particular operating point. Environmental factors such as irradiance and temperature variations greatly affect the maximum power point (MPP. Diverse offline and online techniques have been introduced for tracking the MPP. Here, to track the MPP, an augmented-state feedback linearized (AFL non-linear controller combined with an artificial neural network (ANN is proposed. This approach linearizes the non-linear characteristics in PV systems and DC/DC converters, for tracking and optimizing the PV system operation. It also reduces the dependency of the designed controller on linearized models, to provide global stability. A complete model of the PV system is simulated. The existing maximum power-point tracking (MPPT and DC/DC boost-converter controller techniques are compared with the proposed ANN method. Two case studies, which simulate realistic circumstances, are presented to demonstrate the effectiveness and superiority of the proposed method. The AFL with ANN controller can provide good dynamic operation, faster convergence speed, and fewer operating-point oscillations around the MPP. It also tracks the global maxima under different conditions, especially irradiance-mutating situations, more effectively than the conventional methods. Detailed mathematical models and a control approach for a three-phase grid-connected intelligent hybrid system are proposed using MATLAB/Simulink.
11. Combined feedforward and feedback control of a redundant, nonlinear, dynamic musculoskeletal system.
Science.gov (United States)
Blana, Dimitra; Kirsch, Robert F; Chadwick, Edward K
2009-05-01
A functional electrical stimulation controller is presented that uses a combination of feedforward and feedback for arm control in high-level injury. The feedforward controller generates the muscle activations nominally required for desired movements, and the feedback controller corrects for errors caused by muscle fatigue and external disturbances. The feedforward controller is an artificial neural network (ANN) which approximates the inverse dynamics of the arm. The feedback loop includes a PID controller in series with a second ANN representing the nonlinear properties and biomechanical interactions of muscles and joints. The controller was designed and tested using a two-joint musculoskeletal model of the arm that includes four mono-articular and two bi-articular muscles. Its performance during goal-oriented movements of varying amplitudes and durations showed a tracking error of less than 4 degrees in ideal conditions, and less than 10 degrees even in the case of considerable fatigue and external disturbances.
12. Robust fuzzy output feedback controller for affine nonlinear systems via T-S fuzzy bilinear model: CSTR benchmark.
Science.gov (United States)
Hamdy, M; Hamdan, I
2015-07-01
In this paper, a robust H∞ fuzzy output feedback controller is designed for a class of affine nonlinear systems with disturbance via Takagi-Sugeno (T-S) fuzzy bilinear model. The parallel distributed compensation (PDC) technique is utilized to design a fuzzy controller. The stability conditions of the overall closed loop T-S fuzzy bilinear model are formulated in terms of Lyapunov function via linear matrix inequality (LMI). The control law is robustified by H∞ sense to attenuate external disturbance. Moreover, the desired controller gains can be obtained by solving a set of LMI. A continuous stirred tank reactor (CSTR), which is a benchmark problem in nonlinear process control, is discussed in detail to verify the effectiveness of the proposed approach with a comparative study. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.
13. Nonlinear control of magnetic signatures
Science.gov (United States)
Niemoczynski, Bogdan
Magnetic properties of ferrite structures are known to cause fluctuations in Earth's magnetic field around the object. These fluctuations are known as the object's magnetic signature and are unique based on the object's geometry and material. It is a common practice to neutralize magnetic signatures periodically after certain time intervals, however there is a growing interest to develop real time degaussing systems for various applications. Development of real time degaussing system is a challenging problem because of magnetic hysteresis and difficulties in measurement or estimation of near-field flux data. The goal of this research is to develop a real time feedback control system that can be used to minimize magnetic signatures for ferrite structures. Experimental work on controlling the magnetic signature of a cylindrical steel shell structure with a magnetic disturbance provided evidence that the control process substantially increased the interior magnetic flux. This means near field estimation using interior sensor data is likely to be inaccurate. Follow up numerical work for rectangular and cylindrical cross sections investigated variations in shell wall flux density under a variety of ambient excitation and applied disturbances. Results showed magnetic disturbances could corrupt interior sensor data and magnetic shielding due to the shell walls makes the interior very sensitive to noise. The magnetic flux inside the shell wall showed little variation due to inner disturbances and its high base value makes it less susceptible to noise. This research proceeds to describe a nonlinear controller to use the shell wall data as an input. A nonlinear plant model of magnetics is developed using a constant tau to represent domain rotation lag and a gain function k to describe the magnetic hysteresis curve for the shell wall. The model is justified by producing hysteresis curves for multiple materials, matching experimental data using a particle swarm algorithm, and
14. Adaptive fuzzy dynamic surface control of nonlinear systems with input saturation and time-varying output constraints
Science.gov (United States)
Edalati, L.; Khaki Sedigh, A.; Aliyari Shooredeli, M.; Moarefianpour, A.
2018-02-01
This paper deals with the design of adaptive fuzzy dynamic surface control for uncertain strict-feedback nonlinear systems with asymmetric time-varying output constraints in the presence of input saturation. To approximate the unknown nonlinear functions and overcome the problem of explosion of complexity, a Fuzzy logic system is combined with the dynamic surface control in the backstepping design technique. To ensure the output constraints satisfaction, an asymmetric time-varying Barrier Lyapunov Function (BLF) is used. Moreover, by applying the minimal learning parameter technique, the number of the online parameters update for each subsystem is reduced to 2. Hence, the semi-globally uniformly ultimately boundedness (SGUUB) of all the closed-loop signals with appropriate tracking error convergence is guaranteed. The effectiveness of the proposed control is demonstrated by two simulation examples.
15. Minimal-Approximation-Based Distributed Consensus Tracking of a Class of Uncertain Nonlinear Multiagent Systems With Unknown Control Directions.
Science.gov (United States)
Choi, Yun Ho; Yoo, Sung Jin
2017-03-28
A minimal-approximation-based distributed adaptive consensus tracking approach is presented for strict-feedback multiagent systems with unknown heterogeneous nonlinearities and control directions under a directed network. Existing approximation-based consensus results for uncertain nonlinear multiagent systems in lower-triangular form have used multiple function approximators in each local controller to approximate unmatched nonlinearities of each follower. Thus, as the follower's order increases, the number of the approximators used in its local controller increases. However, the proposed approach employs only one function approximator to construct the local controller of each follower regardless of the order of the follower. The recursive design methodology using a new error transformation is derived for the proposed minimal-approximation-based design. Furthermore, a bounding lemma on parameters of Nussbaum functions is presented to handle the unknown control direction problem in the minimal-approximation-based distributed consensus tracking framework and the stability of the overall closed-loop system is rigorously analyzed in the Lyapunov sense.
16. A model reference and sensitivity model-based self-learning fuzzy logic controller as a solution for control of nonlinear servo systems
NARCIS (Netherlands)
Kovacic, Z.; Bogdan, S.; Balenovic, M.
1999-01-01
In this paper, the design, simulation and experimental verification of a self-learning fuzzy logic controller (SLFLC) suitable for the control of nonlinear servo systems are described. The SLFLC contains a learning algorithm that utilizes a second-order reference model and a sensitivity model
17. Adaptive Critic Nonlinear Robust Control: A Survey.
Science.gov (United States)
Wang, Ding; He, Haibo; Liu, Derong
2017-10-01
Adaptive dynamic programming (ADP) and reinforcement learning are quite relevant to each other when performing intelligent optimization. They are both regarded as promising methods involving important components of evaluation and improvement, at the background of information technology, such as artificial intelligence, big data, and deep learning. Although great progresses have been achieved and surveyed when addressing nonlinear optimal control problems, the research on robustness of ADP-based control strategies under uncertain environment has not been fully summarized. Hence, this survey reviews the recent main results of adaptive-critic-based robust control design of continuous-time nonlinear systems. The ADP-based nonlinear optimal regulation is reviewed, followed by robust stabilization of nonlinear systems with matched uncertainties, guaranteed cost control design of unmatched plants, and decentralized stabilization of interconnected systems. Additionally, further comprehensive discussions are presented, including event-based robust control design, improvement of the critic learning rule, nonlinear H ∞ control design, and several notes on future perspectives. By applying the ADP-based optimal and robust control methods to a practical power system and an overhead crane plant, two typical examples are provided to verify the effectiveness of theoretical results. Overall, this survey is beneficial to promote the development of adaptive critic control methods with robustness guarantee and the construction of higher level intelligent systems.
18. Adaptive Actor-Critic Design-Based Integral Sliding-Mode Control for Partially Unknown Nonlinear Systems With Input Disturbances.
Science.gov (United States)
Fan, Quan-Yong; Yang, Guang-Hong
2016-01-01
This paper is concerned with the problem of integral sliding-mode control for a class of nonlinear systems with input disturbances and unknown nonlinear terms through the adaptive actor-critic (AC) control method. The main objective is to design a sliding-mode control methodology based on the adaptive dynamic programming (ADP) method, so that the closed-loop system with time-varying disturbances is stable and the nearly optimal performance of the sliding-mode dynamics can be guaranteed. In the first step, a neural network (NN)-based observer and a disturbance observer are designed to approximate the unknown nonlinear terms and estimate the input disturbances, respectively. Based on the NN approximations and disturbance estimations, the discontinuous part of the sliding-mode control is constructed to eliminate the effect of the disturbances and attain the expected equivalent sliding-mode dynamics. Then, the ADP method with AC structure is presented to learn the optimal control for the sliding-mode dynamics online. Reconstructed tuning laws are developed to guarantee the stability of the sliding-mode dynamics and the convergence of the weights of critic and actor NNs. Finally, the simulation results are presented to illustrate the effectiveness of the proposed method.
19. Adaptive Constrained Optimal Control Design for Data-Based Nonlinear Discrete-Time Systems With Critic-Only Structure.
Science.gov (United States)
Luo, Biao; Liu, Derong; Wu, Huai-Ning
2018-06-01
Reinforcement learning has proved to be a powerful tool to solve optimal control problems over the past few years. However, the data-based constrained optimal control problem of nonaffine nonlinear discrete-time systems has rarely been studied yet. To solve this problem, an adaptive optimal control approach is developed by using the value iteration-based Q-learning (VIQL) with the critic-only structure. Most of the existing constrained control methods require the use of a certain performance index and only suit for linear or affine nonlinear systems, which is unreasonable in practice. To overcome this problem, the system transformation is first introduced with the general performance index. Then, the constrained optimal control problem is converted to an unconstrained optimal control problem. By introducing the action-state value function, i.e., Q-function, the VIQL algorithm is proposed to learn the optimal Q-function of the data-based unconstrained optimal control problem. The convergence results of the VIQL algorithm are established with an easy-to-realize initial condition . To implement the VIQL algorithm, the critic-only structure is developed, where only one neural network is required to approximate the Q-function. The converged Q-function obtained from the critic-only VIQL method is employed to design the adaptive constrained optimal controller based on the gradient descent scheme. Finally, the effectiveness of the developed adaptive control method is tested on three examples with computer simulation.
20. Computer-Aided Design Methods for Model-Based Nonlinear Engine Control Systems, Phase I
Data.gov (United States)
National Aeronautics and Space Administration — Traditional design methods for aircraft turbine engine control systems have relied on the use of linearized models and linear control theory. While these controllers...
1. Adaptive neural network output feedback control for stochastic nonlinear systems with unknown dead-zone and unmodeled dynamics.
Science.gov (United States)
Tong, Shaocheng; Wang, Tong; Li, Yongming; Zhang, Huaguang
2014-06-01
This paper discusses the problem of adaptive neural network output feedback control for a class of stochastic nonlinear strict-feedback systems. The concerned systems have certain characteristics, such as unknown nonlinear uncertainties, unknown dead-zones, unmodeled dynamics and without the direct measurements of state variables. In this paper, the neural networks (NNs) are employed to approximate the unknown nonlinear uncertainties, and then by representing the dead-zone as a time-varying system with a bounded disturbance. An NN state observer is designed to estimate the unmeasured states. Based on both backstepping design technique and a stochastic small-gain theorem, a robust adaptive NN output feedback control scheme is developed. It is proved that all the variables involved in the closed-loop system are input-state-practically stable in probability, and also have robustness to the unmodeled dynamics. Meanwhile, the observer errors and the output of the system can be regulated to a small neighborhood of the origin by selecting appropriate design parameters. Simulation examples are also provided to illustrate the effectiveness of the proposed approach.
2. Fuzzy combination of fuzzy and switching state-feedback controllers for nonlinear systems subject to parameter uncertainties.
Science.gov (United States)
Lam, H K; Leung, Frank H F
2005-04-01
This paper presents a fuzzy controller, which involves a fuzzy combination of local fuzzy and global switching state-feedback controllers, for nonlinear systems subject to parameter uncertainties with known bounds. The nonlinear system is represented by a fuzzy combined Takagi-Sugeno-Kang model, which is a fuzzy combination of the global and local fuzzy plant models. By combining the local fuzzy and global switching state-feedback controllers using fuzzy logic techniques, the advantages of both controllers can be retained and the undesirable chattering effect introduced by the global switching state-feedback controller can be eliminated. The steady-state error introduced by the global switching state-feedback controller when a saturation function is used can also be removed. Stability conditions, which are related to the system matrices of the local and global closed-loop systems, are derived to guarantee the closed-loop system stability. An application example will be given to demonstrate the merits of the proposed approach.
3. Global output feedback control for a class of high-order feedforward nonlinear systems with input delay.
Science.gov (United States)
Zha, Wenting; Zhai, Junyong; Fei, Shumin
2013-07-01
This paper investigates the problem of output feedback stabilization for a class of high-order feedforward nonlinear systems with time-varying input delay. First, a scaling gain is introduced into the system under a set of coordinate transformations. Then, the authors construct an observer and controller to make the nominal system globally asymptotically stable. Based on homogeneous domination approach and Lyapunov-Krasovskii functional, it is shown that the closed-loop system can be rendered globally asymptotically stable by the scaling gain. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed scheme. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.
4. FRF decoupling of nonlinear systems
Science.gov (United States)
Kalaycıoğlu, Taner; Özgüven, H. Nevzat
2018-03-01
Structural decoupling problem, i.e. predicting dynamic behavior of a particular substructure from the knowledge of the dynamics of the coupled structure and the other substructure, has been well investigated for three decades and led to several decoupling methods. In spite of the inherent nonlinearities in a structural system in various forms such as clearances, friction and nonlinear stiffness, all decoupling studies are for linear systems. In this study, decoupling problem for nonlinear systems is addressed for the first time. A method, named as FRF Decoupling Method for Nonlinear Systems (FDM-NS), is proposed for calculating FRFs of a substructure decoupled from a coupled nonlinear structure where nonlinearity can be modeled as a single nonlinear element. Depending on where nonlinear element is, i.e., either in the known or unknown subsystem, or at the connection point, the formulation differs. The method requires relative displacement information between two end points of the nonlinear element, in addition to point and transfer FRFs at some points of the known subsystem. However, it is not necessary to excite the system from the unknown subsystem even when the nonlinear element is in that subsystem. The validation of FDM-NS is demonstrated with two different case studies using nonlinear lumped parameter systems. Finally, a nonlinear experimental test structure is used in order to show the real-life application and accuracy of FDM-NS.
5. An Error-Entropy Minimization Algorithm for Tracking Control of Nonlinear Stochastic Systems with Non-Gaussian Variables
Energy Technology Data Exchange (ETDEWEB)
Liu, Yunlong; Wang, Aiping; Guo, Lei; Wang, Hong
2017-07-09
This paper presents an error-entropy minimization tracking control algorithm for a class of dynamic stochastic system. The system is represented by a set of time-varying discrete nonlinear equations with non-Gaussian stochastic input, where the statistical properties of stochastic input are unknown. By using Parzen windowing with Gaussian kernel to estimate the probability densities of errors, recursive algorithms are then proposed to design the controller such that the tracking error can be minimized. The performance of the error-entropy minimization criterion is compared with the mean-square-error minimization in the simulation results.
6. On Stabilization of Nonautonomous Nonlinear Systems
International Nuclear Information System (INIS)
Bogdanov, A. Yu.
2008-01-01
The procedures to obtain the sufficient conditions of asymptotic stability for nonlinear nonstationary continuous-time systems are discussed. We consider different types of the following general controlled system: x = X(t,x,u) = F(t,x)+B(t,x)u, x(t 0 ) = x 0 . (*) The basis of investigation is limiting equations, limiting Lyapunov functions, etc. The improved concept of observability of the pair of functional matrices is presented. By these results the problem of synthesis of asymptotically stable control nonlinear nonautonomous systems (with linear parts) involving the quadratic time-dependent Lyapunov functions is solved as well as stabilizing a given unstable system with nonlinear control law.
7. Response analysis and energy transmissibility of a vibration isolation system with real-power nonlinearities under a NMPPF controller
International Nuclear Information System (INIS)
Huang, Dongmei; Xu, Wei; Shi, Lingling
2016-01-01
Highlights: • The nonlinear modified positive position feedback (NMPPF) scheme and the real-power form of restoring and damping forces are combined to improve the response performance of a vibration isolation system. • The primary resonance, dynamical stability and energy transmissibility of the real-power vibration isolation system are studied. • The sensitivity of the controller parameters on the responses has been analyzed. • In order to suppress the amplitude peak, the feedback parameters have been determined by the frequency response. • The energy transmissibility is investigated. - Abstract: In this paper, the nonlinear modified positive position feedback (NMPPF) scheme and the real-power form of restoring and damping forces are combined to improve the response performance of a vibration isolation system. Based on the method of multiple scales, the frequency response, the stability and the energy transmissibility of the real-power vibration isolation system are studied. It is found that the controlled isolation system exhibits a softening behavior for sub-linear restoring force, while it exhibits the two peak response characteristic rather than a hardening behavior for over-linear restoring force. Further, the sensitivity of the feedback parameters on the responses is discussed. The results, compared to the conventional PPF and IRC methods, show that the proposed method is significantly more effective in controlling the steady-state response, and slightly advantageous for the steady-state dynamics control. The effectiveness of this method is also verified by time domain analysis. Then, the suitable feedback and controller parameters are derived by simulation results in which the amplitude peak is suppressed and the resonance stability is maintained. Finally, the energy transmissibility of the vibration isolation system is investigated. The results show that the feedback gain can reduce the whole transmissibility level and greatly suppress vibration
8. Adaptive NN tracking control of uncertain nonlinear discrete-time systems with nonaffine dead-zone input.
Science.gov (United States)
Liu, Yan-Jun; Tong, Shaocheng
2015-03-01
In the paper, an adaptive tracking control design is studied for a class of nonlinear discrete-time systems with dead-zone input. The considered systems are of the nonaffine pure-feedback form and the dead-zone input appears nonlinearly in the systems. The contributions of the paper are that: 1) it is for the first time to investigate the control problem for this class of discrete-time systems with dead-zone; 2) there are major difficulties for stabilizing such systems and in order to overcome the difficulties, the systems are transformed into an n-step-ahead predictor but nonaffine function is still existent; and 3) an adaptive compensative term is constructed to compensate for the parameters of the dead-zone. The neural networks are used to approximate the unknown functions in the transformed systems. Based on the Lyapunov theory, it is proven that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to a small neighborhood of zero. Two simulation examples are provided to verify the effectiveness of the control approach in the paper.
9. Nonlinear model predictive control theory and algorithms
CERN Document Server
Grüne, Lars
2017-01-01
This book offers readers a thorough and rigorous introduction to nonlinear model predictive control (NMPC) for discrete-time and sampled-data systems. NMPC schemes with and without stabilizing terminal constraints are detailed, and intuitive examples illustrate the performance of different NMPC variants. NMPC is interpreted as an approximation of infinite-horizon optimal control so that important properties like closed-loop stability, inverse optimality and suboptimality can be derived in a uniform manner. These results are complemented by discussions of feasibility and robustness. An introduction to nonlinear optimal control algorithms yields essential insights into how the nonlinear optimization routine—the core of any nonlinear model predictive controller—works. Accompanying software in MATLAB® and C++ (downloadable from extras.springer.com/), together with an explanatory appendix in the book itself, enables readers to perform computer experiments exploring the possibilities and limitations of NMPC. T...
10. Discrete-time online learning control for a class of unknown nonaffine nonlinear systems using reinforcement learning.
Science.gov (United States)
Yang, Xiong; Liu, Derong; Wang, Ding; Wei, Qinglai
2014-07-01
In this paper, a reinforcement-learning-based direct adaptive control is developed to deliver a desired tracking performance for a class of discrete-time (DT) nonlinear systems with unknown bounded disturbances. We investigate multi-input-multi-output unknown nonaffine nonlinear DT systems and employ two neural networks (NNs). By using Implicit Function Theorem, an action NN is used to generate the control signal and it is also designed to cancel the nonlinearity of unknown DT systems, for purpose of utilizing feedback linearization methods. On the other hand, a critic NN is applied to estimate the cost function, which satisfies the recursive equations derived from heuristic dynamic programming. The weights of both the action NN and the critic NN are directly updated online instead of offline training. By utilizing Lyapunov's direct method, the closed-loop tracking errors and the NN estimated weights are demonstrated to be uniformly ultimately bounded. Two numerical examples are provided to show the effectiveness of the present approach. Copyright © 2014 Elsevier Ltd. All rights reserved.
11. Chaotic behaviour in the non-linear optimal control of unilaterally contacting building systems during earthquakes
CERN Document Server
Liolios, A
2003-01-01
The paper presents a new numerical approach for a non-linear optimal control problem arising in earthquake civil engineering. This problem concerns the elastoplastic softening-fracturing unilateral contact between neighbouring buildings during earthquakes when Coulomb friction is taken into account under second-order instabilizing effects. So, the earthquake response of the adjacent structures can appear instabilities and chaotic behaviour. The problem formulation presented here leads to a set of equations and inequalities, which is equivalent to a dynamic hemivariational inequality in the way introduced by Panagiotopoulos [Hemivariational Inequalities. Applications in Mechanics and Engineering, Springer-Verlag, Berlin, 1993]. The numerical procedure is based on an incremental problem formulation and on a double discretization, in space by the finite element method and in time by the Wilson-theta method. The generally non-convex constitutive contact laws are piecewise linearized, and in each time-step a non-c...
12. Indirect adaptive fuzzy fault-tolerant tracking control for MIMO nonlinear systems with actuator and sensor failures.
Science.gov (United States)
Bounemeur, Abdelhamid; Chemachema, Mohamed; Essounbouli, Najib
2018-05-10
13. DESIGN AN INTELLIGENT CONTROLLER FOR FULL VEHICLE NONLINEAR ACTIVE SUSPENSION SYSTEMS
OpenAIRE
Aldair, A. A.; Wang, W. J.
2011-01-01
The main objective of designed the controller for a vehicle suspension system is to reduce the discomfort sensed by passengers which arises from road roughness and to increase the ride handling associated with the pitching and rolling movements. This necessitates a very fast and accurate controller to meet as much control objectives, as possible. Therefore, this paper deals with an artificial intelligence Neuro-Fuzzy (NF) technique to design a robust controller to meet the control objectives....
14. Event-triggered decentralized adaptive fault-tolerant control of uncertain interconnected nonlinear systems with actuator failures.
Science.gov (United States)
Choi, Yun Ho; Yoo, Sung Jin
2018-06-01
This paper investigates the event-triggered decentralized adaptive tracking problem of a class of uncertain interconnected nonlinear systems with unexpected actuator failures. It is assumed that local control signals are transmitted to local actuators with time-varying faults whenever predefined conditions for triggering events are satisfied. Compared with the existing control-input-based event-triggering strategy for adaptive control of uncertain nonlinear systems, the aim of this paper is to propose a tracking-error-based event-triggering strategy in the decentralized adaptive fault-tolerant tracking framework. The proposed approach can relax drastic changes in control inputs caused by actuator faults in the existing triggering strategy. The stability of the proposed event-triggering control system is analyzed in the Lyapunov sense. Finally, simulation comparisons of the proposed and existing approaches are provided to show the effectiveness of the proposed theoretical result in the presence of actuator faults. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.
15. Balancing for Unstable Nonlinear Systems
NARCIS (Netherlands)
Scherpen, J.M.A.
1993-01-01
A previously obtained method of balancing for stable nonlinear systems is extended to unstable nonlinear systems. The similarity invariants obtained by the concept of LQG balancing for an unstable linear system can also be obtained by considering a past and future energy function of the system. By
16. Nonlinear dynamic analysis and robust controller design for Francis hydraulic turbine regulating system with a straight-tube surge tank
Science.gov (United States)
Liang, Ji; Yuan, Xiaohui; Yuan, Yanbin; Chen, Zhihuan; Li, Yuanzheng
2017-02-01
The safety and stability of hydraulic turbine regulating system (HTRS) in hydropower plants become increasingly important since the rapid development and the broad application of hydro energy technology. In this paper, a novel mathematical model of Francis hydraulic turbine regulating system with a straight-tube surge tank based on a few state-space equations is introduced to study the dynamic behaviors of the HTRS system, where the existence of possible unstable oscillations of this model is studied extensively and presented in the forms of the bifurcation diagram, time waveform plot, phase trajectories, and power spectrum. To eliminate these undesirable behaviors, a specified fuzzy sliding mode controller is designed. In this hybrid controller, the sliding mode control law makes full use of the proposed model to guarantee the robust control in the presence of system uncertainties, while the fuzzy system is applied to approximate the proper gains of the switching control in sliding mode technique to reduce the chattering effect, and particle swarm optimization is developed to search the optimal gains of the controller. Numerical simulations are presented to verify the effectiveness of the designed controller, and the results show that the performances of the nonlinear HTRS system assisted with the proposed controller is much better than that with the commonly used optimal PID controller.
17. Observer-Based Controller Design for a Class of Nonlinear Networked Control Systems with Random Time-Delays Modeled by Markov Chains
Directory of Open Access Journals (Sweden)
Yanfeng Wang
2017-01-01
Full Text Available This paper investigates the observer-based controller design problem for a class of nonlinear networked control systems with random time-delays. The nonlinearity is assumed to satisfy a global Lipschitz condition and two dependent Markov chains are employed to describe the time-delay from sensor to controller (S-C delay and the time-delay from controller to actuator (C-A delay, respectively. The transition probabilities of S-C delay and C-A delay are both assumed to be partly inaccessible. Sufficient conditions on the stochastic stability for the closed-loop systems are obtained by constructing proper Lyapunov functional. The methods of calculating the controller and the observer gain matrix are also given. Two numerical examples are used to illustrate the effectiveness of the proposed method.
18. An Interval Type-2 Fuzzy System with a Species-Based Hybrid Algorithm for Nonlinear System Control Design
Directory of Open Access Journals (Sweden)
Chung-Ta Li
2014-01-01
Full Text Available We propose a species-based hybrid of the electromagnetism-like mechanism (EM and back-propagation algorithms (SEMBP for an interval type-2 fuzzy neural system with asymmetric membership functions (AIT2FNS design. The interval type-2 asymmetric fuzzy membership functions (IT2 AFMFs and the TSK-type consequent part are adopted to implement the network structure in AIT2FNS. In addition, the type reduction procedure is integrated into an adaptive network structure to reduce computational complexity. Hence, the AIT2FNS can enhance the approximation accuracy effectively by using less fuzzy rules. The AIT2FNS is trained by the SEMBP algorithm, which contains the steps of uniform initialization, species determination, local search, total force calculation, movement, and evaluation. It combines the advantages of EM and back-propagation (BP algorithms to attain a faster convergence and a lower computational complexity. The proposed SEMBP algorithm adopts the uniform method (which evenly scatters solution agents over the feasible solution region and the species technique to improve the algorithm’s ability to find the global optimum. Finally, two illustrative examples of nonlinear systems control are presented to demonstrate the performance and the effectiveness of the proposed AIT2FNS with the SEMBP algorithm.
19. elative controllability of nonlinear neutral Volterra Integrodiferential ...
African Journals Online (AJOL)
In this paper we established sufficient conditions for the relative controllability of the nonlinear neutral volterra integro-differential systems with distributed delays in the control. The results were established using the Schauder's fixed point theorem which is an extension of known results. Journal of the Nigerian Association of ...
20. Recurrent-Neural-Network-Based Multivariable Adaptive Control for a Class of Nonlinear Dynamic Systems With Time-Varying Delay.
Science.gov (United States)
Hwang, Chih-Lyang; Jan, Chau
2016-02-01
At the beginning, an approximate nonlinear autoregressive moving average (NARMA) model is employed to represent a class of multivariable nonlinear dynamic systems with time-varying delay. It is known that the disadvantages of robust control for the NARMA model are as follows: 1) suitable control parameters for larger time delay are more sensitive to achieving desirable performance; 2) it only deals with bounded uncertainty; and 3) the nominal NARMA model must be learned in advance. Due to the dynamic feature of the NARMA model, a recurrent neural network (RNN) is online applied to learn it. However, the system performance becomes deteriorated due to the poor learning of the larger variation of system vector functions. In this situation, a simple network is employed to compensate the upper bound of the residue caused by the linear parameterization of the approximation error of RNN. An e -modification learning law with a projection for weight matrix is applied to guarantee its boundedness without persistent excitation. Under suitable conditions, the semiglobally ultimately bounded tracking with the boundedness of estimated weight matrix is obtained by the proposed RNN-based multivariable adaptive control. Finally, simulations are presented to verify the effectiveness and robustness of the proposed control.
1. Non-fragile robust stabilization and H{sub {infinity}} control for uncertain stochastic nonlinear time-delay systems
Energy Technology Data Exchange (ETDEWEB)
Zhang Jinhui [Department of Automatic Control, Beijing Institute of Technology, Beijing 100081 (China)], E-mail: jinhuizhang82@gmail.com; Shi Peng [Faculty of Advanced Technology, University of Glamorgan, Pontypridd CF37 1DL (United Kingdom); ILSCM, School of Science and Engineering, Victoria University, Melbourne, Vic. 8001 (Australia); School of Mathematics and Statistics, University of South Australia, Mawson Lakes, SA 5095 (Australia)], E-mail: pshi@glam.ac.uk; Yang Hongjiu [Department of Automatic Control, Beijing Institute of Technology, Beijing 100081 (China)], E-mail: yanghongjiu@gmail.com
2009-12-15
This paper deals with the problem of non-fragile robust stabilization and H{sub {infinity}} control for a class of uncertain stochastic nonlinear time-delay systems. The parametric uncertainties are real time-varying as well as norm bounded. The time-delay factors are unknown and time-varying with known bounds. The aim is to design a memoryless non-fragile state feedback control law such that the closed-loop system is stochastically asymptotically stable in the mean square and the effect of the disturbance input on the controlled output is less than a prescribed level for all admissible parameter uncertainties. New sufficient conditions for the existence of such controllers are presented based on the linear matrix inequalities (LMIs) approach. Numerical example is given to illustrate the effectiveness of the developed techniques.
2. Identification of the Response of a Controlled Building Structure Subjected to Seismic Load by Using Nonlinear System Models
Directory of Open Access Journals (Sweden)
Mosbeh R. Kaloop
2016-10-01
Full Text Available The present study investigates the prediction efficiency of nonlinear system-identification models, in assessing the behavior of a coupled structure-passive vibration controller. Two system-identification models, including Nonlinear AutoRegresive with eXogenous inputs (NARX and adaptive neuro-fuzzy inference system (ANFIS, are used to model the behavior of an experimentally scaled three-story building incorporated with a tuned mass damper (TMD subjected to seismic loads. The experimental study is performed to generate the input and output data sets for training and testing the designed models. The parameters of root-mean-squared error, mean absolute error and determination coefficient statistics are used to compare the performance of the aforementioned models. A TMD controller system works efficiently to mitigate the structural vibration. The results revealed that the NARX and ANFIS models could be used to identify the response of a controlled structure. The parameters of both two time-delays of the structure response and the seismic load were proven to be effective tools in identifying the performance of the models. A comparison based on the parametric evaluation of the two methods showed that the NARX model outperforms the ANFIS model in identifying structures response.
3. Robust finite-time tracking control for nonlinear suspension systems via disturbance compensation
Science.gov (United States)
Pan, Huihui; Jing, Xingjian; Sun, Weichao
2017-05-01
This paper focuses on the finite-time tracking control with external disturbance for active suspension systems. In order to compensate unknown disturbance efficiently, a disturbance compensator with finite-time convergence property is studied. By analyzing the discontinuous phenomenon of classical disturbance compensation techniques, this study presents a simple approach to construct a continuous compensator satisfying the finite-time disturbance rejection performance. According to the finite-time separation principle, the design procedures of the nominal controller for the suspension system without disturbance and the disturbance compensator can be implemented in a completely independent manner. Therefore, the overall control law for the closed-loop system is continuous, which offers some distinct advantages over the existing discontinuous ones. From the perspective of practical implementation, the continuous controller can avoid effectively the unexpected chattering in active suspension control. Comparative experimental results are presented and discussed to illustrate the advantage and effectiveness of the proposed control strategy.
4. Feedforward Nonlinear Control Using Neural Gas Network
Directory of Open Access Journals (Sweden)
Iván Machón-González
2017-01-01
Full Text Available Nonlinear systems control is a main issue in control theory. Many developed applications suffer from a mathematical foundation not as general as the theory of linear systems. This paper proposes a control strategy of nonlinear systems with unknown dynamics by means of a set of local linear models obtained by a supervised neural gas network. The proposed approach takes advantage of the neural gas feature by which the algorithm yields a very robust clustering procedure. The direct model of the plant constitutes a piece-wise linear approximation of the nonlinear system and each neuron represents a local linear model for which a linear controller is designed. The neural gas model works as an observer and a controller at the same time. A state feedback control is implemented by estimation of the state variables based on the local transfer function that was provided by the local linear model. The gradient vectors obtained by the supervised neural gas algorithm provide a robust procedure for feedforward nonlinear control, that is, supposing the inexistence of disturbances.
5. Distributed Adaptive Finite-Time Approach for Formation-Containment Control of Networked Nonlinear Systems Under Directed Topology.
Science.gov (United States)
Wang, Yujuan; Song, Yongduan; Ren, Wei
2017-07-06
This paper presents a distributed adaptive finite-time control solution to the formation-containment problem for multiple networked systems with uncertain nonlinear dynamics and directed communication constraints. By integrating the special topology feature of the new constructed symmetrical matrix, the technical difficulty in finite-time formation-containment control arising from the asymmetrical Laplacian matrix under single-way directed communication is circumvented. Based upon fractional power feedback of the local error, an adaptive distributed control scheme is established to drive the leaders into the prespecified formation configuration in finite time. Meanwhile, a distributed adaptive control scheme, independent of the unavailable inputs of the leaders, is designed to keep the followers within a bounded distance from the moving leaders and then to make the followers enter the convex hull shaped by the formation of the leaders in finite time. The effectiveness of the proposed control scheme is confirmed by the simulation.
6. Neuroadaptive Fault-Tolerant Control of Nonlinear Systems Under Output Constraints and Actuation Faults.
Science.gov (United States)
Zhao, Kai; Song, Yongduan; Shen, Zhixi
2018-02-01
In this paper, a neuroadaptive fault-tolerant tracking control method is proposed for a class of time-delay pure-feedback systems in the presence of external disturbances and actuation faults. The proposed controller can achieve prescribed transient and steady-state performance, despite uncertain time delays and output constraints as well as actuation faults. By combining a tangent barrier Lyapunov-Krasovskii function with the dynamic surface control technique, the neural network unit in the developed control scheme is able to take its action from the very beginning and play its learning/approximating role safely during the entire system operational envelope, leading to enhanced control performance without the danger of violating compact set precondition. Furthermore, prescribed transient performance and output constraints are strictly ensured in the presence of nonaffine uncertainties, external disturbances, and undetectable actuation faults. The control strategy is also validated by numerical simulation.
7. Model and Sensor Based Nonlinear Adaptive Flight Control with Online System Identification
NARCIS (Netherlands)
Sun, L.G.
2014-01-01
Consensus exists that many loss-of-control (LOC) in flight accidents caused by severe aircraft damage or system failure could be prevented if flight performance could be recovered using the valid and remaining control authorities. However, the safe maneuverability of a post-failure aircraft will
8. Evaluation of Linear and Non-Linear Control Schemes Applied to a Hydraulic Servo System
DEFF Research Database (Denmark)
Andersen, Torben Ole; Hansen, Michael Rygaard; Pedersen, Henrik Clemmensen
2005-01-01
Due to the innovation of low-cost electronics such as sensors, microcontrollers etc., the focus on highperformance motion control is increasing. This work focuses on position control of single-input single-output hydraulic servo-systems in general. A hydraulically actuated robotic manipulator...
9. Modeling and Nonlinear Control of Fuel Cell / Supercapacitor Hybrid Energy Storage System for Electric Vehicles
DEFF Research Database (Denmark)
2014-01-01
This paper deals with the problem of controlling hybrid energy storage system (HESS) for electric vehicle. The storage system consists of a fuel cell (FC), serving as the main power source, and a supercapacitor (SC), serving as an auxiliary power source. It also contains a power block for energy...
10. Chaotic behaviour in the non-linear optimal control of unilaterally contacting building systems during earthquakes
International Nuclear Information System (INIS)
Liolios, A.A.; Boglou, A.K.
2003-01-01
The paper presents a new numerical approach for a non-linear optimal control problem arising in earthquake civil engineering. This problem concerns the elastoplastic softening-fracturing unilateral contact between neighbouring buildings during earthquakes when Coulomb friction is taken into account under second-order instabilizing effects. So, the earthquake response of the adjacent structures can appear instabilities and chaotic behaviour. The problem formulation presented here leads to a set of equations and inequalities, which is equivalent to a dynamic hemivariational inequality in the way introduced by Panagiotopoulos [Hemivariational Inequalities. Applications in Mechanics and Engineering, Springer-Verlag, Berlin, 1993]. The numerical procedure is based on an incremental problem formulation and on a double discretization, in space by the finite element method and in time by the Wilson-θ method. The generally non-convex constitutive contact laws are piecewise linearized, and in each time-step a non-convex linear complementarity problem is solved with a reduced number of unknowns
11. Singularity-Free Neural Control for the Exponential Trajectory Tracking in Multiple-Input Uncertain Systems with Unknown Deadzone Nonlinearities
Directory of Open Access Journals (Sweden)
J. Humberto Pérez-Cruz
2014-01-01
Full Text Available The trajectory tracking for a class of uncertain nonlinear systems in which the number of possible states is equal to the number of inputs and each input is preceded by an unknown symmetric deadzone is considered. The unknown dynamics is identified by means of a continuous time recurrent neural network in which the control singularity is conveniently avoided by guaranteeing the invertibility of the coupling matrix. Given this neural network-based mathematical model of the uncertain system, a singularity-free feedback linearization control law is developed in order to compel the system state to follow a reference trajectory. By means of Lyapunov-like analysis, the exponential convergence of the tracking error to a bounded zone can be proven. Likewise, the boundedness of all closed-loop signals can be guaranteed.
12. Control-based method to identify underlying delays of a nonlinear dynamical system.
Science.gov (United States)
Yu, Dongchuan; Frasca, Mattia; Liu, Fang
2008-10-01
We suggest several stationary state control-based delay identification methods which do not require any structural information about the controlled systems and are applicable to systems described by delayed ordinary differential equations. This proposed technique includes three steps: (i) driving a system to a steady state; (ii) perturbing the control signal for shifting the steady state; and (iii) identifying all delays by detecting the time that the system is abruptly drawn out of stationarity. Some aspects especially important for applications are discussed as well, including interaction delay identification, stationary state convergence speed, performance comparison, and the influence of noise on delay identification. Several examples are presented to illustrate the reliability and robustness of all delay identification methods suggested.
13. Interval type-2 fuzzy PID controller for uncertain nonlinear inverted pendulum system.
Science.gov (United States)
2014-05-01
In this paper, the interval type-2 fuzzy proportional-integral-derivative controller (IT2F-PID) is proposed for controlling an inverted pendulum on a cart system with an uncertain model. The proposed controller is designed using a new method of type-reduction that we have proposed, which is called the simplified type-reduction method. The proposed IT2F-PID controller is able to handle the effect of structure uncertainties due to the structure of the interval type-2 fuzzy logic system (IT2-FLS). The results of the proposed IT2F-PID controller using a new method of type-reduction are compared with the other proposed IT2F-PID controller using the uncertainty bound method and the type-1 fuzzy PID controller (T1F-PID). The simulation and practical results show that the performance of the proposed controller is significantly improved compared with the T1F-PID controller. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.
14. A nonlinear controller design for permanent magnet motors using a synchronization-based technique inspired from the Lorenz system.
Science.gov (United States)
Zaher, Ashraf A
2008-03-01
The dynamic behavior of a permanent magnet synchronous machine (PMSM) is analyzed. Nominal and special operating conditions are explored to show that the PMSM can experience chaos. A nonlinear controller is introduced to control these unwanted chaotic oscillations and to bring the PMSM to a stable steady state. The designed controller uses a pole-placement approach to force the closed-loop system to follow the performance of a simple first-order linear system with zero steady-state error to a desired set point. The similarity between the mathematical model of the PMSM and the famous chaotic Lorenz system is utilized to design a synchronization-based state observer using only the angular speed for feedback. Simulation results verify the effectiveness of the proposed controller in eliminating the chaotic oscillations while using a single feedback signal. The superiority of the proposed controller is further demonstrated by comparing it with a conventional PID controller. Finally, a laboratory-based experiment was conducted using the MCK2812 C Pro-MS(BL) motion control kit to confirm the theoretical results and to verify both the causality and versatility of the proposed controller.
15. Feedback control systems for non-linear simulation of operational transients in LMFBRs
International Nuclear Information System (INIS)
Khatib-Rahbar, M.; Agrawal, A.K.; Srinivasan, E.S.
Adequate modeling of Plant Control Systems (PCS) for the study of Anticipated Transients Without Scram (ATWS) is of considerable significance in the design, operation and safety evaluation of Liquid-Metal-Cooled Fast Breeder Reactor (LMFBR) systems. To assess the system response to high frequency, low consequence events, the plant needs to be dynamically simulated. The description of analytical and numerical models for PCS that have been developed and incorporated into the loop version of the Super System Code (SSC-L) are described. The importance of detailed modeling of control systems is discussed. Sample transient results obtained for a 10% ramp change of load in 40 s in the Clinch River Breeder Reactor Plant (CRBRP) are also shown
16. Performance of a Nonlinear Real-Time Optimal Control System for HEVs/PHEVs during Car Following
Directory of Open Access Journals (Sweden)
Kaijiang Yu
2014-01-01
Full Text Available This paper presents a real-time optimal control approach for the energy management problem of hybrid electric vehicles (HEVs and plug-in hybrid electric vehicles (PHEVs with slope information during car following. The new features of this study are as follows. First, the proposed method can optimize the engine operating points and the driving profile simultaneously. Second, the proposed method gives the freedom of vehicle spacing between the preceding vehicle and the host vehicle. Third, using the HEV/PHEV property, the desired battery state of charge is designed according to the road slopes for better recuperation of free braking energy. Fourth, all of the vehicle operating modes engine charge, electric vehicle, motor assist and electric continuously variable transmission, and regenerative braking, can be realized using the proposed real-time optimal control approach. Computer simulation results are shown among the nonlinear real-time optimal control approach and the ADVISOR rule-based approach. The conclusion is that the nonlinear real-time optimal control approach is effective for the energy management problem of the HEV/PHEV system during car following.
17. A case study in nonlinear dynamics and control of articulated spacecraft: The Space Station Freedom with a mobile remote manipulator system
Science.gov (United States)
Bennett, William H.; Kwatny, Harry G.; Lavigna, Chris; Blankenship, Gilmer
1994-01-01
The following topics are discussed: (1) modeling of articulated spacecraft as multi-flex-body systems; (2) nonlinear attitude control by adaptive partial feedback linearizing (PFL) control; (3) attitude dynamics and control for SSF/MRMS; and (4) performance analysis results for attitude control of SSF/MRMS.
18. Distributed Cooperative Control of Multiple Nonlinear Systems with Nonholonomic Constraints and Uncertainty
Science.gov (United States)
2015-04-04
this testbed, there are four P3-AT mobile robots. Each robot is equipped with a camera and a laser sensor. Between robots, there is wireless...shows the formation tracking of the 4 followers, the blue spots represent each follower robot, the black spot represent the trajectory of centroid of...P. Jiang, “Lyapunov design of global state and output trackers for nonholonomic control systems,” Int. J. of Control, pp. 744–761, 2000. [97] Y. P
19. Adaptive nonlinear control for a research reactor
International Nuclear Information System (INIS)
Benitez R, J.S.
1994-01-01
Linearization by feedback of states is based on the idea of transform the nonlinear dynamic equation of a system in a linear form. This linear behavior can be achieve well in a complete way (input state) or in partial way (input output). This can be applied to systems of single or multiple inputs, and can be used to solve problems of stabilization and tracking of references trajectories. Comparing this method with conventional ones, linearization by feedback of states is exact in certain region of the space of state, instead of linear approximations of the equations in a certain point of the operation. In the presence of parametric uncertainties in the model of the system, the introduction of adaptive schemes provide a type toughness to the control system by nonlinear feedback, which gives as result the eventual cancellation of the nonlinear terms in the dynamic relationship between the output and the input of the auxiliary control. In the same way, it has been presented the design of a nonlinearizing control for the non lineal model of a TRIGA Mark III type reactor, with the aim of tracking a predetermined power profile. The asymptotic tracking of such profile is, at the present moment, in the stage of verification by computerized simulation the relative easiness in the design of auxiliary variable of control, as well as the decoupling action of the output variable, make very attractive the utilization of the method herein presented. (Author)
20. Cooperative learning neural network output feedback control of uncertain nonlinear multi-agent systems under directed topologies
Science.gov (United States)
Wang, W.; Wang, D.; Peng, Z. H.
2017-09-01
Without assuming that the communication topologies among the neural network (NN) weights are to be undirected and the states of each agent are measurable, the cooperative learning NN output feedback control is addressed for uncertain nonlinear multi-agent systems with identical structures in strict-feedback form. By establishing directed communication topologies among NN weights to share their learned knowledge, NNs with cooperative learning laws are employed to identify the uncertainties. By designing NN-based κ-filter observers to estimate the unmeasurable states, a new cooperative learning output feedback control scheme is proposed to guarantee that the system outputs can track nonidentical reference signals with bounded tracking errors. A simulation example is given to demonstrate the effectiveness of the theoretical results.
1. Policy Iteration for $H_\\infty$ Optimal Control of Polynomial Nonlinear Systems via Sum of Squares Programming.
Science.gov (United States)
Zhu, Yuanheng; Zhao, Dongbin; Yang, Xiong; Zhang, Qichao
2018-02-01
Sum of squares (SOS) polynomials have provided a computationally tractable way to deal with inequality constraints appearing in many control problems. It can also act as an approximator in the framework of adaptive dynamic programming. In this paper, an approximate solution to the optimal control of polynomial nonlinear systems is proposed. Under a given attenuation coefficient, the Hamilton-Jacobi-Isaacs equation is relaxed to an optimization problem with a set of inequalities. After applying the policy iteration technique and constraining inequalities to SOS, the optimization problem is divided into a sequence of feasible semidefinite programming problems. With the converged solution, the attenuation coefficient is further minimized to a lower value. After iterations, approximate solutions to the smallest -gain and the associated optimal controller are obtained. Four examples are employed to verify the effectiveness of the proposed algorithm.
2. Robust Adaptive Backstepping Control Design for a Nonlinear Hydraulic-Mechanical System
DEFF Research Database (Denmark)
Choux, Martin; Karimi, Hamid Reza; Hovland, Geir
2009-01-01
converge to zero despite the uncertainties in the system according to the Barbalat lemma. The resulting controllers are able to take into account the interval uncertainties in Coulomb friction parameters and in the internal leakage parameters in the cylinders. Two adaptation laws are obtained by using...
3. Control of nonlinear systems using periodic parametric perturbations with application to a reversed field pinch
International Nuclear Information System (INIS)
Mirus, K.A.
1998-06-01
In this thesis, the possibility of controlling low- and high-dimensional chaotic systems by periodically driving an accessible system parameter is examined. This method has been carried out on several numerical systems and the MST Reversed Field Pinch. The numerical systems investigated include the logistic equation, the Lorenz equations, the Roessler equations, a coupled lattice of logistic equations, a coupled lattice of Lorenz equations, the Yoshida equations, which model tearing mode fluctuations in a plasma, and a neural net model for magnetic fluctuations on MST. This method was tested on the MST by sinusoidally driving a magnetic flux through the toroidal gap of the device. Numerically, periodic drives were found to be most effective at producing limit cycle behavior or significantly reducing the dimension of the system when the perturbation frequency was near natural frequencies of unstable periodic orbits embedded in the attractor of the unperturbed system. Several different unstable periodic orbits have been stabilized in this way for the low-dimensional numerical systems, sometimes with perturbation amplitudes that were less than 5% of the nominal value of the parameter being perturbed. In high-dimensional systems, limit cycle behavior and significant decreases in the system dimension were also achieved using perturbations with frequencies near the natural unstable periodic orbit frequencies. Results for the MST were not this encouraging, most likely because of an insufficient drive amplitude, the extremely high dimension of the plasma behavior, large amounts of noise, and a lack of stationarity in the transient plasma pulses
4. Control of nonlinear systems using periodic parametric perturbations with application to a reversed field pinch
Energy Technology Data Exchange (ETDEWEB)
Mirus, Kevin A. [Univ. of Wisconsin, Madison, WI (United States)
1998-01-01
In this thesis, the possibility of controlling low- and high-dimensional chaotic systems by periodically driving an accessible system parameter is examined. This method has been carried out on several numerical systems and the MST Reversed Field Pinch. The numerical systems investigated include the logistic equation, the Lorenz equations, the Roessler equations, a coupled lattice of logistic equations, a coupled lattice of Lorenz equations, the Yoshida equations, which model tearing mode fluctuations in a plasma, and a neural net model for magnetic fluctuations on MST. This method was tested on the MST by sinusoidally driving a magnetic flux through the toroidal gap of the device. Numerically, periodic drives were found to be most effective at producing limit cycle behavior or significantly reducing the dimension of the system when the perturbation frequency was near natural frequencies of unstable periodic orbits embedded in the attractor of the unperturbed system. Several different unstable periodic orbits have been stabilized in this way for the low-dimensional numerical systems, sometimes with perturbation amplitudes that were less than 5% of the nominal value of the parameter being perturbed. In high-dimensional systems, limit cycle behavior and significant decreases in the system dimension were also achieved using perturbations with frequencies near the natural unstable periodic orbit frequencies. Results for the MST were not this encouraging, most likely because of an insufficient drive amplitude, the extremely high dimension of the plasma behavior, large amounts of noise, and a lack of stationarity in the transient plasma pulses.
5. Control of nonlinear systems using periodic parametric perturbations with application to a reversed field pinch
Science.gov (United States)
Mirus, Kevin Andrew
In this thesis, the possibility of controlling low- and high-dimensional chaotic systems by periodically driving an accessible system parameter is examined. This method has been carried out on several numerical systems and the MST Reversed Field Pinch. The numerical systems investigated include the logistic equation, the Lorenz equations, the Rossler equations, a coupled lattice of logistic equations, a coupled lattice of Lorenz equations, the Yoshida equations, which model tearing mode fluctuations in a plasma, and a neural net model for magnetic fluctuations on MST. This method was tested on the MST by sinusoidally driving a magnetic flux through the toroidal gap of the device. Numerically, periodic drives were found to be most effective at producing limit cycle behavior or significantly reducing the dimension of the system when the perturbation frequency was near natural frequencies of unstable periodic orbits embedded in the attractor of the unperturbed system. Several different unstable periodic orbits have been stabilized in this way for the low-dimensional numerical systems, sometimes with perturbation amplitudes that were less than 5% of the nominal value of the parameter being perturbed. In high- dimensional systems, limit cycle behavior and significant decreases in the system dimension were also achieved using perturbations with frequencies near the natural unstable periodic orbit frequencies. Results for the MST were not this encouraging, most likely because of an insufficient drive amplitude, the extremely high dimension of the plasma behavior, large amounts of noise, and a lack of stationarity in the transient plasma pulses.
6. Efficient start–up energy management via nonlinear control for eco–traction systems
International Nuclear Information System (INIS)
Becherif, M.; Ramadan, H.S.; Ayad, M.Y.; Hissel, D.; Desideri, U.; Antonelli, M.
2017-01-01
Highlights: • Renewable HPS for the train start-up within feeding durations. • Dynamic modelling of the modern HPS applied to traction systems. • Port-Controlled Hamiltonian (PCH) design for supercapacitors’ charge/discharge operation. • Experimental validation and applicability of HPSs for energy management in eco-tractions. - Abstract: Electrochemical capacitors, called supercapacitors (SCs) or ultracapacitors, are devices conveniently used for embedded electrical energy management owing to their huge capacitance, low internal resistance and flexible control through power electronic conversion. This paper proposes a main power supply of hybrid Wind Generator (WG)–SC within the train station for feeding the traction onboard SC through specified limited feeding transit durations. Onboard SCs provide the train with the requested start–up self–energy. The hybrid WG–SCs system is an environmental–friendly source that enables the independency on national grid and guarantees an efficient bidirectional power transfer for energy management with enhanced dynamic performance. Therefore, the dynamic modelling and the experimental analysis of the modern hybrid WG–SCs used for managing the charge/discharge operation of SCs at Unity Power Factor (UPF) mode are presented. For this purpose, the Port–Controlled Hamiltonian (PCH) methodology is deduced and explicitly presented. Simulation results, via MATLAB™, reveal that the proposed PCH control methodology can be successfully implemented to ensure acceptable system dynamic behavior. Numerical results are validated with experimental measurements to investigate the significance of the PCH approach for the energy management operation in eco-tractions.
7. Pulsed Nonlinear Automatic Control System for Guidance of a Caterpillar Tractor Unit in Vineyards
Directory of Open Access Journals (Sweden)
Sit M.L.
2018-04-01
Full Text Available The automatic guidance systems of tractors for soil cultivation in vineyards have attracted the attention of researchers since the second half of the twentieth century. The purpose of this paper is to investigate the driving quality of an automatic guidance system (AGS for a caterpillar tractor unit (CTU consisting of a crawler tractor and a vineyard plow and having the orientation system by grapes stamps. Compared with the known works (in which GPS, LIDAR, and video cameras are used for orientation, the proposed system is the least expensive. For this, the existence of stability of the AGS as a whole in the range of operating speeds of the unit was proved. The dynamic model of the vineyard plow was verified on a three-point hitching system of the tractor, field tests of the AGS were carried out, which confirmed the results of theoretical studies, and suggested directions for further research. The shape and parameters of the modulation characteristic (MC of the pulse-width modulator (PWM of the AGS control system, the rational values of the hydraulic drive speeds of the sequential control mechanism of the clutch of the turn and the crawler tractor belt brake, were established, depending on the slope angle and the speed of the unit, ensuring agrotechnical requirements for driving. New solutions, in comparison with the known ones, are the ways of forming the MC of PWM using a new design probe and the associated driver MC of PWM.
8. High-performance sensorless nonlinear power control of a flywheel energy storage system
International Nuclear Information System (INIS)
Amodeo, S.J.; Chiacchiarini, H.G.; Solsona, J.A.; Busada, C.A.
2009-01-01
The flywheel energy storage systems (FESS) can be used to store and release energy in high power pulsed systems. Based on the use of a homopolar synchronous machine in a FESS, a high performance model-based power flow control law is developed using the feedback linearization methodology. This law is based on the voltage space vector reference frame machine model. To reduce the magnetic losses, a pulse amplitude modulation driver for the armature is more adequate. The restrictions in amplitude and phase imposed by the driver are also included. A full order Luenberger observer for the torque angle and rotor speed is developed to implement a sensorless control strategy. Simulation results are presented to illustrate the performance.
9. Adaptive control for a class of nonlinear complex dynamical systems with uncertain complex parameters and perturbations.
Directory of Open Access Journals (Sweden)
Jian Liu
Full Text Available In this paper, adaptive control is extended from real space to complex space, resulting in a new control scheme for a class of n-dimensional time-dependent strict-feedback complex-variable chaotic (hyperchaotic systems (CVCSs in the presence of uncertain complex parameters and perturbations, which has not been previously reported in the literature. In detail, we have developed a unified framework for designing the adaptive complex scalar controller to ensure this type of CVCSs asymptotically stable and for selecting complex update laws to estimate unknown complex parameters. In particular, combining Lyapunov functions dependent on complex-valued vectors and back-stepping technique, sufficient criteria on stabilization of CVCSs are derived in the sense of Wirtinger calculus in complex space. Finally, numerical simulation is presented to validate our theoretical results.
10. Adaptive control for a class of nonlinear complex dynamical systems with uncertain complex parameters and perturbations.
Science.gov (United States)
Liu, Jian; Liu, Kexin; Liu, Shutang
2017-01-01
In this paper, adaptive control is extended from real space to complex space, resulting in a new control scheme for a class of n-dimensional time-dependent strict-feedback complex-variable chaotic (hyperchaotic) systems (CVCSs) in the presence of uncertain complex parameters and perturbations, which has not been previously reported in the literature. In detail, we have developed a unified framework for designing the adaptive complex scalar controller to ensure this type of CVCSs asymptotically stable and for selecting complex update laws to estimate unknown complex parameters. In particular, combining Lyapunov functions dependent on complex-valued vectors and back-stepping technique, sufficient criteria on stabilization of CVCSs are derived in the sense of Wirtinger calculus in complex space. Finally, numerical simulation is presented to validate our theoretical results.
11. Non-linear model reduction and control of molten carbonate fuel cell systems with internal reforming
Energy Technology Data Exchange (ETDEWEB)
Sheng, Min
2007-10-12
Currently, the process design of fuel cells and the development of control strategies is mainly based on heuristic methods. Fuel cell models are often too complex for control purposes, or they are developed for a specific type of fuel cell and valid only in a small range of operation conditions. The application of fuel cell models to controller design is still limited. Furthermore, suitable and simple-to-implement design strategies for fuel cell control remain an open area. There is thus a motivation for simplifying dynamic models for process control applications and for designing suitable control strategies for fuel cells. This is the main objective of this work. As an application example, the 250 kW industrial molten carbonate fuel cell (MCFC) system HotModule by MTU CFC Solutions, Germany is considered. A detailed dynamic two-dimensional spatially distributed cross-flow model of a MCFC from literature is taken as a starting point for the investigation. In Chapter 2, two simplified model versions are derived by incorporating additional physical assumptions. One of the simplified models is extended to a three-dimensional stack model to deal with physical and chemical phenomena in the stack. Simulations of the stack model are performed in Chapter 3 in order to calculate the mass and temperature distributions in the direction perpendicular to the electrode area. The other simplified model forms the basis for a low order reduced model that is derived in Chapter 4. The reduced-order model is constructed by application of the Karhunen-Loeve Galerkin method. The spatial temperature, concentration and potential profiles are approximated by a set of orthogonal time independent spatial basis functions. Problem specific basis functions are generated numerically from simulation data of the detailed reference model. The advantage of this approach is that a small number of basis functions suffices in order to approximate the solution of the detailed model very well. The
12. Nonlinear Control of Back-to-Back VSC-HVDC System via Command-Filter Backstepping
Directory of Open Access Journals (Sweden)
Jie Huang
2017-01-01
Full Text Available This paper proposed a command-filtered backstepping controller to improve the dynamic performance of back-to-back voltage-source-converter high voltage direct current (BTB VSC-HVDC. First, the principle and model of BTB VSC-HVDC in abc and d-q frame are described. Then, backstepping method is applied to design a controller to maintain the voltage balance and realize coordinated control of active and reactive power. Meanwhile, command filter is introduced to deal with the problem of input saturation and explosion of complexity in conventional backstepping, and a filter compensation signal is designed to diminish the adverse effects caused by the command filter. Next, the stability and convergence of the whole system are proved via the Lyapunov theorem of asymptotic stability. Finally, simulation results are given to demonstrate that proposed controller has a better dynamic performance and stronger robustness compared to the traditional PID algorithm, which also proves the effectiveness and possibility of the designed controller.
13. Measurement and control of optical nonlinearities of importance to glass laser fusion systems
International Nuclear Information System (INIS)
Kurnit, N.A.; Shimada, T.; Sorem, M.S.; Taylor, A.J.; Rodriguez, G.; Clement, T.S.; James, D.F.V.; Milonni, P.W.
1996-01-01
Results of a number of studies carried out at Los Alamos, both experimental and theoretical, of nonlinear optical phenomena important to the design of the National Ignition Facility are summarized. These include measurements of nonlinear index coefficients, Raman scattering in atmospheric oxygen, and theoretical studies of harmonic conversion. The measurements were made by two different techniques in order to increase confidence in the results. One method was an application of a recently-developed technique for measuring the amplitude and phase of an ultrashort pulse by Frequency-Resolved Optical Gating (FROG). The other utilized a modified version of the Z-scan technique that measures beam distortion introduced by scanning a sample through the focus of a beam. The measurements by both techniques for fused silica were consistent with the lower range of previously measured values, indicating that it should not be necessary to further expand the beam size in the NIF to stay below the self-focusing threshold
14. A single network adaptive critic (SNAC) architecture for optimal control synthesis for a class of nonlinear systems.
Science.gov (United States)
2006-12-01
Even though dynamic programming offers an optimal control solution in a state feedback form, the method is overwhelmed by computational and storage requirements. Approximate dynamic programming implemented with an Adaptive Critic (AC) neural network structure has evolved as a powerful alternative technique that obviates the need for excessive computations and storage requirements in solving optimal control problems. In this paper, an improvement to the AC architecture, called the "Single Network Adaptive Critic (SNAC)" is presented. This approach is applicable to a wide class of nonlinear systems where the optimal control (stationary) equation can be explicitly expressed in terms of the state and costate variables. The selection of this terminology is guided by the fact that it eliminates the use of one neural network (namely the action network) that is part of a typical dual network AC setup. As a consequence, the SNAC architecture offers three potential advantages: a simpler architecture, lesser computational load and elimination of the approximation error associated with the eliminated network. In order to demonstrate these benefits and the control synthesis technique using SNAC, two problems have been solved with the AC and SNAC approaches and their computational performances are compared. One of these problems is a real-life Micro-Electro-Mechanical-system (MEMS) problem, which demonstrates that the SNAC technique is applicable to complex engineering systems.
15. Output-Feedback Nonlinear Adaptive Control Strategy of the Single-Phase Grid-Connected Photovoltaic System
Directory of Open Access Journals (Sweden)
Abdelmajid Abouloifa
2018-01-01
Full Text Available This paper addresses the problem of controlling the single-phase grid connected to the photovoltaic system through a full bridge inverter with LCL-filter. The control aims are threefold: (i imposing the voltage in the output of PV panel to track a reference provided by the MPPT block; (ii regulating the DC-link voltage to guarantee the power exchange between the source and AC grid; (iii ensuring a satisfactory power factor correction (PFC. The problem is dealt with using a cascade nonlinear adaptive controller that is developed making use of sliding-mode technique and observers in order to estimate the state variables and grid parameters, by measuring only the grid current, PV voltage, and the DC bus voltage. The control problem addressed by this work involves several difficulties, including the uncertainty of some parameters of the system and the numerous state variables are inaccessible to measurements. The results are confirmed by simulation under MATLAB∖Simulink∖SimPowerSystems, which show that the proposed regulator is robust with respect to climate changes.
16. OPTIMAL CONTROL OF A NONLINEAR COUPLED ELECTROMAGNETIC INDUCTION HEATING SYSTEM WITH POINTWISE STATE CONSTRAINTS
Directory of Open Access Journals (Sweden)
Irwin Yousept
2010-07-01
Full Text Available An optimal control problem arising in the context of 3D electromagnetic induction heating is investigated. The state equation is given by a quasilinear stationary heat equation coupled with a semilinear time harmonic eddy current equation. The temperature-dependent electrical conductivity and the presence of pointwise inequality state-constraints represent the main challenge of the paper. In the first part of the paper, the existence and regularity of the state are addressed. The second part of the paper deals with the analysis of the corresponding linearized equation. Some suffcient conditions are presented which guarantee thesolvability of the linearized system. The final part of the paper is concerned with the optimal control. The aim of the optimization is to find the optimal voltage such that a desired temperature can be achieved optimally. The corresponding first-order necessary optimality condition is presented.
17. A Modified LQG Algorithm (MLQG for Robust Control of Nonlinear Multivariable Systems
Directory of Open Access Journals (Sweden)
Jens G. Balchen
1993-07-01
Full Text Available The original LQG algorithm is often characterized for its lack of robustness. This is because in the design of the estimator (Kalman filter the process disturbance is assumed to be white noise. If the estimator is to give good estimates, the Kalman gain is increased which means that the estimator fails to become robust. A solution to this problem is to replace the proportional Kalman gain matrix by a dynamic PI algorithm and the proportional LQ feedback gain matrix by a PI algorithm. A tuning method is developed which facilitates the tuning of a modified LQG control system (MLQG by only two tuning parameters.
18. APPLICATION OF NONLINEAR PID CONTROLLER IN SUPERCONDUCTING MAGNETIC ENERGY STORAGE
OpenAIRE
PENG, Xiaotao; CHENG, Shijie
2011-01-01
As a new control strategy, Nonlinear PID(NLPID) controller has been introduced in the power system successfully. The controller is free of planting model foundation in the design procedure and realized simply. In this paper, a nonlinear PID controller used for superconducting magnetic energy storage (SMES) unit connected to a power system is proposed. Purpose of designing such controller is to improve the stability of the power system in a relatively wide operation range. The design procedure...
19. Explicit Nonlinear Model Predictive Control Theory and Applications
CERN Document Server
Grancharova, Alexandra
2012-01-01
Nonlinear Model Predictive Control (NMPC) has become the accepted methodology to solve complex control problems related to process industries. The main motivation behind explicit NMPC is that an explicit state feedback law avoids the need for executing a numerical optimization algorithm in real time. The benefits of an explicit solution, in addition to the efficient on-line computations, include also verifiability of the implementation and the possibility to design embedded control systems with low software and hardware complexity. This book considers the multi-parametric Nonlinear Programming (mp-NLP) approaches to explicit approximate NMPC of constrained nonlinear systems, developed by the authors, as well as their applications to various NMPC problem formulations and several case studies. The following types of nonlinear systems are considered, resulting in different NMPC problem formulations: Ø Nonlinear systems described by first-principles models and nonlinear systems described by black-box models; �...
20. Tradeoffs between quality-of-control and quality-of-service in large-scale nonlinear networked control systems
NARCIS (Netherlands)
Borgers, D. P.; Geiselhart, R.; Heemels, W. P. M. H.
2017-01-01
In this paper we study input-to-state stability (ISS) of large-scale networked control systems (NCSs) in which sensors, controllers and actuators are connected via multiple (local) communication networks which operate asynchronously and independently of each other. We model the large-scale NCS as an
1. Stabilization of nonlinear systems using sampled-data output-feedback fuzzy controller based on polynomial-fuzzy-model-based control approach.
Science.gov (United States)
Lam, H K
2012-02-01
This paper investigates the stability of sampled-data output-feedback (SDOF) polynomial-fuzzy-model-based control systems. Representing the nonlinear plant using a polynomial fuzzy model, an SDOF fuzzy controller is proposed to perform the control process using the system output information. As only the system output is available for feedback compensation, it is more challenging for the controller design and system analysis compared to the full-state-feedback case. Furthermore, because of the sampling activity, the control signal is kept constant by the zero-order hold during the sampling period, which complicates the system dynamics and makes the stability analysis more difficult. In this paper, two cases of SDOF fuzzy controllers, which either share the same number of fuzzy rules or not, are considered. The system stability is investigated based on the Lyapunov stability theory using the sum-of-squares (SOS) approach. SOS-based stability conditions are obtained to guarantee the system stability and synthesize the SDOF fuzzy controller. Simulation examples are given to demonstrate the merits of the proposed SDOF fuzzy control approach.
2. Robust adaptive controller design for a class of uncertain nonlinear systems using online T-S fuzzy-neural modeling approach.
Science.gov (United States)
Chien, Yi-Hsing; Wang, Wei-Yen; Leu, Yih-Guang; Lee, Tsu-Tian
2011-04-01
This paper proposes a novel method of online modeling and control via the Takagi-Sugeno (T-S) fuzzy-neural model for a class of uncertain nonlinear systems with some kinds of outputs. Although studies about adaptive T-S fuzzy-neural controllers have been made on some nonaffine nonlinear systems, little is known about the more complicated uncertain nonlinear systems. Because the nonlinear functions of the systems are uncertain, traditional T-S fuzzy control methods can model and control them only with great difficulty, if at all. Instead of modeling these uncertain functions directly, we propose that a T-S fuzzy-neural model approximates a so-called virtual linearized system (VLS) of the system, which includes modeling errors and external disturbances. We also propose an online identification algorithm for the VLS and put significant emphasis on robust tracking controller design using an adaptive scheme for the uncertain systems. Moreover, the stability of the closed-loop systems is proven by using strictly positive real Lyapunov theory. The proposed overall scheme guarantees that the outputs of the closed-loop systems asymptotically track the desired output trajectories. To illustrate the effectiveness and applicability of the proposed method, simulation results are given in this paper.
3. Nonlinear Superheat Control of a Refrigeration Plant using Backstepping
DEFF Research Database (Denmark)
Rasmussen, Henrik
2008-01-01
This paper proposes a novel method for superheat and capacity control of refrigeration systems. The main idea is to control the superheat by the compressor speed and capacity by the refrigerant flow. A new low order nonlinear model of the evaporator is developed and used in a backstepping design...... of a nonlinear controller. The proposed method is validated by experimental results....
4. Nonlinear dynamical system approaches towards neural prosthesis
International Nuclear Information System (INIS)
Torikai, Hiroyuki; Hashimoto, Sho
2011-01-01
An asynchronous discrete-state spiking neurons is a wired system of shift registers that can mimic nonlinear dynamics of an ODE-based neuron model. The control parameter of the neuron is the wiring pattern among the registers and thus they are suitable for on-chip learning. In this paper an asynchronous discrete-state spiking neuron is introduced and its typical nonlinear phenomena are demonstrated. Also, a learning algorithm for a set of neurons is presented and it is demonstrated that the algorithm enables the set of neurons to reconstruct nonlinear dynamics of another set of neurons with unknown parameter values. The learning function is validated by FPGA experiments.
5. Nonlinear control techniques of a controllable rectifier/inverter-motor drive system with a small dc-link capacitor
International Nuclear Information System (INIS)
Liutanakul, Pisit; Pierfederici, Serge; Meibody-Tabar, Farid
2008-01-01
The necessity of the converters compactness in many applications imposes the reduction of their different components size when it is possible. In this paper, a control method allowing the use of a small size dc-link capacitor for the cascade of voltage controlled-rectifier/inverter-motor drive system is proposed. This is achieved by adding the power balance equation in the system's model and the application of an exact input/output feedback linearization technique in a way that the rectifier controller compensates any sudden change in the inverter load, which is here an induction motor. Since the exact input/output feedback linearization technique is sensitive to the uncertainties over system parameters, a robust control strategy based on sliding mode controller is proposed. By this approach, the dc-link voltage becomes almost insensitive to the load variations. As a result, the level of the dc-link voltage could be stabilized with a small size dc-link capacitor. Without any considerations of the RMS current stress on this dc-link capacitor, a calculation method of a minimum value of this capacitor based on its storage energy is proposed. All the investigations are shown by computer simulations and the performance of controlled system is verified by experimentation results
6. Reinforcement learning design-based adaptive tracking control with less learning parameters for nonlinear discrete-time MIMO systems.
Science.gov (United States)
Liu, Yan-Jun; Tang, Li; Tong, Shaocheng; Chen, C L Philip; Li, Dong-Juan
2015-01-01
Based on the neural network (NN) approximator, an online reinforcement learning algorithm is proposed for a class of affine multiple input and multiple output (MIMO) nonlinear discrete-time systems with unknown functions and disturbances. In the design procedure, two networks are provided where one is an action network to generate an optimal control signal and the other is a critic network to approximate the cost function. An optimal control signal and adaptation laws can be generated based on two NNs. In the previous approaches, the weights of critic and action networks are updated based on the gradient descent rule and the estimations of optimal weight vectors are directly adjusted in the design. Consequently, compared with the existing results, the main contributions of this paper are: 1) only two parameters are needed to be adjusted, and thus the number of the adaptation laws is smaller than the previous results and 2) the updating parameters do not depend on the number of the subsystems for MIMO systems and the tuning rules are replaced by adjusting the norms on optimal weight vectors in both action and critic networks. It is proven that the tracking errors, the adaptation laws, and the control inputs are uniformly bounded using Lyapunov analysis method. The simulation examples are employed to illustrate the effectiveness of the proposed algorithm.
7. Nonlinear Control Structure of Grid Connected Modular Multilevel Converters
DEFF Research Database (Denmark)
2017-01-01
in the prediction step in order to preserve the stochastic characteristics of a nonlinear system. In order to design adaptive robust control strategy and nonlinear observer, mathematical model of MMC using rotating d-q theory has been used. Digital time-domain simulation studies are carried out in the Matlab......This paper implements nonlinear control structure based on Adaptive Fuzzy Sliding Mode (AFSM) Current Control and Unscented Kalman Filter (UKF) to estimate the capacitor voltages from the measurement of arm currents of Modular Multilevel Converter (MMC). UKF use nonlinear unscented transforms....../Simulink environment to verify the performance of the overall proposed control structure during different case studies....
8. Nonlinear closed-loop control theory
International Nuclear Information System (INIS)
Perez, R.B.; Otaduy, P.J.; Abdalla, M.
1992-01-01
Traditionally, the control of nuclear power plants has been implemented by the use of proportional-integral (PI) control systems. PI controllers are both simple and, within their calibration range, highly reliable. However, PIs provide little performance information that could be used to diagnose out-of-range events or the nature of unanticipated transients that may occur in the plant. To go beyond the PI controller, the new control algorithms must deal with the physical system nonlinearities and with the reality of uncertain dynamics terms in its mathematical model. The tool to develop a new kind of control algorithm is provided by Optimal Control Theory. In this theory, a norm is minimized which incorporates the constraint that the model equations should be satisfied at all times by means of the Lagrange multipliers. Optimal control algorithms consist of two sets of coupled equations: (1) the model equations, integrated forward in time; and (2) the equations for the Lagrange multipliers (adjoints), integrated backwards in time. There are two challenges: dealing with large sets of coupled nonlinear equations and with a two-point boundary value problem that must be solved iteratively. In this paper, the rigorous conversion of the two-point boundary value problem into an initial value problem is presented. In addition, the incorporation into the control algorithm of ''real world'' constraints such as sensors and actuators, dynamic response functions and time lags introduced by the digitalization of analog signals is presented. (Author)
9. Internal Decoupling in Nonlinear Process Control
Directory of Open Access Journals (Sweden)
Jens G. Balchen
1988-07-01
Full Text Available A simple method has been investigated for the total or partial removal of the effect of non-linear process phenomena in multi-variable feedback control systems. The method is based upon computing the control variables which will drive the process at desired rates. It is shown that the effect of model errors in the linearization of the process can be partly removed through the use of large feedback gains. In practice there will be limits on how large gains can he used. The sensitivity to parameter errors is less pronounced and the transient behaviour is superior to that of ordinary PI controllers.
10. Nonlinear superheat and capacity control of a refrigeration plant
DEFF Research Database (Denmark)
Rasmussen, Henrik; Larsen, Lars F. S.
2009-01-01
This paper proposes a novel method for superheat and capacity control of refrigeration systems. A new low order nonlinear model of the evaporator is developed and used in a backstepping design of a nonlinear controller. The stability of the proposed method is validated theoretically by Lyapunov...
11. Nonlinear transport of dynamic system phase space
International Nuclear Information System (INIS)
Xie Xi; Xia Jiawen
1993-01-01
The inverse transform of any order solution of the differential equation of general nonlinear dynamic systems is derived, realizing theoretically the nonlinear transport for the phase space of nonlinear dynamic systems. The result is applicable to general nonlinear dynamic systems, with the transport of accelerator beam phase space as a typical example
12. Novel probabilistic and distributed algorithms for guidance, control, and nonlinear estimation of large-scale multi-agent systems
Science.gov (United States)
global exponential convergence of tracking errors with finite-gain Lp stability in the presence of modeling uncertainties and disturbances, and reduces the resultant disturbance torque. Further, this control law permits the use of any attitude representation and its integral control formulation eliminates any constant disturbance. Under small uncertainties, the best strategy for stabilizing the combined system is to track a fuel-optimal reference trajectory using this nonlinear control law, because it consumes the least amount of fuel. In the presence of large uncertainties, the most effective strategy is to track the derivative plus proportional-derivative based reference trajectory, because it reduces the resultant disturbance torque. The effectiveness of the proposed attitude control law is demonstrated by using results of numerical simulation based on an Asteroid Redirect Mission concept. The new algorithms proposed in this dissertation will facilitate the development of versatile autonomous multi-agent systems that are capable of performing a variety of complex tasks in a robust and scalable manner.
13. Robust flight control using incremental nonlinear dynamic inversion and angular acceleration prediction
NARCIS (Netherlands)
Sieberling, S.; Chu, Q.P.; Mulder, J.A.
2010-01-01
This paper presents a flight control strategy based on nonlinear dynamic inversion. The approach presented, called incremental nonlinear dynamic inversion, uses properties of general mechanical systems and nonlinear dynamic inversion by feeding back angular accelerations. Theoretically, feedback of
14. Neuromechanical tuning of nonlinear postural control dynamics
Science.gov (United States)
Ting, Lena H.; van Antwerp, Keith W.; Scrivens, Jevin E.; McKay, J. Lucas; Welch, Torrence D. J.; Bingham, Jeffrey T.; DeWeerth, Stephen P.
2009-06-01
Postural control may be an ideal physiological motor task for elucidating general questions about the organization, diversity, flexibility, and variability of biological motor behaviors using nonlinear dynamical analysis techniques. Rather than presenting "problems" to the nervous system, the redundancy of biological systems and variability in their behaviors may actually be exploited to allow for the flexible achievement of multiple and concurrent task-level goals associated with movement. Such variability may reflect the constant "tuning" of neuromechanical elements and their interactions for movement control. The problem faced by researchers is that there is no one-to-one mapping between the task goal and the coordination of the underlying elements. We review recent and ongoing research in postural control with the goal of identifying common mechanisms underlying variability in postural control, coordination of multiple postural strategies, and transitions between them. We present a delayed-feedback model used to characterize the variability observed in muscle coordination patterns during postural responses to perturbation. We emphasize the significance of delays in physiological postural systems, requiring the modulation and coordination of both the instantaneous, "passive" response to perturbations as well as the delayed, "active" responses to perturbations. The challenge for future research lies in understanding the mechanisms and principles underlying neuromechanical tuning of and transitions between the diversity of postural behaviors. Here we describe some of our recent and ongoing studies aimed at understanding variability in postural control using physical robotic systems, human experiments, dimensional analysis, and computational models that could be enhanced from a nonlinear dynamics approach.
15. Nonlinear adaptive inverse control via the unified model neural network
Science.gov (United States)
Jeng, Jin-Tsong; Lee, Tsu-Tian
1999-03-01
In this paper, we propose a new nonlinear adaptive inverse control via a unified model neural network. In order to overcome nonsystematic design and long training time in nonlinear adaptive inverse control, we propose the approximate transformable technique to obtain a Chebyshev Polynomials Based Unified Model (CPBUM) neural network for the feedforward/recurrent neural networks. It turns out that the proposed method can use less training time to get an inverse model. Finally, we apply this proposed method to control magnetic bearing system. The experimental results show that the proposed nonlinear adaptive inverse control architecture provides a greater flexibility and better performance in controlling magnetic bearing systems.
16. A Conic Sector-Based Methodology for Nonlinear Control Design
OpenAIRE
Doyle, Francis J., III; Morari, Manfred
1990-01-01
A design method is presented for the analysis and synthesis of robust nonlinear controllers for chemical engineering systems. The method rigorously treats the effect of unmeasured disturbances and unmodeled dynamics on the stability and performance properties of a nonlinear system. The results utilise new extensions of structured singular value theory for analysis and recent synthesis results for approximate linearisation.
17. Reinforcement-learning-based output-feedback control of nonstrict nonlinear discrete-time systems with application to engine emission control.
Science.gov (United States)
Shih, Peter; Kaul, Brian C; Jagannathan, Sarangapani; Drallmeier, James A
2009-10-01
A novel reinforcement-learning-based output adaptive neural network (NN) controller, which is also referred to as the adaptive-critic NN controller, is developed to deliver the desired tracking performance for a class of nonlinear discrete-time systems expressed in nonstrict feedback form in the presence of bounded and unknown disturbances. The adaptive-critic NN controller consists of an observer, a critic, and two action NNs. The observer estimates the states and output, and the two action NNs provide virtual and actual control inputs to the nonlinear discrete-time system. The critic approximates a certain strategic utility function, and the action NNs minimize the strategic utility function and control inputs. All NN weights adapt online toward minimization of a performance index, utilizing the gradient-descent-based rule, in contrast with iteration-based adaptive-critic schemes. Lyapunov functions are used to show the stability of the closed-loop tracking error, weights, and observer estimates. Separation and certainty equivalence principles, persistency of excitation condition, and linearity in the unknown parameter assumption are not needed. Experimental results on a spark ignition (SI) engine operating lean at an equivalence ratio of 0.75 show a significant (25%) reduction in cyclic dispersion in heat release with control, while the average fuel input changes by less than 1% compared with the uncontrolled case. Consequently, oxides of nitrogen (NO(x)) drop by 30%, and unburned hydrocarbons drop by 16% with control. Overall, NO(x)'s are reduced by over 80% compared with stoichiometric levels.
18. Adaptive control of nonlinear system using online error minimum neural networks.
Science.gov (United States)
Jia, Chao; Li, Xiaoli; Wang, Kang; Ding, Dawei
2016-11-01
19. NON-LINEAR STATE SPACE MODEL AND CONTROL STRATEGY FOR PEM FUEL CELL SYSTEMS
Directory of Open Access Journals (Sweden)
RICHARD RIOS
2011-01-01
Full Text Available Este artículo presenta un modelo no lineal en el espacio de estado y un sistema de control lineal para una celda de combustible de Membrana de Intercambio Protónico. El modelo tiene como dinámicas la temperatura de la pila y el fl ujo de aire, y su principal rasgo es la reproducción del comportamiento de la razón de exceso de oxigeno. El sistema de control lineal es un regulador optimo cuadrático y un fi ltro de Kalman, cuyo objetivo de control es evitar el agotamiento de oxigeno y minimizar el consumo de combustible, a través del seguimiento de un perfi l optimo de potencia de carga. El observador es diseñado con el fi nde obtener una completa información de los estados.
20. Control mechanisms for a nonlinear model of international relations
Energy Technology Data Exchange (ETDEWEB)
Pentek, A.; Kadtke, J. [Univ. of California, San Diego, La Jolla, CA (United States). Inst. for Pure and Applied Physical Sciences; Lenhart, S. [Univ. of Tennessee, Knoxville, TN (United States). Mathematics Dept.; Protopopescu, V. [Oak Ridge National Lab., TN (United States). Computer Science and Mathematics Div.
1997-07-15
Some issues of control in complex dynamical systems are considered. The authors discuss two control mechanisms, namely: a short range, reactive control based on the chaos control idea and a long-term strategic control based on an optimal control algorithm. They apply these control ideas to simple examples in a discrete nonlinear model of a multi-nation arms race.
1. L2-gain and passivity techniques in nonlinear control
CERN Document Server
van der Schaft, Arjan
2017-01-01
This standard text gives a unified treatment of passivity and L2-gain theory for nonlinear state space systems, preceded by a compact treatment of classical passivity and small-gain theorems for nonlinear input-output maps. The synthesis between passivity and L2-gain theory is provided by the theory of dissipative systems. Specifically, the small-gain and passivity theorems and their implications for nonlinear stability and stabilization are discussed from this standpoint. The connection between L2-gain and passivity via scattering is detailed. Feedback equivalence to a passive system and resulting stabilization strategies are discussed. The passivity concepts are enriched by a generalised Hamiltonian formalism, emphasising the close relations with physical modeling and control by interconnection, and leading to novel control methodologies going beyond passivity. The potential of L2-gain techniques in nonlinear control, including a theory of all-pass factorizations of nonlinear systems, and of parametrization...
2. Nonlinear Model Predictive Control for Cooperative Control and Estimation
Science.gov (United States)
Ru, Pengkai
Recent advances in computational power have made it possible to do expensive online computations for control systems. It is becoming more realistic to perform computationally intensive optimization schemes online on systems that are not intrinsically stable and/or have very small time constants. Being one of the most important optimization based control approaches, model predictive control (MPC) has attracted a lot of interest from the research community due to its natural ability to incorporate constraints into its control formulation. Linear MPC has been well researched and its stability can be guaranteed in the majority of its application scenarios. However, one issue that still remains with linear MPC is that it completely ignores the system's inherent nonlinearities thus giving a sub-optimal solution. On the other hand, if achievable, nonlinear MPC, would naturally yield a globally optimal solution and take into account all the innate nonlinear characteristics. While an exact solution to a nonlinear MPC problem remains extremely computationally intensive, if not impossible, one might wonder if there is a middle ground between the two. We tried to strike a balance in this dissertation by employing a state representation technique, namely, the state dependent coefficient (SDC) representation. This new technique would render an improved performance in terms of optimality compared to linear MPC while still keeping the problem tractable. In fact, the computational power required is bounded only by a constant factor of the completely linearized MPC. The purpose of this research is to provide a theoretical framework for the design of a specific kind of nonlinear MPC controller and its extension into a general cooperative scheme. The controller is designed and implemented on quadcopter systems.
3. Nonlinear Response of Strong Nonlinear System Arisen in Polymer Cushion
Directory of Open Access Journals (Sweden)
Jun Wang
2013-01-01
Full Text Available A dynamic model is proposed for a polymer foam-based nonlinear cushioning system. An accurate analytical solution for the nonlinear free vibration of the system is derived by applying He's variational iteration method, and conditions for resonance are obtained, which should be avoided in the cushioning design.
4. Nonlinear dynamics in biological systems
CERN Document Server
Carballido-Landeira, Jorge
2016-01-01
This book presents recent research results relating to applications of nonlinear dynamics, focusing specifically on four topics of wide interest: heart dynamics, DNA/RNA, cell mobility, and proteins. The book derives from the First BCAM Workshop on Nonlinear Dynamics in Biological Systems, held in June 2014 at the Basque Center of Applied Mathematics (BCAM). At this international meeting, researchers from different but complementary backgrounds, including molecular dynamics, physical chemistry, bio-informatics and biophysics, presented their most recent results and discussed the future direction of their studies using theoretical, mathematical modeling and experimental approaches. Such was the level of interest stimulated that the decision was taken to produce this publication, with the organizers of the event acting as editors. All of the contributing authors are researchers working on diverse biological problems that can be approached using nonlinear dynamics. The book will appeal especially to applied math...
5. Nonlinear dynamics and control strategies: On a energy harvester vibrating system with a linear form to non-ideal motor torquet
Directory of Open Access Journals (Sweden)
de Pontes B. R.
2012-07-01
Full Text Available In this paper, we deal with the research of a vibrating model of an energy harvester device, including the nonlinearities in the model of the piezoelectric coupling and the non-ideal excitation. We show, using numerical simulations, in the analysis of the dynamic responses, that the harvested power is influenced by non-linear vibrations of the structure. Chaotic behavior was also observed, causing of the loss of energy throughout the simulation time. Using a perturbation technique, we find an approximate analytical solution for the non-ideal system. Then, we apply both two control techniques, to keep the considered system, into a stable condition. Both the State Dependent Ricatti Equation (SDRE control as the feedback control by changing the energy of the oscillator, were efficient in controlling of the considered non-ideal system.
6. Neural Networks for Non-linear Control
DEFF Research Database (Denmark)
Sørensen, O.
1994-01-01
This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process.......This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process....
7. MOEA based design of decentralized controllers for LFC of interconnected power systems with nonlinearities, AC-DC parallel tie-lines and SMES units
International Nuclear Information System (INIS)
Ganapathy, S.; Velusami, S.
2010-01-01
A new design of Multi-Objective Evolutionary Algorithm based decentralized controllers for load-frequency control of interconnected power systems with Governor Dead Band and Generation Rate Constraint nonlinearities, AC-DC parallel tie-lines and Superconducting Magnetic Energy Storage (SMES) units, is proposed in this paper. The HVDC link is used as system interconnection in parallel with AC tie-line to effectively damp the frequency oscillations of AC system while the SMES unit provides bulk energy storage and release, thereby achieving combined benefits. The proposed controller satisfies two main objectives, namely, minimum Integral Squared Error of the system output and maximum closed-loop stability of the system. Simulation studies are conducted on a two area interconnected power system with nonlinearities, AC-DC tie-lines and SMES units. Results indicate that the proposed controller improves the transient responses and guarantees the closed-loop stability of the overall system even in the presence of system nonlinearities and with parameter changes.
8. Frequency response functions for nonlinear convergent systems
NARCIS (Netherlands)
Pavlov, A.V.; Wouw, van de N.; Nijmeijer, H.
2007-01-01
Convergent systems constitute a practically important class of nonlinear systems that extends the class of asymptotically stable linear time-invariant systems. In this note, we extend frequency response functions defined for linear systems to nonlinear convergent systems. Such nonlinear frequency
9. Higher-order techniques for some problems of nonlinear control
Directory of Open Access Journals (Sweden)
Sarychev Andrey V.
2002-01-01
Full Text Available A natural first step when dealing with a nonlinear problem is an application of some version of linearization principle. This includes the well known linearization principles for controllability, observability and stability and also first-order optimality conditions such as Lagrange multipliers rule or Pontryagin's maximum principle. In many interesting and important problems of nonlinear control the linearization principle fails to provide a solution. In the present paper we provide some examples of how higher-order methods of differential geometric control theory can be used for the study nonlinear control systems in such cases. The presentation includes: nonlinear systems with impulsive and distribution-like inputs; second-order optimality conditions for bang–bang extremals of optimal control problems; methods of high-order averaging for studying stability and stabilization of time-variant control systems.
10. Data-Driven Zero-Sum Neuro-Optimal Control for a Class of Continuous-Time Unknown Nonlinear Systems With Disturbance Using ADP.
Science.gov (United States)
Wei, Qinglai; Song, Ruizhuo; Yan, Pengfei
2016-02-01
This paper is concerned with a new data-driven zero-sum neuro-optimal control problem for continuous-time unknown nonlinear systems with disturbance. According to the input-output data of the nonlinear system, an effective recurrent neural network is introduced to reconstruct the dynamics of the nonlinear system. Considering the system disturbance as a control input, a two-player zero-sum optimal control problem is established. Adaptive dynamic programming (ADP) is developed to obtain the optimal control under the worst case of the disturbance. Three single-layer neural networks, including one critic and two action networks, are employed to approximate the performance index function, the optimal control law, and the disturbance, respectively, for facilitating the implementation of the ADP method. Convergence properties of the ADP method are developed to show that the system state will converge to a finite neighborhood of the equilibrium. The weight matrices of the critic and the two action networks are also convergent to finite neighborhoods of their optimal ones. Finally, the simulation results will show the effectiveness of the developed data-driven ADP methods.
11. Success Stories in Control: Nonlinear Dynamic Inversion Control
Science.gov (United States)
Bosworth, John T.
2010-01-01
NASA plays an important role in advancing the state of the art in flight control systems. In the case of Nonlinear Dynamic Inversion (NDI) NASA supported initial implementation of the theory in an aircraft and demonstration in a space vehicle. Dr. Dale Enns of Honeywell Aerospace Advanced Technology performed this work in cooperation with NASA and under NASA contract. Honeywell and Lockheed Martin were subsequently contracted by AFRL to create "Design Guidelines for Multivariable Control Theory". This foundational work directly contributed to the advancement of the technology and the credibility of the control law as a design option. As a result Honeywell collaborated with Lockheed Martin to produce a Nonlinear Dynamic Inversion controller for the X-35 and subsequently Lockheed Martin did the same for the production Lockheed Martin F-35 vehicle. The theory behind NDI is to use a systematic generalized approach to controlling a vehicle. Using general aircraft nonlinear equations of motion and onboard aerodynamic, mass properties, and engine models specific to the vehicle, a relationship between control effectors and desired aircraft motion can be formulated. Using this formulation a control combination is used that provides a predictable response to commanded motion. Control loops around this formulation shape the response as desired and provide robustness to modeling errors. Once the control law is designed it can be used on a similar class of vehicle with only an update to the vehicle specific onboard models.
12. Augmented nonlinear differentiator design and application to nonlinear uncertain systems.
Science.gov (United States)
Shao, Xingling; Liu, Jun; Li, Jie; Cao, Huiliang; Shen, Chong; Zhang, Xiaoming
2017-03-01
13. An analytical fuzzy-based approach to ?-gain optimal control of input-affine nonlinear systems using Newton-type algorithm
Science.gov (United States)
Milic, Vladimir; Kasac, Josip; Novakovic, Branko
2015-10-01
This paper is concerned with ?-gain optimisation of input-affine nonlinear systems controlled by analytic fuzzy logic system. Unlike the conventional fuzzy-based strategies, the non-conventional analytic fuzzy control method does not require an explicit fuzzy rule base. As the first contribution of this paper, we prove, by using the Stone-Weierstrass theorem, that the proposed fuzzy system without rule base is universal approximator. The second contribution of this paper is an algorithm for solving a finite-horizon minimax problem for ?-gain optimisation. The proposed algorithm consists of recursive chain rule for first- and second-order derivatives, Newton's method, multi-step Adams method and automatic differentiation. Finally, the results of this paper are evaluated on a second-order nonlinear system.
14. Nonlinear dynamics and control of a vibrating rectangular plate
Science.gov (United States)
Shebalin, J. V.
1983-01-01
The von Karman equations of nonlinear elasticity are solved for the case of a vibrating rectangular plate by meams of a Fourier spectral transform method. The amplification of a particular Fourier mode by nonlinear transfer of energy is demonstrated for this conservative system. The multi-mode system is reduced to a minimal (two mode) system, retaining the qualitative features of the multi-mode system. The effect of a modal control law on the dynamics of this minimal nonlinear elastic system is examined.
15. Delay-Dependent Finite-Time H∞ Controller Design for a Kind of Nonlinear Descriptor Systems via a T-S Fuzzy Model
Directory of Open Access Journals (Sweden)
Baoyan Zhu
2015-01-01
Full Text Available Delay-dependent finite-time H∞ controller design problems are investigated for a kind of nonlinear descriptor system via a T-S fuzzy model in this paper. The solvable conditions of finite-time H∞ controller are given to guarantee that the loop-closed system is impulse-free and finite-time bounded and holds the H∞ performance to a prescribed disturbance attenuation level γ. The method given is the ability to eliminate the impulsive behavior caused by descriptor systems in a finite-time interval, which confirms the existence and uniqueness of solutions in the interval. By constructing a nonsingular matrix, we overcome the difficulty that results in an infeasible linear matrix inequality (LMI. Using the FEASP solver and GEVP solver of the LMI toolbox, we perform simulations to validate the proposed methods for a nonlinear descriptor system via the T-S fuzzy model, which shows the application of the T-S fuzzy method in studying the finite-time control problem of a nonlinear system. Meanwhile the method was also applied to the biological economy system to eliminate impulsive behavior at the bifurcation value, stabilize the loop-closed system in a finite-time interval, and achieve a H∞ performance level.
16. A Nonlinear Fuel Optimal Reaction Jet Control Law
National Research Council Canada - National Science Library
Breitfeller, Eric
2002-01-01
We derive a nonlinear fuel optimal attitude control system (ACS) that drives the final state to the desired state according to a cost function that weights the final state angular error relative to the angular rate error...
17. Complex motions and chaos in nonlinear systems
CERN Document Server
2016-01-01
This book brings together 10 chapters on a new stream of research examining complex phenomena in nonlinear systems—including engineering, physics, and social science. Complex Motions and Chaos in Nonlinear Systems provides readers a particular vantage of the nature and nonlinear phenomena in nonlinear dynamics that can develop the corresponding mathematical theory and apply nonlinear design to practical engineering as well as the study of other complex phenomena including those investigated within social science.
18. Application of nonlinear transformations to automatic flight control
Science.gov (United States)
Meyer, G.; Su, R.; Hunt, L. R.
1984-01-01
The theory of transformations of nonlinear systems to linear ones is applied to the design of an automatic flight controller for the UH-1H helicopter. The helicopter mathematical model is described and it is shown to satisfy the necessary and sufficient conditions for transformability. The mapping is constructed, taking the nonlinear model to canonical form. The performance of the automatic control system in a detailed simulation on the flight computer is summarized.
19. Distributed ESO based cooperative tracking control for high-order nonlinear multiagent systems with lumped disturbance and application in multi flight simulators systems.
Science.gov (United States)
Cong, Zhang
2018-03-01
Based on extended state observer, a novel and practical design method is developed to solve the distributed cooperative tracking problem of higher-order nonlinear multiagent systems with lumped disturbance in a fixed communication topology directed graph. The proposed method is designed to guarantee all the follower nodes ultimately and uniformly converge to the leader node with bounded residual errors. The leader node, modeled as a higher-order non-autonomous nonlinear system, acts as a command generator giving commands only to a small portion of the networked follower nodes. Extended state observer is used to estimate the local states and lumped disturbance of each follower node. Moreover, each distributed controller can work independently only requiring the relative states and/or the estimated relative states information between itself and its neighbors. Finally an engineering application of multi flight simulators systems is demonstrated to test and verify the effectiveness of the proposed algorithm. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.
20. Non-linear model predictive supervisory controller for building, air handling unit with recuperator and refrigeration system with heat waste recovery
DEFF Research Database (Denmark)
Minko, Tomasz; Wisniewski, Rafal; Bendtsen, Jan Dimon
2016-01-01
. The retrieved heat excess can be stored in the water tank. For this purpose the charging and the discharging water loops has been designed. We present the non-linear model of the above described system and a non-linear model predictive supervisory controller that according to the received price signal......, occupancy information and ambient temperature minimizes the operation cost of the whole system and distributes set points to local controllers of supermarkets subsystems. We find that when reliable information about the high price period is available, it is profitable to use the refrigeration system...... to generate heat during the low price period, store it and use it to substitute the conventional heater during the high price period....
1. Adaptive projective synchronization of different chaotic systems with nonlinearity inputs
International Nuclear Information System (INIS)
Niu Yu-Jun; Pei Bing-Nan; Wang Xing-Yuan
2012-01-01
We investigate the projective synchronization of different chaotic systems with nonlinearity inputs. Based on the adaptive technique, sliding mode control method and pole assignment technique, a novel adaptive projective synchronization scheme is proposed to ensure the drive system and the response system with nonlinearity inputs can be rapidly synchronized up to the given scaling factor. (general)
2. Nonlinear time heteronymous damping in nonlinear parametric planetary systems
Czech Academy of Sciences Publication Activity Database
Hortel, Milan; Škuderová, Alena
2014-01-01
Roč. 225, č. 7 (2014), s. 2059-2073 ISSN 0001-5970 Institutional support: RVO:61388998 Keywords : nonlinear dynamics * planetary systems * heteronymous damping Subject RIV: JT - Propulsion, Motors ; Fuels Impact factor: 1.465, year: 2014
3. Nonlinear estimation and control of automotive drivetrains
CERN Document Server
Chen, Hong
2014-01-01
Nonlinear Estimation and Control of Automotive Drivetrains discusses the control problems involved in automotive drivetrains, particularly in hydraulic Automatic Transmission (AT), Dual Clutch Transmission (DCT) and Automated Manual Transmission (AMT). Challenging estimation and control problems, such as driveline torque estimation and gear shift control, are addressed by applying the latest nonlinear control theories, including constructive nonlinear control (Backstepping, Input-to-State Stable) and Model Predictive Control (MPC). The estimation and control performance is improved while the calibration effort is reduced significantly. The book presents many detailed examples of design processes and thus enables the readers to understand how to successfully combine purely theoretical methodologies with actual applications in vehicles. The book is intended for researchers, PhD students, control engineers and automotive engineers. Hong Chen is a professor at the State Key Laboratory of Automotive Simulation and...
4. Nonlinearity of colloid systems oxyhydrate systems
CERN Document Server
Sucharev, Yuri I
2008-01-01
The present monograph is the first systematic study of the non-linear characteristic of gel oxy-hydrate systems involving d- and f- elements. These are the oxyhydrates of rare-earth elements and oxides - hydroxides of d- elements (zirconium, niobium, titanium, etc.) The non-linearity of these gel systems introduces fundamental peculiarities into their structure and, consequently, their properties. The polymer-conformational diversity of energetically congenial gel fragments, which continu-ously transform under the effect of, for instance, system dissipation heat, is central to the au-thor's hy
5. Analysis, Adaptive Control and Adaptive Synchronization of a Nine-Term Novel 3-D Chaotic System with Four Quadratic Nonlinearities and its Circuit Simulation
Directory of Open Access Journals (Sweden)
S. Vaidyanathan
2014-11-01
Full Text Available This research work describes a nine-term novel 3-D chaotic system with four quadratic nonlinearities and details its qualitative properties. The phase portraits of the 3-D novel chaotic system simulated using MATLAB, depict the strange chaotic attractor of the system. For the parameter values chosen in this work, the Lyapunov exponents of the novel chaotic system are obtained as L1 = 6.8548, L2 = 0 and L3 = −32.8779. Also, the Kaplan-Yorke dimension of the novel chaotic system is obtained as DKY = 2.2085. Next, an adaptive controller is design to achieve global stabilization of the 3-D novel chaotic system with unknown system parameters. Moreover, an adaptive controller is designed to achieve global chaos synchronization of two identical novel chaotic systems with unknown system parameters. Finally, an electronic circuit realization of the novel chaotic system is presented using SPICE to confirm the feasibility of the theoretical model.
6. Nonlinear predictive control in the LHC accelerator
CERN Document Server
Blanco, E; Cristea, S; Casas, J
2009-01-01
This paper describes the application of a nonlinear model-based control strategy in a real challenging process. A predictive controller based on a nonlinear model derived from physical relationships, mainly heat and mass balances, has been developed and commissioned in the inner triplet heat exchanger unit (IT-HXTU) of the large hadron collider (LHC) particle accelerator at European Center for Nuclear Research (CERN). The advanced regulation\\ maintains the magnets temperature at about 1.9 K. The development includes a constrained nonlinear state estimator with a receding horizon estimation procedure to improve the regulator predictions.
7. Introduction to geometric nonlinear control; Controllability and lie bracket
Energy Technology Data Exchange (ETDEWEB)
Jakubczyk, B [Institute of Mathematics, Polish Academy of Sciences, Warsaw (Poland)
2002-07-15
We present an introduction to the qualitative theory of nonlinear control systems, with the main emphasis on controllability properties of such systems. We introduce the differential geometric language of vector fields, Lie bracket, distributions, foliations etc. One of the basic tools is the orbit theorem of Stefan and Sussmann. We analyse the basic controllability problems and give criteria for complete controllability, accessibility and related properties, using certain Lie algebras of ve fields defined by the system. A problem of path approximation is considered as an application of the developed theory. We illustrate our considerations with examples of simple systems or systems appearing in applications. The notes start from an elementary level and are self-contained. (author)
8. Identification of Nonlinear Dynamic Systems Possessing Some Non-linearities
Directory of Open Access Journals (Sweden)
Y. N. Pavlov
2015-01-01
Full Text Available The subject of this work is the problem of identification of nonlinear dynamic systems based on the experimental data obtained by applying test signals to the system. The goal is to determinate coefficients of differential equations of systems by experimental frequency hodographs and separate similar, but different, in essence, forces: dissipative forces with the square of the first derivative in the motion equations and dissipative force from the action of dry friction. There was a proposal to use the harmonic linearization method to approximate each of the nonlinearity of "quadratic friction" and "dry friction" by linear friction with the appropriate harmonic linearization coefficient.Assume that a frequency transfer function of the identified system has a known form. Assume as well that there are disturbances while obtaining frequency characteristics of the realworld system. As a result, the points of experimentally obtained hodograph move randomly. Searching for solution of the identification problem was in the hodograph class, specified by the system model, which has the form of the frequency transfer function the same as the form of the frequency transfer function of the system identified. Minimizing a proximity criterion (measure of the experimentally obtained system hodograph and the system hodograph model for all the experimental points described and previously published by one of the authors allowed searching for the unknown coefficients of the frequenc ransfer function of the system model. The paper shows the possibility to identify a nonlinear dynamic system with multiple nonlinearities, obtained on the experimental samples of the frequency system hodograph. The proposed algorithm allows to select the nonlinearity of the type "quadratic friction" and "dry friction", i.e. also in the case where the nonlinearity is dependent on the same dynamic parameter, in particular, on the derivative of the system output value. For the dynamic
9. Robust fast controller design via nonlinear fractional differential equations.
Science.gov (United States)
Zhou, Xi; Wei, Yiheng; Liang, Shu; Wang, Yong
2017-07-01
A new method for linear system controller design is proposed whereby the closed-loop system achieves both robustness and fast response. The robustness performance considered here means the damping ratio of closed-loop system can keep its desired value under system parameter perturbation, while the fast response, represented by rise time of system output, can be improved by tuning the controller parameter. We exploit techniques from both the nonlinear systems control and the fractional order systems control to derive a novel nonlinear fractional order controller. For theoretical analysis of the closed-loop system performance, two comparison theorems are developed for a class of fractional differential equations. Moreover, the rise time of the closed-loop system can be estimated, which facilitates our controller design to satisfy the fast response performance and maintain the robustness. Finally, numerical examples are given to illustrate the effectiveness of our methods. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
10. Robust LS-SVM-based adaptive constrained control for a class of uncertain nonlinear systems with time-varying predefined performance
Science.gov (United States)
Luo, Jianjun; Wei, Caisheng; Dai, Honghua; Yuan, Jianping
2018-03-01
This paper focuses on robust adaptive control for a class of uncertain nonlinear systems subject to input saturation and external disturbance with guaranteed predefined tracking performance. To reduce the limitations of classical predefined performance control method in the presence of unknown initial tracking errors, a novel predefined performance function with time-varying design parameters is first proposed. Then, aiming at reducing the complexity of nonlinear approximations, only two least-square-support-vector-machine-based (LS-SVM-based) approximators with two design parameters are required through norm form transformation of the original system. Further, a novel LS-SVM-based adaptive constrained control scheme is developed under the time-vary predefined performance using backstepping technique. Wherein, to avoid the tedious analysis and repeated differentiations of virtual control laws in the backstepping technique, a simple and robust finite-time-convergent differentiator is devised to only extract its first-order derivative at each step in the presence of external disturbance. In this sense, the inherent demerit of backstepping technique-;explosion of terms; brought by the recursive virtual controller design is conquered. Moreover, an auxiliary system is designed to compensate the control saturation. Finally, three groups of numerical simulations are employed to validate the effectiveness of the newly developed differentiator and the proposed adaptive constrained control scheme.
11. Topological equivalence of nonlinear autonomous dynamical systems
International Nuclear Information System (INIS)
Nguyen Huynh Phan; Tran Van Nhung
1995-12-01
We show in this paper that the autonomous nonlinear dynamical system Σ(A,B,F): x' = Ax+Bu+F(x) is topologically equivalent to the linear dynamical system Σ(A,B,O): x' = Ax+Bu if the projection of A on the complement in R n of the controllable vectorial subspace is hyperbolic and if lipschitz constant of F is sufficiently small ( * ) and F(x) = 0 when parallel x parallel is sufficiently large ( ** ). In particular, if Σ(A,B,O) is controllable, it is topologically equivalent to Σ(A,B,F) when it is only that F satisfy ( ** ). (author). 18 refs
12. Sensorless Estimation and Nonlinear Control of a Rotational Energy Harvester
Science.gov (United States)
Nunna, Kameswarie; Toh, Tzern T.; Mitcheson, Paul D.; Astolfi, Alessandro
2013-12-01
It is important to perform sensorless monitoring of parameters in energy harvesting devices in order to determine the operating states of the system. However, physical measurements of these parameters is often a challenging task due to the unavailability of access points. This paper presents, as an example application, the design of a nonlinear observer and a nonlinear feedback controller for a rotational energy harvester. A dynamic model of a rotational energy harvester with its power electronic interface is derived and validated. This model is then used to design a nonlinear observer and a nonlinear feedback controller which yield a sensorless closed-loop system. The observer estimates the mechancial quantities from the measured electrical quantities while the control law sustains power generation across a range of source rotation speeds. The proposed scheme is assessed through simulations and experiments.
13. Empirical Differential Balancing for Nonlinear Systems
NARCIS (Netherlands)
Kawano, Yu; Scherpen, Jacquelien M.A.; Dochain, Denis; Henrion, Didier; Peaucelle, Dimitri
In this paper, we consider empirical balancing of nonlinear systems by using its prolonged system, which consists of the original nonlinear system and its variational system. For the prolonged system, we define differential reachability and observability Gramians, which are matrix valued functions
14. Transient stability improvement by nonlinear controllers based on tracking
Energy Technology Data Exchange (ETDEWEB)
Ramirez, Juan M. [Centro de Investigacion y Estudios Avanzados, Guadalajara, Mexico. Av. Cientifica 1145. Col. El Bajio. Zapopan, Jal. 45015 (Mexico); Arroyave, Felipe Valencia; Correa Gutierrez, Rosa Elvira [Universidad Nacional de Colombia, Sede Medellin. Facultad de Minas, Escuela de Mecatronica (Colombia)
2011-02-15
This paper deals with the control problem in multi-machine electric power systems, which represent complex great scale nonlinear systems. Thus, the controller design is a challenging problem. These systems are subjected to different perturbations, such as short circuits, connection and/or disconnection of loads, lines, or generators. Then, the utilization of controllers which guarantee good performance under those perturbations is required in order to provide electrical energy to the loads with admissible stability margins. The proposed controllers are based on a systematic strategy, which calculate nonlinear controllers for generating units in a power plant, both for voltage and velocity regulation. The formulation allows designing controllers in a multi-machine power system without intricate calculations. Results on a power system of the open research indicate the proposition's suitability. The problem is formulated as a tracking problem. The designed controllers may be implemented in any electric power system. (author)
15. Implementation of neural network based non-linear predictive control
DEFF Research Database (Denmark)
Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole
1999-01-01
This paper describes a control method for non-linear systems based on generalized predictive control. Generalized predictive control (GPC) was developed to control linear systems, including open-loop unstable and non-minimum phase systems, but has also been proposed to be extended for the control...... of non-linear systems. GPC is model based and in this paper we propose the use of a neural network for the modeling of the system. Based on the neural network model, a controller with extended control horizon is developed and the implementation issues are discussed, with particular emphasis...... on an efficient quasi-Newton algorithm. The performance is demonstrated on a pneumatic servo system....
16. A data-driven adaptive controller for a class of unknown nonlinear discrete-time systems with estimated PPD
Directory of Open Access Journals (Sweden)
Chidentree Treesatayapun
2015-06-01
Full Text Available An adaptive control scheme based on data-driven controller (DDC is proposed in this article. Unlike several DDC techniques, the proposed controller is constructed by an adaptive fuzzy rule emulated network (FREN which is able to include human knowledge based on controlled plant's input–output signals within the format of IF-THEN rules. Regarding to this advantage, an on-line estimation of pseudo partial derivative (PPD and resetting algorithms, which are commonly used by DDC, can be omitted here. Furthermore, a novel adaptive algorithm is introduced to minimize for both tracking error and control effort with stability analysis for the closed-loop system. The experimental system with brushed DC-motor current control is constructed to validate the performance of the proposed control scheme. Comparative results with conventional DDC and radial basis function (RBF controllers demonstrate that the proposed controller can provide the less tracking error and minimize the control effort.
17. Nonlinear control of the Salnikov model reaction
DEFF Research Database (Denmark)
Recke, Bodil; Jørgensen, Sten Bay
1999-01-01
This paper explores different nonlinear control schemes, applied to a simple model reaction. The model is the Salnikov model, consisting of two ordinary differential equations. The control strategies investigated are I/O-linearisation, Exact linearisation, exact linearisation combined with LQR...
18. Control Design of a Nonlinear Controller to Stabilize the Nonlinear ...
African Journals Online (AJOL)
inyangs
is used to formularize the delay differential equation in equation. (13), which accounts for the delayed terms in the system. By applying the Leibniz integration rule, the derivative. •. V shows that the system is asymptotically stable with a negative definite solution in equation (14). The conditions for the stability are: •. The delay ...
19. Nonlinear Control of Marine Surface Vessels
Science.gov (United States)
Das, Swarup; Talole, S. E.
2018-03-01
In the present study, a robust yaw control law design derived from nonlinear extended state observer (NESO) based nonlinear state error feedback controller (NSEFC) in conjunction with nonlinear tracking differentiator (NTD) for marine surface vessels is presented. As marine vessel operates in an environment where significant uncertainties and disturbances are present, an NESO is used to estimate the effect of the uncertainties and disturbances along with the plant states leading to a robust design through disturbance estimation and compensation. Convergence of NESO and NTD is demonstrated. The notable feature of the formulation is that to achieve robustness, accurate plant model or any characterization of the uncertainties and disturbances is not needed. Efficacy of the design is illustrated by simulation. Further, performance of the proposed design is compared with some existing controllers to showcase the effectiveness of the proposed design.
20. Control Design of a Nonlinear Controller to Stabilize the Nonlinear ...
African Journals Online (AJOL)
inyangs
protocol employed to combat the problem of proper queue utilization, busty packet drop and adaptable delay. TCP .... This case considers a delay on the control input only and the link capacity is made to be very large to ... We take the derivative of equation (13) with respect to t and apply the Leibniz integrator rule to obtain.
1. Nonlinear Waves in Complex Systems
DEFF Research Database (Denmark)
2007-01-01
The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations, it is the ......The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations...
2. Discontinuity and complexity in nonlinear physical systems
CERN Document Server
Baleanu, Dumitru; Luo, Albert
2014-01-01
This unique book explores recent developments in experimental research in this broad field, organized in four distinct sections. Part I introduces the reader to the fractional dynamics and Lie group analysis for nonlinear partial differential equations. Part II covers chaos and complexity in nonlinear Hamiltonian systems, important to understand the resonance interactions in nonlinear dynamical systems, such as Tsunami waves and wildfire propagations; as well as Lev flights in chaotic trajectories, dynamical system synchronization and DNA information complexity analysis. Part III examines chaos and periodic motions in discontinuous dynamical systems, extensively present in a range of systems, including piecewise linear systems, vibro-impact systems and drilling systems in engineering. And in Part IV, engineering and financial nonlinearity are discussed. The mechanism of shock wave with saddle-node bifurcation and rotating disk stability will be presented, and the financial nonlinear models will be discussed....
3. Analysis of MPPT Failure and Development of an Augmented Nonlinear Controller for MPPT of Photovoltaic Systems under Partial Shading Conditions
Directory of Open Access Journals (Sweden)
Mingxuan Chen
2017-01-01
Full Text Available The output–voltage–power curves of photovoltaic (PV arrays exhibit complex multi-peak shapes when local shading occurs. The existing maximum power point tracking (MPPT algorithms to solve this multi-peak problem do not consider the possibility of tracking failures due to the time of the irradiance change. In this study, first, the reason for the failure of the global MPPT (GMPPT algorithm is analyzed based on the PV array mathematical model and its output characteristics under partial shading conditions; then, in order to estimate the MPP voltage, an artificial neural network (ANN is trained using environmental information such as irradiance. A hybrid MPPT method using an augmented state feedback precise linearization (AFL controller combined with an ANN is proposed to solve problems such as the shift of the static operating point of the DC/DC boost converter. Finally, numerical simulations are conducted to validate the proposed method and eliminate the possibility of MPPT failure. The proposed hybrid MPPT method is compared with the conventional perturb and observe (P & O method and the improved P & O method through simulations. Using the proposed neural network and nonlinear control strategy, the MPP can be tracked rapidly, accurately, and statically, proving that the method is feasible and effective.
4. Nonlinear saturation controller for vibration supersession of a nonlinear composite beam
Energy Technology Data Exchange (ETDEWEB)
Hamed, Y. S. [Menofia University, Menouf (Egypt); Amer, Y. A. [Zagazig University, Zagazig (Egypt)
2014-08-15
In this paper, a study for nonlinear saturation controller (NSC) is presented that used to suppress the vibration amplitude of a structural dynamic model simulating nonlinear composite beam at simultaneous sub-harmonic and internal resonance excitation. The absorber exploits the saturation phenomenon that is known to occur in dynamical systems with quadratic non-linearities of the feedback gain and a two-to-one internal resonance. The analytical solution for the system and the nonlinear saturation controller are obtained using method of multiple time scales perturbation up to the second order approximation. All possible resonance cases were extracted at this approximation order and studied numerically. The stability of the system at the worst resonance case (Ω = 2ω{sub s} and ω{sub s} =2ω{sub C}) is investigated using both frequency response equations and phase-plane trajectories. The effects of different parameters on the system and the controller are studied numerically. The effect of some types of controller on the system is investigated numerically. The simulation results are achieved using Matlab and Maple programs.
5. Stability analysis of nonlinear systems with slope restricted nonlinearities.
Science.gov (United States)
Liu, Xian; Du, Jiajia; Gao, Qing
2014-01-01
The problem of absolute stability of Lur'e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP) lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.
6. Stability Analysis of Nonlinear Systems with Slope Restricted Nonlinearities
Directory of Open Access Journals (Sweden)
Xian Liu
2014-01-01
Full Text Available The problem of absolute stability of Lur’e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.
7. Nonlinear control of permanent magnet synchronous motor driving a ...
African Journals Online (AJOL)
This paper presents a non-linear control of permanent magnet synchronous motor (PMSM) fed by a PWM voltage source inverter. To improve the performance of this control technique, the input-output linearization technique is proposed for a system driving a mechanical load with two masses. In order to ensure a steady ...
8. Nonlinear Dynamic Inversion Baseline Control Law: Flight-Test Results for the Full-scale Advanced Systems Testbed F/A-18 Airplane
Science.gov (United States)
Miller, Christopher J.
2011-01-01
A model reference nonlinear dynamic inversion control law has been developed to provide a baseline controller for research into simple adaptive elements for advanced flight control laws. This controller has been implemented and tested in a hardware-in-the-loop simulation and in flight. The flight results agree well with the simulation predictions and show good handling qualities throughout the tested flight envelope with some noteworthy deficiencies highlighted both by handling qualities metrics and pilot comments. Many design choices and implementation details reflect the requirements placed on the system by the nonlinear flight environment and the desire to keep the system as simple as possible to easily allow the addition of the adaptive elements. The flight-test results and how they compare to the simulation predictions are discussed, along with a discussion about how each element affected pilot opinions. Additionally, aspects of the design that performed better than expected are presented, as well as some simple improvements that will be suggested for follow-on work.
9. Fault Diagnosis Scheme for Nonlinear Stochastic Systems with Time-Varying Fault: Application to the Rigid Spacecraft Control
Czech Academy of Sciences Publication Activity Database
Nguyen, H.Q.; Čelikovský, Sergej
2012-01-01
Roč. 1, č. 3 (2012), s. 179-187 ISSN 2223-7038 R&D Projects: GA ČR(CZ) GAP103/12/1794 Institutional support: RVO:67985556 Keywords : Attitude control * adaptive fault estimation * LMI * PDF Subject RIV: BC - Control Systems Theory http://lib.physcon.ru/doc?id=02c925f7e4ab
10. Propeller-Pendulum for Nonlinear UAVs Control
Directory of Open Access Journals (Sweden)
Tomáš Huba
2013-02-01
Full Text Available This paper presents basic information about new experiment and about the wrapped-around learning objects for nonlinear control and other relevant topics from the mechatronics area. Its primary aim is to motivate students within the framework of the “learning by playing”, “learning by discovering”, or through “experiential learning” approaches to drag them to study this highly sophisticated stuff. The experiment may deal with simple but challenging positional or velocity control tasks requiring knowledge of basic physical principals of mechanics and of the associated mathematical apparatus of nonlinear differential equations. Furthermore, it is also used to master related measurement and communication problems, to carry out embedded control design and programming of embedded devices. Finally, it is also useful and illustrative in comparing traditional control methods that may be confronted towards the latest development in several areas of modern control theory.
11. Genetic design of interpolated non-linear controllers for linear plants
International Nuclear Information System (INIS)
Ajlouni, N.
2000-01-01
The techniques of genetic algorithms are proposed as a means of designing non-linear PID control systems. It is shown that the use of genetic algorithms for this purpose results in highly effective non-linear PID control systems. These results are illustrated by using genetic algorithms to design a non-linear PID control system and contrasting the results with an optimally tuned linear PID controller. (author)
12. Tracking control of DC motors via mimo nonlinear fuzzy control
International Nuclear Information System (INIS)
2009-01-01
This paper proposed a nonlinear controller for speed tracking of separately excited DC motors (SEDCM's) using the multi-input multi-output (MIMO) fuzzy logic controller (FLC's). Based on a nonlinear mathematical model of SEDCM, a FLC is designed to achieve high performance speed tracking through rejection load disturbance. Computer simulations are presented to show speed tracking performance and the effectiveness of the proposed controller.
13. Nonlinear vibration with control for flexible and adaptive structures
CERN Document Server
Wagg, David
2015-01-01
This book provides a comprehensive discussion of nonlinear multi-modal structural vibration problems, and shows how vibration suppression can be applied to such systems by considering a sample set of relevant control techniques. It covers the basic principles of nonlinear vibrations that occur in flexible and/or adaptive structures, with an emphasis on engineering analysis and relevant control techniques. Understanding nonlinear vibrations is becoming increasingly important in a range of engineering applications, particularly in the design of flexible structures such as aircraft, satellites, bridges, and sports stadia. There is an increasing trend towards lighter structures, with increased slenderness, often made of new composite materials and requiring some form of deployment and/or active vibration control. There are also applications in the areas of robotics, mechatronics, micro electrical mechanical systems, non-destructive testing and related disciplines such as structural health monitoring. Two broader ...
14. Passivity Based Stabilization of Non-minimum Phase Nonlinear Systems
Czech Academy of Sciences Publication Activity Database
Travieso-Torres, J.C.; Duarte-Mermoud, M.A.; Zagalak, Petr
2009-01-01
Roč. 45, č. 3 (2009), s. 417-426 ISSN 0023-5954 R&D Projects: GA ČR(CZ) GA102/07/1596 Institutional research plan: CEZ:AV0Z10750506 Keywords : nonlinear systems * stabilisation * passivity * state feedback Subject RIV: BC - Control Systems Theory Impact factor: 0.445, year: 2009 http://library.utia.cas.cz/separaty/2009/AS/zagalak-passivity based stabilization of non-minimum phase nonlinear systems.pdf
15. Positive real balancing for nonlinear systems
NARCIS (Netherlands)
Ionescu, Tudor C.; Scherpen, Jacquelien M.A.; Ciuprina, G; Ioan, D
2007-01-01
We extend the positive real balancing procedure for passive linear systems to the nonlinear systems case. We show that, just like in the linear case, model reduction based on this technique preserves passivity.
16. Neural network based adaptive control for nonlinear dynamic regimes
Science.gov (United States)
Shin, Yoonghyun
17. Fluctuations in Nonlinear Systems: A Short Review
International Nuclear Information System (INIS)
Rubia, F.J. de la; Buceta, J.; Cabrera, J.L.; Olarrea, J.; Parrondo, J.M.R.
2003-01-01
We review some results that illustrate the constructive role of noise in nonlinear systems. Several phenomena are briefly discussed: optimal localization of orbits in a system with limit cycle behavior and perturbed by colored noise; stochastic branch selection at secondary bifurcations; noise- induced order/disorder transitions and pattern formation in spatially extended systems. In all cases the presence of noise is crucial, and the results reinforce the modern view of the importance of noise in the evolution of nonlinear systems. (author)
18. Optimization of nonlinear controller with an enhanced biogeography approach
Directory of Open Access Journals (Sweden)
Mohammed Salem
2014-07-01
Full Text Available This paper is dedicated to the optimization of nonlinear controllers basing of an enhanced Biogeography Based Optimization (BBO approach. Indeed, The BBO is combined to a predator and prey model where several predators are used with introduction of a modified migration operator to increase the diversification along the optimization process so as to avoid local optima and reach the optimal solution quickly. The proposed approach is used in tuning the gains of PID controller for nonlinear systems. Simulations are carried out over a Mass spring damper and an inverted pendulum and has given remarkable results when compared to genetic algorithm and BBO.
19. Analysis, Adaptive Control and Anti-Synchronization of a Six-Term Novel Jerk Chaotic System with two Exponential Nonlinearities and its Circuit Simulation
Directory of Open Access Journals (Sweden)
S. Vaidyanathan
2014-11-01
Full Text Available This research work proposes a six-term novel 3-D jerk chaotic system with two exponential nonlinearities. This work also analyses system’s fundamental properties such as dissipativity, equilibria, Lyapunov exponents and Kaplan-Yorke dimension. The phase portraits of the jerk chaotic system simulated using MATLAB, depict the strange chaotic attractor of the system. For the parameter values and initial conditions chosen in this work, the Lyapunov exponents of the novel jerk chaotic system are obtained as L1 = 0.24519, L2 = 0 and L3 = −0.84571. Also, the Kaplan-Yorke dimension of the novel jerk chaotic system is obtained as DKY = 2.2899. Next, an adaptive backstepping controller is designed to stabilize the novel jerk chaotic system having two unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve global chaos anti-synchronization of two identical novel jerk chaotic systems with two unknown system parameters. Finally, an electronic circuit realization of the novel jerk chaotic system is presented using SPICE to confirm the feasibility of the theoretical model.
20. Fractional-Order Control of a Nonlinear Time-Delay System: Case Study in Oxygen Regulation in the Heart-Lung Machine
Directory of Open Access Journals (Sweden)
2012-01-01
Full Text Available A fractional-order controller will be proposed to regulate the inlet oxygen into the heart-lung machine. An analytical approach will be explained to satisfy some requirements together with practical implementation of some restrictions for the first time. Primarily a nonlinear single-input single-output (SISO time-delay model which was obtained previously in the literature is introduced for the oxygen generation process in the heart-lung machine system and we will complete it by adding some new states to control it. Thereafter, the system is linearized using the state feedback linearization approach to find a third-order time-delay dynamics. Consequently classical PID and fractional order controllers are gained to assess the quality of the proposed technique. A set of optimal parameters of those controllers are achieved through the genetic algorithm optimization procedure through minimizing a cost function. Our design method focuses on minimizing some famous performance criterions such as IAE, ISE, and ITSE. In the genetic algorithm, the controller parameters are chosen as a random population. The best relevant values are achieved by reducing the cost function. A time-domain simulation signifies the performance of controller with respect to a traditional optimized PID controller.
1. Introduction to geometric nonlinear control; Linearization, observability, decoupling
Energy Technology Data Exchange (ETDEWEB)
Respondek, W [Laboratoire de Mathematiques, INSA de Rouen (France)
2002-07-15
These notes are devoted to the problems of linearization, observability, and decoupling of nonlinear control systems. Together with notes of Bronislaw Jakubczyk in the same volume, they form an introduction to geometric methods in nonlinear control theory. In the first part we discuss equivalence of control systems. We consider various aspects of the problem: state-space and feedback equivalence, local and global equivalence, equivalence to linear and partially linear systems. In the second part we present the notion of observability and give a geometric rank condition for local observability and an algebraic characterization of local observability. We discuss unm observability, decompositions of non-observable systems, and properties of generic observable systems. In the third part we introduce the notion of invariant distributions and discuss disturbance decoupling and input-output decoupling. Many concepts and results are illustrated with examples. (author)
2. A Linear Programming Approach to Routing Control in Networks of Constrained Nonlinear Positive Systems with Concave Flow Rates
Science.gov (United States)
Arneson, Heather M.; Dousse, Nicholas; Langbort, Cedric
2014-01-01
We consider control design for positive compartmental systems in which each compartment's outflow rate is described by a concave function of the amount of material in the compartment.We address the problem of determining the routing of material between compartments to satisfy time-varying state constraints while ensuring that material reaches its intended destination over a finite time horizon. We give sufficient conditions for the existence of a time-varying state-dependent routing strategy which ensures that the closed-loop system satisfies basic network properties of positivity, conservation and interconnection while ensuring that capacity constraints are satisfied, when possible, or adjusted if a solution cannot be found. These conditions are formulated as a linear programming problem. Instances of this linear programming problem can be solved iteratively to generate a solution to the finite horizon routing problem. Results are given for the application of this control design method to an example problem. Key words: linear programming; control of networks; positive systems; controller constraints and structure.
3. Nonlinear stability control and λ-bifurcation
International Nuclear Information System (INIS)
Erneux, T.; Reiss, E.L.; Magnan, J.F.; Jayakumar, P.K.
1987-01-01
Passive techniques for nonlinear stability control are presented for a model of fluidelastic instability. They employ the phenomena of λ-bifurcation and a generalization of it. λ-bifurcation occurs when a branch of flutter solutions bifurcates supercritically from a basic solution and terminates with an infinite period orbit at a branch of divergence solutions which bifurcates subcritically from the basic solution. The shape of the bifurcation diagram then resembles the greek letter λ. When the system parameters are in the range where flutter occurs by λ-bifurcation, then as the flow velocity increase the flutter amplitude also increases, but the frequencies of the oscillations decrease to zero. This diminishes the damaging effects of structural fatigue by flutter, and permits the flow speed to exceed the critical flutter speed. If generalized λ-bifurcation occurs, then there is a jump transition from the flutter states to a divergence state with a substantially smaller amplitude, when the flow speed is sufficiently larger than the critical flutter speed
4. Nonlinear discrete-time multirate adaptive control of non-linear vibrations of smart beams
Science.gov (United States)
Georgiou, Georgios; Foutsitzi, Georgia A.; Stavroulakis, Georgios E.
2018-06-01
The nonlinear adaptive digital control of a smart piezoelectric beam is considered. It is shown that in the case of a sampled-data context, a multirate control strategy provides an appropriate framework in order to achieve vibration regulation, ensuring the stability of the whole control system. Under parametric uncertainties in the model parameters (damping ratios, frequencies, levels of non linearities and cross coupling, control input parameters), the scheme is completed with an adaptation law deduced from hyperstability concepts. This results in the asymptotic satisfaction of the control objectives at the sampling instants. Simulation results are presented.
5. Nonlinear Control of Hydraulic Manipulator for Decommissioning Nuclear Reactor
International Nuclear Information System (INIS)
Kim, Myoung-Ho; Lee, Sung-Uk; Kim, Chang-Hoi; Choi, Byung-Seon; Moon, Jei-Kwon
2016-01-01
Robot technique is need to decommission nuclear reactor because of high radiation environment. Especially, Manipulator systems are useful for dismantling complex structure in a nuclear facility. In addition, Hydraulic system is applied to handle heavy duty object. Since hydraulic system can demonstrate high power. The manipulator with hydraulic power is already developed. To solve this problem, various nonlinear control method includes acceleration control. But, it is difficult because acceleration value is highly noisy. In this paper, the nonlinear control algorithm without acceleration control is studied. To verify, the hydraulic manipulator model had been developed. Furthermore, the numerical simulation is carried out. The nonlinear control without acceleration parameter method is developed for hydraulic manipulator. To verify control algorithm, the manipulator is modeled by MBD and the hydraulic servo system is also derived. In addition, the numerical simulation is also carried out. Especially, PID gain is determined though TDC algorithm. In the result of numerical simulation, tracking performance is good without acceleration control. Thus, the PID though TDC with SMC is good for hydraulic manipulator control
6. Nonlinear Control of Hydraulic Manipulator for Decommissioning Nuclear Reactor
Energy Technology Data Exchange (ETDEWEB)
Kim, Myoung-Ho; Lee, Sung-Uk; Kim, Chang-Hoi; Choi, Byung-Seon; Moon, Jei-Kwon [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2016-10-15
Robot technique is need to decommission nuclear reactor because of high radiation environment. Especially, Manipulator systems are useful for dismantling complex structure in a nuclear facility. In addition, Hydraulic system is applied to handle heavy duty object. Since hydraulic system can demonstrate high power. The manipulator with hydraulic power is already developed. To solve this problem, various nonlinear control method includes acceleration control. But, it is difficult because acceleration value is highly noisy. In this paper, the nonlinear control algorithm without acceleration control is studied. To verify, the hydraulic manipulator model had been developed. Furthermore, the numerical simulation is carried out. The nonlinear control without acceleration parameter method is developed for hydraulic manipulator. To verify control algorithm, the manipulator is modeled by MBD and the hydraulic servo system is also derived. In addition, the numerical simulation is also carried out. Especially, PID gain is determined though TDC algorithm. In the result of numerical simulation, tracking performance is good without acceleration control. Thus, the PID though TDC with SMC is good for hydraulic manipulator control.
7. Design of polynomial fuzzy observer-controller for nonlinear systems with state delay: sum of squares approach
Science.gov (United States)
Gassara, H.; El Hajjaji, A.; Chaabane, M.
2017-07-01
This paper investigates the problem of observer-based control for two classes of polynomial fuzzy systems with time-varying delay. The first class concerns a special case where the polynomial matrices do not depend on the estimated state variables. The second one is the general case where the polynomial matrices could depend on unmeasurable system states that will be estimated. For the last case, two design procedures are proposed. The first one gives the polynomial fuzzy controller and observer gains in two steps. In the second procedure, the designed gains are obtained using a single-step approach to overcome the drawback of a two-step procedure. The obtained conditions are presented in terms of sum of squares (SOS) which can be solved via the SOSTOOLS and a semi-definite program solver. Illustrative examples show the validity and applicability of the proposed results.
8. Distributed cooperative H∞ optimal tracking control of MIMO nonlinear multi-agent systems in strict-feedback form via adaptive dynamic programming
Science.gov (United States)
Luy, N. T.
2018-04-01
The design of distributed cooperative H∞ optimal controllers for multi-agent systems is a major challenge when the agents' models are uncertain multi-input and multi-output nonlinear systems in strict-feedback form in the presence of external disturbances. In this paper, first, the distributed cooperative H∞ optimal tracking problem is transformed into controlling the cooperative tracking error dynamics in affine form. Second, control schemes and online algorithms are proposed via adaptive dynamic programming (ADP) and the theory of zero-sum differential graphical games. The schemes use only one neural network (NN) for each agent instead of three from ADP to reduce computational complexity as well as avoid choosing initial NN weights for stabilising controllers. It is shown that despite not using knowledge of cooperative internal dynamics, the proposed algorithms not only approximate values to Nash equilibrium but also guarantee all signals, such as the NN weight approximation errors and the cooperative tracking errors in the closed-loop system, to be uniformly ultimately bounded. Finally, the effectiveness of the proposed method is shown by simulation results of an application to wheeled mobile multi-robot systems.
9. Incremental passivity and output regulation for switched nonlinear systems
Science.gov (United States)
Pang, Hongbo; Zhao, Jun
2017-10-01
This paper studies incremental passivity and global output regulation for switched nonlinear systems, whose subsystems are not required to be incrementally passive. A concept of incremental passivity for switched systems is put forward. First, a switched system is rendered incrementally passive by the design of a state-dependent switching law. Second, the feedback incremental passification is achieved by the design of a state-dependent switching law and a set of state feedback controllers. Finally, we show that once the incremental passivity for switched nonlinear systems is assured, the output regulation problem is solved by the design of global nonlinear regulator controllers comprising two components: the steady-state control and the linear output feedback stabilising controllers, even though the problem for none of subsystems is solvable. Two examples are presented to illustrate the effectiveness of the proposed approach.
10. Nonlinear PDEs a dynamical systems approach
CERN Document Server
Schneider, Guido
2017-01-01
This is an introductory textbook about nonlinear dynamics of PDEs, with a focus on problems over unbounded domains and modulation equations. The presentation is example-oriented, and new mathematical tools are developed step by step, giving insight into some important classes of nonlinear PDEs and nonlinear dynamics phenomena which may occur in PDEs. The book consists of four parts. Parts I and II are introductions to finite- and infinite-dimensional dynamics defined by ODEs and by PDEs over bounded domains, respectively, including the basics of bifurcation and attractor theory. Part III introduces PDEs on the real line, including the Korteweg-de Vries equation, the Nonlinear Schrödinger equation and the Ginzburg-Landau equation. These examples often occur as simplest possible models, namely as amplitude or modulation equations, for some real world phenomena such as nonlinear waves and pattern formation. Part IV explores in more detail the connections between such complicated physical systems and the reduced...
11. Universal formats for nonlinear ordinary differential systems
International Nuclear Information System (INIS)
Kerner, E.H.
1981-01-01
It is shown that very general nonlinear ordinary differential systems (embracing all that arise in practice) may, first, be brought down to polynomial systems (where the nonlinearities occur only as polynomials in the dependent variables) by introducing suitable new variables into the original system; second, that polynomial systems are reducible to ''Riccati systems,'' where the nonlinearities are quadratic at most; third, that Riccati systems may be brought to elemental universal formats containing purely quadratic terms with simple arrays of coefficients that are all zero or unity. The elemental systems have representations as novel types of matrix Riccati equations. Different starting systems and their associated Riccati systems differ from one another, at the final elemental level, in order and in initial data, but not in format
12. Nonlinear and Complex Dynamics in Real Systems
OpenAIRE
William Barnett; Apostolos Serletis; Demitre Serletis
2005-01-01
This paper was produced for the El-Naschie Symposium on Nonlinear Dynamics in Shanghai in December 2005. In this paper we provide a review of the literature with respect to fluctuations in real systems and chaos. In doing so, we contrast the order and organization hypothesis of real systems with nonlinear chaotic dynamics and discuss some techniques used in distinguishing between stochastic and deterministic behavior. Moreover, we look at the issue of where and when the ideas of chaos could p...
13. NONLINEAR MODEL PREDICTIVE CONTROL OF CHEMICAL PROCESSES
Directory of Open Access Journals (Sweden)
SILVA R. G.
1999-01-01
Full Text Available A new algorithm for model predictive control is presented. The algorithm utilizes a simultaneous solution and optimization strategy to solve the model's differential equations. The equations are discretized by equidistant collocation, and along with the algebraic model equations are included as constraints in a nonlinear programming (NLP problem. This algorithm is compared with the algorithm that uses orthogonal collocation on finite elements. The equidistant collocation algorithm results in simpler equations, providing a decrease in computation time for the control moves. Simulation results are presented and show a satisfactory performance of this algorithm.
14. Linear and nonlinear schemes applied to pitch control of wind turbines.
Science.gov (United States)
Geng, Hua; Yang, Geng
2014-01-01
Linear controllers have been employed in industrial applications for many years, but sometimes they are noneffective on the system with nonlinear characteristics. This paper discusses the structure, performance, implementation cost, advantages, and disadvantages of different linear and nonlinear schemes applied to the pitch control of the wind energy conversion systems (WECSs). The linear controller has the simplest structure and is easily understood by the engineers and thus is widely accepted by the industry. In contrast, nonlinear schemes are more complicated, but they can provide better performance. Although nonlinear algorithms can be implemented in a powerful digital processor nowadays, they need time to be accepted by the industry and their reliability needs to be verified in the commercial products. More information about the system nonlinear feature is helpful to simplify the controller design. However, nonlinear schemes independent of the system model are more robust to the uncertainties or deviations of the system parameters.
15. Synchronization of two different chaotic systems via nonlinear ...
African Journals Online (AJOL)
ABSTRACT: This work reports the synchronization of a pair of four chaotic systems via nonlinear control technique. This method has been found to be easy to implement and effective especially on two different chaotic systems. We paired four chaotic systems out of which one is new and we have six possible pairs.
16. Burn Control in Fusion Reactors via Nonlinear Stabilization Techniques
International Nuclear Information System (INIS)
Schuster, Eugenio; Krstic, Miroslav; Tynan, George
2003-01-01
Control of plasma density and temperature magnitudes, as well as their profiles, are among the most fundamental problems in fusion reactors. Existing efforts on model-based control use control techniques for linear models. In this work, a zero-dimensional nonlinear model involving approximate conservation equations for the energy and the densities of the species was used to synthesize a nonlinear feedback controller for stabilizing the burn condition of a fusion reactor. The subignition case, where the modulation of auxiliary power and fueling rate are considered as control forces, and the ignition case, where the controlled injection of impurities is considered as an additional actuator, are treated separately.The model addresses the issue of the lag due to the finite time for the fresh fuel to diffuse into the plasma center. In this way we make our control system independent of the fueling system and the reactor can be fed either by pellet injection or by puffing. This imposed lag is treated using nonlinear backstepping.The nonlinear controller proposed guarantees a much larger region of attraction than the previous linear controllers. In addition, it is capable of rejecting perturbations in initial conditions leading to both thermal excursion and quenching, and its effectiveness does not depend on whether the operating point is an ignition or a subignition point.The controller designed ensures setpoint regulation for the energy and plasma parameter β with robustness against uncertainties in the confinement times for different species. Hence, the controller can increase or decrease β, modify the power, the temperature or the density, and go from a subignition to an ignition point and vice versa
17. Nonlinear chaos control in a permanent magnet reluctance machine
International Nuclear Information System (INIS)
2004-01-01
The dynamics of a permanent magnet synchronous machine (PMSM) is analyzed. The study shows that under certain conditions the PMSM is experiencing chaotic behavior. To control these unwanted chaotic oscillations, a nonlinear controller based on the backstepping nonlinear control theory is designed. The objective of the designed control is to stabilize the output chaotic trajectory by forcing it to the nearest constant solution in the basin of attraction. The result is compared with a nonlinear sliding mode controller. The designed controller that based on backstepping nonlinear control was able to eliminate the chaotic oscillations. Also the study shows that the designed controller is mush better than the sliding mode control
18. Robust stabilization of nonlinear systems: The LMI approach
Directory of Open Access Journals (Sweden)
iljak D. D.
2000-01-01
Full Text Available This paper presents a new approach to robust quadratic stabilization of nonlinear systems within the framework of Linear Matrix Inequalities (LMI. The systems are composed of a linear constant part perturbed by an additive nonlinearity which depends discontinuously on both time and state. The only information about the nonlinearity is that it satisfies a quadratic constraint. Our major objective is to show how linear constant feedback laws can be formulated to stabilize this type of systems and, at the same time, maximize the bounds on the nonlinearity which the system can tolerate without going unstable. We shall broaden the new setting to include design of decentralized control laws for robust stabilization of interconnected systems. Again, the LMI methods will be used to maximize the class of uncertain interconnections which leave the overall system connectively stable. It is useful to learn that the proposed LMI formulation “recognizes” the matching conditions by returning a feedback gain matrix for any prescribed bound on the interconnection terms. More importantly, the new formulation provides a suitable setting for robust stabilization of nonlinear systems where the nonlinear perturbations satisfy the generalized matching conditions.
19. Nonlinear Tracking Control of a Conductive Supercoiled Polymer Actuator.
Science.gov (United States)
Luong, Tuan Anh; Cho, Kyeong Ho; Song, Min Geun; Koo, Ja Choon; Choi, Hyouk Ryeol; Moon, Hyungpil
2018-04-01
Artificial muscle actuators made from commercial nylon fishing lines have been recently introduced and shown as a new type of actuator with high performance. However, the actuators also exhibit significant nonlinearities, which make them difficult to control, especially in precise trajectory-tracking applications. In this article, we present a nonlinear mathematical model of a conductive supercoiled polymer (SCP) actuator driven by Joule heating for model-based feedback controls. Our efforts include modeling of the hysteresis behavior of the actuator. Based on nonlinear modeling, we design a sliding mode controller for SCP actuator-driven manipulators. The system with proposed control law is proven to be asymptotically stable using the Lyapunov theory. The control performance of the proposed method is evaluated experimentally and compared with that of a proportional-integral-derivative (PID) controller through one-degree-of-freedom SCP actuator-driven manipulators. Experimental results show that the proposed controller's performance is superior to that of a PID controller, such as the tracking errors are nearly 10 times smaller compared with those of a PID controller, and it is more robust to external disturbances such as sensor noise and actuator modeling error.
20. Machine learning control taming nonlinear dynamics and turbulence
CERN Document Server
Duriez, Thomas; Noack, Bernd R
2017-01-01
This is the first book on a generally applicable control strategy for turbulence and other complex nonlinear systems. The approach of the book employs powerful methods of machine learning for optimal nonlinear control laws. This machine learning control (MLC) is motivated and detailed in Chapters 1 and 2. In Chapter 3, methods of linear control theory are reviewed. In Chapter 4, MLC is shown to reproduce known optimal control laws for linear dynamics (LQR, LQG). In Chapter 5, MLC detects and exploits a strongly nonlinear actuation mechanism of a low-dimensional dynamical system when linear control methods are shown to fail. Experimental control demonstrations from a laminar shear-layer to turbulent boundary-layers are reviewed in Chapter 6, followed by general good practices for experiments in Chapter 7. The book concludes with an outlook on the vast future applications of MLC in Chapter 8. Matlab codes are provided for easy reproducibility of the presented results. The book includes interviews with leading r...
1. Nonlinear force feedback control of piezoelectric-hydraulic pump actuator for automotive transmission shift control
Science.gov (United States)
Kim, Gi-Woo; Wang, K. W.
2008-03-01
In recent years, researchers have investigated the feasibility of utilizing piezoelectric-hydraulic pump based actuation systems for automotive transmission controls. This new concept could eventually reduce the complexity, weight, and fuel consumption of the current transmissions. In this research, we focus on how to utilize this new approach on the shift control of automatic transmissions (AT), which generally requires pressure profiling for friction elements during the operation. To illustrate the concept, we will consider the 1--> 2 up shift control using band brake friction elements. In order to perform the actuation force tracking for AT shift control, nonlinear force feedback control laws are designed based on the sliding mode theory for the given nonlinear system. This paper will describe the modeling of the band brake actuation system, the design of the nonlinear force feedback controller, and simulation and experimental results for demonstration of the new concept.
2. Optimal and robust control of a class of nonlinear systems using dynamically re-optimised single network adaptive critic design
Science.gov (United States)
2018-01-01
Following the philosophy of adaptive optimal control, a neural network-based state feedback optimal control synthesis approach is presented in this paper. First, accounting for a nominal system model, a single network adaptive critic (SNAC) based multi-layered neural network (called as NN1) is synthesised offline. However, another linear-in-weight neural network (called as NN2) is trained online and augmented to NN1 in such a manner that their combined output represent the desired optimal costate for the actual plant. To do this, the nominal model needs to be updated online to adapt to the actual plant, which is done by synthesising yet another linear-in-weight neural network (called as NN3) online. Training of NN3 is done by utilising the error information between the nominal and actual states and carrying out the necessary Lyapunov stability analysis using a Sobolev norm based Lyapunov function. This helps in training NN2 successfully to capture the required optimal relationship. The overall architecture is named as 'Dynamically Re-optimised single network adaptive critic (DR-SNAC)'. Numerical results for two motivating illustrative problems are presented, including comparison studies with closed form solution for one problem, which clearly demonstrate the effectiveness and benefit of the proposed approach.
3. Adaptive nonlinear control using input normalized neural networks
International Nuclear Information System (INIS)
Leeghim, Henzeh; Seo, In Ho; Bang, Hyo Choong
2008-01-01
An adaptive feedback linearization technique combined with the neural network is addressed to control uncertain nonlinear systems. The neural network-based adaptive control theory has been widely studied. However, the stability analysis of the closed-loop system with the neural network is rather complicated and difficult to understand, and sometimes unnecessary assumptions are involved. As a result, unnecessary assumptions for stability analysis are avoided by using the neural network with input normalization technique. The ultimate boundedness of the tracking error is simply proved by the Lyapunov stability theory. A new simple update law as an adaptive nonlinear control is derived by the simplification of the input normalized neural network assuming the variation of the uncertain term is sufficiently small
4. Self-Organized Biological Dynamics and Nonlinear Control
Science.gov (United States)
Walleczek, Jan
2006-04-01
The frontiers and challenges of biodynamics research Jan Walleczek; Part I. Nonlinear Dynamics in Biology and Response to Stimuli: 1. External signals and internal oscillation dynamics - principal aspects and response of stimulated rhythmic processes Friedemann Kaiser; 2. Nonlinear dynamics in biochemical and biophysical systems: from enzyme kinetics to epilepsy Raima Larter, Robert Worth and Brent Speelman; 3. Fractal mechanisms in neural control: human heartbeat and gait dynamics in health and disease Chung-Kang Peng, Jeffrey M. Hausdorff and Ary L. Goldberger; 4. Self-organising dynamics in human coordination and perception Mingzhou Ding, Yanqing Chen, J. A. Scott Kelso and Betty Tuller; 5. Signal processing in biochemical reaction networks Adam P. Arkin; Part II. Nonlinear Sensitivity of Biological Systems to Electromagnetic Stimuli: 6. Electrical signal detection and noise in systems with long-range coherence Paul C. Gailey; 7. Oscillatory signals in migrating neutrophils: effects of time-varying chemical and electrical fields Howard R. Petty; 8. Enzyme kinetics and nonlinear biochemical amplification in response to static and oscillating magnetic fields Jan Walleczek and Clemens F. Eichwald; 9. Magnetic field sensitivity in the hippocampus Stefan Engström, Suzanne Bawin and W. Ross Adey; Part III. Stochastic Noise-Induced Dynamics and Transport in Biological Systems: 10. Stochastic resonance: looking forward Frank Moss; 11. Stochastic resonance and small-amplitude signal transduction in voltage-gated ion channels Sergey M. Bezrukov and Igor Vodyanoy; 12. Ratchets, rectifiers and demons: the constructive role of noise in free energy and signal transduction R. Dean Astumian; 13. Cellular transduction of periodic and stochastic energy signals by electroconformational coupling Tian Y. Tsong; Part IV. Nonlinear Control of Biological and Other Excitable Systems: 14. Controlling chaos in dynamical systems Kenneth Showalter; 15. Electromagnetic fields and biological
5. Application of H∞ control theory to power control of a nonlinear reactor model
International Nuclear Information System (INIS)
Suzuki, Katsuo; Shimazaki, Junya; Shinohara, Yoshikuni
1993-01-01
The H∞ control theory is applied to the compensator design of a nonlinear nuclear reactor model, and the results are compared with standard linear quadratic Gaussian (LQG) control. The reactor model is assumed to be provided with a control rod drive system having the compensation of rod position feedback. The nonlinearity of the reactor model exerts a great influence on the stability of the control system, and hence, it is desirable for a power control system of a nuclear reactor to achieve robust stability and to improve the sensitivity of the feedback control system. A computer simulation based on a power control system synthesized by LQG control was performed revealing that the control system has some stationary offset and less stability. Therefore, here, attention is given to the development of a methodology for robust control that can withstand exogenous disturbances and nonlinearity in view of system parameter changes. The developed methodology adopts H∞ control theory in the feedback system and shows interesting features of robustness. The results of the computer simulation indicate that the feedback control system constructed by the developed H∞ compensator possesses sufficient robustness of control on the stability and disturbance attenuation, which are essential for the safe operation of a nuclear reactor
6. Parametric model of servo-hydraulic actuator coupled with a nonlinear system: Experimental validation
Science.gov (United States)
Maghareh, Amin; Silva, Christian E.; Dyke, Shirley J.
2018-05-01
Hydraulic actuators play a key role in experimental structural dynamics. In a previous study, a physics-based model for a servo-hydraulic actuator coupled with a nonlinear physical system was developed. Later, this dynamical model was transformed into controllable canonical form for position tracking control purposes. For this study, a nonlinear device is designed and fabricated to exhibit various nonlinear force-displacement profiles depending on the initial condition and the type of materials used as replaceable coupons. Using this nonlinear system, the controllable canonical dynamical model is experimentally validated for a servo-hydraulic actuator coupled with a nonlinear physical system.
7. Adaptive Optimizing Nonlinear Control Design for an Over-actuated Aircraft Model
NARCIS (Netherlands)
Van Oort, E.R.; Sonneveldt, L.; Chu, Q.P.; Mulder, J.A.
2011-01-01
In this paper nonlinear adaptive flight control laws based on the backstepping approach are proposed which are applicable to over-actuated nonlinear systems. Instead of solving the control allocation exactly, update laws for the desired control effector signals are defined such that they converge to
8. Parametric Identification of Nonlinear Dynamical Systems
Science.gov (United States)
Feeny, Brian
2002-01-01
In this project, we looked at the application of harmonic balancing as a tool for identifying parameters (HBID) in a nonlinear dynamical systems with chaotic responses. The main idea is to balance the harmonics of periodic orbits extracted from measurements of each coordinate during a chaotic response. The periodic orbits are taken to be approximate solutions to the differential equations that model the system, the form of the differential equations being known, but with unknown parameters to be identified. Below we summarize the main points addressed in this work. The details of the work are attached as drafts of papers, and a thesis, in the appendix. Our study involved the following three parts: (1) Application of the harmonic balance to a simulation case in which the differential equation model has known form for its nonlinear terms, in contrast to a differential equation model which has either power series or interpolating functions to represent the nonlinear terms. We chose a pendulum, which has sinusoidal nonlinearities; (2) Application of the harmonic balance to an experimental system with known nonlinear forms. We chose a double pendulum, for which chaotic response were easily generated. Thus we confronted a two-degree-of-freedom system, which brought forth challenging issues; (3) A study of alternative reconstruction methods. The reconstruction of the phase space is necessary for the extraction of periodic orbits from the chaotic responses, which is needed in this work. Also, characterization of a nonlinear system is done in the reconstructed phase space. Such characterizations are needed to compare models with experiments. Finally, some nonlinear prediction methods can be applied in the reconstructed phase space. We developed two reconstruction methods that may be considered if the common method (method of delays) is not applicable.
9. A study of discrete nonlinear systems
International Nuclear Information System (INIS)
Dhillon, H.S.
2001-04-01
An investigation of various spatially discrete time-independent nonlinear models was undertaken. These models are generically applicable to many different physical systems including electron-phonon interactions in solids, magnetic multilayers, layered superconductors and classical lattice systems. To characterise the possible magnetic structures created on magnetic multilayers a model has been formulated and studied. The Euler-Lagrange equation for this model is a discrete version of the Sine-Gordon equation. Solutions of this equation are generated by applying the methods of Chaotic Dynamics - treating the space variable associated with the layer number as a discrete time variable. The states found indicate periodic, quasiperiodic and chaotic structures. Analytic solutions to the discrete nonlinear Schroedinger Equation (DNSE) with cubic nonlinearity are presented in the strong coupling limit. Using these as a starting point, a procedure is developed to determine the wave function and the energy eigenvalue for moderate coupling. The energy eigenvalues of the different structures of the wave function are found to be in excellent agreement with the exact strong coupling result. The solutions to the DNSE indicate commensurate and incommensurate spatial structures associated with different localisation patterns of the wave function. The states which arise may be fractal, periodic, quasiperiodic or chaotic. This work is then extended to solve a first order discrete nonlinear equation. The exact solutions for both the first and second order discrete nonlinear equations with cubic nonlinearity suggests that this method of studying discrete nonlinear equations may be applied to solve discrete equations with any order difference and cubic nonlinearity. (author)
10. Nonlinear observer based phase synchronization of chaotic systems
International Nuclear Information System (INIS)
Meng Juan; Wang Xingyuan
2007-01-01
This Letter analyzes the phase synchronization problem of autonomous chaotic systems. Based on the nonlinear state observer algorithm and the pole placement technique, a phase synchronization scheme is designed. The phase synchronization of a new chaotic system is achieved by using this observer controller. Numerical simulations further demonstrate the effectiveness of the proposed phase synchronization scheme
11. Resonant driving of a nonlinear Hamiltonian system
International Nuclear Information System (INIS)
Palmisano, Carlo; Gervino, Gianpiero; Balma, Massimo; Devona, Dorina; Wimberger, Sandro
2013-01-01
As a proof of principle, we show how a classical nonlinear Hamiltonian system can be driven resonantly over reasonably long times by appropriately shaped pulses. To keep the parameter space reasonably small, we limit ourselves to a driving force which consists of periodic pulses additionally modulated by a sinusoidal function. The main observables are the average increase of kinetic energy and of the action variable (of the non-driven system) with time. Applications of our scheme aim for driving high frequencies of a nonlinear system with a fixed modulation signal.
12. Asymptotic stabilization of nonlinear systems using state feedback
International Nuclear Information System (INIS)
D'Attellis, Carlos
1990-01-01
This paper studies the design of state-feedback controllers for the stabilization of single-input single-output nonlinear systems x = f(x) + g(x)u, y = h(x). Two approaches for the stabilization problem are given; the asymptotic stability is achieved by means of: a) nonlinear state feedback: two nonlinear feedbacks are used; the first separates the system in a controllable linear part and in the zeros-dynamic part. The second feedback generates an asymptotically stable equilibrium on the manifold where this dynamics evolves; b) nonlinear dynamic feedback: conditions are established under which the system can follow the output of a completely controllable bilinear system which uses bounded controls. This fact enables the system to reach, using bounded controls too, a desired output value in finite time. As this value corresponds to a state that lays in the attraction basin of a stable equilibrium with the same output, the system evolves to that point. The two methods are illustrated by examples. (Author) [es
13. Nonlinear Analysis and Intelligent Control of Integrated Vehicle Dynamics
Directory of Open Access Journals (Sweden)
C. Huang
2014-01-01
Full Text Available With increasing and more stringent requirements for advanced vehicle integration, including vehicle dynamics and control, traditional control and optimization strategies may not qualify for many applications. This is because, among other factors, they do not consider the nonlinear characteristics of practical systems. Moreover, the vehicle wheel model has some inadequacies regarding the sideslip angle, road adhesion coefficient, vertical load, and velocity. In this paper, an adaptive neural wheel network is introduced, and the interaction between the lateral and vertical dynamics of the vehicle is analyzed. By means of nonlinear analyses such as the use of a bifurcation diagram and the Lyapunov exponent, the vehicle is shown to exhibit complicated motions with increasing forward speed. Furthermore, electric power steering (EPS and active suspension system (ASS, which are based on intelligent control, are used to reduce the nonlinear effect, and a negotiation algorithm is designed to manage the interdependences and conflicts among handling stability, driving smoothness, and safety. Further, a rapid control prototype was built using the hardware-in-the-loop simulation platform dSPACE and used to conduct a real vehicle test. The results of the test were consistent with those of the simulation, thereby validating the proposed control.
14. A hierarchy of systems of nonlinear equations
International Nuclear Information System (INIS)
Falkensteiner, P.; Grosse, H.
1985-01-01
Imposing isospectral invariance for the one-dimensional Dirac operator yields an infinite hierarchy of systems of chiral invariant nonlinear partial differential equations. The same system is obtained through a Lax pair construction and finally a formulation in terms of Kac-Moody generators is given. (Author)
15. Nonlinear analysis and control of a continuous fermentation process
DEFF Research Database (Denmark)
Szederkényi, G.; Kristensen, Niels Rode; Hangos, K.M
2002-01-01
Different types of nonlinear controllers are designed and compared for a simple continuous bioreactor operating near optimal productivity. This operating point is located close to a fold bifurcation point. Nonlinear analysis of stability, controllability and zero dynamics is used to investigate o...... are recommended for the simple fermenter. Passivity based controllers have been found to be globally stable, not very sensitive to the uncertainties in the reaction rate and controller parameter but they require full nonlinear state feedback....
16. Fault detection for nonlinear systems - A standard problem approach
DEFF Research Database (Denmark)
Stoustrup, Jakob; Niemann, Hans Henrik
1998-01-01
The paper describes a general method for designing (nonlinear) fault detection and isolation (FDI) systems for nonlinear processes. For a rich class of nonlinear systems, a nonlinear FDI system can be designed using convex optimization procedures. The proposed method is a natural extension...
17. A Model Predictive Algorithm for Active Control of Nonlinear Noise Processes
Directory of Open Access Journals (Sweden)
Qi-Zhi Zhang
2005-01-01
Full Text Available In this paper, an improved nonlinear Active Noise Control (ANC system is achieved by introducing an appropriate secondary source. For ANC system to be successfully implemented, the nonlinearity of the primary path and time delay of the secondary path must be overcome. A nonlinear Model Predictive Control (MPC strategy is introduced to deal with the time delay in the secondary path and the nonlinearity in the primary path of the ANC system. An overall online modeling technique is utilized for online secondary path and primary path estimation. The secondary path is estimated using an adaptive FIR filter, and the primary path is estimated using a Neural Network (NN. The two models are connected in parallel with the two paths. In this system, the mutual disturbances between the operation of the nonlinear ANC controller and modeling of the secondary can be greatly reduced. The coefficients of the adaptive FIR filter and weight vector of NN are adjusted online. Computer simulations are carried out to compare the proposed nonlinear MPC method with the nonlinear Filter-x Least Mean Square (FXLMS algorithm. The results showed that the convergence speed of the proposed nonlinear MPC algorithm is faster than that of nonlinear FXLMS algorithm. For testing the robust performance of the proposed nonlinear ANC system, the sudden changes in the secondary path and primary path of the ANC system are considered. Results indicated that the proposed nonlinear ANC system can rapidly track the sudden changes in the acoustic paths of the nonlinear ANC system, and ensure the adaptive algorithm stable when the nonlinear ANC system is time variable.
18. Network science, nonlinear science and infrastructure systems
CERN Document Server
2007-01-01
Network Science, Nonlinear Science and Infrastructure Systems has been written by leading scholars in these areas. Its express purpose is to develop common theoretical underpinnings to better solve modern infrastructural problems. It is felt by many who work in these fields that many modern communication problems, ranging from transportation networks to telecommunications, Internet, supply chains, etc., are fundamentally infrastructure problems. Moreover, these infrastructure problems would benefit greatly from a confluence of theoretical and methodological work done with the areas of Network Science, Dynamical Systems and Nonlinear Science. This book is dedicated to the formulation of infrastructural tools that will better solve these types of infrastructural problems. .
19. Nonlinearity measure and internal model control based linearization in anti-windup design
Energy Technology Data Exchange (ETDEWEB)
Perev, Kamen [Systems and Control Department, Technical University of Sofia, 8 Cl. Ohridski Blvd., 1756 Sofia (Bulgaria)
2013-12-18
This paper considers the problem of internal model control based linearization in anti-windup design. The nonlinearity measure concept is used for quantifying the control system degree of nonlinearity. The linearizing effect of a modified internal model control structure is presented by comparing the nonlinearity measures of the open-loop and closed-loop systems. It is shown that the linearization properties are improved by increasing the control system local feedback gain. However, it is emphasized that at the same time the stability of the system deteriorates. The conflicting goals of stability and linearization are resolved by solving the design problem in different frequency ranges.
20. Nonlinear dynamics of fractional order Duffing system
International Nuclear Information System (INIS)
Li, Zengshan; Chen, Diyi; Zhu, Jianwei; Liu, Yongjian
2015-01-01
In this paper, we analyze the nonlinear dynamics of fractional order Duffing system. First, we present the fractional order Duffing system and the numerical algorithm. Second, nonlinear dynamic behaviors of Duffing system with a fixed fractional order is studied by using bifurcation diagrams, phase portraits, Poincare maps and time domain waveforms. The fractional order Duffing system shows some interesting dynamical behaviors. Third, a series of Duffing systems with different fractional orders are analyzed by using bifurcation diagrams. The impacts of fractional orders on the tendency of dynamical motion, the periodic windows in chaos, the bifurcation points and the distance between the first and the last bifurcation points are respectively studied, in which some basic laws are discovered and summarized. This paper reflects that the integer order system and the fractional order one have close relationship and an integer order system is a special case of fractional order ones. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6900767087936401, "perplexity": 1245.7342823921654}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376825512.37/warc/CC-MAIN-20181214092734-20181214114234-00562.warc.gz"} |
https://www.physicsforums.com/threads/a-problem-on-quadratic-functions.703060/ | 1. Jul 26, 2013
Mabs
1. The problem statement, all variables and given/known data
a) Let f(x) = ax^2+ bx + c; ∀x ∈ ℝ; where a(≠ 0), b and c ∈ ℝ are constants,
(i) Prove that f(k) =(64+(b^2−4ac)^2)/(64a) ; where k = −(b/2a)+(1/a)+(b^2−4ac)/(8a).
(ii) Hence, without using graphs and without using your knowledge on quadratic
functions and equations, prove that (∀x ∈ ℝ f(x) > 0) $\Rightarrow$ (a > 0 and b^2 − 4ac< 0).
2. Relevant equations
3. The attempt at a solution
i have already proven the first part but i m stuck in the 2nd part that says prove from "hence" . otherwise i can show that there exist M in R such that for all x in R ,M<=f(x) and M=inf(f(x)), and there exist x' in R such that f(x')=M, so i can take an argument that x' to be in real and if this happens (a>0 and b^2-4ac<0) ,M>0, so f(x)<0, but on that approach i m not using any above proven things to get my second answer(hence). if any one can help would be great. sorry for my english.
2. Jul 26, 2013
Dods
You want to prove that the statement ∀x ∈ ℝ f(x) > 0) $\Rightarrow$ (a > 0 and b^2 − 4ac< 0) is a true statement. In this paticular case, if I were you I would start by thinking about when/under what conditions this statement isn't true. Do you know when an implication (p implies q) isn't true?
Then I would try to find a contradiction. Are you familiar with proof by contradiction? If not, I would be happy to explain.
This probably isn't the only way to do this, but it's the first solution I thought of and it seems well suited to this problem (I checked that the method works here).
Dods
3. Jul 26, 2013
Mabs
thanks for the reply , p$\Rightarrow$q is false only when the p is true and q is false. the problem I'm having is i cant find a way to say it from using f(k). it just a constant right ?. i cant use it to talk show that for all x f(x) is greater than 0. you mean that I should show the p (for all x f(x)>0 ) implies the negation of (a>0 & b^2-4ac<0) proposition is always false right ?
4. Jul 26, 2013
Dods
I'm sorry, I didn't get the emphasis on "hence"...I just suggested a less convoluted way of proving it (if you take (∀x ∈ ℝ f(x) > 0) to be true and (a > 0 and b^2 − 4ac< 0) to be false you can easily arrive at a contradiction). I'll look at it again, although off the top of my head I don't see a connection to the part you've already proved.
Can you clarify the context here? What sort of level is this book/course? Have you recently covered a method that could be relevant?
I'll try to help as much as I can, however there are plenty of people waaay smarter than me on these forums who might be better able to help, or see something I'm missing.
5. Jul 26, 2013
Mabs
its on Mathematics of Bsc Engineering , level 1. its came up with the real analysis topic of functions.
Draft saved Draft deleted
Similar Discussions: A Problem on quadratic functions | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8471406102180481, "perplexity": 576.3471156951596}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886106367.1/warc/CC-MAIN-20170820092918-20170820112918-00595.warc.gz"} |
http://jsts.org/jsts/XmlViewer/f402210 | Mobile QR Code
1. (Department of Electronic and Electrical Engineering, Pohang University of Science and Technology, Pohang 37673, Korea)
2. (Department of Electrical Engineering, Rämistrasse 101, 8092 Zürich, Switzerland)
3. (Department of Electronic and Electrical Engineering, Pohang University of Science and Technology, Pohang 37673, Korea)
Temperature sensor, subthreshold, bandgap reference
## I. INTRODUCTION
Ultra-low-power (ULP) sensor applications often necessitate a continuous monitoring of temperature sensor. It is not only to obtain the accurate sensor output by calibrating the measurement results but also to compensate strong temperature sensitivity of circuit operation. For a continuous thermal monitoring block to work with a nW-consuming sensor node, the power consumption needs to be even lower, e.g. in sub-nW level. However, extreme reduction of the power consumption eventually faces challenges in using analog circuits which require a nonzero bias current.
On-chip temperature sensing schemes utilize inherent temperature dependence of devices provided in CMOS technology. Key coefficients of complementary-to-absolute-temperature (CTAT) and proportional-to-absolute-temperature (PTAT) can be obtained from CMOS compatible circuits and converted through an analog-to-digital (AD) conversion. Using BJT devices in temperature sensing references the bandgap voltage (V$_{\mathrm{BG}}$) which shows superiority in robustness against process variations (1-5). It is because the temperature coefficients of CTAT and PTAT are well-defined by inherent PN junction characteristic and design parameters, respectively. However, previous works use a high-precision oversampling ADC that dissipates a significant power of ${μ}$W range (1-5). As an alternative, the use of a temperature-dependent frequency generation followed by an edge counting is one of the most popular ways in ULP applications (6-12) since an oscillator circuit can be designed to consume a low power and can be implemented in a small area. This approach suffers from nonlinear die-to-die variations and necessitates a 2-point calibration. In addition, the temperature coefficient of the oscillator frequency is very low and takes a long conversion time for the edge counting. To further reduce power consumption of the on-chip temperature sensor, a leakage-based temperature-sensing circuits was combined with a Nyquist-rate asynchronous successive approximation register (SAR) ADC (13). Though it achieved the lowest power consumption of 490 pW, the minimum temperature resolution given by the 1-b resolution of the ADC is about 0.6 $^{\circ}$C.
This paper presents a ULP temperature sensor based on a leakage-based reference generator (14). A reference divider with a switched-capacitor circuit effectively achieves a finer resolution of SAR ADC. The internal nodes of the reference circuit are directly sampled to be passed to the ADC. It minimizes the use of analog circuits which necessitate bias current. The designed temperature sensor is implemented using 180 nm CMOS process. It achieves a 62.6-pJ/conversion with a resolution of 0.37 $^{\circ}$C. Section II describes circuits of the proposed temperature sensor, and Section III shows implementation results. Section IV concludes this work.
Fig. 1. Overall circuit diagram of the proposed temperature sensor (*SMP : SAMPLE).
## II. CIRCUIT DESCRIPTION
Fig. 1 shows an overall circuit diagram of the proposed temperature sensor. The sensor consists of a bias generator part, a regulator part, an asynchronous SAR ADC, a switched-capacitor (SC) voltage divider and a timing control block with an oscillator. The regulator is formed with a conventional differential amplifier (Fig. 2). Since the bias current, I$_{\mathrm{B}}$, is in a pA level, a large output resistance associated at OUT node causes a pole at a low frequency. However, since AVDD is the supply voltage for ADC, AVDD node is desired to be the dominant pole with a large power-decoupling capacitance connected at AVDD. We connected an off-chip capacitor of 50 nF at AVDD node to make it the dominant pole in the regulator loop.
The bias generator is based on the leakage-based hybrid V$_{\mathrm{BG}}$-V$_{\mathrm{TH}}$ voltage reference (14) which provides a PTAT (V$_{\mathrm{PTAT}}$), a CTAT (V$_{\mathrm{CTAT}}$) and a reference voltage (V$_{\mathrm{REF}}$). The V$_{\mathrm{REF}}$ is divided by half using SC voltage divider. The reduced supply voltage by the SC voltage divider decreases the input conversion range of ADC and effectively achieves a finer temperature resolution. With the 180 nm CMOS process used in this work, the V$_{\mathrm{REF}}$ and the AVDD is about 0.8 V and 0.4 V, respectively. A static voltage divider using resistors should flow a nonzero static current.
Fig. 2. Amplifier circuit in the regulator and DC characteristics.
Fig. 3. (a) SC voltage divider circuit, (b) simulated transients.
The SC voltage divider is formed with three capacitors (Fig. 3(a)). They are two identical capacitors (C$_{1}$) of 2.5~pF and a larger storage capacitor (C$_{2}$) of 10 pF. The voltage division is performed using two phases, a receiving phase (${Φ}$$_{1}) and a transferring phase ({Φ}$$_{2}$). In ${Φ}$$_{1}, the two identical capacitors (C_{1}) are connected in series to sample V_{\mathrm{REF}} while C_{2} is disconnected. In {Φ}$$_{2}$, all the three capacitors are connected in parallel while V$_{\mathrm{REF}}$ is disconnected. Repetition of switching eventually makes C$_{2}$ hold V$_{\mathrm{REF}}$/2. Simulated transients of V$_{\mathrm{HF}}$ and V$_{\mathrm{DIV}}$ are shown in Fig. 3(b). In the steady state, the voltage stored at all the three capacitors approaches V$_{\mathrm{REF}}$/2, and there would be no charge transferring among the capacitors. Since the leakage current (I$_{\mathrm{leak}}$) through off-state switch (Fig. 3(a)) has a strong temperature dependency, the V$_{\mathrm{HF}}$ at high temperature significantly decays by the leakage. We adopted a switch in (15) which minimizes the effect of leakage current.
In addition, frequency for the switching needs to be designed so that the leakage current can be compensated to maintain V$_{\mathrm{REF}}$/2. We employed a leakage-based oscillator as the clock generator (Fig. 4). Designed parameters are summarized in Table 1. Bold characters indicate thick MOSFET. A capacitor of 30 pF is used for C$_{\mathrm{OSC}}$.
## III. MEASUREMENT RESULTS
The proposed temperature sensor is implemented using a standard 180 nm CMOS process. Fig. 5 shows chip microphotograph. The active die area is 0.128 mm$^{2}$. 37 chips are tested in a temperature range of -30~100 $^{\circ}$C. Fig. 6 shows measurements of the internally generated voltages which are V$_{\mathrm{REF}}$, V$_{\mathrm{CTAT}}$ and AVDD. The V$_{\mathrm{PTAT}}$ is calculated by V$_{\mathrm{REF}}$-V$_{\mathrm{CTAT}}$. The V$_{\mathrm{REF}}$ and AVDD are about 0.8 V and 0.4 V, respectively, showing a good agreement with designed levels. Fig. 7 shows digital codes measured from 37 samples. The dynamic range of the temperature-dependent voltage is about 150 mV (see Fig. 6) which corresponds to about 35% of AVDD. Thus, the range of the output code is also about 35% (from 250 to 600) of the total 10-b code range.
Fig. 4. Circuit diagram of oscillator.
Table 1. Design parameters.
Component Parameters Width (μm) Length (μm) Multiplier M$_{\mathrm{N1}}$ 0.42 1.2 1 M$_{1}$ 20 1 7 M$_{2}$ 1 1 1 M$_{\mathbf{PASS}}$ 0.5 0.85 1 M$_{\mathbf{P}}$ 5 5 5* M$_{\mathbf{N}}$ 4 10 5* M$_{\mathbf{B}}$ 1 1 12* M$_{\mathbf{O}}$ 20 1 21 M$_{\mathbf{DIS}}$ 1 0.35 3* Q$_{1}$ 2 2 2
* The number of stacks
Fig. 5. Chip microphotograph.
Fig. 6. Measured internal voltages of bias generator. The V$_{\mathrm{PTAT}}$ is calculated by subtracting V$_{\mathrm{CTAT}}$ from V$_{\mathrm{REF}}$.
Fig. 7. Measured digital code output.
Fig. 8. Error temperature after a 1-point calibration at 40 $^{\circ}$C calculated with the measured bias voltages and an ideal ADC.
Fig. 9. Measured error temperature after a 1-point calibration at 40 $^{\circ}$C.
To exclude imperfections of ADC operation in temperature sensing, error temperatures are calculated from the measured bias voltages (Fig. 6). An ideal ADC is modeled by MATLAB for the calculation. We compared the calculated error with the measured error using the implemented ADC. Fig. 8 and 9 show the calculated and the measured error temperature after a 1-point calibration at 40 $^{\circ}$C, respectively. The two figures indicate an overall good agreement with an increased error of about 1-LSB by ADC nonlinearity. The ADC simulation shows an input-referred comparator noise of about 550 ${μ}$Vrms which corresponds to 1.37-LSB of the ADC with an AVDD of 0.4 V. The capacitor DACs were implemented by a MIM structure with the unit C of 5 fF, indicating a 12-b level matching according to given 0.18~${μ}$m CMOS process documents. Therefore, the inaccuracy of temperature sensing is rather limited by the temperature dependences of the bias voltages than by the linearity performance of ADC.
Fig. 10. Measured error temperature after a 2-point calibration at -10 $^{\circ}$C and 80 $^{\circ}$C.
Fig. 11. Measured oscillator frequency from 37 samples over a temperature range of -30-to-100 $^{\circ}$C.
Fig. 12. Measured RMS resolution (1-${\upsigma}$) after 500 sensor readings from each of 37 samples.
Fig. 13. Measured supply sensitivities when the supply voltage varies from 1 V to 2.2 V.
Fig. 14. Average power consumption of each core block and the energy/conversion.
A 2-point calibration at -10 $^{\circ}$C and 80 $^{\circ}$C reduces the peak-to-peak inaccuracy from -3.43 $^{\circ}$C/+2.77 $^{\circ}$C to -1.63~$^{\circ}$C/+1.63~$^{\circ}$C (Fig. 10). Fig. 11 shows measured frequency of the oscillator. The strong dependence of the oscillator frequency helps suppression of the effect of leakage current on the operation of the SC voltage divider. Fig. 12 shows the RMS resolutions (16) of 500 cases. The RMS resolution refers to the standard deviation of the converted temperature when the test temperature is fixed. The RMS resolution for the whole temperature range is less than 1-LSB, also revealing that the resolution of the sensor is rather limited by the quantized 1-b temperature resolution of 0.37 $^{\circ}$C. Fig. 13 shows measured supply sensitivity at 20 $^{\circ}$C, showing 0.61 $^{\circ}$C/V in a supply range of 1 V-to-2.2 V. By placing a stacked native NMOS transistors at the header of the bias generator, the effect of supply variation is greatly suppressed. Fig. 14 summarizes average power consumption and energy/conversion. The average power consumption at 20~$^{\circ}$C is 487 pW, indicating an energy/conversion of 62.6 pJ. The energy/conversion in the whole temperature range varies from 60 pJ to 110 pJ. Table 2 compares performance with previously reported low-power temperature sensors.
Table 2. Performance comparison
This work [13] [1] [2] [6] [7] [8] Process (nm) 180 180 180 180 65 180 180 Supply Voltage (V) 1.2 1 1.6~2.2 1 0.5, 0.9~1.2+ 0.8 0.6~1.2 Type PNP & MOS NPN & MOS NPN PNP MOS (Gate Leak.) MOS MOS Digital Conversion SAR SAR ΣΔ ΣΔ FDC FDC FDC Supply Sensitivity (°C/V) 0.61 1.073 0.0082 N/A N/A 3.8 1.9 Power (nW) 0.487 0.49 8960 720 0.64 11 3.92 Conversion Time (ms) 128.6 200 213 40 34.3 839 300 Energy/Conversion (nJ) 0.0626 0.098 1908.5 28.8 0.022 9.2 1.2 Temperature Range (°C) -30~100 -10~100 -40~125 0~100 -20~100 -20~80 0~100 Resolution (K) 0.37 0.59 0.00167 0.04 0.25 0.145 0.55 Calibration 1-point 2-point 1-point 1-point 1-point 2-point 2-point 2-point Inaccuracy (°C) -3.43/2.77* (37 smps) ±1.63* (37 smps) ±2.35* (15 smps) ±0.13** (16 smps) ±0.18** (15 smps) -2.7/1.8* (7 smps) -0.9/1.2* (9 smps) -1.64/0.67* (3 smps) Area (mm$^{2}$) 0.1278 0.12 0.35 0.18 0.013 0.074 0.007 FoM$_1$ (pJK$^{2}$)# 8.57 34.1 5.32 46.08 1.4 193.4 363 FoM$_2$ (nJ°C$^{2}$)## 0.74 0.17 0.54 32.25 0.93 0.16 13.25 3.23
+ : two supply voltages
* : peak-to-peak inaccuracy
** : 3σ inaccuracy
# : FoM$_{1}$ = energy/conversion ${\times}$ (resolution)$^{2}$
## FoM$_{2}$ = energy/conversion ${\times}$ (max inaccuracy)$^{2}$
## IV. CONCLUSIONS
This work proposes a leakage-based temperature sensor with a SC voltage divider. The temperature sensor consists of a temperature sensing part and an asynchronous SAR ADC. The SC voltage divider performs a division of V$_{\mathrm{REF}}$ by half to provide supply voltage for ADC. It effectively achieves a finer temperature resolution with given ADC. The proposed temperature sensor chip is fabricated in an active area of 0.1278 mm$^{2}$ using 180 nm CMOS technology. The implemented sensor consumes 487 pW with an energy/conversion of 62.6 pJ. The proposed work minimally dissipates standby power for analog circuits and is promising for ULP sensor applications which necessitate continuous thermal monitoring.
### REFERENCES
1
Kumar Rushil K., Nov 2019, An Energy-Efficient BJT-Based Temperature-to-Digital Converter with ±0.13ºC (3σ) Inaccuracy from -40 to 125ºC, IEEE ASSCC, pp. 107-108
2
Zhan Tan-Tan, Apr 2018, Nano-Watt Class Energy-Efficient Capacitive Sensor Interface With On-Chip Temperature Drift Compensation, IEEE Sensors Journal, Vol. 18, No. 7, pp. 2870-2882
3
Tang Zhong, Nov 2018, A CMOS Temperature Sensor With Versatile Readout Scheme and High Accuracy for Multi-Sensor Systems, IEEE Trans. Circuits Syst. I, Vol. 65, No. 11, pp. 3821-3829
4
Yousefzadeh B., Jun 2016, A BJT-based Temperature-to-Digital Converter with ±60mK (3σ) Inaccuracy from -70ºC to 125ºC in 160nm CMOS, IEEE Symp. VLSI Circuits
5
Oshita Takao, Mar 2015, Compact BJT-Based Thermal Sensor for Processor Applications in a 14nm tri-Gate CMOS Process, IEEE JSSC, Vol. 50, No. 3, pp. 799-807
6
Truesdell Daniel S., Apr 2019, A 640pW 22pJ/Sample Gate Leakage-Based Digital CMOS Temperature Sensor with 0.25ºC Resolution, CICC, pp. 1-4
7
Someya Teruki, Mar 2019, An 11-nW CMOS Temperature-to-Digital Converter Utilizing Sub-Threshold Current at Sub-Thermal Drain Voltage, IEEE JSSC, Vol. 54, No. 2, pp. 613-622
8
Ku Chia-Yuan, Oct 2019, A Voltage-Scalable Low-Power All-Digital Temperature Sensor for On-Chip Thermal Monitoring, IEEE Trans. Circuits Syst. II, Vol. 66, No. 10, pp. 1658-1662
9
Y. K., Feb 2017, A 0.6nJ -0.22/0.19ºC Inaccuracy Temperature Sensor Using Exponential Subthreshold Oscillation Dependence, IEEE ISSCC, pp. 160-162
10
Anand Tejasvi, Jun 2015, A Self-referenced VCO-based Temperature Sensor with 0.034ºC/mV Supply Sensitivity in 65nm CMOS, IEEE Symp. VLSI Circuits
11
Islam A. K. M. Mahfuzul, Nov 2015, Wide-Supply-Range All-Digital Leakage Variation Sensor for On-Chip Process and Temperature Monitoring, IEEE JSSC, Vol. 50, No. 11, pp. 2475-2490
12
Jeong Seokhyeon, Aug 2014, A Fully-Integrated 71nW CMOS Temperature Sensor for Low Power Wireless Sensor Nodes, IEEE Journal of Solid-State Circuits, Vol. 49, No. 8, pp. 1682-1693
13
Tang Zhong, Nov 2018, A CMOS Temperature Sensor With Versatile Readout Scheme and High Accuracy for Multi-Sensor Systems, IEEE Trans. Circuits Syst. I, Vol. 65, No. 11, pp. 3821-3829
14
Ji Youngwoo, Feb 2019, A 192pW Hybrid Bandgap-Vth Reference with Process Dependence Compensated by a Dimension-Induced Side-Effect, in IEEE Int. Solid-State Circuits Conf. (ISSCC), pp. 308-310
15
Ishida K., Arl 2006, Managing Subthreshold Leakage in Charge-Based Analog Circuits With Low-VTH Transistors by Analog T- Switch (AT-Switch) and Super Cut-off CMOS (SCCMOS), IEEE JSSC, Vol. 41, No. 4, pp. 859-867
16
Makinwa K.A.A., Delft Tu, Smart Temperature Sensor Survey, Rev. 04022020, Arl. 2020. Accessed on Dec. 24, 2020. https://ei.tudelft.nl/smart_temperature/
## Author
##### Bumjin Park
Bumjin Park received the B.S. and M.S. degrees in Electronic and Electrical Engineering from Pohang University of Science and Technology, South Korea, in 2014, and 2016, respectively.
He is currently pursuing the Ph.D. degree in the Department of Electronic and Electrical Engineering from Pohang University of Science and Technology (POSTECH), Korea.
His interests include and ultra-low-power sensor interface circuits
##### Youngwoo Ji
Youngwoo Ji received the B.S. and Ph.D. degrees in electronic and electrical engineering from the Pohang University of Science and Technology (POSTECH), Pohang, South Korea, in 2013 and 2020, respectively.
He is currently a Post-Doctoral Researcher with the Integrated Systems Laboratory, ETH Zürich, Zürich, Switzerland.
His research interests include subthreshold circuit designs, sensor interface circuits, and data converters.
##### Jae-Yoon Sim
Jae-Yoon Sim received the B.S., M.S., and Ph.D. degrees in electronic and electrical engineering from the Pohang University of Science and Technology (POSTECH), South Korea, in 1993, 1995, and 1999, respectively.,
From 1999 to 2005, he was a Senior Engineer with Samsung Electronics, South Korea.
From 2003 to 2005, he was a Postdoctoral Researcher with the University of Southern California, Los Angeles.
From 2011 to 2012, he was a Visiting Scholar with the University of Michigan, Ann Arbor.
In 2005, he joined the Department of Electrical Engineering, POSTECH, where he is currently a Professor.
His research interests include serial and parallel links, PLLs, data converters, ultra-low-power sensor circuits, and power module for plasma generation.
Dr. Sim received the Special Author-Recognition Award at ISSCC 2013 and was a co-recipient of the Takuo Sugano Award at ISSCC 2001.
He has served on the Technical Program Committee of the IEEE International Solid-State Circuits Conference (ISSCC), the Symposium on VLSI Circuits, and the Asian Solid-State Circuits Conference (ASSCC). | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5279847383499146, "perplexity": 5749.4877590585265}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038863420.65/warc/CC-MAIN-20210419015157-20210419045157-00628.warc.gz"} |
https://www.fuzzingbook.org/html/LangFuzzer.html | # Fuzzing with Input Fragments¶
In this chapter, we introduce how to combine parsing and fuzzing. This allows to mutate existing inputs while preserving syntactical correctness, and to reuse fragments from existing inputs while generating new ones. The combination of parsing and fuzzing, as demonstrated in this chapter, has been highly successful in practice: The LangFuzz fuzzer for JavaScript has found more than 2,600 bugs in JavaScript interpreters this way.
Prerequisites
import fuzzingbook_utils
from Parser import PEGParser
from GrammarFuzzer import GrammarFuzzer
## Recombining Parsed Inputs¶
Recombining parsed inputs was pioneered by Langfuzz [Holler et al, 2012.]. The main challenge is that program inputs often carry additional constraints beyond what is described by the syntax. For example, in Java, one needs to declare a variable (using a specific format for declaration) before it can be used in an expression. This restriction is not captured in the Java CFG. Checking for type correctness is another example for additional restrictions carried by program definitions.
When fuzzing compilers and interpreters, naive generation of programs using the language CFG often fails to achieve significant deeper coverage due to these kinds of checks external to the grammar. Holler et al. suggests using pre-existing valid code fragments to get around these restrictions. The idea is that the pre-existing valid code fragments already conform to the restrictions external to the grammar, and can often provide a means to evade validity checks.
### A Grammar-based Mutational Fuzzer¶
The idea is that one can treat the derivation tree of a preexisting program as the scaffolding, poke holes in it, and patch it with generated inputs from our grammar. Given below is a grammar for a language that allows assignment of variables.
import string
from Grammars import crange, syntax_diagram
VAR_GRAMMAR = {
'<start>': ['<statements>'],
'<statements>': ['<statement>;<statements>', '<statement>'],
'<statement>': ['<assignment>'],
'<assignment>': ['<identifier>=<expr>'],
'<identifier>': ['<word>'],
'<word>': ['<alpha><word>', '<alpha>'],
'<alpha>': list(string.ascii_letters),
'<expr>': ['<term>+<expr>', '<term>-<expr>', '<term>'],
'<term>': ['<factor>*<term>', '<factor>/<term>', '<factor>'],
'<factor>':
['+<factor>', '-<factor>', '(<expr>)', '<identifier>', '<number>'],
'<number>': ['<integer>.<integer>', '<integer>'],
'<integer>': ['<digit><integer>', '<digit>'],
'<digit>': crange('0', '9')
}
syntax_diagram(VAR_GRAMMAR)
start
statements
statement
assignment
identifier
word
alpha
expr
term
factor
number
integer
digit
Let us use our new grammar to parse a program.
mystring = 'va=10;vb=20'
def hl_predicate(_d, _n, symbol, _a): return symbol in {
'<number>', '<identifier>'}
from Parser import PEGParser, highlight_node
from GrammarFuzzer import display_tree
parser = PEGParser(VAR_GRAMMAR)
for tree in parser.parse(mystring):
display_tree(tree, node_attr=highlight_node(hl_predicate))
As can be seen from the above example, our grammar is rather detailed. So we need to define our token nodes, which correspond to the red nodes above.
VAR_TOKENS = {'<number>', '<identifier>'}
These tokens are pruned using the prune_tree method that we mentioned previously. Here is a slightly more complex program to parse, but with the tree pruned using tokens:
mystring = 'avar=1.3;bvar=avar-3*(4+300)'
parser = PEGParser(VAR_GRAMMAR, tokens=VAR_TOKENS)
for tree in parser.parse(mystring):
display_tree(tree, node_attr=highlight_node(hl_predicate))
We develop a LangFuzzer class that generates recombined inputs. To apply the Langfuzz approach, we need a few parsed strings.
mystrings = [
'abc=12+(3+3.3)',
'a=1;b=2;c=a+b',
'avar=1.3;bvar=avar-3*(4+300)',
'a=1.3;b=a-1*(4+3+(2/a))',
'a=10;b=20;c=34;d=-b+(b*b-4*a*c)/(2*a)',
'x=10;y=20;z=(x+y)*(x-y)',
'x=23;y=51;z=x*x-y*y',
]
We recurse through any given tree, collecting parsed fragments corresponding to each nonterminal. Further, we also name each node so that we can address each node separately.
from Fuzzer import Fuzzer
class LangFuzzer(Fuzzer):
def __init__(self, parser):
self.parser = parser
self.fragments = {k: [] for k in self.parser.cgrammar}
def traverse_tree(self, node):
counter = 1
nodes = {}
def helper(node, id):
nonlocal counter
name, children = node
new_children = []
nodes[id] = node
for child in children:
counter += 1
new_children.append(helper(child, counter))
return name, new_children, id
return helper(node, counter), nodes
def fragment(self, strings):
self.trees = []
for string in strings:
for tree in self.parser.parse(string):
tree, nodes = self.traverse_tree(tree)
self.trees.append((tree, nodes))
for node in nodes:
symbol = nodes[node][0]
if symbol in self.fragments:
self.fragments[symbol].append(nodes[node])
return self.fragments
We thus obtain all valid fragments from our parsed strings.
lf = LangFuzzer(PEGParser(VAR_GRAMMAR, tokens=VAR_TOKENS))
fragments = lf.fragment(mystrings)
for key in fragments:
print("%s: %d" % (key, len(fragments[key])))
<start>: 7
<statements>: 18
<statement>: 18
<assignment>: 18
<identifier>: 37
<word>: 0
<alpha>: 0
<expr>: 39
<term>: 50
<factor>: 51
<number>: 23
<integer>: 0
<digit>: 0
All that remains is to actually find a place to poke a hole using candidate(), and patch that hole using generate_new_tree(). We will explain how to do this next.
But before that, we update our initialization method with a call to fragment().
import random
class LangFuzzer(LangFuzzer):
def __init__(self, parser, strings):
self.parser = parser
self.fragments = {k: [] for k in self.parser.cgrammar}
self.fragment(strings)
#### Candidate¶
LangFuzzer accepts a list of strings, which are stored as derivation trees in the object.
The method candidate() chooses one of the derivation trees randomly as the template, and identifies a node such that it can be replaced by another node that is different from itself. That is, it chooses a node such that, if the non-terminal name of the node is node_type, there is at least one other entry in fragment[node_type])
class LangFuzzer(LangFuzzer):
def candidate(self):
tree, nodes = random.choice(self.trees)
interesting_nodes = [
n for n in nodes if nodes[n][0] in self.fragments
and len(self.fragments[nodes[n][0]]) > 1
]
node = random.choice(interesting_nodes)
return tree, node
Here is how it is used -- the red node is the node chosen.
random.seed(1)
lf = LangFuzzer(PEGParser(VAR_GRAMMAR, tokens=VAR_TOKENS), mystrings)
tree, node = lf.candidate()
def hl_predicate(_d, nid, _s, _a): return nid in {node}
display_tree(tree, node_attr=highlight_node(hl_predicate))
#### Generate New Tree¶
Once we have identified the node, one can generate a new tree by replacing that node with another node of similar type from our fragment pool.
class LangFuzzer(LangFuzzer):
def generate_new_tree(self, node, choice):
name, children, id = node
if id == choice:
return random.choice(self.fragments[name])
else:
return (name, [self.generate_new_tree(c, choice)
for c in children])
Again, the red node indicates where the replacement has occurred.
random.seed(1)
lf = LangFuzzer(PEGParser(VAR_GRAMMAR, tokens=VAR_TOKENS), mystrings)
tree, node = lf.candidate()
def hl_predicate(_d, nid, _s, _a): return nid in {node}
from GrammarFuzzer import tree_to_string
new_tree = lf.generate_new_tree(tree, node)
for s in [tree_to_string(i) for i in [tree, new_tree]]:
print(s)
display_tree(new_tree, node_attr=highlight_node(hl_predicate))
a=1;b=2;c=a+b
a=1;b=2;b=2
#### Fuzz¶
The fuzz() method simply calls the procedures defined before in order.
class LangFuzzer(LangFuzzer):
def fuzz(self):
tree, node = self.candidate()
modified = self.generate_new_tree(tree, node)
return tree_to_string(modified)
Here is our fuzzer in action.
lf = LangFuzzer(PEGParser(VAR_GRAMMAR, tokens=VAR_TOKENS), mystrings)
for i in range(10):
print(lf.fuzz())
x=23;bvar=avar-3*(4+300)
x=23;y=51;z=x*x-(x+y)*(x-y)
x=10;y=20;z=(1.3)*(x-y)
abc=12+(12+3.3)
x=23;y=51;z=y*x-y*y
a=10;b=20;c=34;d=-b+(b*b-4*y)/(2*a)
abc=12+((4+3+(2/a))+3.3)
x=10;y=20;z=(x+y)*(x-y)
abc=12+(3+3.3)
x=10;y=20;z=(x+y)*(x-y)
How effective was our fuzzing? Let us find out!
from Timer import Timer
trials = 100
lf = LangFuzzer(PEGParser(VAR_GRAMMAR, tokens=VAR_TOKENS), mystrings)
valid = []
time = 0
for i in range(trials):
with Timer() as t:
s = lf.fuzz()
try:
exec(s, {}, {})
valid.append((s, t.elapsed_time()))
except:
pass
time += t.elapsed_time()
print("%d valid strings, that is LangFuzzer generated %f%% valid entries" %
(len(valid), len(valid) * 100.0 / trials))
print("Total time of %f seconds" % time)
61 valid strings, that is LangFuzzer generated 61.000000% valid entries
Total time of 0.011114 seconds
gf = GrammarFuzzer(VAR_GRAMMAR)
valid = []
time = 0
for i in range(trials):
with Timer() as t:
s = gf.fuzz()
try:
exec(s, {}, {})
valid.append(s)
except:
pass
time += t.elapsed_time()
print("%d valid strings, that is GrammarFuzzer generated %f%% valid entries" %
(len(valid), len(valid) * 100.0 / trials))
print("Total time of %f seconds" % time)
4 valid strings, that is GrammarFuzzer generated 4.000000% valid entries
Total time of 1.366280 seconds
That is, our LangFuzzer is rather effective on generating valid entries when compared to the GrammarFuzzer.
## Grammar-Based Mutation¶
General idea: Take a derivation tree and a matching grammar; apply a random mutation.
from Grammars import EXPR_GRAMMAR
from GrammarFuzzer import display_tree
from Parser import EarleyParser
parser = EarleyParser(EXPR_GRAMMAR)
tree,*_ = parser.parse("1 + 2 * 3")
display_tree(tree)
1. Pick any node in the tree
2. Produce a new expansion.
We have seen this for LangFuzzer already, right?
How about we factor this out (from the Parser notebook), and have two notebook on mutational (and genetic fuzzing):
1. LangFuzzer – a chapter on
• Mutating trees (randomly)
• Mutating trees from a given population (the LangFuzz approach)
• Tree recombination (and crossover)
2. EvoGrammarFuzzer – a chapter on
• Genetic improvement (using coverage only)
• Genetic improvement (using a fitness function from search-based fuzzing)
def mutate_tree(tree, grammar):
pass
## Lessons Learned¶
• We can generate a pool of fragments using the LangFuzz approach, and use it to generate nearly valid strings.
## Next Steps¶
• In the chapter on evolutionary fuzzing, we discuss how to systematically evolve a population of inputs through mutation and crossover operations (as discussed in this chapter) to achieve a specific goal such as code coverage.
## Background¶
Recombining parsed inputs was pioneered by Langfuzz [Holler et al, 2012.], which also gave its name to the main class of this chapter.
## Exercises¶
### Exercise 1: A Different LangFuzzer¶
Sometimes we do not want to use our pool of strings for various reasons – the number of items in the pool may be inadequate, or not varied enough. Extend the LangFuzzer to use a separate function to check if the number of items in the pool corresponding to the selected non-terminal is large enough (say greater than 10), and if not, use the tree expansion technique from GrammarFuzzer` to patch the hole. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.341887503862381, "perplexity": 12390.29657510978}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578721441.77/warc/CC-MAIN-20190425114058-20190425140058-00479.warc.gz"} |
https://chemistry.stackexchange.com/questions/73198/why-is-ots-a-good-leaving-group-and-how-does-it-work | Why is OTs a good leaving group and how does it work?
I've been told that $\ce{OTs}$ is a good leaving group for substitution reactions, but I'm not sure how it works or why it is a good leaving group. Can someone please explain?
$\ce{Ts}$ comes from Toluenesulfonyl chloride, and when the $\ce{Ts-}$ ion replaces and H in an alcohol, it becomes an $\ce{OTs}$ group.
Tosylate groups ($\ce{CH3C6H4SO3-}$) are good leaving groups because their conjugate base forms are quite stabilized by resonance: | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6570507287979126, "perplexity": 1428.2615826575998}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195530385.82/warc/CC-MAIN-20190724041048-20190724063048-00120.warc.gz"} |
https://ai.stackexchange.com/questions/15752/will-quantum-computing-have-any-kind-of-effect-on-the-development-of-ai | # Will quantum computing have any kind of effect on the development of AI? [duplicate]
Recently, according to some reports Google achieved something called 'Quantum Supremacy'. Whether its true or not remains to be seen.
But my question is does Quantum Computers or the principle they work on has any effect on AI. We know that according to Shor's Algorithm Quantum Computing can reduce the complexity of breaking an encryption from $$O(2^n)$$ to $$O(2^{\frac{n}{2}})$$ (not sure).
So similar to this, will Quantum computing have any kind of effect in accelerating AI training or something similar?
## Preface
"Before answering this question, let me preface by stating that the following is simply MY answer as a Machine Learning Researcher and "Hobbyist" Theoretical Physicist, although I have strong feelings that my answer will most certainly be proven as true, I am more than sure that others will have differing opinions as with everything else in this world!" ~ Me
That being said, I would say that the answer to your question, is unequivocally YES! I could write a short book on the subject (that might be a good idea actually) but I will keep this response brief, although I am happy to answer any further questions your may have to which I possess the answers in the comments!
The primary reasons that I believe the newly blossoming field of Quantum Computation will have a massive impact on the field of Machine Learning in general, are as follows:
1. The most simple reason for my belief is that the primary goal of Machine Learning, is to create an entity which is capable of coherent, self-aware thought much like we exhibit as human beings. We know that the brain is what allows us to be capable of such feats, and thus I view the field something like brain counterfeiting. Without going into esoteric detail, there are many subtleties of the brain's workings which are thought to be quantum mechanical in operation, and thus would suggest that the path of least resistance to replicating the system would require a quantum mechanical computational medium.
2. The second primary rationale which solidifies my position, is the point which you briefly touched upon by stating that,
"We know that according to Shor's Algorithm Quantum Computing can reduce the complexity > of breaking an encryption from O(2n) to O(2n2) (not sure)."
This is primarily due to the quantum phenomena referred to as Super Position, which allows for a multiple qubit gate to not only work with the options of 00, 01, 10 and 11 (assuming a two qubit gate) but to also work with any combination in-between, during the computation. Although when the result is obtained (this is what is referred to as collapsing the wave function) you will only still have a resulting state space with 2^n possibilities, where n is the number of qubits. This being said, there are very clever ways, by which one can design their algorithms to make full use of this technically infinite computational space before observing the final results.
## Conclusion
I hope that my answer is helpful to you in some way, although I am aware that it is not a very in-depth answer, I feel that it hits the primary reasons why my personal belief is that there will be a wall which is hit, in the pursuit of a general AI, while we are limited to classical computation faculties; and thus will require quantum based computation before we are able to truly mimic the brain's most well kept secrets! The next couple decades should be VERY interesting in the fields, keep a close eye on the latest happenings! | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 2, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6754682660102844, "perplexity": 460.85052486747117}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154089.6/warc/CC-MAIN-20210731105716-20210731135716-00025.warc.gz"} |
http://www.wowinterface.com/downloads/fileinfo.php?id=8533&so=&page=119 | (1 MB)
Updated: 10-07-13 11:09 AM
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File Info
Compatibility: Siege of Orgrimmar (5.4)Escalation (5.3)Thunder Isle (5.2)Landfall (5.1)Mists of Pandaria (5.0.4) Updated: 10-07-13 11:09 AM Created: unknown Downloads: 203,026 Favorites: 1,919 MD5:
5.4
Altoholic
Version: 5.4.004
by: Thaoky [More]
Hi, my name is Thaoky, and I'm an Altoholic
Altoholic is an Ace 3 addon written for people who dedicate most of their time to leveling alts, and who want to have as much information as possible in one addon. The main feature of the addon is the search functionality which allows users to search their alts' bags or loot tables in an Auction-House-like frame (see screenshots). All this with multiple-realms/accounts support.
Paypal donations accepted at : thaoky.altoholic@yahoo.com
I've been playing WoW since the European release, and I used to rely on addons like character viewer to check my alts' inventory, but since it was more or less abandoned and not always stable for me, I decided to write an addon myself and to improve the search feature as much as I could. I hope you'll enjoy it as much as I do
The addon has been in development since December 2007 and was officially released in late March 2008. It's still not final, and although it has considerably evolved since the initial release, there are still a lot of things I haven't had time to implement yet.
Please note that this is my first addon, and that English is not my native language.
Features:
- Languages supported: enUS, frFR, deDE, esES, ruRU, zhCN & zhTW.
- Account-wide data summary:
• Characters' talents: Full talent trees & glyphs are supported for both specializations.
• Money, /played, rest xp for each character, subtotals by realm, and grandtotals for the account.
• Bag usage: see at a glance which characters should get bigger bags (bag size, free slots and types included)
• Characters' skills: skill summary on one screen, namely the 2 main professions + the 3 secondary skills as well as riding. I may add more if there's demand. Profession cooldowns included.
• Reputations: a list of all the reputations of the current realm's characters. You can see at a glance if all your alts are at least honored with Honor Hold if you want to get the new 2.4 blue PVP set. Suggestions on how to gring reputations will be available soon.
- View containers (bags, bank, keyring) of all alts, on all realms.
- Guild banks : You have 10 alts in 10 different guilds on the same server, all of them with access to a guild bank ? Not a problem, you can see them all here.
- E-mail: allows you to see which alts have mail without having to reconnect them. The addon will tell you when mail is about to expire on a character. Threshold configurable (up to 15 days). Multiple realm support as well. Mails sent to a known alt (one you've logged on at least once) will be visible in the addon without having to reconnect it.
- Equipment: See the equipment of the current realm's alts in one screen. Very useful when purchasing stuff for your alts at the AH. Multiple realms supported. Right-clicking any equipment piece will allow you to find an upgrade, this feature is similar to the official wow armory feature, and is quite performant, even though it doesn't match the accuracy of the official one.
- Search: the most important feature of the addon, it uses an AH-like frame to display search results. You can either search bags on the current realm, on all realms, or a loot table.
The loot table is a table based on AtlasLoot, but which contains only item id's, and therefore keeps memory usage minimal.
The Search menu allows you to find items based on their name (even partial), level, type or rarity, almost like at the AH. It is also possible to search known recipes.
- Quest Log: See the quest logs of all your alts, as well as an indication of which alts are on a specific quest. Clicking on a quest link in the chat log will tell you which alts are on that quest.
- Suggestions: Currently, only profession leveling suggestions are available when mousing over your current level in a specific profession. Suggestions are based on the leveling guides posted on the official US forums (credit goes to their respective authors). The addon also suggests you where to quest/grind xp depending on your character level.
Suggestions were also added for the most recent factions. More to come later.
- Auction house: You can see which auctions/bids you've placed with an alt without being logged in or being at the AH.
- Professions: You can browse all known recipes in a thotbot like frame (see screenshot).
- Mounts & Pets of all your alts.
- Achievements are tracked for all you alts (see screenshot).
- Guild Members: a list of your connected guildmates, along with their alts (if they're using Altoholic too), and their average item level. Clicking their AiL will also allow you to "remotely" inspect their equipment.
- Guild Skills: a list of altoholic users in your guild, along with their alts and direct profession links. All professions are available in one click.
- Guild Bank tabs: a list of altoholic users and the time at which they last visited the guild bank. If you haven't visited the guild bank for a few days, you can remotely update your local data without going to a capital city.
FAQ
The FAQ has been moved here : http://www.wowinterface.com/portal.php?id=372&a=faq
Credits
- I'd like to thank my guild, Odysseüs on EU-Marécages de Zangar, for assisting me since the earliest phases, thanks guys for everything you've done
- Thanks to the wowace community, you've been very helpful and this addon would not be there without the technical answers you gave me (especially Xinhuan, author of BankItems)
- Thanks to all the guys who are behind AtlasLoot, keeping the loot table up-to-date is a tremendous work, and the search functionality of Altoholic would not be what it is without your hard work.
- Thanks to Ayindi (wowace) & sLiz3r (curse) for the German translation.
- Thanks to NightOwl (wowace) for the zhTW translation.
- Thanks to Wang (wowace) for the zhCN translation.
- Thanks to Hellbot for the ruRU translation.
- Thanks to Laumac for the frFR translation.
- Thanks to IrregularByte for the esES translation.
- Brykrys for the LinkWrangler support.
Join the #altoholic IRC channel on Freenode : irc://irc.freenode.net:6667/
IMPORTANT NOTE: If you're upgrading from 4.x :
- Make sure you delete the addon's databases in SavedVariables. ie: Altoholic.lua and all DataStore*.lua.
- Make sure to delete the old addon directories (Altoholic & all DataStore modules) as many files have changed/moved. A patch like this one is always a good opportunity for a fresh install.
5.4.004 (07/10/2013)
- Fixed showing the item source for crafts in the tooltip.
- Fixed LibCraftInfo.
5.4.003 (06/10/2013)
- Created and added support for 3 new libraries : LibCraftInfo, LibCraftLevels, LibCraftReagents.
These libraries intend to replace the lost functionality caused by tables reset to zero in LibPeriodicTable.
I now have my own dataminer, so these tables should be easier to maintain when a patch hits.
I also cleaned up some hard coded tables to now use the libraries instead.
Overall, the addon now consumes a little bit more memory, but the data sources are way more complete than before.
- Replaced the internal list of recipes by LibCraftInfo.
- Fixed the Characters -> Profession pane no longer showing reagents due to LPT changes.
- Fixed the Grids -> Tradeskills pane no longer correct due to LPT changes.
5.4.002 (17/09/2013)
- Fixed profession levels reported as 0.
5.4.001 (11/09/2013)
- Removed a call to GetArenaTeam in DataStore_Stats.
5.3.003 (01/08/2013)
- Added missing reputations (Thanks Daovan !)
- The source of an item is no longer read/displayed in the tooltip if combat lockdown is active.
- Fixed a risk of profile reset when DataStore_Agenda is disabled.
- Updated glyphs (Thanks Zartsoft)
- Implemented RGriedel's fix for profession cooldown, hopefully they should be correct for both US & EU now (Thanks RGriedel!)
- Fixed a tainting issue in DataStore_Talents. (Thanks Warloxx!)
5.3.002 (29/05/2013)
- Fixed skill levels reported as 0.
Note: The problems does not fix itself with this new version. To fully fix it, you need to populate the database with new profession links.
To do this, log all your alts one by one, open their tradeskills, and ONLY THEN, open the skills pane in Altoholic to see that this character's
skill levels are ok. If not, it is merely a refresh issue.
As I said, the problem comes from the format of the profession links which has been changed by Blizzard, reload the whole thing, and you will be fine.
5.3.001 (28/05/2013)
- Fixed recipe colors at the Auction House (Thanks Elandril !).
- Fixed a lua error when DataStore_Agenda is disabled.
- Fixed profession cooldowns warnings, they are now hardcoded at 3 am (the game sometimes still returns midnight).
- Added a total AiL per realm in the account summary.
5.2.001 (12/03/2013)
- Added new pane in the 'Grids' tab to track dailies across all alts. Dailies are stored in DataStore_Quests and reset at 3am.
- Fixed a bug while scanning reputations (Thanks Sylvannis !).
- Fixed a Lua error in the tabards pane.
- Added a safeguard to prevent tooltip errors when mousing over a recipe, this seems to be caused by other tooltip addons/libs.
- Added the Mantid archaeology race.
- Fixed scanning quest history.
Note: I have tried to look into an issue where profession cooldowns are announced at the wrong time, mostly for people playing on US realms.
Unfortunately, I could not make any solid tests (UK realms return me the same realm time as other EU realms .. weird).
Places to check in the code:
Altoholic\Events.lua: as of line 427
DataStore_Agenda\DataStore_Agenda.lua: look at how I set the variable clientServerTimeGap, see if results are consistent.
5.1.002 (24/02/2013)
- Updated both Achievements & Grids tab to show 11 characters per realm.
- Support for tabards is back.
5.1.001 (29/11/2012)
- Fixed 5.0.003 archive, DataStore_Achievements was missing.
- Fixed .Toc files not updated for 5.1 in previous release.
5.0.003 (28/11/2012)
- Re-fixed searching for heirlooms (Thanks JCinDE !).
- Scanning tabards is temporarily disabled, as it triggers an error I cannot fix right now.
5.0.002 (06/10/2012)
- Integrated the Void Storage to the container's UI (Characters -> Containers).
- Added Mists of Pandaria factions (Grids -> Reputations).
- Added Mists of Pandaria archaeology artefacts (Grids -> Archaeology).
- Added Mists of Pandaria crafts for each professions (Grids -> Tradeskills).
- Fixed a few Lua errors related to Battle Pets. They are temporarily NOT scanned at the Auction House.
Some features related to Battle Pets are now fully working, this is on my (neverending) to-do-list.
5.0.001d (13/09/2012)
- Fixed tooltips sometime being incorrect in Grids -> reputations & currencies.
- Fixed potential tainting issues due to the usage of the underscore in the code.
- Cleared a few source files that were no longer used.
- Fixed scanning of partially completed achievements.
- Fixed Lua errors that appeared in 5.0.5 due to a wrong spell ID for fishing.
Achievements partially completed on one alt. They will now appear a bit differently in the UI (especially when part of a series).
This is due to the values the game is returning.
Sometimes, the results may seem weird, BUT THERE IS NOTHING I CAN DO TO FIX THAT !
It also makes no sense for me that some achievements in a series are character based, while some others are account based.
Ex: 100 HK is character based, but 25000 HK is account based ?
If you too think there is a problem here, then complain about it to Blizzard, as I will not write code to work around those inconsistencies.
5.0.001c (03/09/2012)
- Fixed tooltip showing "No data" for herbalism in the Skills pane.. for good this time !
- Fixed a Lua error when scanning glyphs.. for good this time too ! (Thanks Sylvannis)
- Fixed a Lua error when clicking on glyphs, blaming DataStore_Crafts and/or DataStore_Achievements.
- Note: About pets & mounts. I know that they are now account wide, but I will leave things as they are for a little while, that is at least until the expansion launches.
I want to see how things actually turn out to see what has value or not, or what could be modified to remain useful.
5.0.001b (02/09/2012)
- Fixed a Lua error when trying to scan glyphs on a low level character.
- Fixed a Lua error when scanning Inscription.
- Fixed invalid profession spell id's for Fishing & Herbalism.
- Fixed version number in .TOC
- Fixed a Lua error when mousing over a specific cell in the guild members pane.
5.0.001 (02/09/2012)
- Updated Achievement lists, please advise if you notice errors (especially for horde players).
- Fixed many issues related to changes in MoP. Too much to list.
- Talent pane is temporarily disabled. It will be back soon.
- Changed all drop down definitions to prevent tainting (Thanks ckaotik !)
- Fixed a Lua error in Grids->Reputations when selecting guild reputation.
- Fixed a few UI issues related to account sharing.
- Fixed searching item upgrades based on iLevel
- Moved the sumary tab into its own module, this is in preparation of future new features. If you encounter a problem due to this, please roll back to 4.3.003b. (Should be ok though)
- Fixed pets not sorted alphabetically in Grids->Pets.
- Added back the All-in-one view in Grids->Pets.
Older patch notes : see changelog.txt
Archived Files (36)
File Name Version Size Author Date 5.4.003 1MB Thaoky 10-06-13 02:37 AM 5.4.002 1MB Thaoky 09-17-13 11:26 AM 5.4.001 1MB Thaoky 09-11-13 10:46 AM 5.3.003 2MB Thaoky 08-01-13 08:10 AM 5.3.002 1MB Thaoky 05-29-13 01:28 PM 5.3.001 1MB Thaoky 05-28-13 12:29 PM 5.2.001 1MB Thaoky 03-12-13 05:02 AM 5.1.002 1MB Thaoky 02-24-13 06:19 AM 5.1.001 1MB Thaoky 11-29-12 11:00 AM 5.0.003 1MB Thaoky 11-28-12 12:14 PM 5.0.002 1MB Thaoky 10-06-12 05:56 AM 5.0.001d 1MB Thaoky 09-13-12 01:08 PM 5.0.001c 1MB Thaoky 09-03-12 11:59 AM 5.0.001b 1MB Thaoky 09-02-12 12:38 PM 5.0.001 1MB Thaoky 09-02-12 06:27 AM 4.3.003b 1MB Thaoky 05-05-12 04:43 AM 4.3.003 1MB Thaoky 05-04-12 09:51 AM 4.3.002 1MB Thaoky 01-29-12 05:05 AM 4.3.001 1MB Thaoky 12-10-11 03:24 PM 4.2.002 1MB Thaoky 10-30-11 05:59 AM 4.2.001 1MB Thaoky 06-29-11 01:20 PM 4.1.001b 1MB Thaoky 05-01-11 10:31 AM 4.1.001 1MB Thaoky 04-30-11 02:06 PM 4.0.006b 1MB Thaoky 04-03-11 12:55 AM 4.0.006 1MB Thaoky 03-02-11 08:03 AM 4.0.005d 1MB Thaoky 02-16-11 10:11 AM 4.0.005c 1MB Thaoky 02-15-11 07:28 AM 4.0.005b 1MB Thaoky 02-11-11 09:23 AM 4.0.005 1MB Thaoky 12-03-10 09:24 AM 4.0.004c 1MB Thaoky 11-24-10 12:25 PM 4.0.004b 1MB Thaoky 11-21-10 08:00 AM 4.0.004 1MB Thaoky 11-20-10 07:28 AM 4.0.003 1MB Thaoky 10-26-10 05:49 AM 4.0.002 1MB Thaoky 10-17-10 07:39 AM 4.0.001 1MB Thaoky 10-15-10 10:02 AM 4.0.001 1MB Thaoky 10-15-10 09:04 AM
Comment Options
02-09-09, 12:36 AM Myster A Kobold Labourer Forum posts: 0 File comments: 175 Uploads: 11 3 errors [2009/02/09 17:57:24-611-x54]: Altoholic-3.0.006b\Altoholic.lua:1613: attempt to concatenate a nil value Altoholic-3.0.006b\Altoholic.lua:1625: in function GetAccountItemCount' Altoholic-3.0.006b\Altoholic.lua:1686: in function GetItemCount' Altoholic-3.0.006b\Altoholic.lua:1983: in function ProcessTooltip' Altoholic-3.0.006b\Altoholic.lua:1871: in function Skillet-1.10-LS-153\Skillet.lua:431: in function : ? : ? TekKompare-3.0.1.4\tekKompare.lua:44: in function TekKompare-3.0.1.4\TipIcon.lua:8: in function : ? : ? : in function SetBagItem' Interface\FrameXML\ContainerFrame.lua:673: in function ContainerFrameItemButton_OnEnter': Combuctor-2.0.7\item.lua:242: in function --- [2009/02/09 18:04:13-611-x4]: Altoholic-3.0.006b\Altoholic.lua:1613: attempt to concatenate a nil value Altoholic-3.0.006b\Altoholic.lua:1625: in function GetAccountItemCount' Altoholic-3.0.006b\Altoholic.lua:1686: in function GetItemCount' Altoholic-3.0.006b\Altoholic.lua:1983: in function ProcessTooltip' Altoholic-3.0.006b\Altoholic.lua:1871: in function Skillet-1.10-LS-153\Skillet.lua:431: in function : ? : ? TekKompare-3.0.1.4\tekKompare.lua:44: in function TekKompare-3.0.1.4\TipIcon.lua:8: in function : ? : ? : in function SetGuildBankItem' Blizzard_GuildBankUI\Blizzard_GuildBankUI.lua:556: in function GuildBankItemButton_OnEnter' :"*:OnEnter":1: in function <[string "*:OnEnter"]:1> --- [2009/02/09 19:35:57-611-x1]: Altoholic-3.0.006b\Frames\GuildMembers.lua:126: bad argument #2 to 'format' (string expected, got nil) Altoholic-3.0.006b\Frames\GuildMembers.lua:126: in function GuildMembers_Update' Altoholic-3.0.006b\Frames\TabSummary.lua:78: in function SummaryMenuOnClick' :"*:OnClick":1: in function <[string "*:OnClick"]:1> ---
02-08-09, 05:29 AM
Thaoky
An Aku'mai Servant
Forum posts: 30
Originally posted by Gruffness This is a really nice add-on. The search (and browsing) is much faster than Armory (the add-on)! One feature I thought for sure I'd find was a guild notes and rank display for each character (and last seen/refreshed) info on the notes. Am I missing it? If not, could it be added? I think the most logical place would be under the Guild Members tab where I can view currently online guild members as well as my own currently online character and offline alts. A "last seen" option to keep a history of guild members we've seen (and their info) instead of only showing currently online members might be nice too.
I'll see what can be done easily, I'm ok to provide some more information if it's available through the API, but quite honestly, my goal is not to replace the default guild frame
However, I intend to do something about offline members, so chances are you'll see some info about them too.
02-08-09, 04:12 AM Gruffness A Deviate Faerie Dragon Forum posts: 18 File comments: 94 Uploads: 0 This is a really nice add-on. The search (and browsing) is much faster than Armory (the add-on)! One feature I thought for sure I'd find was a guild notes and rank display for each character (and last seen/refreshed) info on the notes. Am I missing it? If not, could it be added? I think the most logical place would be under the Guild Members tab where I can view currently online guild members as well as my own currently online character and offline alts. A "last seen" option to keep a history of guild members we've seen (and their info) instead of only showing currently online members might be nice too. Last edited by Gruffness : 02-08-09 at 04:18 AM.
02-07-09, 06:38 PM
stqn
A Deviate Faerie Dragon
Forum posts: 10
Re: Re: Re: Re: Searching recipes
Originally posted by Thaoky A search will always search in the bags, but the option allows you to look also in the recipes (or not, if you disabled it). You can find the option into Options->Search.
I just tried with the latest version of Altoholic, and it worked . I didn't have to check the option, it was already active... Though I wasn't on the same character this time.
Last edited by stqn : 02-07-09 at 06:38 PM.
02-07-09, 04:57 PM
Thaoky
An Aku'mai Servant
Forum posts: 30
Re: Re: Re: Searching recipes
Originally posted by stqn Hm, well, err, thanks. But last time I tried, I went to the list of enchanting recipes of one of my alts, then typed something in the search field, and it searched containers...? I'll look again, I guess.
A search will always search in the bags, but the option allows you to look also in the recipes (or not, if you disabled it).
You can find the option into Options->Search.
Also, the addon can only search recipes it knows, so make sure you have logged in this character at least once, and opened the professions as well.
Let me know if you need additional directions
02-07-09, 06:17 AM
stqn
A Deviate Faerie Dragon
Forum posts: 10
Re: Re: Searching recipes
Originally posted by Thaoky This has been implemented a long time ago. There's also an option to enable/disable this.
Hm, well, err, thanks. But last time I tried, I went to the list of enchanting recipes of one of my alts, then typed something in the search field, and it searched containers...?
I'll look again, I guess.
02-07-09, 02:17 AM Thaoky An Aku'mai Servant Forum posts: 30 File comments: 602 Uploads: 2 It's a known issue. The explanation is here: http://www.wowinterface.com/portal.p...=faq&faqid=322 I intend to review this in the near future, as I've learned a lot about the API since I coded this feature, I've thought about a few ways to circumvent it, and I'd like to test a few things.
02-06-09, 03:07 PM AnrDaemon A Flamescale Wyrmkin Forum posts: 115 File comments: 2348 Uploads: 6 Altoholic does not track JC-only trinkets properly. (Nor does it RecipeRadar, but that's a whole different issue) See, it says "Already known" and "Could be learnable" at the same time. Altoholic DO know that this recipe is known, but it has different name in book. "Figurine - Black Pearl Panther" So, all other figurines.
02-03-09, 03:20 AM Thaoky An Aku'mai Servant Forum posts: 30 File comments: 602 Uploads: 2 @Pseudopath: Thanks @waxie: Same reply as on Curse. You can either disable the option to "show all accounts in the tooltip counters", or completely clean your altoholic.lua from saved variables if you need this option. @harl: Just out of curiosity, since I apparently made a mistake that I can't find in 3.0.006b, what kind of problems did you face ? Edit: I just fixed the same issue with two guildmates, it has to do with a DB that has not been cleaned when upgrading to version 3.0.006 Last edited by Thaoky : 02-03-09 at 05:26 AM.
02-02-09, 09:28 PM harl A Defias Bandit Forum posts: 2 File comments: 48 Uploads: 2 I'm not getting that previously mentioned error. But I had to delete my SavedVariables/Altoholic.lua for Altoholic to be fully functional again, since all of its tooltip parts were just showing 1 everywhere even if I had more than 1 piece of that item with that same character. Everything's fine now again, just wanted to let you know. If it's previously been mentioned already, I'm sorry.
02-02-09, 02:10 PM waxie A Kobold Labourer Forum posts: 0 File comments: 8 Uploads: 0 getting a new error with v3.0.006b Date: 2009-02-02 12:08:06 ID: 4 Error occured in: Global Count: 1 Message: ..\AddOns\Altoholic\Altoholic.lua line 1613: attempt to concatenate a nil value Debug: [C]: ? Altoholic\Altoholic.lua:1613: GetCharacterItemCount() Altoholic\Altoholic.lua:1625: GetAccountItemCount() Altoholic\Altoholic.lua:1686: GetItemCount() Altoholic\Altoholic.lua:1983: ProcessTooltip() Altoholic\Altoholic.lua:1871: Altoholic\Altoholic.lua:1862 ...AddOns\Auc-Advanced\Libs\LibExtraTip\LibExtraTip.lua:279: OnTooltipSetItem() Enchantrix\EnxMain.lua:220: Enchantrix\EnxMain.lua:216 [C]: ? [C]: ? MobInfo2\MI2_Events.lua:615: <-----I have since removed MobInfo2 MobInfo2\MI2_Events.lua:612 <----- MobInfo3\MI3_Events.lua:616: MobInfo3\MI3_Events.lua:613 (tail call): ? (tail call): ? [C]: ? [C]: ? ...AddOns\Auc-Advanced\Libs\LibExtraTip\LibExtraTip.lua:251: ...AddOns\Auc-Advanced\Libs\LibExtraTip\LibExtraTip.lua:245 [C]: ? [C]: pcall() Stubby\Stubby.lua:341: Stubby\Stubby.lua:325 (tail call): ? [C]: ? [C]: ? [C]: ? [C]: ? [C]: Outfitter_OrigSetBagItem() Outfitter\Outfitter.lua:6681: SetBagItem() ..\FrameXML\ContainerFrame.lua:673: ContainerFrameItemButton_OnEnter() ArkInventory\ArkInventory.lua:5178: Frame_Item_OnEnter() [string "*:OnEnter"]:1: [string "*:OnEnter"]:1 AddOns: Swatter, v5.3.4045 (DingoIII) WowheadLooter, v30018 AdvancedTradeSkillWindow, v AHsearch, v3.1 AlarBGHelper, v3.5.7 r35 Altoholic, v3.0.006b Aperture, v1.0 ArkInventory, v3.02 Atlas, v1.13.0 AtlasBattlegrounds, v1.13.0 AtlasDungeonLocs, v1.13.0 AtlasOutdoorRaids, v1.13.0 AtlasLoot, vv5.03.02 AtlasQuest, v4.3.1 AucAdvanced, v5.3.4045 (DingoIII) AucFilterBasic, v5.3.4045 (DingoIII) AucFilterOutlier, v5.3.4045.2531 AucMatchUndercut, v5.3.4045.2531 AucScanData, v5.3.4045 (DingoIII) AucStatClassic, v5.3.4045 (DingoIII) AucStatHistogram, v5.3.4045 (DingoIII) AucStatiLevel, v5.3.4045 (DingoIII) AucStatPurchased, v5.3.4045 (DingoIII) AucStatSales, v5.3.4045.2842 AucStatSimple, v5.3.4045 (DingoIII) AucStatStdDev, v5.3.4045 (DingoIII) 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XPerlRaidMonitor, v XPerlRaidPets, v XPerlTarget, v XPerlTargetTarget, v ZHunterMod, v ZThreatMeter, v1.0.10 ZygorGuidesHorde, v1.0 ZygorGuidesViewer, v1.0 (ck=14b5) Last edited by waxie : 02-02-09 at 02:56 PM.
02-01-09, 02:16 PM Pseudopath A Murloc Raider Forum posts: 4 File comments: 70 Uploads: 1 Thanks I recently found this addon and installed it on a whim, great job! I've just noticed the "Auctions" entry in the Activity pane, that alone justifies me using this and posting my thanks! Great Utility. - Pseudopath.
02-01-09, 06:21 AM
Thaoky
An Aku'mai Servant
Forum posts: 30
Re: Searching recipes
Originally posted by stqn Hi, It would be great to be able to search alt's recipes (enchanting, etc.)
This has been implemented a long time ago. There's also an option to enable/disable this.
02-01-09, 06:16 AM stqn A Deviate Faerie Dragon Forum posts: 10 File comments: 76 Uploads: 0 Searching recipes Hi, It would be great to be able to search alt's recipes (enchanting, etc.)
02-01-09, 02:08 AM
Thaoky
An Aku'mai Servant
Forum posts: 30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5737650990486145, "perplexity": 22596.883914071506}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1393999642518/warc/CC-MAIN-20140305060722-00052-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/503924/is-such-transformation-for-a-given-array-possible | # Is such transformation for a given array possible?
My friend asked me this question and I am not able to solve it even I am not getting how to think about such problem. Please provide a good method?
Given $n$ numbers, you can perform the following operation any number of times : Choose any subset of the numbers (possibly empty), none of which are $0$. Decrement the numbers in the subset by $1$, and increment the numbers not in the subset by $K$. Is it possible to perform operations such that exactly $n - 1$ numbers become $0$?
Constraints :
2 <= n <= 100
1 <= K <= 10
0 <= array element<= 1000
-
What is $K$ in this context? – Dennis Meng Sep 24 '13 at 20:09
I'm assuming $K$ is a given constant? Certainly not possible if $K \geq n-1$. – Calvin Lin Sep 24 '13 at 20:26
@CalvinLin Possibly, but it could also be the size of the subset you choose. Hence why I asked. – Dennis Meng Sep 24 '13 at 20:28
@DennisMeng Indeed, that was why I said it is not possible if $K \geq n-1$. I'm assuming it is fixed, given $n$. – Calvin Lin Sep 24 '13 at 20:29
Could you make the problem clearer? I can't understand exactly what you are asking. – innisfree Sep 24 '13 at 21:32
Assuming that $K$ is some positive integer constant, then there exists a method iff all but one share the same remainder mod $(K+1)$.
To see why solutions exist only when $n-1$ of them share the same remainder, consider any arbitrary set of $s$ operations, and two of the numbers, $x_a$ and $x_b$.
If $x_a$ is decremented $a$ times and incremented $s-a$ times, while $x_b$ is decremented $b$ times and incremented $s-b$ times, the net change of $x_a$ is that it increased by $Ks - (K+1)a$, while $x_b$ increased by $Ks - (K+1)b$. Thus, the difference between them changed by $(K+1)(a - b)$. In other words, $x_a - x_b$ could only have changed by a multiple of $(K+1)$. If the difference between them wasn't a multiple of $(K+1)$ before, it can't be 0 now, and thus $x_a$ and $x_b$ wouldn't even be equal, much less both 0.
Now that we've established that solutions only exist when $n-1$ of them share the same remainder, I will show how to actually do it when this case arises.
Let $x_i$ be one of the numbers. The basic idea is to consider the next $(K+1)$ moves as one iteration. The aggregate result of this iteration is:
• $x_i$ gets incremented twice and decremented $K-1$ times, for a total net increase of $2K - (K-1) = K+1$
• All other numbers will be incremented once and decremented $K$ times, for a total net increase of $K - K = 0$.
It's not too hard to see that we can create and use such an iteration.
So, suppose $x_t$ is the "odd one out". All we do then is do the above $(K+1)$-step iteration on each of the others until they are all equal (which can be done since they all have the same remainder mod $K+1$). Once all $n-1$ are equal, just decrement them all to 0.
Technically, the above iteration might run into problems if one of the variables is less than $K$ (the iteration might make it go negative in the middle). To fix this, what you can do is first prime everything with small singleton decrements until all variables are at least $K$. Then, you can do the iterations as needed. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6944310069084167, "perplexity": 254.40376096853996}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416400373301.1/warc/CC-MAIN-20141119123253-00174-ip-10-235-23-156.ec2.internal.warc.gz"} |
http://th.ai/GC-content | GC-content
Nucleotide bonds showing AT and GC pairs. Arrows point to the hydrogen bonds.
In molecular biology and genetics, GC-content (or guanine-cytosine content) is the percentage of nitrogenous bases on a DNA or RNA molecule that are either guanine or cytosine (from a possibility of four different ones, also including adenine and thymine in DNA and adenine and uracil in RNA).[1] This may refer to a certain fragment of DNA or RNA, or that of the whole genome. When it refers to a fragment of the genetic material, it may denote the GC-content of section of a gene (domain), single gene, group of genes (or gene clusters), or even a non-coding region. G (guanine) and C (cytosine) undergo a specific hydrogen bonding, whereas A (adenine) bonds specifically with T (thymine, in DNA) or U (uracil, in RNA).
The GC pair is bound by three hydrogen bonds, while AT and AU pairs are bound by two hydrogen bonds. To emphasize this difference in the number of hydrogen bonds, the base pairings can be represented as respectively G≡C versus A=T and A=U. DNA with low GC-content is less stable than DNA with high GC-content; however, the hydrogen bonds themselves do not have a particularly significant impact on stabilization, the stabilization is due mainly to interactions of base stacking.[2] In spite of the higher thermostability conferred to the genetic material, it has been observed that at least some bacteria species with DNA of high GC-content undergo autolysis more readily, thereby reducing the longevity of the cell per se.[3] Due to the thermostability given to the genetic materials in high GC organisms, it was commonly believed that the GC content played a necessary role in adaptation temperatures, a hypothesis that was refuted in 2001.[4] However, it has been shown that there is a strong correlation between the prokaryotic optimal growth at higher temperatures and the GC content of structured RNAs (such as ribosomal RNA, transfer RNA, and many other non-coding RNAs).[4][5] The AU base pairs are less stable than the GC base pairs previously attributed to GC bonds containing 3 hydrogen bonds and AU having only 2 hydrogen bonds, making high-GC-content RNA structures more resistant to the effects of high temperatures. More recently, it has been proved that the most stabilizing factor of thermal stability of double stranded nucleic acids is actually due to the base stackings of adjacent bases, rather than the number of hydrogen bonds between the bases.There is more favorable stacking energy for G:C pairs because of the relative positions of exocyclic groups than in the A:U pairs. Additionally, there is a correlation between the order in which the bases stack and thermal stability.[6]
In PCR experiments, the GC-content of primers are used to predict their annealing temperature to the template DNA. A higher GC-content level indicates a relatively higher melting temperature.
Determination
GC content is usually expressed as a percentage value, but sometimes as a ratio (called G+C ratio or GC-ratio). GC-content percentage is calculated as[7]
${\displaystyle {\cfrac {G+C}{A+T+G+C}}\times 100\%}$
whereas the AT/GC ratio is calculated as[8]
${\displaystyle {\cfrac {A+T}{G+C}}}$ .
The GC-content percentages as well as GC-ratio can be measured by several means, but one of the simplest methods is to measure what is called the melting temperature of the DNA double helix using spectrophotometry. The absorbance of DNA at a wavelength of 260 nm increases fairly sharply when the double-stranded DNA separates into two single strands when sufficiently heated.[9] The most commonly used protocol for determining GC ratios uses flow cytometry for large number of samples.[10]
In alternative manner, if the DNA or RNA molecule under investigation has been sequenced then the GC-content can be accurately calculated by simple arithmetic or by using the free online GC calculator.
GC ratio of genomes
GC ratios within a genome is found to be markedly variable. These variations in GC ratio within the genomes of more complex organisms result in a mosaic-like formation with islet regions called isochores.[11] This results in the variations in staining intensity in the chromosomes.[12] GC-rich isochores include in them many protein coding genes, and thus determination of ratio of these specific regions contributes in mapping gene-rich regions of the genome.[13][14]
GC ratios and coding sequence
Within a long region of genomic sequence, genes are often characterised by having a higher GC-content in contrast to the background GC-content for the entire genome. Evidence of GC ratio with that of length of the coding region of a gene has shown that the length of the coding sequence is directly proportional to higher G+C content.[15] This has been pointed to the fact that the stop codon has a bias towards A and T nucleotides, and, thus, the shorter the sequence the higher the AT bias.[16]
Application in systematics
GC content is found to be variable with different organisms, the process of which is envisaged to be contributed to by variation in selection, mutational bias, and biased recombination-associated DNA repair.[17] The species problem in prokaryotic taxonomy has led to various suggestions in classifying bacteria, and the ad hoc committee on reconciliation of approaches to bacterial systematics has recommended use of GC ratios in higher level hierarchical classification.[18] For example, the Actinobacteria are characterised as "high GC-content bacteria".[19] In Streptomyces coelicolor A3(2), GC content is 72%.[20] The GC-content of Yeast (Saccharomyces cerevisiae) is 38%,[21] and that of another common model organism, thale cress (Arabidopsis thaliana), is 36%.[22] Because of the nature of the genetic code, it is virtually impossible for an organism to have a genome with a GC-content approaching either 0% or 100%. A species with an extremely low GC-content is Plasmodium falciparum (GC% = ~20%),[23] and it is usually common to refer to such examples as being AT-rich instead of GC-poor.[24]
Software Tools
GCSpeciesSorter [25] and TopSort [26] are software tools for classifying species based on their GC contents.
References
1. ^
2. ^ Yakovchuk P, Protozanova E, Frank-Kamenetskii MD (2006). "Base-stacking and base-pairing contributions into thermal stability of the DNA double helix". Nucleic Acids Res. 34 (2): 564–74. doi:10.1093/nar/gkj454. PMC . PMID 16449200.
3. ^ Levin RE, Van Sickle C (1976). "Autolysis of high-GC isolates of Pseudomonas putrefaciens". Antonie van Leeuwenhoek. 42 (1–2): 145–55. doi:10.1007/BF00399459. PMID 7999.
4. ^ a b Hurst LD, Merchant AR (March 2001). "High guanine-cytosine content is not an adaptation to high temperature: a comparative analysis amongst prokaryotes". Proc. Biol. Sci. 268 (1466): 493–7. doi:10.1098/rspb.2000.1397. PMC . PMID 11296861.
5. ^ Galtier, N.; Lobry, J.R. (1997). "Relationships between genomic G+C content, RNA secondary structures, and optimal growth temperature in Prokaryotes". Journal of Molecular Evolution. 44 (6): 632–636. doi:10.1007/PL00006186. PMID 9169555.
6. ^ Yakovchuk, Peter; Protozanova, Ekaterina; Frank-Kamenetskii, Maxim D. (2006). "Base-stacking and base-pairing contributions into thermal stability of the DNA double helix". Nucleic Acids Research. 34 (2): 564–574. doi:10.1093/nar/gkj454. ISSN 0305-1048. PMC . PMID 16449200.
7. ^ Madigan,MT. and Martinko JM. (2003). Brock biology of microorganisms (10th ed.). Pearson-Prentice Hall. ISBN 84-205-3679-2.
8. ^ Definition of GC-ratio on Northwestern University, IL, USA
9. ^ Wilhelm J, Pingoud A, Hahn M (May 2003). "Real-time PCR-based method for the estimation of genome sizes". Nucleic Acids Res. 31 (10): e56. doi:10.1093/nar/gng056. PMC . PMID 12736322.
10. ^ Vinogradov AE (May 1994). "Measurement by flow cytometry of genomic AT/GC ratio and genome size". Cytometry. 16 (1): 34–40. doi:10.1002/cyto.990160106. PMID 7518377.
11. ^ Bernardi G (January 2000). "Isochores and the evolutionary genomics of vertebrates". Gene. 241 (1): 3–17. doi:10.1016/S0378-1119(99)00485-0. PMID 10607893.
12. ^ Furey TS, Haussler D (May 2003). "Integration of the cytogenetic map with the draft human genome sequence". Hum. Mol. Genet. 12 (9): 1037–44. doi:10.1093/hmg/ddg113. PMID 12700172.
13. ^ Sumner AT, de la Torre J, Stuppia L (August 1993). "The distribution of genes on chromosomes: a cytological approach". J. Mol. Evol. 37 (2): 117–22. doi:10.1007/BF02407346. PMID 8411200.
14. ^ Aïssani B, Bernardi G (October 1991). "CpG islands, genes and isochores in the genomes of vertebrates". Gene. 106 (2): 185–95. doi:10.1016/0378-1119(91)90198-K. PMID 1937049.
15. ^ Pozzoli U, Menozzi G, Fumagalli M, et al. (2008). "Both selective and neutral processes drive GC content evolution in the human genome". BMC Evol. Biol. 8: 99. doi:10.1186/1471-2148-8-99. PMC . PMID 18371205.
16. ^ Wuitschick JD, Karrer KM (1999). "Analysis of genomic G + C content, codon usage, initiator codon context and translation termination sites in Tetrahymena thermophila". J. Eukaryot. Microbiol. 46 (3): 239–47. doi:10.1111/j.1550-7408.1999.tb05120.x. PMID 10377985.
17. ^ Birdsell JA (1 July 2002). "Integrating genomics, bioinformatics, and classical genetics to study the effects of recombination on genome evolution". Mol. Biol. Evol. 19 (7): 1181–97. doi:10.1093/oxfordjournals.molbev.a004176. PMID 12082137.
18. ^ Wayne LG; et al. (1987). "Report of the ad hoc committee on reconciliation of approaches to bacterial systematic". International Journal of Systematic Bacteriology. 37 (4): 463–4. doi:10.1099/00207713-37-4-463.
19. ^ Taxonomy browser on NCBI
20. ^ Whole genome data of "Streptomyces coelicolor" A3(2) on NCBI
21. ^ Whole genome data of Saccharomyces cerevisiae on NCBI
22. ^ Whole genome data of Arabidopsis thaliana on NCBI
23. ^ Whole genome data of Plasmodium falciparum on NCBI
24. ^ Musto H, Cacciò S, Rodríguez-Maseda H, Bernardi G (1997). "Compositional constraints in the extremely GC-poor genome of Plasmodium falciparum" (PDF). Mem. Inst. Oswaldo Cruz. 92 (6): 835–41. doi:10.1590/S0074-02761997000600020. PMID 9566216.
25. ^ Karimi K, Wuitchik D, Oldach M, Vize P (2018). "Distinguishing Species Using GC Contents in Mixed DNA or RNA Sequences". Evol Bioinform Online. 14 (January 1, 2018). doi:10.1177/1176934318788866. PMID 30038485.
26. ^ Lehnert E, Mouchka M, Burriesci M, Gallo N, Schwarz J, Pringle J (2014). "Extensive differences in gene expression between symbiotic and aposymbiotic cnidarians". G3 (Bethesda). 4 (2). doi:10.1534/g3.113.009084. PMID 24368779. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 2, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8385697603225708, "perplexity": 9821.237225677625}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267162385.84/warc/CC-MAIN-20180925202648-20180925223048-00022.warc.gz"} |
http://ksvanhorn.com/bayes/jaynes/node2.html | ksvanhorn.com
Home
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# Commentary: Note on exchangeability and de Finetti's Theorem
In several places Jaynes refers to exchangeability and de Finetti's Theorem without defining these; finally, in Chapter 18 section 16 (p. 586 onward) he says a little bit about just what de Finetti's Theorem is. For those readers who are unfamiliar with this topic, Bernardo and Smith's book Bayesian Theory has a nice discussion in sections 4.2 and 4.3. Here is a brief, simplified summary of the definitions and theorems given therein, translated into the vocabulary and notation of Jaynes.
Notation. We write for , and for the infinite sequence . For simplicity, we assume that the set of possible values for each variable is the same finite set .
Definition of finite exchangeability. The variables are said to be (finitely) exchangeable for a state of information if, for any constant values , we have
whenever is a permutation of the variables .
Definition of infinite exchangeability. The infinite sequence of variables is said to be infinitely exchangeable for a state of information if every finite subsequence of is exchangeable for .
Theorem. Let be the set of probability mass functions over . If is an infinitely exchangeable sequence of variables for , then there exists a probability density over such that
for any constant . (Note that may involve delta functions, to assign positive probability to a single specific value in .)
In other words, we may reason as if there exists some additional variable such that the variables are independently and identically distributed when the value of is known, and is . | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9775614142417908, "perplexity": 434.3714960557956}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039745015.71/warc/CC-MAIN-20181119023120-20181119045120-00360.warc.gz"} |
https://groups.google.com/g/osemosys/c/0KcxhG1OKo8 | # Open University task (Mismatch of demand and production)
23 views
### alikin...@gmail.com
Sep 22, 2021, 1:59:32 PM9/22/21
to OSeMOSYS
Hi everyone, I got a question. I'm passing the Open University tutorial on osemosys and flextool. Some why I got a mismatch of energy demand end production. Demand was set by using SpecifiedAnnualDemand and was split among INDELC(250,9) COMELC(72,8) and RESELC(160,5).But somehow annual production is 597 which is 114 Pj higher than i expected (250+160+73=483). Is it a mistake and how could that happened?
### Rudolf Yeganyan
Oct 4, 2021, 6:55:29 AM10/4/21
to OSeMOSYS
Hi,
This would be normal in the case that some of the energy generation technologies require large energy inputs in order to produce energy (e.g. hydrogen). If you have added such technologies, check whether the numbers make sense.
Otherwise, since there is extra energy being generated, this could be because you defined another demand parameter (ELC003 possibly?). Check if this is the case firstly, ensuring that ELC003 or any other parameter as such is 0.
Another reason could be that you have constrained certain technologies to produce a certain amount of energy, and thus the overall energy generation is higher than the demand. Check this as well, and ensure that there is no constraint that makes the energy production be higher than demand.
If this does not work, message here again and paste the specified demand profile, INDELC, COMELC, AND RESELC figures here.
Hope this helps.
Best,
Rudolf | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9243303537368774, "perplexity": 2040.9242042640992}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320305006.68/warc/CC-MAIN-20220126222652-20220127012652-00503.warc.gz"} |
https://www.perlmonks.org/?displaytype=print;node_id=508876;replies=1 | http://www.perlmonks.org?node_id=508876
richz has asked for the wisdom of the Perl Monks concerning the following question:
I have an installation of Perl that is bundled with another software application. If I run "perl -V" from the bin directory of this application where the perl executable is located, the @INC variable includes the appropriate perl module directories. If I copy the perl executable to a new directory and run it from this new directory the @INC variable only includes the '.' directory. I'm running windows 2000 and perl 5.6.1. Can anyone shed some light on why/how @INC is changing?
The reason I ask this question is because I have a complicated software build setup that runs some perl scripts by invoking a perl executable it expects to find in a particular directory. It is easier to try and locate a perl executable in this directory as opposed to modifying the build setup.
Thanks.
Replies are listed 'Best First'.
Re: Win32 @INC behavior
by pg (Canon) on Nov 16, 2005 at 04:35 UTC
Set environment variable PERL5LIB to the directory list that you want in your @INC.
set PERL5LIB=\perl\lib;\perl\site\lib
If I do:
set PERL5LIB=foo;bar;%PERL5LIB%
The last piece of perl -V shows:
...... %ENV: PERL5LIB="foo;bar;\perl\lib;\perl\site\lib" @INC: foo bar \perl\lib \perl\site\lib .
Re: Win32 @INC behavior
by blm (Hermit) on Nov 16, 2005 at 04:02 UTC
What do you copy to the new computer? Just perl.exe or the whole bin directory? Do you update the PATH system variable?
This is all on the same computer. I am not relying on my PATH to run perl and I am just copying perl.exe and the perl56.dll. I ran dependency walker and that is the only dynamically linked non-OS library linked in perl.exe.
I was always under the impression that the @INC variable is fixed once you compile perl.exe but there was on thread here that mentioned it seems to be somewhat dynamic but not in the way I'm finding out. That thread seemed to indicate that moving perl.exe around would result in @INC being adjusted so the directories it contains have their path adjusted accordingly.
In my attempts to mimick this problem I got an error about missing Config.pm when running perl -V when I removed all the perl except perl.exe and perl58.dll and perl5.8.0.exe (Yes I am doing this under perl 5.8 because that is all I have on Win32). The config.pm that it is refering to (I think) is c:\perl\lib\Config.pm and it contains alot of the info needed for the -V screen. I don't know if this helps you.
@INC is the result of all perllib additions that have been made by perl upon startup. It is not fixed at all. Although there is a portion of it that is fixed at compile time. The @INC is a combination of compile time settings, PERLLIB environment variable, perl command line -I parameters and use lib statements.
For example on linux, if you do:
PERLLIB=envbar perl -I cmdfoo -V -e "use lib ('usebaz');"
You will see the resulting @INC :
@INC: usebaz cmdfoo envbar /usr/lib/perl5/5.6.1/i386-linux /usr/lib/perl5/5.6.1 /usr/lib/perl5/site_perl/5.6.1/i386-linux /usr/lib/perl5/site_perl/5.6.1 /usr/lib/perl5/site_perl/5.6.0/i386-linux /usr/lib/perl5/site_perl/5.6.0 /usr/lib/perl5/site_perl /usr/lib/perl5/vendor_perl/5.6.1/i386-linux /usr/lib/perl5/vendor_perl/5.6.1 /usr/lib/perl5/vendor_perl .
There appears to be an order of precidence here too. use lib is first, -I option is second, PERLLIB is third and compiled settings is fourth.
Update: added use lib to the example.
Hazah! I'm Employed! But this place sucks
Note: I'm doing a lot of handwaving here... I seem to recall having read about this, but I've not looked it up to confirm my beliefs. I'll look it up later, I promise.
I was always under the impression that the @INC variable is fixed once you compile perl.exe
That's right. That's even the case for Perl on Windows... Except: perl itself changes the directories found in the hardwired @INC inside the perl exectutable, into directories relative to where it currently resides. That happens to lib (relative position to perl: ../lib) and site/lib (relative position: ../site/lib), where the perl executable resides in bin, relative to the perl installation root.
You could say it's a simple s/^\$HARDWIRED_ROOT/\$CURRENT_ROOT/, done inside perl.
Re: Win32 @INC behavior
by jimbojones (Friar) on Nov 16, 2005 at 15:24 UTC
Hi
What I've managed to observe on windows for ActiveState 561 is that @INC is derived based on the invoked location of the perl.exe. Well, actually, the perl5x.dll that is loaded by perl.exe. Basically, it looks up one dir (out of bin/) for lib/ and site/lib. If you move perl.exe and perl56.dll to some remote location that doesn't follow that structure:
bin/ lib/ site/lib
you won't get @INC set. Here's little test, where I copied perl.exe and perl56.dll to a bin/ directory under my "Documents and Settings"
C:\Documents and Settings\jim> C:\Progra~1\Perl\Perl561_638\bin\perl.e +xe -V Summary of my perl5 (revision 5 version 6 subversion 1) configuration: .... Built under MSWin32 Compiled at Apr 13 2004 19:24:21 @INC: C:/Program Files/Perl/Perl561_638/lib C:/Program Files/Perl/Perl561_638/site/lib . C:\Documents and Settings\jim>mkdir bin C:\Documents and Settings\jim>cp C:\Progra~1\Perl\Perl561_638\bin\perl +.exe bin\. C:\Documents and Settings\jim>cp C:\Progra~1\Perl\Perl561_638\bin\perl +56.dll bin\. C:\Documents and Settings\jim>set PATH=C:\Documents and Settings\jim\b +in;%PATH% C:\Documents and Settings\jim>perl.exe -V Can't locate Config.pm in @INC (@INC contains: .). BEGIN failed--compilation aborted. C:\Documents and Settings\jim>mkdir lib C:\Documents and Settings\jim>mkdir site\lib C:\Documents and Settings\jim>perl.exe -V Can't locate Config.pm in @INC (@INC contains: C:/Documents and Settin +gs/jim/lib C:/Documents and Settings/jim/site/lib .). BEGIN failed--compilation aborted.
Note that only when I have a lib/ and site/lib directory does the @INC get set correctly. Also, the main functionality is driven by the location of the perl56.dll, not the perl.exe file. perl.exe loads the .dll through the PATH environment variable, and it appears @INC is set with respect to the location of the .dll. So, if I remove the .dll from my local bin/ dir, the .dll is loaded from its default location, and @INC is set with respect to that location.
C:\Documents and Settings\jim>del bin\perl56.dll C:\Documents and Settings\jim>perl -V Summary of my perl5 (revision 5 version 6 subversion 1) ... ActivePerl Build 638 Built under MSWin32 Compiled at Apr 13 2004 19:24:21 @INC: C:/Program Files/Perl/Perl561_638/lib C:/Program Files/Perl/Perl561_638/site/lib .
HTH, Jim
(Update: fix cut and paste error)
As a follow-up:
The relevant parts of the .c code appear to be in win32.c
char *win32_get_sitelib(const char *pl) { return win32_get_xlib(pl, "sitelib", "site"); } static char *win32_get_xlib(const char *pl, const char *xlib, const ch +ar *libname) { .... sprintf(pathstr, "%s/lib", libname); (void)get_emd_part(&sv2, pathstr, ARCHNAME, "bin", pl, Nullch); /* JJ -- get_emd_part strips 'bin' if possible from the path to the .dll (found in get_emd_part by calling set_w32_module_name(); ) and then adds 'site/lib' to that path */ ... }
Thanks so much. What you describe is definitely the behavior I see. I didn't realize the perl executable would make the @INC directories relative to the location of the dll and if they weren't found it wouldn't include them. It's kind of annoying that perl.exe locates the perl5x.dll via %PATH%; I'd prefer it was done through the registry, but I digress.
Thanks for the help! | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8724977374076843, "perplexity": 10325.643349778793}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141748276.94/warc/CC-MAIN-20201205165649-20201205195649-00419.warc.gz"} |
https://khufkens.com/2016/04/20/modis-hdf-data-extraction-in-r/ | MODIS HDF data extraction in R
The Moderate-resolution imaging spectroradiometer (MODIS) sensors on both Aqua and Terra platforms provide a wealth of (environmental) data. However, manipulating the raw files can be challenging. Although Google Earth Engine provides an easier way to access these data, as most of the MODIS products are hosted, sometimes direct manipulation is still necessary. Here I quickly outline how to extract data from raw MODIS files using R.
Dependencies
To download extract data from a MODIS HDF file in R you need a few packages. Mainly:
After installing these packages make sure you load them to continue.
require(raster)
require(sp)
require(MODIS)
Finding your way on the globe
First you have to determine where your data is located within the tiled format MODIS data is distributed in. All tiles are denoted with a horizontal (h) and a vertical index (v). For the Land Products there are roughly ~350 or so tiles with varying degrees of actual land coverage. All MODIS data are distributed in a custom sinusoidal projection, hence the rather weird looking shape of the map.
Tiles
In order to find the right tile we load a coordinate into R. In this case it’s the location of Harvard Yard, or 42.375028, -71.116493 latitude and longitude respectively.
# the location of Harvard Yard
harvard_yard = cbind(42.375028, -71.116493)
# define the projection system to use
# lat-long in this case
latlon = CRS('+proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0')
# create a spatial object from the coordinate(s)
coordinates = SpatialPoints(harvard_yard, latlon)
# get the horizontal and vertical tile location for the coordinate(s)
horizontal = extract(tiles,coordinates)$h[1] vertical = extract(tiles,coordinates)$v[1]
Once you have the horizontal and vertical tiles you can download only these tiles instead of the entire archive.
Extracting data
As previously mentioned, data is stored in HDF files. These files are readily readable by the GDAL library. However, given the structured nature of these files you have to know what you are looking for. These layers in structured HDF files are called scientific data sets (SDS). You need to specify one to read them individually.
# read in all SDS strings (layer descriptors)
# using the MODIS package
sds <- getSds(filename)
# grab layer 4 of a particular hdf file
my_hdf_layer = raster(readGDAL(sds\$SDS4gdal[4], as.is = TRUE))
# should the HDF file not contain any layers, or a singular one
# you can default to using raster() any additional arguments
my_hdf_file = raster(filename)
Now you have succesfully read in data. However, this data is projected using the sinusoidal projection, not the lat-long. In order to extract data at given locations we have to translate the coordinates of these extraction points to the MODIS sinusoidal projection.
# specify the sinusoidal projection
sinus = CRS("+proj=sinu +lon_0=0 +x_0=0 +y_0=0 +a=6371007.181 +b=6371007.181 +units=m +no_defs")
# transform the coordinates
coordinates_sinus = spTransform(coordinates,sinus)
Finally extract the data at the new sinusoidal coordinates.
# extract data
my_data_point = extract(my_hdf_layer,coordinates_sinus) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5786524415016174, "perplexity": 5319.874966552064}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178365454.63/warc/CC-MAIN-20210303042832-20210303072832-00043.warc.gz"} |
https://fds.duke.edu/db/aas/math/smolka/publications/14134 | Department of Mathematics Search | Help | Login | |
Math @ Duke
....................... ....................... Webpage
## Publications [#14134] of Linda B. Smolka
Papers Submitted
1. L. B. Smolka, A. Belmonte, D. M. Henderson, T. P. Witelski, Exact solution for the extensional flow of a viscoelastic filament, European Journal of Applied Mathematics (November, 2003)
(last updated on 2003/12/19)
Abstract:
We solve the free boundary problem for the dynamics of a cylindrical, axisymmetric viscoelastic filament stretching in a purely extensional flow for the Upper Convected Maxwell and Oldroyd-B constitutive models. Assuming the axial stress in the filament has a spatial dependence provides the simplest coupling of viscoelastic effects to the motion of the filament, and yields a closed system of ODEs with an exact solution for the stretch rate and filament thickness satisfied by both constitutive models. This viscoelastic solution, which is a generalization of the exact solution for Newtonian filaments, converges to the Newtonian power-law scaling as $t \go \infty$. Based on the exact solution, we identify two regimes of dynamical behavior called the weakly- and strongly-viscoelastic limits. For the weakly-viscoelastic case, corresponding to low Deborah numbers, the dynamics are comparable to Newtonian behavior for all times and yield an effective increase in the filament thickness relative to a Newtonian fluid. In the strongly-viscoelastic case, initial transient dynamics are not comparable to Newtonian behavior and the effective filament thickness decreases with increasing Deborah number. We compare the viscoelastic solution to measurements of the thinning filament that forms behind a falling drop for several semi-dilute (strongly-viscoelastic) polymer solutions. We find the exact solution correctly predicts the time-dependence of the filament diameter in all of the experiments. As $t \go \infty$, observations of the filament thickness follow the Newtonian scaling $1/\sqrt{t}$. The transition from viscoelastic to Newtonian scaling in the filament thickness is coupled to a stretch-to-coil transition of the polymer molecules.
dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8746383786201477, "perplexity": 2269.698468966171}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221211719.12/warc/CC-MAIN-20180817045508-20180817065508-00204.warc.gz"} |
https://worldwidescience.org/topicpages/s/solving+partial+differential.html | #### Sample records for solving partial differential
1. Solving Partial Differential Equations Using a New Differential Evolution Algorithm
Directory of Open Access Journals (Sweden)
Natee Panagant
2014-01-01
Full Text Available This paper proposes an alternative meshless approach to solve partial differential equations (PDEs. With a global approximate function being defined, a partial differential equation problem is converted into an optimisation problem with equality constraints from PDE boundary conditions. An evolutionary algorithm (EA is employed to search for the optimum solution. For this approach, the most difficult task is the low convergence rate of EA which consequently results in poor PDE solution approximation. However, its attractiveness remains due to the nature of a soft computing technique in EA. The algorithm can be used to tackle almost any kind of optimisation problem with simple evolutionary operation, which means it is mathematically simpler to use. A new efficient differential evolution (DE is presented and used to solve a number of the partial differential equations. The results obtained are illustrated and compared with exact solutions. It is shown that the proposed method has a potential to be a future meshless tool provided that the search performance of EA is greatly enhanced.
2. Auxiliary equation method for solving nonlinear partial differential equations
International Nuclear Information System (INIS)
Sirendaoreji,; Jiong, Sun
2003-01-01
By using the solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct several kinds of exact travelling wave solutions for some nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation
3. Exp-function method for solving fractional partial differential equations.
Science.gov (United States)
Zheng, Bin
2013-01-01
We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space-time fractional Fokas equation and the nonlinear fractional Sharma-Tasso-Olver (STO) equation. As a result, some new exact solutions for them are successfully established.
4. Solving Nonlinear Partial Differential Equations with Maple and Mathematica
CERN Document Server
Shingareva, Inna K
2011-01-01
The emphasis of the book is given in how to construct different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book). Numerous comparisons and relationships between various types of solutions, different methods and approaches are provided, the results obtained in Maple an
5. Multivariate Padé Approximation for Solving Nonlinear Partial Differential Equations of Fractional Order
Directory of Open Access Journals (Sweden)
Veyis Turut
2013-01-01
Full Text Available Two tecHniques were implemented, the Adomian decomposition method (ADM and multivariate Padé approximation (MPA, for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in Caputo sense. First, the fractional differential equation has been solved and converted to power series by Adomian decomposition method (ADM, then power series solution of fractional differential equation was put into multivariate Padé series. Finally, numerical results were compared and presented in tables and figures.
6. A New Numerical Technique for Solving Systems Of Nonlinear Fractional Partial Differential Equations
Directory of Open Access Journals (Sweden)
Mountassir Hamdi Cherif
2017-11-01
Full Text Available In this paper, we apply an efficient method called the Aboodh decomposition method to solve systems of nonlinear fractional partial differential equations. This method is a combined form of Aboodh transform with Adomian decomposition method. The theoretical analysis of this investigated for systems of nonlinear fractional partial differential equations is calculated in the explicit form of a power series with easily computable terms. Some examples are given to shows that this method is very efficient and accurate. This method can be applied to solve others nonlinear systems problems.
7. Local Fractional Laplace Variational Iteration Method for Solving Linear Partial Differential Equations with Local Fractional Derivative
Directory of Open Access Journals (Sweden)
Ai-Min Yang
2014-01-01
Full Text Available The local fractional Laplace variational iteration method was applied to solve the linear local fractional partial differential equations. The local fractional Laplace variational iteration method is coupled by the local fractional variational iteration method and Laplace transform. The nondifferentiable approximate solutions are obtained and their graphs are also shown.
8. A boundary value approach for solving three-dimensional elliptic and hyperbolic partial differential equations.
Science.gov (United States)
Biala, T A; Jator, S N
2015-01-01
In this article, the boundary value method is applied to solve three dimensional elliptic and hyperbolic partial differential equations. The partial derivatives with respect to two of the spatial variables (y, z) are discretized using finite difference approximations to obtain a large system of ordinary differential equations (ODEs) in the third spatial variable (x). Using interpolation and collocation techniques, a continuous scheme is developed and used to obtain discrete methods which are applied via the Block unification approach to obtain approximations to the resulting large system of ODEs. Several test problems are investigated to elucidate the solution process.
9. The Adomian decomposition method for solving partial differential equations of fractal order in finite domains
Energy Technology Data Exchange (ETDEWEB)
El-Sayed, A.M.A. [Faculty of Science University of Alexandria (Egypt)]. E-mail: amasyed@hotmail.com; Gaber, M. [Faculty of Education Al-Arish, Suez Canal University (Egypt)]. E-mail: mghf408@hotmail.com
2006-11-20
The Adomian decomposition method has been successively used to find the explicit and numerical solutions of the time fractional partial differential equations. A different examples of special interest with fractional time and space derivatives of order {alpha}, 0<{alpha}=<1 are considered and solved by means of Adomian decomposition method. The behaviour of Adomian solutions and the effects of different values of {alpha} are shown graphically for some examples.
10. An Efficient Numerical Approach for Solving Nonlinear Coupled Hyperbolic Partial Differential Equations with Nonlocal Conditions
Directory of Open Access Journals (Sweden)
A. H. Bhrawy
2014-01-01
Full Text Available One of the most important advantages of collocation method is the possibility of dealing with nonlinear partial differential equations (PDEs as well as PDEs with variable coefficients. A numerical solution based on a Jacobi collocation method is extended to solve nonlinear coupled hyperbolic PDEs with variable coefficients subject to initial-boundary nonlocal conservation conditions. This approach, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled hyperbolic PDEs with variable coefficients to a system of nonlinear ordinary differential equation which is far easier to solve. In fact, we deal with initial-boundary coupled hyperbolic PDEs with variable coefficients as well as initial-nonlocal conditions. Using triangular, soliton, and exponential-triangular solutions as exact solutions, the obtained results show that the proposed numerical algorithm is efficient and very accurate.
11. An Accurate Approximate-Analytical Technique for Solving Time-Fractional Partial Differential Equations
Directory of Open Access Journals (Sweden)
M. Bishehniasar
2017-01-01
Full Text Available The demand of many scientific areas for the usage of fractional partial differential equations (FPDEs to explain their real-world systems has been broadly identified. The solutions may portray dynamical behaviors of various particles such as chemicals and cells. The desire of obtaining approximate solutions to treat these equations aims to overcome the mathematical complexity of modeling the relevant phenomena in nature. This research proposes a promising approximate-analytical scheme that is an accurate technique for solving a variety of noninteger partial differential equations (PDEs. The proposed strategy is based on approximating the derivative of fractional-order and reducing the problem to the corresponding partial differential equation (PDE. Afterwards, the approximating PDE is solved by using a separation-variables technique. The method can be simply applied to nonhomogeneous problems and is proficient to diminish the span of computational cost as well as achieving an approximate-analytical solution that is in excellent concurrence with the exact solution of the original problem. In addition and to demonstrate the efficiency of the method, it compares with two finite difference methods including a nonstandard finite difference (NSFD method and standard finite difference (SFD technique, which are popular in the literature for solving engineering problems.
12. A New Fractional Projective Riccati Equation Method for Solving Fractional Partial Differential Equations
International Nuclear Information System (INIS)
Feng Qing-Hua
2014-01-01
In this paper, a new fractional projective Riccati equation method is proposed to establish exact solutions for fractional partial differential equations in the sense of modified Riemann—Liouville derivative. This method can be seen as the fractional version of the known projective Riccati equation method. For illustrating the validity of this method, we apply this method to solve the space-time fractional Whitham—Broer—Kaup (WBK) equations and the nonlinear fractional Sharma—Tasso—Olever (STO) equation, and as a result, some new exact solutions for them are obtained. (general)
13. Solving variational problems and partial differential equations that map between manifolds via the closest point method
Science.gov (United States)
King, Nathan D.; Ruuth, Steven J.
2017-05-01
Maps from a source manifold M to a target manifold N appear in liquid crystals, color image enhancement, texture mapping, brain mapping, and many other areas. A numerical framework to solve variational problems and partial differential equations (PDEs) that map between manifolds is introduced within this paper. Our approach, the closest point method for manifold mapping, reduces the problem of solving a constrained PDE between manifolds M and N to the simpler problems of solving a PDE on M and projecting to the closest points on N. In our approach, an embedding PDE is formulated in the embedding space using closest point representations of M and N. This enables the use of standard Cartesian numerics for general manifolds that are open or closed, with or without orientation, and of any codimension. An algorithm is presented for the important example of harmonic maps and generalized to a broader class of PDEs, which includes p-harmonic maps. Improved efficiency and robustness are observed in convergence studies relative to the level set embedding methods. Harmonic and p-harmonic maps are computed for a variety of numerical examples. In these examples, we denoise texture maps, diffuse random maps between general manifolds, and enhance color images.
14. A dynamical regularization algorithm for solving inverse source problems of elliptic partial differential equations
Science.gov (United States)
Zhang, Ye; Gong, Rongfang; Cheng, Xiaoliang; Gulliksson, Mårten
2018-06-01
This study considers the inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary data. The unknown source term is to be determined by additional boundary conditions. Unlike the existing methods found in the literature, which usually employ the first-order in time gradient-like system (such as the steepest descent methods) for numerically solving the regularized optimization problem with a fixed regularization parameter, we propose a novel method with a second-order in time dissipative gradient-like system and a dynamical selected regularization parameter. A damped symplectic scheme is proposed for the numerical solution. Theoretical analysis is given for both the continuous model and the numerical algorithm. Several numerical examples are provided to show the robustness of the proposed algorithm.
15. From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Angstmann, C.N.; Donnelly, I.C. [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia); Henry, B.I., E-mail: B.Henry@unsw.edu.au [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia); Jacobs, B.A. [School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050 (South Africa); DST–NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) (South Africa); Langlands, T.A.M. [Department of Mathematics and Computing, University of Southern Queensland, Toowoomba QLD 4350 (Australia); Nichols, J.A. [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia)
2016-02-15
We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also show that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.
16. The orthogonal gradients method: A radial basis functions method for solving partial differential equations on arbitrary surfaces
KAUST Repository
Piret, Cé cile
2012-01-01
Much work has been done on reconstructing arbitrary surfaces using the radial basis function (RBF) method, but one can hardly find any work done on the use of RBFs to solve partial differential equations (PDEs) on arbitrary surfaces. In this paper
17. Use of fast Fourier transforms for solving partial differential equations in physics
CERN Document Server
Le Bail, R C
1972-01-01
The use of fast Fourier techniques for the direct solution of an important class of elliptic, parabolic, and hyperbolic partial differential equations in two dimensions is described. Extensions to higher-order and higher-dimension equations as well as to integrodifferential equations are presented, and several numerical examples with their resulting precision and timing are reported. (12 refs).
18. ICM: an Integrated Compartment Method for numerically solving partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Yeh, G.T.
1981-05-01
An integrated compartment method (ICM) is proposed to construct a set of algebraic equations from a system of partial differential equations. The ICM combines the utility of integral formulation of finite element approach, the simplicity of interpolation of finite difference approximation, and the flexibility of compartment analyses. The integral formulation eases the treatment of boundary conditions, in particular, the Neumann-type boundary conditions. The simplicity of interpolation provides great economy in computation. The flexibility of discretization with irregular compartments of various shapes and sizes offers advantages in resolving complex boundaries enclosing compound regions of interest. The basic procedures of ICM are first to discretize the region of interest into compartments, then to apply three integral theorems of vectors to transform the volume integral to the surface integral, and finally to use interpolation to relate the interfacial values in terms of compartment values to close the system. The Navier-Stokes equations are used as an example of how to derive the corresponding ICM alogrithm for a given set of partial differential equations. Because of the structure of the algorithm, the basic computer program remains the same for cases in one-, two-, or three-dimensional problems.
19. Beginning partial differential equations
CERN Document Server
O'Neil, Peter V
2014-01-01
A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is or
20. The orthogonal gradients method: A radial basis functions method for solving partial differential equations on arbitrary surfaces
KAUST Repository
Piret, Cécile
2012-05-01
Much work has been done on reconstructing arbitrary surfaces using the radial basis function (RBF) method, but one can hardly find any work done on the use of RBFs to solve partial differential equations (PDEs) on arbitrary surfaces. In this paper, we investigate methods to solve PDEs on arbitrary stationary surfaces embedded in . R3 using the RBF method. We present three RBF-based methods that easily discretize surface differential operators. We take advantage of the meshfree character of RBFs, which give us a high accuracy and the flexibility to represent the most complex geometries in any dimension. Two out of the three methods, which we call the orthogonal gradients (OGr) methods are the result of our work and are hereby presented for the first time. © 2012 Elsevier Inc.
1. An ansatz for solving nonlinear partial differential equations in mathematical physics.
Science.gov (United States)
Akbar, M Ali; Ali, Norhashidah Hj Mohd
2016-01-01
In this article, we introduce an ansatz involving exact traveling wave solutions to nonlinear partial differential equations. To obtain wave solutions using direct method, the choice of an appropriate ansatz is of great importance. We apply this ansatz to examine new and further general traveling wave solutions to the (1+1)-dimensional modified Benjamin-Bona-Mahony equation. Abundant traveling wave solutions are derived including solitons, singular solitons, periodic solutions and general solitary wave solutions. The solutions emphasize the nobility of this ansatz in providing distinct solutions to various tangible phenomena in nonlinear science and engineering. The ansatz could be more efficient tool to deal with higher dimensional nonlinear evolution equations which frequently arise in many real world physical problems.
2. Solving Differential Equations in R: Package deSolve
Science.gov (United States)
In this paper we present the R package deSolve to solve initial value problems (IVP) written as ordinary differential equations (ODE), differential algebraic equations (DAE) of index 0 or 1 and partial differential equations (PDE), the latter solved using the method of lines appr...
3. Solving Differential Equations in R: Package deSolve
NARCIS (Netherlands)
Soetaert, K.E.R.; Petzoldt, T.; Setzer, R.W.
2010-01-01
In this paper we present the R package deSolve to solve initial value problems (IVP) written as ordinary differential equations (ODE), differential algebraic equations (DAE) of index 0 or 1 and partial differential equations (PDE), the latter solved using the method of lines approach. The
4. Solving nonlinear, High-order partial differential equations using a high-performance isogeometric analysis framework
KAUST Repository
Cortes, Adriano Mauricio; Vignal, Philippe; Sarmiento, Adel; Garcí a, Daniel O.; Collier, Nathan; Dalcin, Lisandro; Calo, Victor M.
2014-01-01
In this paper we present PetIGA, a high-performance implementation of Isogeometric Analysis built on top of PETSc. We show its use in solving nonlinear and time-dependent problems, such as phase-field models, by taking advantage of the high-continuity of the basis functions granted by the isogeometric framework. In this work, we focus on the Cahn-Hilliard equation and the phase-field crystal equation.
5. Solving Linear Differential Equations
NARCIS (Netherlands)
Nguyen, K.A.; Put, M. van der
2010-01-01
The theme of this paper is to 'solve' an absolutely irreducible differential module explicitly in terms of modules of lower dimension and finite extensions of the differential field K. Representations of semi-simple Lie algebras and differential Galo is theory are the main tools. The results extend
6. Introduction to partial differential equations
CERN Document Server
Greenspan, Donald
2000-01-01
Designed for use in a one-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, second-order partial differential equations, wave equation, potential equation, heat equation, approximate solution of partial differential equations, and more. Exercises appear at the ends of most chapters. 1961 edition.
7. PARALLEL SOLUTION METHODS OF PARTIAL DIFFERENTIAL EQUATIONS
Directory of Open Access Journals (Sweden)
Korhan KARABULUT
1998-03-01
Full Text Available Partial differential equations arise in almost all fields of science and engineering. Computer time spent in solving partial differential equations is much more than that of in any other problem class. For this reason, partial differential equations are suitable to be solved on parallel computers that offer great computation power. In this study, parallel solution to partial differential equations with Jacobi, Gauss-Siedel, SOR (Succesive OverRelaxation and SSOR (Symmetric SOR algorithms is studied.
8. Issues in developing parallel iterative algorithms for solving partial differential equations on a (transputer-based) distributed parallel computing system
International Nuclear Information System (INIS)
Rajagopalan, S.; Jethra, A.; Khare, A.N.; Ghodgaonkar, M.D.; Srivenkateshan, R.; Menon, S.V.G.
1990-01-01
Issues relating to implementing iterative procedures, for numerical solution of elliptic partial differential equations, on a distributed parallel computing system are discussed. Preliminary investigations show that a speed-up of about 3.85 is achievable on a four transputer pipeline network. (author). 2 figs., 3 a ppendixes., 7 refs
9. Applied partial differential equations
CERN Document Server
Logan, J David
2004-01-01
This primer on elementary partial differential equations presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. What makes this book unique is that it is a brief treatment, yet it covers all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. Mathematical ideas are motivated from physical problems, and the exposition is presented in a concise style accessible to science and engineering students; emphasis is on motivation, concepts, methods, and interpretation, rather than formal theory. This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation; epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of t...
10. A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations
Science.gov (United States)
Bhrawy, A. H.; Zaky, M. A.
2015-01-01
In this paper, we propose and analyze an efficient operational formulation of spectral tau method for multi-term time-space fractional differential equation with Dirichlet boundary conditions. The shifted Jacobi operational matrices of Riemann-Liouville fractional integral, left-sided and right-sided Caputo fractional derivatives are presented. By using these operational matrices, we propose a shifted Jacobi tau method for both temporal and spatial discretizations, which allows us to present an efficient spectral method for solving such problem. Furthermore, the error is estimated and the proposed method has reasonable convergence rates in spatial and temporal discretizations. In addition, some known spectral tau approximations can be derived as special cases from our algorithm if we suitably choose the corresponding special cases of Jacobi parameters θ and ϑ. Finally, in order to demonstrate its accuracy, we compare our method with those reported in the literature.
11. Hyperbolic partial differential equations
CERN Document Server
Witten, Matthew
1986-01-01
Hyperbolic Partial Differential Equations III is a refereed journal issue that explores the applications, theory, and/or applied methods related to hyperbolic partial differential equations, or problems arising out of hyperbolic partial differential equations, in any area of research. This journal issue is interested in all types of articles in terms of review, mini-monograph, standard study, or short communication. Some studies presented in this journal include discretization of ideal fluid dynamics in the Eulerian representation; a Riemann problem in gas dynamics with bifurcation; periodic M
12. Beginning partial differential equations
CERN Document Server
O'Neil, Peter V
2011-01-01
A rigorous, yet accessible, introduction to partial differential equations-updated in a valuable new edition Beginning Partial Differential Equations, Second Edition provides a comprehensive introduction to partial differential equations (PDEs) with a special focus on the significance of characteristics, solutions by Fourier series, integrals and transforms, properties and physical interpretations of solutions, and a transition to the modern function space approach to PDEs. With its breadth of coverage, this new edition continues to present a broad introduction to the field, while also addres
13. Parallel Algorithm Solves Coupled Differential Equations
Science.gov (United States)
Hayashi, A.
1987-01-01
Numerical methods adapted to concurrent processing. Algorithm solves set of coupled partial differential equations by numerical integration. Adapted to run on hypercube computer, algorithm separates problem into smaller problems solved concurrently. Increase in computing speed with concurrent processing over that achievable with conventional sequential processing appreciable, especially for large problems.
14. Partial differential equations
CERN Document Server
Evans, Lawrence C
2010-01-01
This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...
15. Solving Ordinary Differential Equations
Science.gov (United States)
Krogh, F. T.
1987-01-01
Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.
16. Fitted Fourier-pseudospectral methods for solving a delayed reaction-diffusion partial differential equation in biology
Science.gov (United States)
Adam, A. M. A.; Bashier, E. B. M.; Hashim, M. H. A.; Patidar, K. C.
2017-07-01
In this work, we design and analyze a fitted numerical method to solve a reaction-diffusion model with time delay, namely, a delayed version of a population model which is an extension of the logistic growth (LG) equation for a food-limited population proposed by Smith [F.E. Smith, Population dynamics in Daphnia magna and a new model for population growth, Ecology 44 (1963) 651-663]. Seeing that the analytical solution (in closed form) is hard to obtain, we seek for a robust numerical method. The method consists of a Fourier-pseudospectral semi-discretization in space and a fitted operator implicit-explicit scheme in temporal direction. The proposed method is analyzed for convergence and we found that it is unconditionally stable. Illustrative numerical results will be presented at the conference.
17. Numerical Analysis of Partial Differential Equations
CERN Document Server
Lui, S H
2011-01-01
A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the numerical analysis
18. Partial differential equations
CERN Document Server
Agranovich, M S
2002-01-01
Mark Vishik's Partial Differential Equations seminar held at Moscow State University was one of the world's leading seminars in PDEs for over 40 years. This book celebrates Vishik's eightieth birthday. It comprises new results and survey papers written by many renowned specialists who actively participated over the years in Vishik's seminars. Contributions include original developments and methods in PDEs and related fields, such as mathematical physics, tomography, and symplectic geometry. Papers discuss linear and nonlinear equations, particularly linear elliptic problems in angles and gener
19. Partial differential equations
CERN Document Server
Levine, Harold
1997-01-01
The subject matter, partial differential equations (PDEs), has a long history (dating from the 18th century) and an active contemporary phase. An early phase (with a separate focus on taut string vibrations and heat flow through solid bodies) stimulated developments of great importance for mathematical analysis, such as a wider concept of functions and integration and the existence of trigonometric or Fourier series representations. The direct relevance of PDEs to all manner of mathematical, physical and technical problems continues. This book presents a reasonably broad introductory account of the subject, with due regard for analytical detail, applications and historical matters.
20. Partial differential equations
CERN Document Server
Sloan, D; Süli, E
2001-01-01
/homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! Over the second half of the 20th century the subject area loosely referred to as numerical analysis of partial differential equations (PDEs) has undergone unprecedented development. At its practical end, the vigorous growth and steady diversification of the field were stimulated by the demand for accurate and reliable tools for computational modelling in physical sciences and engineering, and by the rapid development of computer hardware and architecture. At the more theoretical end, the analytical insight in
1. Elliptic partial differential equations
CERN Document Server
Han, Qing
2011-01-01
Elliptic Partial Differential Equations by Qing Han and FangHua Lin is one of the best textbooks I know. It is the perfect introduction to PDE. In 150 pages or so it covers an amazing amount of wonderful and extraordinary useful material. I have used it as a textbook at both graduate and undergraduate levels which is possible since it only requires very little background material yet it covers an enormous amount of material. In my opinion it is a must read for all interested in analysis and geometry, and for all of my own PhD students it is indeed just that. I cannot say enough good things abo
2. Solving Differential Equations in R: Package deSolve
Directory of Open Access Journals (Sweden)
Karline Soetaert
2010-02-01
Full Text Available In this paper we present the R package deSolve to solve initial value problems (IVP written as ordinary differential equations (ODE, differential algebraic equations (DAE of index 0 or 1 and partial differential equations (PDE, the latter solved using the method of lines approach. The differential equations can be represented in R code or as compiled code. In the latter case, R is used as a tool to trigger the integration and post-process the results, which facilitates model development and application, whilst the compiled code significantly increases simulation speed. The methods implemented are efficient, robust, and well documented public-domain Fortran routines. They include four integrators from the ODEPACK package (LSODE, LSODES, LSODA, LSODAR, DVODE and DASPK2.0. In addition, a suite of Runge-Kutta integrators and special-purpose solvers to efficiently integrate 1-, 2- and 3-dimensional partial differential equations are available. The routines solve both stiff and non-stiff systems, and include many options, e.g., to deal in an efficient way with the sparsity of the Jacobian matrix, or finding the root of equations. In this article, our objectives are threefold: (1 to demonstrate the potential of using R for dynamic modeling, (2 to highlight typical uses of the different methods implemented and (3 to compare the performance of models specified in R code and in compiled code for a number of test cases. These comparisons demonstrate that, if the use of loops is avoided, R code can efficiently integrate problems comprising several thousands of state variables. Nevertheless, the same problem may be solved from 2 to more than 50 times faster by using compiled code compared to an implementation using only R code. Still, amongst the benefits of R are a more flexible and interactive implementation, better readability of the code, and access to R’s high-level procedures. deSolve is the successor of package odesolve which will be deprecated in
3. On Degenerate Partial Differential Equations
OpenAIRE
Chen, Gui-Qiang G.
2010-01-01
Some of recent developments, including recent results, ideas, techniques, and approaches, in the study of degenerate partial differential equations are surveyed and analyzed. Several examples of nonlinear degenerate, even mixed, partial differential equations, are presented, which arise naturally in some longstanding, fundamental problems in fluid mechanics and differential geometry. The solution to these fundamental problems greatly requires a deep understanding of nonlinear degenerate parti...
4. Convergence of hybrid methods for solving non-linear partial ...
African Journals Online (AJOL)
This paper is concerned with the numerical solution and convergence analysis of non-linear partial differential equations using a hybrid method. The solution technique involves discretizing the non-linear system of PDE to obtain a corresponding non-linear system of algebraic difference equations to be solved at each time ...
5. THREE-POINT BACKWARD FINITE DIFFERENCE METHOD FOR SOLVING A SYSTEM OF MIXED HYPERBOLIC-PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS. (R825549C019)
Science.gov (United States)
A three-point backward finite-difference method has been derived for a system of mixed hyperbolic¯¯parabolic (convection¯¯diffusion) partial differential equations (mixed PDEs). The method resorts to the three-point backward differenci...
6. Partial Differential Equations
CERN Document Server
1988-01-01
The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.
7. Teaching Modeling with Partial Differential Equations: Several Successful Approaches
Science.gov (United States)
Myers, Joseph; Trubatch, David; Winkel, Brian
2008-01-01
We discuss the introduction and teaching of partial differential equations (heat and wave equations) via modeling physical phenomena, using a new approach that encompasses constructing difference equations and implementing these in a spreadsheet, numerically solving the partial differential equations using the numerical differential equation…
8. Elements of partial differential equations
CERN Document Server
Sneddon, Ian Naismith
1957-01-01
Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory.Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems of surfaces, and solutions to the odd-numbered problems appear at the end of the book. Readers pursuing independent st
9. Reduced differential transform method for partial differential equations within local fractional derivative operators
Directory of Open Access Journals (Sweden)
Hossein Jafari
2016-04-01
Full Text Available The non-differentiable solution of the linear and non-linear partial differential equations on Cantor sets is implemented in this article. The reduced differential transform method is considered in the local fractional operator sense. The four illustrative examples are given to show the efficiency and accuracy features of the presented technique to solve local fractional partial differential equations.
10. Nonlinear partial differential equations of second order
CERN Document Server
Dong, Guangchang
1991-01-01
This book addresses a class of equations central to many areas of mathematics and its applications. Although there is no routine way of solving nonlinear partial differential equations, effective approaches that apply to a wide variety of problems are available. This book addresses a general approach that consists of the following: Choose an appropriate function space, define a family of mappings, prove this family has a fixed point, and study various properties of the solution. The author emphasizes the derivation of various estimates, including a priori estimates. By focusing on a particular approach that has proven useful in solving a broad range of equations, this book makes a useful contribution to the literature.
11. Boundary value problems and partial differential equations
CERN Document Server
Powers, David L
2005-01-01
Boundary Value Problems is the leading text on boundary value problems and Fourier series. The author, David Powers, (Clarkson) has written a thorough, theoretical overview of solving boundary value problems involving partial differential equations by the methods of separation of variables. Professors and students agree that the author is a master at creating linear problems that adroitly illustrate the techniques of separation of variables used to solve science and engineering.* CD with animations and graphics of solutions, additional exercises and chapter review questions* Nearly 900 exercises ranging in difficulty* Many fully worked examples
12. Basic linear partial differential equations
CERN Document Server
Treves, Francois
1975-01-01
Focusing on the archetypes of linear partial differential equations, this text for upper-level undergraduates and graduate students features most of the basic classical results. The methods, however, are decidedly nontraditional: in practically every instance, they tend toward a high level of abstraction. This approach recalls classical material to contemporary analysts in a language they can understand, as well as exploiting the field's wealth of examples as an introduction to modern theories.The four-part treatment covers the basic examples of linear partial differential equations and their
13. Introduction to partial differential equations and Hilbert space methods
CERN Document Server
Gustafson, Karl E
1997-01-01
Easy-to-use text examines principal method of solving partial differential equations, 1st-order systems, computation methods, and much more. Over 600 exercises, with answers for many. Ideal for a 1-semester or full-year course.
14. Introduction to partial differential equations
CERN Document Server
Borthwick, David
2016-01-01
This modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series, drawing on tools from analysis only as they arise.Within each section the author creates a narrative that answers the five questions: (1) What is the scientific problem we are trying to understand? (2) How do we model that with PDE? (3) What techniques can we use to analyze the PDE? (4) How do those techniques apply to this equation? (5) What information or insight did we obtain by developing and analyzing the PDE? The text stresses the interplay between modeling and mathematical analysis, providing a thorough source of problems and an inspiration for the development of methods.
15. Dynamics of partial differential equations
CERN Document Server
Wayne, C Eugene
2015-01-01
This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently. Wayne reviews recent results on the global dynamics of the two-dimensional Navier-Stokes equations. This system exhibits stable vortex solutions: the topic of Wayne's contribution is how solutions that start from arbitrary initial conditions evolve towards stable vortices. Weinstein considers the dynamics of localized states in nonlinear Schrodinger and Gross-Pitaevskii equations that describe many optical and quantum systems. In this contribution, Weinstein reviews recent bifurcations results of solitary waves, their linear and nonlinear stability properties, and results about radiation damping where waves lose energy through radiation. The articles, written independently, are combined into one volume to showcase the tools of dynamical systems theory at work in explaining qualitative phenomena associated with two classes of partial differential equ...
16. Solving Differential Equations in R
Science.gov (United States)
Although R is still predominantly applied for statistical analysis and graphical representation, it is rapidly becoming more suitable for mathematical computing. One of the fields where considerable progress has been made recently is the solution of differential equations. Here w...
17. Nonlinear elliptic partial differential equations an introduction
CERN Document Server
Le Dret, Hervé
2018-01-01
This textbook presents the essential parts of the modern theory of nonlinear partial differential equations, including the calculus of variations. After a short review of results in real and functional analysis, the author introduces the main mathematical techniques for solving both semilinear and quasilinear elliptic PDEs, and the associated boundary value problems. Key topics include infinite dimensional fixed point methods, the Galerkin method, the maximum principle, elliptic regularity, and the calculus of variations. Aimed at graduate students and researchers, this textbook contains numerous examples and exercises and provides several comments and suggestions for further study.
18. Solving Nonlinear Coupled Differential Equations
Science.gov (United States)
Mitchell, L.; David, J.
1986-01-01
Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.
19. Partial differential equations an introduction
CERN Document Server
Colton, David
2004-01-01
Intended for a college senior or first-year graduate-level course in partial differential equations, this text offers students in mathematics, engineering, and the applied sciences a solid foundation for advanced studies in mathematics. Classical topics presented in a modern context include coverage of integral equations and basic scattering theory. This complete and accessible treatment includes a variety of examples of inverse problems arising from improperly posed applications. Exercises at the ends of chapters, many with answers, offer a clear progression in developing an understanding of
20. Abstract methods in partial differential equations
CERN Document Server
Carroll, Robert W
2012-01-01
Detailed, self-contained treatment examines modern abstract methods in partial differential equations, especially abstract evolution equations. Suitable for graduate students with some previous exposure to classical partial differential equations. 1969 edition.
1. The Cousin problems in the viewpoint of partial differential equations
International Nuclear Information System (INIS)
Le Hung Son.
1990-01-01
In this paper we consider the Cousin problems for overdetermined systems of partial differential equations, which are generalizations of the Cauchy-Riemann system. The general methods for solving these problems are given. Applying the given methods we can solve the Cousin problems for many important systems in theoretical physics. (author). 19 refs
2. Modified Chebyshev Collocation Method for Solving Differential Equations
Directory of Open Access Journals (Sweden)
M Ziaul Arif
2015-05-01
Full Text Available This paper presents derivation of alternative numerical scheme for solving differential equations, which is modified Chebyshev (Vieta-Lucas Polynomial collocation differentiation matrices. The Scheme of modified Chebyshev (Vieta-Lucas Polynomial collocation method is applied to both Ordinary Differential Equations (ODEs and Partial Differential Equations (PDEs cases. Finally, the performance of the proposed method is compared with finite difference method and the exact solution of the example. It is shown that modified Chebyshev collocation method more effective and accurate than FDM for some example given.
3. Differential equation analysis in biomedical science and engineering partial differential equation applications with R
CERN Document Server
Schiesser, William E
2014-01-01
Features a solid foundation of mathematical and computational tools to formulate and solve real-world PDE problems across various fields With a step-by-step approach to solving partial differential equations (PDEs), Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R successfully applies computational techniques for solving real-world PDE problems that are found in a variety of fields, including chemistry, physics, biology, and physiology. The book provides readers with the necessary knowledge to reproduce and extend the com
4. Partial differential equations & boundary value problems with Maple
CERN Document Server
Articolo, George A
2009-01-01
Partial Differential Equations and Boundary Value Problems with Maple presents all of the material normally covered in a standard course on partial differential equations, while focusing on the natural union between this material and the powerful computational software, Maple. The Maple commands are so intuitive and easy to learn, students can learn what they need to know about the software in a matter of hours- an investment that provides substantial returns. Maple''s animation capabilities allow students and practitioners to see real-time displays of the solutions of partial differential equations. Maple files can be found on the books website. Ancillary list: Maple files- http://www.elsevierdirect.com/companion.jsp?ISBN=9780123747327 Provides a quick overview of the software w/simple commands needed to get startedIncludes review material on linear algebra and Ordinary Differential equations, and their contribution in solving partial differential equationsIncorporates an early introduction to Sturm-L...
5. Partial differential equations of mathematical physics
CERN Document Server
Sobolev, S L
1964-01-01
Partial Differential Equations of Mathematical Physics emphasizes the study of second-order partial differential equations of mathematical physics, which is deemed as the foundation of investigations into waves, heat conduction, hydrodynamics, and other physical problems. The book discusses in detail a wide spectrum of topics related to partial differential equations, such as the theories of sets and of Lebesgue integration, integral equations, Green's function, and the proof of the Fourier method. Theoretical physicists, experimental physicists, mathematicians engaged in pure and applied math
6. Partial Differential Equations and Solitary Waves Theory
CERN Document Server
Wazwaz, Abdul-Majid
2009-01-01
"Partial Differential Equations and Solitary Waves Theory" is a self-contained book divided into two parts: Part I is a coherent survey bringing together newly developed methods for solving PDEs. While some traditional techniques are presented, this part does not require thorough understanding of abstract theories or compact concepts. Well-selected worked examples and exercises shall guide the reader through the text. Part II provides an extensive exposition of the solitary waves theory. This part handles nonlinear evolution equations by methods such as Hirota’s bilinear method or the tanh-coth method. A self-contained treatment is presented to discuss complete integrability of a wide class of nonlinear equations. This part presents in an accessible manner a systematic presentation of solitons, multi-soliton solutions, kinks, peakons, cuspons, and compactons. While the whole book can be used as a text for advanced undergraduate and graduate students in applied mathematics, physics and engineering, Part II w...
7. Introduction to partial differential equations with applications
CERN Document Server
Zachmanoglou, E C
1988-01-01
This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.
8. Parameter Estimation of Partial Differential Equation Models.
Science.gov (United States)
Xun, Xiaolei; Cao, Jiguo; Mallick, Bani; Carroll, Raymond J; Maity, Arnab
2013-01-01
Partial differential equation (PDE) models are commonly used to model complex dynamic systems in applied sciences such as biology and finance. The forms of these PDE models are usually proposed by experts based on their prior knowledge and understanding of the dynamic system. Parameters in PDE models often have interesting scientific interpretations, but their values are often unknown, and need to be estimated from the measurements of the dynamic system in the present of measurement errors. Most PDEs used in practice have no analytic solutions, and can only be solved with numerical methods. Currently, methods for estimating PDE parameters require repeatedly solving PDEs numerically under thousands of candidate parameter values, and thus the computational load is high. In this article, we propose two methods to estimate parameters in PDE models: a parameter cascading method and a Bayesian approach. In both methods, the underlying dynamic process modeled with the PDE model is represented via basis function expansion. For the parameter cascading method, we develop two nested levels of optimization to estimate the PDE parameters. For the Bayesian method, we develop a joint model for data and the PDE, and develop a novel hierarchical model allowing us to employ Markov chain Monte Carlo (MCMC) techniques to make posterior inference. Simulation studies show that the Bayesian method and parameter cascading method are comparable, and both outperform other available methods in terms of estimation accuracy. The two methods are demonstrated by estimating parameters in a PDE model from LIDAR data.
9. Partial differential equations for scientists and engineers
CERN Document Server
Farlow, Stanley J
1993-01-01
Most physical phenomena, whether in the domain of fluid dynamics, electricity, magnetism, mechanics, optics, or heat flow, can be described in general by partial differential equations. Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations.This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing th
10. Multigrid methods for partial differential equations - a short introduction
International Nuclear Information System (INIS)
Linden, J.; Stueben, K.
1993-01-01
These notes summarize the multigrid methods and emphasis is laid on the algorithmic concepts of multigrid for solving linear and non-linear partial differential equations. In this paper there is brief description of the basic structure of multigrid methods. Detailed introduction is also contained with applications to VLSI process simulation. (A.B.)
11. Solution of partial differential equations by agent-based simulation
International Nuclear Information System (INIS)
Szilagyi, Miklos N
2014-01-01
The purpose of this short note is to demonstrate that partial differential equations can be quickly solved by agent-based simulation with high accuracy. There is no need for the solution of large systems of algebraic equations. This method is especially useful for quick determination of potential distributions and demonstration purposes in teaching electromagnetism. (letters and comments)
12. Convergence criteria for systems of nonlinear elliptic partial differential equations
International Nuclear Information System (INIS)
Sharma, R.K.
1986-01-01
This thesis deals with convergence criteria for a special system of nonlinear elliptic partial differential equations. A fixed-point algorithm is used, which iteratively solves one linearized elliptic partial differential equation at a time. Conditions are established that help foresee the convergence of the algorithm. Under reasonable hypotheses it is proved that the algorithm converges for such nonlinear elliptic systems. Extensive experimental results are reported and they show the algorithm converges in a wide variety of cases and the convergence is well correlated with the theoretical conditions introduced in this thesis
13. Partial Differential Equations Modeling and Numerical Simulation
CERN Document Server
Glowinski, Roland
2008-01-01
This book is dedicated to Olivier Pironneau. For more than 250 years partial differential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural at first and then those originating from human activity and technological development. Mechanics, physics and their engineering applications were the first to benefit from the impact of partial differential equations on modeling and design, but a little less than a century ago the Schrödinger equation was the key opening the door to the application of partial differential equations to quantum chemistry, for small atomic and molecular systems at first, but then for systems of fast growing complexity. Mathematical modeling methods based on partial differential equations form an important part of contemporary science and are widely used in engineering and scientific applications. In this book several experts in this field present their latest results and discuss trends in the numerical analy...
14. Parameter Estimation of Partial Differential Equation Models
KAUST Repository
Xun, Xiaolei
2013-09-01
Partial differential equation (PDE) models are commonly used to model complex dynamic systems in applied sciences such as biology and finance. The forms of these PDE models are usually proposed by experts based on their prior knowledge and understanding of the dynamic system. Parameters in PDE models often have interesting scientific interpretations, but their values are often unknown and need to be estimated from the measurements of the dynamic system in the presence of measurement errors. Most PDEs used in practice have no analytic solutions, and can only be solved with numerical methods. Currently, methods for estimating PDE parameters require repeatedly solving PDEs numerically under thousands of candidate parameter values, and thus the computational load is high. In this article, we propose two methods to estimate parameters in PDE models: a parameter cascading method and a Bayesian approach. In both methods, the underlying dynamic process modeled with the PDE model is represented via basis function expansion. For the parameter cascading method, we develop two nested levels of optimization to estimate the PDE parameters. For the Bayesian method, we develop a joint model for data and the PDE and develop a novel hierarchical model allowing us to employ Markov chain Monte Carlo (MCMC) techniques to make posterior inference. Simulation studies show that the Bayesian method and parameter cascading method are comparable, and both outperform other available methods in terms of estimation accuracy. The two methods are demonstrated by estimating parameters in a PDE model from long-range infrared light detection and ranging data. Supplementary materials for this article are available online. © 2013 American Statistical Association.
15. Partial Differential Equations in General Relativity
International Nuclear Information System (INIS)
Choquet-Bruhat, Yvonne
2008-01-01
General relativity is a physical theory basic in the modeling of the universe at the large and small scales. Its mathematical formulation, the Einstein partial differential equations, are geometrically simple, but intricate for the analyst, involving both hyperbolic and elliptic PDE, with local and global problems. Many problems remain open though remarkable progress has been made recently towards their solutions. Alan Rendall's book states, in a down-to-earth form, fundamental results used to solve different types of equations. In each case he gives applications to special models as well as to general properties of Einsteinian spacetimes. A chapter on ODE contains, in particular, a detailed discussion of Bianchi spacetimes. A chapter entitled 'Elliptic systems' treats the Einstein constraints. A chapter entitled 'Hyperbolic systems' is followed by a chapter on the Cauchy problem and a chapter 'Global results' which contains recently proved theorems. A chapter is dedicated to the Einstein-Vlasov system, of which the author is a specialist. On the whole, the book surveys, in a concise though precise way, many essential results of recent interest in mathematical general relativity, and it is very clearly written. Each chapter is followed by an up to date bibliography. In conclusion, this book will be a valuable asset to relativists who wish to learn clearly-stated mathematical results and to mathematicians who want to penetrate into the subtleties of general relativity, as a mathematical and physical theory. (book review)
16. Partial Differential Equations in General Relativity
Energy Technology Data Exchange (ETDEWEB)
Choquet-Bruhat, Yvonne
2008-09-07
General relativity is a physical theory basic in the modeling of the universe at the large and small scales. Its mathematical formulation, the Einstein partial differential equations, are geometrically simple, but intricate for the analyst, involving both hyperbolic and elliptic PDE, with local and global problems. Many problems remain open though remarkable progress has been made recently towards their solutions. Alan Rendall's book states, in a down-to-earth form, fundamental results used to solve different types of equations. In each case he gives applications to special models as well as to general properties of Einsteinian spacetimes. A chapter on ODE contains, in particular, a detailed discussion of Bianchi spacetimes. A chapter entitled 'Elliptic systems' treats the Einstein constraints. A chapter entitled 'Hyperbolic systems' is followed by a chapter on the Cauchy problem and a chapter 'Global results' which contains recently proved theorems. A chapter is dedicated to the Einstein-Vlasov system, of which the author is a specialist. On the whole, the book surveys, in a concise though precise way, many essential results of recent interest in mathematical general relativity, and it is very clearly written. Each chapter is followed by an up to date bibliography. In conclusion, this book will be a valuable asset to relativists who wish to learn clearly-stated mathematical results and to mathematicians who want to penetrate into the subtleties of general relativity, as a mathematical and physical theory. (book review)
17. Darboux transformations and linear parabolic partial differential equations
International Nuclear Information System (INIS)
Arrigo, Daniel J.; Hickling, Fred
2002-01-01
Solutions for a class of linear parabolic partial differential equation are provided. These solutions are obtained by first solving a system of (n+1) nonlinear partial differential equations. This system arises as the coefficients of a Darboux transformation and is equivalent to a matrix Burgers' equation. This matrix equation is solved using a generalized Hopf-Cole transformation. The solutions for the original equation are given in terms of solutions of the heat equation. These results are applied to the (1+1)-dimensional Schroedinger equation where all bound state solutions are obtained for a 2n-parameter family of potentials. As a special case, the solutions for integral members of the regular and modified Poeschl-Teller potentials are recovered. (author). Letter-to-the-editor
18. Particle Systems and Partial Differential Equations I
CERN Document Server
Gonçalves, Patricia
2014-01-01
This book presents the proceedings of the international conference Particle Systems and Partial Differential Equations I, which took place at the Centre of Mathematics of the University of Minho, Braga, Portugal, from the 5th to the 7th of December, 2012. The purpose of the conference was to bring together world leaders to discuss their topics of expertise and to present some of their latest research developments in those fields. Among the participants were researchers in probability, partial differential equations and kinetics theory. The aim of the meeting was to present to a varied public the subject of interacting particle systems, its motivation from the viewpoint of physics and its relation with partial differential equations or kinetics theory, and to stimulate discussions and possibly new collaborations among researchers with different backgrounds. The book contains lecture notes written by François Golse on the derivation of hydrodynamic equations (compressible and incompressible Euler and Navie...
19. Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (3).
Science.gov (United States)
Murase, Kenya
2016-01-01
In this issue, simultaneous differential equations were introduced. These differential equations are often used in the field of medical physics. The methods for solving them were also introduced, which include Laplace transform and matrix methods. Some examples were also introduced, in which Laplace transform and matrix methods were applied to solving simultaneous differential equations derived from a three-compartment kinetic model for analyzing the glucose metabolism in tissues and Bloch equations for describing the behavior of the macroscopic magnetization in magnetic resonance imaging.In the next (final) issue, partial differential equations and various methods for solving them will be introduced together with some examples in medical physics.
20. A Novel Partial Differential Algebraic Equation (PDAE) Solver
DEFF Research Database (Denmark)
Lim, Young-il; Chang, Sin-Chung; Jørgensen, Sten Bay
2004-01-01
For solving partial differential algebraic equations (PDAEs), the space-time conservation element/solution element (CE/SE) method is addressed in this study. The method of lines (MOL) using an implicit time integrator is compared with the CE/SE method in terms of computational efficiency, solution...... or nonlinear adsorption isotherm are solved by the two methods. The CE/SE method enforces both local and global flux conservation in space and time, and uses a simple stencil structure (two points at the previous time level and one point at the present time level). Thus, accurate and computationally...
1. Generalized solutions of nonlinear partial differential equations
CERN Document Server
Rosinger, EE
1987-01-01
During the last few years, several fairly systematic nonlinear theories of generalized solutions of rather arbitrary nonlinear partial differential equations have emerged. The aim of this volume is to offer the reader a sufficiently detailed introduction to two of these recent nonlinear theories which have so far contributed most to the study of generalized solutions of nonlinear partial differential equations, bringing the reader to the level of ongoing research.The essence of the two nonlinear theories presented in this volume is the observation that much of the mathematics concernin
2. Asymptotic problems for stochastic partial differential equations
Science.gov (United States)
Salins, Michael
Stochastic partial differential equations (SPDEs) can be used to model systems in a wide variety of fields including physics, chemistry, and engineering. The main SPDEs of interest in this dissertation are the semilinear stochastic wave equations which model the movement of a material with constant mass density that is exposed to both determinstic and random forcing. Cerrai and Freidlin have shown that on fixed time intervals, as the mass density of the material approaches zero, the solutions of the stochastic wave equation converge uniformly to the solutions of a stochastic heat equation, in probability. This is called the Smoluchowski-Kramers approximation. In Chapter 2, we investigate some of the multi-scale behaviors that these wave equations exhibit. In particular, we show that the Freidlin-Wentzell exit place and exit time asymptotics for the stochastic wave equation in the small noise regime can be approximated by the exit place and exit time asymptotics for the stochastic heat equation. We prove that the exit time and exit place asymptotics are characterized by quantities called quasipotentials and we prove that the quasipotentials converge. We then investigate the special case where the equation has a gradient structure and show that we can explicitly solve for the quasipotentials, and that the quasipotentials for the heat equation and wave equation are equal. In Chapter 3, we study the Smoluchowski-Kramers approximation in the case where the material is electrically charged and exposed to a magnetic field. Interestingly, if the system is frictionless, then the Smoluchowski-Kramers approximation does not hold. We prove that the Smoluchowski-Kramers approximation is valid for systems exposed to both a magnetic field and friction. Notably, we prove that the solutions to the second-order equations converge to the solutions of the first-order equation in an Lp sense. This strengthens previous results where convergence was proved in probability.
3. Canonical coordinates for partial differential equations
Science.gov (United States)
Hunt, L. R.; Villarreal, Ramiro
1988-01-01
Necessary and sufficient conditions are found under which operators of the form Sigma (m, j=1) x (2) sub j + X sub O can be made constant coefficient. In addition, necessary and sufficient conditions are derived which classify those linear partial differential operators that can be moved to the Kolmogorov type.
4. Canonical coordinates for partial differential equations
Science.gov (United States)
Hunt, L. R.; Villarreal, Ramiro
1987-01-01
Necessary and sufficient conditions are found under which operators of the form Sigma(m, j=1) X(2)sub j + X sub 0 can be made constant coefficient. In addition, necessary and sufficient conditions are derived which classify those linear partial differential operators that can be moved to the Kolmogorov type.
5. A Numerical Method for Partial Differential Algebraic Equations Based on Differential Transform Method
Directory of Open Access Journals (Sweden)
Murat Osmanoglu
2013-01-01
Full Text Available We have considered linear partial differential algebraic equations (LPDAEs of the form , which has at least one singular matrix of . We have first introduced a uniform differential time index and a differential space index. The initial conditions and boundary conditions of the given system cannot be prescribed for all components of the solution vector here. To overcome this, we introduced these indexes. Furthermore, differential transform method has been given to solve LPDAEs. We have applied this method to a test problem, and numerical solution of the problem has been compared with analytical solution.
6. Partial differential operators of elliptic type
CERN Document Server
Shimakura, Norio
1992-01-01
This book, which originally appeared in Japanese, was written for use in an undergraduate course or first year graduate course in partial differential equations and is likely to be of interest to researchers as well. This book presents a comprehensive study of the theory of elliptic partial differential operators. Beginning with the definitions of ellipticity for higher order operators, Shimakura discusses the Laplacian in Euclidean spaces, elementary solutions, smoothness of solutions, Vishik-Sobolev problems, the Schauder theory, and degenerate elliptic operators. The appendix covers such preliminaries as ordinary differential equations, Sobolev spaces, and maximum principles. Because elliptic operators arise in many areas, readers will appreciate this book for the way it brings together a variety of techniques that have arisen in different branches of mathematics.
7. RECTC/RECTCF, 2. Order Elliptical Partial Differential Equation, Arbitrary Boundary Conditions
International Nuclear Information System (INIS)
Hackbusch, W.
1983-01-01
1 - Description of problem or function: A general linear elliptical second order partial differential equation on a rectangle with arbitrary boundary conditions is solved. 2 - Method of solution: Multi-grid iteration
8. Applying homotopy analysis method for solving differential-difference equation
International Nuclear Information System (INIS)
Wang Zhen; Zou Li; Zhang Hongqing
2007-01-01
In this Letter, we apply the homotopy analysis method to solving the differential-difference equations. A simple but typical example is applied to illustrate the validity and the great potential of the generalized homotopy analysis method in solving differential-difference equation. Comparisons are made between the results of the proposed method and exact solutions. The results show that the homotopy analysis method is an attractive method in solving the differential-difference equations
9. Non-linear partial differential equations an algebraic view of generalized solutions
CERN Document Server
Rosinger, Elemer E
1990-01-01
A massive transition of interest from solving linear partial differential equations to solving nonlinear ones has taken place during the last two or three decades. The availability of better computers has often made numerical experimentations progress faster than the theoretical understanding of nonlinear partial differential equations. The three most important nonlinear phenomena observed so far both experimentally and numerically, and studied theoretically in connection with such equations have been the solitons, shock waves and turbulence or chaotical processes. In many ways, these phenomen
10. Constructing general partial differential equations using polynomial and neural networks.
Science.gov (United States)
2016-01-01
Sum fraction terms can approximate multi-variable functions on the basis of discrete observations, replacing a partial differential equation definition with polynomial elementary data relation descriptions. Artificial neural networks commonly transform the weighted sum of inputs to describe overall similarity relationships of trained and new testing input patterns. Differential polynomial neural networks form a new class of neural networks, which construct and solve an unknown general partial differential equation of a function of interest with selected substitution relative terms using non-linear multi-variable composite polynomials. The layers of the network generate simple and composite relative substitution terms whose convergent series combinations can describe partial dependent derivative changes of the input variables. This regression is based on trained generalized partial derivative data relations, decomposed into a multi-layer polynomial network structure. The sigmoidal function, commonly used as a nonlinear activation of artificial neurons, may transform some polynomial items together with the parameters with the aim to improve the polynomial derivative term series ability to approximate complicated periodic functions, as simple low order polynomials are not able to fully make up for the complete cycles. The similarity analysis facilitates substitutions for differential equations or can form dimensional units from data samples to describe real-world problems. Copyright © 2015 Elsevier Ltd. All rights reserved.
11. A novel method to solve functional differential equations
International Nuclear Information System (INIS)
Tapia, V.
1990-01-01
A method to solve differential equations containing the variational operator as the derivation operation is presented. They are called variational differential equations (VDE). The solution to a VDE should be a function containing the derivatives, with respect to the base space coordinates, of the fields up to a generic order s: a s-th-order function. The variational operator doubles the order of the function on which it acts. Therefore, in order to make compatible the orders of the different terms appearing in a VDE, the solution should be a function containing the derivatives of the fields at all orders. But this takes us again back to the functional methods. In order to avoid this, one must restrict the considerations, in the case of second-order VDEs, to the space of s-th-order functions on which the variational operator acts transitively. These functions have been characterized for a one-dimensional base space for the first- and second-order cases. These functions turn out to be polynomial in the highest-order derivatives of the fields with functions of the lower-order derivatives as coefficients. Then VDEs reduce to a system of coupled partial differential equations for the coefficients above mentioned. The importance of the method lies on the fact that the solutions to VDEs are in a one-to-one correspondence with the solutions of functional differential equations. The previous method finds direct applications in quantum field theory, where the Schroedinger equation plays a central role. Since the Schroedinger equation is reduced to a system of coupled partial differential equations, this provides a nonperturbative scheme for quantum field theory. As an example, the massless scalar field is considered
12. System Entropy Measurement of Stochastic Partial Differential Systems
Directory of Open Access Journals (Sweden)
Bor-Sen Chen
2016-03-01
Full Text Available System entropy describes the dispersal of a system’s energy and is an indication of the disorder of a physical system. Several system entropy measurement methods have been developed for dynamic systems. However, most real physical systems are always modeled using stochastic partial differential dynamic equations in the spatio-temporal domain. No efficient method currently exists that can calculate the system entropy of stochastic partial differential systems (SPDSs in consideration of the effects of intrinsic random fluctuation and compartment diffusion. In this study, a novel indirect measurement method is proposed for calculating of system entropy of SPDSs using a Hamilton–Jacobi integral inequality (HJII-constrained optimization method. In other words, we solve a nonlinear HJII-constrained optimization problem for measuring the system entropy of nonlinear stochastic partial differential systems (NSPDSs. To simplify the system entropy measurement of NSPDSs, the global linearization technique and finite difference scheme were employed to approximate the nonlinear stochastic spatial state space system. This allows the nonlinear HJII-constrained optimization problem for the system entropy measurement to be transformed to an equivalent linear matrix inequalities (LMIs-constrained optimization problem, which can be easily solved using the MATLAB LMI-toolbox (MATLAB R2014a, version 8.3. Finally, several examples are presented to illustrate the system entropy measurement of SPDSs.
13. Calculation of similarity solutions of partial differential equations
International Nuclear Information System (INIS)
Dresner, L.
1980-08-01
When a partial differential equation in two independent variables is invariant to a group G of stretching transformations, it has similarity solutions that can be found by solving an ordinary differential equation. Under broad conditions, this ordinary differential equation is also invariant to another stretching group G', related to G. The invariance of the ordinary differential equation to G' can be used to simplify its solution, particularly if it is of second order. Then a method of Lie's can be used to reduce it to a first-order equation, the study of which is greatly facilitated by analysis of its direction field. The method developed here is applied to three examples: Blasius's equation for boundary layer flow over a flat plate and two nonlinear diffusion equations, cc/sub t/ = c/sub zz/ and c/sub t/ = (cc/sub z/)/sub z/
14. Computational partial differential equations using Matlab
CERN Document Server
Li, Jichun
2008-01-01
Brief Overview of Partial Differential Equations The parabolic equations The wave equations The elliptic equations Differential equations in broader areasA quick review of numerical methods for PDEsFinite Difference Methods for Parabolic Equations Introduction Theoretical issues: stability, consistence, and convergence 1-D parabolic equations2-D and 3-D parabolic equationsNumerical examples with MATLAB codesFinite Difference Methods for Hyperbolic Equations IntroductionSome basic difference schemes Dissipation and dispersion errors Extensions to conservation lawsThe second-order hyperbolic PDE
15. Stochastic partial differential equations an introduction
CERN Document Server
Liu, Wei
2015-01-01
This book provides an introduction to the theory of stochastic partial differential equations (SPDEs) of evolutionary type. SPDEs are one of the main research directions in probability theory with several wide ranging applications. Many types of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations. The theory of SPDEs is based both on the theory of deterministic partial differential equations, as well as on modern stochastic analysis. Whilst this volume mainly follows the ‘variational approach’, it also contains a short account on the ‘semigroup (or mild solution) approach’. In particular, the volume contains a complete presentation of the main existence and uniqueness results in the case of locally monotone coefficients. Various types of generalized coercivity conditions are shown to guarantee non-explosion, but also a systematic approach to treat SPDEs with explosion in finite time is developed. It is, so far, the only book where the latter and t...
16. Hamiltonian partial differential equations and applications
CERN Document Server
Nicholls, David; Sulem, Catherine
2015-01-01
This book is a unique selection of work by world-class experts exploring the latest developments in Hamiltonian partial differential equations and their applications. Topics covered within are representative of the field’s wide scope, including KAM and normal form theories, perturbation and variational methods, integrable systems, stability of nonlinear solutions as well as applications to cosmology, fluid mechanics and water waves. The volume contains both surveys and original research papers and gives a concise overview of the above topics, with results ranging from mathematical modeling to rigorous analysis and numerical simulation. It will be of particular interest to graduate students as well as researchers in mathematics and physics, who wish to learn more about the powerful and elegant analytical techniques for Hamiltonian partial differential equations.
17. Observability of discretized partial differential equations
Science.gov (United States)
Cohn, Stephen E.; Dee, Dick P.
1988-01-01
It is shown that complete observability of the discrete model used to assimilate data from a linear partial differential equation (PDE) system is necessary and sufficient for asymptotic stability of the data assimilation process. The observability theory for discrete systems is reviewed and applied to obtain simple observability tests for discretized constant-coefficient PDEs. Examples are used to show how numerical dispersion can result in discrete dynamics with multiple eigenvalues, thereby detracting from observability.
18. Ambit processes and stochastic partial differential equations
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole; Benth, Fred Espen; Veraart, Almut
Ambit processes are general stochastic processes based on stochastic integrals with respect to Lévy bases. Due to their flexible structure, they have great potential for providing realistic models for various applications such as in turbulence and finance. This papers studies the connection betwe...... ambit processes and solutions to stochastic partial differential equations. We investigate this relationship from two angles: from the Walsh theory of martingale measures and from the viewpoint of the Lévy noise analysis....
19. First-order partial differential equations
CERN Document Server
Rhee, Hyun-Ku; Amundson, Neal R
2001-01-01
This first volume of a highly regarded two-volume text is fully usable on its own. After going over some of the preliminaries, the authors discuss mathematical models that yield first-order partial differential equations; motivations, classifications, and some methods of solution; linear and semilinear equations; chromatographic equations with finite rate expressions; homogeneous and nonhomogeneous quasilinear equations; formation and propagation of shocks; conservation equations, weak solutions, and shock layers; nonlinear equations; and variational problems. Exercises appear at the end of mo
20. Differential geometry techniques for sets of nonlinear partial differential equations
Science.gov (United States)
Estabrook, Frank B.
1990-01-01
An attempt is made to show that the Cartan theory of partial differential equations can be a useful technique for applied mathematics. Techniques for finding consistent subfamilies of solutions that are generically rich and well-posed and for introducing potentials or other usefully consistent auxiliary fields are introduced. An extended sample calculation involving the Korteweg-de Vries equation is given.
1. Representations of Lie algebras and partial differential equations
CERN Document Server
Xu, Xiaoping
2017-01-01
This book provides explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic codes, combinatorics and algebraic varieties, summarizing the author’s works and his joint works with his former students. Further, it presents various oscillator generalizations of the classical representation theorem on harmonic polynomials, and highlights new functors from the representation category of a simple Lie algebra to that of another simple Lie algebra. Partial differential equations play a key role in solving certain representation problems. The weight matrices of the minimal and adjoint representations over the simple Lie algebras of types E and F are proved to generate ternary orthogonal linear codes with large minimal distances. New multi-variable hypergeometric functions related to the root systems of simple Lie algebras are introduced in connection with quantum many-body systems in one dimension. In addition, the book identifies certai...
2. Semi-bounded partial differential operators
CERN Document Server
Cialdea, Alberto
2014-01-01
This book examines the conditions for the semi-boundedness of partial differential operators, which are interpreted in different ways. For example, today we know a great deal about L2-semibounded differential and pseudodifferential operators, although their complete characterization in analytic terms still poses difficulties, even for fairly simple operators. In contrast, until recently almost nothing was known about analytic characterizations of semi-boundedness for differential operators in other Hilbert function spaces and in Banach function spaces. This book works to address that gap. As such, various types of semi-boundedness are considered and a number of relevant conditions which are either necessary and sufficient or best possible in a certain sense are presented. The majority of the results reported on are the authors’ own contributions.
3. A comparison of the Method of Lines to finite difference techniques in solving time-dependent partial differential equations. [with applications to Burger equation and stream function-vorticity problem
Science.gov (United States)
Kurtz, L. A.; Smith, R. E.; Parks, C. L.; Boney, L. R.
1978-01-01
Steady state solutions to two time dependent partial differential systems have been obtained by the Method of Lines (MOL) and compared to those obtained by efficient standard finite difference methods: (1) Burger's equation over a finite space domain by a forward time central space explicit method, and (2) the stream function - vorticity form of viscous incompressible fluid flow in a square cavity by an alternating direction implicit (ADI) method. The standard techniques were far more computationally efficient when applicable. In the second example, converged solutions at very high Reynolds numbers were obtained by MOL, whereas solution by ADI was either unattainable or impractical. With regard to 'set up' time, solution by MOL is an attractive alternative to techniques with complicated algorithms, as much of the programming difficulty is eliminated.
4. Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (4).
Science.gov (United States)
Murase, Kenya
2016-01-01
Partial differential equations are often used in the field of medical physics. In this (final) issue, the methods for solving the partial differential equations were introduced, which include separation of variables, integral transform (Fourier and Fourier-sine transforms), Green's function, and series expansion methods. Some examples were also introduced, in which the integral transform and Green's function methods were applied to solving Pennes' bioheat transfer equation and the Fourier series expansion method was applied to Navier-Stokes equation for analyzing the wall shear stress in blood vessels.Finally, the author hopes that this series will be helpful for people who engage in medical physics.
5. Analytical solutions for systems of partial differential-algebraic equations.
Science.gov (United States)
Benhammouda, Brahim; Vazquez-Leal, Hector
2014-01-01
This work presents the application of the power series method (PSM) to find solutions of partial differential-algebraic equations (PDAEs). Two systems of index-one and index-three are solved to show that PSM can provide analytical solutions of PDAEs in convergent series form. What is more, we present the post-treatment of the power series solutions with the Laplace-Padé (LP) resummation method as a useful strategy to find exact solutions. The main advantage of the proposed methodology is that the procedure is based on a few straightforward steps and it does not generate secular terms or depends of a perturbation parameter.
6. Solving Differential Equations Using Modified Picard Iteration
Science.gov (United States)
Robin, W. A.
2010-01-01
Many classes of differential equations are shown to be open to solution through a method involving a combination of a direct integration approach with suitably modified Picard iterative procedures. The classes of differential equations considered include typical initial value, boundary value and eigenvalue problems arising in physics and…
7. Partial differential equations in several complex variables
CERN Document Server
Chen, So-Chin
2001-01-01
This book is intended both as an introductory text and as a reference book for those interested in studying several complex variables in the context of partial differential equations. In the last few decades, significant progress has been made in the fields of Cauchy-Riemann and tangential Cauchy-Riemann operators. This book gives an up-to-date account of the theories for these equations and their applications. The background material in several complex variables is developed in the first three chapters, leading to the Levi problem. The next three chapters are devoted to the solvability and regularity of the Cauchy-Riemann equations using Hilbert space techniques. The authors provide a systematic study of the Cauchy-Riemann equations and the \\bar\\partial-Neumann problem, including L^2 existence theorems on pseudoconvex domains, \\frac 12-subelliptic estimates for the \\bar\\partial-Neumann problems on strongly pseudoconvex domains, global regularity of \\bar\\partial on more general pseudoconvex domains, boundary ...
8. A partial differential equation for pseudocontact shift.
Science.gov (United States)
Charnock, G T P; Kuprov, Ilya
2014-10-07
It is demonstrated that pseudocontact shift (PCS), viewed as a scalar or a tensor field in three dimensions, obeys an elliptic partial differential equation with a source term that depends on the Hessian of the unpaired electron probability density. The equation enables straightforward PCS prediction and analysis in systems with delocalized unpaired electrons, particularly for the nuclei located in their immediate vicinity. It is also shown that the probability density of the unpaired electron may be extracted, using a regularization procedure, from PCS data.
9. Partial differential equation models in macroeconomics.
Science.gov (United States)
Achdou, Yves; Buera, Francisco J; Lasry, Jean-Michel; Lions, Pierre-Louis; Moll, Benjamin
2014-11-13
10. Nonlinear partial differential equations and their applications
CERN Document Server
Lions, Jacques Louis
2002-01-01
This book contains the written versions of lectures delivered since 1997 in the well-known weekly seminar on Applied Mathematics at the Collège de France in Paris, directed by Jacques-Louis Lions. It is the 14th and last of the series, due to the recent and untimely death of Professor Lions. The texts in this volume deal mostly with various aspects of the theory of nonlinear partial differential equations. They present both theoretical and applied results in many fields of growing importance such as Calculus of variations and optimal control, optimization, system theory and control, op
11. Partial differential equations and their applications
International Nuclear Information System (INIS)
Gauthier-Villars
1998-01-01
This book is dedicated to the French mathematician J.L.Lions. It represents a compilation of articles from about 80 authors. The topics treated are diverse but the more or less commune matter is the study of the characteristics of some partial differential equations. Stability, optimal approximation, numerical resolution, particular applications are among the subjects reviewed. An article deals with the MHD stability of fusion plasmas in tokamaks, another presents the scientific and technical challenges of nuclear energy in France. The latter that contains no equations can be considered as an enjoyable break in a sea of about 40 mathematical articles. (A.C.)
12. ERC Workshop on Geometric Partial Differential Equations
CERN Document Server
Novaga, Matteo; Valdinoci, Enrico
2013-01-01
This book is the outcome of a conference held at the Centro De Giorgi of the Scuola Normale of Pisa in September 2012. The aim of the conference was to discuss recent results on nonlinear partial differential equations, and more specifically geometric evolutions and reaction-diffusion equations. Particular attention was paid to self-similar solutions, such as solitons and travelling waves, asymptotic behaviour, formation of singularities and qualitative properties of solutions. These problems arise in many models from Physics, Biology, Image Processing and Applied Mathematics in general, and have attracted a lot of attention in recent years.
13. Numerical Methods for Partial Differential Equations
CERN Document Server
Guo, Ben-yu
1987-01-01
These Proceedings of the first Chinese Conference on Numerical Methods for Partial Differential Equations covers topics such as difference methods, finite element methods, spectral methods, splitting methods, parallel algorithm etc., their theoretical foundation and applications to engineering. Numerical methods both for boundary value problems of elliptic equations and for initial-boundary value problems of evolution equations, such as hyperbolic systems and parabolic equations, are involved. The 16 papers of this volume present recent or new unpublished results and provide a good overview of current research being done in this field in China.
14. Reconsidering harmonic and anharmonic coherent states: Partial differential equations approach
Energy Technology Data Exchange (ETDEWEB)
2015-02-15
This article presents a new approach to dealing with time dependent quantities such as autocorrelation function of harmonic and anharmonic systems using coherent states and partial differential equations. The approach that is normally used to evaluate dynamical quantities involves formidable operator algebra. That operator algebra becomes insurmountable when employing Morse oscillator coherent states. This problem becomes even more complicated in case of Morse oscillator as it tends to exhibit divergent dynamics. This approach employs linear partial differential equations, some of which may be solved exactly and analytically, thereby avoiding the cumbersome noncommutative algebra required to manipulate coherent states of Morse oscillator. Additionally, the arising integrals while using the herein presented method feature stability and high numerical efficiency. The correctness, applicability, and utility of the above approach are tested by reproducing the partition and optical autocorrelation function of the harmonic oscillator. A closed-form expression for the equilibrium canonical partition function of the Morse oscillator is derived using its coherent states and partial differential equations. Also, a nonequilibrium autocorrelation function expression for weak electron–phonon coupling in condensed systems is derived for displaced Morse oscillator in electronic state. Finally, the utility of the method is demonstrated through further simplifying the Morse oscillator partition function or autocorrelation function expressions reported by other researchers in unevaluated form of second-order derivative exponential. Comparison with exact dynamics shows identical results.
15. A new efficient analytical method for a system of vibration. Structural analysis using a new technique of partially solving method
International Nuclear Information System (INIS)
Gunyasu, Kenzo; Hiramoto, Tsuneyuki; Tanimoto, Mitsumori; Osano, Minetada
2002-01-01
We describe a new method for solving large-scale system of linear equations resulting from discretization of ordinary differential equation and partial differential equation directly. This new method effectively reduces the memory capacity requirements and computing time problems for analyses using finite difference method and finite element method. In this paper we have tried to solve one-million linear equations directly for the case that initial displacement and boundary displacement are known about the finite difference scheme of second order inhomogeneous differential equation for vibration of a 10 story structure. Excellent results were got. (author)
16. Adams Predictor-Corrector Systems for Solving Fuzzy Differential Equations
Directory of Open Access Journals (Sweden)
Dequan Shang
2013-01-01
Full Text Available A predictor-corrector algorithm and an improved predictor-corrector (IPC algorithm based on Adams method are proposed to solve first-order differential equations with fuzzy initial condition. These algorithms are generated by updating the Adams predictor-corrector method and their convergence is also analyzed. Finally, the proposed methods are illustrated by solving an example.
17. Inverse problems for partial differential equations
CERN Document Server
Isakov, Victor
2017-01-01
This third edition expands upon the earlier edition by adding nearly 40 pages of new material reflecting the analytical and numerical progress in inverse problems in last 10 years. As in the second edition, the emphasis is on new ideas and methods rather than technical improvements. These new ideas include use of the stationary phase method in the two-dimensional elliptic problems and of multi frequencies\\temporal data to improve stability and numerical resolution. There are also numerous corrections and improvements of the exposition throughout. This book is intended for mathematicians working with partial differential equations and their applications, physicists, geophysicists, and financial, electrical, and mechanical engineers involved with nondestructive evaluation, seismic exploration, remote sensing, and various kinds of tomography. Review of the second edition: "The first edition of this excellent book appeared in 1998 and became a standard reference for everyone interested in analysis and numerics of...
18. Partial differential equations mathematical techniques for engineers
CERN Document Server
Epstein, Marcelo
2017-01-01
This monograph presents a graduate-level treatment of partial differential equations (PDEs) for engineers. The book begins with a review of the geometrical interpretation of systems of ODEs, the appearance of PDEs in engineering is motivated by the general form of balance laws in continuum physics. Four chapters are devoted to a detailed treatment of the single first-order PDE, including shock waves and genuinely non-linear models, with applications to traffic design and gas dynamics. The rest of the book deals with second-order equations. In the treatment of hyperbolic equations, geometric arguments are used whenever possible and the analogy with discrete vibrating systems is emphasized. The diffusion and potential equations afford the opportunity of dealing with questions of uniqueness and continuous dependence on the data, the Fourier integral, generalized functions (distributions), Duhamel's principle, Green's functions and Dirichlet and Neumann problems. The target audience primarily comprises graduate s...
19. Handbook of differential equations stationary partial differential equations
CERN Document Server
Chipot, Michel
2006-01-01
This handbook is volume III in a series devoted to stationary partial differential quations. Similarly as volumes I and II, it is a collection of self contained state-of-the-art surveys written by well known experts in the field. The topics covered by this handbook include singular and higher order equations, problems near critically, problems with anisotropic nonlinearities, dam problem, T-convergence and Schauder-type estimates. These surveys will be useful for both beginners and experts and speed up the progress of corresponding (rapidly developing and fascinating) areas of mathematics. Ke
20. Lagrange-Noether method for solving second-order differential equations
Institute of Scientific and Technical Information of China (English)
Wu Hui-Bin; Wu Run-Heng
2009-01-01
The purpose of this paper is to provide a new method called the Lagrange-Noether method for solving second-order differential equations. The method is,firstly,to write the second-order differential equations completely or partially in the form of Lagrange equations,and secondly,to obtain the integrals of the equations by using the Noether theory of the Lagrange system. An example is given to illustrate the application of the result.
1. Solving Fuzzy Fractional Differential Equations Using Zadeh's Extension Principle
Science.gov (United States)
Ahmad, M. Z.; Hasan, M. K.; Abbasbandy, S.
2013-01-01
We study a fuzzy fractional differential equation (FFDE) and present its solution using Zadeh's extension principle. The proposed study extends the case of fuzzy differential equations of integer order. We also propose a numerical method to approximate the solution of FFDEs. To solve nonlinear problems, the proposed numerical method is then incorporated into an unconstrained optimisation technique. Several numerical examples are provided. PMID:24082853
2. The convergence of the order sequence and the solution function sequence on fractional partial differential equation
Science.gov (United States)
Rusyaman, E.; Parmikanti, K.; Chaerani, D.; Asefan; Irianingsih, I.
2018-03-01
One of the application of fractional ordinary differential equation is related to the viscoelasticity, i.e., a correlation between the viscosity of fluids and the elasticity of solids. If the solution function develops into function with two or more variables, then its differential equation must be changed into fractional partial differential equation. As the preliminary study for two variables viscoelasticity problem, this paper discusses about convergence analysis of function sequence which is the solution of the homogenous fractional partial differential equation. The method used to solve the problem is Homotopy Analysis Method. The results show that if given two real number sequences (αn) and (βn) which converge to α and β respectively, then the solution function sequences of fractional partial differential equation with order (αn, βn) will also converge to the solution function of fractional partial differential equation with order (α, β).
3. Compatible Spatial Discretizations for Partial Differential Equations
Energy Technology Data Exchange (ETDEWEB)
Arnold, Douglas, N, ed.
2004-11-25
From May 11--15, 2004, the Institute for Mathematics and its Applications held a hot topics workshop on Compatible Spatial Discretizations for Partial Differential Equations. The numerical solution of partial differential equations (PDE) is a fundamental task in science and engineering. The goal of the workshop was to bring together a spectrum of scientists at the forefront of the research in the numerical solution of PDEs to discuss compatible spatial discretizations. We define compatible spatial discretizations as those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. A wide variety of discretization methods applied across a wide range of scientific and engineering applications have been designed to or found to inherit or mimic intrinsic spatial structure and reproduce fundamental properties of the solution of the continuous PDE model at the finite dimensional level. A profusion of such methods and concepts relevant to understanding them have been developed and explored: mixed finite element methods, mimetic finite differences, support operator methods, control volume methods, discrete differential forms, Whitney forms, conservative differencing, discrete Hodge operators, discrete Helmholtz decomposition, finite integration techniques, staggered grid and dual grid methods, etc. This workshop seeks to foster communication among the diverse groups of researchers designing, applying, and studying such methods as well as researchers involved in practical solution of large scale problems that may benefit from advancements in such discretizations; to help elucidate the relations between the different methods and concepts; and to generally advance our understanding in the area of compatible spatial discretization methods for PDE. Particular points of emphasis included: + Identification of intrinsic properties of PDE models that are critical for the fidelity of numerical
4. A Line-Tau Collocation Method for Partial Differential Equations ...
African Journals Online (AJOL)
This paper deals with the numerical solution of second order linear partial differential equations with the use of the method of lines coupled with the tau collocation method. The method of lines is used to convert the partial differential equation (PDE) to a sequence of ordinary differential equations (ODEs) which is then ...
5. Parameter Estimation of Partial Differential Equation Models
KAUST Repository
Xun, Xiaolei; Cao, Jiguo; Mallick, Bani; Maity, Arnab; Carroll, Raymond J.
2013-01-01
PDEs used in practice have no analytic solutions, and can only be solved with numerical methods. Currently, methods for estimating PDE parameters require repeatedly solving PDEs numerically under thousands of candidate parameter values, and thus
6. Path integral solution of linear second order partial differential equations I: the general construction
International Nuclear Information System (INIS)
LaChapelle, J.
2004-01-01
A path integral is presented that solves a general class of linear second order partial differential equations with Dirichlet/Neumann boundary conditions. Elementary kernels are constructed for both Dirichlet and Neumann boundary conditions. The general solution can be specialized to solve elliptic, parabolic, and hyperbolic partial differential equations with boundary conditions. This extends the well-known path integral solution of the Schroedinger/diffusion equation in unbounded space. The construction is based on a framework for functional integration introduced by Cartier/DeWitt-Morette
7. Partial differential equations methods, applications and theories
CERN Document Server
Hattori, Harumi
2013-01-01
This volume is an introductory level textbook for partial differential equations (PDE's) and suitable for a one-semester undergraduate level or two-semester graduate level course in PDE's or applied mathematics. Chapters One to Five are organized according to the equations and the basic PDE's are introduced in an easy to understand manner. They include the first-order equations and the three fundamental second-order equations, i.e. the heat, wave and Laplace equations. Through these equations we learn the types of problems, how we pose the problems, and the methods of solutions such as the separation of variables and the method of characteristics. The modeling aspects are explained as well. The methods introduced in earlier chapters are developed further in Chapters Six to Twelve. They include the Fourier series, the Fourier and the Laplace transforms, and the Green's functions. The equations in higher dimensions are also discussed in detail. This volume is application-oriented and rich in examples. Going thr...
8. Solving SAT Problem Based on Hybrid Differential Evolution Algorithm
Science.gov (United States)
Liu, Kunqi; Zhang, Jingmin; Liu, Gang; Kang, Lishan
Satisfiability (SAT) problem is an NP-complete problem. Based on the analysis about it, SAT problem is translated equally into an optimization problem on the minimum of objective function. A hybrid differential evolution algorithm is proposed to solve the Satisfiability problem. It makes full use of strong local search capacity of hill-climbing algorithm and strong global search capability of differential evolution algorithm, which makes up their disadvantages, improves the efficiency of algorithm and avoids the stagnation phenomenon. The experiment results show that the hybrid algorithm is efficient in solving SAT problem.
9. Reproducing Kernel Method for Solving Nonlinear Differential-Difference Equations
Directory of Open Access Journals (Sweden)
Reza Mokhtari
2012-01-01
Full Text Available On the basis of reproducing kernel Hilbert spaces theory, an iterative algorithm for solving some nonlinear differential-difference equations (NDDEs is presented. The analytical solution is shown in a series form in a reproducing kernel space, and the approximate solution , is constructed by truncating the series to terms. The convergence of , to the analytical solution is also proved. Results obtained by the proposed method imply that it can be considered as a simple and accurate method for solving such differential-difference problems.
10. Workload Characterization of CFD Applications Using Partial Differential Equation Solvers
Science.gov (United States)
Waheed, Abdul; Yan, Jerry; Saini, Subhash (Technical Monitor)
1998-01-01
Workload characterization is used for modeling and evaluating of computing systems at different levels of detail. We present workload characterization for a class of Computational Fluid Dynamics (CFD) applications that solve Partial Differential Equations (PDEs). This workload characterization focuses on three high performance computing platforms: SGI Origin2000, EBM SP-2, a cluster of Intel Pentium Pro bases PCs. We execute extensive measurement-based experiments on these platforms to gather statistics of system resource usage, which results in workload characterization. Our workload characterization approach yields a coarse-grain resource utilization behavior that is being applied for performance modeling and evaluation of distributed high performance metacomputing systems. In addition, this study enhances our understanding of interactions between PDE solver workloads and high performance computing platforms and is useful for tuning these applications.
11. Approximate Method for Solving the Linear Fuzzy Delay Differential Equations
Directory of Open Access Journals (Sweden)
S. Narayanamoorthy
2015-01-01
Full Text Available We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.
12. On Solving the Lorenz System by Differential Transformation Method
International Nuclear Information System (INIS)
Al-Sawalha, M. Mossa; Noorani, M. S. M.
2008-01-01
The differential transformation method (DTM) is employed to solve a nonlinear differential equation, namely the Lorenz system. Numerical results are compared to those obtained by the Runge–Kutta method to illustrate the preciseness and effectiveness of the proposed method. In particular, we examine the accuracy of the (DTM) as the Lorenz system changes from a non-chaotic system to a chaotic one. It is shown that the (DTM) is robust, accurate and easy to apply
13. A Simple Derivation of Kepler's Laws without Solving Differential Equations
Science.gov (United States)
Provost, J.-P.; Bracco, C.
2009-01-01
Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls for non-trivial properties of ellipses, is avoided by the introduction of polar coordinates. Then a simple…
14. Using Computer Symbolic Algebra to Solve Differential Equations.
Science.gov (United States)
Mathews, John H.
1989-01-01
This article illustrates that mathematical theory can be incorporated into the process to solve differential equations by a computer algebra system, muMATH. After an introduction to functions of muMATH, several short programs for enhancing the capabilities of the system are discussed. Listed are six references. (YP)
15. Dielectric metasurfaces solve differential and integro-differential equations.
Science.gov (United States)
2017-04-01
Leveraging subwavelength resonant nanostructures, plasmonic metasurfaces have recently attracted much attention as a breakthrough concept for engineering optical waves both spatially and spectrally. However, inherent ohmic losses concomitant with low coupling efficiencies pose fundamental impediments over their practical applications. Not only can all-dielectric metasurfaces tackle such substantial drawbacks, but also their CMOS-compatible configurations support both Mie resonances that are invariant to the incident angle. Here, we report on a transmittive metasurface comprising arrayed silicon nanodisks embedded in a homogeneous dielectric medium to manipulate phase and amplitude of incident light locally and almost independently. By taking advantage of the interplay between the electric/magnetic resonances and employing general concepts of spatial Fourier transformation, a highly efficient metadevice is proposed to perform mathematical operations including solution of ordinary differential and integro-differential equations with constant coefficients. Our findings further substantiate dielectric metasurfaces as promising candidates for miniaturized, two-dimensional, and planar optical analog computing systems that are much thinner than their conventional lens-based counterparts.
16. A neuro approach to solve fuzzy Riccati differential equations
Energy Technology Data Exchange (ETDEWEB)
Shahrir, Mohammad Shazri, E-mail: mshazri@gmail.com [InstitutSainsMatematik, Universiti Malaya 50603 Kuala Lumpur, Wilayah Persekutuan Kuala Lumpur (Malaysia); Telekom Malaysia, R& D TM Innovation Centre, LingkaranTeknokrat Timur, 63000 Cyberjaya, Selangor (Malaysia); Kumaresan, N., E-mail: drnk2008@gmail.com; Kamali, M. Z. M.; Ratnavelu, Kurunathan [InstitutSainsMatematik, Universiti Malaya 50603 Kuala Lumpur, Wilayah Persekutuan Kuala Lumpur (Malaysia)
2015-10-22
There are many applications of optimal control theory especially in the area of control systems in engineering. In this paper, fuzzy quadratic Riccati differential equation is estimated using neural networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). The solution can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that NN approach shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over RK4.
17. Topics in numerical partial differential equations and scientific computing
CERN Document Server
2016-01-01
Numerical partial differential equations (PDEs) are an important part of numerical simulation, the third component of the modern methodology for science and engineering, besides the traditional theory and experiment. This volume contains papers that originated with the collaborative research of the teams that participated in the IMA Workshop for Women in Applied Mathematics: Numerical Partial Differential Equations and Scientific Computing in August 2014.
18. Lagrangian vector field and Lagrangian formulation of partial differential equations
Directory of Open Access Journals (Sweden)
M.Chen
2005-01-01
Full Text Available In this paper we consider the Lagrangian formulation of a system of second order quasilinear partial differential equations. Specifically we construct a Lagrangian vector field such that the flows of the vector field satisfy the original system of partial differential equations.
19. A note on the Lie symmetries of complex partial differential
Folklore suggests that the split Lie-like operators of a complex partial differential equation are symmetries of the split system of real partial differential equations. However, this is not the case generally. We illustrate this by using the complex heat equation, wave equation with dissipation, the nonlinear Burgers equation and ...
20. Parameter Estimation for Partial Differential Equations by Collage-Based Numerical Approximation
Directory of Open Access Journals (Sweden)
Xiaoyan Deng
2009-01-01
into a minimization problem of a function of several variables after the partial differential equation is approximated by a differential dynamical system. Then numerical schemes for solving this minimization problem are proposed, including grid approximation and ant colony optimization. The proposed schemes are applied to a parameter estimation problem for the Belousov-Zhabotinskii equation, and the results show that the proposed approximation method is efficient for both linear and nonlinear partial differential equations with respect to unknown parameters. At worst, the presented method provides an excellent starting point for traditional inversion methods that must first select a good starting point.
1. Effective action for stochastic partial differential equations
International Nuclear Information System (INIS)
Hochberg, David; Molina-Paris, Carmen; Perez-Mercader, Juan; Visser, Matt
1999-01-01
Stochastic partial differential equations (SPDEs) are the basic tool for modeling systems where noise is important. SPDEs are used for models of turbulence, pattern formation, and the structural development of the universe itself. It is reasonably well known that certain SPDEs can be manipulated to be equivalent to (nonquantum) field theories that nevertheless exhibit deep and important relationships with quantum field theory. In this paper we systematically extend these ideas: We set up a functional integral formalism and demonstrate how to extract all the one-loop physics for an arbitrary SPDE subject to arbitrary Gaussian noise. It is extremely important to realize that Gaussian noise does not imply that the field variables undergo Gaussian fluctuations, and that these nonquantum field theories are fully interacting. The limitation to one loop is not as serious as might be supposed: Experience with quantum field theories (QFTs) has taught us that one-loop physics is often quite adequate to give a good description of the salient issues. The limitation to one loop does, however, offer marked technical advantages: Because at one loop almost any field theory can be rendered finite using zeta function technology, we can sidestep the complications inherent in the Martin-Siggia-Rose formalism (the SPDE analog of the Becchi-Rouet-Stora-Tyutin formalism used in QFT) and instead focus attention on a minimalist approach that uses only the physical fields (this ''direct approach'' is the SPDE analog of canonical quantization using physical fields). After setting up the general formalism for the characteristic functional (partition function), we show how to define the effective action to all loops, and then focus on the one-loop effective action and its specialization to constant fields: the effective potential. The physical interpretation of the effective action and effective potential for SPDEs is addressed and we show that key features carry over from QFT to the case of
2. Effective action for stochastic partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Hochberg, David [Laboratorio de Astrofisica Espacial y Fisica Fundamental, Apartado 50727, 28080 Madrid, (Spain); Centro de Astrobiologia, INTA, Carratera Ajalvir, Km. 4, 28850 Torrejon, Madrid, (Spain); Molina-Paris, Carmen [Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Perez-Mercader, Juan [Laboratorio de Astrofisica Espacial y Fisica Fundamental, Apartado 50727, 28080 Madrid, (Spain); Visser, Matt [Physics Department, Washington University, Saint Louis, Missouri 63130-4899 (United States)
1999-12-01
Stochastic partial differential equations (SPDEs) are the basic tool for modeling systems where noise is important. SPDEs are used for models of turbulence, pattern formation, and the structural development of the universe itself. It is reasonably well known that certain SPDEs can be manipulated to be equivalent to (nonquantum) field theories that nevertheless exhibit deep and important relationships with quantum field theory. In this paper we systematically extend these ideas: We set up a functional integral formalism and demonstrate how to extract all the one-loop physics for an arbitrary SPDE subject to arbitrary Gaussian noise. It is extremely important to realize that Gaussian noise does not imply that the field variables undergo Gaussian fluctuations, and that these nonquantum field theories are fully interacting. The limitation to one loop is not as serious as might be supposed: Experience with quantum field theories (QFTs) has taught us that one-loop physics is often quite adequate to give a good description of the salient issues. The limitation to one loop does, however, offer marked technical advantages: Because at one loop almost any field theory can be rendered finite using zeta function technology, we can sidestep the complications inherent in the Martin-Siggia-Rose formalism (the SPDE analog of the Becchi-Rouet-Stora-Tyutin formalism used in QFT) and instead focus attention on a minimalist approach that uses only the physical fields (this ''direct approach'' is the SPDE analog of canonical quantization using physical fields). After setting up the general formalism for the characteristic functional (partition function), we show how to define the effective action to all loops, and then focus on the one-loop effective action and its specialization to constant fields: the effective potential. The physical interpretation of the effective action and effective potential for SPDEs is addressed and we show that key features carry over from
3. CPDS3, Coupled 3-D Partial Differential Equation Solution
International Nuclear Information System (INIS)
Anderson, D.V.; Koniges, A.E.; Shumaker, D.E.
1992-01-01
1 - Description of program or function: CPDES3 solves the linear asymmetric matrix equations arising from coupled partial differential equations in three dimensions. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximation employed. CPDES3 allows each spatial operator to have 7, 15, 19, or 27 point stencils, permits general couplings between all of the component PDE's, and automatically generates the matrix structures needed to perform the algorithm. 2 - Method of solution: The resulting sparse matrix equation with a complicated sub-band structure and generally asymmetric is solved by either the preconditioned conjugate gradient (CG) method or the preconditioned bi-conjugate gradient (BCG) algorithm. BCG enjoys faster convergence in most cases but in rare instances diverges. Then, CG iterations must be used. 3 - Restrictions on the complexity of the problem: The discretization of the coupled three-dimensional PDE's and their boundary conditions must result in an operator stencil which fits in the Cray2 memory. In addition, the matrix must possess a reasonable amount of diagonal dominance for the preconditioning technique to be effective
4. CPDES2, Coupled 2-D Partial Differential Equation Solution
International Nuclear Information System (INIS)
Anderson, D.V.; Koniges, A.E.; Shumaker, D.E.
1992-01-01
1 - Description of program or function: CPDES2 solves the linear asymmetric equations arising from coupled partial differential equations in two dimensions. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximation employed. CPDES2 allows each spatial operator to have 5 or 9 point stencils, permits general coupling between all of the component PDE's, and automatically generates the matrix structures needed to perform the algorithm. 2 - Method of solution: The resulting sparse matrix equation with a complicated sub-band structure and generally asymmetric is solved by either the preconditioned conjugate gradient (CG) method or the preconditioned bi-conjugate gradient (BCG) algorithm. BCG enjoys faster convergence in most cases but in rare instances diverges. Then, CG iterations must be used. 3 - Restrictions on the complexity of the problem: The discretization of the coupled two-dimensional PDE's and their boundary conditions must result in an operator stencil which fits in the Cray2 memory. In addition, the matrix must possess a reasonable amount of diagonal dominance for the preconditioning technique to be effective
5. Approximate analytical methods for solving ordinary differential equations
CERN Document Server
2015-01-01
Approximate Analytical Methods for Solving Ordinary Differential Equations (ODEs) is the first book to present all of the available approximate methods for solving ODEs, eliminating the need to wade through multiple books and articles. It covers both well-established techniques and recently developed procedures, including the classical series solution method, diverse perturbation methods, pioneering asymptotic methods, and the latest homotopy methods.The book is suitable not only for mathematicians and engineers but also for biologists, physicists, and economists. It gives a complete descripti
6. On the hierarchy of partially invariant submodels of differential equations
OpenAIRE
Golovin, Sergey V.
2007-01-01
It is noticed, that partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PIS of the higher rank. This introduce a hierarchic structure in the set of all PISs of a given system of differential equations. By using this structure one can significantly decrease an amount of calculations required in enumeration of all PISs for a given system of partially differential equations. An equivalence of the two-step and the direct ...
7. Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear partial differential evolution equations of dynamical systems
Institute of Scientific and Technical Information of China (English)
2008-01-01
Using functional derivative technique in quantum field theory, the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations. The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynam-ics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new nu-merical algorithm—algebraic dynamics algorithm was proposed for partial differ-ential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.
8. Solving polynomial differential equations by transforming them to linear functional-differential equations
OpenAIRE
Nahay, John Michael
2008-01-01
We present a new approach to solving polynomial ordinary differential equations by transforming them to linear functional equations and then solving the linear functional equations. We will focus most of our attention upon the first-order Abel differential equation with two nonlinear terms in order to demonstrate in as much detail as possible the computations necessary for a complete solution. We mention in our section on further developments that the basic transformation idea can be generali...
9. On the hierarchy of partially invariant submodels of differential equations
Energy Technology Data Exchange (ETDEWEB)
Golovin, Sergey V [Lavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk 630090 (Russian Federation)], E-mail: sergey@hydro.nsc.ru
2008-07-04
It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given.
10. On the hierarchy of partially invariant submodels of differential equations
Science.gov (United States)
Golovin, Sergey V.
2008-07-01
It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given.
11. On the hierarchy of partially invariant submodels of differential equations
International Nuclear Information System (INIS)
Golovin, Sergey V
2008-01-01
It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given
12. Flow visualization via partial differential equations
NARCIS (Netherlands)
Preusser, T.; Rumpf, M.; Telea, A.C.; Möller, T.; Hamann, B.; Russell, R.D.
2009-01-01
The visualization of stationary and time-dependent flow is an important and chaltenging topic in scientific visualization. lts aim is 10 represent transport phenomena govemed by vector fjelds in an intuitively understandable way. In this paper. we review the use of methods based on partial
13. From ordinary to partial differential equations
CERN Document Server
Esposito, Giampiero
2017-01-01
This book is addressed to mathematics and physics students who want to develop an interdisciplinary view of mathematics, from the age of Riemann, Poincaré and Darboux to basic tools of modern mathematics. It enables them to acquire the sensibility necessary for the formulation and solution of difficult problems, with an emphasis on concepts, rigour and creativity. It consists of eight self-contained parts: ordinary differential equations; linear elliptic equations; calculus of variations; linear and non-linear hyperbolic equations; parabolic equations; Fuchsian functions and non-linear equations; the functional equations of number theory; pseudo-differential operators and pseudo-differential equations. The author leads readers through the original papers and introduces new concepts, with a selection of topics and examples that are of high pedagogical value.
14. Sparse dynamics for partial differential equations.
Science.gov (United States)
Schaeffer, Hayden; Caflisch, Russel; Hauck, Cory D; Osher, Stanley
2013-04-23
We investigate the approximate dynamics of several differential equations when the solutions are restricted to a sparse subset of a given basis. The restriction is enforced at every time step by simply applying soft thresholding to the coefficients of the basis approximation. By reducing or compressing the information needed to represent the solution at every step, only the essential dynamics are represented. In many cases, there are natural bases derived from the differential equations, which promote sparsity. We find that our method successfully reduces the dynamics of convection equations, diffusion equations, weak shocks, and vorticity equations with high-frequency source terms.
15. Unified algorithm for partial differential equations and examples of numerical computation
International Nuclear Information System (INIS)
Watanabe, Tsuguhiro
1999-01-01
A new unified algorithm is proposed to solve partial differential equations which describe nonlinear boundary value problems, eigenvalue problems and time developing boundary value problems. The algorithm is composed of implicit difference scheme and multiple shooting scheme and is named as HIDM (Higher order Implicit Difference Method). A new prototype computer programs for 2-dimensional partial differential equations is constructed and tested successfully to several problems. Extension of the computer programs to 3 or more higher order dimension problems will be easy due to the direct product type difference scheme. (author)
16. Partial differential equation models in the socio-economic sciences
KAUST Repository
Burger, Martin; Caffarelli, Luis; Markowich, Peter A.
2014-01-01
Mathematical models based on partial differential equations (PDEs) have become an integral part of quantitative analysis in most branches of science and engineering, recently expanding also towards biomedicine and socio-economic sciences
17. A Priori Regularity of Parabolic Partial Differential Equations
KAUST Repository
Berkemeier, Francisco
2018-01-01
In this thesis, we consider parabolic partial differential equations such as the heat equation, the Fokker-Planck equation, and the porous media equation. Our aim is to develop methods that provide a priori estimates for solutions with singular
18. Exact solutions of some nonlinear partial differential equations using ...
Nonlinear partial differential equations (NPDEs) are encountered in various ... such as physics, mechanics, chemistry, biology, mathematics and engineering. ... In §3, this method is applied to the generalized forms of Klein–Gordon equation,.
19. Formulae of differentiation for solving differential equations with complex-valued random coefficients
International Nuclear Information System (INIS)
Kim, Ki Hong; Lee, Dong Hun
1999-01-01
Generalizing the work of Shapiro and Loginov, we derive new formulae of differentiation useful for solving differential equations with complex-valued random coefficients. We apply the formulae to the quantum-mechanical problem of noninteracting electrons moving in a correlated random potential in one dimension
20. Handbook of Nonlinear Partial Differential Equations
CERN Document Server
Polyanin, Andrei D
2011-01-01
New to the Second Edition More than 1,000 pages with over 1,500 new first-, second-, third-, fourth-, and higher-order nonlinear equations with solutions Parabolic, hyperbolic, elliptic, and other systems of equations with solutions Some exact methods and transformations Symbolic and numerical methods for solving nonlinear PDEs with Maple(t), Mathematica(R), and MATLAB(R) Many new illustrative examples and tables A large list of references consisting of over 1,300 sources To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology. They
1. International Conference on Multiscale Methods and Partial Differential Equations.
Energy Technology Data Exchange (ETDEWEB)
Thomas Hou
2006-12-12
The International Conference on Multiscale Methods and Partial Differential Equations (ICMMPDE for short) was held at IPAM, UCLA on August 26-27, 2005. The conference brought together researchers, students and practitioners with interest in the theoretical, computational and practical aspects of multiscale problems and related partial differential equations. The conference provided a forum to exchange and stimulate new ideas from different disciplines, and to formulate new challenging multiscale problems that will have impact in applications.
2. Numerical Analysis for Stochastic Partial Differential Delay Equations with Jumps
OpenAIRE
Li, Yan; Hu, Junhao
2013-01-01
We investigate the convergence rate of Euler-Maruyama method for a class of stochastic partial differential delay equations driven by both Brownian motion and Poisson point processes. We discretize in space by a Galerkin method and in time by using a stochastic exponential integrator. We generalize some results of Bao et al. (2011) and Jacob et al. (2009) in finite dimensions to a class of stochastic partial differential delay equations with jumps in infinite dimensions.
3. Preconditioning for partial differential equation constrained optimization with control constraints
KAUST Repository
Stoll, Martin; Wathen, Andy
2011-01-01
Optimal control problems with partial differential equations play an important role in many applications. The inclusion of bound constraints for the control poses a significant additional challenge for optimization methods. In this paper, we propose preconditioners for the saddle point problems that arise when a primal-dual active set method is used. We also show for this method that the same saddle point system can be derived when the method is considered as a semismooth Newton method. In addition, the projected gradient method can be employed to solve optimization problems with simple bounds, and we discuss the efficient solution of the linear systems in question. In the case when an acceleration technique is employed for the projected gradient method, this again yields a semismooth Newton method that is equivalent to the primal-dual active set method. We also consider the Moreau-Yosida regularization method for control constraints and efficient preconditioners for this technique. Numerical results illustrate the competitiveness of these approaches. © 2011 John Wiley & Sons, Ltd.
4. Preconditioning for partial differential equation constrained optimization with control constraints
KAUST Repository
Stoll, Martin
2011-10-18
Optimal control problems with partial differential equations play an important role in many applications. The inclusion of bound constraints for the control poses a significant additional challenge for optimization methods. In this paper, we propose preconditioners for the saddle point problems that arise when a primal-dual active set method is used. We also show for this method that the same saddle point system can be derived when the method is considered as a semismooth Newton method. In addition, the projected gradient method can be employed to solve optimization problems with simple bounds, and we discuss the efficient solution of the linear systems in question. In the case when an acceleration technique is employed for the projected gradient method, this again yields a semismooth Newton method that is equivalent to the primal-dual active set method. We also consider the Moreau-Yosida regularization method for control constraints and efficient preconditioners for this technique. Numerical results illustrate the competitiveness of these approaches. © 2011 John Wiley & Sons, Ltd.
5. Neural network error correction for solving coupled ordinary differential equations
Science.gov (United States)
Shelton, R. O.; Darsey, J. A.; Sumpter, B. G.; Noid, D. W.
1992-01-01
A neural network is presented to learn errors generated by a numerical algorithm for solving coupled nonlinear differential equations. The method is based on using a neural network to correctly learn the error generated by, for example, Runge-Kutta on a model molecular dynamics (MD) problem. The neural network programs used in this study were developed by NASA. Comparisons are made for training the neural network using backpropagation and a new method which was found to converge with fewer iterations. The neural net programs, the MD model and the calculations are discussed.
6. Partial differential equations with numerical methods
CERN Document Server
2003-01-01
The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering. The main theme is the integration of the theory of linear PDEs and the numerical solution of such equations. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. As preparation, the two-point boundary value problem and the initial-value problem for ODEs are discussed in separate chapters. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. Some background on linear functional analysis and Sobolev spaces, and also on numerical linear algebra, is reviewed in two appendices.
7. Elliptic partial differential equations of second order
CERN Document Server
Gilbarg, David
2001-01-01
From the reviews: "This is a book of interest to any having to work with differential equations, either as a reference or as a book to learn from. The authors have taken trouble to make the treatment self-contained. It (is) suitable required reading for a PhD student. Although the material has been developed from lectures at Stanford, it has developed into an almost systematic coverage that is much longer than could be covered in a year's lectures". Newsletter, New Zealand Mathematical Society, 1985 "Primarily addressed to graduate students this elegant book is accessible and useful to a broad spectrum of applied mathematicians". Revue Roumaine de Mathématiques Pures et Appliquées,1985.
8. A linearizing transformation for the Korteweg-de Vries equation; generalizations to higher-dimensional nonlinear partial differential equations
NARCIS (Netherlands)
Dorren, H.J.S.
1998-01-01
It is shown that the Korteweg–de Vries (KdV) equation can be transformed into an ordinary linear partial differential equation in the wave number domain. Explicit solutions of the KdV equation can be obtained by subsequently solving this linear differential equation and by applying a cascade of
9. On the relation between elementary partial difference equations and partial differential equations
NARCIS (Netherlands)
van den Berg, I.P.
1998-01-01
The nonstandard stroboscopy method links discrete-time ordinary difference equations of first-order and continuous-time, ordinary differential equations of first order. We extend this method to the second order, and also to an elementary, yet general class of partial difference/differential
10. Integrator Performance Analysis In Solving Stiff Differential Equation System
International Nuclear Information System (INIS)
2001-01-01
In this paper we discuss the four-stage index-2 singly diagonally implicit Runge-Kutta method, which is used to solve stiff ordinary differential equations (SODE). Stiff problems require a method where step size is not restricted by the method's stability. We desire SDIRK to be A-stable that has no stability restrictions when solving y'= λy with Reλ>0 and h>0, so by choosing suitable stability function we can determine appropriate constant g) to formulate SDIRK integrator to solve SODE. We select the second stage of the internal stage as embedded method to perform low order estimate for error predictor. The strategy for choosing the step size is adopted from the strategy proposed by Hall(1996:6). And the algorithm that is developed in this paper is implemented using MATLAB 5.3, which is running on Window's 95 environment. Our performance measurement's local truncation error accuracy, and efficiency were evaluated by statistical results of sum of steps, sum of calling functions, average of Newton iterations and elapsed times.As the results, our numerical experiment show that SDIRK is unconditionally stable. By using Hall's step size strategy, the method can be implemented efficiently, provided that suitable parameters are used
11. [Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (2)].
Science.gov (United States)
Murase, Kenya
2015-01-01
In this issue, symbolic methods for solving differential equations were firstly introduced. Of the symbolic methods, Laplace transform method was also introduced together with some examples, in which this method was applied to solving the differential equations derived from a two-compartment kinetic model and an equivalent circuit model for membrane potential. Second, series expansion methods for solving differential equations were introduced together with some examples, in which these methods were used to solve Bessel's and Legendre's differential equations. In the next issue, simultaneous differential equations and various methods for solving these differential equations will be introduced together with some examples in medical physics.
12. Construction and accuracy of partial differential equation approximations to the chemical master equation.
Science.gov (United States)
Grima, Ramon
2011-11-01
The mesoscopic description of chemical kinetics, the chemical master equation, can be exactly solved in only a few simple cases. The analytical intractability stems from the discrete character of the equation, and hence considerable effort has been invested in the development of Fokker-Planck equations, second-order partial differential equation approximations to the master equation. We here consider two different types of higher-order partial differential approximations, one derived from the system-size expansion and the other from the Kramers-Moyal expansion, and derive the accuracy of their predictions for chemical reactive networks composed of arbitrary numbers of unimolecular and bimolecular reactions. In particular, we show that the partial differential equation approximation of order Q from the Kramers-Moyal expansion leads to estimates of the mean number of molecules accurate to order Ω(-(2Q-3)/2), of the variance of the fluctuations in the number of molecules accurate to order Ω(-(2Q-5)/2), and of skewness accurate to order Ω(-(Q-2)). We also show that for large Q, the accuracy in the estimates can be matched only by a partial differential equation approximation from the system-size expansion of approximate order 2Q. Hence, we conclude that partial differential approximations based on the Kramers-Moyal expansion generally lead to considerably more accurate estimates in the mean, variance, and skewness than approximations of the same order derived from the system-size expansion.
13. [Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (1)].
Science.gov (United States)
Murase, Kenya
2014-01-01
Utilization of differential equations and methods for solving them in medical physics are presented. First, the basic concept and the kinds of differential equations were overviewed. Second, separable differential equations and well-known first-order and second-order differential equations were introduced, and the methods for solving them were described together with several examples. In the next issue, the symbolic and series expansion methods for solving differential equations will be mainly introduced.
14. PDASAC, Partial Differential Sensitivity Analysis of Stiff System
International Nuclear Information System (INIS)
Caracotsios, M.; Stewart, W.E.
2001-01-01
1 - Description of program or function: PDASAC solves stiff, nonlinear initial-boundary-value problems in a timelike dimension t and a space dimension x. Plane, circular cylindrical or spherical boundaries can be handled. Mixed-order systems of partial differential and algebraic equations can be analyzed with members of order or 0 or 1 in t, 0, 1 or 2 in x. Parametric sensitivities of the calculated states are computed simultaneously on request, via the Jacobian of the state equations. Initial and boundary conditions are efficiently reconciled. Local error control (in the max-norm or the 2-norm) is provided for the state vector and can include the parametric sensitivities if desired. 2 - Method of solution: The method of lines is used, with a user- selected x-grid and a minimum-bandwidth finite-difference approximations of the x-derivatives. Starting conditions are reconciled with a damped Newton algorithm adapted from Bain and Stewart (1991). Initial step selection is done by the first-order algorithms of Shampine (1987), extended here to differential- algebraic equation systems. The solution is continued with the DASSL predictor-corrector algorithm (Petzold 1983, Brenan et al. 1989) with the initial acceleration phase deleted and with row scaling of the Jacobian added. The predictor and corrector are expressed in divided-difference form, with the fixed-leading-coefficient form of corrector (Jackson and Sacks-Davis 1989; Brenan et al. 1989). Weights for the error tests are updated in each step with the user's tolerances at the predicted state. Sensitivity analysis is performed directly on the corrector equations of Caracotsios and Stewart (1985) and is extended here to the initialization when needed. 3 - Restrictions on the complexity of the problem: This algorithm, like DASSL, performs well on differential-algebraic equation systems of index 0 and 1 but not on higher-index systems; see Brenan et al. (1989). The user assigned the work array lengths and the output
15. Analytical Solutions for Systems of Singular Partial Differential-Algebraic Equations
Directory of Open Access Journals (Sweden)
U. Filobello-Nino
2015-01-01
Full Text Available This paper proposes power series method (PSM in order to find solutions for singular partial differential-algebraic equations (SPDAEs. We will solve three examples to show that PSM method can be used to search for analytical solutions of SPDAEs. What is more, we will see that, in some cases, Padé posttreatment, besides enlarging the domain of convergence, may be employed in order to get the exact solution from the truncated series solutions of PSM.
16. Explicit finite difference predictor and convex corrector with applications to hyperbolic partial differential equations
Science.gov (United States)
Dey, C.; Dey, S. K.
1983-01-01
An explicit finite difference scheme consisting of a predictor and a corrector has been developed and applied to solve some hyperbolic partial differential equations (PDEs). The corrector is a convex-type function which is applied at each time level and at each mesh point. It consists of a parameter which may be estimated such that for larger time steps the algorithm should remain stable and generate a fast speed of convergence to the steady-state solution. Some examples have been given.
17. New finite volume methods for approximating partial differential equations on arbitrary meshes
International Nuclear Information System (INIS)
Hermeline, F.
2008-12-01
This dissertation presents some new methods of finite volume type for approximating partial differential equations on arbitrary meshes. The main idea lies in solving twice the problem to be dealt with. One addresses the elliptic equations with variable (anisotropic, antisymmetric, discontinuous) coefficients, the parabolic linear or non linear equations (heat equation, radiative diffusion, magnetic diffusion with Hall effect), the wave type equations (Maxwell, acoustics), the elasticity and Stokes'equations. Numerous numerical experiments show the good behaviour of this type of method. (author)
18. Entropy and convexity for nonlinear partial differential equations.
Science.gov (United States)
Ball, John M; Chen, Gui-Qiang G
2013-12-28
Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological and social processes. The concept of entropy originated in thermodynamics and statistical physics during the nineteenth century to describe the heat exchanges that occur in the thermal processes in a thermodynamic system, while the original notion of convexity is for sets and functions in mathematics. Since then, entropy and convexity have become two of the most important concepts in mathematics. In particular, nonlinear methods via entropy and convexity have been playing an increasingly important role in the analysis of nonlinear partial differential equations in recent decades. This opening article of the Theme Issue is intended to provide an introduction to entropy, convexity and related nonlinear methods for the analysis of nonlinear partial differential equations. We also provide a brief discussion about the content and contributions of the papers that make up this Theme Issue.
19. Student Solutions Manual to Boundary Value Problems and Partial Differential Equations
CERN Document Server
Powers, David L
2005-01-01
This student solutions manual accompanies the text, Boundary Value Problems and Partial Differential Equations, 5e. The SSM is available in print via PDF or electronically, and provides the student with the detailed solutions of the odd-numbered problems contained throughout the book.Provides students with exercises that skillfully illustrate the techniques used in the text to solve science and engineering problemsNearly 900 exercises ranging in difficulty from basic drills to advanced problem-solving exercisesMany exercises based on current engineering applications
20. Optimal moving grids for time-dependent partial differential equations
Science.gov (United States)
Wathen, A. J.
1992-01-01
Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of PDE solutions in the least-squares norm are reported.
1. A simple derivation of Kepler's laws without solving differential equations
International Nuclear Information System (INIS)
Provost, J-P; Bracco, C
2009-01-01
Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls for non-trivial properties of ellipses, is avoided by the introduction of polar coordinates. Then a simple reconsideration of Newton's figure naturally leads to an explicit expression of the velocity and to the equation of the trajectory. This derivation, which can be fully apprehended by undergraduates or by secondary school teachers (who might use it with their pupils), can be considered as a first application of mechanical concepts to a physical problem of great historical and pedagogical interest
2. Advances in nonlinear partial differential equations and stochastics
CERN Document Server
Kawashima, S
1998-01-01
In the past two decades, there has been great progress in the theory of nonlinear partial differential equations. This book describes the progress, focusing on interesting topics in gas dynamics, fluid dynamics, elastodynamics etc. It contains ten articles, each of which discusses a very recent result obtained by the author. Some of these articles review related results.
3. Mild Solutions of Neutral Stochastic Partial Functional Differential Equations
Directory of Open Access Journals (Sweden)
T. E. Govindan
2011-01-01
Full Text Available This paper studies the existence and uniqueness of a mild solution for a neutral stochastic partial functional differential equation using a local Lipschitz condition. When the neutral term is zero and even in the deterministic special case, the result obtained here appears to be new. An example is included to illustrate the theory.
4. Exact solutions of some nonlinear partial differential equations using ...
The functional variable method is a powerful solution method for obtaining exact solutions of some nonlinear partial differential equations. In this paper, the functional variable method is used to establish exact solutions of the generalized forms of Klein–Gordon equation, the (2 + 1)-dimensional Camassa–Holm ...
5. Function spaces and partial differential equations 2 volume set
CERN Document Server
Taheri, Ali
2015-01-01
This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour.
6. Function spaces and partial differential equations volume 2 : contemporary analysis
CERN Document Server
Taheri, Ali
2015-01-01
This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour.
7. Energy preserving integration of bi-Hamiltonian partial differential equations
NARCIS (Netherlands)
Karasozen, B.; Simsek, G.
2013-01-01
The energy preserving average vector field (AVF) integrator is applied to evolutionary partial differential equations (PDEs) in bi-Hamiltonian form with nonconstant Poisson structures. Numerical results for the Korteweg de Vries (KdV) equation and for the Ito type coupled KdV equation confirm the
8. Stability test for a parabolic partial differential equation
NARCIS (Netherlands)
Vajta, Miklos
2001-01-01
The paper describes a stability test applied to coupled parabolic partial differential equations. The PDE's describe the temperature distribution of composite structures with linear inner heat sources. The distributed transfer functions are developed based on the transmission matrix of each layer.
9. Book review: Partial Differential Equations and Fluid Mechanics
NARCIS (Netherlands)
Muntean, A.
2011-01-01
The baak is the result of the workshop Partial Differential Equations and Fluid Dynamics that look place at the Mathematics Institute of the University of Warwick. May 21st - 23rd, 2007. It contains ten review and research papers which provide an accessible summary of a wide range of active research
10. Functional Determinants for Radially Separable Partial Differential Operators
Directory of Open Access Journals (Sweden)
G. V. Dunne
2007-01-01
Full Text Available Functional determinants of differential operators play a prominent role in many fields of theoretical and mathematical physics, ranging from condensed matter physics, to atomic, molecular and particle physics. They are, however, difficult to compute reliably in non-trivial cases. In one dimensional problems (i.e. functional determinants of ordinary differential operators, a classic result of Gel’fand and Yaglom greatly simplifies the computation of functional determinants. Here I report some recent progress in extending this approach to higher dimensions (i.e., functional determinants of partial differential operators, with applications in quantum field theory.
11. Solving differential equations with unknown constitutive relations as recurrent neural networks
Energy Technology Data Exchange (ETDEWEB)
Hagge, Tobias J.; Stinis, Panagiotis; Yeung, Enoch H.; Tartakovsky, Alexandre M.
2017-12-08
We solve a system of ordinary differential equations with an unknown functional form of a sink (reaction rate) term. We assume that the measurements (time series) of state variables are partially available, and use a recurrent neural network to “learn” the reaction rate from this data. This is achieved by including discretized ordinary differential equations as part of a recurrent neural network training problem. We extend TensorFlow’s recurrent neural network architecture to create a simple but scalable and effective solver for the unknown functions, and apply it to a fedbatch bioreactor simulation problem. Use of techniques from recent deep learning literature enables training of functions with behavior manifesting over thousands of time steps. Our networks are structurally similar to recurrent neural networks, but differ in purpose, and require modified training strategies.
12. Role reversal and problem solving in international negotiations: the Partial Nuclear Test Ban case
International Nuclear Information System (INIS)
King, T.D.
1978-01-01
To facilitate finding bargaining space and to reinforce cooperative potential, a number of analysts have promoted the use of role reversal and problem solving. Role reversal involves restating the positions of one's adversary to demonstrate understanding and to develop empathy, while problem solving involves searching for alternatives that promote joint interests. The case of the negotiations in the Eighteen Nation Disarmament Conference from 1962--1963 leading to the Partial Nuclear Test Ban Treaty provided the context for examining bargaining relationships involving role reversal and problem solving. Interactions among the United States, the United Kingdom, and the Soviet Union, as recorded in transcripts of 112 sessions, were coded using Bargaining Process Analysis II, a content analysis instrument used to classify negotiation behaviors. Role reversal was measured by the frequency of paraphrases of the adversary's positions. Problem solving was measured by the frequency of themes promoting the exploration of alternatives and the search for mutually beneficial outcomes. The findings on the use of paraphrasing suggest that it can be used to restrict exploration as well as to promote it. The exploratory focus of problem solving was somewhat limited by its use in association with demands, suggesting that problem solving was interpreted as a sign of weakness
13. Plane waves and spherical means applied to partial differential equations
CERN Document Server
John, Fritz
2004-01-01
Elementary and self-contained, this heterogeneous collection of results on partial differential equations employs certain elementary identities for plane and spherical integrals of an arbitrary function, showing how a variety of results on fairly general differential equations follow from those identities. The first chapter deals with the decomposition of arbitrary functions into functions of the type of plane waves. Succeeding chapters introduce the first application of the Radon transformation and examine the solution of the initial value problem for homogeneous hyperbolic equations with con
14. CIME course on Control of Partial Differential Equations
CERN Document Server
Alabau-Boussouira, Fatiha; Glass, Olivier; Le Rousseau, Jérôme; Zuazua, Enrique
2012-01-01
The term “control theory” refers to the body of results - theoretical, numerical and algorithmic - which have been developed to influence the evolution of the state of a given system in order to meet a prescribed performance criterion. Systems of interest to control theory may be of very different natures. This monograph is concerned with models that can be described by partial differential equations of evolution. It contains five major contributions and is connected to the CIME Course on Control of Partial Differential Equations that took place in Cetraro (CS, Italy), July 19 - 23, 2010. Specifically, it covers the stabilization of evolution equations, control of the Liouville equation, control in fluid mechanics, control and numerics for the wave equation, and Carleman estimates for elliptic and parabolic equations with application to control. We are confident this work will provide an authoritative reference work for all scientists who are interested in this field, representing at the same time a fri...
15. Spectral methods for time dependent partial differential equations
Science.gov (United States)
Gottlieb, D.; Turkel, E.
1983-01-01
The theory of spectral methods for time dependent partial differential equations is reviewed. When the domain is periodic Fourier methods are presented while for nonperiodic problems both Chebyshev and Legendre methods are discussed. The theory is presented for both hyperbolic and parabolic systems using both Galerkin and collocation procedures. While most of the review considers problems with constant coefficients the extension to nonlinear problems is also discussed. Some results for problems with shocks are presented.
16. Nonclassical Symmetries for Nonlinear Partial Differential Equations via Compatibility
International Nuclear Information System (INIS)
El-Sabbagh, Mostafa F.; Ahmad, Ali T.
2011-01-01
The determining equations for the nonclassical symmetry reductions of nonlinear partial differential equations with arbitrary order can be obtained by requiring the compatibility between the original equations and the invariant surface conditions. The (2+1)-dimensional shallow water wave equation, Boussinesq equation, and the dispersive wave equations in shallow water serve as examples illustrating how compatibility leads quickly and easily to the determining equations for their nonclassical symmetries. (general)
17. Unconditionally stable difference methods for delay partial differential equations
OpenAIRE
Huang, Chengming; Vandewalle, Stefan
2012-01-01
This paper is concerned with the numerical solution of parabolic partial differential equations with time-delay. We focus in particular on the delay dependent stability analysis of difference methods that use a non-constrained mesh, i.e., the time step-size is not required to be a submultiple of the delay. We prove that the fully discrete system unconditionally preserves the delay dependent asymptotic stability of the linear test problem under consideration, when the following discretizati...
18. Some overdetermined systems of complex partial differential equations
International Nuclear Information System (INIS)
Le Hung Son.
1990-01-01
In this paper we extend some properties of analytic functions on several complex variables to solutions of overdetermined systems of complex partial differential equations. It is proved that many global properties of analytic functions are true for solutions of the Vekua system in special cases. The relation between analytic functions and solutions of quasi-linear systems is discussed in the paper. (author). 8 refs
19. A higher order numerical method for time fractional partial differential equations with nonsmooth data
Science.gov (United States)
Xing, Yanyuan; Yan, Yubin
2018-03-01
Gao et al. [11] (2014) introduced a numerical scheme to approximate the Caputo fractional derivative with the convergence rate O (k 3 - α), 0 equation is sufficiently smooth, Lv and Xu [20] (2016) proved by using energy method that the corresponding numerical method for solving time fractional partial differential equation has the convergence rate O (k 3 - α), 0 equation has low regularity and in this case the numerical method fails to have the convergence rate O (k 3 - α), 0 quadratic interpolation polynomials. Based on this scheme, we introduce a time discretization scheme to approximate the time fractional partial differential equation and show by using Laplace transform methods that the time discretization scheme has the convergence rate O (k 3 - α), 0 0 for smooth and nonsmooth data in both homogeneous and inhomogeneous cases. Numerical examples are given to show that the theoretical results are consistent with the numerical results.
20. Hidden physics models: Machine learning of nonlinear partial differential equations
Science.gov (United States)
2018-03-01
While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from small data. In particular, we introduce hidden physics models, which are essentially data-efficient learning machines capable of leveraging the underlying laws of physics, expressed by time dependent and nonlinear partial differential equations, to extract patterns from high-dimensional data generated from experiments. The proposed methodology may be applied to the problem of learning, system identification, or data-driven discovery of partial differential equations. Our framework relies on Gaussian processes, a powerful tool for probabilistic inference over functions, that enables us to strike a balance between model complexity and data fitting. The effectiveness of the proposed approach is demonstrated through a variety of canonical problems, spanning a number of scientific domains, including the Navier-Stokes, Schrödinger, Kuramoto-Sivashinsky, and time dependent linear fractional equations. The methodology provides a promising new direction for harnessing the long-standing developments of classical methods in applied mathematics and mathematical physics to design learning machines with the ability to operate in complex domains without requiring large quantities of data.
1. A new RBF-Trefftz meshless method for partial differential equations
International Nuclear Information System (INIS)
Cao Leilei; Zhao Ning; Qin Qinghua
2010-01-01
Based on the radial basis functions (RBF) and T-Trefftz solution, this paper presents a new meshless method for numerically solving various partial differential equation systems. First, the analog equation method (AEM) is used to convert the original patial differential equation to an equivalent Poisson's equation. Then, the radial basis functions (RBF) are employed to approxiamate the inhomogeneous term, while the homogeneous solution is obtained by linear combination of a set of T-Trefftz solutions. The present scheme, named RBF-Trefftz has the advantage over the fundamental solution (MFS) method due to the use of nonsingular T-Trefftz solution rather than singular fundamental solutions, so it does not require the artificial boundary. The application and efficiency of the proposed method are validated through several examples which include different type of differential equations, such as Laplace equation, Hellmholtz equation, convectin-diffusion equation and time-dependent equation.
2. Solving the Telegraph and Oscillatory Differential Equations by a Block Hybrid Trigonometrically Fitted Algorithm
Directory of Open Access Journals (Sweden)
F. F. Ngwane
2015-01-01
Full Text Available We propose a block hybrid trigonometrically fitted (BHT method, whose coefficients are functions of the frequency and the step-size for directly solving general second-order initial value problems (IVPs, including systems arising from the semidiscretization of hyperbolic Partial Differential Equations (PDEs, such as the Telegraph equation. The BHT is formulated from eight discrete hybrid formulas which are provided by a continuous two-step hybrid trigonometrically fitted method with two off-grid points. The BHT is implemented in a block-by-block fashion; in this way, the method does not suffer from the disadvantages of requiring starting values and predictors which are inherent in predictor-corrector methods. The stability property of the BHT is discussed and the performance of the method is demonstrated on some numerical examples to show accuracy and efficiency advantages.
3. Simple equation method for nonlinear partial differential equations and its applications
Directory of Open Access Journals (Sweden)
Taher A. Nofal
2016-04-01
Full Text Available In this article, we focus on the exact solution of the some nonlinear partial differential equations (NLPDEs such as, Kodomtsev–Petviashvili (KP equation, the (2 + 1-dimensional breaking soliton equation and the modified generalized Vakhnenko equation by using the simple equation method. In the simple equation method the trial condition is the Bernoulli equation or the Riccati equation. It has been shown that the method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering problems.
4. Solution of Nonlinear Partial Differential Equations by New Laplace Variational Iteration Method
Directory of Open Access Journals (Sweden)
Eman M. A. Hilal
2014-01-01
Full Text Available The aim of this study is to give a good strategy for solving some linear and nonlinear partial differential equations in engineering and physics fields, by combining Laplace transform and the modified variational iteration method. This method is based on the variational iteration method, Laplace transforms, and convolution integral, introducing an alternative Laplace correction functional and expressing the integral as a convolution. Some examples in physical engineering are provided to illustrate the simplicity and reliability of this method. The solutions of these examples are contingent only on the initial conditions.
5. Analytical solutions to time-fractional partial differential equations in a two-dimensional multilayer annulus
Science.gov (United States)
Chen, Shanzhen; Jiang, Xiaoyun
2012-08-01
In this paper, analytical solutions to time-fractional partial differential equations in a multi-layer annulus are presented. The final solutions are obtained in terms of Mittag-Leffler function by using the finite integral transform technique and Laplace transform technique. In addition, the classical diffusion equation (α=1), the Helmholtz equation (α→0) and the wave equation (α=2) are discussed as special cases. Finally, an illustrative example problem for the three-layer semi-circular annular region is solved and numerical results are presented graphically for various kind of order of fractional derivative.
6. The Spectral/hp-Finite Element Method for Partial Differential Equations
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter
2009-01-01
dimensions. In the course the chosen programming environment is Matlab, however, this is by no means a necessary requirement. The mathematical level needed to grasp the details of this set of notes requires an elementary background in mathematical analysis and linear algebra. Each chapter is supplemented......This set of lecture notes provides an elementary introduction to both the classical Finite Element Method (FEM) and the extended Spectral/$hp$-Finite Element Method for solving Partial Differential Equations (PDEs). Many problems in science and engineering can be formulated mathematically...
7. Lattice Boltzmann model for high-order nonlinear partial differential equations
Science.gov (United States)
Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang
2018-01-01
In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂tϕ +∑k=1mαk∂xkΠk(ϕ ) =0 (1 ≤k ≤m ≤6 ), αk are constant coefficients, Πk(ϕ ) are some known differential functions of ϕ . As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K (n ,n ) -Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009), 10.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009), 10.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.
8. Lattice Boltzmann model for high-order nonlinear partial differential equations.
Science.gov (United States)
Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang
2018-01-01
In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂_{t}ϕ+∑_{k=1}^{m}α_{k}∂_{x}^{k}Π_{k}(ϕ)=0 (1≤k≤m≤6), α_{k} are constant coefficients, Π_{k}(ϕ) are some known differential functions of ϕ. As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K(n,n)-Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009)1672-179910.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009)PHYADX0378-437110.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.
9. Optimal Control Problems for Partial Differential Equations on Reticulated Domains
CERN Document Server
Kogut, Peter I
2011-01-01
In the development of optimal control, the complexity of the systems to which it is applied has increased significantly, becoming an issue in scientific computing. In order to carry out model-reduction on these systems, the authors of this work have developed a method based on asymptotic analysis. Moving from abstract explanations to examples and applications with a focus on structural network problems, they aim at combining techniques of homogenization and approximation. Optimal Control Problems for Partial Differential Equations on Reticulated Domains is an excellent reference tool for gradu
10. Estimating varying coefficients for partial differential equation models.
Science.gov (United States)
Zhang, Xinyu; Cao, Jiguo; Carroll, Raymond J
2017-09-01
Partial differential equations (PDEs) are used to model complex dynamical systems in multiple dimensions, and their parameters often have important scientific interpretations. In some applications, PDE parameters are not constant but can change depending on the values of covariates, a feature that we call varying coefficients. We propose a parameter cascading method to estimate varying coefficients in PDE models from noisy data. Our estimates of the varying coefficients are shown to be consistent and asymptotically normally distributed. The performance of our method is evaluated by a simulation study and by an empirical study estimating three varying coefficients in a PDE model arising from LIDAR data. © 2017, The International Biometric Society.
11. Partial differential equation models in the socio-economic sciences.
Science.gov (United States)
Burger, Martin; Caffarelli, Luis; Markowich, Peter A
2014-11-13
Mathematical models based on partial differential equations (PDEs) have become an integral part of quantitative analysis in most branches of science and engineering, recently expanding also towards biomedicine and socio-economic sciences. The application of PDEs in the latter is a promising field, but widely quite open and leading to a variety of novel mathematical challenges. In this introductory article of the Theme Issue, we will provide an overview of the field and its recent boosting topics. Moreover, we will put the contributions to the Theme Issue in an appropriate perspective. © 2014 The Author(s) Published by the Royal Society. All rights reserved.
12. Convergence of method of lines approximations to partial differential equations
International Nuclear Information System (INIS)
Verwer, J.G.; Sanz-Serna, J.M.
1984-01-01
Many existing numerical schemes for evolutionary problems in partial differential equations (PDEs) can be viewed as method of lines (MOL) schemes. This paper treats the convergence of one-step MOL schemes. The main purpose is to set up a general framework for a convergence analysis applicable to nonlinear problems. The stability materials for this framework are taken from the field of nonlinear stiff ODEs. In this connection, important concepts are the logarithmic matrix norm and C-stability. A nonlinear parabolic equation and the cubic Schroedinger equation are used for illustrating the ideas. (Auth.)
13. Controllability of partial differential equations governed by multiplicative controls
CERN Document Server
Khapalov, Alexander Y
2010-01-01
The goal of this monograph is to address the issue of the global controllability of partial differential equations in the context of multiplicative (or bilinear) controls, which enter the model equations as coefficients. The mathematical models we examine include the linear and nonlinear parabolic and hyperbolic PDE's, the Schrödinger equation, and coupled hybrid nonlinear distributed parameter systems modeling the swimming phenomenon. The book offers a new, high-quality and intrinsically nonlinear methodology to approach the aforementioned highly nonlinear controllability problems.
14. Constrained Optimization and Optimal Control for Partial Differential Equations
CERN Document Server
Leugering, Günter; Griewank, Andreas
2012-01-01
This special volume focuses on optimization and control of processes governed by partial differential equations. The contributors are mostly participants of the DFG-priority program 1253: Optimization with PDE-constraints which is active since 2006. The book is organized in sections which cover almost the entire spectrum of modern research in this emerging field. Indeed, even though the field of optimal control and optimization for PDE-constrained problems has undergone a dramatic increase of interest during the last four decades, a full theory for nonlinear problems is still lacking. The cont
15. Malliavin Calculus With Applications to Stochastic Partial Differential Equations
CERN Document Server
Sanz-Solé, Marta
2005-01-01
Developed in the 1970s to study the existence and smoothness of density for the probability laws of random vectors, Malliavin calculus--a stochastic calculus of variation on the Wiener space--has proven fruitful in many problems in probability theory, particularly in probabilistic numerical methods in financial mathematics.This book presents applications of Malliavin calculus to the analysis of probability laws of solutions to stochastic partial differential equations driven by Gaussian noises that are white in time and coloured in space. The first five chapters introduce the calculus itself
16. Partial differential equations and boundary-value problems with applications
CERN Document Server
Pinsky, Mark A
2011-01-01
Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems-rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate th
17. Superdiffusions and positive solutions of nonlinear partial differential equations
CERN Document Server
Dynkin, E B
2004-01-01
This book is devoted to the applications of probability theory to the theory of nonlinear partial differential equations. More precisely, it is shown that all positive solutions for a class of nonlinear elliptic equations in a domain are described in terms of their traces on the boundary of the domain. The main probabilistic tool is the theory of superdiffusions, which describes a random evolution of a cloud of particles. A substantial enhancement of this theory is presented that can be of interest for everybody who works on applications of probabilistic methods to mathematical analysis.
18. Partial differential equation models in the socio-economic sciences
KAUST Repository
Burger, Martin
2014-10-06
Mathematical models based on partial differential equations (PDEs) have become an integral part of quantitative analysis in most branches of science and engineering, recently expanding also towards biomedicine and socio-economic sciences. The application of PDEs in the latter is a promising field, but widely quite open and leading to a variety of novel mathematical challenges. In this introductory article of the Theme Issue, we will provide an overview of the field and its recent boosting topics. Moreover, we will put the contributions to the Theme Issue in an appropriate perspective.
19. Using Partial Differential Equations for Pricing of Goods and Services
Directory of Open Access Journals (Sweden)
Traykov Metodi
2016-06-01
Full Text Available This article is based on the methodology of comparative analysis, using an innovative approach for pricing of various goods and services. Benchmarking is the continuous search to find and adapt better pricing methods that leading to increased profits. We will consider the numerical solution of partial differential equations, based on Black-Scholes model for pricing of goods and services within European option. Also, we will present formulation and numerical behavior of explicit and implicit methods that can be use in pricing for company assets within European option.
20. Numerical solution of two-dimensional non-linear partial differential ...
African Journals Online (AJOL)
linear partial differential equations using a hybrid method. The solution technique involves discritizing the non-linear system of partial differential equations (PDEs) to obtain a corresponding nonlinear system of algebraic difference equations to be ...
1. A Priori Regularity of Parabolic Partial Differential Equations
KAUST Repository
Berkemeier, Francisco
2018-05-13
In this thesis, we consider parabolic partial differential equations such as the heat equation, the Fokker-Planck equation, and the porous media equation. Our aim is to develop methods that provide a priori estimates for solutions with singular initial data. These estimates are obtained by understanding the time decay of norms of solutions. First, we derive regularity results for the heat equation by estimating the decay of Lebesgue norms. Then, we apply similar methods to the Fokker-Planck equation with suitable assumptions on the advection and diffusion. Finally, we conclude by extending our techniques to the porous media equation. The sharpness of our results is confirmed by examining known solutions of these equations. The main contribution of this thesis is the use of functional inequalities to express decay of norms as differential inequalities. These are then combined with ODE methods to deduce estimates for the norms of solutions and their derivatives.
2. Improved stochastic approximation methods for discretized parabolic partial differential equations
Science.gov (United States)
Guiaş, Flavius
2016-12-01
We present improvements of the stochastic direct simulation method, a known numerical scheme based on Markov jump processes which is used for approximating solutions of ordinary differential equations. This scheme is suited especially for spatial discretizations of evolution partial differential equations (PDEs). By exploiting the full path simulation of the stochastic method, we use this first approximation as a predictor and construct improved approximations by Picard iterations, Runge-Kutta steps, or a combination. This has as consequence an increased order of convergence. We illustrate the features of the improved method at a standard benchmark problem, a reaction-diffusion equation modeling a combustion process in one space dimension (1D) and two space dimensions (2D).
3. Numerical methods for stochastic partial differential equations with white noise
CERN Document Server
Zhang, Zhongqiang
2017-01-01
This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. The book begins with some motivational and background material in the introductory chapters and is divided into three parts. Part I covers numerical stochastic ordinary differential equations. Here the authors start with numerical methods for SDEs with delay using the Wong-Zakai approximation and finite difference in time. Part II covers temporal white noise. Here the authors consider SPDEs as PDEs driven by white noise, where discretization of white noise (Brownian motion) leads to PDEs with smooth noise, which can then be treated by numerical methods for PDEs. In this part, recursive algorithms based on Wiener chaos expansion and stochastic collocation methods are presented for linear stochastic advection-diffusion-reaction equations. In addition, stochastic Euler equations are exploited as an application of stochastic collocation methods, where a numerical compa...
4. Variational and potential formulation for stochastic partial differential equations
International Nuclear Information System (INIS)
Munoz S, A G; Ojeda, J; Sierra D, P; Soldovieri, T
2006-01-01
Recently there has been interest in finding a potential formulation for stochastic partial differential equations (SPDEs). The rationale behind this idea lies in obtaining all the dynamical information of the system under study from one single expression. In this letter we formally provide a general Lagrangian formalism for SPDEs using the Hojman et al method. We show that it is possible to write the corresponding effective potential starting from an s-equivalent Lagrangian, and that this potential is able to reproduce all the dynamics of the system once a special differential operator has been applied. This procedure can be used to study the complete time evolution and spatial inhomogeneities of the system under consideration, and is also suitable for the statistical mechanics description of the problem. (letter to the editor)
5. Application of Monte Carlo method to solving boundary value problem of differential equations
International Nuclear Information System (INIS)
Zuo Yinghong; Wang Jianguo
2012-01-01
This paper introduces the foundation of the Monte Carlo method and the way how to generate the random numbers. Based on the basic thought of the Monte Carlo method and finite differential method, the stochastic model for solving the boundary value problem of differential equations is built. To investigate the application of the Monte Carlo method to solving the boundary value problem of differential equations, the model is used to solve Laplace's equations with the first boundary condition and the unsteady heat transfer equation with initial values and boundary conditions. The results show that the boundary value problem of differential equations can be effectively solved with the Monte Carlo method, and the differential equations with initial condition can also be calculated by using a stochastic probability model which is based on the time-domain finite differential equations. Both the simulation results and theoretical analyses show that the errors of numerical results are lowered as the number of simulation particles is increased. (authors)
6. Bäcklund transformation of fractional Riccati equation and its applications to nonlinear fractional partial differential equations
International Nuclear Information System (INIS)
Lu, Bin
2012-01-01
In this Letter, the fractional derivatives in the sense of modified Riemann–Liouville derivative and the Bäcklund transformation of fractional Riccati equation are employed for constructing the exact solutions of nonlinear fractional partial differential equations. The power of this manageable method is presented by applying it to several examples. This approach can also be applied to other nonlinear fractional differential equations. -- Highlights: ► Backlund transformation of fractional Riccati equation is presented. ► A new method for solving nonlinear fractional differential equations is proposed. ► Three important fractional differential equations are solved successfully. ► Some new exact solutions of the fractional differential equations are obtained.
7. Rapid Fourier space solution of linear partial integro-differential equations in toroidal magnetic confinement geometries
International Nuclear Information System (INIS)
McMillan, B.F.; Jolliet, S.; Tran, T.M.; Villard, L.; Bottino, A.; Angelino, P.
2010-01-01
Fluctuating quantities in magnetic confinement geometries often inherit a strong anisotropy along the field lines. One technique for describing these structures is the use of a certain set of Fourier components on the tori of nested flux surfaces. We describe an implementation of this approach for solving partial differential equations, like Poisson's equation, where a different set of Fourier components may be chosen on each surface according to the changing safety factor profile. Allowing the resolved components to change to follow the anisotropy significantly reduces the total number of degrees of freedom in the description. This can permit large gains in computational performance. We describe, in particular, how this approach can be applied to rapidly solve the gyrokinetic Poisson equation in a particle code, ORB5 (Jolliet et al. (2007) [5]), with a regular (non-field-aligned) mesh. (authors)
8. Stable multi-domain spectral penalty methods for fractional partial differential equations
Science.gov (United States)
Xu, Qinwu; Hesthaven, Jan S.
2014-01-01
We propose stable multi-domain spectral penalty methods suitable for solving fractional partial differential equations with fractional derivatives of any order. First, a high order discretization is proposed to approximate fractional derivatives of any order on any given grids based on orthogonal polynomials. The approximation order is analyzed and verified through numerical examples. Based on the discrete fractional derivative, we introduce stable multi-domain spectral penalty methods for solving fractional advection and diffusion equations. The equations are discretized in each sub-domain separately and the global schemes are obtained by weakly imposed boundary and interface conditions through a penalty term. Stability of the schemes are analyzed and numerical examples based on both uniform and nonuniform grids are considered to highlight the flexibility and high accuracy of the proposed schemes.
9. Advanced Topics in Computational Partial Differential Equations: Numerical Methods and Diffpack Programming
International Nuclear Information System (INIS)
Katsaounis, T D
2005-01-01
The scope of this book is to present well known simple and advanced numerical methods for solving partial differential equations (PDEs) and how to implement these methods using the programming environment of the software package Diffpack. A basic background in PDEs and numerical methods is required by the potential reader. Further, a basic knowledge of the finite element method and its implementation in one and two space dimensions is required. The authors claim that no prior knowledge of the package Diffpack is required, which is true, but the reader should be at least familiar with an object oriented programming language like C++ in order to better comprehend the programming environment of Diffpack. Certainly, a prior knowledge or usage of Diffpack would be a great advantage to the reader. The book consists of 15 chapters, each one written by one or more authors. Each chapter is basically divided into two parts: the first part is about mathematical models described by PDEs and numerical methods to solve these models and the second part describes how to implement the numerical methods using the programming environment of Diffpack. Each chapter closes with a list of references on its subject. The first nine chapters cover well known numerical methods for solving the basic types of PDEs. Further, programming techniques on the serial as well as on the parallel implementation of numerical methods are also included in these chapters. The last five chapters are dedicated to applications, modelled by PDEs, in a variety of fields. In summary, the book focuses on the computational and implementational issues involved in solving partial differential equations. The potential reader should have a basic knowledge of PDEs and the finite difference and finite element methods. The examples presented are solved within the programming framework of Diffpack and the reader should have prior experience with the particular software in order to take full advantage of the book. Overall
10. Variable-mesh method of solving differential equations
Science.gov (United States)
Van Wyk, R.
1969-01-01
Multistep predictor-corrector method for numerical solution of ordinary differential equations retains high local accuracy and convergence properties. In addition, the method was developed in a form conducive to the generation of effective criteria for the selection of subsequent step sizes in step-by-step solution of differential equations.
11. On mixed derivatives type high dimensional multi-term fractional partial differential equations approximate solutions
Science.gov (United States)
2017-01-01
In this research article, we derive and analyze an efficient spectral method based on the operational matrices of three dimensional orthogonal Jacobi polynomials to solve numerically the mixed partial derivatives type multi-terms high dimensions generalized class of fractional order partial differential equations. We transform the considered fractional order problem to an easily solvable algebraic equations with the aid of the operational matrices. Being easily solvable, the associated algebraic system leads to finding the solution of the problem. Some test problems are considered to confirm the accuracy and validity of the proposed numerical method. The convergence of the method is ensured by comparing our Matlab software simulations based obtained results with the exact solutions in the literature, yielding negligible errors. Moreover, comparative results discussed in the literature are extended and improved in this study.
12. Solution of Fractional Partial Differential Equations in Fluid Mechanics by Extension of Some Iterative Method
Directory of Open Access Journals (Sweden)
A. A. Hemeda
2013-01-01
Full Text Available An extension of the so-called new iterative method (NIM has been used to handle linear and nonlinear fractional partial differential equations. The main property of the method lies in its flexibility and ability to solve nonlinear equations accurately and conveniently. Therefore, a general framework of the NIM is presented for analytical treatment of fractional partial differential equations in fluid mechanics. The fractional derivatives are described in the Caputo sense. Numerical illustrations that include the fractional wave equation, fractional Burgers equation, fractional KdV equation, fractional Klein-Gordon equation, and fractional Boussinesq-like equation are investigated to show the pertinent features of the technique. Comparison of the results obtained by the NIM with those obtained by both Adomian decomposition method (ADM and the variational iteration method (VIM reveals that the NIM is very effective and convenient. The basic idea described in this paper is expected to be further employed to solve other similar linear and nonlinear problems in fractional calculus.
13. ADM For Solving Linear Second-Order Fredholm Integro-Differential Equations
Science.gov (United States)
Karim, Mohd F.; Mohamad, Mahathir; Saifullah Rusiman, Mohd; Che-Him, Norziha; Roslan, Rozaini; Khalid, Kamil
2018-04-01
In this paper, we apply Adomian Decomposition Method (ADM) as numerically analyse linear second-order Fredholm Integro-differential Equations. The approximate solutions of the problems are calculated by Maple package. Some numerical examples have been considered to illustrate the ADM for solving this equation. The results are compared with the existing exact solution. Thus, the Adomian decomposition method can be the best alternative method for solving linear second-order Fredholm Integro-Differential equation. It converges to the exact solution quickly and in the same time reduces computational work for solving the equation. The result obtained by ADM shows the ability and efficiency for solving these equations.
14. Partial wave analysis for folded differential cross sections
Science.gov (United States)
Machacek, J. R.; McEachran, R. P.
2018-03-01
The value of modified effective range theory (MERT) and the connection between differential cross sections and phase shifts in low-energy electron scattering has long been recognized. Recent experimental techniques involving magnetically confined beams have introduced the concept of folded differential cross sections (FDCS) where the forward (θ ≤ π/2) and backward scattered (θ ≥ π/2) projectiles are unresolved, that is the value measured at the angle θ is the sum of the signal for particles scattered into the angles θ and π - θ. We have developed an alternative approach to MERT in order to analyse low-energy folded differential cross sections for positrons and electrons. This results in a simplified expression for the FDCS when it is expressed in terms of partial waves and thereby enables one to extract the first few phase shifts from a fit to an experimental FDCS at low energies. Thus, this method predicts forward and backward angle scattering (0 to π) using only experimental FDCS data and can be used to determine the total elastic cross section solely from experimental results at low-energy, which are limited in angular range.
15. Analytical approach to linear fractional partial differential equations arising in fluid mechanics
International Nuclear Information System (INIS)
Momani, Shaher; Odibat, Zaid
2006-01-01
In this Letter, we implement relatively new analytical techniques, the variational iteration method and the Adomian decomposition method, for solving linear fractional partial differential equations arising in fluid mechanics. The fractional derivatives are described in the Caputo sense. The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of fractional differential equations. In these methods, the solution takes the form of a convergent series with easily computable components. The corresponding solutions of the integer order equations are found to follow as special cases of those of fractional order equations. Some numerical examples are presented to illustrate the efficiency and reliability of the two methods
16. Wavelet Methods for Solving Fractional Order Differential Equations
OpenAIRE
A. K. Gupta; S. Saha Ray
2014-01-01
Fractional calculus is a field of applied mathematics which deals with derivatives and integrals of arbitrary orders. The fractional calculus has gained considerable importance during the past decades mainly due to its application in diverse fields of science and engineering such as viscoelasticity, diffusion of biological population, signal processing, electromagnetism, fluid mechanics, electrochemistry, and many more. In this paper, we review different wavelet methods for solving both linea...
17. Paleomagnetic evidence for a partially differentiated H chondrite parent planetesimal
Science.gov (United States)
Bryson, J. F. J.; Weiss, B. P.; Scholl, A.; Getzin, B. L.; Abrahams, J. N. H.; Nimmo, F.
2016-12-01
The texture, composition and ages of chondrites have all been used to argue that the parent bodies of these meteorites did not undergo planetary differentiation. Without a core, these planetesimals could not have generated planetary magnetic fields, hence chondrites are predicted to be unmagnetized. Here, we test this hypothesis by applying synchrotron x-ray microscopy to the metallic melt veins in the metamorphosed H chondrite breccia Portales Valley. We find that tetrataenite nanostructures in these veins are uniformly magnetized, suggesting that the H chondrite parent body generated a stable, 10 µT ancient field. We also performed alternating field (AF) demagnetization on bulk silicate-rich portions of Portales Valley, finding that both the large grain size of the metal in these subsamples and the presence of tetrataenite hinder the reliable interpretation of these measurements. Based on 40Ar/39Ar dating and the metallographic cooling rate, we propose that this field inferred from x-ray microscopy was generated 100 Myr after solar system formation and lasted >5 Myr. These properties are consistent with a dynamo field generated by core solidification, implying that the H chondrite parent body was partially differentiated. This conclusion is supported by our analyses of the H4 chondrite Forest Vale, which show that H chondrite magnetization is unlikely to be a relic signature of early nebular or solar wind fields (Getzin et al., this meeting; Oran et al., this meeting). We propose that partial differentiation could result form prolonged accretion over millions of years, possibly in two stages. In this scenario, the earliest accreted material melted from the radioactive decay of abundant 26Al, forming a core and rocky achondritic mantle, while the later accreted material was less metamorphosed, forming an undifferentiated crust. We demonstrate that, with the inclusion of an insulating regolith, the thermal evolution of such a body is consistent with the measured
18. High-order quantum algorithm for solving linear differential equations
International Nuclear Information System (INIS)
Berry, Dominic W
2014-01-01
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms to general inhomogeneous sparse linear differential equations, which describe many classical physical systems. We examine the use of high-order methods (where the error over a time step is a high power of the size of the time step) to improve the efficiency. These provide scaling close to Δt 2 in the evolution time Δt. As with other algorithms of this type, the solution is encoded in amplitudes of the quantum state, and it is possible to extract global features of the solution. (paper)
19. A concise course on stochastic partial differential equations
CERN Document Server
Prévôt, Claudia
2007-01-01
These lectures concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. All kinds of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations. To keep the technicalities minimal we confine ourselves to the case where the noise term is given by a stochastic integral w.r.t. a cylindrical Wiener process.But all results can be easily generalized to SPDE with more general noises such as, for instance, stochastic integral w.r.t. a continuous local martingale. There are basically three approaches to analyze SPDE: the "martingale measure approach", the "mild solution approach" and the "variational approach". The purpose of these notes is to give a concise and as self-contained as possible an introduction to the "variational approach". A large part of necessary background material, such as definitions and results from the theory of Hilbert spaces, are included in appendices.
20. Partial differential equations in action from modelling to theory
CERN Document Server
Salsa, Sandro
2016-01-01
The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background in numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In turn the second part, chapters 6 to 11, concentrates on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear bo...
1. Reduced basis methods for partial differential equations an introduction
CERN Document Server
Quarteroni, Alfio; Negri, Federico
2016-01-01
This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied sciences, such as PDEs depending on several parameters and PDE-constrained optimization. The book presents a general mathematical formulation of RB methods, analyzes their fundamental theoretical properties, discusses the related algorithmic and implementation aspects, and highlights their built-in algebraic and geometric structures. More specifically, the authors discuss alternative strategies for constructing accurate RB spaces using greedy algorithms and proper orthogonal decomposition techniques, investigate their approximation properties and analyze offline-online decomposition strategies aimed at the reduction of computational complexity. Furthermore, they carry out both a priori and a posteriori error analysis. The whole mathematical presentation is made more stimulating by the use of representative examp...
2. Essential partial differential equations analytical and computational aspects
CERN Document Server
Griffiths, David F; Silvester, David J
2015-01-01
This volume provides an introduction to the analytical and numerical aspects of partial differential equations (PDEs). It unifies an analytical and computational approach for these; the qualitative behaviour of solutions being established using classical concepts: maximum principles and energy methods. Notable inclusions are the treatment of irregularly shaped boundaries, polar coordinates and the use of flux-limiters when approximating hyperbolic conservation laws. The numerical analysis of difference schemes is rigorously developed using discrete maximum principles and discrete Fourier analysis. A novel feature is the inclusion of a chapter containing projects, intended for either individual or group study, that cover a range of topics such as parabolic smoothing, travelling waves, isospectral matrices, and the approximation of multidimensional advection–diffusion problems. The underlying theory is illustrated by numerous examples and there are around 300 exercises, designed to promote and test unde...
3. Nonlinear partial differential equations for scientists and engineers
CERN Document Server
Debnath, Lokenath
1997-01-01
"An exceptionally complete overview. There are numerous examples and the emphasis is on applications to almost all areas of science and engineering. There is truly something for everyone here. This reviewer feels that it is a very hard act to follow, and recommends it strongly. [This book] is a jewel." ---Applied Mechanics Review (Review of First Edition) This expanded and revised second edition is a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied applications. Building upon the successful material of the first book, this edition contains updated modern examples and applications from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation. Methods and properties of solutions are presented, along with their physical significance, making the book more useful for a diverse readership. Topics and key features: * Thorough coverage of derivation and methods of soluti...
4. Partial differential equations in action from modelling to theory
CERN Document Server
Salsa, Sandro
2015-01-01
The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background in numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In turn the second part, chapters 6 to 11, concentrates on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear bo...
5. Learning partial differential equations via data discovery and sparse optimization.
Science.gov (United States)
Schaeffer, Hayden
2017-01-01
We investigate the problem of learning an evolution equation directly from some given data. This work develops a learning algorithm to identify the terms in the underlying partial differential equations and to approximate the coefficients of the terms only using data. The algorithm uses sparse optimization in order to perform feature selection and parameter estimation. The features are data driven in the sense that they are constructed using nonlinear algebraic equations on the spatial derivatives of the data. Several numerical experiments show the proposed method's robustness to data noise and size, its ability to capture the true features of the data, and its capability of performing additional analytics. Examples include shock equations, pattern formation, fluid flow and turbulence, and oscillatory convection.
6. Optimized difference schemes for multidimensional hyperbolic partial differential equations
Directory of Open Access Journals (Sweden)
2009-04-01
Full Text Available In numerical solutions to hyperbolic partial differential equations in multidimensions, in addition to dispersion and dissipation errors, there is a grid-related error (referred to as isotropy error or numerical anisotropy that affects the directional dependence of the wave propagation. Difference schemes are mostly analyzed and optimized in one dimension, wherein the anisotropy correction may not be effective enough. In this work, optimized multidimensional difference schemes with arbitrary order of accuracy are designed to have improved isotropy compared to conventional schemes. The derivation is performed based on Taylor series expansion and Fourier analysis. The schemes are restricted to equally-spaced Cartesian grids, so the generalized curvilinear transformation method and Cartesian grid methods are good candidates.
7. Modeling tree crown dynamics with 3D partial differential equations.
Science.gov (United States)
Beyer, Robert; Letort, Véronique; Cournède, Paul-Henry
2014-01-01
We characterize a tree's spatial foliage distribution by the local leaf area density. Considering this spatially continuous variable allows to describe the spatiotemporal evolution of the tree crown by means of 3D partial differential equations. These offer a framework to rigorously take locally and adaptively acting effects into account, notably the growth toward light. Biomass production through photosynthesis and the allocation to foliage and wood are readily included in this model framework. The system of equations stands out due to its inherent dynamic property of self-organization and spontaneous adaptation, generating complex behavior from even only a few parameters. The density-based approach yields spatially structured tree crowns without relying on detailed geometry. We present the methodological fundamentals of such a modeling approach and discuss further prospects and applications.
8. Data-driven discovery of partial differential equations.
Science.gov (United States)
Rudy, Samuel H; Brunton, Steven L; Proctor, Joshua L; Kutz, J Nathan
2017-04-01
We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with the dynamics. The method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Moreover, the method is capable of disambiguating between potentially nonunique dynamical terms by using multiple time series taken with different initial data. Thus, for a traveling wave, the method can distinguish between a linear wave equation and the Korteweg-de Vries equation, for instance. The method provides a promising new technique for discovering governing equations and physical laws in parameterized spatiotemporal systems, where first-principles derivations are intractable.
9. Solving Differential Equations Analytically. Elementary Differential Equations. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Unit 335.
Science.gov (United States)
Goldston, J. W.
This unit introduces analytic solutions of ordinary differential equations. The objective is to enable the student to decide whether a given function solves a given differential equation. Examples of problems from biology and chemistry are covered. Problem sets, quizzes, and a model exam are included, and answers to all items are provided. The…
10. Workshop on Recent Trends in Complex Methods for Partial Differential Equations
CERN Document Server
Celebi, A; Tutschke, Wolfgang
1999-01-01
This volume is a collection of manscripts mainly originating from talks and lectures given at the Workshop on Recent Trends in Complex Methods for Par tial Differential Equations held from July 6 to 10, 1998 at the Middle East Technical University in Ankara, Turkey, sponsored by The Scientific and Tech nical Research Council of Turkey and the Middle East Technical University. This workshop is a continuation oftwo workshops from 1988 and 1993 at the In ternational Centre for Theoretical Physics in Trieste, Italy entitled Functional analytic Methods in Complex Analysis and Applications to Partial Differential Equations. Since classical complex analysis of one and several variables has a long tra dition it is of high level. But most of its basic problems are solved nowadays so that within the last few decades it has lost more and more attention. The area of complex and functional analytic methods in partial differential equations, however, is still a growing and flourishing field, in particular as these ...
11. On method of solving third-order ordinary differential equations directly using Bernstein polynomials
Science.gov (United States)
Khataybeh, S. N.; Hashim, I.
2018-04-01
In this paper, we propose for the first time a method based on Bernstein polynomials for solving directly a class of third-order ordinary differential equations (ODEs). This method gives a numerical solution by converting the equation into a system of algebraic equations which is solved directly. Some numerical examples are given to show the applicability of the method.
12. BOOK REVIEW: Partial Differential Equations in General Relativity
Science.gov (United States)
Halburd, Rodney G.
2008-11-01
Although many books on general relativity contain an overview of the relevant background material from differential geometry, very little attention is usually paid to background material from the theory of differential equations. This is understandable in a first course on relativity but it often limits the kinds of problems that can be studied rigorously. Einstein's field equations lie at the heart of general relativity. They are a system of partial differential equations (PDEs) relating the curvature of spacetime to properties of matter. A central part of most problems in general relativity is to extract information about solutions of these equations. Most standard texts achieve this by studying exact solutions or numerical and analytical approximations. In the book under review, Alan Rendall emphasises the role of rigorous qualitative methods in general relativity. There has long been a need for such a book, giving a broad overview of the relevant background from the theory of partial differential equations, and not just from differential geometry. It should be noted that the book also covers the basic theory of ordinary differential equations. Although there are many good books on the rigorous theory of PDEs, methods related to the Einstein equations deserve special attention, not only because of the complexity and importance of these equations, but because these equations do not fit into any of the standard classes of equations (elliptic, parabolic, hyperbolic) that one typically encounters in a course on PDEs. Even specifying exactly what ones means by a Cauchy problem in general relativity requires considerable care. The main problem here is that the manifold on which the solution is defined is determined by the solution itself. This means that one does not simply define data on a submanifold. Rendall's book gives a good overview of applications and results from the qualitative theory of PDEs to general relativity. It would be impossible to give detailed
13. Derivation of a macroscale formulation for a class of nonlinear partial differential equations
International Nuclear Information System (INIS)
Pantelis, G.
1995-05-01
A macroscale formulation is constructed from a system of partial differential equations which govern the microscale dependent variables. The construction is based upon the requirement that the solutions of the macroscale partial differential equations satisfy, in some approximate sense, the system of partial differential equations associated with the microscale. These results are restricted to the class of nonlinear partial differential equations which can be expressed as polynomials of the dependent variables and their partial derivatives up to second order. A linear approximation of transformations of second order contact manifolds is employed. 6 refs
14. DISPL-1, 2. Order Nonlinear Partial Differential Equation System Solution for Kinetics Diffusion Problems
International Nuclear Information System (INIS)
Leaf, G.K.; Minkoff, M.
1982-01-01
1 - Description of problem or function: DISPL1 is a software package for solving second-order nonlinear systems of partial differential equations including parabolic, elliptic, hyperbolic, and some mixed types. The package is designed primarily for chemical kinetics- diffusion problems, although not limited to these problems. Fairly general nonlinear boundary conditions are allowed as well as inter- face conditions for problems in an inhomogeneous medium. The spatial domain is one- or two-dimensional with rectangular Cartesian, cylindrical, or spherical (in one dimension only) geometry. 2 - Method of solution: The numerical method is based on the use of Galerkin's procedure combined with the use of B-Splines (C.W.R. de-Boor's B-spline package) to generate a system of ordinary differential equations. These equations are solved by a sophisticated ODE software package which is a modified version of Hindmarsh's GEAR package, NESC Abstract 592. 3 - Restrictions on the complexity of the problem: The spatial domain must be rectangular with sides parallel to the coordinate geometry. Cross derivative terms are not permitted in the PDE. The order of the B-Splines is at most 12. Other parameters such as the number of mesh points in each coordinate direction, the number of PDE's etc. are set in a macro table used by the MORTRAn2 preprocessor in generating the object code
15. Application of the Generalized Differential Quadrature Method in Solving Burgers' Equations
International Nuclear Information System (INIS)
Mokhtari, R.; Toodar, A. Samadi; Chegini, N.G.
2011-01-01
The aim of this paper is to obtain numerical solutions of the one-dimensional, two-dimensional and coupled Burgers' equations through the generalized differential quadrature method (GDQM). The polynomial-based differential quadrature (PDQ) method is employed and the obtained system of ordinary differential equations is solved via the total variation diminishing Runge-Kutta (TVD-RK) method. The numerical solutions are satisfactorily coincident with the exact solutions. The method can compete against the methods applied in the literature. (general)
16. Application of differential transformation method for solving dengue transmission mathematical model
Science.gov (United States)
Ndii, Meksianis Z.; Anggriani, Nursanti; Supriatna, Asep K.
2018-03-01
The differential transformation method (DTM) is a semi-analytical numerical technique which depends on Taylor series and has application in many areas including Biomathematics. The aim of this paper is to employ the differential transformation method (DTM) to solve system of non-linear differential equations for dengue transmission mathematical model. Analytical and numerical solutions are determined and the results are compared to that of Runge-Kutta method. We found a good agreement between DTM and Runge-Kutta method.
17. Grid generation for the solution of partial differential equations
Science.gov (United States)
Eiseman, Peter R.; Erlebacher, Gordon
1989-01-01
A general survey of grid generators is presented with a concern for understanding why grids are necessary, how they are applied, and how they are generated. After an examination of the need for meshes, the overall applications setting is established with a categorization of the various connectivity patterns. This is split between structured grids and unstructured meshes. Altogether, the categorization establishes the foundation upon which grid generation techniques are developed. The two primary categories are algebraic techniques and partial differential equation techniques. These are each split into basic parts, and accordingly are individually examined in some detail. In the process, the interrelations between the various parts are accented. From the established background in the primary techniques, consideration is shifted to the topic of interactive grid generation and then to adaptive meshes. The setting for adaptivity is established with a suitable means to monitor severe solution behavior. Adaptive grids are considered first and are followed by adaptive triangular meshes. Then the consideration shifts to the temporal coupling between grid generators and PDE-solvers. To conclude, a reflection upon the discussion, herein, is given.
18. A hybrid perturbation-Galerkin technique for partial differential equations
Science.gov (United States)
Geer, James F.; Anderson, Carl M.
1990-01-01
A two-step hybrid perturbation-Galerkin technique for improving the usefulness of perturbation solutions to partial differential equations which contain a parameter is presented and discussed. In the first step of the method, the leading terms in the asymptotic expansion(s) of the solution about one or more values of the perturbation parameter are obtained using standard perturbation methods. In the second step, the perturbation functions obtained in the first step are used as trial functions in a Bubnov-Galerkin approximation. This semi-analytical, semi-numerical hybrid technique appears to overcome some of the drawbacks of the perturbation and Galerkin methods when they are applied by themselves, while combining some of the good features of each. The technique is illustrated first by a simple example. It is then applied to the problem of determining the flow of a slightly compressible fluid past a circular cylinder and to the problem of determining the shape of a free surface due to a sink above the surface. Solutions obtained by the hybrid method are compared with other approximate solutions, and its possible application to certain problems associated with domain decomposition is discussed.
19. Final Report: Symposium on Adaptive Methods for Partial Differential Equations
Energy Technology Data Exchange (ETDEWEB)
Pernice, M.; Johnson, C.R.; Smith, P.J.; Fogelson, A.
1998-12-10
OAK-B135 Final Report: Symposium on Adaptive Methods for Partial Differential Equations. Complex physical phenomena often include features that span a wide range of spatial and temporal scales. Accurate simulation of such phenomena can be difficult to obtain, and computations that are under-resolved can even exhibit spurious features. While it is possible to resolve small scale features by increasing the number of grid points, global grid refinement can quickly lead to problems that are intractable, even on the largest available computing facilities. These constraints are particularly severe for three dimensional problems that involve complex physics. One way to achieve the needed resolution is to refine the computational mesh locally, in only those regions where enhanced resolution is required. Adaptive solution methods concentrate computational effort in regions where it is most needed. These methods have been successfully applied to a wide variety of problems in computational science and engineering. Adaptive methods can be difficult to implement, prompting the development of tools and environments to facilitate their use. To ensure that the results of their efforts are useful, algorithm and tool developers must maintain close communication with application specialists. Conversely it remains difficult for application specialists who are unfamiliar with the methods to evaluate the trade-offs between the benefits of enhanced local resolution and the effort needed to implement an adaptive solution method.
20. Towards information-optimal simulation of partial differential equations.
Science.gov (United States)
Leike, Reimar H; Enßlin, Torsten A
2018-03-01
Most simulation schemes for partial differential equations (PDEs) focus on minimizing a simple error norm of a discretized version of a field. This paper takes a fundamentally different approach; the discretized field is interpreted as data providing information about a real physical field that is unknown. This information is sought to be conserved by the scheme as the field evolves in time. Such an information theoretic approach to simulation was pursued before by information field dynamics (IFD). In this paper we work out the theory of IFD for nonlinear PDEs in a noiseless Gaussian approximation. The result is an action that can be minimized to obtain an information-optimal simulation scheme. It can be brought into a closed form using field operators to calculate the appearing Gaussian integrals. The resulting simulation schemes are tested numerically in two instances for the Burgers equation. Their accuracy surpasses finite-difference schemes on the same resolution. The IFD scheme, however, has to be correctly informed on the subgrid correlation structure. In certain limiting cases we recover well-known simulation schemes like spectral Fourier-Galerkin methods. We discuss implications of the approximations made.
1. Application of Stochastic Partial Differential Equations to Reservoir Property Modelling
KAUST Repository
Potsepaev, R.
2010-09-06
Existing algorithms of geostatistics for stochastic modelling of reservoir parameters require a mapping (the \\'uvt-transform\\') into the parametric space and reconstruction of a stratigraphic co-ordinate system. The parametric space can be considered to represent a pre-deformed and pre-faulted depositional environment. Existing approximations of this mapping in many cases cause significant distortions to the correlation distances. In this work we propose a coordinate free approach for modelling stochastic textures through the application of stochastic partial differential equations. By avoiding the construction of a uvt-transform and stratigraphic coordinates, one can generate realizations directly in the physical space in the presence of deformations and faults. In particular the solution of the modified Helmholtz equation driven by Gaussian white noise is a zero mean Gaussian stationary random field with exponential correlation function (in 3-D). This equation can be used to generate realizations in parametric space. In order to sample in physical space we introduce a stochastic elliptic PDE with tensor coefficients, where the tensor is related to correlation anisotropy and its variation is physical space.
2. Partial differential equations an accessible route through theory and applications
CERN Document Server
Vasy, András
2015-01-01
This text on partial differential equations is intended for readers who want to understand the theoretical underpinnings of modern PDEs in settings that are important for the applications without using extensive analytic tools required by most advanced texts. The assumed mathematical background is at the level of multivariable calculus and basic metric space material, but the latter is recalled as relevant as the text progresses. The key goal of this book is to be mathematically complete without overwhelming the reader, and to develop PDE theory in a manner that reflects how researchers would think about the material. A concrete example is that distribution theory and the concept of weak solutions are introduced early because while these ideas take some time for the students to get used to, they are fundamentally easy and, on the other hand, play a central role in the field. Then, Hilbert spaces that are quite important in the later development are introduced via completions which give essentially all the fea...
3. Stochastic partial differential equations a modeling, white noise functional approach
CERN Document Server
Holden, Helge; Ubøe, Jan; Zhang, Tusheng
1996-01-01
This book is based on research that, to a large extent, started around 1990, when a research project on fluid flow in stochastic reservoirs was initiated by a group including some of us with the support of VISTA, a research coopera tion between the Norwegian Academy of Science and Letters and Den norske stats oljeselskap A.S. (Statoil). The purpose of the project was to use stochastic partial differential equations (SPDEs) to describe the flow of fluid in a medium where some of the parameters, e.g., the permeability, were stochastic or "noisy". We soon realized that the theory of SPDEs at the time was insufficient to handle such equations. Therefore it became our aim to develop a new mathematically rigorous theory that satisfied the following conditions. 1) The theory should be physically meaningful and realistic, and the corre sponding solutions should make sense physically and should be useful in applications. 2) The theory should be general enough to handle many of the interesting SPDEs that occur in r...
4. On new classes of solutions of nonlinear partial differential equations in the form of convergent special series
Science.gov (United States)
Filimonov, M. Yu.
2017-12-01
The method of special series with recursively calculated coefficients is used to solve nonlinear partial differential equations. The recurrence of finding the coefficients of the series is achieved due to a special choice of functions, in powers of which the solution is expanded in a series. We obtain a sequence of linear partial differential equations to find the coefficients of the series constructed. In many cases, one can deal with a sequence of linear ordinary differential equations. We construct classes of solutions in the form of convergent series for a certain class of nonlinear evolution equations. A new class of solutions of generalized Boussinesque equation with an arbitrary function in the form of a convergent series is constructed.
5. Nonlocal symmetry generators and explicit solutions of some partial differential equations
International Nuclear Information System (INIS)
Qin Maochang
2007-01-01
The nonlocal symmetry of a partial differential equation is studied in this paper. The partial differential equation written as a conservation law can be transformed into an equivalent system by introducing a suitable potential. The nonlocal symmetry group generators of original partial differential equations can be obtained through their equivalent system. Further, new explicit solutions can be constructed from the newly obtained symmetry generators. The Burgers equation is chosen as an example; many new valuable explicit solutions and nonlocal symmetry generators are presented
6. Basis adaptation and domain decomposition for steady-state partial differential equations with random coefficients
Energy Technology Data Exchange (ETDEWEB)
Tipireddy, R.; Stinis, P.; Tartakovsky, A. M.
2017-12-01
We present a novel approach for solving steady-state stochastic partial differential equations (PDEs) with high-dimensional random parameter space. The proposed approach combines spatial domain decomposition with basis adaptation for each subdomain. The basis adaptation is used to address the curse of dimensionality by constructing an accurate low-dimensional representation of the stochastic PDE solution (probability density function and/or its leading statistical moments) in each subdomain. Restricting the basis adaptation to a specific subdomain affords finding a locally accurate solution. Then, the solutions from all of the subdomains are stitched together to provide a global solution. We support our construction with numerical experiments for a steady-state diffusion equation with a random spatially dependent coefficient. Our results show that highly accurate global solutions can be obtained with significantly reduced computational costs.
7. Partial differential equations of first order and their applications to physics
CERN Document Server
López, Gustavo
2012-01-01
This book tries to point out the mathematical importance of the Partial Differential Equations of First Order (PDEFO) in Physics and Applied Sciences. The intention is to provide mathematicians with a wide view of the applications of this branch in physics, and to give physicists and applied scientists a powerful tool for solving some problems appearing in Classical Mechanics, Quantum Mechanics, Optics, and General Relativity. This book is intended for senior or first year graduate students in mathematics, physics, or engineering curricula. This book is unique in the sense that it covers the applications of PDEFO in several branches of applied mathematics, and fills the theoretical gap between the formal mathematical presentation of the theory and the pure applied tool to physical problems that are contained in other books. Improvements made in this second edition include corrected typographical errors; rewritten text to improve the flow and enrich the material; added exercises in all chapters; new applicati...
8. A Table Lookup Method for Exact Analytical Solutions of Nonlinear Fractional Partial Differential Equations
Directory of Open Access Journals (Sweden)
Ji Juan-Juan
2017-01-01
Full Text Available A table lookup method for solving nonlinear fractional partial differential equations (fPDEs is proposed in this paper. Looking up the corresponding tables, we can quickly obtain the exact analytical solutions of fPDEs by using this method. To illustrate the validity of the method, we apply it to construct the exact analytical solutions of four nonlinear fPDEs, namely, the time fractional simplified MCH equation, the space-time fractional combined KdV-mKdV equation, the (2+1-dimensional time fractional Zoomeron equation, and the space-time fractional ZKBBM equation. As a result, many new types of exact analytical solutions are obtained including triangular periodic solution, hyperbolic function solution, singular solution, multiple solitary wave solution, and Jacobi elliptic function solution.
9. Solving inverse problems for biological models using the collage method for differential equations.
Science.gov (United States)
Capasso, V; Kunze, H E; La Torre, D; Vrscay, E R
2013-07-01
In the first part of this paper we show how inverse problems for differential equations can be solved using the so-called collage method. Inverse problems can be solved by minimizing the collage distance in an appropriate metric space. We then provide several numerical examples in mathematical biology. We consider applications of this approach to the following areas: population dynamics, mRNA and protein concentration, bacteria and amoeba cells interaction, tumor growth.
10. Iterative Observer-based Estimation Algorithms for Steady-State Elliptic Partial Differential Equation Systems
KAUST Repository
2017-07-19
Steady-state elliptic partial differential equations (PDEs) are frequently used to model a diverse range of physical phenomena. The source and boundary data estimation problems for such PDE systems are of prime interest in various engineering disciplines including biomedical engineering, mechanics of materials and earth sciences. Almost all existing solution strategies for such problems can be broadly classified as optimization-based techniques, which are computationally heavy especially when the problems are formulated on higher dimensional space domains. However, in this dissertation, feedback based state estimation algorithms, known as state observers, are developed to solve such steady-state problems using one of the space variables as time-like. In this regard, first, an iterative observer algorithm is developed that sweeps over regular-shaped domains and solves boundary estimation problems for steady-state Laplace equation. It is well-known that source and boundary estimation problems for the elliptic PDEs are highly sensitive to noise in the data. For this, an optimal iterative observer algorithm, which is a robust counterpart of the iterative observer, is presented to tackle the ill-posedness due to noise. The iterative observer algorithm and the optimal iterative algorithm are then used to solve source localization and estimation problems for Poisson equation for noise-free and noisy data cases respectively. Next, a divide and conquer approach is developed for three-dimensional domains with two congruent parallel surfaces to solve the boundary and the source data estimation problems for the steady-state Laplace and Poisson kind of systems respectively. Theoretical results are shown using a functional analysis framework, and consistent numerical simulation results are presented for several test cases using finite difference discretization schemes.
11. Preconditioners based on windowed Fourier frames applied to elliptic partial differential equations
NARCIS (Netherlands)
Bhowmik, S.K.; Stolk, C.C.
2011-01-01
We investigate the application of windowed Fourier frames to the numerical solution of partial differential equations, focussing on elliptic equations. The action of a partial differential operator (PDO) on a windowed plane wave is close to a multiplication, where the multiplication factor is given
12. Higher order multi-term time-fractional partial differential equations involving Caputo-Fabrizio derivative
Directory of Open Access Journals (Sweden)
Erkinjon Karimov
2017-10-01
Full Text Available In this work we discuss higher order multi-term partial differential equation (PDE with the Caputo-Fabrizio fractional derivative in time. Using method of separation of variables, we reduce fractional order partial differential equation to the integer order. We represent explicit solution of formulated problem in particular case by Fourier series.
13. Higher order multi-term time-fractional partial differential equations involving Caputo-Fabrizio derivative
OpenAIRE
Erkinjon Karimov; Sardor Pirnafasov
2017-01-01
In this work we discuss higher order multi-term partial differential equation (PDE) with the Caputo-Fabrizio fractional derivative in time. Using method of separation of variables, we reduce fractional order partial differential equation to the integer order. We represent explicit solution of formulated problem in particular case by Fourier series.
14. Controllability and Stabilization of Bilinear and Semilinear Partial Differential Equations
DEFF Research Database (Denmark)
Krishnaswamy, Vijayaraghavan
The topic of the thesis is the investigation of the question of controllability of weakly nonlinear partial differntial equations. The method is based on the Hilbert Uniqueness Method.......The topic of the thesis is the investigation of the question of controllability of weakly nonlinear partial differntial equations. The method is based on the Hilbert Uniqueness Method....
15. Optimal Control Method of Parabolic Partial Differential Equations and Its Application to Heat Transfer Model in Continuous Cast Secondary Cooling Zone
Directory of Open Access Journals (Sweden)
Yuan Wang
2015-01-01
Full Text Available Our work is devoted to a class of optimal control problems of parabolic partial differential equations. Because of the partial differential equations constraints, it is rather difficult to solve the optimization problem. The gradient of the cost function can be found by the adjoint problem approach. Based on the adjoint problem approach, the gradient of cost function is proved to be Lipschitz continuous. An improved conjugate method is applied to solve this optimization problem and this algorithm is proved to be convergent. This method is applied to set-point values in continuous cast secondary cooling zone. Based on the real data in a plant, the simulation experiments show that the method can ensure the steel billet quality. From these experiment results, it is concluded that the improved conjugate gradient algorithm is convergent and the method is effective in optimal control problem of partial differential equations.
16. Advantages and Disadvantages of Using MATLAB/ode45 for Solving Differential Equations in Engineering Applications
OpenAIRE
Waleed K. Ahmed
2013-01-01
The present paper demonstrates the route used for solving differential equations for the engineering applications at UAEU. Usually students at the Engineering Requirements Unit (ERU) stage of the Faculty of Engineering at the UAEU must enroll in a course of Differential Equations and Engineering Applications (MATH 2210) as a prerequisite for the subsequent stages of their study. Mainly, one of the objectives of this course is that the students practice MATLAB software package during the cours...
17. An efficient computer based wavelets approximation method to solve Fuzzy boundary value differential equations
Science.gov (United States)
Alam Khan, Najeeb; Razzaq, Oyoon Abdul
2016-03-01
In the present work a wavelets approximation method is employed to solve fuzzy boundary value differential equations (FBVDEs). Essentially, a truncated Legendre wavelets series together with the Legendre wavelets operational matrix of derivative are utilized to convert FB- VDE into a simple computational problem by reducing it into a system of fuzzy algebraic linear equations. The capability of scheme is investigated on second order FB- VDE considered under generalized H-differentiability. Solutions are represented graphically showing competency and accuracy of this method.
18. A semi-analytical approach for solving of nonlinear systems of functional differential equations with delay
Science.gov (United States)
Rebenda, Josef; Šmarda, Zdeněk
2017-07-01
In the paper, we propose a correct and efficient semi-analytical approach to solve initial value problem for systems of functional differential equations with delay. The idea is to combine the method of steps and differential transformation method (DTM). In the latter, formulas for proportional arguments and nonlinear terms are used. An example of using this technique for a system with constant and proportional delays is presented.
19. Analytic Solutions and Resonant Solutions of Hyperbolic Partial Differential Equations
Science.gov (United States)
Wagenmaker, Timothy Roger
This dissertation contains two main subject areas. The first deals with solutions to the wave equation Du/Dt + a Du/Dx = 0, where D/Dt and D/Dx represent partial derivatives and a(t,x) is real valued. The question I studied, which arises in control theory, is whether solutions which are real analytic with respect to the time variable are dense in the space of all solutions. If a is real analytic in t and x, the Cauchy-Kovalevsky Theorem implies that the solutions real analytic in t and x are dense, since it suffices to approximate the initial data by polynomials. The same positive result is valid when a is continuously differentiable and independent of t. This is proved by regularization in time. The hypothesis that a is independent of t cannot be replaced by the weaker assumption that a is real analytic in t, even when it is infinitely smooth. I construct a(t,x) for which the solutions which are analytic in time are automatically periodic in time. In particular these solutions are not dense in the space of all solutions. The second area concerns the resonant interaction of oscillatory waves propagating in a compressible inviscid fluid. An asymptotic description given by Andrew Majda, Rodolfo Rosales, and Maria Schonbek (MRS) involves the genuinely nonlinear quasilinear hyperbolic system Du/Dt + D(uu/2)/Dt + v = 0, Dv/Dt - D(vv/2)/Dt - u = 0. They performed many numerical simulations which indicated that small amplitude solutions of this system tend to evade shock formation, and conjectured that "smooth initial data with a sufficiently small amplitude never develop shocks throughout a long time interval of integration.". I proved that for smooth periodic U(x), V(x) and initial data u(0,x) = epsilonU(x), v(0,x) = epsilonV(x), the solution is smooth for time at least constant times | ln epsilon| /epsilon. This is longer than the lifetime order 1/ epsilon of the solution to the decoupled Burgers equations. The decoupled equation describes nonresonant interaction of
20. New Exact Solutions for New Model Nonlinear Partial Differential Equation
OpenAIRE
Maher, A.; El-Hawary, H. M.; Al-Amry, M. S.
2013-01-01
In this paper we propose a new form of Padé-II equation, namely, a combined Padé-II and modified Padé-II equation. The mapping method is a promising method to solve nonlinear evaluation equations. Therefore, we apply it, to solve the combined Padé-II and modified Padé-II equation. Exact travelling wave solutions are obtained and expressed in terms of hyperbolic functions, trigonometric functions, rational functions, and elliptic functions.
1. Fast solution of elliptic partial differential equations using linear combinations of plane waves.
Science.gov (United States)
Pérez-Jordá, José M
2016-02-01
Given an arbitrary elliptic partial differential equation (PDE), a procedure for obtaining its solution is proposed based on the method of Ritz: the solution is written as a linear combination of plane waves and the coefficients are obtained by variational minimization. The PDE to be solved is cast as a system of linear equations Ax=b, where the matrix A is not sparse, which prevents the straightforward application of standard iterative methods in order to solve it. This sparseness problem can be circumvented by means of a recursive bisection approach based on the fast Fourier transform, which makes it possible to implement fast versions of some stationary iterative methods (such as Gauss-Seidel) consuming O(NlogN) memory and executing an iteration in O(Nlog(2)N) time, N being the number of plane waves used. In a similar way, fast versions of Krylov subspace methods and multigrid methods can also be implemented. These procedures are tested on Poisson's equation expressed in adaptive coordinates. It is found that the best results are obtained with the GMRES method using a multigrid preconditioner with Gauss-Seidel relaxation steps.
2. Solving Nonlinear Fractional Differential Equation by Generalized Mittag-Leffler Function Method
Science.gov (United States)
Arafa, A. A. M.; Rida, S. Z.; Mohammadein, A. A.; Ali, H. M.
2013-06-01
In this paper, we use Mittag—Leffler function method for solving some nonlinear fractional differential equations. A new solution is constructed in power series. The fractional derivatives are described by Caputo's sense. To illustrate the reliability of the method, some examples are provided.
3. Who Solved the Bernoulli Differential Equation and How Did They Do It?
Science.gov (United States)
2013-01-01
The Bernoulli brothers, Jacob and Johann, and Leibniz: Any of these might have been first to solve what is called the Bernoulli differential equation. We explore their ideas and the chronology of their work, finding out, among other things, that variation of parameters was used in 1697, 78 years before 1775, when Lagrange introduced it in general.
4. Construction of Interval Wavelet Based on Restricted Variational Principle and Its Application for Solving Differential Equations
OpenAIRE
Mei, Shu-Li; Lv, Hong-Liang; Ma, Qin
2008-01-01
Based on restricted variational principle, a novel method for interval wavelet construction is proposed. For the excellent local property of quasi-Shannon wavelet, its interval wavelet is constructed, and then applied to solve ordinary differential equations. Parameter choices for the interval wavelet method are discussed and its numerical performance is demonstrated.
5. Solving Second-Order Ordinary Differential Equations without Using Complex Numbers
Science.gov (United States)
Kougias, Ioannis E.
2009-01-01
Ordinary differential equations (ODEs) is a subject with a wide range of applications and the need of introducing it to students often arises in the last year of high school, as well as in the early stages of tertiary education. The usual methods of solving second-order ODEs with constant coefficients, among others, rely upon the use of complex…
6. New Solutions of Three Nonlinear Space- and Time-Fractional Partial Differential Equations in Mathematical Physics
International Nuclear Information System (INIS)
Yao Ruo-Xia; Wang Wei; Chen Ting-Hua
2014-01-01
Motivated by the widely used ansätz method and starting from the modified Riemann—Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional partial differential equations to nonlinear ordinary differential equations, new types of exact traveling wave solutions to three important nonlinear space- and time-fractional partial differential equations are obtained simultaneously in terms of solutions of a Riccati equation. The results are new and first reported in this paper. (general)
7. Partial differential equations with variable exponents variational methods and qualitative analysis
CERN Document Server
2015-01-01
Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis provides researchers and graduate students with a thorough introduction to the theory of nonlinear partial differential equations (PDEs) with a variable exponent, particularly those of elliptic type. The book presents the most important variational methods for elliptic PDEs described by nonhomogeneous differential operators and containing one or more power-type nonlinearities with a variable exponent. The authors give a systematic treatment of the basic mathematical theory and constructive meth
8. Pure soliton solutions of some nonlinear partial differential equations
International Nuclear Information System (INIS)
Fuchssteiner, B.
1977-01-01
A general approach is given to obtain the system of ordinary differential equations which determines the pure soliton solutions for the class of generalized Korteweg-de Vries equations. This approach also leads to a system of ordinary differential equations for the pure soliton solutions of the sine-Gordon equation. (orig.) [de
9. Parallels between control PDE's (Partial Differential Equations) and systems of ODE's (Ordinary Differential Equations)
Science.gov (United States)
Hunt, L. R.; Villarreal, Ramiro
1987-01-01
System theorists understand that the same mathematical objects which determine controllability for nonlinear control systems of ordinary differential equations (ODEs) also determine hypoellipticity for linear partial differentail equations (PDEs). Moreover, almost any study of ODE systems begins with linear systems. It is remarkable that Hormander's paper on hypoellipticity of second order linear p.d.e.'s starts with equations due to Kolmogorov, which are shown to be analogous to the linear PDEs. Eigenvalue placement by state feedback for a controllable linear system can be paralleled for a Kolmogorov equation if an appropriate type of feedback is introduced. Results concerning transformations of nonlinear systems to linear systems are similar to results for transforming a linear PDE to a Kolmogorov equation.
10. Solving differential-algebraic equation systems by means of index reduction methodology
DEFF Research Database (Denmark)
Sørensen, Kim; Houbak, Niels; Condra, Thomas Joseph
2006-01-01
of a number of differential equations and algebraic equations - a so called DAE system. Two of the DAE systems are of index 1 and they can be solved by means of standard DAE-solvers. For the actual application, the equation systems are integrated by means of MATLAB’s solver: ode23t, that solves moderately...... stiff ODE’s and index 1 DAE’s by means of the trapezoidal rule. The last sub-model that models the boilers steam drum consist of two differential and three algebraic equations. The index of this model is greater than 1, which means that ode23t cannot integrate this equation system. In this paper......, it is shown how the equation system, by means of an index reduction methodology, can be reduced to a system of Ordinary- Differential-Equations - ODE’s....
11. The Embedding Method for Linear Partial Differential Equations
The recently suggested embedding method to solve linear boundary value problems is here extended to cover situations where the domain of interest is unbounded or multiply connected. The extensions involve the use of complete sets of exterior and interior eigenfunctions on canonical domains. Applications to typical ...
12. New numerical approximation for solving fractional delay differential equations of variable order using artificial neural networks
Science.gov (United States)
Zúñiga-Aguilar, C. J.; Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Alvarado-Martínez, V. M.; Romero-Ugalde, H. M.
2018-02-01
In this paper, we approximate the solution of fractional differential equations with delay using a new approach based on artificial neural networks. We consider fractional differential equations of variable order with the Mittag-Leffler kernel in the Liouville-Caputo sense. With this new neural network approach, an approximate solution of the fractional delay differential equation is obtained. Synaptic weights are optimized using the Levenberg-Marquardt algorithm. The neural network effectiveness and applicability were validated by solving different types of fractional delay differential equations, linear systems with delay, nonlinear systems with delay and a system of differential equations, for instance, the Newton-Leipnik oscillator. The solution of the neural network was compared with the analytical solutions and the numerical simulations obtained through the Adams-Bashforth-Moulton method. To show the effectiveness of the proposed neural network, different performance indices were calculated.
13. Solving of some Problems with On-Line Mode Measurement of Partial Discharges
Directory of Open Access Journals (Sweden)
Karel Zalis
2004-01-01
Full Text Available This paper deals with the problems discussing the transition from off-line diagnostic methods to on-line ones. Based on the experience with commercial partial discharge measuring equipment a new digital system for the evaluation of partial discharge measurement including software and hardware facilities has been developed at the Czech Technical University in Prague. Two expert systems work in this complex evaluating system: a rule-based expert system performing an amplitude analysis of partial discharge impulses for determining the damage of the insulation system, and a neural network which is used for a phase analysis of partial discharge impulses to determine the kind of partial discharge activity. Problem of the elimination of disturbances is also discussed.
14. OSCILLATION OF IMPULSIVE HYPERBOLIC PARTIAL DIFFERENTIAL EQUATION WITH DELAY
Institute of Scientific and Technical Information of China (English)
2006-01-01
In this paper, oscillation properties of the solutions of impulsive hyperbolic equation with delay are investigated via the method of differential inequalities. Sufficient conditions for oscillations of the solutions are established.
15. Atmospheres of partially differentiated super-Earth exoplanets
Science.gov (United States)
Schaefer, Laura; Sasselov, Dimitar
2015-11-01
Terrestrial exoplanets have been discovered in a range of sizes, densities and orbital locations that defy our expectations based upon the Solar System. Planets discovered to date with radii less than ~1.5-1.6 Earth radii all seem to fall on an iso-density curve with the Earth [1]. However, mass and radius determinations, which depend on the known properties of the host star, are not accurate enough to distinguish between a fully differentiated three-layer planet (core, mantle, ocean/atmosphere) and an incompletely differentiated planet [2]. Full differentiation of a planet will depend upon the conditions at the time of accretion, including the abundance of short-lived radioisotopes, which will vary from system to system, as well as the number of giant impacts the planet experiences. Furthermore, separation of metal and silicates at the much larger pressures found inside super-Earths will depend on how the chemistry of these materials change at high pressures. There are therefore hints emerging that not all super-Earths will be fully differentiated. Incomplete differentiation will result in a more reduced mantle oxidation state and may have implications for the composition of an outgassed atmosphere. Here we will present the first results from a chemical equilibrium model of the composition of such an outgassed atmosphere and discuss the possibility of distinguishing between fully and incompletely differentiated planets through atmospheric observations.[1] Rogers, L. 2015. ApJ, 801, 41. [2] Zeng, L. & Sasselov, D. 2013. PASP, 125, 227.
16. On the strong solution of a class of partial differential equations that arise in the pricing of mortgage backed securities
KAUST Repository
2011-01-01
We consider a reduced form pricing model for mortgage backed securities, formulated as a non-linear partial differential equation. We prove that the model possesses a weak solution. We then show that under additional regularity assumptions on the initial data, we also have a mild solution. This mild solution is shown to be a strong solution via further regularity arguments. We also numerically solve the reduced model via a Fourier spectral method. Lastly, we compare our numerical solution to real market data. We observe interestingly that the reduced model captures a number of recent market trends in this data, that have escaped previous models.
17. Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions
Directory of Open Access Journals (Sweden)
Fukang Yin
2013-01-01
Full Text Available A numerical method is presented to obtain the approximate solutions of the fractional partial differential equations (FPDEs. The basic idea of this method is to achieve the approximate solutions in a generalized expansion form of two-dimensional fractional-order Legendre functions (2D-FLFs. The operational matrices of integration and derivative for 2D-FLFs are first derived. Then, by these matrices, a system of algebraic equations is obtained from FPDEs. Hence, by solving this system, the unknown 2D-FLFs coefficients can be computed. Three examples are discussed to demonstrate the validity and applicability of the proposed method.
18. Matrix form of Legendre polynomials for solving linear integro-differential equations of high order
Science.gov (United States)
Kammuji, M.; Eshkuvatov, Z. K.; Yunus, Arif A. M.
2017-04-01
This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods.
19. A differential transformation approach for solving functional differential equations with multiple delays
Science.gov (United States)
Rebenda, Josef; Šmarda, Zdeněk
2017-07-01
In the paper an efficient semi-analytical approach based on the method of steps and the differential transformation is proposed for numerical approximation of solutions of functional differential models of delayed and neutral type on a finite interval of arbitrary length, including models with several constant delays. Algorithms for both commensurate and non-commensurate delays are described, applications are shown in examples. Validity and efficiency of the presented algorithms is compared with the variational iteration method, the Adomian decomposition method and the polynomial least squares method numerically. Matlab package DDE23 is used to produce reference numerical values.
20. FORSIM, Solution of Ordinary or Partial Differential Equation with Initial Conditions
International Nuclear Information System (INIS)
Carver, M.B.
1985-01-01
1 - Description of problem or function: FORSIM is a FORTRAN oriented simulation program which automates the continuous transient solution of systems of ordinary and/or partial differential equations. The user writes his equations in a FORTRAN subroutine, following prescribed rules, and loads this routine along with the executive routines. The executive routines then read in initial data supplied by the user and proceed with the integration. 2 - Method of solution: Partial differential equations are converted to coupled ordinary differential equations by suitable discretization formulae. Integration is done by variable order, variable step-size error controlled algorithms. 3 - Restrictions on the complexity of the problem - Maximum of: 1000 ordinary differential equations
1. BOOK REVIEW: Advanced Topics in Computational Partial Differential Equations: Numerical Methods and Diffpack Programming
Science.gov (United States)
Katsaounis, T. D.
2005-02-01
The scope of this book is to present well known simple and advanced numerical methods for solving partial differential equations (PDEs) and how to implement these methods using the programming environment of the software package Diffpack. A basic background in PDEs and numerical methods is required by the potential reader. Further, a basic knowledge of the finite element method and its implementation in one and two space dimensions is required. The authors claim that no prior knowledge of the package Diffpack is required, which is true, but the reader should be at least familiar with an object oriented programming language like C++ in order to better comprehend the programming environment of Diffpack. Certainly, a prior knowledge or usage of Diffpack would be a great advantage to the reader. The book consists of 15 chapters, each one written by one or more authors. Each chapter is basically divided into two parts: the first part is about mathematical models described by PDEs and numerical methods to solve these models and the second part describes how to implement the numerical methods using the programming environment of Diffpack. Each chapter closes with a list of references on its subject. The first nine chapters cover well known numerical methods for solving the basic types of PDEs. Further, programming techniques on the serial as well as on the parallel implementation of numerical methods are also included in these chapters. The last five chapters are dedicated to applications, modelled by PDEs, in a variety of fields. The first chapter is an introduction to parallel processing. It covers fundamentals of parallel processing in a simple and concrete way and no prior knowledge of the subject is required. Examples of parallel implementation of basic linear algebra operations are presented using the Message Passing Interface (MPI) programming environment. Here, some knowledge of MPI routines is required by the reader. Examples solving in parallel simple PDEs using
2. Improving Teaching Quality and Problem Solving Ability through Contextual Teaching and Learning in Differential Equations: A Lesson Study Approach
Science.gov (United States)
Khotimah, Rita Pramujiyanti; Masduki
2016-01-01
Differential equations is a branch of mathematics which is closely related to mathematical modeling that arises in real-world problems. Problem solving ability is an essential component to solve contextual problem of differential equations properly. The purposes of this study are to describe contextual teaching and learning (CTL) model in…
3. Factors Affecting Differential Equation Problem Solving Ability of Students at Pre-University Level: A Conceptual Model
Science.gov (United States)
Aisha, Bibi; Zamri, Sharifa NorulAkmar Syed; Abdallah, Nabeel; Abedalaziz, Mohammad; Ahmad, Mushtaq; Satti, Umbreen
2017-01-01
In this study, different factors affecting students' differential equations (DEs) solving abilities were explored at pre university level. To explore main factors affecting students' differential equations problem solving ability, articles for a 19-year period, from 1996 to 2015, were critically reviewed and analyzed. It was revealed that…
4. Consistency of direct integral estimator for partially observed systems of ordinary differential equations
NARCIS (Netherlands)
Vujačić, Ivan; Dattner, Itai
In this paper we use the sieve framework to prove consistency of the ‘direct integral estimator’ of parameters for partially observed systems of ordinary differential equations, which are commonly used for modeling dynamic processes.
5. The generalized tanh method to obtain exact solutions of nonlinear partial differential equation
OpenAIRE
Gómez, César
2007-01-01
In this paper, we present the generalized tanh method to obtain exact solutions of nonlinear partial differential equations, and we obtain solitons and exact solutions of some important equations of the mathematical physics.
6. 3rd International Conference on Particle Systems and Partial Differential Equations
CERN Document Server
Soares, Ana
2016-01-01
The main focus of this book is on different topics in probability theory, partial differential equations and kinetic theory, presenting some of the latest developments in these fields. It addresses mathematical problems concerning applications in physics, engineering, chemistry and biology that were presented at the Third International Conference on Particle Systems and Partial Differential Equations, held at the University of Minho, Braga, Portugal in December 2014. The purpose of the conference was to bring together prominent researchers working in the fields of particle systems and partial differential equations, providing a venue for them to present their latest findings and discuss their areas of expertise. Further, it was intended to introduce a vast and varied public, including young researchers, to the subject of interacting particle systems, its underlying motivation, and its relation to partial differential equations. This book will appeal to probabilists, analysts and those mathematicians whose wor...
7. Modulating Function-Based Method for Parameter and Source Estimation of Partial Differential Equations
KAUST Repository
Asiri, Sharefa M.
2017-01-01
Partial Differential Equations (PDEs) are commonly used to model complex systems that arise for example in biology, engineering, chemistry, and elsewhere. The parameters (or coefficients) and the source of PDE models are often unknown
8. Intuitive Understanding of Solutions of Partially Differential Equations
Science.gov (United States)
Kobayashi, Y.
2008-01-01
This article uses diagrams that help the observer see how solutions of the wave equation and heat conduction equation are obtained. The analytical approach cannot necessarily show the mechanisms of the key to the solution without transforming the differential equation into a more convenient form by separation of variables. The visual clues based…
9. Coverings and the fundamental group for partial differential equations
NARCIS (Netherlands)
Igonin, S.
2003-01-01
Following I. S. Krasilshchik and A. M. Vinogradov, we regard systems of PDEs as manifolds with involutive distributions and consider their special morphisms called differential coverings, which include constructions like Lax pairs and B\\"acklund transformations in soliton theory. We show that,
10. Hyperbolic partial differential equations populations, reactors, tides and waves theory and applications
CERN Document Server
Witten, Matthew
1983-01-01
Hyperbolic Partial Differential Equations, Volume 1: Population, Reactors, Tides and Waves: Theory and Applications covers three general areas of hyperbolic partial differential equation applications. These areas include problems related to the McKendrick/Von Foerster population equations, other hyperbolic form equations, and the numerical solution.This text is composed of 15 chapters and begins with surveys of age specific population interactions, populations models of diffusion, nonlinear age dependent population growth with harvesting, local and global stability for the nonlinear renewal eq
11. Modeling Solution of Nonlinear Dispersive Partial Differential Equations using the Marker Method
International Nuclear Information System (INIS)
Lewandowski, Jerome L.V.
2005-01-01
A new method for the solution of nonlinear dispersive partial differential equations is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details
12. Analytic continuation of solutions of some nonlinear convolution partial differential equations
Directory of Open Access Journals (Sweden)
Hidetoshi Tahara
2015-01-01
Full Text Available The paper considers a problem of analytic continuation of solutions of some nonlinear convolution partial differential equations which naturally appear in the summability theory of formal solutions of nonlinear partial differential equations. Under a suitable assumption it is proved that any local holomorphic solution has an analytic extension to a certain sector and its extension has exponential growth when the variable goes to infinity in the sector.
13. Calculus for cognitive scientists partial differential equation models
CERN Document Server
Peterson, James K
2016-01-01
This book shows cognitive scientists in training how mathematics, computer science and science can be usefully and seamlessly intertwined. It is a follow-up to the first two volumes on mathematics for cognitive scientists, and includes the mathematics and computational tools needed to understand how to compute the terms in the Fourier series expansions that solve the cable equation. The latter is derived from first principles by going back to cellular biology and the relevant biophysics. A detailed discussion of ion movement through cellular membranes, and an explanation of how the equations that govern such ion movement leading to the standard transient cable equation are included. There are also solutions for the cable model using separation of variables, as well an explanation of why Fourier series converge and a description of the implementation of MatLab tools to compute the solutions. Finally, the standard Hodgkin - Huxley model is developed for an excitable neuron and is solved using MatLab.
14. Give me a hand: Differential effects of gesture type in guiding young children's problem-solving
OpenAIRE
Vallotton, Claire; Fusaro, Maria; Hayden, Julia; Decker, Kalli; Gutowski, Elizabeth
2015-01-01
Adults’ gestures support children's learning in problem-solving tasks, but gestures may be differentially useful to children of different ages, and different features of gestures may make them more or less useful to children. The current study investigated parents’ use of gestures to support their young children (1.5 – 6 years) in a block puzzle task (N = 126 parent-child dyads), and identified patterns in parents’ gesture use indicating different gestural strategies. Further, we examined the...
15. The ATOMFT integrator - Using Taylor series to solve ordinary differential equations
Science.gov (United States)
Berryman, Kenneth W.; Stanford, Richard H.; Breckheimer, Peter J.
1988-01-01
This paper discusses the application of ATOMFT, an integration package based on Taylor series solution with a sophisticated user interface. ATOMFT has the capabilities to allow the implementation of user defined functions and the solution of stiff and algebraic equations. Detailed examples, including the solutions to several astrodynamics problems, are presented. Comparisons with its predecessor ATOMCC and other modern integrators indicate that ATOMFT is a fast, accurate, and easy method to use to solve many differential equation problems.
16. A Regularized Approach for Solving Magnetic Differential Equations and a Revised Iterative Equilibrium Algorithm
International Nuclear Information System (INIS)
Hudson, S.R.
2010-01-01
A method for approximately solving magnetic differential equations is described. The approach is to include a small diffusion term to the equation, which regularizes the linear operator to be inverted. The extra term allows a 'source-correction' term to be defined, which is generally required in order to satisfy the solvability conditions. The approach is described in the context of computing the pressure and parallel currents in the iterative approach for computing magnetohydrodynamic equilibria.
17. T-Stability of the Heun Method and Balanced Method for Solving Stochastic Differential Delay Equations
Directory of Open Access Journals (Sweden)
Xiaolin Zhu
2014-01-01
Full Text Available This paper studies the T-stability of the Heun method and balanced method for solving stochastic differential delay equations (SDDEs. Two T-stable conditions of the Heun method are obtained for two kinds of linear SDDEs. Moreover, two conditions under which the balanced method is T-stable are obtained for two kinds of linear SDDEs. Some numerical examples verify the theoretical results proposed.
18. Fibonacci collocation method with a residual error Function to solve linear Volterra integro differential equations
Directory of Open Access Journals (Sweden)
Salih Yalcinbas
2016-01-01
Full Text Available In this paper, a new collocation method based on the Fibonacci polynomials is introduced to solve the high-order linear Volterra integro-differential equations under the conditions. Numerical examples are included to demonstrate the applicability and validity of the proposed method and comparisons are made with the existing results. In addition, an error estimation based on the residual functions is presented for this method. The approximate solutions are improved by using this error estimation.
19. A Sequential, Implicit, Wavelet-Based Solver for Multi-Scale Time-Dependent Partial Differential Equations
Directory of Open Access Journals (Sweden)
Donald A. McLaren
2013-04-01
Full Text Available This paper describes and tests a wavelet-based implicit numerical method for solving partial differential equations. Intended for problems with localized small-scale interactions, the method exploits the form of the wavelet decomposition to divide the implicit system created by the time-discretization into multiple smaller systems that can be solved sequentially. Included is a test on a basic non-linear problem, with both the results of the test, and the time required to calculate them, compared with control results based on a single system with fine resolution. The method is then tested on a non-trivial problem, its computational time and accuracy checked against control results. In both tests, it was found that the method requires less computational expense than the control. Furthermore, the method showed convergence towards the fine resolution control results.
20. Stepwise Analysis of Differential Item Functioning Based on Multiple-Group Partial Credit Model.
Science.gov (United States)
Muraki, Eiji
1999-01-01
Extended an Item Response Theory (IRT) method for detection of differential item functioning to the partial credit model and applied the method to simulated data using a stepwise procedure. Then applied the stepwise DIF analysis based on the multiple-group partial credit model to writing trend data from the National Assessment of Educational…
1. Highly Scalable Asynchronous Computing Method for Partial Differential Equations: A Path Towards Exascale
Science.gov (United States)
Many natural and engineering systems are governed by nonlinear partial differential equations (PDEs) which result in a multiscale phenomena, e.g. turbulent flows. Numerical simulations of these problems are computationally very expensive and demand for extreme levels of parallelism. At realistic conditions, simulations are being carried out on massively parallel computers with hundreds of thousands of processing elements (PEs). It has been observed that communication between PEs as well as their synchronization at these extreme scales take up a significant portion of the total simulation time and result in poor scalability of codes. This issue is likely to pose a bottleneck in scalability of codes on future Exascale systems. In this work, we propose an asynchronous computing algorithm based on widely used finite difference methods to solve PDEs in which synchronization between PEs due to communication is relaxed at a mathematical level. We show that while stability is conserved when schemes are used asynchronously, accuracy is greatly degraded. Since message arrivals at PEs are random processes, so is the behavior of the error. We propose a new statistical framework in which we show that average errors drop always to first-order regardless of the original scheme. We propose new asynchrony-tolerant schemes that maintain accuracy when synchronization is relaxed. The quality of the solution is shown to depend, not only on the physical phenomena and numerical schemes, but also on the characteristics of the computing machine. A novel algorithm using remote memory access communications has been developed to demonstrate excellent scalability of the method for large-scale computing. Finally, we present a path to extend this method in solving complex multi-scale problems on Exascale machines.
2. Approximate Solutions of Nonlinear Partial Differential Equations by Modified q-Homotopy Analysis Method
Directory of Open Access Journals (Sweden)
Shaheed N. Huseen
2013-01-01
Full Text Available A modified q-homotopy analysis method (mq-HAM was proposed for solving nth-order nonlinear differential equations. This method improves the convergence of the series solution in the nHAM which was proposed in (see Hassan and El-Tawil 2011, 2012. The proposed method provides an approximate solution by rewriting the nth-order nonlinear differential equation in the form of n first-order differential equations. The solution of these n differential equations is obtained as a power series solution. This scheme is tested on two nonlinear exactly solvable differential equations. The results demonstrate the reliability and efficiency of the algorithm developed.
3. Memory functioning and negative symptoms as differential predictors of social problem solving skills in schizophrenia.
Science.gov (United States)
Ventura, Joseph; Tom, Shelley R; Jetton, Chris; Kern, Robert S
2013-02-01
Neurocognition in general, and memory functioning in particular, as well as symptoms have all been shown to be related to social problem solving (SPS) in schizophrenia. However, few studies have directly compared the relative contribution of neurocognition vs. psychiatric symptoms to the components of SPS. Sixty outpatients (aged 21-65) who met DSM-IV criteria for schizophrenia or schizoaffective disorder were administered a broad battery of memory tests and assessed for severity of positive and negative symptoms as part of a baseline assessment of a study of psychiatric rehabilitation. Multiple regression analyses were used to examine the contribution of memory functioning vs. symptoms on receiving, processing, and sending skill areas of social problem solving ability. An index of verbal learning was the strongest predictor of processing skills whereas negative symptoms were the strongest predictor of sending skills. Positive symptoms were not related to any of the three skill areas of social problem solving. Memory functioning and psychiatric symptoms differentially predict selected areas of social problem solving ability in persons with schizophrenia. Consistent with other reports, positive symptoms were not related to social problem solving. Consideration of both neurocognition and negative symptoms may be important to the development of rehabilitation interventions in this area of functioning. Copyright © 2012 Elsevier B.V. All rights reserved.
4. High-order asynchrony-tolerant finite difference schemes for partial differential equations
Science.gov (United States)
2017-12-01
Synchronizations of processing elements (PEs) in massively parallel simulations, which arise due to communication or load imbalances between PEs, significantly affect the scalability of scientific applications. We have recently proposed a method based on finite-difference schemes to solve partial differential equations in an asynchronous fashion - synchronization between PEs is relaxed at a mathematical level. While standard schemes can maintain their stability in the presence of asynchrony, their accuracy is drastically affected. In this work, we present a general methodology to derive asynchrony-tolerant (AT) finite difference schemes of arbitrary order of accuracy, which can maintain their accuracy when synchronizations are relaxed. We show that there are several choices available in selecting a stencil to derive these schemes and discuss their effect on numerical and computational performance. We provide a simple classification of schemes based on the stencil and derive schemes that are representative of different classes. Their numerical error is rigorously analyzed within a statistical framework to obtain the overall accuracy of the solution. Results from numerical experiments are used to validate the performance of the schemes.
5. A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
KAUST Repository
Babuška, Ivo; Nobile, Fabio; Tempone, Raul
2010-01-01
This work proposes and analyzes a stochastic collocation method for solving elliptic partial differential equations with random coefficients and forcing terms. These input data are assumed to depend on a finite number of random variables. The method consists of a Galerkin approximation in space and a collocation in the zeros of suitable tensor product orthogonal polynomials (Gauss points) in the probability space, and naturally leads to the solution of uncoupled deterministic problems as in the Monte Carlo approach. It treats easily a wide range of situations, such as input data that depend nonlinearly on the random variables, diffusivity coefficients with unbounded second moments, and random variables that are correlated or even unbounded. We provide a rigorous convergence analysis and demonstrate exponential convergence of the “probability error” with respect to the number of Gauss points in each direction of the probability space, under some regularity assumptions on the random input data. Numerical examples show the effectiveness of the method. Finally, we include a section with developments posterior to the original publication of this work. There we review sparse grid stochastic collocation methods, which are effective collocation strategies for problems that depend on a moderately large number of random variables.
6. Partial differential equation-based approach for empirical mode decomposition: application on image analysis.
Science.gov (United States)
Niang, Oumar; Thioune, Abdoulaye; El Gueirea, Mouhamed Cheikh; Deléchelle, Eric; Lemoine, Jacques
2012-09-01
The major problem with the empirical mode decomposition (EMD) algorithm is its lack of a theoretical framework. So, it is difficult to characterize and evaluate this approach. In this paper, we propose, in the 2-D case, the use of an alternative implementation to the algorithmic definition of the so-called "sifting process" used in the original Huang's EMD method. This approach, especially based on partial differential equations (PDEs), was presented by Niang in previous works, in 2005 and 2007, and relies on a nonlinear diffusion-based filtering process to solve the mean envelope estimation problem. In the 1-D case, the efficiency of the PDE-based method, compared to the original EMD algorithmic version, was also illustrated in a recent paper. Recently, several 2-D extensions of the EMD method have been proposed. Despite some effort, 2-D versions for EMD appear poorly performing and are very time consuming. So in this paper, an extension to the 2-D space of the PDE-based approach is extensively described. This approach has been applied in cases of both signal and image decomposition. The obtained results confirm the usefulness of the new PDE-based sifting process for the decomposition of various kinds of data. Some results have been provided in the case of image decomposition. The effectiveness of the approach encourages its use in a number of signal and image applications such as denoising, detrending, or texture analysis.
7. RBSDE's with jumps and the related obstacle problems for integral-partial differential equations
Institute of Scientific and Technical Information of China (English)
FAN; Yulian
2006-01-01
The author proves, when the noise is driven by a Brownian motion and an independent Poisson random measure, the one-dimensional reflected backward stochastic differential equation with a stopping time terminal has a unique solution. And in a Markovian framework, the solution can provide a probabilistic interpretation for the obstacle problem for the integral-partial differential equation.
8. A direct algebraic method applied to obtain complex solutions of some nonlinear partial differential equations
International Nuclear Information System (INIS)
Zhang Huiqun
2009-01-01
By using some exact solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct the exact complex solutions for nonlinear partial differential equations. The method is implemented for the NLS equation, a new Hamiltonian amplitude equation, the coupled Schrodinger-KdV equations and the Hirota-Maccari equations. New exact complex solutions are obtained.
9. In silico ordinary differential equation/partial differential equation hemodialysis model estimates methadone removal during dialysis
Science.gov (United States)
Linares, Oscar A; Schiesser, William E; Fudin, Jeffrey; Pham, Thien C; Bettinger, Jeffrey J; Mathew, Roy O; Daly, Annemarie L
2015-01-01
10. In silico ordinary differential equation/partial differential equation hemodialysis model estimates methadone removal during dialysis.
Science.gov (United States)
Linares, Oscar A; Schiesser, William E; Fudin, Jeffrey; Pham, Thien C; Bettinger, Jeffrey J; Mathew, Roy O; Daly, Annemarie L
2015-01-01
11. When problem size matters: differential effects of brain stimulation on arithmetic problem solving and neural oscillations.
Directory of Open Access Journals (Sweden)
Bruno Rütsche
Full Text Available The problem size effect is a well-established finding in arithmetic problem solving and is characterized by worse performance in problems with larger compared to smaller operand size. Solving small and large arithmetic problems has also been shown to involve different cognitive processes and distinct electroencephalography (EEG oscillations over the left posterior parietal cortex (LPPC. In this study, we aimed to provide further evidence for these dissociations by using transcranial direct current stimulation (tDCS. Participants underwent anodal (30min, 1.5 mA, LPPC and sham tDCS. After the stimulation, we recorded their neural activity using EEG while the participants solved small and large arithmetic problems. We found that the tDCS effects on performance and oscillatory activity critically depended on the problem size. While anodal tDCS improved response latencies in large arithmetic problems, it decreased solution rates in small arithmetic problems. Likewise, the lower-alpha desynchronization in large problems increased, whereas the theta synchronization in small problems decreased. These findings reveal that the LPPC is differentially involved in solving small and large arithmetic problems and demonstrate that the effects of brain stimulation strikingly differ depending on the involved neuro-cognitive processes.
12. A universal concept based on cellular neural networks for ultrafast and flexible solving of differential equations.
Science.gov (United States)
Chedjou, Jean Chamberlain; Kyamakya, Kyandoghere
2015-04-01
This paper develops and validates a comprehensive and universally applicable computational concept for solving nonlinear differential equations (NDEs) through a neurocomputing concept based on cellular neural networks (CNNs). High-precision, stability, convergence, and lowest-possible memory requirements are ensured by the CNN processor architecture. A significant challenge solved in this paper is that all these cited computing features are ensured in all system-states (regular or chaotic ones) and in all bifurcation conditions that may be experienced by NDEs.One particular quintessence of this paper is to develop and demonstrate a solver concept that shows and ensures that CNN processors (realized either in hardware or in software) are universal solvers of NDE models. The solving logic or algorithm of given NDEs (possible examples are: Duffing, Mathieu, Van der Pol, Jerk, Chua, Rössler, Lorenz, Burgers, and the transport equations) through a CNN processor system is provided by a set of templates that are computed by our comprehensive templates calculation technique that we call nonlinear adaptive optimization. This paper is therefore a significant contribution and represents a cutting-edge real-time computational engineering approach, especially while considering the various scientific and engineering applications of this ultrafast, energy-and-memory-efficient, and high-precise NDE solver concept. For illustration purposes, three NDE models are demonstratively solved, and related CNN templates are derived and used: the periodically excited Duffing equation, the Mathieu equation, and the transport equation.
13. Multiscale functions, scale dynamics, and applications to partial differential equations
Science.gov (United States)
Cresson, Jacky; Pierret, Frédéric
2016-05-01
Modeling phenomena from experimental data always begins with a choice of hypothesis on the observed dynamics such as determinism, randomness, and differentiability. Depending on these choices, different behaviors can be observed. The natural question associated to the modeling problem is the following: "With a finite set of data concerning a phenomenon, can we recover its underlying nature? From this problem, we introduce in this paper the definition of multi-scale functions, scale calculus, and scale dynamics based on the time scale calculus [see Bohner, M. and Peterson, A., Dynamic Equations on Time Scales: An Introduction with Applications (Springer Science & Business Media, 2001)] which is used to introduce the notion of scale equations. These definitions will be illustrated on the multi-scale Okamoto's functions. Scale equations are analysed using scale regimes and the notion of asymptotic model for a scale equation under a particular scale regime. The introduced formalism explains why a single scale equation can produce distinct continuous models even if the equation is scale invariant. Typical examples of such equations are given by the scale Euler-Lagrange equation. We illustrate our results using the scale Newton's equation which gives rise to a non-linear diffusion equation or a non-linear Schrödinger equation as asymptotic continuous models depending on the particular fractional scale regime which is considered.
14. The Use of Generalized Laguerre Polynomials in Spectral Methods for Solving Fractional Delay Differential Equations.
Science.gov (United States)
2013-10-01
In this paper, an efficient numerical method for solving the fractional delay differential equations (FDDEs) is considered. The fractional derivative is described in the Caputo sense. The proposed method is based on the derived approximate formula of the Laguerre polynomials. The properties of Laguerre polynomials are utilized to reduce FDDEs to a linear or nonlinear system of algebraic equations. Special attention is given to study the error and the convergence analysis of the proposed method. Several numerical examples are provided to confirm that the proposed method is in excellent agreement with the exact solution.
15. A numerical technique for solving fractional optimal control problems and fractional Riccati differential equations
Directory of Open Access Journals (Sweden)
F. Ghomanjani
2016-10-01
Full Text Available In the present paper, we apply the Bezier curves method for solving fractional optimal control problems (OCPs and fractional Riccati differential equations. The main advantage of this method is that it can reduce the error of the approximate solutions. Hence, the solutions obtained using the Bezier curve method give good approximations. Some numerical examples are provided to confirm the accuracy of the proposed method. All of the numerical computations have been performed on a PC using several programs written in MAPLE 13.
16. A toolbox to solve coupled systems of differential and difference equations
International Nuclear Information System (INIS)
Ablinger, Jakob; Schneider, Carsten; Bluemlein, Johannes; Freitas, Abilio de
2016-01-01
We present algorithms to solve coupled systems of linear differential equations, arising in the calculation of massive Feynman diagrams with local operator insertions at 3-loop order, which do not request special choices of bases. Here we assume that the desired solution has a power series representation and we seek for the coefficients in closed form. In particular, if the coefficients depend on a small parameter ε (the dimensional parameter), we assume that the coefficients themselves can be expanded in formal Laurent series w.r.t. ε and we try to compute the first terms in closed form. More precisely, we have a decision algorithm which solves the following problem: if the terms can be represented by an indefinite nested hypergeometric sum expression (covering as special cases the harmonic sums, cyclotomic sums, generalized harmonic sums or nested binomial sums), then we can calculate them. If the algorithm fails, we obtain a proof that the terms cannot be represented by the class of indefinite nested hypergeometric sum expressions. Internally, this problem is reduced by holonomic closure properties to solving a coupled system of linear difference equations. The underlying method in this setting relies on decoupling algorithms, difference ring algorithms and recurrence solving. We demonstrate by a concrete example how this algorithm can be applied with the new Mathematica package SolveCoupledSystem which is based on the packages Sigma, HarmonicSums and OreSys. In all applications the representation in x-space is obtained as an iterated integral representation over general alphabets, generalizing Poincare iterated integrals.
17. A toolbox to solve coupled systems of differential and difference equations
Energy Technology Data Exchange (ETDEWEB)
Ablinger, Jakob; Schneider, Carsten [Linz Univ. (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, Johannes; Freitas, Abilio de [DESY Zeuthen (Germany)
2016-01-15
We present algorithms to solve coupled systems of linear differential equations, arising in the calculation of massive Feynman diagrams with local operator insertions at 3-loop order, which do not request special choices of bases. Here we assume that the desired solution has a power series representation and we seek for the coefficients in closed form. In particular, if the coefficients depend on a small parameter ε (the dimensional parameter), we assume that the coefficients themselves can be expanded in formal Laurent series w.r.t. ε and we try to compute the first terms in closed form. More precisely, we have a decision algorithm which solves the following problem: if the terms can be represented by an indefinite nested hypergeometric sum expression (covering as special cases the harmonic sums, cyclotomic sums, generalized harmonic sums or nested binomial sums), then we can calculate them. If the algorithm fails, we obtain a proof that the terms cannot be represented by the class of indefinite nested hypergeometric sum expressions. Internally, this problem is reduced by holonomic closure properties to solving a coupled system of linear difference equations. The underlying method in this setting relies on decoupling algorithms, difference ring algorithms and recurrence solving. We demonstrate by a concrete example how this algorithm can be applied with the new Mathematica package SolveCoupledSystem which is based on the packages Sigma, HarmonicSums and OreSys. In all applications the representation in x-space is obtained as an iterated integral representation over general alphabets, generalizing Poincare iterated integrals.
18. In silico ordinary differential equation/partial differential equation hemodialysis model estimates methadone removal during dialysis
Directory of Open Access Journals (Sweden)
Linares OA
2015-07-01
19. Solving differential equations for Feynman integrals by expansions near singular points
Science.gov (United States)
Lee, Roman N.; Smirnov, Alexander V.; Smirnov, Vladimir A.
2018-03-01
We describe a strategy to solve differential equations for Feynman integrals by powers series expansions near singular points and to obtain high precision results for the corresponding master integrals. We consider Feynman integrals with two scales, i.e. non-trivially depending on one variable. The corresponding algorithm is oriented at situations where canonical form of the differential equations is impossible. We provide a computer code constructed with the help of our algorithm for a simple example of four-loop generalized sunset integrals with three equal non-zero masses and two zero masses. Our code gives values of the master integrals at any given point on the real axis with a required accuracy and a given order of expansion in the regularization parameter ɛ.
20. Mobile point sensors and actuators in the controllability theory of partial differential equations
CERN Document Server
Khapalov, Alexander Y
2017-01-01
This book presents a concise study of controllability theory of partial differential equations when they are equipped with actuators and/or sensors that are finite dimensional at every moment of time. Based on the author’s extensive research in the area of controllability theory, this monograph specifically focuses on the issues of controllability, observability, and stabilizability for parabolic and hyperbolic partial differential equations. The topics in this book also cover related applied questions such as the problem of localization of unknown pollution sources based on information obtained from point sensors that arise in environmental monitoring. Researchers and graduate students interested in controllability theory of partial differential equations and its applications will find this book to be an invaluable resource to their studies.
1. Methods for partial differential equations qualitative properties of solutions, phase space analysis, semilinear models
CERN Document Server
Ebert, Marcelo R
2018-01-01
This book provides an overview of different topics related to the theory of partial differential equations. Selected exercises are included at the end of each chapter to prepare readers for the “research project for beginners” proposed at the end of the book. It is a valuable resource for advanced graduates and undergraduate students who are interested in specializing in this area. The book is organized in five parts: In Part 1 the authors review the basics and the mathematical prerequisites, presenting two of the most fundamental results in the theory of partial differential equations: the Cauchy-Kovalevskaja theorem and Holmgren's uniqueness theorem in its classical and abstract form. It also introduces the method of characteristics in detail and applies this method to the study of Burger's equation. Part 2 focuses on qualitative properties of solutions to basic partial differential equations, explaining the usual properties of solutions to elliptic, parabolic and hyperbolic equations for the archetypes...
2. ON PARTIAL DIFFERENTIAL AND DIFFERENCE EQUATIONS WITH SYMMETRIES DEPENDING ON ARBITRARY FUNCTIONS
Directory of Open Access Journals (Sweden)
Giorgio Gubbiotti
2016-06-01
Full Text Available In this note we present some ideas on when Lie symmetries, both point and generalized, can depend on arbitrary functions. We show a few examples, both in partial differential and partial difference equations where this happens. Moreover we show that the infinitesimal generators of generalized symmetries depending on arbitrary functions, both for continuous and discrete equations, effectively play the role of master symmetries.
3. Implementation of geomechanical models for engineered clay barriers in multi-physic partial differential equation solvers
International Nuclear Information System (INIS)
Navarro, V.; Alonso, J.; Asensio, L.; Yustres, A.; Pintado, X.
2012-01-01
Document available in extended abstract form only. The use of numerical methods, especially the Finite Element Method (FEM), for solving boundary problems in Unsaturated Soil Mechanics has experienced significant progress. Several codes, both built mainly for research purposes and commercial software, are now available. In the last years, Multi-physic Partial Differentiation Equation Solvers (MPDES) have turned out to be an interesting proposal. In this family of solvers, the user defines the governing equations and the behaviour models, generally using a computer algebra environment. The code automatically assembles and solves the equation systems, saving the user having to redefine the structures of memory storage or to implement solver algorithms. The user can focus on the definition of the physics of the problem, while it is possible to couple virtually any physical or chemical process that can be described by a PDE. This can be done, for instance, in COMSOL Multiphysics (CM). Nonetheless, the versatility of CM is compromised by the impossibility to implement models with variables defined by implicit functions. Elasto-plastic models involve an implicit coupling among stress increments, plastic strains and plastic variables increments. For this reason, they cannot be implemented in CM in a straightforward way. This means a very relevant limitation for the use of this tool in the analysis of geomechanical boundary value problems. In this work, a strategy to overcome this problem using the multi-physics concept is presented. A mixed method is proposed, considering the constitutive stresses, the pre-consolidation pressure and the plastic variables as main unknowns of the model. Mixed methods usually present stability problems. However, the algorithmics present in CM include several numerical strategies to minimise this kind of problems. Besides, CM is based on the application of the FEM with Lagrange multipliers, an approach that significantly contributes stability
4. Soliton solution for nonlinear partial differential equations by cosine-function method
International Nuclear Information System (INIS)
Ali, A.H.A.; Soliman, A.A.; Raslan, K.R.
2007-01-01
In this Letter, we established a traveling wave solution by using Cosine-function algorithm for nonlinear partial differential equations. The method is used to obtain the exact solutions for five different types of nonlinear partial differential equations such as, general equal width wave equation (GEWE), general regularized long wave equation (GRLW), general Korteweg-de Vries equation (GKdV), general improved Korteweg-de Vries equation (GIKdV), and Coupled equal width wave equations (CEWE), which are the important soliton equations
5. Formulae and Bounds connected to Optimal Design and Homogenization of Partial Differential Operators and Integral Functionals
Energy Technology Data Exchange (ETDEWEB)
Lukkassen, D.
1996-12-31
When partial differential equations are set up to model physical processes in strongly heterogeneous materials, effective parameters for heat transfer, electric conductivity etc. are usually required. Averaging methods often lead to convergence problems and in homogenization theory one is therefore led to study how certain integral functionals behave asymptotically. This mathematical doctoral thesis discusses (1) means and bounds connected to homogenization of integral functionals, (2) reiterated homogenization of integral functionals, (3) bounds and homogenization of some particular partial differential operators, (4) applications and further results. 154 refs., 11 figs., 8 tabs.
6. Introductory Applications of Partial Differential Equations With Emphasis on Wave Propagation and Diffusion
CERN Document Server
Lamb, George L
1995-01-01
INTRODUCTORY APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS. With Emphasis on Wave Propagation and Diffusion. This is the ideal text for students and professionals who have some familiarity with partial differential equations, and who now wish to consolidate and expand their knowledge. Unlike most other texts on this topic, it interweaves prior knowledge of mathematics and physics, especially heat conduction and wave motion, into a presentation that demonstrates their interdependence. The result is a superb teaching text that reinforces the reader's understanding of both mathematics and physic
7. Algorithms to solve coupled systems of differential equations in terms of power series
International Nuclear Information System (INIS)
Ablinger, Jakob; Schneider, Carsten
2016-08-01
Using integration by parts relations, Feynman integrals can be represented in terms of coupled systems of differential equations. In the following we suppose that the unknown Feynman integrals can be given in power series representations, and that sufficiently many initial values of the integrals are given. Then there exist algorithms that decide constructively if the coefficients of their power series representations can be given within the class of nested sums over hypergeometric products. In this article we work out the calculation steps that solve this problem. First, we present a successful tactic that has been applied recently to challenging problems coming from massive 3-loop Feynman integrals. Here our main tool is to solve scalar linear recurrences within the class of nested sums over hypergeometric products. Second, we will present a new variation of this tactic which relies on more involved summation technologies but succeeds in reducing the problem to solve scalar recurrences with lower recurrence orders. The article works out the different challenges of this new tactic and demonstrates how they can be treated efficiently with our existing summation technologies.
8. Reducing the memory requirement in reverse mode automatic differentiation by solving TBR flow equations
International Nuclear Information System (INIS)
Naumann, U.
2002-01-01
The fast computation of gradients in reverse mode Automatic Differentiation (AD) requires the generation of adjoint versions of every statement in the original code. Due to the resulting reversal of the control flow certain intermediate values have to be made available in reverse order to compute the local partial derivatives. This can be achieved by storing these values or by recomputing them when they become required. In any case one is interested in minimizing the size of this set. Following an extensive introduction of the ''To-Be-Recorded'' (TBR) problem the authors present flow equations for propagating the TBR status of variables in the context of reverse mode AD of structured programs
9. A pertinent approach to solve nonlinear fuzzy integro-differential equations.
Science.gov (United States)
Narayanamoorthy, S; Sathiyapriya, S P
2016-01-01
Fuzzy integro-differential equations is one of the important parts of fuzzy analysis theory that holds theoretical as well as applicable values in analytical dynamics and so an appropriate computational algorithm to solve them is in essence. In this article, we use parametric forms of fuzzy numbers and suggest an applicable approach for solving nonlinear fuzzy integro-differential equations using homotopy perturbation method. A clear and detailed description of the proposed method is provided. Our main objective is to illustrate that the construction of appropriate convex homotopy in a proper way leads to highly accurate solutions with less computational work. The efficiency of the approximation technique is expressed via stability and convergence analysis so as to guarantee the efficiency and performance of the methodology. Numerical examples are demonstrated to verify the convergence and it reveals the validity of the presented numerical technique. Numerical results are tabulated and examined by comparing the obtained approximate solutions with the known exact solutions. Graphical representations of the exact and acquired approximate fuzzy solutions clarify the accuracy of the approach.
10. Solving delay differential equations in S-ADAPT by method of steps.
Science.gov (United States)
Bauer, Robert J; Mo, Gary; Krzyzanski, Wojciech
2013-09-01
11. Solving ordinary differential equations by electrical analogy: a multidisciplinary teaching tool
Science.gov (United States)
Sanchez Perez, J. F.; Conesa, M.; Alhama, I.
2016-11-01
Ordinary differential equations are the mathematical formulation for a great variety of problems in science and engineering, and frequently, two different problems are equivalent from a mathematical point of view when they are formulated by the same equations. Students acquire the knowledge of how to solve these equations (at least some types of them) using protocols and strict algorithms of mathematical calculation without thinking about the meaning of the equation. The aim of this work is that students learn to design network models or circuits in this way; with simple knowledge of them, students can establish the association of electric circuits and differential equations and their equivalences, from a formal point of view, that allows them to associate knowledge of two disciplines and promote the use of this interdisciplinary approach to address complex problems. Therefore, they learn to use a multidisciplinary tool that allows them to solve these kinds of equations, even students of first course of engineering, whatever the order, grade or type of non-linearity. This methodology has been implemented in numerous final degree projects in engineering and science, e.g., chemical engineering, building engineering, industrial engineering, mechanical engineering, architecture, etc. Applications are presented to illustrate the subject of this manuscript.
12. Sparse grid spectral methods for the numerical solution of partial differential equations with periodic boundary conditions
International Nuclear Information System (INIS)
Kupka, F.
1997-11-01
This thesis deals with the extension of sparse grid techniques to spectral methods for the solution of partial differential equations with periodic boundary conditions. A review on boundary and initial-boundary value problems and a discussion on numerical resolution is used to motivate this research. Spectral methods are introduced by projection techniques, and by three model problems: the stationary and the transient Helmholtz equations, and the linear advection equation. The approximation theory on the hyperbolic cross is reviewed and its close relation to sparse grids is demonstrated. This approach extends to non-periodic problems. Various Sobolev spaces with dominant mixed derivative are introduced to provide error estimates for Fourier approximation and interpolation on the hyperbolic cross and on sparse grids by means of Sobolev norms. The theorems are immediately applicable to the stability and convergence analysis of sparse grid spectral methods. This is explicitly demonstrated for the three model problems. A variant of the von Neumann condition is introduced to simplify the stability analysis of the time-dependent model problems. The discrete Fourier transformation on sparse grids is discussed together with its software implementation. Results on numerical experiments are used to illustrate the performance of the new method with respect to the smoothness properties of each example. The potential of the method in mathematical modelling is estimated and generalizations to other sparse grid methods are suggested. The appendix includes a complete Fortran90 program to solve the linear advection equation by the sparse grid Fourier collocation method and a third-order Runge-Kutta routine for integration in time. (author)
13. High-order fractional partial differential equation transform for molecular surface construction.
Science.gov (United States)
Hu, Langhua; Chen, Duan; Wei, Guo-Wei
2013-01-01
Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model
14. 3D early embryogenesis image filtering by nonlinear partial differential equations.
Science.gov (United States)
Krivá, Z; Mikula, K; Peyriéras, N; Rizzi, B; Sarti, A; Stasová, O
2010-08-01
We present nonlinear diffusion equations, numerical schemes to solve them and their application for filtering 3D images obtained from laser scanning microscopy (LSM) of living zebrafish embryos, with a goal to identify the optimal filtering method and its parameters. In the large scale applications dealing with analysis of 3D+time embryogenesis images, an important objective is a correct detection of the number and position of cell nuclei yielding the spatio-temporal cell lineage tree of embryogenesis. The filtering is the first and necessary step of the image analysis chain and must lead to correct results, removing the noise, sharpening the nuclei edges and correcting the acquisition errors related to spuriously connected subregions. In this paper we study such properties for the regularized Perona-Malik model and for the generalized mean curvature flow equations in the level-set formulation. A comparison with other nonlinear diffusion filters, like tensor anisotropic diffusion and Beltrami flow, is also included. All numerical schemes are based on the same discretization principles, i.e. finite volume method in space and semi-implicit scheme in time, for solving nonlinear partial differential equations. These numerical schemes are unconditionally stable, fast and naturally parallelizable. The filtering results are evaluated and compared first using the Mean Hausdorff distance between a gold standard and different isosurfaces of original and filtered data. Then, the number of isosurface connected components in a region of interest (ROI) detected in original and after the filtering is compared with the corresponding correct number of nuclei in the gold standard. Such analysis proves the robustness and reliability of the edge preserving nonlinear diffusion filtering for this type of data and lead to finding the optimal filtering parameters for the studied models and numerical schemes. Further comparisons consist in ability of splitting the very close objects which
15. Modulating Function-Based Method for Parameter and Source Estimation of Partial Differential Equations
KAUST Repository
Asiri, Sharefa M.
2017-10-08
Partial Differential Equations (PDEs) are commonly used to model complex systems that arise for example in biology, engineering, chemistry, and elsewhere. The parameters (or coefficients) and the source of PDE models are often unknown and are estimated from available measurements. Despite its importance, solving the estimation problem is mathematically and numerically challenging and especially when the measurements are corrupted by noise, which is often the case. Various methods have been proposed to solve estimation problems in PDEs which can be classified into optimization methods and recursive methods. The optimization methods are usually heavy computationally, especially when the number of unknowns is large. In addition, they are sensitive to the initial guess and stop condition, and they suffer from the lack of robustness to noise. Recursive methods, such as observer-based approaches, are limited by their dependence on some structural properties such as observability and identifiability which might be lost when approximating the PDE numerically. Moreover, most of these methods provide asymptotic estimates which might not be useful for control applications for example. An alternative non-asymptotic approach with less computational burden has been proposed in engineering fields based on the so-called modulating functions. In this dissertation, we propose to mathematically and numerically analyze the modulating functions based approaches. We also propose to extend these approaches to different situations. The contributions of this thesis are as follows. (i) Provide a mathematical analysis of the modulating function-based method (MFBM) which includes: its well-posedness, statistical properties, and estimation errors. (ii) Provide a numerical analysis of the MFBM through some estimation problems, and study the sensitivity of the method to the modulating functions\\' parameters. (iii) Propose an effective algorithm for selecting the method\\'s design parameters
16. Numerical solutions of ordinary and partial differential equations in the frequency domain
International Nuclear Information System (INIS)
Hazi, G.; Por, G.
1997-01-01
Numerical problems during the noise simulation in a nuclear power plant are discussed. The solutions of ordinary and partial differential equations are studied in the frequency domain. Numerical methods by the transfer function method are applied. It is shown that the correctness of the numerical methods is limited for ordinary differential equations in the frequency domain. To overcome the difficulties, step-size selection is suggested. (author)
17. Modeling biological gradient formation: combining partial differential equations and Petri nets.
Science.gov (United States)
Bertens, Laura M F; Kleijn, Jetty; Hille, Sander C; Heiner, Monika; Koutny, Maciej; Verbeek, Fons J
2016-01-01
Both Petri nets and differential equations are important modeling tools for biological processes. In this paper we demonstrate how these two modeling techniques can be combined to describe biological gradient formation. Parameters derived from partial differential equation describing the process of gradient formation are incorporated in an abstract Petri net model. The quantitative aspects of the resulting model are validated through a case study of gradient formation in the fruit fly.
18. A Novel Method for Analytical Solutions of Fractional Partial Differential Equations
OpenAIRE
Mehmet Ali Akinlar; Muhammet Kurulay
2013-01-01
A new solution technique for analytical solutions of fractional partial differential equations (FPDEs) is presented. The solutions are expressed as a finite sum of a vector type functional. By employing MAPLE software, it is shown that the solutions might be extended to an arbitrary degree which makes the present method not only different from the others in the literature but also quite efficient. The method is applied to special Bagley-Torvik and Diethelm fractional differential equations as...
19. Spectral finite element methods for solving fractional differential equations with applications in anomalous transport
Energy Technology Data Exchange (ETDEWEB)
Carella, Alfredo Raul
2012-09-15
Quantifying species transport rates is a main concern in chemical and petrochemical industries. In particular, the design and operation of many large-scale industrial chemical processes is as much dependent on diffusion as it is on reaction rates. However, the existing diffusion models sometimes fail to predict experimentally observed behaviors and their accuracy is usually insufficient for process optimization purposes. Fractional diffusion models offer multiple possibilities for generalizing Flick's law in a consistent manner in order to account for history dependence and nonlocal effects. These models have not been extensively applied to the study of real systems, mainly due to their computational cost and mathematical complexity. A least squares spectral formulation was developed for solving fractional differential equations. The proposed method was proven particularly well-suited for dealing with the numerical difficulties inherent to fractional differential operators. The practical implementation was explained in detail in order to enhance reproducibility, and directions were specified for extending it to multiple dimensions and arbitrarily shaped domains. A numerical framework based on the least-squares spectral element method was developed for studying and comparing anomalous diffusion models in pellets. This simulation tool is capable of solving arbitrary integro-differential equations and can be effortlessly adapted to various problems in any number of dimensions. Simulations of the flow around a cylindrical particle were achieved by extending the functionality of the developed framework. A test case was analyzed by coupling the boundary condition yielded by the fluid model with two families of anomalous diffusion models: hyperbolic diffusion and fractional diffusion. Qualitative guidelines for determining the suitability of diffusion models can be formulated by complementing experimental data with the results obtained from this approach.(Author)
20. Solving (2 + 1)-dimensional sine-Poisson equation by a modified variable separated ordinary differential equation method
International Nuclear Information System (INIS)
Ka-Lin, Su; Yuan-Xi, Xie
2010-01-01
By introducing a more general auxiliary ordinary differential equation (ODE), a modified variable separated ordinary differential equation method is presented for solving the (2 + 1)-dimensional sine-Poisson equation. As a result, many explicit and exact solutions of the (2 + 1)-dimensional sine-Poisson equation are derived in a simple manner by this technique. (general)
1. Numerical and computational analysis of the partial differential equations in hydrocodes and wavecodes
International Nuclear Information System (INIS)
Hicks, D.L.; Walsh, R.T.
1976-06-01
Discrete methods for the solution of the partial differential equations arising in hydrocodes and wavecodes are presented in a tutorial fashion. By discrete methods is meant, for example, the methods of finite differences, finite elements, discretized characteristics, etc. The concepts of stability, consistency, convergence, order of accuracy, true accuracy, etc., and their relevance to the hydrocodes and wavecodes are discussed
2. Nonlinear perturbations of systems of partial differential equations with constant coefficients
Directory of Open Access Journals (Sweden)
Carmen J. Vanegas
2000-01-01
Full Text Available In this article, we show the existence of solutions to boundary-value problems, consisting of nonlinear systems of partial differential equations with constant coefficients. For this purpose, we use the right inverse of an associated operator and a fix point argument. As illustrations, we apply this method to Helmholtz equations and to second order systems of elliptic equations.
3. Application of partial differential equation modeling of the control/structural dynamics of flexible spacecraft
Science.gov (United States)
Taylor, Lawrence W., Jr.; Rajiyah, H.
1991-01-01
Partial differential equations for modeling the structural dynamics and control systems of flexible spacecraft are applied here in order to facilitate systems analysis and optimization of these spacecraft. Example applications are given, including the structural dynamics of SCOLE, the Solar Array Flight Experiment, the Mini-MAST truss, and the LACE satellite. The development of related software is briefly addressed.
4. Functional analytic methods in complex analysis and applications to partial differential equations
International Nuclear Information System (INIS)
Mshimba, A.S.A.; Tutschke, W.
1990-01-01
The volume contains 24 lectures given at the Workshop on Functional Analytic Methods in Complex Analysis and Applications to Partial Differential Equations held in Trieste, Italy, between 8-19 February 1988, at the ICTP. A separate abstract was prepared for each of these lectures. Refs and figs
5. Oscillation of certain higher-order neutral partial functional differential equations.
Science.gov (United States)
Li, Wei Nian; Sheng, Weihong
2016-01-01
In this paper, we study the oscillation of certain higher-order neutral partial functional differential equations with the Robin boundary conditions. Some oscillation criteria are established. Two examples are given to illustrate the main results in the end of this paper.
6. Parent Ratings of ADHD Symptoms: Generalized Partial Credit Model Analysis of Differential Item Functioning across Gender
Science.gov (United States)
Gomez, Rapson
2012-01-01
Objective: Generalized partial credit model, which is based on item response theory (IRT), was used to test differential item functioning (DIF) for the "Diagnostic and Statistical Manual of Mental Disorders" (4th ed.), inattention (IA), and hyperactivity/impulsivity (HI) symptoms across boys and girls. Method: To accomplish this, parents completed…
7. On k-summability of formal solutions for certain partial differential operators with polynomial coefficients
Directory of Open Access Journals (Sweden)
Kunio Ichinobe
2015-01-01
Full Text Available We study the \\(k\\-summability of divergent formal solutions for the Cauchy problem of certain linear partial differential operators with coefficients which are polynomial in \\(t\\. We employ the method of successive approximation in order to construct the formal solutions and to obtain the properties of analytic continuation of the solutions of convolution equations and their exponential growth estimates.
8. Multigrid for high dimensional elliptic partial differential equations on non-equidistant grids
NARCIS (Netherlands)
bin Zubair, H.; Oosterlee, C.E.; Wienands, R.
2006-01-01
This work presents techniques, theory and numbers for multigrid in a general d-dimensional setting. The main focus is the multigrid convergence for high-dimensional partial differential equations (PDEs). As a model problem we have chosen the anisotropic diffusion equation, on a unit hypercube. We
9. Lp Theory for Super-Parabolic Backward Stochastic Partial Differential Equations in the Whole Space
International Nuclear Information System (INIS)
Du Kai; Qiu, Jinniao; Tang Shanjian
2012-01-01
This paper is concerned with semi-linear backward stochastic partial differential equations (BSPDEs for short) of super-parabolic type. An L p -theory is given for the Cauchy problem of BSPDEs, separately for the case of p∈(1,2] and for the case of p∈(2,∞). A comparison theorem is also addressed.
10. The modified simplest equation method to look for exact solutions of nonlinear partial differential equations
OpenAIRE
Efimova, Olga Yu.
2010-01-01
The modification of simplest equation method to look for exact solutions of nonlinear partial differential equations is presented. Using this method we obtain exact solutions of generalized Korteweg-de Vries equation with cubic source and exact solutions of third-order Kudryashov-Sinelshchikov equation describing nonlinear waves in liquids with gas bubbles.
11. Image denoising using new pixon representation based on fuzzy filtering and partial differential equations
DEFF Research Database (Denmark)
2012-01-01
In this paper, we have proposed two extensions to pixon-based image modeling. The first one is using bicubic interpolation instead of bilinear interpolation and the second one is using fuzzy filtering method, aiming to improve the quality of the pixonal image. Finally, partial differential...
12. Mixed problem with integral boundary condition for a high order mixed type partial differential equation
OpenAIRE
M. Denche; A. L. Marhoune
2003-01-01
In this paper, we study a mixed problem with integral boundary conditions for a high order partial differential equation of mixed type. We prove the existence and uniqueness of the solution. The proof is based on energy inequality, and on the density of the range of the operator generated by the considered problem.
13. An approximation theory for nonlinear partial differential equations with applications to identification and control
Science.gov (United States)
Banks, H. T.; Kunisch, K.
1982-01-01
Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.
14. New model reduction technique for a class of parabolic partial differential equations
NARCIS (Netherlands)
Vajta, Miklos
1991-01-01
A model reduction (or lumping) technique for a class of parabolic-type partial differential equations is given, and its application is discussed. The frequency response of the temperature distribution in any multilayer solid is developed and given by a matrix expression. The distributed transfer
15. Introduction to partial differential equations from Fourier series to boundary-value problems
CERN Document Server
Broman, Arne
2010-01-01
This well-written, advanced-level text introduces students to Fourier analysis and some of its applications. The self-contained treatment covers Fourier series, orthogonal systems, Fourier and Laplace transforms, Bessel functions, and partial differential equations of the first and second orders. Over 260 exercises with solutions reinforce students' grasp of the material. 1970 edition.
16. Rail-to-rail low-power fully differential OTA utilizing adaptive biasing and partial feedback
DEFF Research Database (Denmark)
Tuan Vu, Cao; Wisland, Dag T.; Lande, Tor Sverre
consumption. The DC-gain of the proposed OTA is improved by adding a partial feedback loop. A Common-Mode Feedback (CMFB) circuit is required for fully differential rail-to-rail operation. Simulations show that the OTA topology has a low stand-by power consumption of 96μW and a high FoM of 3.84 [(V...
17. A Novel Method for Analytical Solutions of Fractional Partial Differential Equations
Directory of Open Access Journals (Sweden)
Mehmet Ali Akinlar
2013-01-01
Full Text Available A new solution technique for analytical solutions of fractional partial differential equations (FPDEs is presented. The solutions are expressed as a finite sum of a vector type functional. By employing MAPLE software, it is shown that the solutions might be extended to an arbitrary degree which makes the present method not only different from the others in the literature but also quite efficient. The method is applied to special Bagley-Torvik and Diethelm fractional differential equations as well as a more general fractional differential equation.
18. Rail-to-rail low-power fully differential OTA utilizing adaptive biasing and partial feedback
DEFF Research Database (Denmark)
Tuan Vu, Cao; Wisland, Dag T.; Lande, Tor Sverre
A fully differential rail-to-rail Operational Transconductance Amplifier (OTA) with improved DC-gain and reduced power consumption is proposed in this paper. By using the adaptive biasing circuit and two differential inputs, a low stand-by current can be obtained together with reduced power...... consumption. The DC-gain of the proposed OTA is improved by adding a partial feedback loop. A Common-Mode Feedback (CMFB) circuit is required for fully differential rail-to-rail operation. Simulations show that the OTA topology has a low stand-by power consumption of 96μW and a high FoM of 3.84 [(V...
19. An Equation-Type Approach for the Numerical Solution of the Partial Differential Equations Governing Transport Phenomena in Porous Media
KAUST Repository
Sun, Shuyu; Salama, Amgad; El-Amin, Mohamed
2012-01-01
A new technique for the numerical solution of the partial differential equations governing transport phenomena in porous media is introduced. In this technique, the governing equations as depicted from the physics of the problem are used without extra manipulations. In other words, there is no need to reduce the number of governing equations by some sort of mathematical manipulations. This technique enables the separation of the physics part of the problem and the solver part, which makes coding more robust and could be used in several other applications with little or no modifications (e.g., multi-phase flow in porous media). In this method, one abandons the need to construct the coefficient matrix for the pressure equation. Alternatively, the coefficients are automatically generated within the solver routine. We show examples of using this technique to solving several flow problems in porous media.
20. An Equation-Type Approach for the Numerical Solution of the Partial Differential Equations Governing Transport Phenomena in Porous Media
KAUST Repository
Sun, Shuyu
2012-06-02
A new technique for the numerical solution of the partial differential equations governing transport phenomena in porous media is introduced. In this technique, the governing equations as depicted from the physics of the problem are used without extra manipulations. In other words, there is no need to reduce the number of governing equations by some sort of mathematical manipulations. This technique enables the separation of the physics part of the problem and the solver part, which makes coding more robust and could be used in several other applications with little or no modifications (e.g., multi-phase flow in porous media). In this method, one abandons the need to construct the coefficient matrix for the pressure equation. Alternatively, the coefficients are automatically generated within the solver routine. We show examples of using this technique to solving several flow problems in porous media.
1. On several aspects and applications of the multigrid method for solving partial differential equations
Science.gov (United States)
Dinar, N.
1978-01-01
Several aspects of multigrid methods are briefly described. The main subjects include the development of very efficient multigrid algorithms for systems of elliptic equations (Cauchy-Riemann, Stokes, Navier-Stokes), as well as the development of control and prediction tools (based on local mode Fourier analysis), used to analyze, check and improve these algorithms. Preliminary research on multigrid algorithms for time dependent parabolic equations is also described. Improvements in existing multigrid processes and algorithms for elliptic equations were studied.
2. Effective quadrature formula in solving linear integro-differential equations of order two
Science.gov (United States)
Eshkuvatov, Z. K.; Kammuji, M.; Long, N. M. A. Nik; Yunus, Arif A. M.
2017-08-01
In this note, we solve general form of Fredholm-Volterra integro-differential equations (IDEs) of order 2 with boundary condition approximately and show that proposed method is effective and reliable. Initially, IDEs is reduced into integral equation of the third kind by using standard integration techniques and identity between multiple and single integrals then truncated Legendre series are used to estimate the unknown function. For the kernel integrals, we have applied Gauss-Legendre quadrature formula and collocation points are chosen as the roots of the Legendre polynomials. Finally, reduce the integral equations of the third kind into the system of algebraic equations and Gaussian elimination method is applied to get approximate solutions. Numerical examples and comparisons with other methods reveal that the proposed method is very effective and dominated others in many cases. General theory of existence of the solution is also discussed.
3. Recent symbolic summation methods to solve coupled systems of differential and difference equations
International Nuclear Information System (INIS)
Schneider, Carsten; Bluemlein, Johannes; Freitas, Abilio de
2014-07-01
We outline a new algorithm to solve coupled systems of differential equations in one continuous variable x (resp. coupled difference equations in one discrete variable N) depending on a small parameter ε: given such a system and given sufficiently many initial values, we can determine the first coefficients of the Laurent-series solutions in ε if they are expressible in terms of indefinite nested sums and products. This systematic approach is based on symbolic summation algorithms in the context of difference rings/fields and uncoupling algorithms. The proposed method gives rise to new interesting applications in connection with integration by parts (IBP) methods. As an illustrative example, we will demonstrate how one can calculate the ε-expansion of a ladder graph with 6 massive fermion lines.
4. Robustness of Operational Matrices of Differentiation for Solving State-Space Analysis and Optimal Control Problems
Directory of Open Access Journals (Sweden)
Emran Tohidi
2013-01-01
Full Text Available The idea of approximation by monomials together with the collocation technique over a uniform mesh for solving state-space analysis and optimal control problems (OCPs has been proposed in this paper. After imposing the Pontryagins maximum principle to the main OCPs, the problems reduce to a linear or nonlinear boundary value problem. In the linear case we propose a monomial collocation matrix approach, while in the nonlinear case, the general collocation method has been applied. We also show the efficiency of the operational matrices of differentiation with respect to the operational matrices of integration in our numerical examples. These matrices of integration are related to the Bessel, Walsh, Triangular, Laguerre, and Hermite functions.
5. Recent symbolic summation methods to solve coupled systems of differential and difference equations
Energy Technology Data Exchange (ETDEWEB)
Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, Johannes; Freitas, Abilio de [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2014-07-15
We outline a new algorithm to solve coupled systems of differential equations in one continuous variable x (resp. coupled difference equations in one discrete variable N) depending on a small parameter ε: given such a system and given sufficiently many initial values, we can determine the first coefficients of the Laurent-series solutions in ε if they are expressible in terms of indefinite nested sums and products. This systematic approach is based on symbolic summation algorithms in the context of difference rings/fields and uncoupling algorithms. The proposed method gives rise to new interesting applications in connection with integration by parts (IBP) methods. As an illustrative example, we will demonstrate how one can calculate the ε-expansion of a ladder graph with 6 massive fermion lines.
6. Give me a hand: Differential effects of gesture type in guiding young children's problem-solving.
Science.gov (United States)
Vallotton, Claire; Fusaro, Maria; Hayden, Julia; Decker, Kalli; Gutowski, Elizabeth
2015-11-01
Adults' gestures support children's learning in problem-solving tasks, but gestures may be differentially useful to children of different ages, and different features of gestures may make them more or less useful to children. The current study investigated parents' use of gestures to support their young children (1.5 - 6 years) in a block puzzle task (N = 126 parent-child dyads), and identified patterns in parents' gesture use indicating different gestural strategies. Further, we examined the effect of child age on both the frequency and types of gestures parents used, and on their usefulness to support children's learning. Children attempted to solve the puzzle independently before and after receiving help from their parent; half of the parents were instructed to sit on their hands while they helped. Parents who could use their hands appear to use gestures in three strategies: orienting the child to the task, providing abstract information, and providing embodied information; further, they adapted their gesturing to their child's age and skill level. Younger children elicited more frequent and more proximal gestures from parents. Despite the greater use of gestures with younger children, it was the oldest group (4.5-6.0 years) who were most affected by parents' gestures. The oldest group was positively affected by the total frequency of parents' gestures, and in particular, parents' use of embodying gestures (indexes that touched their referents, representational demonstrations with object in hand, and physically guiding child's hands). Though parents rarely used the embodying strategy with older children, it was this strategy which most enhanced the problem-solving of children 4.5 - 6 years.
7. Give me a hand: Differential effects of gesture type in guiding young children's problem-solving
Science.gov (United States)
Vallotton, Claire; Fusaro, Maria; Hayden, Julia; Decker, Kalli; Gutowski, Elizabeth
2015-01-01
Adults’ gestures support children's learning in problem-solving tasks, but gestures may be differentially useful to children of different ages, and different features of gestures may make them more or less useful to children. The current study investigated parents’ use of gestures to support their young children (1.5 – 6 years) in a block puzzle task (N = 126 parent-child dyads), and identified patterns in parents’ gesture use indicating different gestural strategies. Further, we examined the effect of child age on both the frequency and types of gestures parents used, and on their usefulness to support children's learning. Children attempted to solve the puzzle independently before and after receiving help from their parent; half of the parents were instructed to sit on their hands while they helped. Parents who could use their hands appear to use gestures in three strategies: orienting the child to the task, providing abstract information, and providing embodied information; further, they adapted their gesturing to their child's age and skill level. Younger children elicited more frequent and more proximal gestures from parents. Despite the greater use of gestures with younger children, it was the oldest group (4.5-6.0 years) who were most affected by parents’ gestures. The oldest group was positively affected by the total frequency of parents’ gestures, and in particular, parents’ use of embodying gestures (indexes that touched their referents, representational demonstrations with object in hand, and physically guiding child's hands). Though parents rarely used the embodying strategy with older children, it was this strategy which most enhanced the problem-solving of children 4.5 – 6 years. PMID:26848192
8. Analytical solutions for coupling fractional partial differential equations with Dirichlet boundary conditions
Science.gov (United States)
Ding, Xiao-Li; Nieto, Juan J.
2017-11-01
In this paper, we consider the analytical solutions of coupling fractional partial differential equations (FPDEs) with Dirichlet boundary conditions on a finite domain. Firstly, the method of successive approximations is used to obtain the analytical solutions of coupling multi-term time fractional ordinary differential equations. Then, the technique of spectral representation of the fractional Laplacian operator is used to convert the coupling FPDEs to the coupling multi-term time fractional ordinary differential equations. By applying the obtained analytical solutions to the resulting multi-term time fractional ordinary differential equations, the desired analytical solutions of the coupling FPDEs are given. Our results are applied to derive the analytical solutions of some special cases to demonstrate their applicability.
9. PSsolver: A Maple implementation to solve first order ordinary differential equations with Liouvillian solutions
Science.gov (United States)
Avellar, J.; Duarte, L. G. S.; da Mota, L. A. C. P.
2012-10-01
We present a set of software routines in Maple 14 for solving first order ordinary differential equations (FOODEs). The package implements the Prelle-Singer method in its original form together with its extension to include integrating factors in terms of elementary functions. The package also presents a theoretical extension to deal with all FOODEs presenting Liouvillian solutions. Applications to ODEs taken from standard references show that it solves ODEs which remain unsolved using Maple's standard ODE solution routines. New version program summary Program title: PSsolver Catalogue identifier: ADPR_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADPR_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 2302 No. of bytes in distributed program, including test data, etc.: 31962 Distribution format: tar.gz Programming language: Maple 14 (also tested using Maple 15 and 16). Computer: Intel Pentium Processor P6000, 1.86 GHz. Operating system: Windows 7. RAM: 4 GB DDR3 Memory Classification: 4.3. Catalogue identifier of previous version: ADPR_v1_0 Journal reference of previous version: Comput. Phys. Comm. 144 (2002) 46 Does the new version supersede the previous version?: Yes Nature of problem: Symbolic solution of first order differential equations via the Prelle-Singer method. Solution method: The method of solution is based on the standard Prelle-Singer method, with extensions for the cases when the FOODE contains elementary functions. Additionally, an extension of our own which solves FOODEs with Liouvillian solutions is included. Reasons for new version: The program was not running anymore due to changes in the latest versions of Maple. Additionally, we corrected/changed some bugs/details that were hampering the smoother functioning of the routines. Summary
10. A deterministic partial differential equation model for dose calculation in electron radiotherapy.
Science.gov (United States)
Duclous, R; Dubroca, B; Frank, M
2010-07-07
High-energy ionizing radiation is a prominent modality for the treatment of many cancers. The approaches to electron dose calculation can be categorized into semi-empirical models (e.g. Fermi-Eyges, convolution-superposition) and probabilistic methods (e.g.Monte Carlo). A third approach to dose calculation has only recently attracted attention in the medical physics community. This approach is based on the deterministic kinetic equations of radiative transfer. We derive a macroscopic partial differential equation model for electron transport in tissue. This model involves an angular closure in the phase space. It is exact for the free streaming and the isotropic regime. We solve it numerically by a newly developed HLLC scheme based on Berthon et al (2007 J. Sci. Comput. 31 347-89) that exactly preserves the key properties of the analytical solution on the discrete level. We discuss several test cases taken from the medical physics literature. A test case with an academic Henyey-Greenstein scattering kernel is considered. We compare our model to a benchmark discrete ordinate solution. A simplified model of electron interactions with tissue is employed to compute the dose of an electron beam in a water phantom, and a case of irradiation of the vertebral column. Here our model is compared to the PENELOPE Monte Carlo code. In the academic example, the fluences computed with the new model and a benchmark result differ by less than 1%. The depths at half maximum differ by less than 0.6%. In the two comparisons with Monte Carlo, our model gives qualitatively reasonable dose distributions. Due to the crude interaction model, these so far do not have the accuracy needed in clinical practice. However, the new model has a computational cost that is less than one-tenth of the cost of a Monte Carlo simulation. In addition, simulations can be set up in a similar way as a Monte Carlo simulation. If more detailed effects such as coupled electron-photon transport, bremsstrahlung
11. A deterministic partial differential equation model for dose calculation in electron radiotherapy
Science.gov (United States)
Duclous, R.; Dubroca, B.; Frank, M.
2010-07-01
High-energy ionizing radiation is a prominent modality for the treatment of many cancers. The approaches to electron dose calculation can be categorized into semi-empirical models (e.g. Fermi-Eyges, convolution-superposition) and probabilistic methods (e.g. Monte Carlo). A third approach to dose calculation has only recently attracted attention in the medical physics community. This approach is based on the deterministic kinetic equations of radiative transfer. We derive a macroscopic partial differential equation model for electron transport in tissue. This model involves an angular closure in the phase space. It is exact for the free streaming and the isotropic regime. We solve it numerically by a newly developed HLLC scheme based on Berthon et al (2007 J. Sci. Comput. 31 347-89) that exactly preserves the key properties of the analytical solution on the discrete level. We discuss several test cases taken from the medical physics literature. A test case with an academic Henyey-Greenstein scattering kernel is considered. We compare our model to a benchmark discrete ordinate solution. A simplified model of electron interactions with tissue is employed to compute the dose of an electron beam in a water phantom, and a case of irradiation of the vertebral column. Here our model is compared to the PENELOPE Monte Carlo code. In the academic example, the fluences computed with the new model and a benchmark result differ by less than 1%. The depths at half maximum differ by less than 0.6%. In the two comparisons with Monte Carlo, our model gives qualitatively reasonable dose distributions. Due to the crude interaction model, these so far do not have the accuracy needed in clinical practice. However, the new model has a computational cost that is less than one-tenth of the cost of a Monte Carlo simulation. In addition, simulations can be set up in a similar way as a Monte Carlo simulation. If more detailed effects such as coupled electron-photon transport, bremsstrahlung
12. Collage-based approaches for elliptic partial differential equations inverse problems
Science.gov (United States)
Yodzis, Michael; Kunze, Herb
2017-01-01
The collage method for inverse problems has become well-established in the literature in recent years. Initial work developed a collage theorem, based upon Banach's fixed point theorem, for treating inverse problems for ordinary differential equations (ODEs). Amongst the subsequent work was a generalized collage theorem, based upon the Lax-Milgram representation theorem, useful for treating inverse problems for elliptic partial differential equations (PDEs). Each of these two different approaches can be applied to elliptic PDEs in one space dimension. In this paper, we explore and compare how the two different approaches perform for the estimation of the diffusivity for a steady-state heat equation.
13. The application of Legendre-tau approximation to parameter identification for delay and partial differential equations
Science.gov (United States)
Ito, K.
1983-01-01
Approximation schemes based on Legendre-tau approximation are developed for application to parameter identification problem for delay and partial differential equations. The tau method is based on representing the approximate solution as a truncated series of orthonormal functions. The characteristic feature of the Legendre-tau approach is that when the solution to a problem is infinitely differentiable, the rate of convergence is faster than any finite power of 1/N; higher accuracy is thus achieved, making the approach suitable for small N.
14. Discrete variational derivative method a structure-preserving numerical method for partial differential equations
CERN Document Server
Furihata, Daisuke
2010-01-01
Nonlinear Partial Differential Equations (PDEs) have become increasingly important in the description of physical phenomena. Unlike Ordinary Differential Equations, PDEs can be used to effectively model multidimensional systems. The methods put forward in Discrete Variational Derivative Method concentrate on a new class of ""structure-preserving numerical equations"" which improves the qualitative behaviour of the PDE solutions and allows for stable computing. The authors have also taken care to present their methods in an accessible manner, which means that the book will be useful to engineer
15. Partial differential equations II elements of the modern theory equations with constant coefficients
CERN Document Server
Shubin, M
1994-01-01
This book, the first printing of which was published as Volume 31 of the Encyclopaedia of Mathematical Sciences, contains a survey of the modern theory of general linear partial differential equations and a detailed review of equations with constant coefficients. Readers will be interested in an introduction to microlocal analysis and its applications including singular integral operators, pseudodifferential operators, Fourier integral operators and wavefronts, a survey of the most important results about the mixed problem for hyperbolic equations, a review of asymptotic methods including short wave asymptotics, the Maslov canonical operator and spectral asymptotics, a detailed description of the applications of distribution theory to partial differential equations with constant coefficients including numerous interesting special topics.
16. Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations
Science.gov (United States)
Arqub, Omar Abu; El-Ajou, Ahmad; Momani, Shaher
2015-07-01
Building fractional mathematical models for specific phenomena and developing numerical or analytical solutions for these fractional mathematical models are crucial issues in mathematics, physics, and engineering. In this work, a new analytical technique for constructing and predicting solitary pattern solutions of time-fractional dispersive partial differential equations is proposed based on the generalized Taylor series formula and residual error function. The new approach provides solutions in the form of a rapidly convergent series with easily computable components using symbolic computation software. For method evaluation and validation, the proposed technique was applied to three different models and compared with some of the well-known methods. The resultant simulations clearly demonstrate the superiority and potentiality of the proposed technique in terms of the quality performance and accuracy of substructure preservation in the construct, as well as the prediction of solitary pattern solutions for time-fractional dispersive partial differential equations.
17. Algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations with the use of parallel computations
Energy Technology Data Exchange (ETDEWEB)
Moryakov, A. V., E-mail: sailor@orc.ru [National Research Centre Kurchatov Institute (Russian Federation)
2016-12-15
An algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations is presented. The algorithm for systems of first-order differential equations is implemented in the EDELWEISS code with the possibility of parallel computations on supercomputers employing the MPI (Message Passing Interface) standard for the data exchange between parallel processes. The solution is represented by a series of orthogonal polynomials on the interval [0, 1]. The algorithm is characterized by simplicity and the possibility to solve nonlinear problems with a correction of the operator in accordance with the solution obtained in the previous iterative process.
18. Parabolic partial differential equations with discrete state-dependent delay: Classical solutions and solution manifold
Czech Academy of Sciences Publication Activity Database
Krisztin, T.; Rezunenko, Oleksandr
2016-01-01
Roč. 260, č. 5 (2016), s. 4454-4472 ISSN 0022-0396 R&D Projects: GA ČR GAP103/12/2431 Institutional support: RVO:67985556 Keywords : Parabolic partial differential equations * State dependent delay * Solution manifold Subject RIV: BC - Control Systems Theory Impact factor: 1.988, year: 2016 http://library.utia.cas.cz/separaty/2016/AS/rezunenko-0457879.pdf
19. A Posteriori Finite Element Bounds for Sensitivity Derivatives of Partial-Differential-Equation Outputs. Revised
Science.gov (United States)
Lewis, Robert Michael; Patera, Anthony T.; Peraire, Jaume
1998-01-01
We present a Neumann-subproblem a posteriori finite element procedure for the efficient and accurate calculation of rigorous, 'constant-free' upper and lower bounds for sensitivity derivatives of functionals of the solutions of partial differential equations. The design motivation for sensitivity derivative error control is discussed; the a posteriori finite element procedure is described; the asymptotic bounding properties and computational complexity of the method are summarized; and illustrative numerical results are presented.
20. Cellular automata for spatiotemporal pattern formation from reaction–diffusion partial differential equations
International Nuclear Information System (INIS)
Ohmori, Shousuke; Yamazaki, Yoshihiro
2016-01-01
Ultradiscrete equations are derived from a set of reaction–diffusion partial differential equations, and cellular automaton rules are obtained on the basis of the ultradiscrete equations. Some rules reproduce the dynamical properties of the original reaction–diffusion equations, namely, bistability and pulse annihilation. Furthermore, other rules bring about soliton-like preservation and periodic pulse generation with a pacemaker, which are not obtained from the original reaction–diffusion equations. (author)
1. Conservation laws for certain time fractional nonlinear systems of partial differential equations
Science.gov (United States)
Singla, Komal; Gupta, R. K.
2017-12-01
In this study, an extension of the concept of nonlinear self-adjointness and Noether operators is proposed for calculating conserved vectors of the time fractional nonlinear systems of partial differential equations. In our recent work (J Math Phys 2016; 57: 101504), by proposing the symmetry approach for time fractional systems, the Lie symmetries for some fractional nonlinear systems have been derived. In this paper, the obtained infinitesimal generators are used to find conservation laws for the corresponding fractional systems.
2. Scale-invariant solutions to partial differential equations of fractional order with a moving boundary condition
International Nuclear Information System (INIS)
Li Xicheng; Xu Mingyu; Wang Shaowei
2008-01-01
In this paper, we give similarity solutions of partial differential equations of fractional order with a moving boundary condition. The solutions are given in terms of a generalized Wright function. The time-fractional Caputo derivative and two types of space-fractional derivatives are considered. The scale-invariant variable and the form of the solution of the moving boundary are obtained by the Lie group analysis. A comparison between the solutions corresponding to two types of fractional derivative is also given
3. On the solution of elliptic partial differential equations on regions with corners
International Nuclear Information System (INIS)
2016-01-01
In this paper we investigate the solution of boundary value problems on polygonal domains for elliptic partial differential equations. We observe that when the problems are formulated as the boundary integral equations of classical potential theory, the solutions are representable by series of elementary functions. In addition to being analytically perspicuous, the resulting expressions lend themselves to the construction of accurate and efficient numerical algorithms. The results are illustrated by a number of numerical examples.
4. Study of coupled nonlinear partial differential equations for finding exact analytical solutions.
Science.gov (United States)
Khan, Kamruzzaman; Akbar, M Ali; Koppelaar, H
2015-07-01
Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G'/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd-Sokolov-Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics.
5. Existence of pseudo almost periodic solutions for a class of partial functional differential equations
Directory of Open Access Journals (Sweden)
Hui-Sheng Ding
2013-04-01
Full Text Available In this paper, we first introduce a new class of pseudo almost periodic type functions and investigate some properties of pseudo almost periodic type functions; and then we discuss the existence of pseudo almost periodic solutions to the class of abstract partial functional differential equations $x'(t=Ax(t+f(t,x_t$ with finite delay in a Banach space X.
6. Taguchi method for partial differential equations with application in tumor growth.
Science.gov (United States)
Ilea, M; Turnea, M; Rotariu, M; Arotăriţei, D; Popescu, Marilena
2014-01-01
The growth of tumors is a highly complex process. To describe this process, mathematical models are needed. A variety of partial differential mathematical models for tumor growth have been developed and studied. Most of those models are based on the reaction-diffusion equations and mass conservation law. A variety of modeling strategies have been developed, each focusing on tumor growth. Systems of time-dependent partial differential equations occur in many branches of applied mathematics. The vast majority of mathematical models in tumor growth are formulated in terms of partial differential equations. We propose a mathematical model for the interactions between these three cancer cell populations. The Taguchi methods are widely used by quality engineering scientists to compare the effects of multiple variables, together with their interactions, with a simple and manageable experimental design. In Taguchi's design of experiments, variation is more interesting to study than the average. First, Taguchi methods are utilized to search for the significant factors and the optimal level combination of parameters. Except the three parameters levels, other factors levels other factors levels would not be considered. Second, cutting parameters namely, cutting speed, depth of cut, and feed rate are designed using the Taguchi method. Finally, the adequacy of the developed mathematical model is proved by ANOVA. According to the results of ANOVA, since the percentage contribution of the combined error is as small. Many mathematical models can be quantitatively characterized by partial differential equations. The use of MATLAB and Taguchi method in this article illustrates the important role of informatics in research in mathematical modeling. The study of tumor growth cells is an exciting and important topic in cancer research and will profit considerably from theoretical input. Interpret these results to be a permanent collaboration between math's and medical oncologists.
7. Study of coupled nonlinear partial differential equations for finding exact analytical solutions
Science.gov (United States)
Khan, Kamruzzaman; Akbar, M. Ali; Koppelaar, H.
2015-01-01
Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G′/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd–Sokolov–Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics. PMID:26587256
8. Baecklund transformations and zero-curvature representations of systems of partial differential equations
International Nuclear Information System (INIS)
Brandt, F.
1993-01-01
It is shown that Baecklund transformations (BTs) and zero-curvature representations (ZCRs) of systems of partial differential equations (PDEs) are closely related. The connection is established by nonlinear representations of the symmetry group underlying the ZCR which induce gauge transformations relating different BTs. This connection is used to construct BTs from ZCRs (and vice versa). Furthermore a procedure is outlined which allows a systematic search for ZCRs of a given system of PDEs. (orig.)
9. Semi-groups of operators and some of their applications to partial differential equations
International Nuclear Information System (INIS)
Kisynski, J.
1976-01-01
Basic notions and theorems of the theory of one-parameter semi-groups of linear operators are given, illustrated by some examples concerned with linear partial differential operators. For brevity, some important and widely developed parts of the semi-group theory such as the general theory of holomorphic semi-groups or the theory of temporally inhomogeneous evolution equations are omitted. This omission includes also the very important application of semi-groups to investigating stochastic processes. (author)
10. Discontinuous Galerkin finite element methods for hyperbolic nonconservative partial differential equations
International Nuclear Information System (INIS)
Rhebergen, S.; Bokhove, O.; Vegt, J.J.W. van der
2008-01-01
We present space- and space-time discontinuous Galerkin finite element (DGFEM) formulations for systems containing nonconservative products, such as occur in dispersed multiphase flow equations. The main criterium we pose on the weak formulation is that if the system of nonconservative partial differential equations can be transformed into conservative form, then the formulation must reduce to that for conservative systems. Standard DGFEM formulations cannot be applied to nonconservative systems of partial differential equations. We therefore introduce the theory of weak solutions for nonconservative products into the DGFEM formulation leading to the new question how to define the path connecting left and right states across a discontinuity. The effect of different paths on the numerical solution is investigated and found to be small. We also introduce a new numerical flux that is able to deal with nonconservative products. Our scheme is applied to two different systems of partial differential equations. First, we consider the shallow water equations, where topography leads to nonconservative products, in which the known, possibly discontinuous, topography is formally taken as an unknown in the system. Second, we consider a simplification of a depth-averaged two-phase flow model which contains more intrinsic nonconservative products
11. A higher-order conservation element solution element method for solving hyperbolic differential equations on unstructured meshes
Science.gov (United States)
Bilyeu, David
This dissertation presents an extension of the Conservation Element Solution Element (CESE) method from second- to higher-order accuracy. The new method retains the favorable characteristics of the original second-order CESE scheme, including (i) the use of the space-time integral equation for conservation laws, (ii) a compact mesh stencil, (iii) the scheme will remain stable up to a CFL number of unity, (iv) a fully explicit, time-marching integration scheme, (v) true multidimensionality without using directional splitting, and (vi) the ability to handle two- and three-dimensional geometries by using unstructured meshes. This algorithm has been thoroughly tested in one, two and three spatial dimensions and has been shown to obtain the desired order of accuracy for solving both linear and non-linear hyperbolic partial differential equations. The scheme has also shown its ability to accurately resolve discontinuities in the solutions. Higher order unstructured methods such as the Discontinuous Galerkin (DG) method and the Spectral Volume (SV) methods have been developed for one-, two- and three-dimensional application. Although these schemes have seen extensive development and use, certain drawbacks of these methods have been well documented. For example, the explicit versions of these two methods have very stringent stability criteria. This stability criteria requires that the time step be reduced as the order of the solver increases, for a given simulation on a given mesh. The research presented in this dissertation builds upon the work of Chang, who developed a fourth-order CESE scheme to solve a scalar one-dimensional hyperbolic partial differential equation. The completed research has resulted in two key deliverables. The first is a detailed derivation of a high-order CESE methods on unstructured meshes for solving the conservation laws in two- and three-dimensional spaces. The second is the code implementation of these numerical methods in a computer code. For
12. Linear differential equations to solve nonlinear mechanical problems: A novel approach
OpenAIRE
2004-01-01
Often a non-linear mechanical problem is formulated as a non-linear differential equation. A new method is introduced to find out new solutions of non-linear differential equations if one of the solutions of a given non-linear differential equation is known. Using the known solution of the non-linear differential equation, linear differential equations are set up. The solutions of these linear differential equations are found using standard techniques. Then the solutions of the linear differe...
13. Homotopy perturbation method with Laplace Transform (LT-HPM) for solving Lane-Emden type differential equations (LETDEs).
Science.gov (United States)
2016-01-01
In this communication, we describe the Homotopy Perturbation Method with Laplace Transform (LT-HPM), which is used to solve the Lane-Emden type differential equations. It's very difficult to solve numerically the Lane-Emden types of the differential equation. Here we implemented this method for two linear homogeneous, two linear nonhomogeneous, and four nonlinear homogeneous Lane-Emden type differential equations and use their appropriate comparisons with exact solutions. In the current study, some examples are better than other existing methods with their nearer results in the form of power series. The Laplace transform used to accelerate the convergence of power series and the results are shown in the tables and graphs which have good agreement with the other existing method in the literature. The results show that LT-HPM is very effective and easy to implement.
14. Total, partial and differential ionization cross sections in proton-hydrogen collisions at low energy
Energy Technology Data Exchange (ETDEWEB)
Zou, Shiyang [Graduate University for Advanced Studies, School of Mathematical and Physical Science, Toki, Gifu (Japan); Pichl, Lukas [University of Aizu, Foundation of Computer Science Laboratory, Aizuwakamatsu, Fukushima (Japan); Kimura, Mineo [Yamaguchi Univ., Graduate School of Science and Engineering, Ube, Yamaguchi (Japan); Kato, Takako [National Inst. for Fusion Science, Toki, Gifu (Japan)
2003-01-01
Single-differential, partial and total ionization cross sections for the proton-hydrogen collision system at low energy range (0.1-10 keV/amu) are determined by using the electron translation factor corrected molecular-orbital close-coupling method. Full convergence of ionization cross sections as a function of H{sub 2}{sup +} molecular basis size is achieved by including up to 10 bound states, and 11 continuum partial waves. The present cross sections are in an excellent agreement with the recent experiments of Shah et al., but decrease more rapidly than the cross sections measured by Pieksma et al. with decreasing energy. The calculated cross section data are included in this report. (author)
15. Differentiation of mucosal disease from partial development of the paranasal sinuses in pediatric patients
International Nuclear Information System (INIS)
Duerinckx, A.J.; Whyte, A.M.; Lufkin, R.B.; Hall, T.R.; Kangarloo, H.
1988-01-01
On magnetic resonance (MR) images of pediatric patients, sinus mucosal disease may have an appearance similar to that of the normal partially developed sinus, leading to an increase in the number of patients labeled as having incidental sinusitis. The paranasal sinuses were retrospectively evaluated in 27 infants and children aged 0-11 years undergoing brain MR imaging for indications both unrelated and related to sinus disease. The authors developed criteria for grading paranasal sinus development and mucosal disease. Incidental mucosal disease is not uncommon, occurring in 28% of patients aged 0-7 years. In children under 3 years of age, inflammatory mucosal thickening and marrow surrounding the partially developed sinus have a high signal on many MR sequences and may be confused. Recognition of the low-intensity peripheral cortical margin of the sinus and awareness of the stages of normal sinus development allow differentiation
16. ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing
KAUST Repository
Calatroni, Luca
2013-08-01
We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H -1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation.
17. Survey of the status of finite element methods for partial differential equations
Science.gov (United States)
Temam, Roger
1986-01-01
The finite element methods (FEM) have proved to be a powerful technique for the solution of boundary value problems associated with partial differential equations of either elliptic, parabolic, or hyperbolic type. They also have a good potential for utilization on parallel computers particularly in relation to the concept of domain decomposition. This report is intended as an introduction to the FEM for the nonspecialist. It contains a survey which is totally nonexhaustive, and it also contains as an illustration, a report on some new results concerning two specific applications, namely a free boundary fluid-structure interaction problem and the Euler equations for inviscid flows.
18. Building bridges connections and challenges in modern approaches to numerical partial differential equations
CERN Document Server
Brezzi, Franco; Cangiani, Andrea; Georgoulis, Emmanuil
2016-01-01
This volume contains contributed survey papers from the main speakers at the LMS/EPSRC Symposium “Building bridges: connections and challenges in modern approaches to numerical partial differential equations”. This meeting took place in July 8-16, 2014, and its main purpose was to gather specialists in emerging areas of numerical PDEs, and explore the connections between the different approaches. The type of contributions ranges from the theoretical foundations of these new techniques, to the applications of them, to new general frameworks and unified approaches that can cover one, or more than one, of these emerging techniques.
19. ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing
KAUST Repository
Calatroni, Luca; Dü ring, Bertram; Schö nlieb, Carola-Bibiane
2013-01-01
We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H -1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation.
20. New Generalized Hyperbolic Functions to Find New Exact Solutions of the Nonlinear Partial Differential Equations
Directory of Open Access Journals (Sweden)
Yusuf Pandir
2013-01-01
Full Text Available We firstly give some new functions called generalized hyperbolic functions. By the using of the generalized hyperbolic functions, new kinds of transformations are defined to discover the exact approximate solutions of nonlinear partial differential equations. Based on the generalized hyperbolic function transformation of the generalized KdV equation and the coupled equal width wave equations (CEWE, we find new exact solutions of two equations and analyze the properties of them by taking different parameter values of the generalized hyperbolic functions. We think that these solutions are very important to explain some physical phenomena.
1. 2013 CIME Course Vector-valued Partial Differential Equations and Applications
CERN Document Server
Marcellini, Paolo
2017-01-01
Collating different aspects of Vector-valued Partial Differential Equations and Applications, this volume is based on the 2013 CIME Course with the same name which took place at Cetraro, Italy, under the scientific direction of John Ball and Paolo Marcellini. It contains the following contributions: The pullback equation (Bernard Dacorogna), The stability of the isoperimetric inequality (Nicola Fusco), Mathematical problems in thin elastic sheets: scaling limits, packing, crumpling and singularities (Stefan Müller), and Aspects of PDEs related to fluid flows (Vladimir Sverák). These lectures are addressed to graduate students and researchers in the field.
2. Parametric Borel summability for some semilinear system of partial differential equations
Directory of Open Access Journals (Sweden)
Hiroshi Yamazawa
2015-01-01
Full Text Available In this paper we study the Borel summability of formal solutions with a parameter of first order semilinear system of partial differential equations with \\(n\\ independent variables. In [Singular perturbation of linear systems with a regular singularity, J. Dynam. Control. Syst. 8 (2002, 313-322], Balser and Kostov proved the Borel summability of formal solutions with respect to a singular perturbation parameter for a linear equation with one independent variable. We shall extend their results to a semilinear system of equations with general independent variables.
3. A lattice Boltzmann model with an amending function for simulating nonlinear partial differential equations
International Nuclear Information System (INIS)
Lin-Jie, Chen; Chang-Feng, Ma
2010-01-01
This paper proposes a lattice Boltzmann model with an amending function for one-dimensional nonlinear partial differential equations (NPDEs) in the form u t + αuu x + βu n u x + γu xx + δu xxx + ζu xxxx = 0. This model is different from existing models because it lets the time step be equivalent to the square of the space step and derives higher accuracy and nonlinear terms in NPDEs. With the Chapman–Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The numerical results agree well with the analytical solutions. (general)
4. First-order systems of linear partial differential equations: normal forms, canonical systems, transform methods
Directory of Open Access Journals (Sweden)
Heinz Toparkus
2014-04-01
Full Text Available In this paper we consider first-order systems with constant coefficients for two real-valued functions of two real variables. This is both a problem in itself, as well as an alternative view of the classical linear partial differential equations of second order with constant coefficients. The classification of the systems is done using elementary methods of linear algebra. Each type presents its special canonical form in the associated characteristic coordinate system. Then you can formulate initial value problems in appropriate basic areas, and you can try to achieve a solution of these problems by means of transform methods.
5. Distribution of the Discretization and Algebraic Error in Numerical Solution of Partial Differential Equations
Czech Academy of Sciences Publication Activity Database
Papež, Jan; Liesen, J.; Strakoš, Z.
2014-01-01
Roč. 449, 15 May (2014), s. 89-114 ISSN 0024-3795 R&D Projects: GA AV ČR IAA100300802; GA ČR GA201/09/0917 Grant - others:GA MŠk(CZ) LL1202; GA UK(CZ) 695612 Institutional support: RVO:67985807 Keywords : numerical solution of partial differential equations * finite element method * adaptivity * a posteriori error analysis * discretization error * algebra ic error * spatial distribution of the error Subject RIV: BA - General Mathematics Impact factor: 0.939, year: 2014
6. "Real-Time Optical Laboratory Linear Algebra Solution Of Partial Differential Equations"
Science.gov (United States)
Casasent, David; Jackson, James
1986-03-01
A Space Integrating (SI) Optical Linear Algebra Processor (OLAP) employing space and frequency-multiplexing, new partitioning and data flow, and achieving high accuracy performance with a non base-2 number system is described. Laboratory data on the performance of this system and the solution of parabolic Partial Differential Equations (PDEs) is provided. A multi-processor OLAP system is also described for the first time. It use in the solution of multiple banded matrices that frequently arise is then discussed. The utility and flexibility of this processor compared to digital systolic architectures should be apparent.
7. Mathematical Methods for Engineers and Scientists 3 Fourier Analysis, Partial Differential Equations and Variational Methods
CERN Document Server
Tang, Kwong-Tin
2007-01-01
Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis, integral transforms, ordinary and partial differential equations are presented in a discursive style that is readable and easy to follow. Numerous clearly stated, completely worked out examples together with carefully selected problem sets with answers are used to enhance students' understanding and manipulative skill. The goal is to make students comfortable and confident in using advanced mathematical tools in junior, senior, and beginning graduate courses.
8. Maillet type theorem for singular first order nonlinear partial differential equations of totally characteristic type. Part II
Directory of Open Access Journals (Sweden)
Akira Shirai
2015-01-01
Full Text Available In this paper, we study the following nonlinear first order partial differential equation: \$f(t,x,u,\\partial_t u,\\partial_x u=0\\quad\\text{with}\\quad u(0,x\\equiv 0.\$ The purpose of this paper is to determine the estimate of Gevrey order under the condition that the equation is singular of a totally characteristic type. The Gevrey order is indicated by the rate of divergence of a formal power series. This paper is a continuation of the previous papers [Convergence of formal solutions of singular first order nonlinear partial differential equations of totally characteristic type, Funkcial. Ekvac. 45 (2002, 187-208] and [Maillet type theorem for singular first order nonlinear partial differential equations of totally characteristic type, Surikaiseki Kenkyujo Kokyuroku, Kyoto University 1431 (2005, 94-106]. Especially the last-mentioned paper is regarded as part I of this paper.
9. Partial differential equation-based localization of a monopole source from a circular array.
Science.gov (United States)
Ando, Shigeru; Nara, Takaaki; Levy, Tsukassa
2013-10-01
Wave source localization from a sensor array has long been the most active research topics in both theory and application. In this paper, an explicit and time-domain inversion method for the direction and distance of a monopole source from a circular array is proposed. The approach is based on a mathematical technique, the weighted integral method, for signal/source parameter estimation. It begins with an exact form of the source-constraint partial differential equation that describes the unilateral propagation of wide-band waves from a single source, and leads to exact algebraic equations that include circular Fourier coefficients (phase mode measurements) as their coefficients. From them, nearly closed-form, single-shot and multishot algorithms are obtained that is suitable for use with band-pass/differential filter banks. Numerical evaluation and several experimental results obtained using a 16-element circular microphone array are presented to verify the validity of the proposed method.
10. Matrix-oriented implementation for the numerical solution of the partial differential equations governing flows and transport in porous media
KAUST Repository
Sun, Shuyu; Salama, Amgad; El-Amin, Mohamed
2012-01-01
In this paper we introduce a new technique for the numerical solution of the various partial differential equations governing flow and transport phenomena in porous media. This method is proposed to be used in high level programming languages like
11. Modulating functions-based method for parameters and source estimation in one-dimensional partial differential equations
KAUST Repository
Asiri, Sharefa M.; Laleg-Kirati, Taous-Meriem
2016-01-01
In this paper, modulating functions-based method is proposed for estimating space–time-dependent unknowns in one-dimensional partial differential equations. The proposed method simplifies the problem into a system of algebraic equations linear
12. A model and variance reduction method for computing statistical outputs of stochastic elliptic partial differential equations
International Nuclear Information System (INIS)
Vidal-Codina, F.; Nguyen, N.C.; Giles, M.B.; Peraire, J.
2015-01-01
We present a model and variance reduction method for the fast and reliable computation of statistical outputs of stochastic elliptic partial differential equations. Our method consists of three main ingredients: (1) the hybridizable discontinuous Galerkin (HDG) discretization of elliptic partial differential equations (PDEs), which allows us to obtain high-order accurate solutions of the governing PDE; (2) the reduced basis method for a new HDG discretization of the underlying PDE to enable real-time solution of the parameterized PDE in the presence of stochastic parameters; and (3) a multilevel variance reduction method that exploits the statistical correlation among the different reduced basis approximations and the high-fidelity HDG discretization to accelerate the convergence of the Monte Carlo simulations. The multilevel variance reduction method provides efficient computation of the statistical outputs by shifting most of the computational burden from the high-fidelity HDG approximation to the reduced basis approximations. Furthermore, we develop a posteriori error estimates for our approximations of the statistical outputs. Based on these error estimates, we propose an algorithm for optimally choosing both the dimensions of the reduced basis approximations and the sizes of Monte Carlo samples to achieve a given error tolerance. We provide numerical examples to demonstrate the performance of the proposed method
13. 4th International Conference on Particle Systems and Partial Differential Equations
CERN Document Server
Soares, Ana
2017-01-01
'This book addresses mathematical problems motivated by various applications in physics, engineering, chemistry and biology. It gathers the lecture notes from the mini-course presented by Jean-Christophe Mourrat on the construction of the various stochastic “basic” terms involved in the formulation of the dynamic Ö4 theory in three space dimensions, as well as selected contributions presented at the fourth meeting on Particle Systems and PDEs, which was held at the University of Minho’s Centre of Mathematics in December 2015. The purpose of the conference was to bring together prominent researchers working in the fields of particle systems and partial differential equations, offering them a forum to present their recent results and discuss their topics of expertise. The meeting was also intended to present to a vast and varied public, including young researchers, the area of interacting particle systems, its underlying motivation, and its relation to partial differential equations. The book w...
14. Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations
Directory of Open Access Journals (Sweden)
2006-05-01
Full Text Available In this paper we present an algorithmic approach to the generation of fully conservative difference schemes for linear partial differential equations. The approach is based on enlargement of the equations in their integral conservation law form by extra integral relations between unknown functions and their derivatives, and on discretization of the obtained system. The structure of the discrete system depends on numerical approximation methods for the integrals occurring in the enlarged system. As a result of the discretization, a system of linear polynomial difference equations is derived for the unknown functions and their partial derivatives. A difference scheme is constructed by elimination of all the partial derivatives. The elimination can be achieved by selecting a proper elimination ranking and by computing a Gröbner basis of the linear difference ideal generated by the polynomials in the discrete system. For these purposes we use the difference form of Janet-like Gröbner bases and their implementation in Maple. As illustration of the described methods and algorithms, we construct a number of difference schemes for Burgers and Falkowich-Karman equations and discuss their numerical properties.
15. Using packaged software for solving two differential equation problems that arise in plasma physics
International Nuclear Information System (INIS)
Gaffney, P.W.
1980-01-01
Experience in using packaged numerical software for solving two related problems that arise in Plasma physics is described. These problems are (i) the solution of the reduced resistive MHD equations and (ii) the solution of the Grad-Shafranov equation
16. Aumann Fuzzy Improper Integral and Its Application to Solve Fuzzy Integro-Differential Equations by Laplace Transform Method
Directory of Open Access Journals (Sweden)
Elhassan Eljaoui
2018-01-01
Full Text Available We introduce the Aumann fuzzy improper integral to define the convolution product of a fuzzy mapping and a crisp function in this paper. The Laplace convolution formula is proved in this case and used to solve fuzzy integro-differential equations with kernel of convolution type. Then, we report and correct an error in the article by Salahshour et al. dealing with the same topic.
17. On a partial differential equation method for determining the free energies and coexisting phase compositions of ternary mixtures from light scattering data.
Science.gov (United States)
Ross, David S; Thurston, George M; Lutzer, Carl V
2008-08-14
In this paper we present a method for determining the free energies of ternary mixtures from light scattering data. We use an approximation that is appropriate for liquid mixtures, which we formulate as a second-order nonlinear partial differential equation. This partial differential equation (PDE) relates the Hessian of the intensive free energy to the efficiency of light scattering in the forward direction. This basic equation applies in regions of the phase diagram in which the mixtures are thermodynamically stable. In regions in which the mixtures are unstable or metastable, the appropriate PDE is the nonlinear equation for the convex hull. We formulate this equation along with continuity conditions for the transition between the two equations at cloud point loci. We show how to discretize this problem to obtain a finite-difference approximation to it, and we present an iterative method for solving the discretized problem. We present the results of calculations that were done with a computer program that implements our method. These calculations show that our method is capable of reconstructing test free energy functions from simulated light scattering data. If the cloud point loci are known, the method also finds the tie lines and tie triangles that describe thermodynamic equilibrium between two or among three liquid phases. A robust method for solving this PDE problem, such as the one presented here, can be a basis for optical, noninvasive means of characterizing the thermodynamics of multicomponent mixtures.
18. A fast direct method for block triangular Toeplitz-like with tri-diagonal block systems from time-fractional partial differential equations
Science.gov (United States)
Ke, Rihuan; Ng, Michael K.; Sun, Hai-Wei
2015-12-01
In this paper, we study the block lower triangular Toeplitz-like with tri-diagonal blocks system which arises from the time-fractional partial differential equation. Existing fast numerical solver (e.g., fast approximate inversion method) cannot handle such linear system as the main diagonal blocks are different. The main contribution of this paper is to propose a fast direct method for solving this linear system, and to illustrate that the proposed method is much faster than the classical block forward substitution method for solving this linear system. Our idea is based on the divide-and-conquer strategy and together with the fast Fourier transforms for calculating Toeplitz matrix-vector multiplication. The complexity needs O (MNlog2 M) arithmetic operations, where M is the number of blocks (the number of time steps) in the system and N is the size (number of spatial grid points) of each block. Numerical examples from the finite difference discretization of time-fractional partial differential equations are also given to demonstrate the efficiency of the proposed method.
19. Uniqueness of global quasi-classical solutions of the Cauchy problems for first-order nonlinear partial differential equations
International Nuclear Information System (INIS)
Tran Duc Van
1994-01-01
The notion of global quasi-classical solutions of the Cauchy problems for first-order nonlinear partial differential equations is presented, some uniqueness theorems and a stability result are established by the method based on the theory of differential inclusions. In particular, the answer to an open problem of S.N. Kruzhkov is given. (author). 10 refs, 1 fig
20. A novel technique to solve nonlinear higher-index Hessenberg differential-algebraic equations by Adomian decomposition method.
Science.gov (United States)
Benhammouda, Brahim
2016-01-01
Since 1980, the Adomian decomposition method (ADM) has been extensively used as a simple powerful tool that applies directly to solve different kinds of nonlinear equations including functional, differential, integro-differential and algebraic equations. However, for differential-algebraic equations (DAEs) the ADM is applied only in four earlier works. There, the DAEs are first pre-processed by some transformations like index reductions before applying the ADM. The drawback of such transformations is that they can involve complex algorithms, can be computationally expensive and may lead to non-physical solutions. The purpose of this paper is to propose a novel technique that applies the ADM directly to solve a class of nonlinear higher-index Hessenberg DAEs systems efficiently. The main advantage of this technique is that; firstly it avoids complex transformations like index reductions and leads to a simple general algorithm. Secondly, it reduces the computational work by solving only linear algebraic systems with a constant coefficient matrix at each iteration, except for the first iteration where the algebraic system is nonlinear (if the DAE is nonlinear with respect to the algebraic variable). To demonstrate the effectiveness of the proposed technique, we apply it to a nonlinear index-three Hessenberg DAEs system with nonlinear algebraic constraints. This technique is straightforward and can be programmed in Maple or Mathematica to simulate real application problems.
1. The large discretization step method for time-dependent partial differential equations
Science.gov (United States)
Haras, Zigo; Taasan, Shlomo
1995-01-01
A new method for the acceleration of linear and nonlinear time dependent calculations is presented. It is based on the Large Discretization Step (LDS) approximation, defined in this work, which employs an extended system of low accuracy schemes to approximate a high accuracy discrete approximation to a time dependent differential operator. Error bounds on such approximations are derived. These approximations are efficiently implemented in the LDS methods for linear and nonlinear hyperbolic equations, presented here. In these algorithms the high and low accuracy schemes are interpreted as the same discretization of a time dependent operator on fine and coarse grids, respectively. Thus, a system of correction terms and corresponding equations are derived and solved on the coarse grid to yield the fine grid accuracy. These terms are initialized by visiting the fine grid once in many coarse grid time steps. The resulting methods are very general, simple to implement and may be used to accelerate many existing time marching schemes.
2. Reciprocal links among differential parenting, perceived partiality, and self-worth: a three-wave longitudinal study.
Science.gov (United States)
Shebloski, Barbara; Conger, Katherine J; Widaman, Keith F
2005-12-01
This study examined reciprocal links between parental differential treatment, siblings' perception of partiality, and self-worth with 3 waves of data from 384 adolescent sibling dyads. Results suggest that birth-order status was significantly associated with self-worth and perception of maternal and paternal differential treatment. There was a consistent across-time effect of self-worth on perception of parental partiality for later born siblings, but not earlier born siblings, and a consistent effect of differential treatment on perception of partiality for earlier born but not later born siblings. The results contribute new insight into the associations between perception of differential parenting and adolescents' adjustment and the role of birth order. Copyright 2006 APA, all rights reserved).
3. Some operational tools for solving fractional and higher integer order differential equations: A survey on their mutual relations
Science.gov (United States)
Kiryakova, Virginia S.
2012-11-01
The Laplace Transform (LT) serves as a basis of the Operational Calculus (OC), widely explored by engineers and applied scientists in solving mathematical models for their practical needs. This transform is closely related to the exponential and trigonometric functions (exp, cos, sin) and to the classical differentiation and integration operators, reducing them to simple algebraic operations. Thus, the classical LT and the OC give useful tool to handle differential equations and systems with constant coefficients. Several generalizations of the LT have been introduced to allow solving, in a similar way, of differential equations with variable coefficients and of higher integer orders, as well as of fractional (arbitrary non-integer) orders. Note that fractional order mathematical models are recently widely used to describe better various systems and phenomena of the real world. This paper surveys briefly some of our results on classes of such integral transforms, that can be obtained from the LT by means of "transmutations" which are operators of the generalized fractional calculus (GFC). On the list of these Laplace-type integral transforms, we consider the Borel-Dzrbashjan, Meijer, Krätzel, Obrechkoff, generalized Obrechkoff (multi-index Borel-Dzrbashjan) transforms, etc. All of them are G- and H-integral transforms of convolutional type, having as kernels Meijer's G- or Fox's H-functions. Besides, some special functions (also being G- and H-functions), among them - the generalized Bessel-type and Mittag-Leffler (M-L) type functions, are generating Gel'fond-Leontiev (G-L) operators of generalized differentiation and integration, which happen to be also operators of GFC. Our integral transforms have operational properties analogous to those of the LT - they do algebrize the G-L generalized integrations and differentiations, and thus can serve for solving wide classes of differential equations with variable coefficients of arbitrary, including non-integer order
4. Differentiation of Self, Personal Adjustment, Problem Solving, and Ethnic Group Belonging among Persons of Color.
Science.gov (United States)
Skowron, Elizabeth A.
2004-01-01
This study focused on examining the cross-cultural validity of Bowen family systems theory (M. Bowen, 1978), namely differentiation of self for individuals of color. Ethnic minority men and women completed measures of differentiation of self, ethnic group belonging, and 3 indices of personal adjustment. Initial support for the cross-cultural…
5. Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models.
Science.gov (United States)
Shah, A A; Xing, W W; Triantafyllidis, V
2017-04-01
In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach.
6. Computable Error Estimates for Finite Element Approximations of Elliptic Partial Differential Equations with Rough Stochastic Data
KAUST Repository
Hall, Eric Joseph
2016-12-08
We derive computable error estimates for finite element approximations of linear elliptic partial differential equations with rough stochastic coefficients. In this setting, the exact solutions contain high frequency content that standard a posteriori error estimates fail to capture. We propose goal-oriented estimates, based on local error indicators, for the pathwise Galerkin and expected quadrature errors committed in standard, continuous, piecewise linear finite element approximations. Derived using easily validated assumptions, these novel estimates can be computed at a relatively low cost and have applications to subsurface flow problems in geophysics where the conductivities are assumed to have lognormal distributions with low regularity. Our theory is supported by numerical experiments on test problems in one and two dimensions.
7. On Direct Transformation Approach to Asymptotical Analytical Solutions of Perturbed Partial Differential Equation
International Nuclear Information System (INIS)
Liu Hongzhun; Pan Zuliang; Li Peng
2006-01-01
In this article, we will derive an equality, where the Taylor series expansion around ε = 0 for any asymptotical analytical solution of the perturbed partial differential equation (PDE) with perturbing parameter ε must be admitted. By making use of the equality, we may obtain a transformation, which directly map the analytical solutions of a given unperturbed PDE to the asymptotical analytical solutions of the corresponding perturbed one. The notion of Lie-Baecklund symmetries is introduced in order to obtain more transformations. Hence, we can directly create more transformations in virtue of known Lie-Baecklund symmetries and recursion operators of corresponding unperturbed equation. The perturbed Burgers equation and the perturbed Korteweg-de Vries (KdV) equation are used as examples.
8. Isostable reduction with applications to time-dependent partial differential equations.
Science.gov (United States)
Wilson, Dan; Moehlis, Jeff
2016-07-01
Isostables and isostable reduction, analogous to isochrons and phase reduction for oscillatory systems, are useful in the study of nonlinear equations which asymptotically approach a stationary solution. In this work, we present a general method for isostable reduction of partial differential equations, with the potential power to reduce the dimensionality of a nonlinear system from infinity to 1. We illustrate the utility of this reduction by applying it to two different models with biological relevance. In the first example, isostable reduction of the Fokker-Planck equation provides the necessary framework to design a simple control strategy to desynchronize a population of pathologically synchronized oscillatory neurons, as might be relevant to Parkinson's disease. Another example analyzes a nonlinear reaction-diffusion equation with relevance to action potential propagation in a cardiac system.
9. Harmonic analysis, partial differential equations and applications in honor of Richard L. Wheeden
CERN Document Server
Franchi, Bruno; Lu, Guozhen; Perez, Carlos; Sawyer, Eric
2017-01-01
This is a collection of contributed papers by many eminent Harmonic Analysts and specialists of Partial Differential equations. The papers focus on weighted norm equalities for singular integrals, focusing wave equations, degenerate elliptic equations, Navier-Stokes flow in two dimensions and Poincare-Sobolev inequalities in the setting of metric spaces equipped with measures among others. Many topics considered in this volume stem from the interests of Richard L. Wheeden whose contributions to Potential Theory, singular integral theory and degenerate elliptic PDE theory this volume honors. Luis Caffarelli, Sagun Chanillo, Bruno Franchi, Cristian Guttierez, Xiaojun Huang, Carlos Kenig, Ermanno Lanconelli, Eric Sawyer and Alexander Volberg, are some of the many contributors to this volume. .
10. Elliptic–hyperbolic partial differential equations a mini-course in geometric and quasilinear methods
CERN Document Server
Otway, Thomas H
2015-01-01
This text is a concise introduction to the partial differential equations which change from elliptic to hyperbolic type across a smooth hypersurface of their domain. These are becoming increasingly important in diverse sub-fields of both applied mathematics and engineering, for example: • The heating of fusion plasmas by electromagnetic waves • The behaviour of light near a caustic • Extremal surfaces in the space of special relativity • The formation of rapids; transonic and multiphase fluid flow • The dynamics of certain models for elastic structures • The shape of industrial surfaces such as windshields and airfoils • Pathologies of traffic flow • Harmonic fields in extended projective space They also arise in models for the early universe, for cosmic acceleration, and for possible violation of causality in the interiors of certain compact stars. Within the past 25 years, they have become central to the isometric embedding of Riemannian manifolds and the prescription of Gauss curvatur...
11. Mathematical and numerical methods for partial differential equations applications for engineering sciences
CERN Document Server
2014-01-01
This self-tutorial offers a concise yet thorough introduction into the mathematical analysis of approximation methods for partial differential equation. A particular emphasis is put on finite element methods. The unique approach first summarizes and outlines the finite-element mathematics in general and then, in the second and major part, formulates problem examples that clearly demonstrate the techniques of functional analysis via numerous and diverse exercises. The solutions of the problems are given directly afterwards. Using this approach, the author motivates and encourages the reader to actively acquire the knowledge of finite- element methods instead of passively absorbing the material, as in most standard textbooks. This English edition is based on the Finite Element Methods for Engineering Sciences by Joel Chaskalovic
12. Partial differential equations for self-organization in cellular and developmental biology
International Nuclear Information System (INIS)
Baker, R E; Gaffney, E A; Maini, P K
2008-01-01
Understanding the mechanisms governing and regulating the emergence of structure and heterogeneity within cellular systems, such as the developing embryo, represents a multiscale challenge typifying current integrative biology research, namely, explaining the macroscale behaviour of a system from microscale dynamics. This review will focus upon modelling how cell-based dynamics orchestrate the emergence of higher level structure. After surveying representative biological examples and the models used to describe them, we will assess how developments at the scale of molecular biology have impacted on current theoretical frameworks, and the new modelling opportunities that are emerging as a result. We shall restrict our survey of mathematical approaches to partial differential equations and the tools required for their analysis. We will discuss the gap between the modelling abstraction and biological reality, the challenges this presents and highlight some open problems in the field. (invited article)
13. An odor interaction model of binary odorant mixtures by a partial differential equation method.
Science.gov (United States)
Yan, Luchun; Liu, Jiemin; Wang, Guihua; Wu, Chuandong
2014-07-09
A novel odor interaction model was proposed for binary mixtures of benzene and substituted benzenes by a partial differential equation (PDE) method. Based on the measurement method (tangent-intercept method) of partial molar volume, original parameters of corresponding formulas were reasonably displaced by perceptual measures. By these substitutions, it was possible to relate a mixture's odor intensity to the individual odorant's relative odor activity value (OAV). Several binary mixtures of benzene and substituted benzenes were respectively tested to establish the PDE models. The obtained results showed that the PDE model provided an easily interpretable method relating individual components to their joint odor intensity. Besides, both predictive performance and feasibility of the PDE model were proved well through a series of odor intensity matching tests. If combining the PDE model with portable gas detectors or on-line monitoring systems, olfactory evaluation of odor intensity will be achieved by instruments instead of odor assessors. Many disadvantages (e.g., expense on a fixed number of odor assessors) also will be successfully avoided. Thus, the PDE model is predicted to be helpful to the monitoring and management of odor pollutions.
14. A Differential Evolution Based MPPT Method for Photovoltaic Modules under Partial Shading Conditions
Directory of Open Access Journals (Sweden)
Kok Soon Tey
2014-01-01
Full Text Available Partially shaded photovoltaic (PV modules have multiple peaks in the power-voltage (P-V characteristic curve and conventional maximum power point tracking (MPPT algorithm, such as perturbation and observation (P&O, which is unable to track the global maximum power point (GMPP accurately due to its localized search space. Therefore, this paper proposes a differential evolution (DE based optimization algorithm to provide the globalized search space to track the GMPP. The direction of mutation in the DE algorithm is modified to ensure that the mutation always converges to the best solution among all the particles in the generation. This helps to provide the rapid convergence of the algorithm. Simulation of the proposed PV system is carried out in PSIM and the results are compared to P&O algorithm. In the hardware implementation, a high step-up DC-DC converter is employed to verify the proposed algorithm experimentally on partial shading conditions, load variation, and solar intensity variation. The experimental results show that the proposed algorithm is able to converge to the GMPP within 1.2 seconds with higher efficiency than P&O.
15. An Odor Interaction Model of Binary Odorant Mixtures by a Partial Differential Equation Method
Directory of Open Access Journals (Sweden)
Luchun Yan
2014-07-01
Full Text Available A novel odor interaction model was proposed for binary mixtures of benzene and substituted benzenes by a partial differential equation (PDE method. Based on the measurement method (tangent-intercept method of partial molar volume, original parameters of corresponding formulas were reasonably displaced by perceptual measures. By these substitutions, it was possible to relate a mixture’s odor intensity to the individual odorant’s relative odor activity value (OAV. Several binary mixtures of benzene and substituted benzenes were respectively tested to establish the PDE models. The obtained results showed that the PDE model provided an easily interpretable method relating individual components to their joint odor intensity. Besides, both predictive performance and feasibility of the PDE model were proved well through a series of odor intensity matching tests. If combining the PDE model with portable gas detectors or on-line monitoring systems, olfactory evaluation of odor intensity will be achieved by instruments instead of odor assessors. Many disadvantages (e.g., expense on a fixed number of odor assessors also will be successfully avoided. Thus, the PDE model is predicted to be helpful to the monitoring and management of odor pollutions.
16. Solutions to an advanced functional partial differential equation of the pantograph type.
Science.gov (United States)
Zaidi, Ali A; Van Brunt, B; Wake, G C
2015-07-08
A model for cells structured by size undergoing growth and division leads to an initial boundary value problem that involves a first-order linear partial differential equation with a functional term. Here, size can be interpreted as DNA content or mass. It has been observed experimentally and shown analytically that solutions for arbitrary initial cell distributions are asymptotic as time goes to infinity to a certain solution called the steady size distribution. The full solution to the problem for arbitrary initial distributions, however, is elusive owing to the presence of the functional term and the paucity of solution techniques for such problems. In this paper, we derive a solution to the problem for arbitrary initial cell distributions. The method employed exploits the hyperbolic character of the underlying differential operator, and the advanced nature of the functional argument to reduce the problem to a sequence of simple Cauchy problems. The existence of solutions for arbitrary initial distributions is established along with uniqueness. The asymptotic relationship with the steady size distribution is established, and because the solution is known explicitly, higher-order terms in the asymptotics can be readily obtained.
17. Method for solving the periodic problem for integro-differential equations
Directory of Open Access Journals (Sweden)
Snezhana G. Hristova
1989-05-01
Full Text Available In the paper a monotone-iterative method for approximate finding a couple of minimal and maximal quasisolutions of the periodic problem for a system of integro-differential equations of Volterra type is justified.
18. Solving Variable Coefficient Fourth-Order Parabolic Equation by ...
African Journals Online (AJOL)
Solving Variable Coefficient Fourth-Order Parabolic Equation by Modified initial guess Variational ... variable coefficient fourth order parabolic partial differential equations. The new method shows rapid convergence to the exact solution.
19. XMDS2: Fast, scalable simulation of coupled stochastic partial differential equations
Science.gov (United States)
Dennis, Graham R.; Hope, Joseph J.; Johnsson, Mattias T.
2013-01-01
XMDS2 is a cross-platform, GPL-licensed, open source package for numerically integrating initial value problems that range from a single ordinary differential equation up to systems of coupled stochastic partial differential equations. The equations are described in a high-level XML-based script, and the package generates low-level optionally parallelised C++ code for the efficient solution of those equations. It combines the advantages of high-level simulations, namely fast and low-error development, with the speed, portability and scalability of hand-written code. XMDS2 is a complete redesign of the XMDS package, and features support for a much wider problem space while also producing faster code. Program summaryProgram title: XMDS2 Catalogue identifier: AENK_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENK_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 2 No. of lines in distributed program, including test data, etc.: 872490 No. of bytes in distributed program, including test data, etc.: 45522370 Distribution format: tar.gz Programming language: Python and C++. Computer: Any computer with a Unix-like system, a C++ compiler and Python. Operating system: Any Unix-like system; developed under Mac OS X and GNU/Linux. RAM: Problem dependent (roughly 50 bytes per grid point) Classification: 4.3, 6.5. External routines: The external libraries required are problem-dependent. Uses FFTW3 Fourier transforms (used only for FFT-based spectral methods), dSFMT random number generation (used only for stochastic problems), MPI message-passing interface (used only for distributed problems), HDF5, GNU Scientific Library (used only for Bessel-based spectral methods) and a BLAS implementation (used only for non-FFT-based spectral methods). Nature of problem: General coupled initial-value stochastic partial differential equations. Solution method: Spectral method
20. Asymptotic behavior of solutions of diffusion-like partial differential equations invariant to a family of affine groups
International Nuclear Information System (INIS)
Dresner, L.
1990-07-01
This report deals with the asymptotic behavior of certain solutions of partial differential equations in one dependent and two independent variables (call them c, z, and t, respectively). The partial differential equations are invariant to one-parameter families of one-parameter affine groups of the form: c' = λ α c, t' = λ β t, z' = λz, where λ is the group parameter that labels the individual transformations and α and β are parameters that label groups of the family. The parameters α and β are connected by a linear relation, Mα + Nβ = L, where M, N, and L are numbers determined by the structure of the partial differential equation. It is shown that when L/M and N/M are L/M t -N/M for large z or small t. Some practical applications of this result are discussed. 8 refs
1. Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals.
Science.gov (United States)
Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel Antonio; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Marin-Hernandez, Antonio; Herrera-May, Agustin Leobardo; Diaz-Sanchez, Alejandro; Huerta-Chua, Jesus
2014-01-01
In this article, we propose the application of a modified Taylor series method (MTSM) for the approximation of nonlinear problems described on finite intervals. The issue of Taylor series method with mixed boundary conditions is circumvented using shooting constants and extra derivatives of the problem. In order to show the benefits of this proposal, three different kinds of problems are solved: three-point boundary valued problem (BVP) of third-order with a hyperbolic sine nonlinearity, two-point BVP for a second-order nonlinear differential equation with an exponential nonlinearity, and a two-point BVP for a third-order nonlinear differential equation with a radical nonlinearity. The result shows that the MTSM method is capable to generate easily computable and highly accurate approximations for nonlinear equations. 34L30.
2. Three tesla magnetic resonance imaging of the anterior cruciate ligament of the knee: can we differentiate complete from partial tears?
Energy Technology Data Exchange (ETDEWEB)
Dyck, Pieter van; Gielen, Jan L.; Parizel, Paul M. [University Hospital Antwerp and University of Antwerp, Department of Radiology, Antwerp (Edegem) (Belgium); Vanhoenacker, Filip M. [University Hospital Antwerp and University of Antwerp, Department of Radiology, Antwerp (Edegem) (Belgium); AZ St-Maarten Duffel/Mechelen, Department of Radiology, Duffel (Belgium); Dossche, Lieven; Gestel, Jozef van [University Hospital Antwerp and University of Antwerp, Department of Orthopedics, Antwerp (Edegem) (Belgium); Wouters, Kristien [University Hospital Antwerp and University of Antwerp, Department of Scientific Coordination and Biostatistics, Antwerp (Edegem) (Belgium)
2011-06-15
To determine the ability of 3.0T magnetic resonance (MR) imaging to identify partial tears of the anterior cruciate ligament (ACL) and to allow distinction of complete from partial ACL tears. One hundred seventy-two patients were prospectively studied by 3.0T MR imaging and arthroscopy in our institution. MR images were interpreted in consensus by two experienced reviewers, and the ACL was diagnosed as being normal, partially torn, or completely torn. Diagnostic accuracy of 3.0T MR for the detection of both complete and partial tears of the ACL was calculated using arthroscopy as the standard of reference. There were 132 patients with an intact ACL, 17 had a partial, and 23 had a complete tear of the ACL seen at arthroscopy. Sensitivity, specificity, and accuracy of 3.0T MR for complete ACL tears were 83, 99, and 97%, respectively, and, for partial ACL tears, 77, 97, and 95%, respectively. Five of 40 ACL lesions (13%) could not correctly be identified as complete or partial ACL tears. MR imaging at 3.0T represents a highly accurate method for identifying tears of the ACL. However, differentiation between complete and partial ACL tears and identification of partial tears of this ligament remains difficult, even at 3.0T. (orig.)
3. Three tesla magnetic resonance imaging of the anterior cruciate ligament of the knee: can we differentiate complete from partial tears?
International Nuclear Information System (INIS)
Dyck, Pieter van; Gielen, Jan L.; Parizel, Paul M.; Vanhoenacker, Filip M.; Dossche, Lieven; Gestel, Jozef van; Wouters, Kristien
2011-01-01
To determine the ability of 3.0T magnetic resonance (MR) imaging to identify partial tears of the anterior cruciate ligament (ACL) and to allow distinction of complete from partial ACL tears. One hundred seventy-two patients were prospectively studied by 3.0T MR imaging and arthroscopy in our institution. MR images were interpreted in consensus by two experienced reviewers, and the ACL was diagnosed as being normal, partially torn, or completely torn. Diagnostic accuracy of 3.0T MR for the detection of both complete and partial tears of the ACL was calculated using arthroscopy as the standard of reference. There were 132 patients with an intact ACL, 17 had a partial, and 23 had a complete tear of the ACL seen at arthroscopy. Sensitivity, specificity, and accuracy of 3.0T MR for complete ACL tears were 83, 99, and 97%, respectively, and, for partial ACL tears, 77, 97, and 95%, respectively. Five of 40 ACL lesions (13%) could not correctly be identified as complete or partial ACL tears. MR imaging at 3.0T represents a highly accurate method for identifying tears of the ACL. However, differentiation between complete and partial ACL tears and identification of partial tears of this ligament remains difficult, even at 3.0T. (orig.)
4. WKB: an interactive code for solving differential equations using phase integral methods
International Nuclear Information System (INIS)
White, R.B.
1978-01-01
A small code for the analysis of ordinary differential equations interactively through the use of Phase Integral Methods (WKB) has been written for use on the DEC 10. This note is a descriptive manual for those interested in using the code
5. An implementation of Kovacic's algorithm for solving ordinary differential equations in FORMAC
International Nuclear Information System (INIS)
Zharkov, A.Yu.
1987-01-01
An implementation of Kovacic's algorithm for finding Liouvillian solutions of the differential equations y'' + a(x)y' + b(x)y = 0 with rational coefficients a(x) and b(x) in the Computer Algebra System FORMAC is described. The algorithm description is presented in such a way that one can easily implement it in a suitable Computer Algebra System
6. Tracer kinetics: Modelling by partial differential equations of inhomogeneous compartments with age-dependent elimination rates. Pt. 2
International Nuclear Information System (INIS)
Winkler, E.
1991-01-01
The general theory of inhomogeneous compartments with age-dependent elimination rates is illustrated by examples. Mathematically, it turns out that models consisting of partial differential equations include ordinary, delayed and integro-differential equations, a general fact which is treated here in the context of linear tracer kinetics. The examples include standard compartments as a degenerate case, systems of standard compartments (compartment blocks), models resulting in special residence time distributions, models with pipes, and systems with heterogeneous particles. (orig./BBR) [de
7. Computation of Green function of the Schroedinger-like partial differential equations by the numerical functional integration
International Nuclear Information System (INIS)
Lobanov, Yu.Yu.; Shahbagian, R.R.; Zhidkov, E.P.
1991-01-01
A new method for numerical solution of the boundary problem for Schroedinger-like partial differential equations in R n is elaborated. The method is based on representation of multidimensional Green function in the form of multiple functional integral and on the use of approximation formulas which are constructed for such integrals. The convergence of approximations to the exact value is proved, the remainder of the formulas is estimated. Method reduces the initial differential problem to quadratures. 16 refs.; 7 tabs
8. Direct application of Padé approximant for solving nonlinear differential equations.
Science.gov (United States)
Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Garcia-Gervacio, Jose Luis; Huerta-Chua, Jesus; Morales-Mendoza, Luis Javier; Gonzalez-Lee, Mario
2014-01-01
This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value problem, a differential-algebraic oscillator problem, and an asymptotic problem. The high accurate handy approximations obtained by the direct application of Padé method shows the high potential if the proposed scheme to approximate a wide variety of problems. What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant. 34L30.
9. On a numerical method for solving integro-differential equations with variable coefficients with applications in finance
Science.gov (United States)
Kudryavtsev, O.; Rodochenko, V.
2018-03-01
We propose a new general numerical method aimed to solve integro-differential equations with variable coefficients. The problem under consideration arises in finance where in the context of pricing barrier options in a wide class of stochastic volatility models with jumps. To handle the effect of the correlation between the price and the variance, we use a suitable substitution for processes. Then we construct a Markov-chain approximation for the variation process on small time intervals and apply a maturity randomization technique. The result is a system of boundary problems for integro-differential equations with constant coefficients on the line in each vertex of the chain. We solve the arising problems using a numerical Wiener-Hopf factorization method. The approximate formulae for the factors are efficiently implemented by means of the Fast Fourier Transform. Finally, we use a recurrent procedure that moves backwards in time on the variance tree. We demonstrate the convergence of the method using Monte-Carlo simulations and compare our results with the results obtained by the Wiener-Hopf method with closed-form expressions of the factors.
10. Analyses of glass transition phenomena by solving differential equation with delay effect
International Nuclear Information System (INIS)
Takeuchi, A.; Inoue, A.
2007-01-01
A linear differential equation for the analyses of glass transition phenomena has been proposed by taking into account the delay effect due to the change in transportation of atoms near the glass transition temperature (T g ). Under the condition maintaining the order of the differential equation as the second, the non-linear differential equation proposed by Van Den Beukel and Sietsma is modified to obtain the analytic solution for a linear equation by introducing the following points: the delay effect which is described with a term of Mackey-Glass model, a concept of effective free volume (x fe eff ) and its concentration expression (C fe eff ) which correspond to the equilibrium, and an additional term associated with C fe eff . In analyzing the linear equation, Doyle's p-function was used for the integral of reaction rate with respect to temperature (T). It is found that the linear equation proposed in the present study can describe the changes in free volume (x) with increasing temperature in the dx/dT-T chart, the sharp increase in free volume at T g , and over shooting phenomena of free volume slightly above the T g , as experimentally in thermal analyses for metallic glasses. The linear solution obtained in the present study is of great importance for the analyses of the glass transition because the change in free volume with increasing temperature on heating is described with fundamental functions
11. A model reduction approach to numerical inversion for a parabolic partial differential equation
International Nuclear Information System (INIS)
Borcea, Liliana; Druskin, Vladimir; Zaslavsky, Mikhail; Mamonov, Alexander V
2014-01-01
We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where the unknown is the subsurface electrical resistivity and the data are time resolved surface measurements of the magnetic field. The algorithm presented in this paper considers inversion in one and two dimensions. The reduced model is obtained with rational interpolation in the frequency (Laplace) domain and a rational Krylov subspace projection method. It amounts to a nonlinear mapping from the function space of the unknown resistivity to the small dimensional space of the parameters of the reduced model. We use this mapping as a nonlinear preconditioner for the Gauss–Newton iterative solution of the inverse problem. The advantage of the inversion algorithm is twofold. First, the nonlinear preconditioner resolves most of the nonlinearity of the problem. Thus the iterations are less likely to get stuck in local minima and the convergence is fast. Second, the inversion is computationally efficient because it avoids repeated accurate simulations of the time-domain response. We study the stability of the inversion algorithm for various rational Krylov subspaces, and assess its performance with numerical experiments. (paper)
12. A model reduction approach to numerical inversion for a parabolic partial differential equation
Science.gov (United States)
Borcea, Liliana; Druskin, Vladimir; Mamonov, Alexander V.; Zaslavsky, Mikhail
2014-12-01
We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where the unknown is the subsurface electrical resistivity and the data are time resolved surface measurements of the magnetic field. The algorithm presented in this paper considers inversion in one and two dimensions. The reduced model is obtained with rational interpolation in the frequency (Laplace) domain and a rational Krylov subspace projection method. It amounts to a nonlinear mapping from the function space of the unknown resistivity to the small dimensional space of the parameters of the reduced model. We use this mapping as a nonlinear preconditioner for the Gauss-Newton iterative solution of the inverse problem. The advantage of the inversion algorithm is twofold. First, the nonlinear preconditioner resolves most of the nonlinearity of the problem. Thus the iterations are less likely to get stuck in local minima and the convergence is fast. Second, the inversion is computationally efficient because it avoids repeated accurate simulations of the time-domain response. We study the stability of the inversion algorithm for various rational Krylov subspaces, and assess its performance with numerical experiments.
13. Partial differential equation techniques for analysing animal movement: A comparison of different methods.
Science.gov (United States)
Wang, Yi-Shan; Potts, Jonathan R
2017-03-07
Recent advances in animal tracking have allowed us to uncover the drivers of movement in unprecedented detail. This has enabled modellers to construct ever more realistic models of animal movement, which aid in uncovering detailed patterns of space use in animal populations. Partial differential equations (PDEs) provide a popular tool for mathematically analysing such models. However, their construction often relies on simplifying assumptions which may greatly affect the model outcomes. Here, we analyse the effect of various PDE approximations on the analysis of some simple movement models, including a biased random walk, central-place foraging processes and movement in heterogeneous landscapes. Perhaps the most commonly-used PDE method dates back to a seminal paper of Patlak from 1953. However, our results show that this can be a very poor approximation in even quite simple models. On the other hand, more recent methods, based on transport equation formalisms, can provide more accurate results, as long as the kernel describing the animal's movement is sufficiently smooth. When the movement kernel is not smooth, we show that both the older and newer methods can lead to quantitatively misleading results. Our detailed analysis will aid future researchers in the appropriate choice of PDE approximation for analysing models of animal movement. Copyright © 2017 Elsevier Ltd. All rights reserved.
14. Research on odor interaction between aldehyde compounds via a partial differential equation (PDE) model.
Science.gov (United States)
Yan, Luchun; Liu, Jiemin; Qu, Chen; Gu, Xingye; Zhao, Xia
2015-01-28
In order to explore the odor interaction of binary odor mixtures, a series of odor intensity evaluation tests were performed using both individual components and binary mixtures of aldehydes. Based on the linear relation between the logarithm of odor activity value and odor intensity of individual substances, the relationship between concentrations of individual constituents and their joint odor intensity was investigated by employing a partial differential equation (PDE) model. The obtained results showed that the binary odor interaction was mainly influenced by the mixing ratio of two constituents, but not the concentration level of an odor sample. Besides, an extended PDE model was also proposed on the basis of the above experiments. Through a series of odor intensity matching tests for several different binary odor mixtures, the extended PDE model was proved effective at odor intensity prediction. Furthermore, odorants of the same chemical group and similar odor type exhibited similar characteristics in the binary odor interaction. The overall results suggested that the PDE model is a more interpretable way of demonstrating the odor interactions of binary odor mixtures.
15. Mesh refinement and numerical sensitivity analysis for parameter calibration of partial differential equations
Science.gov (United States)
Becker, Roland; Vexler, Boris
2005-06-01
We consider the calibration of parameters in physical models described by partial differential equations. This task is formulated as a constrained optimization problem with a cost functional of least squares type using information obtained from measurements. An important issue in the numerical solution of this type of problem is the control of the errors introduced, first, by discretization of the equations describing the physical model, and second, by measurement errors or other perturbations. Our strategy is as follows: we suppose that the user defines an interest functional I, which might depend on both the state variable and the parameters and which represents the goal of the computation. First, we propose an a posteriori error estimator which measures the error with respect to this functional. This error estimator is used in an adaptive algorithm to construct economic meshes by local mesh refinement. The proposed estimator requires the solution of an auxiliary linear equation. Second, we address the question of sensitivity. Applying similar techniques as before, we derive quantities which describe the influence of small changes in the measurements on the value of the interest functional. These numbers, which we call relative condition numbers, give additional information on the problem under consideration. They can be computed by means of the solution of the auxiliary problem determined before. Finally, we demonstrate our approach at hand of a parameter calibration problem for a model flow problem.
16. Statistical mechanics of normal grain growth in one dimension: A partial integro-differential equation model
International Nuclear Information System (INIS)
Ng, Felix S.L.
2016-01-01
We develop a statistical-mechanical model of one-dimensional normal grain growth that does not require any drift-velocity parameterization for grain size, such as used in the continuity equation of traditional mean-field theories. The model tracks the population by considering grain sizes in neighbour pairs; the probability of a pair having neighbours of certain sizes is determined by the size-frequency distribution of all pairs. Accordingly, the evolution obeys a partial integro-differential equation (PIDE) over ‘grain size versus neighbour grain size’ space, so that the grain-size distribution is a projection of the PIDE's solution. This model, which is applicable before as well as after statistically self-similar grain growth has been reached, shows that the traditional continuity equation is invalid outside this state. During statistically self-similar growth, the PIDE correctly predicts the coarsening rate, invariant grain-size distribution and spatial grain size correlations observed in direct simulations. The PIDE is then reducible to the standard continuity equation, and we derive an explicit expression for the drift velocity. It should be possible to formulate similar parameterization-free models of normal grain growth in two and three dimensions.
17. Patch Similarity Modulus and Difference Curvature Based Fourth-Order Partial Differential Equation for Image Denoising
Directory of Open Access Journals (Sweden)
Yunjiao Bai
2015-01-01
Full Text Available The traditional fourth-order nonlinear diffusion denoising model suffers the isolated speckles and the loss of fine details in the processed image. For this reason, a new fourth-order partial differential equation based on the patch similarity modulus and the difference curvature is proposed for image denoising. First, based on the intensity similarity of neighbor pixels, this paper presents a new edge indicator called patch similarity modulus, which is strongly robust to noise. Furthermore, the difference curvature which can effectively distinguish between edges and noise is incorporated into the denoising algorithm to determine the diffusion process by adaptively adjusting the size of the diffusion coefficient. The experimental results show that the proposed algorithm can not only preserve edges and texture details, but also avoid isolated speckles and staircase effect while filtering out noise. And the proposed algorithm has a better performance for the images with abundant details. Additionally, the subjective visual quality and objective evaluation index of the denoised image obtained by the proposed algorithm are higher than the ones from the related methods.
18. The solids-flux theory--confirmation and extension by using partial differential equations.
Science.gov (United States)
Diehl, Stefan
2008-12-01
The solids-flux theory has been used for half a century as a tool for estimating concentration and fluxes in the design and operation of secondary settling tanks during stationary conditions. The flux theory means that the conservation of mass is used in one dimension together with the batch-settling flux function according to the Kynch assumption. The flux theory results correspond to stationary solutions of a partial differential equation, a conservation law, with discontinuous coefficients modelling the continuous-sedimentation process in one dimension. The mathematical analysis of such an equation is intricate, partly since it cannot be interpreted in the classical sense. Recent results, however, make it possible to partly confirm and extend the previous flux theory statements, partly draw new conclusions also on the dynamic behaviour and the possibilities and limitations for control. We use here a single example of an ideal settling tank and a given batch-settling flux in a whole series of calculations. The mathematical results are adapted towards the application and many of them are conveniently presented in terms of operating charts.
19. A multiple-scale power series method for solving nonlinear ordinary differential equations
Directory of Open Access Journals (Sweden)
Chein-Shan Liu
2016-02-01
Full Text Available The power series solution is a cheap and effective method to solve nonlinear problems, like the Duffing-van der Pol oscillator, the Volterra population model and the nonlinear boundary value problems. A novel power series method by considering the multiple scales $R_k$ in the power term $(t/R_k^k$ is developed, which are derived explicitly to reduce the ill-conditioned behavior in the data interpolation. In the method a huge value times a tiny value is avoided, such that we can decrease the numerical instability and which is the main reason to cause the failure of the conventional power series method. The multiple scales derived from an integral can be used in the power series expansion, which provide very accurate numerical solutions of the problems considered in this paper.
20. Solving binary-state multi-objective reliability redundancy allocation series-parallel problem using efficient epsilon-constraint, multi-start partial bound enumeration algorithm, and DEA
International Nuclear Information System (INIS)
Khalili-Damghani, Kaveh; Amiri, Maghsoud
2012-01-01
In this paper, a procedure based on efficient epsilon-constraint method and data envelopment analysis (DEA) is proposed for solving binary-state multi-objective reliability redundancy allocation series-parallel problem (MORAP). In first module, a set of qualified non-dominated solutions on Pareto front of binary-state MORAP is generated using an efficient epsilon-constraint method. In order to test the quality of generated non-dominated solutions in this module, a multi-start partial bound enumeration algorithm is also proposed for MORAP. The performance of both procedures is compared using different metrics on well-known benchmark instance. The statistical analysis represents that not only the proposed efficient epsilon-constraint method outperform the multi-start partial bound enumeration algorithm but also it improves the founded upper bound of benchmark instance. Then, in second module, a DEA model is supplied to prune the generated non-dominated solutions of efficient epsilon-constraint method. This helps reduction of non-dominated solutions in a systematic manner and eases the decision making process for practical implementations. - Highlights: ► A procedure based on efficient epsilon-constraint method and DEA was proposed for solving MORAP. ► The performance of proposed procedure was compared with a multi-start PBEA. ► Methods were statistically compared using multi-objective metrics.
1. Advances in phase space analysis of partial differential equations in honor of Ferruccio Colombini's 60th birthday
CERN Document Server
Bove, Antonio; Murthy, MK Venkatesha
2009-01-01
This collection of original articles and surveys addresses the recent advances in linear and nonlinear aspects of the theory of partial differential equations. The key topics include operators as "sums of squares" of real and complex vector fields, nonlinear evolution equations, local solvability, and hyperbolic questions.
2. Dimensional analysis to transform the differential equations in partial derivates in the theory of heat transmission into ordinary ones
International Nuclear Information System (INIS)
Diaz Sanchidrian, C.
1989-01-01
The present paper applies dimensional analysis with spatial discrimination to transform the differential equations in partial derivatives developed in the theory of heat transmission into ordinary ones. The effectivity of the method is comparable to that methods based in transformations of uni or multiparametric groups, with the advantage of being more direct and simple. (Author)
3. Mixed problem with nonlocal boundary conditions for a third-order partial differential equation of mixed type
OpenAIRE
Denche, M.; Marhoune, A. L.
2001-01-01
We study a mixed problem with integral boundary conditions for a third-order partial differential equation of mixed type. We prove the existence and uniqueness of the solution. The proof is based on two-sided a priori estimates and on the density of the range of the operator generated by the considered problem.
4. CPDES2: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in two dimensions
Science.gov (United States)
Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.
1988-11-01
Many physical problems require the solution of coupled partial differential equations on two-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES2 allows each spatial operator to have 5 or 9 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect indices which is vectorizable on some of the newer scientific computers.
5. Inclusion of exact exchange in the noniterative partial-differential-equation method of electron-molecule scattering - Application to e-N2
Science.gov (United States)
Weatherford, C. A.; Onda, K.; Temkin, A.
1985-01-01
The noniterative partial-differential-equation (PDE) approach to electron-molecule scattering of Onda and Temkin (1983) is modified to account for the effects of exchange explicitly. The exchange equation is reduced to a set of inhomogeneous equations containing no integral terms and solved noniteratively in a difference form; a method for propagating the solution to large values of r is described; the changes in the polarization potential of the original PDE method required by the inclusion of exact static exchange are indicated; and the results of computations for e-N2 scattering in the fixed-nuclei approximation are presented in tables and graphs and compared with previous calculations and experimental data. Better agreement is obtained using the modified PDE method.
6. A Numerical Algorithm for Solving a Four-Point Nonlinear Fractional Integro-Differential Equations
OpenAIRE
Gao, Er; Song, Songhe; Zhang, Xinjian
2012-01-01
We provide a new algorithm for a four-point nonlocal boundary value problem of nonlinear integro-differential equations of fractional order q∈(1,2] based on reproducing kernel space method. According to our work, the analytical solution of the equations is represented in the reproducing kernel space which we construct and so the n-term approximation. At the same time, the n-term approximation is proved to converge to the analytical solution. An illustrative example is also presented, which sh...
7. Newton-Raphson based modified Laplace Adomian decomposition method for solving quadratic Riccati differential equations
Directory of Open Access Journals (Sweden)
Mishra Vinod
2016-01-01
Full Text Available Numerical Laplace transform method is applied to approximate the solution of nonlinear (quadratic Riccati differential equations mingled with Adomian decomposition method. A new technique is proposed in this work by reintroducing the unknown function in Adomian polynomial with that of well known Newton-Raphson formula. The solutions obtained by the iterative algorithm are exhibited in an infinite series. The simplicity and efficacy of method is manifested with some examples in which comparisons are made among the exact solutions, ADM (Adomian decomposition method, HPM (Homotopy perturbation method, Taylor series method and the proposed scheme.
8. Two-dimensional differential transform method for solving linear and non-linear Schroedinger equations
International Nuclear Information System (INIS)
Ravi Kanth, A.S.V.; Aruna, K.
2009-01-01
In this paper, we propose a reliable algorithm to develop exact and approximate solutions for the linear and nonlinear Schroedinger equations. The approach rest mainly on two-dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and nonlinear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. Several illustrative examples are given to demonstrate the effectiveness of the present method.
9. A Numerical Algorithm for Solving a Four-Point Nonlinear Fractional Integro-Differential Equations
Directory of Open Access Journals (Sweden)
Er Gao
2012-01-01
Full Text Available We provide a new algorithm for a four-point nonlocal boundary value problem of nonlinear integro-differential equations of fractional order q∈(1,2] based on reproducing kernel space method. According to our work, the analytical solution of the equations is represented in the reproducing kernel space which we construct and so the n-term approximation. At the same time, the n-term approximation is proved to converge to the analytical solution. An illustrative example is also presented, which shows that the new algorithm is efficient and accurate.
10. A Four-Stage Fifth-Order Trigonometrically Fitted Semi-Implicit Hybrid Method for Solving Second-Order Delay Differential Equations
Directory of Open Access Journals (Sweden)
2016-01-01
Full Text Available We derived a two-step, four-stage, and fifth-order semi-implicit hybrid method which can be used for solving special second-order ordinary differential equations. The method is then trigonometrically fitted so that it is suitable for solving problems which are oscillatory in nature. The methods are then used for solving oscillatory delay differential equations. Numerical results clearly show the efficiency of the new method when compared to the existing explicit and implicit methods in the scientific literature.
11. Magnetic Evidence for a Partially Differentiated Carbonaceous Chondrite Parent Body and Possible Implications for Asteroid 21 Lutetia
Science.gov (United States)
Weiss, Benjamin; Carporzen, L.; Elkins-Tanton, L.; Shuster, D. L.; Ebel, D. S.; Gattacceca, J.; Binzel, R. P.
2010-10-01
The origin of remanent magnetization in the CV carbonaceous chondrite Allende has been a longstanding mystery. The possibility of a core dynamo like that known for achondrite parent bodies has been discounted because chondrite parent bodies are assumed to be undifferentiated. Here we report that Allende's magnetization was acquired over several million years (Ma) during metasomatism on the parent planetesimal in a > 20 microtesla field 8-9 Ma after solar system formation. This field was present too recently and directionally stable for too long to have been the generated by the protoplanetary disk or young Sun. The field intensity is in the range expected for planetesimal core dynamos (Weiss et al. 2010), suggesting that CV chondrites are derived from the outer, unmelted layer of a partially differentiated body with a convecting metallic core (Elkins-Tanton et al. 2010). This suggests that asteroids with differentiated interiors could be present today but masked under chondritic surfaces. In fact, CV chondrites are spectrally similar to many members of the Eos asteroid family whose spectral diversity has been interpreted as evidence for a partially differentiated parent asteroid (Mothe-Diniz et al. 2008). CV chondrite spectral and polarimetric data also resemble those of asteroid 21 Lutetia (e.g., Belskaya et al. 2010), recently encountered by the Rosetta spacecraft. Ground-based measurements of Lutetia indicate a high density of 2.4-5.1 g cm-3 (Drummond et al. 2010), while radar data seem to rule out a metallic surface composition (Shepard et al. 2008). If Rosetta spacecraft measurements confirm a high density and a CV-like surface composition for Lutetia, then we propose Lutetia may be an example of a partially differentiated carbonaceous chondrite parent body. Regardless, the very existence of primitive achondrites, which contain evidence of both relict chondrules and partial melting, are prima facie evidence for the formation of partially differentiated bodies.
12. A Simple Differential Modulation Scheme for Quasi-Orthogonal Space-Time Block Codes with Partial Transmit Diversity
Directory of Open Access Journals (Sweden)
Lingyang Song
2007-04-01
Full Text Available We report a simple differential modulation scheme for quasi-orthogonal space-time block codes. A new class of quasi-orthogonal coding structures that can provide partial transmit diversity is presented for various numbers of transmit antennas. Differential encoding and decoding can be simplified for differential Alamouti-like codes by grouping the signals in the transmitted matrix and decoupling the detection of data symbols, respectively. The new scheme can achieve constant amplitude of transmitted signals, and avoid signal constellation expansion; in addition it has a linear signal detector with very low complexity. Simulation results show that these partial-diversity codes can provide very useful results at low SNR for current communication systems. Extension to more than four transmit antennas is also considered.
13. A hybrid algorithm for coupling partial differential equation and compartment-based dynamics.
Science.gov (United States)
Harrison, Jonathan U; Yates, Christian A
2016-09-01
Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing particle numbers. An alternative description of many of these systems can be derived in the diffusive limit as a deterministic, continuum system of partial differential equations (PDEs). Although the numerical solution of such PDEs is, in general, much more efficient than the full stochastic simulation, the deterministic continuum description is generally not valid when copy numbers are low and stochastic effects dominate. Therefore, to take advantage of the benefits of both of these types of models, each of which may be appropriate in different parts of a spatial domain, we have developed an algorithm that can be used to couple these two types of model together. This hybrid coupling algorithm uses an overlap region between the two modelling regimes. By coupling fluxes at one end of the interface and using a concentration-matching condition at the other end, we ensure that mass is appropriately transferred between PDE- and compartment-based regimes. Our methodology gives notable reductions in simulation time in comparison with using a fully stochastic model, while maintaining the important stochastic features of the system and providing detail in appropriate areas of the domain. We test our hybrid methodology robustly by applying it to several biologically motivated problems including diffusion and morphogen gradient formation. Our analysis shows that the resulting error is small, unbiased and does not grow over time. © 2016 The Authors.
14. Ionic diffusion through confined geometries: from Langevin equations to partial differential equations
International Nuclear Information System (INIS)
Nadler, Boaz; Schuss, Zeev; Singer, Amit; Eisenberg, R S
2004-01-01
Ionic diffusion through and near small domains is of considerable importance in molecular biophysics in applications such as permeation through protein channels and diffusion near the charged active sites of macromolecules. The motion of the ions in these settings depends on the specific nanoscale geometry and charge distribution in and near the domain, so standard continuum type approaches have obvious limitations. The standard machinery of equilibrium statistical mechanics includes microscopic details, but is also not applicable, because these systems are usually not in equilibrium due to concentration gradients and to the presence of an external applied potential, which drive a non-vanishing stationary current through the system. We present a stochastic molecular model for the diffusive motion of interacting particles in an external field of force and a derivation of effective partial differential equations and their boundary conditions that describe the stationary non-equilibrium system. The interactions can include electrostatic, Lennard-Jones and other pairwise forces. The analysis yields a new type of Poisson-Nernst-Planck equations, that involves conditional and unconditional charge densities and potentials. The conditional charge densities are the non-equilibrium analogues of the well studied pair correlation functions of equilibrium statistical physics. Our proposed theory is an extension of equilibrium statistical mechanics of simple fluids to stationary non-equilibrium problems. The proposed system of equations differs from the standard Poisson-Nernst-Planck system in two important aspects. First, the force term depends on conditional densities and thus on the finite size of ions, and second, it contains the dielectric boundary force on a discrete ion near dielectric interfaces. Recently, various authors have shown that both of these terms are important for diffusion through confined geometries in the context of ion channels
15. Fourier method for three-dimensional partial differential equations in periodic geometry. Application: HELIAC
International Nuclear Information System (INIS)
Shestakov, A.I.; Mirin, A.A.
1984-01-01
A numerical method based on Fourier expansions and finite differences is presented. The method is demonstrated by solving a scalar, three-dimensional elliptic equation arising in MFE research, but has applicability to a wider class of problems. The scheme solves equations whose solutions are expected to be periodic in one or more of the independent variables
16. Iterative Observer-based Estimation Algorithms for Steady-State Elliptic Partial Differential Equation Systems
KAUST Repository
2017-01-01
the problems are formulated on higher dimensional space domains. However, in this dissertation, feedback based state estimation algorithms, known as state observers, are developed to solve such steady-state problems using one of the space variables as time
17. A Solution Space for a System of Null-State Partial Differential Equations: Part 1
Science.gov (United States)
Flores, Steven M.; Kleban, Peter
2015-01-01
This article is the first of four that completely and rigorously characterize a solution space for a homogeneous system of 2 N + 3 linear partial differential equations (PDEs) in 2 N variables that arises in conformal field theory (CFT) and multiple Schramm-Löwner evolution (SLE). In CFT, these are null-state equations and conformal Ward identities. They govern partition functions for the continuum limit of a statistical cluster or loop-gas model, such as percolation, or more generally the Potts models and O( n) models, at the statistical mechanical critical point. (SLE partition functions also satisfy these equations.) For such a lattice model in a polygon with its 2 N sides exhibiting a free/fixed side-alternating boundary condition , this partition function is proportional to the CFT correlation function where the w i are the vertices of and where is a one-leg corner operator. (Partition functions for "crossing events" in which clusters join the fixed sides of in some specified connectivity are linear combinations of such correlation functions.) When conformally mapped onto the upper half-plane, methods of CFT show that this correlation function satisfies the system of PDEs that we consider. In this first article, we use methods of analysis to prove that the dimension of this solution space is no more than C N , the Nth Catalan number. While our motivations are based in CFT, our proofs are completely rigorous. This proof is contained entirely within this article, except for the proof of Lemma 14, which constitutes the second article (Flores and Kleban, in Commun Math Phys, arXiv:1404.0035, 2014). In the third article (Flores and Kleban, in Commun Math Phys, arXiv:1303.7182, 2013), we use the results of this article to prove that the solution space of this system of PDEs has dimension C N and is spanned by solutions constructed with the CFT Coulomb gas (contour integral) formalism. In the fourth article (Flores and Kleban, in Commun Math Phys, arXiv:1405
18. A Solution Space for a System of Null-State Partial Differential Equations: Part 2
Science.gov (United States)
Flores, Steven M.; Kleban, Peter
2015-01-01
19. A Solution Space for a System of Null-State Partial Differential Equations: Part 4
Science.gov (United States)
Flores, Steven M.; Kleban, Peter
2015-01-01
This article is the last of four that completely and rigorously characterize a solution space for a homogeneous system of 2 N + 3 linear partial differential equations in 2 N variables that arises in conformal field theory (CFT) and multiple Schramm-Löwner evolution (SLE). The system comprises 2 N null-state equations and three conformal Ward identities that govern CFT correlation functions of 2 N one-leg boundary operators. In the first two articles (Flores and Kleban in Commun Math Phys, 2012; Flores and Kleban, in Commun Math Phys, 2014), we use methods of analysis and linear algebra to prove that dim , with C N the Nth Catalan number. Using these results in the third article (Flores and Kleban, in Commun Math Phys, 2013), we prove that dim and is spanned by (real-valued) solutions constructed with the Coulomb gas (contour integral) formalism of CFT. In this article, we use these results to prove some facts concerning the solution space . First, we show that each of its elements equals a sum of at most two distinct Frobenius series in powers of the difference between two adjacent points (unless is odd, in which case a logarithmic term may appear). This establishes an important element in the operator product expansion for one-leg boundary operators, assumed in CFT. We also identify particular elements of , which we call connectivity weights, and exploit their special properties to conjecture a formula for the probability that the curves of a multiple-SLE process join in a particular connectivity. This leads to new formulas for crossing probabilities of critical lattice models inside polygons with a free/fixed side-alternating boundary condition, which we derive in Flores et al. (Partition functions and crossing probabilities for critical systems inside polygons, in preparation). Finally, we propose a reason for why the exceptional speeds [certain values that appeared in the analysis of the Coulomb gas solutions in Flores and Kleban (Commun Math Phys, 2013)] and
20. A Solution Space for a System of Null-State Partial Differential Equations: Part 3
Science.gov (United States)
Flores, Steven M.; Kleban, Peter
2015-01-01
This article is the third of four that completely and rigorously characterize a solution space for a homogeneous system of 2 N + 3 linear partial differential equations (PDEs) in 2 N variables that arises in conformal field theory (CFT) and multiple Schramm-Löwner evolution (SLE κ ). The system comprises 2 N null-state equations and three conformal Ward identities that govern CFT correlation functions of 2 N one-leg boundary operators. In the first two articles (Flores and Kleban, in Commun Math Phys, arXiv:1212.2301, 2012; Commun Math Phys, arXiv:1404.0035, 2014), we use methods of analysis and linear algebra to prove that dim , with C N the Nth Catalan number. Extending these results, we prove in this article that dim and entirely consists of (real-valued) solutions constructed with the CFT Coulomb gas (contour integral) formalism. In order to prove this claim, we show that a certain set of C N such solutions is linearly independent. Because the formulas for these solutions are complicated, we prove linear independence indirectly. We use the linear injective map of Lemma 15 in Flores and Kleban (Commun Math Phys, arXiv:1212.2301, 2012) to send each solution of the mentioned set to a vector in , whose components we find as inner products of elements in a Temperley-Lieb algebra. We gather these vectors together as columns of a symmetric matrix, with the form of a meander matrix. If the determinant of this matrix does not vanish, then the set of C N Coulomb gas solutions is linearly independent. And if this determinant does vanish, then we construct an alternative set of C N Coulomb gas solutions and follow a similar procedure to show that this set is linearly independent. The latter situation is closely related to CFT minimal models. We emphasize that, although the system of PDEs arises in CFT in away that is typically non-rigorous, our treatment of this system here and in Flores and Kleban (Commun Math Phys, arXiv:1212.2301, 2012; Commun Math Phys, arXiv:1404 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8367392420768738, "perplexity": 847.5544810341227}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178362899.14/warc/CC-MAIN-20210301182445-20210301212445-00537.warc.gz"} |
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Mar 26 comment PlayRange option ignored when exporting Try Block[{Rescale = # &}, Export[...]] Mar 24 comment Why is the range from $-\pi$ to $\pi$ in polar coordinates? Another possible factor in the decision is to ensure that FromPolarCoordinates and ToPolarCoordinates are exact inverses. Mar 22 comment General techniques for creating complex animations @LLlAMnYP, thanks. I think the code is confusing too! I had the idea to use an association so that chunks of graphics could be named, which then drove the whole thing in a weird direction. I have a much better version now which I'll try to post later. Mar 17 comment Has compilation of big programs become excessively sluggish in v 10.4? It looks like it's the typesetting that takes all the time. Try using SetSystemOptions["TypesetOptions" -> {"IconicElidedForms" -> False}] Mar 9 comment Create “Ostagram” like Images using Wavelet Transforms Do you have any reason to expect that this wavelet operation can give anything remotely like the deep neural network images? Mar 9 comment Create “Ostagram” like Images using Wavelet Transforms It would help to include example images Mar 8 comment How can I generate this “domain coloring” plot? @Mr.Wizard, I'll update it. The original contained two errors and I only fixed one. Feb 24 comment Export audio with frames? I'm pretty sure there is no way to export any kind of movie file with an audio stream. You will probably have to use a separate application. Feb 24 comment Calculate area of black sea from image Possible duplicate Feb 22 comment Using BandpassFilter delta is given in Hz so you need to multiply it by 2Pi Feb 20 comment Automatic Ticks on x-axis, but not first 5% of x-range @AlexeyPopkov, good point. I had forgotten that you could supply a function for Ticks. Feb 20 comment Why is ListPlot so slow here? I wondered about injecting timing information into the Trace to help locate the problem area in the huge output, but Trace adds its own delays. Feb 20 comment Why is ListPlot so slow here? It's no better in 10.3.1. I tried this but it wasn't as informative as I'd hoped: Module[{a = AbsoluteTime[]}, Block[{ChartingdbPrint = Print[AbsoluteTime[] - a, " ", #] &}, ListPlot[dat]]] Feb 20 comment Automatic Ticks on x-axis, but not first 5% of x-range I don't think so. Ticks are either fully automatic or explicitly specified. Feb 20 comment How to put Magnification control in docked cell related Feb 16 comment Memory limit hit: optimize code for finding twin primes Yes p was included twice in the original code - once in primesList and again explicitly in twinPrimes. 5 also appears in both. You can remove both of those from primesList and also work from small numbers up by changing the range in primesList to Range[PrimePi[p-1], 4, -1] Feb 16 comment Memory limit hit: optimize code for finding twin primes Checking all possible products would rapidly become impractical. For the m'th prime the number of products to check is (pl+1)^(m-3), for example in testPrime[Prime[100],1] you would be testing 2^97 products. I'm getting a loop time of around 3ms so you'd be looking at something over 10^19 years for it to complete, or a billion times the age of the universe. Feb 16 comment Memory limit hit: optimize code for finding twin primes You should be able to use testPrime in parallel, e.g. ParallelTable[testPrime[Prime[j], 1], {j, 4, 1000}] Feb 15 comment Brackets around each item in matrix I get similar results, to within a scaling factor for my slow CPU. Interesting that Join is much worse on packed arrays! Feb 14 comment Role of Accuracy in numerical evaluations, SplitBy vs GatherBy A simpler formulation of the same fundamental question: Given list = SetAccuracy[{1, 1, 1.01, 1.01, 1.02, 1.02}, 2] why does Gather[list] give a different result from Split[list] | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3832150399684906, "perplexity": 2150.8827091281846}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461860126377.4/warc/CC-MAIN-20160428161526-00082-ip-10-239-7-51.ec2.internal.warc.gz"} |
http://math.stackexchange.com/users/25159/matt-pressland?tab=activity&sort=reviews | # Matt Pressland
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Postgraduate student at the University of Bath, UK, studying geometry and representation theory. Currently thinking about cluster algebras and related objects.
# 482 Reviews
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https://rd.springer.com/article/10.1007%2Fs10584-018-2320-1 | Climatic Change
pp 1–18
# Risk perception and decision-making: do farmers consider risks from climate change?
• Anton Eitzinger
• Claudia R. Binder
• Markus A. Meyer
Open Access
Article
## Abstract
Small-scale farmers are highly threatened by climate change. Experts often base their interventions to support farmers to adapt to climate change on their own perception of farmers’ livelihood risks. However, if differences in risk perception between farmers and experts exist, these interventions might fail. Thus, for effective design and implementation of adaptation strategies for farmers, it is necessary to understand farmers’ perception and how it influences their decision-making. We analyze farmers’ and experts’ systemic view on climate change threats in relation to other agricultural livelihood risks and assess the differences between their perceptions. For Cauca, Colombia, we found that experts and farmers perceived climate-related and other livelihood risks differently. While farmers’ perceived risks were a failure in crop production and lack of access to health and educational services, experts, in contrast, perceived insecurity and the unreliable weather to be the highest risks for farmers. On barriers that prevent farmers from taking action against risks, experts perceived both external factors such as the national policy and internal factors such as the adaptive capacity of farmers to be the main barriers. Farmers ranked the lack of information, especially about weather and climate, as their main barrier to adapt. Effective policies aiming at climate change adaptation need to relate climate change risks to other production risks as farmers often perceive climate change in the context of other risks. Policymakers in climate change need to consider differences in risk perception.
## 1 Introduction
Climate change poses major challenges to our society, especially in the agricultural sector in developing countries (Vermeulen et al. 2011). Experts have argued that adaptation and mitigation actions are urgently needed to pave climate-resilient pathways for the future (IPCC 2014a). One major challenge with the design and implementation of adequate actions is the complexity of the systems characterized by interactions between environmental and human dynamics at different scales (Turner et al. 2003). Delayed and unexpected feedback loops, nonlinearities, and abrupt rather than gradual changes render the climate system exceedingly hard to predict and the reactions of the exposed human system even less foreseeable (Alley et al. 2003). These entailed uncertainties make decision- and policymaking a difficult task.
The difficulties in climate-relevant decision- and policymaking in agriculture are further aggravated by differing perceptions of climate change by experts and farmers. Despite the scientific consensus about existence, risks, and possible solutions to climate change, nonspecialists largely seem to underestimate and misinterpret these causes and risks (Ding et al. 2011). This is partly due to two key facts: first, most people do not differentiate between weather and climate (Weber 2010) and are thereby unable to distinguish climate variability from climate change (Finnis et al. 2015). Second, most people still perceive the likelihood that climate change might affect them directly as low (Weber 2010; Barnes and Toma 2011; Lee et al. 2015). When taking decisions towards adaptation, people tend to relate possible actions to probable consequences in a linear manner without considering feedback loops, delays, and nonlinearities (Weber 2006). The success of agricultural climate policies relies to a large extent on farmers’ awareness of climate change including their knowledge and beliefs regarding climate change and how it will affect them (Patt and Schröter 2008; Carlton et al. 2016).
Scholars have found that small-scale farmers in Latin America are highly vulnerable to climate change (Baca et al. 2014; Eitzinger et al. 2014). While farmers have adapted continuously to social and environmental change in the past, the magnitude of climate change strikes the already stressed rural population. In Latin America, inequality and economic vulnerability call for an approach that tackles the underlying causes of vulnerability before implementing adaptation strategies (Eakin and Lemos 2010). Without visualizing climate change as one of the multiple exposures, small-scale farmers rarely adapt their farming practices even if suggested by climate policies (Niles et al. 2015). This reluctance is greatly influenced by the farmers’ beliefs and perception concerning causes and local impacts of climate change (Haden et al. 2012).
Furthermore, adaptive actions are driven by individuals and groups ideally supported by institutions and governmental organizations. In many countries in Latin America, the influence of governments has become weaker due to economic liberalization. Thus, governance mechanisms have lost their capacity to manage risks and to address issues of social vulnerability, especially in rural areas (Eakin and Lemos 2006).
“By 2050, climate change in Colombia will likely impact 3.5 million people” (Ramirez-Villegas et al. 2012, p. 1), and scenarios of impacts from long-term climate change will likely threaten socioeconomics of Colombian agriculture. In Colombia’s southwestern department Cauca, the average increase in annual temperature to the 2050s is estimated to be 2.1 °C with a minor increase in precipitation (Ramirez-Villegas et al. 2012). In this region, coffee farmers face several challenges through climate change, like shifting suitable areas into higher altitudes, implying reduced yields and increasing pest and disease pressure (Ovalle-Rivera et al. 2015). Ovalle-Rivera et al. (2015) estimate a national average of 16% decrease of climate suitability for coffee in Colombia by 2050, mostly for areas below 1800 m a.s.l.
During the twentieth century, Colombia’s agrarian reform was the best example of failed top-down approaches to promote self-reliant grassroots organizations in agriculture (Gutiérrez 2014), which might be more likely to adapt to climate change. Vulnerabilities in Colombia are structural and need to be addressed through transformative adaptation (Feola 2013). First, rural populations in Colombia, and especially resource-limited farmers, depend on natural resources and are particularly sensitive to environmental stress. Second, the level of human security is low and tied to deeply rooted socioeconomic and political inequality. Third, the institutional setting is a mix of formal and informal institutions that facilitate or impede building adaptive capacity of farmers (Eakin and Lemos 2010; Feola 2013).
For the successful adaptation of Colombian agriculture to agricultural risks from climate, the government should set up enabling policies and release funds for research and development to subsectors (Ramirez-Villegas and Khoury 2013). Adaptation options should be developed based on underlying vulnerability analysis and participatory processes with farmers and experts (Feola 2013). The interaction between grassroots organizations (bottom-up) and institutions (top-down) is crucial for transformative adaptation (Bizikova et al. 2012).
The development of adaptation options is hampered by the fact that experts often have an incomplete view of farmers’ perceptions which might have vast implications for effective risk communication, e.g., regarding climate change, and during the participatory design process of adaptation strategies (Thomas et al. 2015). These findings imply that an improved, in-depth understanding of the differences in risk perception between farmers and experts is necessary for the design of more effective and successful policies to promote adaptation initiatives.
To gauge the prevailing perception of various groups, mental models (MMs) have been successfully employed in the past, for example, to elicit farmers’ perceptions and underlying views on livelihood risks (Schoell and Binder 2009; Binder and Schöll 2010; Jones et al. 2011). MMs provide insight into perceptions and priority setting of individuals (Morgan et al. 2002) and can help to understand risk perceptions and to inform the design of effective risk communication strategies. In risk analysis, MMs have been used to identify how individuals construct representations of risk (Atman et al. 1994; Schöll and Binder 2010; Binder and Schöll 2010). Based on the mental model approach (MMA) (Morgan et al. 2002), Binder and Schöll (2010) developed the structured mental model approach (SMMA). The SMMA combines the so-called sustainable livelihood framework (SLF) (Scoones 1998)—a framework that shows how sustainable livelihoods are achieved through access to resources of livelihood capitals with the MMA (Morgan et al. 2002). The SMMA can help to understand how farmers perceive and balance livelihood risks for their agricultural practices (Schoell and Binder 2009; Binder and Schöll 2010).
This study aims (i) to understand how climate risks are integrated in the context of other risks in the farmers’ perception and decision-making process for taking action, (ii) to identify differences between farmers’ and experts’ mental models regarding farmers’ agricultural risk perception, and (iii) to elaborate on possible consequences for policies addressing farmers’ livelihood risks and their agricultural adaptation strategies in the face of climate change.
The paper is structured as follows: first, we present material and methods on how we analyze climate risks in the context of farmers’ livelihood risks and analyze differences in perception between farmers’ and experts’ MMs. Second, we present results from applying our approach to the Cauca Department in Colombia (South America) as an exemplary study for a region for small-scale farmers in a developing country. Finally, we discuss our findings concerning other literature and draw our conclusions.
## 2 Material and methods
### 2.1 Study area
The Cauca Department is located in the southwestern part of Colombia with a size of approximately 30,000 km2. Cauca is composed of a lowland coastal region, two Cordilleras of the Andes, and an inner Andean valley. Agricultural land is concentrated in the inner Andean valley. According to the latest agricultural census (DANE 2014), 83% of the farmers in Cauca have a low educational achievement (elementary school only), 22% are illiterate, and 52% live in poverty according to Colombia’s Multidimensional Poverty Index (Salazar et al. 2011). The main stressors for agriculture and farmers alongside climate change are trade liberalization and violent conflicts (Feola et al. 2015). Colombia has one of the longest ongoing civil conflicts and one of the highest rates of internal displacement, estimated to be 7% of the country’s population and 29% of the rural population (Ibáñez and Vélez 2008). Cauca is one of the regions in Colombia with a high rate of violence from armed conflicts (Holmes et al. 2006). Especially for small farm households, weak institutional support and absence of the state in rural areas have led to unequal land distribution and lacking technical assistance as well as financial services for agricultural transformation (Pérez Correa and Pérez Martínez 2002).
Due to Cauca’s proximity to the Pacific Ocean, the region is subject to inter-annual climate variability mainly driven by the El Niño Southern Oscillation (ENSO) (Poveda et al. 2001), a feature that has great influence on agricultural productivity and, in consequence, farmers’ livelihood. A study by the CGIAR Research Program on Climate Change, Agriculture and Food Security (CCAFS) shows that farmers in the study area are mostly affected by more frequent droughts, storm and hail events, more erratic rains, and landslides as a consequence of heavy rains (Garlick 2016). Even if uncertainty in future scenarios of extreme events is still high, changes in inter-annual climate variability are of high relevance for farmers; there is agreement that more intense and frequent extreme events are likely to be observed in the future (IPCC 2014b).
The Cauca region is particularly relevant for these types of analyses as (i) the region has a high potential of being affected by climate change, (ii) interventions for rural development by the government have been weak in the past, and (iii) because of the national and international efforts to implement the peace process, Cauca has caught attention for implementing development interventions. Many of these interventions could benefit from an in-depth understanding of farmers’ perceptions regarding the climate and nonclimate risks affecting their livelihoods.
Exemplary for Cauca, we selected a geographical domain of 10 km2 with altitudes between 1600 and 1800 m a.s.l. within the boundaries of the municipality Popayan. We conducted the interviews with experts and farmers in five rural villages and selected randomly 11 to 12 farmers each village (see details on sampling design in Chapter 2.4). The farm size of interviewees was between 1 and 4 ha, half of them (45%) possessed legal land titles, and 41% of farmers have started the legalization process recently. The average age of interviewees was 47 years old, 48% of them were women farmer, and the average household size was five people. Overall, 74% of farmers depend on coffee (Coffea arabica) as their main agricultural livelihood besides other crops and some livestock to complement income and for self-consumption. Other crops and livestock that are managed in the farming systems are cassava (Manihot esculenta), dry beans (Phaseolus vulgaris), maize (Zea mays), banana (Musa acuminata), cattle, and poultry. As the second most important crop, 19% of interviewed households depend on sugarcane (Saccharum officinarum) and the derived product panela, which is unrefined sugar in compact loaves of a rectangular shape. Most of farmers’ income is coming from on-farm agricultural activities and also from off-farm day labor activities in the agricultural sector (harvest coffee in other farms). Generally, there are few job opportunities in the study area.
### 2.2 Assessment of climate risks
Before we started analyzing risk perceptions, we conducted an assessment of climate risks and impacts on main crops grown in the region and reviewed existing literature on the vulnerability of farmers in the study area. First, we compared anomalies of precipitation, maximum temperature, and minimum temperature in the study area with records about ENSO events. We used data of a local weather station from the Instituto de Hidrologia, Meteorologia y Estudios Ambientales de Colombia (IDEAM) and data of the Oceanic Niño Index (ONI) from the National Oceanic and Atmospheric Administration (NOAA) (NOAA 2014). Second, we used a simple climate envelope model to analyze the current and future climate suitability of six crops in the study area. Finally, we reviewed the existing literature on climate change impact assessment for Colombia. Detailed results of climate risk assessment in the study area are presented in Online Resource 1.
### 2.3 Analyzing mental models to understand perceptions
Figure 1 presents the conceptual approach of the study. Farmers’ perceptions regarding climate risks are shaped by their knowledge about the causes of climate change, their beliefs, social norms, and values as well as through their experience with climate-related information and past climate-related events. However, farmers’ decision-making is not only shaped by climate risks, but other agricultural production risks are also equal or even more important for farmers. Farmers consider the complete mental model of risks when envisioning goals concerning their livelihood strategy and make appropriate decisions about investments and adaptations of the agricultural production system. In applying our approach, we captured experts’ external views of farmers’ perception and compared it to the farmers’ internal views.
To assess the importance of climate risks in the context of another risk in farmers’ agricultural production system, we identified differences between the perception of farmers and that of experts regarding climate risks as placed in the context of other risks within the farmers’ livelihood system by analyzing and comparing each group’s MMs. The experts’ perspective on farmers’ perceptions represented the external view, whereas the perspective of the farmers themselves represented the internal one. We captured the external and internal views on climate risks with two sets of structured interviews with experts and farmers, and we used ranking techniques to show differences in perception.
### 2.4 Interviews with experts and farmers
A qualitative semi-structured interview study was conducted between June and September 2014 to examine perceptions of experts and farmers about farmers’ livelihood risks and farmers’ barriers for adaptation to cope with risks they face in agricultural production. In a first step, we conducted open interviews with 13 experts. In order to obtain a holistic view of experts’ perceptions, we included regional, national, and international experts from different fields of the analyzed agro-environmental system, namely four agronomists, three economists, one environmental lawyer, one public government administrator, one nutritionist, one climate change scientist, one ecologist, and one veterinarian. All experts have been regularly working with farmers in the study region during the last 5 to 10 yrs and have still been working with them at the time of the study. Following the expert interviews, we conducted 58 semi-structured interviews with farmers from five different villages in the municipality of Popayan, performing between 10 and 12 farmer interviews from different households and for each village. The total population of farmers of the five villages was 499 at the time of the interviews. We included farmers aged 20 to 60, and we designed the sample to ensure an equal representation of women and men. Morgan et al. (2002) judge a small sample for interviews within a population group that has relatively similar beliefs as reasonable. Schoell and Binder (2009) found for the case of small farmers in Boyacá, Colombia, that after 5–10 interviews, no more new concepts emerged (Binder et al. 2015). To avoid interruption from notes taken by the interviewer and to keep the natural flow of conversation, we recorded all interviews with the consent of the participants. Subsequently, we transcribed the records of the interviews for the analysis. The used guidebook for expert interviews can be found in Online Resource 2 and the guidebook for farmer interviews in Online Resource 3.
First, we assessed the experts’ views on the farmers’ concerns, risks, barriers for taking action, and enablers to take action by asking the following questions:
• What are the farmers’ main livelihood concerns?
• Which risks do farmers face in agricultural production?
• Which are farmers’ barriers to cope with these risks?
• What motivates (enablers) farmers to cope and adapt?
In the expert interviews, we received answers and explanations to the four guiding questions about farmers’ concerns, risks, barriers for taking action, and enablers to take action when facing risks in agricultural production. We noted all answers of experts for each question on small cards. Answers from all experts were pooled after finishing all the interviews; we got 16 concerns, 10 risks, 13 barriers for taking action, and eight enablers to take action. Based on the pooled elements, we used an online survey tool to ask the same group of experts to rank all compiled elements according to the importance of the elements for farmers. The highest ranked elements by experts were then selected to start the farmer interviews.
Second, we carried out the farmers’ interviews. After explaining the overall purpose of the study briefly as part of informed consent with farmers, we visualized the elements of the experts through drawings we created for each question and then asked farmers to rank them according to their priorities. After piloting the interviews with farmers, we decided to use only the six highest ranked elements by experts to keep the ranking exercise for farmers simple. In addition, we asked farmers at the end of each ranking if they would consider other elements to be more important for them that the ones we used for the ranking (see Online Resource 3). We did not mention climate change during the interviews for a specific purpose. Farmers should rank the card elements without being biased by knowing the purpose of the interview, namely to understand how they perceive climate risks in relation to other livelihood risks.
After finishing both interview series, we analyzed the differences in perception between experts and farmers. To aggregate the individual rankings, we calculated a weighted average based on the ranking of each element for the four questions. The overall ranking of experts and farmers was calculated separately as follows:
$${f}_{\mathrm{ranking}}=\frac{\sum_{i=0}^n\left({x}_i\times {w}_i\right)}{n}$$
where w is the weight, x the response count of an answer choice of each question, and n the total number of answer elements. In our case of six elements per question, we calculated the average ranking using weights starting at 6 for the highest ranked element and decreasing towards 1 for the lowest ranked element.
We compared the average experts’ rankings to farmers’ rankings stratified by gender and age group and then applied the hierarchical clustering approach (Ward 1963) to the farmers’ rankings to obtain groups of farmers with similar choices. The hierarchical clustering approach by Ward (1963) is a widely used data analysis approach for similarity grouping to determine distinct subgroups with similar characteristics (Vigneau and Qannari 2003). After obtaining groups of farmers from clusters, we described them based on high ranks using first and second ranked answers each question and demographic variables collected during the surveys.
## 3 Results
### 3.1 Climate change risks in the study area
Figure 2 shows that inter-annual rainfall variability is high. High variability in rainfall can be observed between October and February for long-term weather records since 1980. Inter-annual climate variations in the study area are mainly driven by the ENSO. The consequences of ENSO for farmers and agricultural production are prolonged droughts (El Niño) or intense rainfall over more extended periods (La Niña). The assessment of the six most relevant crops in the study area revealed that variation in crop exposure to climate variability in Cauca is high (see Online Resource 1). Farm households in the study area grow coffee, sugarcane, maize, dry beans, banana, and cassava. While banana, sugarcane, and cassava can better cope with long-term climate change scenarios, dry beans and coffee are more likely affected by increasing mean annual temperatures. Production of coffee and dry beans represents an important livelihood for farmers in the study region but will likely face impacts through climate change in the future. See Online Resource 1 for more details on climate change risks in the study area.
### 3.2 Farmers’ rankings and differences to experts’ rankings
We found that experts and farmers perceived farmers’ livelihood concerns and enablers for adaptation to agricultural production risks similarly, but risks and barriers for adaptation differently (see Fig. 3). Also, farmers agreed on the selected answers as the most relevant for them for each question; only a few farmers mentioned other elements. Beyond, the most mentioned elements by farmers were concerns about health (five times) and access to tap water (three times).
Older farmers are more worried about climate change than younger farmers but rank production failure low as risk (see Fig. 4). Interestingly, older farmers saw insecure transport as a major risk and production failure as a lower risk, whereas this was the opposite for younger farmers.
Regarding farmers’ concerns (Fig. 3a), we found two issues experts and farmers agreed upon: poverty is a chief concern in this region (ranked first by experts and second by farmers) and neither climate change nor security problems are perceived to be relevant in the study area. The key differences in perceived concerns were related to government policies, access to credit, and market opportunities. Farmers were highly worried regarding government policies (rank 1). They argued: “The government in the capital, Bogota, is too far away and does not take into account the context of our region when making new laws” (farmer’s interview, translated from Spanish, Colombia, October 2014). Experts ranked government policies lower with respect to concerns (rank 3), but they agreed in their explanations with farmers that: “The government is focusing on international trade agreements and is supporting medium-sized and large farmers, they are not investing in small-scale farmers’ production” (expert’s interview, translated from Spanish, Colombia, August 2014). Both male and female farmers were highly worried regarding their access to credit to be able to pay for labor and to purchase inputs for crop production (rank 3). Experts, on the other hand, did not perceive that farmers need to be worried about having access to credit (rank 6). In contrast, experts believed that farmers were worried about market opportunities—a perception shared more often by women than by men (see Fig. 3a).
The main differences in the rankings between experts and farmers were related to risks (Fig. 3b). For farmers, the highest perceived risks were a failure in crop production and social vulnerability (lack of access to health and educational services). Experts, in contrast, perceived insecurity (theft of products from plots or during transportation) and the unreliable weather to be the highest risks for farmers. From a gender perspective, results showed that women and men disagreed in rankings with experts for few themes. Whereas women agreed with experts that insufficient planning is a major risk (even ranking it higher than experts), men agreed with experts that insecurity is a high risk (for women, this was among the lowest risks). The risk rankings showed clearly that farmers see the symptoms of social inequality (first rank of social vulnerability), agricultural production, and market risks such as unstable prices or production failure. Farmers ranked insufficient planning lower and unreliable weather very low compared to experts. These results showed that experts rather ranked risks from climate higher than farmers did. Experts would rather expect a higher planning activity of the farmers for adaptation to climate risks. Contrastingly, farmers believed that they were doing already as much as they could.
The agreement between experts and farmers was mostly on farmers’ motivations (enablers to adaptation), which were family interests, increased quality of life, and traditional attachment to land (Fig. 3d). Regarding the motivations, one expert mentioned during the interview that: “Farmers in Cauca do have a strong connection to their roots. Territories and family unity are very important” (expert’s interview, translated from Spanish, Colombia, August 2014). Within these motivations, however, men and women placed different emphases. While women ranked food security and traditional attachment to land higher than men, men ranked economic interests and improved quality of life higher than women.
### 3.3 Farmer typologies of risk perception
The cluster analysis of farmers’ first ranked answer to each question yielded four typologies of farmers based on the farmers’ perception of concerns, risks, barriers to adaptation, and enablers for adaptation:
1. i)
Cluster 1—Higher-educated women–dominated farmers that are attributing risks to external factors: farmers belonging to this group are worried about ending up in poverty and fear that they will not be supported by the government. They consider insufficient planning of their farming activities as well as a lack of access to social services (social vulnerability) as key risks for their future. In the view of this group, farmers are dependent on weather forecasts which they consider necessary to adapt to risks in agricultural production; they perceive that not cooperating as a community is a barrier for taking action. Their adaptive capacity could potentially be triggered if they perceived that the quality of life for them and their families would increase from implementing adaptation measures. The group of farmers in cluster 1 consists of 62.5% women and 37.5% men with an average age of 44 years; 50% of the farmers reached the primary education level only, and 38% have obtained a legal land title (50% have started a legal process). The average farm size is 4 ha.
2. ii)
Cluster 2—Lower-educated production–focused farmers with the land title: farmers belonging to this group are worried about a lack of access to credit or money to adapt agricultural production to change, and they are concerned about the government policies for rural development. These farmers perceive production failure due to uncontrollable factors (pest and diseases, climate events) and volatile selling prices for their products as the highest risks. The main barrier to adapt to change is a combination of low adaptive capacity and missing support from institutions. Similar to the first group, production-focused farmers are motivated to adapt to changes if their own and their families’ quality of life would increase. The group of farmers in cluster 2 consists of 43% women and 57% men with an average age of 44 years; 64% of farmers reached the primary education level only, and 57% have obtained a legal land title (29% have started a legal process). The average farm size is 2 ha.
3. iii)
Cluster 3—Vulnerable, less-educated farmers with lower access to land: farmers belonging to this group are worried about unstable markets for selling their products and the associated poverty risk. Compared to the others, their perceived risk is based not only on production but also on insecurity issues on their farms and during the transport of their products to the market. The main barriers for this group of farmers are high costs for implementing adaptation measures to cope with risks and the missing support from institutions. Members of this group share motivation for adapting to change due to being traditionally attached to their land and region. They want to improve the quality of life for themselves and their families. The group of farmers in cluster 3 consists of 47% women and 53% men with an average age of 46 years; 67% of farmers reached the primary education level only, and 27% have obtained a legal land title (47% have started a legal process). The average farm size is 2 ha.
4. iv)
Cluster 4—Risk-aware male–dominated elderly farmers with the land title: farmers of this group are worried about the government, risks from climate change, and the overall security in their region. The risks perceived as the highest by these farmers are social vulnerability such as the lacking access to social services and the risks associated with regional insecurity. The main barriers to adaptation lack weather forecasts and a low adaptive capacity on their farms. Like cluster 3 farmers, they feel traditionally attached to their land and also believe that their land is highly suitable for agricultural activities. The group of farmers in cluster 4 consists of 38% women and 62% men with an average age of 57 years; 69% of farmers reached the primary education level only, and 62% have obtained a legal land title (38% have started a legal process). The average farm size is 3 ha.
Detailed results of all comparisons, gender differences, and the hierarchical clustering of farmers’ rankings are presented in Online Resource 4.
## 4 Discussion
This paper presented an integrative approach to understanding how climate risks are integrated into the context of other risks in the farmers’ decision-making process. We compared the experts’ with the farmers’ view and differentiated between concerns, risks, and barriers for adaptation, and enablers to adaptation. Two explanations in the literature stress why this type of integrated analysis of farmers’ risk is more suitable than an isolated analysis of climate change risks: (i) farming systems of smallholders in the developing world are complex systems of location-specific characteristics integrating agricultural and nonagricultural livelihood strategies, which are vulnerable to a range of climate-related and other stressors (Morton 2007; Feola et al. 2015), and (ii) farmers’ long-term memory of climate events tends to decrease significantly after a few years; therefore, the importance of climate risks in farmers’ perceptions may equally decline very quickly after disturbing climate events (Brondizio and Moran 2008).
In the case of Cauca, the interviews were conducted in 2014, a year with ENSO neutral conditions, the same as the two previous years. Farmers ranked climate risks low among their perceived risks in agricultural production, a perception that might change if the interviews would have taken place in a year affected by ENSO conditions (e.g., with a prolonged drought and high temperatures).
### 4.2 What can we learn about climate risk communication?
While experts focus on communicating climate change risks, in cases such as we found in Cauca, farmers do not see such information as practical since their highest perceived risk is the poverty trap (social vulnerability) and the sum of risks related to the agricultural production of which climate risks are merely a part. In their article, Reid and Vogel (2006) pointed to this fact by stating that farmer’s associate crop losses sometimes with climate events which are, however, not always seen as extraordinary and farmers are accustomed to coping with them. This is also supported by our findings. Farmers in Cauca do not rank climate risks high among their perceived risks, but they rank the lack of weather forecast and weak institutional services as the most important barriers for adaptation to agricultural production risks. Differences between experts’ and farmers’ views related to the weather forecast, seasonal forecast, and climate change projections of long-term changes and inter-annual climate variability are relevant issues in climate risk communication (Weber 2010). In the case of Cauca, experts do not perceive that there is a lack of climate information for farmers. Thus, we recommend that experts should provide context-based–climate-related information in such a way that it becomes tangible and usable for farmers in their everyday and long-term decision-making, for example daily and seasonal weather information associated with agro-advisory services on varieties, planting dates, and water management.
### 4.3 A need for a more holistic perspective on adaptation
Our findings show that farmers in Colombia do not perceive climate risks separately; they are embedded in their mental models of agricultural livelihood risks. Other scholars have shown that in Colombia, climate change, trade liberalization, and violent conflicts act simultaneously on farmers’ livelihoods, but policies address them separately (Feola et al. 2015). If the implementation of policy actions is not coordinated, they might hinder each other or lead to failure. Understanding differences between experts’ and farmers’ mental models about risks is the first step to better design adequate policy actions for adaptation. Additionally, our results show that farmers in Cauca hardly trust national policies as mentioned by some experts as well as by farmers during the interviews. Farmers in Cauca are overall concerned about national policies. Llorente (2015) asserts that this is a result of the violent conflict which, in rural areas like Cauca, has led to profound mistrust in the state. Feola et al. (2015) argue that the institutional integration between different levels of government has been historically difficult in Colombia. Agricultural policies are often not based on the realities of smallholders. However, before designing adaptation strategies for farmers, the deeply rooted social vulnerability and inequality must be addressed and brought to the focus of experts. Ideally, this should be done together with farmers as a social learning process.
“Adaptation is a dynamic social process” (Adger 2003, p. 387), including many different actors. We agree with Vogel and Henstra (2015) to involve local actors in the development process of adaptation plans instead of operationalizing top-down adaptation measures. We suggest starting this process by developing a Local Adaptation Plan of Action (LAPA) in Cauca, aiming at initiating a bottom-up process of adaptation planning, which takes into account the community and individual levels (Jones and Boyd 2011; Regmi et al. 2014). The uptake of adaptation strategies depends on barriers and the adaptive capacity of both the community and the individual farmer.
Effective adaptation at the community level would require a mix of top-down structural measures, often provided by institutions, including national adaptation plans, financial services, economic incentives, and nonstructural measures developed by the community itself as a collective action (Girard et al. 2015).
Finally, transformative adaptation instead of targeting climate change by individual technological solutions would be a better approach for Colombian smallholders because it focuses on the root of vulnerability rather than on the adaptation of production systems only (Feola 2013). Such an approach would bring a more central role to farmers in developing adaptation options together with experts and would stimulate a social learning process in which science engages with lay knowledge and contributes with its transformative role to society (Feola 2013; Mauser et al. 2013). Climate change in the context of Latin America is characterized by complex lay and expert knowledge systems, social coping mechanisms, and ancient resilience mechanisms to adapt to perturbations (Sietz and Feola 2016). Several scholars support the need for an integrated approach to address critical dynamics of vulnerabilities and constraints for adaptation around climate change more integrated into cultural and socioeconomic realities (De los Ríos Cardona and Almeida 2011; Ulloa 2011). Other authors call for identification of causes of vulnerability and transformative solutions to cope with risks from climate change (Ribot 2014). Anyway, the state and its institutions are also important to provide a policy framework for adaptation, to intervene when resources are required, and to enable needed policies (Ramirez-Villegas and Khoury 2013). Finally, cooperatives could play a crucial role and become vehicles for rural development, opposite to previous top-down approaches that have failed in Colombia (Gutiérrez 2014).
For further research, we recommend to study the dynamics in the farmers’ complex livelihood system, to analyze the actor’s network of farmers, and to identify adaptation pathways for farmers to cope with climate change in Cauca, Colombia.
## 5 Conclusions
Since the 2015 Paris Agreement (COP 21), the political commitment to take action on climate change increased. Even in developing countries, policymakers have started working more specifically towards policies for achieving climate resilience, especially in the agricultural sector. Agriculture, both contributing to climate change and being affected by climate change, needs a transformation to become more sustainable and climate resilient by improving farmers’ livelihood system and farm productivity while reducing emissions from agriculture. Especially, transforming smallholders’ agriculture in developing countries such as Colombia requires greater attention to human livelihoods and related concerns, risks, barriers to decision-making, and the adoption of adaptation strategies.
This study applied a mental model approach to understand better climate risks in the context of farmers’ decision-making process. It showed that climate risks need to be seen in the overall context of farmers’ livelihood risks. Climate change adaptation strategies and policies can be more successful if they (i) address specific climate risks, (ii) simultaneously address other risks of major importance for farmers, and (iii) target more climate risk–sensitive groups of farmers. Our research demonstrates that understanding differences in experts’ and farmers’ perception of farmers’ livelihood risks could avoid maladaptation and improve climate risk communication from experts to farmers. Therefore, we recommend to study the dynamics in the farmers’ complex livelihood system, to analyze the actor’s network of farmers, and to identify adaptation pathways for farmers to cope with climate change in Cauca, Colombia.
## Notes
### Acknowledgements
This work was implemented as part of the CGIAR Research Program on Climate Change, Agriculture and Food Security (CCAFS), which is carried out with support from the CGIAR Fund Donors and through bilateral funding agreements. For details, please visit https://ccafs.cgiar.org/donors. The views expressed in this document cannot be taken to reflect the official opinions of these organizations. We thank the International Center for Tropical Agriculture (CIAT) and Fundacion Ecohabitats for supporting the fieldwork.
## Supplementary material
10584_2018_2320_MOESM1_ESM.pdf (1.1 mb)
Online Resource 1 Assessment of climate change risks in Cauca, Colombia (PDF 1098 kb)
10584_2018_2320_MOESM2_ESM.pdf (263 kb)
Online Resource 2 Guidebook for experts’ interviews (PDF 262 kb)
10584_2018_2320_MOESM3_ESM.pdf (706 kb)
Online Resource 3 Guidebook for farmers’ interviews (PDF 705 kb)
10584_2018_2320_MOESM4_ESM.pdf (190 kb)
Online Resource 4 Detailed results of ranking hierarchical clustering of farmers’ perceptions (PDF 190 kb)
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## Authors and Affiliations
• Anton Eitzinger
• 1
• 2
• Claudia R. Binder
• 2
• 3
• Markus A. Meyer
• 2
1. 1.International Center for Tropical Agriculture (CIAT)CaliColombia
2. 2.Department of GeographyUniversity of Munich (LMU)MunichGermany
3. 3.Laboratory for Human-Environment Relations in Urban Systems, IIE, ENACEcole Polytechnique Fédérale de Lausanne (EPFL)LausanneSwitzerland | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.42397141456604004, "perplexity": 7902.781785527056}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039742567.46/warc/CC-MAIN-20181115054518-20181115080518-00148.warc.gz"} |
http://growthecon.com/blog/the-simplest-growth-model/ | # The Simplest Growth Model
This is an idea for a new way of introducing growth theory. Given that productivity growth is the source of long-run growth, it seems to make sense to start with that, rather than with the Solow model.
Let's write down a very simple model of economic growth. Let total output ${Y}$ be determined by
$$Y = A L$$
where ${A}$ is a measure of labor productivity, and ${L}$ is the number of workers. If we divide through by ${L}$, then we get a measure of output per worker. To keep notation clean, let ${y = Y/L}$ be output per worker, so that now we have
$$y = A$$
as our model of economic growth. Basically, output per worker is simply equal to labor productivity ${A}$.
From this we know that the time path of output per worker is simply the same as the time path of labor productivity, ${A}$. So what determines the time path of labor productivity? We'll assume that it is growing at a constant rate, meaning that it goes up by the same percent every period of time,
$$A(t) = A(0) e^{g t}.$$
Here, we've written ${A(t)}$ to be clear that we mean labor productivity at any given time ${t}$. ${A(0)}$ is labor productivity in the initial moment of time. The exponential term says that labor productivity grows at the rate ${g}$ over time.
The exponential term implies, perhaps not surprisingly, exponential growth. You get exponential growth when something goes up by the same percent every period of time. If ${g = 0.02}$, then we have 2% growth. At time zero, labor productivity is just ${A(0)}$. When ${t=2}$, then ${A(2) = A(0)e^{.02(2)} = 1.041 A(0)}$, or labor productivity is a little more than 4% higher than at time zero. When ${t=10}$, ${A(10)=A(0)e{.02(10)}=1.221}$, or labor productivity is more than 22% higher than at time zero.
It may not seem obvious, but output per worker in the U.S. and most other developed nations displays exponential growth. Our model matches that, as
$$y(t) = A(0) e^{g t}.$$
These countries also tend to have a similar growth rate of about 1.8%, or ${g=0.018}$. Seeing this in a figure, though, is difficult. Graphing ${y}$ over time for the U.S. gives you a curve that quickly accelerates upwards and is almost off the page. Graphs like this will also make it difficult to compare countries to one another.
For that reason, among others, we like to work with the natural log of output per worker, ${\ln{y(t)}}$. Taking natural logs of ${y(t)}$ gives us
$$\ln{y(t)} = \ln{A(0)} + g t.$$
This is an equation that says the natural log of output per worker is a linear function of time, ${t}$. If we graph ${\ln{y(t)}}$ against ${t}$, we get a straight line, similar to the trend line we drew in the figure for U.S. output per worker.
We can calculate the growth rate of output per worker by taking the derivative of (5) with respect to time. This results in the following
$$\frac{\dot{y}}{y} = g.$$
The value of ${A(0)}$ is fixed, so the derivative of it with respect to time is just zero. The notation ${\dot{y}/y}$ is a shorthand way of writing the growth rate. ${\dot{y}}$ is the absolute change in output per worker at any given moment, and by dividing by ${y}$ we get that change relative to the level of output per worker. This means that ${\dot{y}/y}$ is essentially the percent change in output per worker at any given moment.
That's it for the simple growth model. Output per worker depends on labor productivity ${A(t)}$, and labor productivity grows at a constant rate ${g}$, which means output per worker grows at that same rate. Despite the mechanical simplicity, this model helps us be clear when we are talking about the growth experiences of different countries. It allows us to distinguish between two forces determining output per worker.
• Level effects: These refer to ${A(0)}$, the intercept of the line in (5)
• Growth effects: These refer to ${g}$, the slope of the line in (5)
Looking at the data over the long run, the general impression we get that the growth rate ${g}$ is similar across countries, and they differ mainly because of level effects. That is, ${A(0)_{Japan}}$ appears to be lower than ${A(0)_{US}}$, but the growth rate ${g}$ is very similar. Theories of economic growth should be consistent with these facts. Things like investment rates, schooling, and social infrastructure are important determinants of level effects, ${A(0)}$, but they have no effect on the growth rate, ${g}$. Under plausible assumptions, theories of endogenous innovation will suggest that the growth rate, ${g}$, is identical across countries.
There are some facts, though, that this simple growth model cannot account for. Namely, there are notable cases where output per worker grows more quickly or more slowly than ${g}$. China, for example, over the last 30 years has grown much faster than the U.S. or Japan. South Korea had a similar growth miracle, starting in about 1960 and lasting until the 2000's. Germany, from World War II until about 1980, grew at a very accelerated pace compared to the U.S. in the same period. How do we reconcile these facts with the assertion above that ${g}$ is the same for all countries?
The key is noting that these growth accelerations were temporary. Germany grew very quickly, but after 1980 its growth rate fell back to a value nearly identical to the U.S. South Korea's growth rate has diminshed as well in the 2000's. What appears to be happening is that once output per worker approaches a frontier level, generally defined by the U.S., growth slows down. While China continues to grow quickly, it has not approached the U.S. level of output per worker.
Looking at these countries, what appears to be happening is that there is a level effect, or their ${A(0)}$ has shifted up. However, it seems to take them a long time to move from their old level to the new, higher level. We call the temporary growth spurt that occurs when a country moves between levels transitional growth. Output per worker grows faster than ${g}$ temporarily - although this could last a few decades - but then growth returns to the rate ${g}$.
Our simple model doesn't offer a way of understanding this transitional growth. The first major extension we'll make to this simple model is to add physical capital, which has to be slowly accumulated over time. Because of this slow accumulation, the economy will take an extended time to fully respond to a level effect. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.861982524394989, "perplexity": 485.6743137328265}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267156554.12/warc/CC-MAIN-20180920175529-20180920195929-00084.warc.gz"} |
https://en.wikipedia.org/wiki/Key_derivation_function | # Key derivation function
In cryptography, a key derivation function (KDF) derives one or more secret keys from a secret value such as a master key, a password, or a passphrase using a pseudo-random function.[1][2] KDFs can be used to stretch keys into longer keys or to obtain keys of a required format, such as converting a group element that is the result of a Diffie–Hellman key exchange into a symmetric key for use with AES. Keyed cryptographic hash functions are popular examples of pseudo-random functions used for key derivation.[3]
## Uses of KDFs
Key derivation functions are often used in conjunction with non-secret parameters to derive one or more keys from a common secret value (which is sometimes also referred to as "key diversification"). Such use may prevent an attacker who obtains a derived key from learning useful information about either the input secret value or any of the other derived keys. A KDF may also be used to ensure that derived keys have other desirable properties, such as avoiding "weak keys" in some specific encryption systems.
The most common use of KDFs is the password hashing approach to password verification, as used by the passwd file or shadow password file. KDFs happen to have the characteristics desired for a "password hash function", even though they were not originally designed for this purpose. The non-secret parameters are called "salt" in this context. In 2013 a "Password Hashing Competition" was announced to choose a new, standard algorithm for password hashing. On 20 July 2015 the competition ended and Argon2 was announced as the final winner. Four other algorithms received special recognition: Catena, Lyra2, Makwa and yescrypt.[4]
Key derivation functions are often used as components of multiparty key-agreement protocols. Examples of such key derivation functions include KDF1, defined in IEEE Std 1363-2000, and similar functions in ANSI X9.42.
Key derivation functions are also used to derive keys from secret passwords or passphrases.
The "HMAC-based Extract-and-Expand Key Derivation Function" or "HKDF" specified in RFC 5869[5] is a simple HMAC-based KDF, which can be used as a building block in various protocols and applications.
### Key stretching
Main article: Key stretching
Key derivation functions are also used in applications to derive keys from secret passwords or passphrases, which typically do not have the desired properties to be used directly as cryptographic keys. In such applications, it is generally recommended that the key derivation function be made deliberately slow so as to frustrate brute-force attack or dictionary attack on the password or passphrase input value.
Such use may be expressed as ${\displaystyle \mathrm {DK} =\mathrm {KDF} (\mathrm {Key} ,\mathrm {Salt} ,\mathrm {Iterations} )}$ where ${\displaystyle \mathrm {DK} }$ is the derived key, ${\displaystyle \mathrm {KDF} }$ is the key derivation function, ${\displaystyle \mathrm {Key} }$ is the original key or password, ${\displaystyle \mathrm {Salt} }$ is a random number which acts as cryptographic salt, and ${\displaystyle \mathrm {Iterations} }$ refers to the number of iterations of a sub-function. The derived key is used instead of the original key or password as the key to the system. The values of the salt and the number of iterations (if it is not fixed) are stored with the hashed password or sent as plaintext with an encrypted message.[6]
The difficulty of a brute force attack increases with the number of iterations. A practical limit on the iteration count is the unwillingness of users to tolerate a perceptible delay in logging in to a computer or seeing a decrypted message. The use of salt prevents the attackers from precomputing a dictionary of derived keys.[6]
An alternative approach, called key strengthening, extends the key with a random salt, but then (unlike in key stretching) securely deletes the salt. This forces both the attacker and legitimate users to perform a brute-force search for the salt value.[7] Although the paper that introduced key stretching [8] referred to this earlier technique and intentionally chose a different name, the term "key strengthening" is now often (arguably incorrectly) used to refer to key stretching.
## History
The first[citation needed] deliberately slow (key stretching) password-based key derivation function was called "crypt" (or "crypt(3)" after its man page), and was invented by Robert Morris in 1978. It would encrypt a constant (zero), using the first 8 characters of the user's password as the key, by performing 25 iterations of a modified DES encryption algorithm (in which a 12-bit number read from the real-time computer clock is used to perturb the calculations). The resulting 64-bit number is encoded as 11 printable characters and then stored in the Unix password file.[9] While it was a great advance at the time, increases in processor speeds since the PDP-11 era have made brute-force attacks against crypt feasible, and advances in storage have rendered the 12-bit salt inadequate. The crypt function's design also limits the user password to 8 characters, which limits the keyspace and makes strong passphrases impossible.[citation needed]
Modern password-based key derivation functions, such as PBKDF2 (specified in RFC 2898), use a cryptographic hash, such as SHA-2, more salt (e.g. 64 bits and greater) and a high iteration count (often tens or hundreds of thousands).
NIST requires at least 128 bits of random salt and a NIST-approved cryptographic function, such as the SHA series or AES (MD5 is not approved).[10] Although high throughput is a desirable property in general-purpose hash functions, the opposite is true in password security applications in which defending against brute-force cracking is a primary concern. The growing use of massively-parallel hardware such as GPUs, FPGAs, and even ASICs for brute-force cracking has made the selection of a suitable algorithms even more critical because the good algorithm should not only enforce a certain amount of computational cost not only on CPUs, but also resist the cost/performance advantages of modern massively-parallel platforms for such tasks. Various algorithms have been designed specifically for this purpose, including bcrypt, scrypt and, more recently, argon2 (the winner of the PHC contest). The large-scale Ashley Madison data breach in which roughly 36 million passwords hashes were stolen by attackers illustrated the importance of algorithm selection in securing passwords. Although bcrypt was employed to protect the hashes (making large scale brute-force cracking expensive and time-consuming), a significant portition of the accounts in the compromised data also contained a password hash based on the general-purpose md5 algorithm which made it possible for over 11 million of the passwords to be cracked in a matter of weeks.[11]
## References
1. ^ Bezzi, Michele; et al. (2011). "Data privacy". In Camenisch, Jan et al. Privacy and Identity Management for Life. Springer. pp. 185–186. ISBN 9783642203176.
2. ^ Kaliski, Burt; RSA Laboratories. "RFC 2898 -- PKCS #5: Password-Based Cryptography Specification, Version 2.0". IETF.
3. ^ Zdziarski, Jonathan (2012). Hacking and Securing IOS Applications: Stealing Data, Hijacking Software, and How to Prevent It. O'Reilly Media. pp. 252–253. ISBN 9781449318741. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 6, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.33665359020233154, "perplexity": 2825.3505787383187}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738661123.53/warc/CC-MAIN-20160924173741-00028-ip-10-143-35-109.ec2.internal.warc.gz"} |
https://worldwidescience.org/topicpages/d/deg+polar+channels.html | #### Sample records for deg polar channels
1. Determination of electron temperature and energy relaxation of 2DEG in AlGaAs/GaAs HEMT channel
Energy Technology Data Exchange (ETDEWEB)
Ari, Mehmet; Turkoglu, Orhan
2003-09-01
We have investigated the electron energy relaxation of two-dimensional electron gas (2DEG) in AlGaAs/GaAs high electron mobility transistor (HEMT) channel at lattice temperature of T{sub L}=1.7 K under zero magnetic field. The electron temperature of 2DEG has been determined by using the absolute power dissipation in HEMT channel in the temperature range of 1.7-60 K. The experimental results are compared with theoretical results which include both acoustic phonon via deformation coupling and polar optic phonon scattering mechanisms. A good agreement is obtained between experimental and theoretical results for all electron temperatures. A transition between acoustic phonon and polar optic phonon regime has been seen at the electron temperature T{sub e}=40 K. The results are consistent with other studies where different techniques but similar sample structures have been used. The results also provide useful information about the relative magnitude of acoustic phonon via deformation potential coupling and polar optic phonon contributions to power loss of 2DEG.
2. Polarization for arbitrary discrete memoryless channels
OpenAIRE
Sasoglu, Eren; Telatar, Emre; Arikan, Erdal
2009-01-01
Channel polarization, originally proposed for binary-input channels, is generalized to arbitrary discrete memoryless channels. Specifically, it is shown that when the input alphabet size is a prime number, a similar construction to that for the binary case leads to polarization. This method can be extended to channels of composite input alphabet sizes by decomposing such channels into a set of channels with prime input alphabet sizes. It is also shown that all discrete memoryless channels can...
3. Observation of Polar Mesosphere Summer Echoes using the Northernmost MST Radar at Eureka (80 deg N)
Science.gov (United States)
Swarnalingam, N.; Hocking, W.; Janches, D.; Drummond, J.
2017-01-01
We investigate long-term Polar Mesosphere Summer Echoes (PMSEs) observations conducted by the northern most geographically located MST radar at Eureka (80 deg N, 86 deg W). While PMSEs are a well recognized summer phenomenon in the polar regions, previous calibrated studies at Resolute Bay and Eureka using 51.5 MHz and33 MHz radars respectively, showed that PMSE backscatter signal strengths are relatively weak in the polar cap sites, compared to the auroral zone sites (Swarnalingam et al., 2009b; Singer et al., 2010). Complications arise with PMSEs in which the echo strength is controlled by the electrons, which are, in turn, influenced by heavily charged ice particles as well as the variability in the D-region plasma. In recent years, PMSE experiments were conducted inside the polar cap utilizing a 51 MHz radar located at Eureka. In this paper, we investigate calibrated observations, conducted during 2009-2015. Seasonal and diurnal variations of the backscatter signal strengths are discussed and compared to previously published results from the ALOMAR radar, which is a radar of similar design located in the auroral zone at Andenes, Norway (69 deg N, 16 deg E). At Eureka, while PMSEs are present with a daily occurrence rate which is comparable to the rate observed at the auroral zone site for at least two seasons, they show a great level of inter-annual variability. The occurrence rate for the strong echoes tends to be low. Furthermore, comparison of the absolute backscatter signal strengths at these two sites clearly indicates that the PMSE backscatter signal strength at Eureka is weak. Although this difference could be caused by several factors, we investigate the intensity of the neutral air turbulence at Eureka from the measurements of the Doppler spectrum of the PMSE backscatter signals. We found that the level of the turbulence intensity at Eureka is weak relative to previously reported results from three high latitude sites.
4. Model to explain the behavior of 2DEG mobility with respect to charge density in N-polar and Ga-polar AlGaN-GaN heterostructures
Science.gov (United States)
Ahmadi, Elaheh; Keller, Stacia; Mishra, Umesh K.
2016-09-01
There are three possible ways of reducing the charge density (ns) in the N-polar high electron mobility transistors (HEMT) structures, by decreasing the channel thickness, applying reverse gate bias, or modifying the back-barrier. Understanding the behavior of 2DEG mobility as a function of ns is essential to design high performance HEMT devices. Experimental data show that in the N-polar HEMT structures, the 2DEG mobility reduces as the ns decreases by applying reverse gate bias or decreasing channel thickness, whereas in the Ga-polar HEMT structures, the 2DEG mobility increases as the ns in the channel decreases by applying reverse gate bias. In this paper, the 2DEG mobility as a function of ns is calculated in N-polar HEMTs for three different aforementioned cases, and is compared to that in the Ga-polar HEMT structures. It is shown that the conventional scattering mechanisms cannot explain these different behaviors. Two new scattering mechanisms, such as scattering from charged interface states and surface state dipoles (SSD), are introduced. It is revealed that in N-polar HEMT structures, reducing ns by applying reverse gate bias or decreasing channel thickness moves the charge centroid closer to the AlGaN-GaN interface. A combination of lower charge density (less screening of the scattering potential) and smaller distance between charge centroid and charged states at the interface leads to a severe mobility degradation in these cases. In contrast, reducing ns by modifying the back-barrier (decreasing back-barrier doping and/or decreasing AlGaN composition) in N-polar HEMT structures moves the charge centroid away from the interface. This behavior is similar to that in the Ga-polar HEMT structures. Therefore, in the last two mentioned cases, the 2DEG mobility first increases slightly as the ns decreases, and decreases slightly at very low charge densities. It is also shown that SSDs have large impact on the 2DEG mobility only in the N-polar (Ga-polar) HEMTs
5. Sexy DEG/ENaC channels involved in gustatory detection of fruit fly pheromones.
Science.gov (United States)
Pikielny, Claudio W
2012-11-06
Hydrocarbon pheromones on the cuticle of Drosophila melanogaster modulate the complex courtship behavior of males. Recently, three members of the degenerin/epithelial Na+ channel (DEG/ENaC) family of sodium channel subunits, Ppk25, Ppk23, and Ppk29 (also known as Nope), have been shown to function in gustatory perception of courtship-modulating contact pheromones. All three proteins are required for the activation of male courtship by female pheromones. Specific interactions between two of them have been demonstrated in cultured cells, suggesting that, in a subset of cells where they are coexpressed, these three subunits function within a common heterotrimeric DEG/ENaC channel. Such a DEG/ENaC channel may be gated by pheromones, either directly or indirectly, or alternatively may control the excitability of pheromone-sensing cells. In addition, these studies identify taste neurons that respond specifically to courtship-modulating pheromones and mediate their effects on male behavior. Two types of pheromone-sensing taste neurons, F and M cells, have been defined on the basis of their specific response to either female or male pheromones. These reports set the stage for the dissection of the molecular and cellular mechanisms that mediate gustatory detection of contact pheromones.
6. Window for Optimal Frequency Operation and Reliability of 3DEG and 2DEG Channels for Oxide Microwave MESFETs and HFETs
Science.gov (United States)
2016-04-01
time.The longest energy relaxation time (1.8 ps) was in a reasonably good agreement with the published values obtained through optical time-resolved...phonon accumulation was taken into account. The assumption of electron density-independent hot- phonon lifetime led to a monotonous increase in the hot...preferable for several reasons : (i) a high-density electron gas is present at equilibrium, (ii) doped channels are of direct interest for FETs
7. A 189 MHz, 2400 deg{sup 2} POLARIZATION SURVEY WITH THE MURCHISON WIDEFIELD ARRAY 32-ELEMENT PROTOTYPE
Energy Technology Data Exchange (ETDEWEB)
Bernardi, G.; Greenhill, L. J.; De Oliveira-Costa, A. [Harvard-Smithsonian Center for Astrophysics, Garden Street 60, Cambridge, MA 02138 (United States); Mitchell, D. A. [The University of Melbourne, Melbourne (Australia); Ord, S. M.; Arcus, W.; Arora, B. S. [International Centre for Radio Astronomy Research, Curtin University, Perth (Australia); Hazelton, B. J.; Morales, M. F. [University of Washington, Seattle, WA (United States); Gaensler, B. M.; Subrahmanyan, R.; Wayth, R. B.; Lenc, E.; Briggs, F. H. [CAASTRO, 44 Rosenhill Street, Redfern, NSW 2016 (Australia); Shankar, N. Udaya [Raman Research Institute, Bangalore (India); Williams, C. L. [MIT Kavli Institute for Astrophysics and Space Research, Cambridge, MA (United States); Barnes, D. G. [Swinburne University of Technology, Melbourne (Australia); Bowman, J. D. [Arizona State University, Tempe, AZ (United States); Bunton, J. D. [CSIRO Astronomy and Space Science, NSW (Australia); Cappallo, R. J., E-mail: gbernardi@cfa.harvard.edu [MIT Haystack Observatory, Westford, MA (United States); and others
2013-07-10
We present a Stokes I, Q and U survey at 189 MHz with the Murchison Widefield Array 32 element prototype covering 2400 deg{sup 2}. The survey has a 15.6 arcmin angular resolution and achieves a noise level of 15 mJy beam{sup -1}. We demonstrate a novel interferometric data analysis that involves calibration of drift scan data, integration through the co-addition of warped snapshot images, and deconvolution of the point-spread function through forward modeling. We present a point source catalog down to a flux limit of 4 Jy. We detect polarization from only one of the sources, PMN J0351-2744, at a level of 1.8% {+-} 0.4%, whereas the remaining sources have a polarization fraction below 2%. Compared to a reported average value of 7% at 1.4 GHz, the polarization fraction of compact sources significantly decreases at low frequencies. We find a wealth of diffuse polarized emission across a large area of the survey with a maximum peak of {approx}13 K, primarily with positive rotation measure values smaller than +10 rad m{sup -2}. The small values observed indicate that the emission is likely to have a local origin (closer than a few hundred parsecs). There is a large sky area at {alpha} {>=} 2{sup h}30{sup m} where the diffuse polarized emission rms is fainter than 1 K. Within this area of low Galactic polarization we characterize the foreground properties in a cold sky patch at ({alpha}, {delta}) = (4{sup h}, -27. Degree-Sign 6) in terms of three-dimensional power spectra.
8. Pressure Loss Through Sharp 180 deg Turn in a Relatively Short Two-Pass Smooth and RibRoughened Channel
Institute of Scientific and Technical Information of China (English)
1995-01-01
The local pressure distributions and resistance coefficients(f1 and f2) through the sharp 180 deg turn in a relatively short (L/De=4) two-pass smooth and rib-roughened channel were investigated for a Reynolds number range of 1.0×103,9.0×103.The rib pitch-to-herght ratios(p/e) were 5,10,and 20,The rib height-to-hydraulic diamter ratios(e/De) were 0.025,0.050 and 0.10,and the rib angles of attack(a) were 90,45,60,-45,and -60 deg.Rids were installed not only in before and after turn regions but also in turn region.The results show that resistance coefficients remain approximately constant when Reynolds number is more than 3.0×104,The effects of the rib configuration(rib spacing,rib height,and rib orientation)on the inlet straight duct resistance coefficient(f2) were significant, however,their effects on the overall resistance coefficient(f1) were diluted by the sharp-180 turn.For this relatively short channel(L/De=4),the overall resistance coefficient(f1) was greatly affected by the sharp turn.Correlations for the overall resistance(f1) and inlet straight duct resistance coefficient (f2) are presented.
9. Atmospheric Channel Characteristics for Quantum Communication with Continuous Polarization Variables
CERN Document Server
Heim, Bettina; Bartley, Tim; Sabuncu, Metin; Wittmann, Christoffer; Sych, Denis; Marquardt, Christoph; Leuchs, Gerd
2009-01-01
We investigate the properties of an atmospheric channel for free space quantum communication with continuous polarization variables. In our prepare-and-measure setup, coherent polarization states are transmitted through an atmospheric quantum channel of 100m length on the roof of our institute's building. The signal states are measured by homodyne detection with the help of a local oscillator (LO) which propagates in the same spatial mode as the signal, orthogonally polarized to it. Thus the interference of signal and LO is excellent and atmospheric fluctuations are autocompensated. The LO also acts as spatial and spectral filter, which allows for unrestrained daylight operation. Important characteristics for our system are atmospheric channel influences that could cause polarization, intensity and position excess noise. Therefore we study these influences in detail. Our results indicate that the channel is suitable for our quantum communication system in most weather conditions.
10. Super Cold Arctic Mesopause Project (CAMP): A research project to investigate the polar middle atmosphere in summer with rocket launches from 65 deg-80 deg N
Science.gov (United States)
Kopp, E.; Philbrick, C. R.; Thomas, G. E.; Witt, G.
A Cold Arctic Mesopause Project for summer to study the structure and dynamics of the middle atmosphere (50 to 150 km) above the north polar region is proposed. It should concentrate on measurements of water vapor, ozone and temperature and their variability as a function of time, and geomagnetic and meteor shower activity; formation, particle size and density, transport and life time of noctilucent cloud (NLC) particles; dynamics and temperature and their effects on ice particle growths and the distribution of minor constituents including the ionospheric plasma; and electric fields, charged aerosols, and massive positive and negative ions in the vicinity of NLC. In situ measurements from rockets, grouped in two to three salvos should be supported by ground, airborne and satellite remote sensing experiments.
11. Measurement of polarization of recoil protons in. pi. /sup 0/ photoproduction for THETAsup(*)sub(. pi. sup(0))=60 deg in the resonance range
Energy Technology Data Exchange (ETDEWEB)
Avakyan, R.O.; Avakyan, Eh.O.; Avetisyan, A.Eh. (Erevanskij Fizicheskij Inst. (USSR))
1983-02-01
The energy dependence of the Psub(y) component of the recoil proton polarization vector in the reaction ..gamma..p ..-->.. p..pi../sup 0/ is presented for the pion production angle thetasub(..pi..sup(2))*=60 deg and ..gamma..-quantum energies Esub(..gamma..)=(0.8-1.5) GeV. The measurement results are compared to the results of various theoretical analyses.
12. Study on target characteristic polarization state in co-polarized channel for the coherent case
Institute of Scientific and Technical Information of China (English)
CHEN Qiang; GAO Gui; ZHOU XiaoGuang; JIANG YongMei; KUANG GangYao
2009-01-01
The target characteristic polarization state in the co-polarized channel for the coherent case was studied in greater detail,with emphasis on the analysis of the characteristic polarization states variable with the target parameters.The Sinclair backscatter matrix was diagonalized under the change of polarization basis via a unitary transformation matrix.Then the diagonal matrix was parameterized by four parameters viz.matrix amplitude,absolute phase,amplitude ratio and phase difference.The behavior of the characteristic polarization states with the varieties of target parameters was discussed together with the power density plot.The characteristic polarization states were displayed on the Poincare sphere and six conclusions were obtained,which provide theoretic support for decreasing the computational complexity of target characteristic polarization state,or anticipating its position in the power density plot.Several simple target cases were considered for validating these conclusions.
13. Inter-calibration of polar imager solar channels using SEVIRI
Directory of Open Access Journals (Sweden)
J. F. Meirink
2013-04-01
Full Text Available Accurate calibration of satellite imagers is a prerequisite for using their measurements in climate applications. Here we present a method for the inter-calibration of geostationary and polar-orbiting imager solar channels based on regressions of collocated near-nadir radiances. Specific attention is paid to correcting for differences in spectral response between instruments. The method is used to calibrate the solar channels of the Spinning Enhanced Visible and Infrared Imager (SEVIRI on the geostationary Meteosat satellite with corresponding channels of the Moderate Resolution Imaging Spectroradiometer (MODIS on the polar-orbiting Aqua satellite. The SEVIRI operational calibration is found to be stable during the years 2004 to 2009 but off by −8, −6, and +3.5% for channels 1 (0.6 μm, 2 (0.8 μm, and 3 (1.6 μm, respectively. These results are robust for a range of choices that can be made regarding data collocation and selection, as long as the viewing and illumination geometries of the two instruments are matched. Uncertainties in the inter-calibration method are estimated to be 1% for channel 1 and 1.5% for channels 2 and 3. A specific application of the method is the inter-calibration of polar imagers using SEVIRI as a transfer instrument. This offers an alternative to direct inter-calibration, which in general has to rely on high-latitude collocations. Using this method we have tied MODIS-Terra and Advanced Very High Resolution Radiometer (AVHRR instruments on National Oceanic and Atmospheric Administration (NOAA satellites 17 and 18 to MODIS-Aqua for the years 2007 to 2009. While reflectances of the two MODIS instruments differ less than 2% for all channels considered, deviations of an existing AVHRR calibration from MODIS-Aqua reach −3.5 and +2.5% for the 0.8 and 1.6 μm channels, respectively.
14. Local heat/mass transfer distributions around sharp 180 deg turns in two-pass smooth and rib-roughened channels
Science.gov (United States)
Han, J. C.; Chandra, P. R.; Lau, S. C.
1988-01-01
The napthalene sublimation technique was employed to study the detailed mass transfer distributions around the sharp 180 deg turns in a two-pass, square, smooth channel and in an identical channel with two rib-roughened opposite walls. Experiments conducted for Reynolds numbers of 15,000, 30,000, and 60,000 indicate that the Sherwood numbers on the top, outer, and inner walls around the turn in the rib-roughened channel are higher than the corresponding Sherwood numbers around the turn in the smooth channel. Sherwood numbers after the sharp turn are found to be higher than those before the turn for both the smooth and the ribbed channels.
15. Study on target characteristic polarization state in co-polarized channel for the coherent case
Institute of Scientific and Technical Information of China (English)
2009-01-01
The target characteristic polarization state in the co-polarized channel for the coherent case was studied in greater detail, with emphasis on the analysis of the characteristic polarization states variable with the target parameters. The Sinclair backscatter matrix was diagonalized under the change of polariza- tion basis via a unitary transformation matrix. Then the diagonal matrix was parameterized by four parameters viz. matrix amplitude, absolute phase, amplitude ratio and phase difference. The behavior of the characteristic polarization states with the varieties of target parameters was discussed together with the power density plot. The characteristic polarization states were displayed on the Poincare sphere and six conclusions were obtained, which provide theoretic support for decreasing the computational complexity of target characteristic polarization state, or anticipating its position in the power density plot. Several simple target cases were considered for validating these conclusions.
16. Identification of Ppk26, a DEG/ENaC Channel Functioning with Ppk1 in a Mutually Dependent Manner to Guide Locomotion Behavior in Drosophila
Directory of Open Access Journals (Sweden)
David A. Gorczyca
2014-11-01
Full Text Available A major gap in our understanding of sensation is how a single sensory neuron can differentially respond to a multitude of different stimuli (polymodality, such as propio- or nocisensation. The prevailing hypothesis is that different stimuli are transduced through ion channels with diverse properties and subunit composition. In a screen for ion channel genes expressed in polymodal nociceptive neurons, we identified Ppk26, a member of the trimeric degenerin/epithelial sodium channel (DEG/ENaC family, as being necessary for proper locomotion behavior in Drosophila larvae in a mutually dependent fashion with coexpressed Ppk1, another member of the same family. Mutants lacking Ppk1 and Ppk26 were defective in mechanical, but not thermal, nociception behavior. Mutants of Piezo, a channel involved in mechanical nociception in the same neurons, did not show a defect in locomotion, suggesting distinct molecular machinery for mediating locomotor feedback and mechanical nociception.
17. Tunable polarization plasma channel undulator for narrow bandwidth photon emission
Science.gov (United States)
Rykovanov, S. G.; Wang, J. W.; Kharin, V. Yu.; Lei, B.; Schroeder, C. B.; Geddes, C. G. R.; Esarey, E.; Leemans, W. P.
2016-09-01
The theory of a plasma undulator excited by a short intense laser pulse in a parabolic plasma channel is presented. The undulator fields are generated either by the laser pulse incident off-axis and/or under the angle with respect to the channel axis. Linear plasma theory is used to derive the wakefield structure. It is shown that the electrons injected into the plasma wakefields experience betatron motion and undulator oscillations. Optimal electron beam injection conditions are derived for minimizing the amplitude of the betatron motion, producing narrow-bandwidth undulator radiation. Polarization control is readily achieved by varying the laser pulse injection conditions.
18. Polar cap flow channel events: spontaneous and driven responses
Directory of Open Access Journals (Sweden)
P. E. Sandholt
2010-11-01
Full Text Available We present two case studies of specific flow channel events appearing at the dusk and/or dawn polar cap boundary during passage at Earth of interplanetary (IP coronal mass ejections (ICMEs on 10 January and 25 July 2004. The channels of enhanced (>1 km/s antisunward convection are documented by SuperDARN radars and dawn-dusk crossings of the polar cap by the DMSP F13 satellite. The relationship with Birkeland currents (C1–C2 located poleward of the traditional R1–R2 currents is demonstrated. The convection events are manifest in ground magnetic deflections obtained from the IMAGE (International Monitor for Auroral Geomagnetic Effects Svalbard chain of ground magnetometer stations located within 71–76° MLAT. By combining the ionospheric convection data and the ground magnetograms we are able to study the temporal behaviour of the convection events. In the two ICME case studies the convection events belong to two different categories, i.e., directly driven and spontaneous events. In the 10 January case two sharp southward turnings of the ICME magnetic field excited corresponding convection events as detected by IMAGE and SuperDARN. We use this case to determine the ground magnetic signature of enhanced flow channel events (the NH-dusk/By<0 variant. In the 25 July case a several-hour-long interval of steady southwest ICME field (Bz<0; By<0 gave rise to a long series of spontaneous convection events as detected by IMAGE when the ground stations swept through the 12:00–18:00 MLT sector. From the ground-satellite conjunction on 25 July we infer the pulsed nature of the polar cap ionospheric flow channel events in this case. The typical duration of these convection enhancements in the polar cap is 10 min.
19. NRA-2, a nicalin homolog, regulates neuronal death by controlling surface localization of toxic Caenorhabditis elegans DEG/ENaC channels.
Science.gov (United States)
Kamat, Shaunak; Yeola, Shrutika; Zhang, Wenying; Bianchi, Laura; Driscoll, Monica
2014-04-25
Hyperactivated DEG/ENaCs induce neuronal death through excessive cation influx and disruption of intracellular calcium homeostasis. Caenorhabditis elegans DEG/ENaC MEC-4 is hyperactivated by the (d) mutation and induces death of touch neurons. The analogous substitution in MEC-10 (MEC-10(d)) co-expressed in the same neurons is only mildly neurotoxic. We exploited the lower toxicity of MEC-10(d) to identify RNAi knockdowns that enhance neuronal death. We report here that knock-out of the C. elegans nicalin homolog NRA-2 enhances MEC-10(d)-induced neuronal death. Cell biological assays in C. elegans neurons show that NRA-2 controls the distribution of MEC-10(d) between the endoplasmic reticulum and the cell surface. Electrophysiological experiments in Xenopus oocytes support this notion and suggest that control of channel distribution by NRA-2 is dependent on the subunit composition. We propose that nicalin/NRA-2 functions in a quality control mechanism to retain mutant channels in the endoplasmic reticulum, influencing the extent of neuronal death. Mammalian nicalin may have a similar role in DEG/ENaC biology, therefore influencing pathological conditions like ischemia.
20. NRA-2, a Nicalin Homolog, Regulates Neuronal Death by Controlling Surface Localization of Toxic Caenorhabditis elegans DEG/ENaC Channels*
Science.gov (United States)
Kamat, Shaunak; Yeola, Shrutika; Zhang, Wenying; Bianchi, Laura; Driscoll, Monica
2014-01-01
Hyperactivated DEG/ENaCs induce neuronal death through excessive cation influx and disruption of intracellular calcium homeostasis. Caenorhabditis elegans DEG/ENaC MEC-4 is hyperactivated by the (d) mutation and induces death of touch neurons. The analogous substitution in MEC-10 (MEC-10(d)) co-expressed in the same neurons is only mildly neurotoxic. We exploited the lower toxicity of MEC-10(d) to identify RNAi knockdowns that enhance neuronal death. We report here that knock-out of the C. elegans nicalin homolog NRA-2 enhances MEC-10(d)-induced neuronal death. Cell biological assays in C. elegans neurons show that NRA-2 controls the distribution of MEC-10(d) between the endoplasmic reticulum and the cell surface. Electrophysiological experiments in Xenopus oocytes support this notion and suggest that control of channel distribution by NRA-2 is dependent on the subunit composition. We propose that nicalin/NRA-2 functions in a quality control mechanism to retain mutant channels in the endoplasmic reticulum, influencing the extent of neuronal death. Mammalian nicalin may have a similar role in DEG/ENaC biology, therefore influencing pathological conditions like ischemia. PMID:24567339
1. Analytical model and new structure of the enhancement-mode polarization-junction HEMT with vertical conduction channel
Science.gov (United States)
Yang, Chao; Xiong, Jiayun; Wei, Jie; Wu, Junfeng; Peng, Fu; Deng, Siyu; Zhang, Bo; Luo, Xiaorong
2016-04-01
A novel enhancement-mode (E-mode) polarization-junction HEMT with vertical conduction channel (PVC-HEMT) is proposed, and its analytical model for threshold voltage (Vth) is presented. It has two features: one is GaN/AlGaN/GaN double hetero-structure, the other is that source and drain locate at the same side of trench-type MOS gate (T-gate), and the source contacts with the T-gate, which forms vertical conduction channel (VC). The 2-D hole gas (2-DHG) and 2-D electron gas (2-DEG) are formed at the GaN-top/AlGaN and AlGaN/GaN-buffer interface, respectively, forming the polarization-junction. First, the E-mode operation is realized because 2-DHG under the source prevents the electrons injecting from source to 2-DEG, breaking through the conventional E-mode method by depleting 2-DEG under the gate. Second, a uniform electric field (E-field) distribution is achieved due to the assisted depletion effect by polarization-junction. Third, the source reduces the E-field peak at the T-gate side and modulates the E-field distribution. The breakdown voltage (BV) of PVC-HEMT is 705 V and specific ON-resistance (RON,sp) is 1.18 mΩ cm2. Compared with conventional HEMT (C-HEMT), PVC-HEMT has a smaller size due to the special location of the source and T-gate. An analytic threshold voltage model is presented and the analytical results agree well with the simulated results.
2. Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels
OpenAIRE
Arikan, Erdal
2008-01-01
A method is proposed, called channel polarization, to construct code sequences that achieve the symmetric capacity $I(W)$ of any given binary-input discrete memoryless channel (B-DMC) $W$. The symmetric capacity is the highest rate achievable subject to using the input letters of the channel with equal probability. Channel polarization refers to the fact that it is possible to synthesize, out of $N$ independent copies of a given B-DMC $W$, a second set of $N$ binary-input channels \\{W_N^{(i)... 3. Double ferromagnetic metal/semiconductor schottky barrier confined quasi-ballistic transport channel as spin polarizer Institute of Scientific and Technical Information of China (English) Wen Wu 2007-01-01 Spin polarizer is one of the most important devices for the newly developing field of spintronics, which may revolute the popular information techniques. Here we present a phenomenal model for a novel spin polarizer, which utilizes two back to back ferromagnetic metal/semiconductor Schottky barriers to define a semiconductor transport channel whose length is less than the spin decoherence length of the host semiconductor. Along this channel, conducting electrons move diffusively in momentum space while they keep ballistic motion in spin space. Across the channel, electrons suffer a spin dependent tunneling, which establishes spin polarization along the channel. 4. Outreach channels for polar science：an expedition to Kerguelen Islands as a case study Institute of Scientific and Technical Information of China (English) Eduardo Dopico; Eva Garcia-Vazquez 2016-01-01 Polar science outreach is strongly needed, because besides promoting the utility of polar studies for society as a whole, it can generate public demand for new projects and expeditions. The dissemination of polar discoveries should be reinforced in countries without polar territories and for which polar science might not be a priority. In this pilot study (N=182 participants) we have contrasted the opinions of polar scientists (French, Belgian, British, Canadian, Australian, German, Italian and Spanish researchers) with those of a potentially interested public (graduate students of pedagogy and biology), in order to assess if the communication channels employed by polar researchers to make their results public align with those used by non-polar experts for learning about polar discoveries. The results revealed that scientiifc publications and presentations were considered a priority by the researchers, and these scientiifc communication channels were preferentially employed. Only a minority of researchers thought that non-scientiifc publications might be a good communication resource. In contrast, both groups of students, which considered polar research important but not a top priority, employed the Internet as their main channel for information about polar discoveries. Students assessed the use of polar discoveries as positive for educational purposes at both Primary and Secondary levels. The information presently received by students was perceived as being too generalist and the main suggestions to improve outreach in this ifeld, in addition to the use of Internet, were more rapid dissemination of new discoveries. 5. Polarized Uniform Linear Array System: Beam Radiation Pattern, Beamforming Diversity Order, and Channel Capacity Directory of Open Access Journals (Sweden) Xin Su 2015-01-01 Full Text Available There have been many studies regarding antenna polarization; however, there have been few publications on the analysis of the channel capacity for polarized antenna systems using the beamforming technique. According to Chung et al., the channel capacity is determined by the density of scatterers and the transmission power, which is obtained based on the assumption that scatterers are uniformly distributed on a 3D spherical scattering model. However, it contradicts the practical scenario, where scatterers may not be uniformly distributed under outdoor environment, and lacks the consideration of fading channel gain. In this study, we derive the channel capacity of polarized uniform linear array (PULA systems using the beamforming technique in a practical scattering environment. The results show that, for PULA systems, the channel capacity, which is boosted by beamforming diversity, can be determined using the channel gain, beam radiation pattern, and beamforming diversity order (BDO, where the BDO is dependent on the antenna characteristics and array configurations. 6. Polarization Drift Channel Model for Coherent Fibre-Optic Systems CERN Document Server Czegledi, Cristian B; Agrell, Erik; Johannisson, Pontus 2015-01-01 A theoretical framework is introduced to model the dynamical changes of the state of polarization during transmission in coherent fibre-optic systems. The model generalizes the one-dimensional phase noise random walk to higher dimensions, accounting for random polarization drifts. The model is described in the Jones, Stokes and real 4-dimensional formalisms, and the mapping between them is derived. Such a model will be increasingly important in simulating and optimizing future optical systems, which to a higher and higher degree rely on transmission and detection on both polarizations jointly using sophisticated digital signal processing. Such analysis cannot be carried out using the more rudimentary polarization drift models in use today, which only account for deterministic effects. The proposed polarization drift model is the first of its kind and will likely be useful in a wide-range of photonics applications where stochastic polarization fluctuation is an issue. 7. thermally poled channel waveguides with polarization independent electro-optic effect DEFF Research Database (Denmark) Ren, Yitao; Marckmann, Carl Johan; Arentoft, Jesper 2002-01-01 We present a systematic investigation of the poling-induced electrooptic (EO) effect in germanium and nitrogen codoped channel waveguides. The channel waveguides show attractive properties: (1) almost polarization independent EO effect; (2) a flat frequency response with the modulation frequency up... 8. Maximum bandwidth snapshot channeled imaging polarimeter with polarization gratings Science.gov (United States) LaCasse, Charles F.; Redman, Brian J.; Kudenov, Michael W.; Craven, Julia M. 2016-05-01 Compact snapshot imaging polarimeters have been demonstrated in literature to provide Stokes parameter estimations for spatially varying scenes using polarization gratings. However, the demonstrated system does not employ aggressive modulation frequencies to take full advantage of the bandwidth available to the focal plane array. A snapshot imaging Stokes polarimeter is described and demonstrated through results. The simulation studies the challenges of using a maximum bandwidth configuration for a snapshot polarization grating based polarimeter, such as the fringe contrast attenuation that results from higher modulation frequencies. Similar simulation results are generated and compared for a microgrid polarimeter. Microgrid polarimeters are instruments where pixelated polarizers are superimposed onto a focal plan array, and this is another type of spatially modulated polarimeter, and the most common design uses a 2x2 super pixel of polarizers which maximally uses the available bandwidth of the focal plane array. 9. Modeling of concentration polarization in a reverse osmosis channel with parabolic crossflow. Science.gov (United States) Liu, Cui; Morse, Audra; Rainwater, Ken; Song, Lianfa 2014-01-01 Concentration polarization in narrow reverse osmosis channels with parabolic crossflow was numerically simulated with finite different equations related to permeate velocity, crossflow velocity, average salt concentration, and wall salt concentration. A significant new theoretical development was the determination of two correction functions, F2 and F3, in the governing equation for average salt concentration. Simulations of concentration polarization under various conditions were then presented to describe the features of the new model as well as discussions about the differences of concentration polarizations of the more realistic parabolic flow with those when plug flow or shear flow was assumed. The situations in which the simpler models based on shear or plug flow can be used were indicated. Concentration polarization was also simulated for various conditions to show the applicability of the model and general features of concentration polarization in a narrow, long reverse osmosis channel. 10. Polar Decomposition of Mutual Information and Applications to Partially Coherent Channels CERN Document Server Goebel, Bernhard; Kramer, Gerhard; Winzer, Peter J; Hanik, Norbert 2010-01-01 The mutual information between a complex-valued channel input and its complex-valued output is decomposed into four parts based on polar coordinates: an amplitude term, a phase term, and two mixed terms. Numerical results for the additive white Gaussian noise (AWGN) channel with various inputs show that, at high signal-to-noise ratio (SNR), the amplitude and phase terms dominate the mixed terms. For the AWGN channel with a Gaussian input, analytical expressions are derived for high SNR. The decomposition method is applied to partially coherent channels and a property of such channels called "spectral loss" is developed. Spectral loss is used to explain the behavior of the capacity of nonlinear fiber-optic channels presented in recent studies, and is applied to simplify a recently published phenomenological channel model. 11. Investigations in Satellite MIMO Channel Modeling: Accent on Polarization Directory of Open Access Journals (Sweden) Péter Horváth 2007-05-01 Full Text Available Due to the much different environment in satellite and terrestrial links, possibilities in and design of MIMO systems are rather different as well. After pointing out these differences and problems arising from them, two MIMO designs are shown rather well adapted to satellite link characteristics. Cooperative diversity seems to be applicable; its concept is briefly presented without a detailed discussion, leaving solving particular satellite problems to later work. On the other hand, a detailed discussion of polarization time-coded diversity (PTC is given. A physical-statistical model for dual-polarized satellite links is presented together with measuring results validating the model. The concept of 3D polarization is presented as well as briefly describing compact 3D-polarized antennas known from the literature and applicable in satellite links. A synthetic satellite-to-indoor link is constructed and its electromagnetic behavior is simulated via the FDTD (finite-difference time-domain method. Previous result of the authors states that in 3D-PTC situations, MIMO capacity can be about two times higher than SIMO (single-input multiple-output capacity while a diversity gain of nearly 2×3 is further verified via extensive FDTD computer simulation. 12. Photoluminescence of a High Mobility 2DEG in the Fractional Quantum Hall Effect Regime Science.gov (United States) Smirnov, D.; Rudenkov, V. V.; Ashkinadze, B. M.; Cohen, E.; Christianen, P. C. M.; Maan, J. C.; Pfeiffer, L. N. The magneto-PL spectra of modulation-doped, ultra-high mobility GaAs/AlGaAs single heterojunctions (HJs) were studied under a perpendicularly applied magnetic field up to 33 T and at temperatures of 0.3 and 1.2 K. The spectra show remarkable intensity redistribution between free (bulk) exciton and 2DEG-hole PL channels occurring at electron filling factors, ν = 2 and 1. At 0.3 K, significant 2DEG-hole PL spectral changes are observed near ν = 2/3 and 1/3. Several heterojunctions with 2DEG density in the range of n2D - (1 - 2.7) · 1011 cm-2 display similar features. These spectral peculiarities are attributed to the modification of the 2DEG energy spectrum caused by the e-e interaction, in particular, the recombination of valence hole with the composite (fractionally-charged) particles of the magnetized 2DEG. In HJs with lower n2D < 1011 cm-2, the observed PL evolution at ν < 1 is mainly determined by an intensity redistribution between the σ+ and σ- circularly-polarized free exciton PL components. In this case, the exciton energy is lower than the energy of the 2DEG-hole system, so that the free excitons do not dissociate near the magnetized 2DEG and thus, the 2DEG-hole PL is barely observed. 13. Achieving the Secrecy Capacity of Wiretap Channels Using Polar Codes CERN Document Server Mahdavifar, Hessam 2010-01-01 Suppose Alice wishes to send messages to Bob through a communication channel C_1, but her transmissions also reach an eavesdropper Eve through another channel C_2. The goal is to design a coding scheme that makes it possible for Alice to communicate both reliably and securely. Reliability is measured in terms of Bob's probability of error in recovering the message, while security is measured in terms of the mutual information between the message and Eve's observations. Wyner showed that the situation is characterized by a single constant C_s, called the secrecy capacity, which has the following meaning: for all\\epsilon > 0$, there exist coding schemes of rate$R \\ge C_s - \\epsilonthat asymptotically achieve both the reliability and the security objectives. However, his proof of this result is based upon a nonconstructive random-coding argument. To date, despite a considerable research effort, the only case where we know how to construct coding schemes that achieve secrecy capacity is when Eve's channel C_... 14. Characterization of dual-polarization LTE radio over a free-space optical turbulence channel. Science.gov (United States) Bohata, J; Zvanovec, S; Korinek, T; Mansour Abadi, M; Ghassemlooy, Z 2015-08-10 A dual polarization (DP) radio over a free-space optical (FSO) communication link using a long-term evolution (LTE) radio signal is proposed and analyzed under different turbulence channel conditions. Radio signal transmission over the DP FSO channel is experimentally verified by means of error vector magnitude (EVM) statistics. We demonstrate that such a system, employing a 64 quadrature amplitude modulation at the frequency bands of 800 MHz and 2.6 GHz, evinces reliability with LTE signal over the FSO channel is a potential solution for last-mile access or backbone networks, when using multiple-input multiple-output based DP signals. 15. Control of Magnetism via Layer Thickness Modification in the LaMnO3/SrMnO3 Digital Superlattices and the Prediction of a Spin-Polarized 2DEG Science.gov (United States) Nanda, Birabar; Satpathy, Sashi 2009-03-01 We study the effect of layer thickness on the magnetic properties in the (LMO)2n/(SMO)n superlattices using density-functional calculations. The change in the magnetic properties is shown to be controlled by the leakage of the Mn-eg electrons from the LMO side to the SMO side. For n = 1 superlattice, the weak potential barrier allows the Mn-eg electrons to spread across the entire superlattice, so that a uniform ferromagnetic behavior is obtained through carrier mediated Zener double exchange. For larger n, the strong potential barrier restricts the eg electron transfer to few layers adjacent to the interface, thus leaving the magnetism unchanged and bulk like away from the interface, while modifying the magnetism in the interfacial region. Finally, taking the example of a delta doped superlattice, (SMO)/(LMO)1/(SMO), we predict the formation of a spin-polarized two dimensional electron gas. The 2DEG, generated due to the confinement of the La (d) electrons in the direction normal to the interface, mediates a ferromagnetic alignment of the Mn-t2g spins via double exchange which in turn spin polarizes the 2DEG. Work supported by the US Department of Energy 1. B. R. K. Nanda and S. Satpathy, arXiv:0810.2126; B. R. K. Nanda and S. Satpathy, Phys. Rev. Lett. 101, 127201 (2008) 16. Secured optical fiber communication using polarization restoration technique and channel characterization Science.gov (United States) Punekar, Nikhil; Darunkar, Bhagyashri; Verma, Pramode 2016-02-01 Optical fiber channels are used as media to transfer the information globally. This paper presents an implementation of a novel procedure using which a secured communication between two parties can be carried out using polarized beam of light over an optical fiber. The paper presents the experimental results obtained of the procedure in the lab environment and a security analysis of the same. It is observed that polarization state of a light pulse cannot be retained as it travels over an optical fiber because of the birefringence phenomenon. Multiple environmental factors such as pressure, vibration, temperature, etc. also add a non-linearity to the birefringence of an optical fiber leading towards an unpredictable polarization state changes over the course of an optical fiber. The proposed procedure helps the receiving party to successfully retrieve the data in the form of a polarization state transmitted by the sending party without having any knowledge about the state of polarization at the transmitting end. The paper also explains an added layer of security the procedure provides to the communicating parties to make it difficult for an adversary to fetch the data being transferred. The proposed system does not depend on the wavelength of the light being used, nor does it depend upon the type of the optical fiber used for the communication. Using this procedure, multiple bits of secured information can be sent over an optical fiber in a single polarized pulse and retrieved at the receiving end, also known as Polarization Shift Keying. 17. Coherent-state constellations and polar codes for thermal Gaussian channels Science.gov (United States) Lacerda, Felipe; Renes, Joseph M.; Scholz, Volkher B. 2017-06-01 Optical communication channels are ultimately quantum mechanical in nature, and we must therefore look beyond classical information theory to determine their communication capacity as well as to find efficient encoding and decoding schemes of the highest rates. Thermal channels, which arise from linear coupling of the field to a thermal environment, are of particular practical relevance; their classical capacity has been recently established, but their quantum capacity remains unknown. While the capacity sets the ultimate limit on reliable communication rates, it does not promise that such rates are achievable by practical means. Here we construct efficiently encodable codes for thermal channels which achieve the classical capacity and the so-called Gaussian coherent information for transmission of classical and quantum information, respectively. Our codes are based on combining polar codes with a discretization of the channel input into a finite "constellation" of coherent states. Encoding of classical information can be done using linear optics. 18. Spatial distribution of spin polarization in a channel on the surface of a topological insulator. Science.gov (United States) Zhou, Xiaoying; Shao, Huaihua; Liu, Yiman; Tang, Dongsheng; Zhou, Guanghui 2012-05-09 We study the spatial distribution of electron spin polarization for a gate-controlled T-shaped channel on the surface of a three-dimensional topological insulator (3D TI). We demonstrate that an energy gap depending on channel geometry parameters is definitely opened due to the spatial confinement. Spin surface locking in momentum space for a uniform wide channel with Hamiltonian linearity in the wavevector is still kept, but it is broken with Hamiltonian nonlinearity in the wavevector, like that for two-dimensional surface states widely studied in the literature. However, the spin surface locking for a T-shaped channel is broken even with Hamiltonian linearity in the wavevector. Interestingly, the magnitude and direction of the in-plane spin polarization are spatially dependent in all regions due to the breaking of translational symmetry of the T-shaped channel system. These interesting findings for an electrically controlled nanostructure based on the 3D TI surface may be testable with the present experimental technique, and may provide further understanding the nature of 3D TI surface states. 19. Achieving the capacity of half-duplex degraded relay channels using polar coding Institute of Scientific and Technical Information of China (English) Duo Bin; Wang Zhenyong; Gu Xuemai; Guo Qing 2014-01-01 In this paper, a novel transmission protocol based on polar coding is proposed for the half-duplex degraded relay channel. In the proposed protocol, referred to as the partial message relaying, the relay only needs to forward a part of the decoded source message that the destination needs according to the exquisite nested structure of polar codes. Theoretically, it is proved that the scheme can achieve the capacity of the half-duplex relay channel under the decode-and-forward (DF) cooperation strategy while enjoying low encoding/decoding complexity. Practically, in order to minimize the global transmission power, the optimization of the power allocation is performed between the source and the relay by using information theoretic tools. Furthermore, a joint iterative soft parallel interference cancellation receiver structure is developed to suit to the proposed scheme. Simulation results show that the proposed scheme outperforms the conventional scheme designed by low-density parity-check (LDPC) codes. 20. Top quark polarization in t-channel single top-quark events with the ATLAS detector CERN Document Server Chitishvili, Mariam 2017-01-01 This summary presents the measurement of the top‐quark polarization in t-channel single top quarks with the ATLAS detector at the LHC. Monte Carlo simulated events are used. Selected events contain one lepton, large missing transverse momentum and exactly two jets, with one of them identified as b-jet. Selection cuts are used to identify the t-channel topology at reconstruction level. The polarization is measured, from an asymmetry in an angular distribution, at parton level by correcting the reconstructed angular distribution for detector effects. This project provides an overview on how a "standard" physics analysis is performed within ATLAS. The analysis is performed in ROOT. Simulation data is reconstructed to perform an unfolded measurement of a given property of a fundamental particle within the Standard Model. Finally results are compared with theoretical predictions. 1. Measurement of thet\\bar{t}$spin correlations and top quark polarization in dileptonic channel CERN Document Server Khatiwada, Ajeeta 2017-01-01 The degree of top polarization and strength of$t\\bar{t}$correlation are dependent on production dynamics, decay mechanism, and choice of the observables. At the LHC, measurement of the top polarization and spin correlations in$t\\bar{t}$production is possible through various observables related to the angular distribution of decay leptons. A measurement of differential distribution provides a precision test of the standard model of particle physics and probes for deviations, which could be a sign of new physics. In particular, the phase space for the super-symmetric partner of the top quark can be constrained. Results from the Compact Muon Solenoid (CMS) collaboration for top quark polarization and spin correlation in the dileptonic channel are reviewed briefly in this proceeding. The measurements are obtained using 19.5 fb$^{-1}$of data collected in pp collisions at the center-of-mass energy of 8 TeV. 2. Experimental demonstration of tunable homodyne detection of WDM and dual-polarization PSK channels by automatically locking the channels to a local pump laser using nonlinear mixing. Science.gov (United States) Almaiman, Ahmed; Ziyadi, Morteza; Mohajerin-Ariaei, Amirhossein; Cao, Yinwen; Chitgarha, Mohammad Reza; Liao, Peicheng; Bao, Changjing; Shamee, Bishara; Ahmed, Nisar; Alishahi, Fatemeh; Fallahpour, Ahmad; Akasaka, Youichi; Yang, Jeng-Yuan; Sekiya, Motoyoshi; Touch, Joseph D; Tur, Moshe; Langrock, Carsten; Fejer, Martin M; Willner, Alan E 2016-06-15 This Letter proposes a method for tunable automatically locked homodyne detection of wavelength-division multiplexing (WDM) dual-polarization (DP) phase-shift keyed (PSK) channels using nonlinear mixing. Two stages of periodically poled lithium niobate (PPLN) waveguides and an LCoS filter enable automatic phase locking of the channels to a local laser. 3. Investigation of polarization effects in the gramicidin A channel from ab initio molecular dynamics simulations. Science.gov (United States) Timko, Jeff; Kuyucak, Serdar 2012-11-28 Polarization is an important component of molecular interactions and is expected to play a particularly significant role in inhomogeneous environments such as pores and interfaces. Here we investigate the effects of polarization in the gramicidin A ion channel by performing quantum mechanics/molecular mechanics molecular dynamics (MD) simulations and comparing the results with those obtained from classical MD simulations with non-polarizable force fields. We consider the dipole moments of backbone carbonyl groups and channel water molecules as well as a number of structural quantities of interest. The ab initio results show that the dipole moments of the carbonyl groups and water molecules are highly sensitive to the hydrogen bonds (H-bonds) they participate in. In the absence of a K(+) ion, water molecules in the channel are quite mobile, making the H-bond network highly dynamic. A central K(+) ion acts as an anchor for the channel waters, stabilizing the H-bond network and thereby increasing their average dipole moments. In contrast, the K(+) ion has little effect on the dipole moments of the neighboring carbonyl groups. The weakness of the ion-peptide interactions helps to explain the near diffusion-rate conductance of K(+) ions through the channel. We also address the sampling issue in relatively short ab initio MD simulations. Results obtained from a continuous 20 ps ab initio MD simulation are compared with those generated by sampling ten windows from a much longer classical MD simulation and running each window for 2 ps with ab initio MD. Both methods yield similar results for a number of quantities of interest, indicating that fluctuations are fast enough to justify the short ab initio MD simulations. 4. The Modulus of the Complex Correlation Coefficient Between Co-Polarized Channels for Oil Spill Observation Science.gov (United States) Khenouchi, H.; Smara, Y.; Migliaccio, M.; Nunziata, F.; Buono, A. 2016-08-01 Sea oil pollution is a matter of great concern since it affects both the environment and human health. Recent studies demonstrated that synthetic aperture radar (SAR) polarimetry is able to provide additional information useful for environmental applications, i. e., oil spill observation. In this context, different approaches based on polarimetric SARs were developed. In this study, a dual-polarimetric feature, namely the modulus of the complex correlation coefficient between the co-polarized channels, is used to discriminate between sea oil spill and weak-damping look-alikes.The proposed approach relies on the fact that high correlation between co-polarized channels is expected over sea surface and weak-damping look- alikes due to the dominant Bragg scattering, while significantly lower correlation is expected over strong-damping oil spills since they are characterized by a no-Bragg scattering behaviour. Experimental results show that the modulus of the complex correlation between the co-polarized chan- nels can be successfully exploited for both the observation of sea oil slicks and their discrimination from weak-damping look-alikes. 5. Evaluation of in-channel amperometric detection using a dual-channel microchip electrophoresis device and a two-electrode potentiostat for reverse polarity separations. Science.gov (United States) Meneses, Diogenes; Gunasekara, Dulan B; Pichetsurnthorn, Pann; da Silva, José A F; de Abreu, Fabiane C; Lunte, Susan M 2015-02-01 In-channel amperometric detection combined with dual-channel microchip electrophoresis is evaluated using a two-electrode isolated potentiostat for reverse polarity separations. The device consists of two separate channels with the working and reference electrodes placed at identical positions relative to the end of the channel, enabling noise subtraction. In previous reports of this configuration, normal polarity and a three-electrode detection system were used. In the two-electrode detection system described here, the electrode in the reference channel acts as both the counter and reference. The effect of electrode placement in the channels on noise and detector response was investigated using nitrite, tyrosine, and hydrogen peroxide as model compounds. The effects of electrode material and size and type of reference electrode on noise and the potential shift of hydrodynamic voltammograms for the model compounds were determined. In addition, the performance of two- and three-electrode configurations using Pt and Ag/AgCl reference electrodes was compared. Although the signal was attenuated with the Pt reference, the noise was also significantly reduced. It was found that lower LOD were obtained for all three compounds with the dual-channel configuration compared to single-channel, in-channel detection. The dual-channel method was then used for the detection of nitrite in a dermal microdialysis sample obtained from a sheep following nitroglycerin administration. 6. Understanding hydrogen sorption in a polar metal-organic framework with constricted channels Science.gov (United States) Stern, Abraham C.; Belof, Jonathan L.; Eddaoudi, Mohamed; Space, Brian 2012-01-01 A high fidelity molecular model is developed for a metal-organic framework (MOF) with narrow (approximately 7.3 Å) nearly square channels. MOF potential models, both with and neglecting explicit polarization, are constructed. Atomic partial point charges for simulation are derived from both fragment-based and fully periodic electronic structure calculations. The molecular models are designed to accurately predict and retrodict material gas sorption properties while assessing the role of induction for molecular packing in highly restricted spaces. Thus, the MOF is assayed via grand canonical Monte Carlo (GCMC) for its potential in hydrogen storage. The confining channels are found to typically accommodate between two to three hydrogen molecules in close proximity to the MOF framework at or near saturation pressures. Further, the net attractive potential energy interactions are dominated by van der Waals interactions in the highly polar MOF - induction changes the structure of the sorbed hydrogen but not the MOF storage capacity. Thus, narrow channels, while providing reasonably promising isosteric heat values, are not the best choice of topology for gas sorption applications from both a molecular and gravimetric perspective. 7. Development of Ribbon Fiber Type Multi-Channel Power Level Monitor with Low-Insertion/Polarization Loss Institute of Scientific and Technical Information of China (English) Maki; Inai; Akira; Haraguchi; Takeo; Komiya; Kiyotaka; Murashima; Takashi; Sasaki; Kazuhito; Saitoh 2003-01-01 We would like to propose a new in-line multi-channel power level monitor, which is applicable as tap-monitor for multi-channel WDM signals. Its ribbon fiber structure has far exceeded PLC performance and realized compact-size and lower insertion/polarization dependent loss. 8. Rate-Dependent Analysis of the Asymptotic Behavior of Channel Polarization CERN Document Server Hassani, S Hamed; Tanaka, Toshiyuki; Urbanke, Rudiger 2011-01-01 For a binary-input memoryless symmetric channel$W$, we consider the asymptotic behavior of the polarization process in the large block-length regime when transmission takes place over$W$. In particular, we study the asymptotics of the cumulative distribution$\\mathbb{P}(Z_n \\leq z)$, where$\\{Z_n\\}$is the Bhattacharyya process defined from$W$, and its dependence on the rate of transmission. On the basis of this result, we characterize the asymptotic behavior, as well as its dependence on the rate, of the block error probability of polar codes using the successive cancellation decoder. This refines the original bounds by Ar{\\i}kan and Telatar. Our results apply to general polar codes based on$\\ell \\times \\ell$kernel matrices. We also provide lower bounds on the block error probability of polar codes using the MAP decoder. The MAP lower bound and the successive cancellation upper bound coincide when$\\ell=2$, but there is a gap for$\\ell>2$. 9. Optimal Multiplexing Gain of K-user Line-of-Sight Interference Channels with Polarization CERN Document Server Chae, Sung ho; Chung, Sae-Young 2009-01-01 We consider the multiplexing gain (MUXG) of the fully connected K-user line-of-sight (LOS) interference channels (ICs). A polarimetric antenna composed of 3 orthogonal electric dipoles and 3 orthogonal magnetic dipoles is considered where all 6 dipoles are co-located. In case of K-user IC with single polarization, the maximum achievable MUXG is K regardless of the number of transmit and receive antennas because of the key-hole effect. With polarization, a trivial upper bound on the MUXG is 2K. We propose a zero forcing (ZF) scheme for the K-user LOS IC, where each user uses one or more polarimetric antennas. By using the proposed ZF scheme, we find minimal antenna configurations that achieve this bound for K 5, we show that the optimal MUXG of 2K is achieved with M = (K+1)/6 polarimetric antennas at each user. 10. Design of a novel multi channel photonic crystal fiber polarization beam splitter Science.gov (United States) Zhao, Yunyan; Li, Shuguang; Wang, Xinyu; Wang, Guangyao; Shi, Min; Wu, Junjun 2017-10-01 A kind of multi channel dual-core photonic crystal fiber polarization beam splitter is designed. We analyze the effects of the lattice parameters and the thickness of gold layer on the beam splitting by the finite element method. Numerical results show that the thickness of metal layer and the size of the air holes near the fiber cores are closely linked with the nature of the polarization beam splitter. We also obtain that extinction ratio can reach -73.87 dB at 1 . 55 μm wavelength and at 1 . 41 μm, 1 . 65 μm extinction ratio can reach 30.8978 dB and 31.1741 dB, respectively. The comparison of the effect on the characteristic of the photonic crystal fiber with coating no gold is also taken into account. 11. Drosophila nociceptors mediate larval aversion to dry surface environments utilizing both the painless TRP channel and the DEG/ENaC subunit, PPK1. Directory of Open Access Journals (Sweden) Wayne A Johnson Full Text Available A subset of sensory neurons embedded within the Drosophila larval body wall have been characterized as high-threshold polymodal nociceptors capable of responding to noxious heat and noxious mechanical stimulation. They are also sensitized by UV-induced tissue damage leading to both thermal hyperalgesia and allodynia very similar to that observed in vertebrate nociceptors. We show that the class IV multiple-dendritic(mdIV nociceptors are also required for a normal larval aversion to locomotion on to a dry surface environment. Drosophila melanogaster larvae are acutely susceptible to desiccation displaying a strong aversion to locomotion on dry surfaces severely limiting the distance of movement away from a moist food source. Transgenic inactivation of mdIV nociceptor neurons resulted in larvae moving inappropriately into regions of low humidity at the top of the vial reflected as an increased overall pupation height and larval desiccation. This larval lethal desiccation phenotype was not observed in wild-type controls and was completely suppressed by growth in conditions of high humidity. Transgenic hyperactivation of mdIV nociceptors caused a reciprocal hypersensitivity to dry surfaces resulting in drastically decreased pupation height but did not induce the writhing nocifensive response previously associated with mdIV nociceptor activation by noxious heat or harsh mechanical stimuli. Larvae carrying mutations in either the Drosophila TRP channel, Painless, or the degenerin/epithelial sodium channel subunit Pickpocket1(PPK1, both expressed in mdIV nociceptors, showed the same inappropriate increased pupation height and lethal desiccation observed with mdIV nociceptor inactivation. Larval aversion to dry surfaces appears to utilize the same or overlapping sensory transduction pathways activated by noxious heat and harsh mechanical stimulation but with strikingly different sensitivities and disparate physiological responses. 12. Electric field induced spin and valley polarization within a magnetically confined silicene channel Energy Technology Data Exchange (ETDEWEB) Liu, Yiman; Zhou, Xiaoying; Zhou, Ma; Zhou, Guanghui, E-mail: ghzhou@hunnu.edu.cn [Department of Physics and Key Laboratory for Low-Dimensional Structures and Quantum Manipulation (Ministry of Education), Hunan Normal University, Changsha 410081 (China); Long, Meng-Qiu [Institute of Super-microstructure and Ultrafast Process in Advanced Materials, School of Physics and Electronics, Central South University, Changsha 410083 (China) 2014-12-28 We study the electronic structure and transport properties of Dirac electrons along a channel created by an exchange field through the proximity of ferromagnets on a silicene sheet. The multiple total internal reflection induces localized states in the channel, which behaves like an electron waveguide. An effect of spin- and valley-filtering originating from the coupling between valley and spin degrees is predicted for such a structure. Interestingly, this feature can be tuned significantly by locally applying electric and exchange fields simultaneously. The parameter condition for observing fully spin- and valley-polarized current is obtained. These findings may be observable in todays' experimental technique and useful for spintronic and valleytronic applications based on silicene. 13. Il teatro degli spiriti. Directory of Open Access Journals (Sweden) Chiara Pussetti 2013-07-01 Full Text Available Questo saggio è dedicato a un culto di possessione, in cui tutte ledonne, investite dagli spiriti degli uomini morti prima dell’iniziazione, compiono un percorso iniziatico parallelo a quello maschile, consentendo a queste anime, potenzialmente pericolose, di completare il cammino che non hanno potuto percorrere da vivi e quindi di raggiungere serenamente il mondo dei morti, come antenati protettori del villaggio 14. Targets detecting in the ocean using the cross-polarized channels of fully polarimetric SAR data Institute of Scientific and Technical Information of China (English) WANG Yunhua; LIU Xiaoyan; LI Huimin; ZHANG Yanmin 2015-01-01 Azimuth ambiguities (ghost targets) discrimination is of great interest with the development of a synthet-ic aperture radar (SAR). And the azimuth ambiguities are often mistaken as actual targets and cause false alarms. For actual targets, HV channel signals acquired by a fully polarimetric SAR are approximately equal to a VH channel in magnitude and phase, i.e., the reciprocity theorem applies, but shifted in phase about ±ʌ for the first-order azimuth ambiguities. Exploiting this physical behavior, the real part of the product of the two cross-polarized channels, i.e.()SHVSV H, hereafter calledA12r, is employed as a new parameter for a target detection at sea. Compared with other parameters, the contrast ofA12r image between a target and the surrounding sea surface will be obviously increased whenA12r image is processed by mean filtering algo-rithm. Here, in order to detect target with constant false-alarm rates (CFARs), an analytical expression for the probability density function (pdf) ofA12r is derived based on the complex Wishart-distribution. Because a value ofA12r is greater/less than 0 for real target/its azimuth ambiguities, the first-order azimuth ambiguities can be completely removed by thisA12r-based CFAR technology. Experiments accomplished over C-band RADARSAT-2 fully polarimetric imageries confirm the validity. 15. High Spectrum Narrowing Tolerant 112 Gb/s Dual Polarization QPSK Optical Communication Systems Using Digital Adaptive Channel Estimation DEFF Research Database (Denmark) Zhang, Xu; Pang, Xiaodan; Dogadaev, Anton Konstantinovich 2012-01-01 We experimentally demonstrate high spectrum narrowing tolerant 112-Gb/s QPSK polarization multiplex system based on digital adaptive channel estimation method. The proposed algorithm is able to detect severe spectrum-narrowed signal even with 20GHz 3dB bandwidth.......We experimentally demonstrate high spectrum narrowing tolerant 112-Gb/s QPSK polarization multiplex system based on digital adaptive channel estimation method. The proposed algorithm is able to detect severe spectrum-narrowed signal even with 20GHz 3dB bandwidth.... 16. Ingegneria degli acquiferi CERN Document Server Molfetta, Antonio 2012-01-01 Il testo fornisce le conoscenze necessarie per affrontare, con un approccio quantitativo, i molteplici aspetti connessi al flusso delle risorse idriche sotterranee (acque di falda) e alla propagazione e bonifica di contaminanti nei sistemi acquiferi. Vengono illustrate le proprietà fondamentali che definiscono la capacità di immagazzinamento, trasporto e rilascio dell’acqua negli acquiferi, e successivamente, descritte le metodiche per la determinazione di tali parametri tramite l’esecuzione e l’interpretazione di prove di falda, di pozzo e di laboratorio. A partire dalla classificazione chimico fisica-tossicologica dei contaminanti vengono, quindi, analizzati i meccanismi di propagazione e illustrate le soluzioni analitiche dell’equazione del trasporto di massa nei mezzi porosi. L’ultima parte del testo è dedicata alla caratterizzazione e bonifica degli acquiferi contaminati. Il testo è rivolto sia agli studenti universitari, sia ai professionisti che debbano affrontare con un approccio quantit... 17. Closed-Form Performance Analysis of Dual Polarization Based MIMO System in Shadowed-Rician Fading LMS Channels Directory of Open Access Journals (Sweden) Suresh Kumar Jindal 2015-04-01 Full Text Available In this paper, the problem of dual polarization based MIMO Processing in Shadowed-Rician (SR fading land mobile satellite (LMS channels is studied. It is shown in literature that polarization is used as a interference rejection method; and, most of the existing analytical results are not in closed-form. In this paper, we derive the closed-form expressions of the moment generating (MGF function of the received signal-to-noise ratio of the MRC based receiver in SR fading LMS channels. Then we provide closed-form expressions of the symbol error rate (SER by using MGF approach. The analytical diversity order and capacity of the considered scheme is also derived. It is shown by by derived closed-form capacity expression that the capacity of the considered dual polarization based scheme is improved; and it is found very useful in practical satellite communication systems. 18. Improved digital backward propagation for the compensation of inter-channel nonlinear effects in polarization-multiplexed WDM systems. Science.gov (United States) Mateo, Eduardo F; Zhou, Xiang; Li, Guifang 2011-01-17 An improved split-step method (SSM) for digital backward propagation (DBP) applicable to wavelength-division multiplexed (WDM) transmission with polarization-division multiplexing (PDM) is presented. A coupled system of nonlinear partial differential equations, derived from the Manakov equations, is used for DBP. The above system enables the implementation of DBP on a channel-by-channel basis, where only the effect of phase-mismatched four-wave mixing (FWM) is neglected. A novel formulation of the SSM for PDM-WDM systems is presented where new terms are included in the nonlinear step to account for inter-polarization mixing effects. In addition, the effect of inter-channel walk-off is included. This substantially reduces the computational load compared to the conventional SSM. 19. Employing circle polarization shift keying in free space optical communication with gamma-gamma atmospheric turbulence channel Science.gov (United States) Wang, Yi; Du, Fan; Ma, Jing; Tan, Liying 2014-12-01 A novel theoretical model of a circular polarization shift keying (CPolSK) system for free space optical links through an atmospheric turbulence channel, is proposed. Intensity scintillation and phase fluctuation induced in atmospheric turbulence, from weak to strong levels, are specifically researched with respect to circular polarization control error caused by the system design. We derive closed form expressions of the bit error rate (BER) and outage probability for evaluating the BER performance and communication interruption in the Gamma-Gamma distributed channel model. Simulation results show that atmospheric turbulence and circular polarization control error have significant effects on the BER performance and interruption of communication in the CPolSK system. The deterioration in BER performance, caused by intensity scintillation and phase fluctuation, is augmented by the power penalty conditioned by the circular polarization control error. This consequently adds to the demand for emissive power from the CPolSK system. Furthermore, we demonstrate that controlling the circular polarization control error below 8° as well as the normalized threshold within 8 dB, 9 dB and 10 dB in turbulent scenarios from weak to strong levels can significantly reduce the probability of communication interruption occurring. This study provides reference material for further design of the CPolSK system. 20. Tunable 13C/1H dual channel matching circuit for dynamic nuclear polarization system with cross-polarization DEFF Research Database (Denmark) Rybalko, Oleksandr; Bowen, Sean; Zhurbenko, Vitaliy 2016-01-01 In this paper we report initial results of design and practical implementation of tuning and matching circuit to estimate a performance of Dynamic Nuclear Polarization (DNP) at a magnetic field of 6.7 T. It is shown that developed circuit for signal observation is compact, easy to make and provides... 1. The structures of Arabidopsis Deg5 and Deg8 reveal new insights into HtrA proteases Energy Technology Data Exchange (ETDEWEB) Sun, Wei [Chinese Academy of Sciences, 5 Datun Road, Chaoyang District, Beijing 100101 (China); University of Chinese Academy of Sciences, 19A Yuquan Road, Beijing 100049 (China); Gao, Feng [Chinese Academy of Sciences, 5 Datun Road, Chaoyang District, Beijing 100101 (China); Fan, Haitian; Shan, Xiaoyue [Chinese Academy of Sciences, 5 Datun Road, Chaoyang District, Beijing 100101 (China); University of Chinese Academy of Sciences, 19A Yuquan Road, Beijing 100049 (China); Sun, Renhua [Chinese Academy of Sciences, 20 Nanxincun, Haidian District, Beijing 100093 (China); University of Chinese Academy of Sciences, 19A Yuquan Road, Beijing 100049 (China); Liu, Lin, E-mail: liulin@ibcas.ac.cn [Chinese Academy of Sciences, 20 Nanxincun, Haidian District, Beijing 100093 (China); Gong, Weimin, E-mail: liulin@ibcas.ac.cn [Chinese Academy of Sciences, 5 Datun Road, Chaoyang District, Beijing 100101 (China) 2013-05-01 The crystal structures of Arabidopsis Deg5 and Deg8 have been determined to resolutions of 2.6 and 2.0 Å, respectively, revealing novel structural features of HtrA proteases. Plant Deg5 and Deg8 are two members of the HtrA proteases, a family of oligomeric serine endopeptidases that are involved in a variety of protein quality-control processes. These two HtrA proteases are located in the thylakoid lumen and participate in high-light stress responses by collaborating with other chloroplast proteins. Deg5 and Deg8 degrade photodamaged D1 protein of the photosystem II reaction centre, allowing its in situ replacement. Here, the crystal structures of Arabidopsis thaliana Deg5 (S266A) and Deg8 (S292A) are reported at 2.6 and 2.0 Å resolution, respectively. The Deg5 trimer contains two calcium ions in a central channel, suggesting a link between photodamage control and calcium ions in chloroplasts. Previous structures of HtrA proteases have indicated that their regulation usually requires C-terminal PDZ domain(s). Deg5 is unique in that it contains no PDZ domain and the trimeric structure of Deg5 (S266A) reveals a novel catalytic triad conformation. A similar triad conformation is observed in the hexameric structure of the single PDZ-domain-containing Deg8 (S292A). These findings suggest a novel activation mechanism for plant HtrA proteases and provide structural clues to their function in light-stress response. 2. A Putative Calcium-Permeable Cyclic Nucleotide-Gated Channel, CNGC18, Regulates Polarized Pollen Tube Growth Institute of Scientific and Technical Information of China (English) 2007-01-01 A tip-focused Ca2+ gradient is tightly coupled to polarized pollen tube growth, and tip-localized influxes of extracellular Ca2+ are required for this process. However the molecular identity and regulation of the potential Ca2+ channels remains elusive.The present study has implicated CNGC18 (cyclic nucleotide-gated channel 18) in polarized pollen tube growth, because its overexpression induced wider and shorter pollen tubes. Moreover, CNGC18 overexpression induced depolarization of pollen tube growth was suppressed by lower extracellular calcium ([Ca2+]ex). CNGC18-yellow fluorescence protein (YFP)was preferentially localized to the apparent post-Golgi vesicles and the plasma membrane (PM) in the apex of pollen tubes.The PM localization was affected by tip-localized ROP1 signaling. Expression of wild type ROP1 or an active form of ROP1enhanced CNGC18-YFP localization to the apical region of the PM, whereas expression of RopGAP1 (a ROP1 deactivator)blocked the PM localization. These results support a role for PM-localized CNGC18 in the regulation of polarized pollen tube growth through Its potential function in the modulation of calcium influxes. 3. Plasma polar lipid profiles of channel catfish with different growth rates Science.gov (United States) Increased growth in channel catfish is an economically important trait and has been used as a criterion for the selection and development of brood fish. Selection of channel catfish toward increased growth usually results in the accumulation of large amounts of fats in their abdomen rather than incr... 4. Efficient cross polarization with simultaneous adiabatic frequency sweep on the source and target channels. Science.gov (United States) Peng, Weng Kung; Takeda, Kazuyuki 2007-10-01 In this work, we propose a new and efficient heteronuclear cross polarization scheme, in which adiabatic frequency sweeps from far off-resonance toward on-resonance are applied simultaneously on both the source and target spins. This technique, which we call as Simultaneous ADIabatic Spin-locking Cross Polarization (SADIS CP), is capable of efficiently locking both the source and target spins with moderate power even in the presence of large spectral distribution and fast relaxation. It is shown that by keeping the time-dependent Hartmann-Hahn mismatch minimal throughout the mixing period, polarization transfer can be accelerated. Experiments are demonstrated in a powder sample of L-alanine. 5. The donut and dynamic polarization effects in proton channeling through carbon nanotubes DEFF Research Database (Denmark) Borka, D.; Mowbray, Duncan; Miskovic, Z.L. 2010-01-01 We investigate the angular and spatial distributions of protons with an energy of 0.223 MeV after channeling them through an (11, 9) single-wall carbon nanotube of 0.2 mu m length. The proton incident angle is varied between 0 and 10 mrad, being close to the critical angle for channeling. We show...... that, as the proton incident angle increases and approaches the critical angle for channeling, a ring-like structure is developed in the angular distribution-the donut effect. We demonstrate that it is the rainbow effect. If the proton incident angle is between zero and half of the critical angle...... for channeling, the image force affects considerably the number and positions of the maxima of the angular and spatial distributions. However, if the proton incident angle is close to the critical angle for channeling, its influence on the angular and spatial distributions is considerably decreased. We... 6. Modeling the Scattering Polarization of the Hydrogen Ly-alpha Line Observed by CLASP in a Filament Channel Science.gov (United States) Stepan, J.; Trujillo Bueno, J.; Gunar, S.; del Pino Aleman, T.; Heinzel, P.; Kano, R.; Ishikawa, R.; Narukage, M.; Bando, T.; Winebarger, Amy; Kobayashi, K.; Auchere, F. 2016-01-01 The 400 arcsec spectrograph slit of CLASP crossed predominantly quiet regions of the solar chromosphere, from the limb towards the solar disk center. Interestingly, in the CLASP slit-jaw images and in the SDO images of the He I line at 304 A, we can identify a filament channel (FC) extending over more than 60 arcsec crossing the spectrograph slit. In order to interpret the peculiar spatial variation of the Q/1 and U/1 signals observed by CLASP in the hydrogen Ly-alpha line (1216 A) and in the Si Ill line (1206 A) in such a filament channel, it is necessary to perform multi-dimensional radiative transfer modeling. In this contribution, we show the first results of the two-dimensional calculations we are carrying out in given filament models, with the aim of determining the filament thermal and magnetic structure by comparing the theoretical and the observed polarization signals. 7. Polarization-mediated Debye-screening of surface potential fluctuations in dual-channel AlN/GaN high electron mobility transistors Science.gov (United States) Deen, David A.; Miller, Ross A.; Osinsky, Andrei V.; Downey, Brian P.; Storm, David F.; Meyer, David J.; Scott Katzer, D.; Nepal, Neeraj 2016-12-01 A dual-channel AlN/GaN/AlN/GaN high electron mobility transistor (HEMT) architecture is proposed, simulated, and demonstrated that suppresses gate lag due to surface-originated trapped charge. Dual two-dimensional electron gas (2DEG) channels are utilized such that the top 2DEG serves as an equipotential that screens potential fluctuations resulting from surface trapped charge. The bottom channel serves as the transistor's modulated channel. Two device modeling approaches have been performed as a means to guide the device design and to elucidate the relationship between the design and performance metrics. The modeling efforts include a self-consistent Poisson-Schrodinger solution for electrostatic simulation as well as hydrodynamic three-dimensional device modeling for three-dimensional electrostatics, steady-state, and transient simulations. Experimental results validated the HEMT design whereby homo-epitaxial growth on free-standing GaN substrates and fabrication of the same-wafer dual-channel and recessed-gate AlN/GaN HEMTs have been demonstrated. Notable pulsed-gate performance has been achieved by the fabricated HEMTs through a gate lag ratio of 0.86 with minimal drain current collapse while maintaining high levels of dc and rf performance. 8. Deficiency in the voltage-gated proton channel Hv1 increases M2 polarization of microglia and attenuates brain damage from photothrombotic ischemic stroke. Science.gov (United States) Tian, Dai-Shi; Li, Chun-Yu; Qin, Chuan; Murugan, Madhuvika; Wu, Long-Jun; Liu, Jun-Li 2016-10-01 Microglia become activated during cerebral ischemia and exert pro-inflammatory or anti-inflammatory role dependent of microglial polarization. NADPH oxidase (NOX)-dependent reactive oxygen species (ROS) production in microglia plays an important role in neuronal damage after ischemic stroke. Recently, NOX and ROS are consistently reported to participate in the microglial activation and polarization; NOX2 inhibition or suppression of ROS production are shown to shift the microglial polarization from M1 toward M2 state after stroke. The voltage-gated proton channel, Hv1, is selectively expressed in microglia and is required for NOX-dependent ROS generation in the brain. However, the effect of Hv1 proton channel on microglial M1/M2 polarization state after cerebral ischemia remains unknown. In this study, we investigated the role of microglial Hv1 proton channel in modulating microglial M1/M2 polarization during the pathogenesis of ischemic cerebral injury using a mouse model of photothrombosis. Following photothrombotic ischemic stroke, wild-type mice presented obvious brain infarct, neuronal damage, and impaired motor coordination. However, mice lacking Hv1 (Hv1(-/-)) were partially protected from brain damage and motor deficits compared to wild-type mice. These rescued phenotypes in Hv1(-/-) mice in ischemic stroke is accompanied by reduced ROS production, shifted the microglial polarization from M1 to M2 state. Hv1 deficiency was also found to shift the M1/M2 polarization in primary cultured microglia. Our study suggests that the microglial Hv1 proton channel is a unique target for modulation of microglial M1/M2 polarization in the pathogenesis of ischemic stroke. The voltage-gated proton channel, Hv1, is selectively expressed in microglia and is required for NOX-dependent generation of reactive oxygen species (ROS) in the brain. ROS participate in microglial activation and polarization. However, the effect of Hv1 on microglial M1/M2 polarization state after 9. 1.28 Tbit/s/channel single-polarization DQPSK transmission over 525 km using ultrafast time-domain optical Fourier transformation DEFF Research Database (Denmark) Guan, P.; Mulvad, Hans Christian Hansen; Tomiyama, Y.; 2010-01-01 A single-channel 1.28 Tbit/s transmission over 525 km is demonstrated for the first time with a single-polarization DQPSK signal. Ultrafast time-domain optical Fourier transformation is successfully applied to DQPSK signals and results in improved performance and increased system margin.......A single-channel 1.28 Tbit/s transmission over 525 km is demonstrated for the first time with a single-polarization DQPSK signal. Ultrafast time-domain optical Fourier transformation is successfully applied to DQPSK signals and results in improved performance and increased system margin.... 10. Polar Codes Science.gov (United States) 2014-12-01 QPSK Gaussian channels . .......................................................................... 39 vi 1. INTRODUCTION Forward error correction (FEC...Capacity of BSC. 7 Figure 5. Capacity of AWGN channel . 8 4. INTRODUCTION TO POLAR CODES Polar codes were introduced by E. Arikan in [1]. This paper...Under authority of C. A. Wilgenbusch, Head ISR Division EXECUTIVE SUMMARY This report describes the results of the project “More reliable wireless 11. Effect of gamma irradiation at various temperatures on air and vacuum packed chicken tissues: Pt. 2; Fatty acid profiles of neutral and polar lipids separated from muscle and skin irradiated at 2-5 deg C Energy Technology Data Exchange (ETDEWEB) Maxwell, R.J. (Deaprtment of Agriculture, Philadelphia, PA (USA)); Rady, A.H. (Nuclear Research Centre, Inshas (Egypt)) 1989-01-01 Chicken muscle and skin were separately irradiated in air and under vacuum packaging at 0, 1, 3, 6 and 10 kGy using {sup 137}Cs (dose rate 0.1 kGy/min). Lipids were isolated as neutral and polar subclasses from muscle samples and as total lipid extracts from skin. Lipids were converted to fatty acid methyl esters, analyzed by capillary gas chromatography and the data compiled as fatty acid profiles by statistical computer analysis. Normalized reports were assembled from this data for the three lipid extract types. Only negligible changes in fatty acid profiles were observed for the neutral lipids of muscle and for the fatty acyl residues of skin lipids. Minor changes of interest, however, were observed for the polyunsaturated fatty acyl residues in the polar lipid fractions of muscle tissue, especially at higher irradiation doses (6 and 10 kGy). Comparisons were made between these results and those of an earlier study were similar tissues were irradiated at -20{sup 0}C. No new fatty acyl residues or other artifacts due to {gamma}-irradiation were found in detectable amounts by gas chromatography in any of the lipid fractions isolated. (author). 12. Construction of polar and hydrophobic pores and channels by assembly of peptide molecules Science.gov (United States) Karle, Isabella; Ranganathan, Darshan 2003-02-01 Selected peptides and hybrid peptides (combinations of peptide sequences with organic moieties in a single molecule) self-assemble to form pores, channels and tubules. The assemblies occur in a variety of motifs. Various physiological functions, such as ion transport through cell membranes, and physical functions, such as solubilizing difficult-to-dissolve molecules, are facilitated by the tubes that are formed by molecular assemblies. Examples from nature are the ionophores zervamicin and antiamoebin that transport K + ions through cell membranes. In the area of the constriction of the hour-glass shaped channel in the ionophores, the channel becomes quite convoluted and contains the double-gating mechanism that controls the ion passage. The formation of fairly straight tubules has been accomplished by designing cyclic peptides that have a relatively flat backbone, with extended side-chains, and with amide groups and carbonyl groups that are perpendicular to the plane of the backbone. Further, the amide groups and carbonyl groups have to be spaced so that they are in register from one peptide to another, stacked over or under it, in order to form intermolecular NH⋯OC hydrogen bonds. Tubules of this type can be made if the amino acid residues alternate between α- and β-residues or between D- and L-residues. In order to obviate the register problem with all α-amino acid residues of the same hand, peptide segments have been interspersed with a number of different organic moieties, such as 1,3-adamantane dicarbonyl, norbornene dicarbonyl, 2,6-pyridyl dicarbonyl, cystine and -(CH 2) n chains. Macrocycles that stacked vertically and formed tubules through hydrogen bonding, are hollow, open-ended, and continue to infinity. The inside diameter of the hollow tubules has varied to more than 10 Å. The hydrophobic tubules are able to accommodate highly lipophilic substances. Successes and failures to make tubules and crystal structures of a number of the tubules 13. Multiphysics simulation of ion concentration polarization induced by a surface-patterned nanoporous membrane in single channel devices. Science.gov (United States) Jia, Mingjie; Kim, Taesung 2014-10-21 Microfluidic devices utilize ion concentration polarization (ICP) phenomena for a variety of applications, but a comprehensive understanding of the generation of ICP is still necessary. Recently, the emergence of a novel single channel ICP (SC-ICP) device has stimulated further research on the mechanism of ICP generation, so that we developed a 2-D model of an SC-ICP device that integrates a nanoporous membrane on the bottom surface of the channel, allowing bulk flow over the membrane. We solved a set of coupled governing equations with appropriate boundary conditions to explore ICP numerically. As a result, we not only showed that the simulation results held a strong qualitative agreement with experimental results, but also found the distribution of ion concentrations in the SC-ICP device that has never been reported in previous studies. We confirmed again that the electrophoretic mobility (EPM) of counterions in the membrane is the most dominant factor determining the generation and strength of ICP, whereas the charge density of the membrane was dominant to the ICP strength only when a high EPM value was assumed. From the viewpoint of practical applications, an SC-ICP device with a long membrane under low buffer strength showed enhanced performance in the preconcentration of charged molecules. Therefore, we believe that the simulation results could not only provide sharp insight into ICP phenomena but also predict and optimize the performance of SC-ICP devices in various microfluidic applications. 14. THz-waves channeling in a monolithic saddle-coil for Dynamic Nuclear Polarization enhanced NMR. Science.gov (United States) Macor, A; de Rijk, E; Annino, G; Alberti, S; Ansermet, J-Ph 2011-10-01 A saddle coil manufactured by electric discharge machining (EDM) from a solid piece of copper has recently been realized at EPFL for Dynamic Nuclear Polarization enhanced Nuclear Magnetic Resonance experiments (DNP-NMR) at 9.4 T. The corresponding electromagnetic behavior of radio-frequency (400 MHz) and THz (263 GHz) waves were studied by numerical simulation in various measurement configurations. Moreover, we present an experimental method by which the results of the THz-wave numerical modeling are validated. On the basis of the good agreement between numerical and experimental results, we conducted by numerical simulation a systematic analysis on the influence of the coil geometry and of the sample properties on the THz-wave field, which is crucial in view of the optimization of DNP-NMR in solids. 15. Cloning and sequencing the degS-degU operon from an alkalophilic Bacillus-brevis CSIR Research Space (South Africa) Louw, M 1994-10-01 Full Text Available at the amino acid level to the B. subtilis degS-degU genes showed 74% and 84% similarity, respectively. On a multicopy vector the B. brevis degS-degU genes were found to cause hypersecretion of several extracellular enzymes in a B. subtilis rec (-) strain... 16. A novel biological activity of praziquantel requiring voltage-operated Ca2+ channel beta subunits: subversion of flatworm regenerative polarity. Directory of Open Access Journals (Sweden) Taisaku Nogi Full Text Available BACKGROUND: Approximately 200 million people worldwide harbour parasitic flatworm infections that cause schistosomiasis. A single drug-praziquantel (PZQ-has served as the mainstay pharmacotherapy for schistosome infections since the 1980s. However, the relevant in vivo target(s of praziquantel remain undefined. METHODS AND FINDINGS: Here, we provide fresh perspective on the molecular basis of praziquantel efficacy in vivo consequent to the discovery of a remarkable action of PZQ on regeneration in a species of free-living flatworm (Dugesia japonica. Specifically, PZQ caused a robust (100% penetrance and complete duplication of the entire anterior-posterior axis during flatworm regeneration to yield two-headed organisms with duplicated, integrated central nervous and organ systems. Exploiting this phenotype as a readout for proteins impacting praziquantel efficacy, we demonstrate that PZQ-evoked bipolarity was selectively ablated by in vivo RNAi of voltage-operated calcium channel (VOCC beta subunits, but not by knockdown of a VOCC alpha subunit. At higher doses of PZQ, knockdown of VOCC beta subunits also conferred resistance to PZQ in lethality assays. CONCLUSIONS: This study identifies a new biological activity of the antischistosomal drug praziquantel on regenerative polarity in a species of free-living flatworm. Ablation of the bipolar regenerative phenotype evoked by PZQ via in vivo RNAi of VOCC beta subunits provides the first genetic evidence implicating a molecular target crucial for in vivo PZQ activity and supports the 'VOCC hypothesis' of PZQ efficacy. Further, in terms of regenerative biology and Ca(2+ signaling, these data highlight a novel role for voltage-operated Ca(2+ entry in regulating in vivo stem cell differentiation and regenerative patterning. 17. Measurement of the$t\\bar{t}$spin correlations and top quark polarization in dileptonic channel with the CMS detector arXiv CERN Document Server Khatiwada, Ajeeta The degree of top polarization and strength of$t\\bar{t}$correlation are dependent on production dynamics, decay mechanism, and choice of the observables. At the LHC, measurement of the top polarization and spin correlations in$t\\bar{t}$production is possible through various observables related to the angular distribution of decay leptons. A measurement of differential distribution provides a precision test of the standard model of particle physics and probes for deviations, which could be a sign of new physics. In particular, the phase space for the super-symmetric partner of the top quark can be constrained. Results from the Compact Muon Solenoid (CMS) collaboration for top quark polarization and spin correlation in the dileptonic channel are reviewed briefly in this proceeding. The measurements are obtained using 19.5 fb$^{-1}$of data collected in pp collisions at the center-of-mass energy of 8 TeV. 18. Fisica degli atomi e dei nuclei CERN Document Server Bernardini, Carlo 1965-01-01 Evidenza della struttura atomica della materia ; le proprietà degli atomi e la meccanica atomica ; gli atomi e le radiazioni elettromagnetiche ; struttura microscopica dello stato gassoso ; struttura microscopica dello stato liquido ; struttura microscopica della stato solido ; proprietà elettriche e magnetiche delle sostanze ; proprietà dei nuclei degli atomi ; le particelle elementari. 19. Rode's iterative calculation of surface optical phonon scattering limited electron mobility in N-polar GaN devices Energy Technology Data Exchange (ETDEWEB) Ghosh, Krishnendu, E-mail: kghosh3@buffalo.edu; Singisetti, Uttam, E-mail: uttamsin@buffalo.edu [Electrical Engineering Department, University at Buffalo, Buffalo, New York 14260 (United States) 2015-02-14 N-polar GaN channel mobility is important for high frequency device applications. Here, we report theoretical calculations on the surface optical (SO) phonon scattering rate of two-dimensional electron gas (2DEG) in N-polar GaN quantum well channels with high-k dielectrics. Rode's iterative calculation is used to predict the scattering rate and mobility. Coupling of the GaN plasmon modes with the SO modes is taken into account and dynamic screening is employed under linear polarization response. The effect of SO phonons on 2DEG mobility was found to be small at >5 nm channel thickness. However, the SO mobility in 3 nm N-polar GaN channels with HfO{sub 2} and ZrO{sub 2} high-k dielectrics is low and limits the total mobility. The SO scattering for SiN dielectric on GaN was found to be negligible due to its high SO phonon energy. Using Al{sub 2}O{sub 3}, the SO phonon scattering does not affect mobility significantly only except the case when the channel is too thin with a low 2DEG density. 20. Engineering the (In, Al, Ga)N back-barrier to achieve high channel-conductivity for extremely scaled channel-thicknesses in N-polar GaN high-electron-mobility-transistors Energy Technology Data Exchange (ETDEWEB) Lu, Jing, E-mail: jing@ece.ucsb.edu; Zheng, Xun; Guidry, Matthew; Denninghoff, Dan; Ahmadi, Elahe; Lal, Shalini; Keller, Stacia; Mishra, Umesh K. [Department of Electrical and Computer Engineering, University of California, Santa Barbara, California 93106 (United States); DenBaars, Steven P. [Department of Electrical and Computer Engineering, University of California, Santa Barbara, California 93106 (United States); Materials Department, University of California, Santa Barbara, California 93106 (United States) 2014-03-03 Scaling down the channel-thickness (t{sub ch}) in GaN/(In, Al, Ga)N high-electron-mobility-transistors (HEMTs) is essential to eliminating short-channel effects in sub 100 nm gate length HEMTs. However, this scaling can degrade both charge density (n{sub s}) and mobility (μ), thereby reducing channel-conductivity. In this study, the back-barrier design in N-polar GaN/(In, Al, Ga)N was engineered to achieve highly conductive-channels with t{sub ch} < 5-nm using metal organic chemical vapor deposition. Compositional-grading was found to be the most effective approach in reducing channel-conductivity for structures with t{sub ch} ∼ 3-nm. For a HEMT with 3-nm-thick-channel, a sheet-resistance of 329 Ω/◻ and a peak-transconductance of 718 mS/mm were demonstrated. 1. Dirac Coupled-channel Analyses of Polarized Proton Scatterings to the 2$^+$Gamma Vibrational Band in$^{24}$Mg and$^{26}$Mg CERN Document Server Shim, Sugie 2016-01-01 Dirac coupled channel calculations are performed phenomenologically for the high-lying excited states that belong to the 2$^+$gamma vibrational band at the 800-MeV polarized proton inelastic scatterings from the s-d shell nuclei,$^{24}$Mg and$^{26}$Mg. Optical potential model is used and scalar and time-like vector potentials are considered as direct potentials. First-order vibrational collective models are used to obtain the transition optical potentials in order to accommodate the high-lying excited vibrational collective states. The complicated Dirac coupled channel equations are solved phenomenologically to reproduce the differential cross section and analyzing power data by varying the optical potential and deformation parameters. It is found that the relativistic Dirac coupled channel calculation could describe the high-lying excited states of the 2$^+$gamma vibrational band at the 800-MeV polarized proton inelastic scatterings from s-d shell nuclei$^{24}$Mg and$^{26}$Mg reasonably well, showing b... 2. Ear-to-Ear On-Body Channel Fading in the ISM-band for Tangentially-Polarized Antennas DEFF Research Database (Denmark) Kvist, Søren Helstrup; Thaysen, Jesper; Jakobsen, Kaj Bjarne 2011-01-01 The ear-to-ear on-body channel fading has been studied in the ISM-band. The ear-to-ear path gain was measured on six persons in an indoor environment for a duration of 200 s. The channel fading has been characterized in terms of empirical cumulative distribution functions (CDF), average fade... 3. Vicarious calibration of the multiviewing channel polarisation imager (3MI) of the EUMETSAT Polar System-Second Generation (EPS-SG) Science.gov (United States) Marbach, T.; Fougnie, B.; Lacan, A.; Schlüssel, P. 2016-10-01 The Multi-Viewing -Channel -Polarization Imager (3MI), planned to fly on the Metop-SG satellite as part of the EPS-SG programme in the timeframe beyond 2020, is a radiometer dedicated to aerosol and cloud characterization for climate monitoring, atmospheric composition, air quality and numerical weather prediction. The purpose of the 3MI is to provide multi-spectral (12 channels between 410 and 2130 nm), multi-polarization (-60°, 0°, and +60°), and multi-angular (10 to 14 views) images of the Earth top of atmosphere outgoing radiance. 3MI does not have an onboard calibration facility and its radiometric and geometric performance will rely on vicarious calibration. The aim of this paper is to present the state of the art of vicarious calibration methods applicable to 3MI. The 3MI measurement principle is based on the French atmospheric mission PARASOL (Polarization and Anisotropy of Reflectances for Atmospheric Sciences coupled with Observations from a Lidar) heritage [1]. This allows adapting the vicarious calibration methods of the PARASOL mission to the needs of 3MI. However, the monitoring of the SWIR (short wave infrared) channels will be a new challenge for the 3MI calibration as this spectral range was not present on PARASOL. The cross-calibration with other instruments flying on the same satellite will support the calibration of 3MI. Indeed the Metop-SG payload includes two other optical instruments covering the same spectral regions. METimage and Sentinel-5 will both be equipped with on-board calibration capabilities and provide valuable measurements for vicarious calibration of 3MI. Further cross-calibration with Earth observation instruments on other satellites, will be studied. 4. Polarity-dependent conformational switching of a peptide mimicking the S4-S5 linker of the voltage-sensitive sodium channel. Science.gov (United States) Helluin, O; Breed, J; Duclohier, H 1996-02-21 The S4-S5 linker (or S45) in voltage-sensitive sodium channels was previously shown to be involved in the permeation pathway. The secondary structure, investigated by circular dichroism, of a S4-S45 peptide from domain IV and its fragments (including S45) is reported here and compared with that of the homologous peptide from domain II as a function of the solvent dielectric constant. The reduction in helicity seen for S4-S45 (II) in polar media is cancelled in membrane-like environment. The most striking result-- a sharp alpha-helix --> beta-sheet transition upon exposure of the S45 moiety to aqueous solvents-- is discussed as regards channel activation and selectivity. 5. Conformational changes and slow dynamics through microsecond polarized atomistic molecular simulation of an integral Kv1.2 ion channel DEFF Research Database (Denmark) Bjelkmar, Pär; Niemelä, Perttu S; Vattulainen, Ilpo; 2009-01-01 Structure and dynamics of voltage-gated ion channels, in particular the motion of the S4 helix, is a highly interesting and hotly debated topic in current membrane protein research. It has critical implications for insertion and stabilization of membrane proteins as well as for finding how...... transitions occur in membrane proteins-not to mention numerous applications in drug design. Here, we present a full 1 micros atomic-detail molecular dynamics simulation of an integral Kv1.2 ion channel, comprising 120,000 atoms. By applying 0.052 V/nm of hyperpolarization, we observe structural rearrangements...... process. The coordinates of the transmembrane part of the simulated channel actually stay closer to the recently determined higher-resolution Kv1.2 chimera channel than the starting structure for the entire second half of the simulation (0.5-1 micros). Together with lipids binding in matching positions... 6. Polarized axonal surface expression of neuronal KCNQ potassium channels is regulated by calmodulin interaction with KCNQ2 subunit. Directory of Open Access Journals (Sweden) John P Cavaretta Full Text Available KCNQ potassium channels composed of KCNQ2 and KCNQ3 subunits give rise to the M-current, a slow-activating and non-inactivating voltage-dependent potassium current that limits repetitive firing of action potentials. KCNQ channels are enriched at the surface of axons and axonal initial segments, the sites for action potential generation and modulation. Their enrichment at the axonal surface is impaired by mutations in KCNQ2 carboxy-terminal tail that cause benign familial neonatal convulsion and myokymia, suggesting that their correct surface distribution and density at the axon is crucial for control of neuronal excitability. However, the molecular mechanisms responsible for regulating enrichment of KCNQ channels at the neuronal axon remain elusive. Here, we show that enrichment of KCNQ channels at the axonal surface of dissociated rat hippocampal cultured neurons is regulated by ubiquitous calcium sensor calmodulin. Using immunocytochemistry and the cluster of differentiation 4 (CD4 membrane protein as a trafficking reporter, we demonstrate that fusion of KCNQ2 carboxy-terminal tail is sufficient to target CD4 protein to the axonal surface whereas inhibition of calmodulin binding to KCNQ2 abolishes axonal surface expression of CD4 fusion proteins by retaining them in the endoplasmic reticulum. Disruption of calmodulin binding to KCNQ2 also impairs enrichment of heteromeric KCNQ2/KCNQ3 channels at the axonal surface by blocking their trafficking from the endoplasmic reticulum to the axon. Consistently, hippocampal neuronal excitability is dampened by transient expression of wild-type KCNQ2 but not mutant KCNQ2 deficient in calmodulin binding. Furthermore, coexpression of mutant calmodulin, which can interact with KCNQ2/KCNQ3 channels but not calcium, reduces but does not abolish their enrichment at the axonal surface, suggesting that apo calmodulin but not calcium-bound calmodulin is necessary for their preferential targeting to the axonal 7. Background Stratospheric Aerosol Investigations Using Multi-Color Wide-Field Polarization Measurements of the Twilight Sky CERN Document Server Ugolnikov, Oleg S 2016-01-01 First results of multi-wavelength polarization measurements of the twilight sky background using Wide-Angle Polarization Camera (WAPC) with RGB-color CCD conducted in spring and early summer of 2016 in central Russia (55.2 deg N, 37.5 deg E) are discussed. They show the effect of aerosol scattering at altitudes up to 35 km which significantly increases to the long-wave range (620 nm, R channel). Analysis of sky color behavior during the light period of twilight with account of ozone Chappuis absorption allows to retrieve the angle dependencies of intensity and polarization of scattering on the stratospheric aerosol particles. This is used to find their effective radius, being close to 0.18-0.19 microns for stratospheric altitude range. 8. Positronium energy levels at order$m \\alpha^7$: vacuum polarization corrections in the two-photon-annihilation channel CERN Document Server Adkins, Gregory S; Salinger, M D; Wang, Ruihan 2015-01-01 We have calculated all contributions to the energy levels of parapositronium at order$m \\alpha^7$coming from vacuum polarization corrections to processes involving virtual annihilation to two photons. This work is motivated by ongoing efforts to improve the experimental determination of the positronium ground-state hyperfine splitting. 9. Positronium energy levels at order mα7: Vacuum polarization corrections in the two-photon-annihilation channel Directory of Open Access Journals (Sweden) Gregory S. Adkins 2015-07-01 Full Text Available We have calculated all contributions to the energy levels of parapositronium at order mα7 coming from vacuum polarization corrections to processes involving virtual annihilation to two photons. This work is motivated by ongoing efforts to improve the experimental determination of the positronium ground-state hyperfine splitting. 10. Coupled-channels analysis of 800 MeV polarized proton inelastic scattering from /sup 18/O Energy Technology Data Exchange (ETDEWEB) Glashausser, C.; De Swiniarski, R.; Jones, K.; Nanda, S. (Rutgers - the State Univ., New Brunswick, NJ (USA)); Baker, F.T.; Grimm, M.; Penumetcha, V.; Scott, A. (Georgia Univ., Athens (USA)); Adams, G.; Igo, G. (California Univ., Los Angeles (USA)) 1982-10-14 Differential cross sections and analyzing powers have been measured for the /sup 18/O(p vector, p')/sup 18/O reaction at 800 MeV. A coupled-channels analysis of the 0/sub 1//sup +/, 2/sub 1//sup +/, and 4/sub 2//sup +/ data yields good agreement with a rotational model description with a large ..beta../sub 4/ deformation. The effects of channel coupling are large. The angular distributions of Asub(y) are reproduced well only with a full Thomas spin-orbit deformation approximately equal to the central deformation. 11. Compensated-power differential calorimeter -196 deg. C/400 deg. C; Calorimetre differentiel a puissance compensee -196 deg. C/400 deg. C Energy Technology Data Exchange (ETDEWEB) Bonjour, E.; Pierre, J.; Agagliate, S.; Bertrand, P.; Faivre, J.; Lagnier, R. [Commissariat a l' Energie Atomique, Grenoble (France). Centre d' Etudes Nucleaires, Section physico-chimie et basses temperatures 1967-06-01 A differential calorimetric device of original design is described. Its allows direct measurements of thermal effects (adsorption or release) during a linear rise of temperature. The self compensated power method which is applied by means of a very sensitive control system, gives a direct value of the different heat capacity between the sample and a dummy of it. The detection threshold is about {+-} 100 micro-watts to {+-} 250 micro-watts. Applications: - Generally measurements of enthalpy changes of massive or powdered samples. - Measurement of Wigner energy after low temperature irradiation (77 deg. K). - Measurements of energy release in low temperature (77 deg. K) cold worked metals. (authors) [French] On decrit un dispositif de calorimetrie differentielle, de conception originale, qui permet de mesurer directement des effets thermiques en absorption ou en degagement de chaleur, au cours d'une montee en temperature lineaire. La methode de compensation automatique de puissance qui est mise en oeuvre au moyen de cha es d'asservissement tres sensibles, conduit a une determination directe de la capacite calorifique differencielle entre l'echantillon et sa reference. Le seuil de detection est de l'ordre de {+-} 100 a {+-} 250 microwatts. Applications: - D'une facon generale, mesure des variations enthalpiques, sur echantillons massifs ou en poudre. - Mesure de l'energie Wigner apres irradiation a basse temperature (77 deg. K). - Mesure de l'energie restauree apres deformation des metaux a basse temperature (77 deg. K). (auteurs) 12. Testimonianze di vittime degli anni di piombo DEFF Research Database (Denmark) Cecchini, Leonardo Testimonianze di vittime degli anni di piombo In un articolo pubblicato nel 2008 sulla webzine Nazione indiana Christian Raimo criticava quello che poi Giovanni De Luna qualche anno dopo nel suo libro La Repubblica del dolore (2011) ha chiamato “paradigma vittimario”; cioè la presenza predominante... 13. Measurements of Channelling Radiation and its Polarization, X-Ray Excitation, together with Deviations from Landau Distributions CERN Multimedia 2002-01-01 This experiment is a continuation of the channelling experiments PS164 and WA64. The following points are investigated : \\item a)~Radiation from channelled 1 to 10 GeV/c positrons and electrons. The results clearly show that the region of 1-10 GeV/c is a very important and interesting momentum range where the onset of relativistic effects in connection with the unharmonicity of the channelling potential can give rise to very sharp pea photon spectra which could be used as a radiation source. With a detector opening angle which is large compared to 1/@g, these peaks appear sharp only on the high energy side. If, on the other hand, only forward emitted channelling radiation is detected, nearly symmetric peaks are expected to emerge. This is measured by means of a position sentitive @g-detector, consisting of an CdTe-array. Here each detector is 0.8~x~0.8~x~3~mm|3 and act as an active converter with the final shower absorbed in a large scintillator. Hereby an angular resolution of 1/3~@g around 40~@mrad is obtai... 14. Comparison of PCBBs and CTs irradiated at 250 deg. C, 300 deg. C, and 350 deg. C Energy Technology Data Exchange (ETDEWEB) Rensman, J.; Nolles, H.N. [ECN-Energy Research Foundation, Research Unit NRG, Westerduinweg, Petten (Netherlands); Lucon, E. [SCK-CEN, Institute of Nuclear Material Science, Boeretang, Mol (Belgium); Spatig, P. [EPFL-CRDP, Centre de Recherches en Physique des Plasmas, Association Euratom-Confederation Suisse, CH Villigen PSI (Switzerland) 2007-07-01 Full text of publication follows: The fracture toughness of irradiated Eurofer steel is difficult to characterise. Several limitations are identified in this paper with respect to the conventional treatment of fracture data of BCC steels in the transition region. It is uncertain that the RPV Master Curve is applicable to unirradiated Eurofer, and low temperature irradiation adds more to this uncertainty. The lack of strain hardening and the dose variation within each batch are two complicating factors. An irradiation has been carried out in the BFR up to a nominal dose of 2.5 dpa at 250 deg. C, 300 deg. C, and 350 deg. C in sodium. Twelve small size pre-cracked bend specimens and eight mini-CT specimens have been irradiated in each temperature section. We analyse the effect of constraint and censoring limit, and the specimen geometry and loading configuration. The fracture data are treated in several ways that are proposed in open literature to investigate the effect of irradiation on a reference temperature like the ASTM E1921 T0. In addition, the relation between the tensile hardening, which is presented in a companion paper, and the shift calculated with the various methods is studied. (authors) 15. Conformational changes and slow dynamics through microsecond polarized atomistic molecular simulation of an integral Kv1.2 ion channel. Directory of Open Access Journals (Sweden) Pär Bjelkmar 2009-02-01 Full Text Available Structure and dynamics of voltage-gated ion channels, in particular the motion of the S4 helix, is a highly interesting and hotly debated topic in current membrane protein research. It has critical implications for insertion and stabilization of membrane proteins as well as for finding how transitions occur in membrane proteins-not to mention numerous applications in drug design. Here, we present a full 1 micros atomic-detail molecular dynamics simulation of an integral Kv1.2 ion channel, comprising 120,000 atoms. By applying 0.052 V/nm of hyperpolarization, we observe structural rearrangements, including up to 120 degrees rotation of the S4 segment, changes in hydrogen-bonding patterns, but only low amounts of translation. A smaller rotation ( approximately 35 degrees of the extracellular end of all S4 segments is present also in a reference 0.5 micros simulation without applied field, which indicates that the crystal structure might be slightly different from the natural state of the voltage sensor. The conformation change upon hyperpolarization is closely coupled to an increase in 3(10 helix contents in S4, starting from the intracellular side. This could support a model for transition from the crystal structure where the hyperpolarization destabilizes S4-lipid hydrogen bonds, which leads to the helix rotating to keep the arginine side chains away from the hydrophobic phase, and the driving force for final relaxation by downward translation is partly entropic, which would explain the slow process. The coordinates of the transmembrane part of the simulated channel actually stay closer to the recently determined higher-resolution Kv1.2 chimera channel than the starting structure for the entire second half of the simulation (0.5-1 micros. Together with lipids binding in matching positions and significant thinning of the membrane also observed in experiments, this provides additional support for the predictive power of microsecond-scale membrane 16. Bacillus subtilis Two-Component System Sensory Kinase DegS Is Regulated by Serine Phosphorylation in Its Input Domain Science.gov (United States) Jers, Carsten; Kobir, Ahasanul; Søndergaard, Elsebeth Oline; Jensen, Peter Ruhdal; Mijakovic, Ivan 2011-01-01 Bacillus subtilis two-component system DegS/U is well known for the complexity of its regulation. The cytosolic sensory kinase DegS does not receive a single predominant input signal like most two-component kinases, instead it integrates a wide array of metabolic inputs that modulate its activity. The phosphorylation state of the response regulator DegU also does not confer a straightforward “on/off” response; it is fine-tuned and at different levels triggers different sub-regulons. Here we describe serine phosphorylation of the DegS sensing domain, which stimulates its kinase activity. We demonstrate that DegS phosphorylation can be carried out by at least two B. subtilis Hanks-type kinases in vitro, and this stimulates the phosphate transfer towards DegU. The consequences of this process were studied in vivo, using phosphomimetic (Ser76Asp) and non-phosphorylatable (Ser76Ala) mutants of DegS. In a number of physiological assays focused on different processes regulated by DegU, DegS S76D phosphomimetic mutant behaved like a strain with intermediate levels of DegU phosphorylation, whereas DegS S76A behaved like a strain with lower levels of DegU phophorylation. These findings suggest a link between DegS phosphorylation at serine 76 and the level of DegU phosphorylation, establishing this post-translational modification as an additional trigger for this two-component system. PMID:21304896 17. Bacillus subtilis two-component system sensory kinase DegS is regulated by serine phosphorylation in its input domain. Directory of Open Access Journals (Sweden) Carsten Jers Full Text Available Bacillus subtilis two-component system DegS/U is well known for the complexity of its regulation. The cytosolic sensory kinase DegS does not receive a single predominant input signal like most two-component kinases, instead it integrates a wide array of metabolic inputs that modulate its activity. The phosphorylation state of the response regulator DegU also does not confer a straightforward "on/off" response; it is fine-tuned and at different levels triggers different sub-regulons. Here we describe serine phosphorylation of the DegS sensing domain, which stimulates its kinase activity. We demonstrate that DegS phosphorylation can be carried out by at least two B. subtilis Hanks-type kinases in vitro, and this stimulates the phosphate transfer towards DegU. The consequences of this process were studied in vivo, using phosphomimetic (Ser76Asp and non-phosphorylatable (Ser76Ala mutants of DegS. In a number of physiological assays focused on different processes regulated by DegU, DegS S76D phosphomimetic mutant behaved like a strain with intermediate levels of DegU phosphorylation, whereas DegS S76A behaved like a strain with lower levels of DegU phophorylation. These findings suggest a link between DegS phosphorylation at serine 76 and the level of DegU phosphorylation, establishing this post-translational modification as an additional trigger for this two-component system. 18. Groove-type channel enhancement-mode AlGaN/GaN MIS HEMT with combined polar and nonpolar AlGaN/GaN heterostructures Science.gov (United States) Duan, Xiao-Ling; Zhang, Jin-Cheng; Xiao, Ming; Zhao, Yi; Ning, Jing; Hao, Yue 2016-08-01 A novel groove-type channel enhancement-mode AlGaN/GaN MIS high electron mobility transistor (GTCE-HEMT) with a combined polar and nonpolar AlGaN/GaN heterostucture is presented. The device simulation shows a threshold voltage of 1.24 V, peak transconductance of 182 mS/mm, and subthreshold slope of 85 mV/dec, which are obtained by adjusting the device parameters. Interestingly, it is possible to control the threshold voltage accurately without precisely controlling the etching depth in fabrication by adopting this structure. Besides, the breakdown voltage (V B) is significantly increased by 78% in comparison with the value of the conventional MIS-HEMT. Moreover, the fabrication process of the novel device is entirely compatible with that of the conventional depletion-mode (D-mode) polar AlGaN/GaN HEMT. It presents a promising way to realize the switch application and the E/D-mode logic circuits. Project supported by the National Science and Technology Major Project, China (Grant No. 2013ZX02308-002) and the National Natural Science Foundation of China (Grant Nos. 11435010, 61474086, and 61404099). 19. Indoor radio channel modeling and mitigation of fading effects using linear and circular polarized antennas in combination for smart home system at 868 MHz Science.gov (United States) Wunderlich, S.; Welpot, M.; Gaspard, I. 2014-11-01 The markets for smart home products and services are expected to grow over the next years, driven by the increasing demands of homeowners considering energy monitoring, management, environmental controls and security. Many of these new systems will be installed in existing homes and offices and therefore using radio based systems for cost reduction. A drawback of radio based systems in indoor environments are fading effects which lead to a high variance of the received signal strength and thereby to a difficult predictability of the encountered path loss of the various communication links. For that reason it is necessary to derive a statistical path loss model which can be used to plan a reliable and cost effective radio network. This paper presents the results of a measurement campaign, which was performed in six buildings to deduce realistic radio channel models for a high variety of indoor radio propagation scenarios in the short range devices (SRD) band at 868 MHz. Furthermore, a potential concept to reduce the variance of the received signal strength using a circular polarized (CP) patch antenna in combination with a linear polarized antenna in an one-to-one communication link is presented. 20. Electrical spin injection and detection in high mobility 2DEG systems Science.gov (United States) Ciorga, M. 2016-11-01 In this review paper we present the current status of research related to the topic of electrical spin injection and detection in two-dimensional electron gas (2DEG) systems, formed typically at the interface between two III-V semiconductor compounds. We discuss both theoretical aspects of spin injection in case of ballistic transport as well as give an overview of available reports on spin injection experiments performed on 2DEG structures. In the experimental part we focus particularly on our recent work on all-semiconductor structures with a 2DEG confined at an inverted GaAs/(Al,Ga)As interface and with a ferromagnetic semiconductor (Ga,Mn)As employed as a source of spin-polarized electrons. 1.$W$boson polarization measurement in the$t\\bar{t}$dilepton channel using the CDF II Detector Energy Technology Data Exchange (ETDEWEB) Aaltonen, T.; /Helsinki Inst. of Phys.; Alvarez Gonzalez, B.; /Oviedo U. /Cantabria Inst. of Phys.; Amerio, S.; /INFN, Padua; Amidei, D.; /Michigan U.; Anastassov, A.; /Northwestern U. /Fermilab; Annovi, A.; /Frascati; Antos, J.; /Comenius U.; Apollinari, G.; /Fermilab; Appel, J.A.; /Fermilab; Arisawa, T.; /Waseda U.; Artikov, A.; /Dubna, JINR /Texas A-M 2012-05-01 We present a measurement of W boson polarization in top-quark decays in t{bar t} events with decays to dilepton final states using 5.1 fb{sup -1} integrated luminosity in p{bar p} collisions collected by the CDF II detector at the Tevatron. A simultaneous measurement of the fractions of longitudinal (f{sub 0}) and right-handed (f{sub +}) W bosons yields the results f{sub 0} = 0.71{sub -0.17}{sup +0.18}(stat) {+-} 0.06(syst) and f{sub +} = -0.07 {+-} 0.09(stat) {+-} 0.03(syst). Combining this measurement with our previous result based on single lepton final states, we obtain f{sub 0} = 0.84 {+-} 0.09(stat) {+-} 0.05(syst) and f{sub +} = -0.16 {+-} 0.05(stat) {+-} 0.04(syst). The results are consistent with standard model expectation. 2. Polarization modulation time-domain terahertz polarimetry CERN Document Server Morris, C M; Stier, A V; Armitage, N P 2012-01-01 We present high precision measurements of polarization rotations in the frequency range from 0.1 to 2.5 THz using a polarization modulation technique. A motorized stage rotates a polarizer at ~80 Hz, and the resulting modulation of the polarization is measured by a lock-in technique. We achieve an accuracy of 0.05{\\deg} (900 {\\mu}rad) and a precision of 0.02{\\deg} (350 {\\mu}rad) for small rotation angles. A detailed mathematical description of the technique is presented, showing its ability to fully characterize elliptical polarizations from 0.1 to 2.5 THz. 3. Electron gas polarization effect induced by heavy H-like ions of moderate velocities channeled in a silicon crystal CERN Document Server Dauvergne, D; Bosch, F; Bräuning, H; Chevallier, M; Cohen, C; Gumberidze, A; Hagmann, S; L'Hoir, A; Kirsch, R; Kozhuharov, C; Liesen, D; Mokler, P H; Poizat, J C; Ray, C; Rozet, J P; Stöhlker, T; Toleikis, S; Toulemonde, M; Verma, P; St\\"{o}hlker, Th. 2006-01-01 We report on the observation of a strong perturbation of the electron gas induced by 20 MeV/u U$^{91+}$ions and 13 MeV/u Pb$^{81+}ions channeled in silicon crystals. This collective response (wake effect) in-duces a shift of the continuum energy level by more than 100 eV, which is observed by means of Radiative Electron Capture into the K and L-shells of the projectiles. We also observe an increase of the REC probability by 20-50% relative to the probability in a non-perturbed electron gas. The energy shift is in agreement with calculations using the linear response theory, whereas the local electron density enhancement is much smaller than predicted by the same model. This shows that, for the small values of the adiabaticity parameter achieved in our experiments, the density fluctuations are not strongly localized at the vicinity of the heavy ions. 4. Electron gas polarization effect induced by heavy H-like ions of moderate velocities channeled in a silicon crystal Energy Technology Data Exchange (ETDEWEB) Testa, E. [Institut de Physique Nucleaire de Lyon, CNRS-IN2P3, Universite Claude Bernard Lyon 1, F-69622 Villeurbanne (France); Dauvergne, D. [Institut de Physique Nucleaire de Lyon, CNRS-IN2P3, Universite Claude Bernard Lyon 1, F-69622 Villeurbanne (France)]. E-mail: d.dauvergne@ipnl.in2p3.fr; Braeuning-Demian, A. [Gesellschaft fuer Schwerionen Forschung (GSI), D-64291 Darmstadt (Germany); Bosch, F. [Gesellschaft fuer Schwerionen Forschung (GSI), D-64291 Darmstadt (Germany); Braeuning, H. [Institut fuer Kernphysik, Justus Liebig Universitaet, D-35392 Giessen (Germany); Chevallier, M. [Institut de Physique Nucleaire de Lyon, CNRS-IN2P3, Universite Claude Bernard Lyon 1, F-69622 Villeurbanne (France); Cohen, C. [Institut des Nano-Sciences de Paris, CNRS-UMR75-88, Universites Paris VI et Paris VII, 75251 Paris cedex 05 (France); Gumberidze, A. [Gesellschaft fuer Schwerionen Forschung (GSI), D-64291 Darmstadt (Germany); Hagmann, S. [Gesellschaft fuer Schwerionen Forschung (GSI), D-64291 Darmstadt (Germany); L' Hoir, A. [Institut des Nano-Sciences de Paris, CNRS-UMR75-88, Universites Paris VI et Paris VII, 75251 Paris cedex 05 (France); Kirsch, R. [Institut de Physique Nucleaire de Lyon, CNRS-IN2P3, Universite Claude Bernard Lyon 1, F-69622 Villeurbanne (France); Kozhuharov, C.; Liesen, D.; Mokler, P.H. [Gesellschaft fuer Schwerionen Forschung (GSI), D-64291 Darmstadt (Germany); Poizat, J.-C.; Ray, C. [Institut de Physique Nucleaire de Lyon, CNRS-IN2P3, Universite Claude Bernard Lyon 1, F-69622 Villeurbanne (France); Rozet, J.-P. [Institut des Nano-Sciences de Paris, CNRS-UMR75-88, Universites Paris VI et Paris VII, 75251 Paris cedex 05 (France); Stoehlker, Th.; Toleikis, S. [Gesellschaft fuer Schwerionen Forschung (GSI), D-64291 Darmstadt (Germany); Toulemonde, M. [Centre Interdisciplinaire de Recherche Ions-Lasers, UMR 11, CEA-CNRS, 14040 Caen cedex (France); Verma, P. [Gesellschaft fuer Schwerionen Forschung (GSI), D-64291 Darmstadt (Germany) 2006-04-15 We report on the observation of a strong perturbation of the electron gas induced by 20 MeV/u U{sup 91+} ions and 13 MeV/u Pb{sup 81+} ions channeled in silicon crystals. This collective response (wake effect) induces a shift of the continuum energy level by more than 100 eV, which is observed by means of radiative electron capture into the K- and L-shells of the projectiles. We also observe an increase of the REC probability by 20-50% relative to the probability in a non-perturbed electron gas. The energy shift is in agreement with calculations using the linear response theory, whereas the local electron density enhancement is much smaller than predicted by the same model. This shows that, for the small values of the adiabaticity parameter achieved in our experiments, the density fluctuations are not strongly localized in the vicinity of the heavy ions. 5. In situ observations of BrO over Antarctica - ER-2 aircraft results from 54 deg S to 72 deg S latitude Science.gov (United States) Brune, W. H.; Anderson, J. G.; Chan, K. R. 1989-01-01 Bromine monoxide was observed in situ during nine flights of the NASA ER-2 aircraft from Punta Arenas, Chile (54 deg S latitude), to 72 deg S latitude over the Palmer Peninsula, Antarctica. The first flight for the BrO detection system was on August 28. The distribution of BrO inside the chemically perturbed region defined by greatly elevated ClO abundances was different from that found just outside. Inside, the BrO mixing ratio was 6.1 + or - 1.1 pptv above the 440 K potential temperature surface, 4.7 + or - 2.0 pptv between the 400 and 440 K surfaces, and less than 4 pptv below the 400 K surface. At high latitudes outside the chemically perturbed region, the BrO mixing ratio was 5.4 + or - 1.4 pptv near the 450 K surface, but decreased to 2.9 + or - 1.2 pptv at the 420 K surface. The abundance of BrO showed no discernible temporal trend during the course of the nine flights. Away from the south polar region, at latitudes between 47 deg S and 37 deg N and potential temperatures between 435 and 500 K (18.5- to 20.7-km altitude), the BrO mixing ratio was 0.5-3.0 pptv. 6. Polar conic current sheets as sources and channels of energetic particles in the high-latitude heliosphere Science.gov (United States) Khabarova, Olga; Malova, Helmi; Kislov, Roman; Zelenyi, Lev; Obridko, Vladimir; Kharshiladze, Alexander; Tokumaru, Munetoshi; Sokół, Justyna; Grzedzielski, Stan; Fujiki, Ken'ichi; Malandraki, Olga 2017-04-01 The existence of a large-scale magnetically separated conic region inside the polar coronal hole has been predicted by the Fisk-Parker hybrid heliospheric magnetic field model in the modification of Burger and co-workers (Burger et al., ApJ, 2008). Recently, long-lived conic (or cylindrical) current sheets (CCSs) have been found from Ulysses observations at high heliolatitudes (Khabarova et al., ApJ, 2017). The characteristic scale of these structures is several times lesser than the typical width of coronal holes, and the CCSs can be observed at 2-3 AU for several months. CCS crossings in 1994 and 2007 are characterized by sharp decreases in the solar wind speed and plasma beta typical for predicted profiles of CCSs. In 2007, a CCS was detected directly over the South Pole and strongly highlighted by the interaction with comet McNaught. The finding is confirmed by restorations of solar coronal magnetic field lines that reveal the occurrence of conic-like magnetic separators over the solar poles both in 1994 and 2007. Interplanetary scintillation data analysis also confirms the existence of long-lived low-speed regions surrounded by the typical polar high-speed solar wind in solar minima. The occurrence of long-lived CCSs in the high-latitude solar wind could shed light on how energetic particles reach high latitudes. Energetic particle enhancements up to tens MeV were observed by Ulysses at edges of CCSs both in 1994 and 2007. In 1994 this effect was clearer, probably due to technical reasons. Accelerated particles could be produced either by magnetic reconnection at the edges of a CCS in the solar corona or in the solar wind. We discuss the role of high-latitude CCSs in propagation of energetic particles in the heliosphere and revisit previous studies of energetic particle enhancements at high heliolatitudes. We also suggest that the existence of a CCS can modify the distribution of the solar wind as a function of heliolatitude and consequently impact ionization 7. Gate control of spin polarization in a quantum Hall regime toward reconfigurable network of helical channels (Conference Presentation) Science.gov (United States) Rokhinson, Leonid; Kazakov, Aleksandr; Simion, George; Lyanda-Geller, Yuli; Kolkovsky, Valery; Karczewski, Grzegorz; Adamus, Zbigniew; Wojtowicz, Tomasz 2016-10-01 Several experiments in nanowires detected signatures of Majorana fermions, building block for topologicaly protected quantum computer. Now the focus of research is shifting toward systems where non-Abelian statistics of excitations can be demonstrated. To achieve this goal we are developing a new dilute magnetic semiconductor-based platform where non-Abelian excitations can be created and manipulated in a two-dimensional plane, with support for Majorana and higher order non-Abelian excitations. Here we report development of heterostructures where spin polarization of a two-dimensional electron gas in a quantum Hall regime can be controlled locally by electrostatic gating. This is demonstrated via voltage induced shift of quantum Hall ferromagnetic transition in the CdTe quantum wells with engineered placement of paramagnetic Mn impurities. The structures can be used to form helical domain walls in integer quantum Hall regime which, coupled to an s-wave superconductor, are expected to support Majorana zero modes. These heterostructures can be used as a testbed to study gate-reconfigurable domain walls networks. 8. Polarized View of Supercooled Liquid Water Clouds Science.gov (United States) Alexandrov, Mikhail D.; Cairns, Brian; Van Diedenhoven, Bastiaan; Ackerman, Andrew S.; Wasilewski, Andrzej P.; McGill, Matthew J.; Yorks, John E.; Hlavka, Dennis L.; Platnick, Steven E.; Arnold, G. Thomas 2016-01-01 Supercooled liquid water (SLW) clouds, where liquid droplets exist at temperatures below 0 C present a well known aviation hazard through aircraft icing, in which SLW accretes on the airframe. SLW clouds are common over the Southern Ocean, and climate-induced changes in their occurrence is thought to constitute a strong cloud feedback on global climate. The two recent NASA field campaigns POlarimeter Definition EXperiment (PODEX, based in Palmdale, California, January-February 2013) and Studies of Emissions and Atmospheric Composition, Clouds and Climate Coupling by Regional Surveys (SEAC4RS, based in Houston, Texas in August- September 2013) provided a unique opportunity to observe SLW clouds from the high-altitude airborne platform of NASA's ER-2 aircraft. We present an analysis of measurements made by the Research Scanning Polarimeter (RSP) during these experiments accompanied by correlative retrievals from other sensors. The RSP measures both polarized and total reflectance in 9 spectral channels with wavelengths ranging from 410 to 2250 nm. It is a scanning sensor taking samples at 0.8deg intervals within 60deg from nadir in both forward and backward directions. This unique angular resolution allows for characterization of liquid water droplet size using the rainbow structure observed in the polarized reflectances in the scattering angle range between 135deg and 165deg. Simple parametric fitting algorithms applied to the polarized reflectance provide retrievals of the droplet effective radius and variance assuming a prescribed size distribution shape (gamma distribution). In addition to this, we use a non-parametric method, Rainbow Fourier Transform (RFT),which allows retrieval of the droplet size distribution without assuming a size distribution shape. We present an overview of the RSP campaign datasets available from the NASA GISS website, as well as two detailed examples of the retrievals. In these case studies we focus on cloud fields with spatial features 9. Polarized View of Supercooled Liquid Water Clouds Science.gov (United States) Alexandrov, Mikhail D.; Cairns, Brian; Van Diedenhoven, Bastiaan; Ackerman, Andrew S.; Wasilewski, Andrzej P.; McGill, Matthew J.; Yorks, John E.; Hlavka, Dennis L.; Platnick, Steven E.; Arnold, G. Thomas 2016-01-01 Supercooled liquid water (SLW) clouds, where liquid droplets exist at temperatures below 0 C present a well known aviation hazard through aircraft icing, in which SLW accretes on the airframe. SLW clouds are common over the Southern Ocean, and climate-induced changes in their occurrence is thought to constitute a strong cloud feedback on global climate. The two recent NASA field campaigns POlarimeter Definition EXperiment (PODEX, based in Palmdale, California, January-February 2013) and Studies of Emissions and Atmospheric Composition, Clouds and Climate Coupling by Regional Surveys (SEAC4RS, based in Houston, Texas in August- September 2013) provided a unique opportunity to observe SLW clouds from the high-altitude airborne platform of NASA's ER-2 aircraft. We present an analysis of measurements made by the Research Scanning Polarimeter (RSP) during these experiments accompanied by correlative retrievals from other sensors. The RSP measures both polarized and total reflectance in 9 spectral channels with wavelengths ranging from 410 to 2250 nm. It is a scanning sensor taking samples at 0.8deg intervals within 60deg from nadir in both forward and backward directions. This unique angular resolution allows for characterization of liquid water droplet size using the rainbow structure observed in the polarized reflectances in the scattering angle range between 135deg and 165deg. Simple parametric fitting algorithms applied to the polarized reflectance provide retrievals of the droplet effective radius and variance assuming a prescribed size distribution shape (gamma distribution). In addition to this, we use a non-parametric method, Rainbow Fourier Transform (RFT),which allows retrieval of the droplet size distribution without assuming a size distribution shape. We present an overview of the RSP campaign datasets available from the NASA GISS website, as well as two detailed examples of the retrievals. In these case studies we focus on cloud fields with spatial features 10. Control of the dipole layer of polar organic molecules adsorbed on metal surfaces via different charge-transfer channels Science.gov (United States) Lin, Meng-Kai; Nakayama, Yasuo; Zhuang, Ying-Jie; Su, Kai-Jun; Wang, Chin-Yung; Pi, Tun-Wen; Metz, Sebastian; Papadopoulos, Theodoros A.; Chiang, T.-C.; Ishii, Hisao; Tang, S.-J. 2017-02-01 Organic molecules with a permanent electric dipole moment have been widely used as a template for further growth of molecular layers in device structures. Key properties of the resulting organic films such as energy level alignment (ELA), work function, and injection/collection barrier are linked to the magnitude and direction of the dipole moment at the interface. Using angle-resolved photoemission spectroscopy (ARPES), we have systematically investigated the coverage-dependent work function and spectral line shapes of occupied molecular energy states (MESs) of chloroaluminium-phthalocyanine (ClAlPc) grown on Ag(111). We demonstrate that the dipole orientation of the first ClAlPc layer can be controlled by adjusting the deposition rate and postannealing conditions, and we find that the ELA at the interface differs by ˜0.4 eV between the Cl up and down configurations of the adsorbed ClAlPc molecules. These observations are rationalized by density functional theory (DFT) calculations based on a realistic model of the ClAlPc/Ag(111) interface, which reveal that the different orientations of the ClAlPc dipole layer lead to different charge-transfer channels between the adsorbed ClAlPc and Ag(111) substrate. Our findings provide a useful framework toward method development for ELA tuning. 11. Global map of lithosphere thermal thickness on a 1 deg x 1 deg grid - digitally available DEFF Research Database (Denmark) Artemieva, Irina 2014-01-01 than 250 km) lithosphere is restrictedsolely to young Archean terranes (3.0–2.6 Ga), while in old Archean cratons (3.6–3.0 Ga) lithospheric roots donot extend deeper than 200–220 km.The TC1 model is presented by a set of maps, which show significant thermal heterogeneity within continentalupper mantle......This presentation reports a 1 deg 1 deg global thermal model for the continental lithosphere (TC1). The modelis digitally available from the author’s web-site: www.lithosphere.info.Geotherms for continental terranes of different ages (early Archean to present) are constrained by reliabledata... 12. The multi-viewing, multi-channel, multi-polarisation imager on board the future EUMETSAT Polar System - Second Generation and its application for the aerosol retrieval Science.gov (United States) Kokhanovsky, Alexander; Munro, Rose; Lang, Ruediger; Lindstrot, Rasmus; Huckle, Roger; Marbach, Thierry; Poli, Gabriele 2017-04-01 Atmospheric aerosol is a global phenomenon. Due to the small size of aerosol particles (typically, 0.1 - 10 micrometers) they are rarely observed by the naked eye. Nevertheless aerosol particles are present in atmospheric air in variable numbers (typically, 100-1000 particles per cubic centimeter of atmospheric air). The particles have different chemical composition, origin, shapes, and internal structure (e.g., dust particles covered by ice, etc.). They influence human health, air quality, climate, downwelling and upwelling radiation, clouds, and precipitation. It is therefore important to monitor aerosol properties on a global scale. Global scale information can only be provided by satellite observations and algorithms for the production of satellite-based aerosol products have been in use already for more than 40 years. In this work we present an update on the recently developed operational EUMETSAT aerosol retrieval algorithm for the Multi-viewing, multi-channel, multi-polarisation Imager (3MI) which will fly on board the future EUMETSAT Polar System Second Generation (EPS-SG), planned for launch in the 2021 timeframe. The 3MI is a two - dimensional push - broom radiometer dedicated to aerosol and cloud characterization for climate monitoring, air quality forecasting and numerical weather prediction with heritage from the POLDER instrument. The first three components of the Stokes vector of the reflected light (I, Q, and U) will be measured at 9 channels in the spectral range from 410 to 2130nm for up to 14 observation directions. Intensity measurements only will be performed at 763, 765, and 910nm. This enables the determination of the degree of linear polarization of reflected light and also the direction of the oscillations of the electric vector in the light beam. The 3MI design consists of a filter and polariser wheel rotating in front of the detectors. For design purposes the spectral channels have been split into VNIR and SWIR filters and polarisers with 13. Electron distribution in polar heterojunctions within a realistic model Energy Technology Data Exchange (ETDEWEB) Tien, Nguyen Thanh, E-mail: thanhtienctu@gmail.com [College of Natural Science, Can Tho University, 3-2 Road, Can Tho City (Viet Nam); Thao, Dinh Nhu [Center for Theoretical and Computational Physics, College of Education, Hue University, 34 Le Loi Street, Hue City (Viet Nam); Thao, Pham Thi Bich [College of Natural Science, Can Tho University, 3-2 Road, Can Tho City (Viet Nam); Quang, Doan Nhat [Institute of Physics, Vietnamese Academy of Science and Technology, 10 Dao Tan Street, Hanoi (Viet Nam) 2015-12-15 We present a theoretical study of the electron distribution, i.e., two-dimensional electron gas (2DEG) in polar heterojunctions (HJs) within a realistic model. The 2DEG is confined along the growth direction by a triangular quantum well with a finite potential barrier and a bent band figured by all confinement sources. Therein, interface polarization charges take a double role: they induce a confining potential and, furthermore, they can make some change in other confinements, e.g., in the Hartree potential from ionized impurities and 2DEG. Confinement by positive interface polarization charges is necessary for the ground state of 2DEG existing at a high sheet density. The 2DEG bulk density is found to be increased in the barrier, so that the scattering occurring in this layer (from interface polarization charges and alloy disorder) becomes paramount in a polar modulation-doped HJ. 14. Electron distribution in polar heterojunctions within a realistic model Science.gov (United States) Tien, Nguyen Thanh; Thao, Dinh Nhu; Thao, Pham Thi Bich; Quang, Doan Nhat 2015-12-01 We present a theoretical study of the electron distribution, i.e., two-dimensional electron gas (2DEG) in polar heterojunctions (HJs) within a realistic model. The 2DEG is confined along the growth direction by a triangular quantum well with a finite potential barrier and a bent band figured by all confinement sources. Therein, interface polarization charges take a double role: they induce a confining potential and, furthermore, they can make some change in other confinements, e.g., in the Hartree potential from ionized impurities and 2DEG. Confinement by positive interface polarization charges is necessary for the ground state of 2DEG existing at a high sheet density. The 2DEG bulk density is found to be increased in the barrier, so that the scattering occurring in this layer (from interface polarization charges and alloy disorder) becomes paramount in a polar modulation-doped HJ. 15. Bacillus subtilis Two-Component System Sensory Kinase DegS Is Regulated by Serine Phosphorylation in Its Input Domain DEFF Research Database (Denmark) Jers, Carsten; Kobir, Ahasanul; Søndergaard, Elsebeth Oline; 2011-01-01 Bacillus subtilis two-component system DegS/U is well known for the complexity of its regulation. The cytosolic sensory kinase DegS does not receive a single predominant input signal like most two-component kinases, instead it integrates a wide array of metabolic inputs that modulate its activity... 16. Angiopatia diabetica e amputazione degli arti inferiori: valutazioni preliminari degli episodi di ricovero ripetuti Directory of Open Access Journals (Sweden) P. Trerotoli 2003-05-01 Full Text Available Obiettivi: l’obiettivo principale dello studio è stata la valutazione dei ricoveri ripetuti nei soggetti con vasculopatia diabetica, rispetto ai soggetti con vasculopatia non diabetica. Materiali e Metodi: sono state selezionate le SDO del triennio 1998-2000 contenenti, in uno dei campi di diagnosi, i codici di diabete mellito, con e senza complicanze (codici ICD9 ed ICD9CM, 250.—, vasculopatia periferica (440.2 e 440.8, ulcera periferica (707.1, 707.8, 707.9, gangrena (785.4. Le SDO con diagnosi di vasculopatia diabetica sono state considerate come angiopatie diabetiche (AD; le altre sono state attribuite agli angiopatici non diabetici (AND. Le SDO con diabete non complicato e arteriopatia periferica sono state eliminate. L’intervento di amputazione è stato individuato dalla presenza del codice ICD9CM di procedura 84.—. La ripetitività degli episodi è stata valutata usando il codice fiscale come identificativo del paziente. Risultati: sono state rilevate 5814 dimissioni di AD e 9010 di AND. Le amputazioni sono state 285 (4,90% negli AD e 485 (5,38% negli AND. I ricoveri ripetuti sono stati 13 negli AD e 12 negli AND. Le amputazioni sono state osservate verso il 4°-5° episodio di ricovero negli AD, mentre già dal 2° episodio negli AND. Le ulcere erano presenti nel 36,05% (il 36,5% nel primo episodio di ricovero, che resta costante negli episodi successivi degli AND e nel 10,97% degli AD (9,84% nel primo episodio, con un incremento fino al 20% del 5° episodio. Un episodio in day-hospital (DH si osserva nel 12,32% degli AD, contro il 4,20% degli AND. Conclusioni: l’accesso degli AD all’assistenza intraospedaliera avviene più frequentemente in DH, i passi successivi sono caratterizzati dalla comparsa dell’ulcera o gangrena e infine dall’amputazione. Nel gruppo degli AD è stato osservato un eccesso di ospedalizzazione, probabilmente per ripetitività del 17. Polarization induced doped transistor Energy Technology Data Exchange (ETDEWEB) Xing, Huili (Grace); Jena, Debdeep; Nomoto, Kazuki; Song, Bo; Zhu, Mingda; Hu, Zongyang 2016-06-07 A nitride-based field effect transistor (FET) comprises a compositionally graded and polarization induced doped p-layer underlying at least one gate contact and a compositionally graded and doped n-channel underlying a source contact. The n-channel is converted from the p-layer to the n-channel by ion implantation, a buffer underlies the doped p-layer and the n-channel, and a drain underlies the buffer. 18. Generalized channeled polarimetry. Science.gov (United States) Alenin, Andrey S; Tyo, J Scott 2014-05-01 Channeled polarimeters measure polarization by modulating the measured intensity in order to create polarization-dependent channels that can be demodulated to reveal the desired polarization information. A number of channeled systems have been described in the past, but their proposed designs often unintentionally sacrifice optimality for ease of algebraic reconstruction. To obtain more optimal systems, a generalized treatment of channeled polarimeters is required. This paper describes methods that enable handling of multi-domain modulations and reconstruction of polarization information using linear algebra. We make practical choices regarding use of either Fourier or direct channels to make these methods more immediately useful. Employing the introduced concepts to optimize existing systems often results in superficial system changes, like changing the order, orientation, thickness, or spacing of polarization elements. For the two examples we consider, we were able to reduce noise in the reconstruction to 34.1% and 57.9% of the original design values. 19. Global map of lithosphere thermal thickness on a 1 deg x 1 deg grid - digitally available Science.gov (United States) Artemieva, Irina 2014-05-01 This presentation reports a 1 deg ×1 deg global thermal model for the continental lithosphere (TC1). The model is digitally available from the author's web-site: www.lithosphere.info. Geotherms for continental terranes of different ages (early Archean to present) are constrained by reliable data on borehole heat flow measurements (Artemieva and Mooney, 2001), checked with the original publications for data quality, and corrected for paleo-temperature effects where needed. These data are supplemented by cratonic geotherms based on xenolith data. Since heat flow measurements cover not more than half of the continents, the remaining areas (ca. 60% of the continents) are filled by the statistical numbers derived from the thermal model constrained by borehole data. Continental geotherms are statistically analyzed as a function of age and are used to estimate lithospheric temperatures in continental regions with no or low quality heat flow data. This analysis requires knowledge of lithosphere age globally. A compilation of tectono-thermal ages of lithospheric terranes on a 1 deg × 1 deg grid forms the basis for the statistical analysis. It shows that, statistically, lithospheric thermal thickness z (in km) depends on tectono-thermal age t (in Ma) as: z=0.04t+93.6. This relationship formed the basis for a global thermal model of the continental lithosphere (TC1). Statistical analysis of continental geotherms also reveals that this relationship holds for the Archean cratons in general, but not in detail. Particularly, thick (more than 250 km) lithosphere is restricted solely to young Archean terranes (3.0-2.6 Ga), while in old Archean cratons (3.6-3.0 Ga) lithospheric roots do not extend deeper than 200-220 km. The TC1 model is presented by a set of maps, which show significant thermal heterogeneity within continental upper mantle. The strongest lateral temperature variations (as large as 800 deg C) are typical of the shallow mantle (depth less than 100 km). A map of the 20. Global map of lithosphere thermal thickness on a 1 deg x 1 deg grid - digitally available DEFF Research Database (Denmark) Artemieva, Irina 2014-01-01 than 250 km) lithosphere is restrictedsolely to young Archean terranes (3.0–2.6 Ga), while in old Archean cratons (3.6–3.0 Ga) lithospheric roots donot extend deeper than 200–220 km.The TC1 model is presented by a set of maps, which show significant thermal heterogeneity within continentalupper mantle......This presentation reports a 1 deg 1 deg global thermal model for the continental lithosphere (TC1). The modelis digitally available from the author’s web-site: www.lithosphere.info.Geotherms for continental terranes of different ages (early Archean to present) are constrained by reliabledata...... of the continents, the remaining areas (ca. 60% ofthe continents) are filled by the statistical numbers derived from the thermal model constrained by boreholedata. Continental geotherms are statistically analyzed as a function of age and are used to estimate lithospherictemperatures in continental regions... 1. OMP Peptides Activate the DegS Stress-Sensor Protease by a Relief of Inhibition Mechanism Energy Technology Data Exchange (ETDEWEB) Sohn, Jungsan; Grant, Robert A.; Sauer, Robert T.; MIT 2010-03-19 In the E. coli periplasm, C-terminal peptides of misfolded outer-membrane porins (OMPs) bind to the PDZ domains of the trimeric DegS protease, triggering cleavage of a transmembrane regulator and transcriptional activation of stress genes. We show that an active-site DegS mutation partially bypasses the requirement for peptide activation and acts synergistically with mutations that disrupt contacts between the protease and PDZ domains. Biochemical results support an allosteric model, in which these mutations, active-site modification, and peptide/substrate binding act in concert to stabilize proteolytically active DegS. Cocrystal structures of DegS in complex with different OMP peptides reveal activation of the protease domain with varied conformations of the PDZ domain and without specific contacts from the bound OMP peptide. Taken together, these results indicate that the binding of OMP peptides activates proteolysis principally by relieving inhibitory contacts between the PDZ domain and the protease domain of DegS. 2. La poesia sabiana degli Anni Venti Directory of Open Access Journals (Sweden) Atilij Rakar 1975-11-01 Full Text Available Muovendo da un confronto fra il Saba del primo Canzoniere e le Figure e canti coi quali l'opera del poeta triestino continua negli anni venti, l'autore cerca di individuare i caratteri che meglio definiscono la poesia sabiana di questo secondo periodo. Messi in evidenza alcuni temi su cui verte il discorso sabiano fin delle Poesie dell'adolescenza e giovanili, le opere degli anni venti si rivelano come esiti di un poliforme compendio in cui il poeta vuol chiarire il senso del cammino percorso e comp:tendere quelle che sono le ragioni prime del suo poetare. Si manifestano qui, anche in maniera esplicita, alcuni motivi fondamentali del Canzionere: basti pensare, ad esempio, a Il borgo che offre la chiave per l'interprezazione di tutto un filone della tematica sabiana, o alle Fughe, con le quali il poeta vuol esprimere l'essenza del proprio sentire. La poetica delle »figure« e dei »canti« composti negli anni venti, non segnerebbe dunque una conversione di Saba ai »miti della forma«, come inducono a credere anche certe apostrofi del poeta stesso, rna può esser definita solo se vista in funzione dei contenuti che determinano il suo formarsi. 3. Spin Interference in Rashba 2DEG Systems Science.gov (United States) Nitta, Junsaku The gate controllable SOI provides useful information about spin interference.1 Spin interference effects are studied in two different interference loop structures. It is known that sample specific conductance fluctuations affect the conductance in the interference loop. By using array of many interference loops, we carefully pick up TRS Altshuler-Aronov-Spivak (AAS)-type oscillation which is not sample specific and depends on the spin phase. The experimentally obtained gate voltage dependence of AAS oscillations indicates that the spin precession angle can be controlled by the gate voltage.2 We demonstrate the time reversal Aharonov-Casher (AC) effect in small arrays of mesoscopic rings.3 By using an electrostatic gate we can control the spin precession angle rate and follow the AC phase over several interference periods. We also see the second harmonic of the AC interference, oscillating with half the period. The spin interference is still visible after more than 20π precession angle. We have proposed a Stern-Gerlach type spin filter based on the Rashba SOI.4 A spatial gradient of effective magnetic field due to the nonuniform SOI separates spin up and down electrons. This spin filter works even without any external magnetic fields and ferromagnetic contacts. We show the semiconductor/ferromagnet hybrid structure is an effective way to detect magnetization process of submicron magnets. The problem of the spin injection from ferromagnetic contact into 2DEG is also disicussed. Note from Publisher: This article contains the abstract only. 4. Evaluation of reconstruction arc in myocardial SPECT imaging using a cardiac phantom. Comparison between 360deg and 180deg arcs Energy Technology Data Exchange (ETDEWEB) Kashikura, Kenichi [Japan Science and Technology Corp., Tokyo (Japan); Kashikura, Akemi; Terada, Shinichirou; Kobayashi, Hideki 1996-10-01 In order to investigate the effect of reconstruction arc on myocardial SPECT images, a series of phantom studies was performed with and without plastic chambers simulating perfusion defects using {sup 201}Tl and {sup 99m}Tc. Coefficient of variations (CV) of the counts among the ROIs and defect contrast were evaluated in 360deg and 180deg images reconstructed from the same 360deg projection data. Reconstruction processes were identical for all images. In the absence of defects, the CV of the counts were approximately the same in 360deg and 180deg images. The CV of the counts in the 360deg {sup 201}Tl image, among 4 defects located on the anterior, lateral, inferoposterior, and septal walls, was superior to those in the 180deg images. In contrast, in the {sup 99m}Tc images, the CV of the counts among the 4 defects in the 180deg image was superior to those of the 360deg image. The defect contrast was changed both by the location of the defect and by the reconstruction arc ({sup 201}Tl, {sup 99m}Tc). The defect contrast of the 180deg images, in both {sup 201}Tl and {sup 99m}Tc experiments, was closer to the true contrast value as calculated by the count ratio between myocardium and defect. Although the defect contrast in the anterior, lateral and septal walls was more emphasized in the 180deg images, the defect contrast in the inferoposterior wall was less emphasized in the 180deg images compared to the 360deg ({sup 201}Tl, {sup 99m}Tc). (author) 5. The Structure of Dark Molecular Gas in the Galaxy - I: A Pilot Survey for 18-cm OH Emission Towardsl \\approx 105^{\\deg}, b \\approx +1^{\\deg}$CERN Document Server Allen, Ronald J; Engelke, Philip D 2015-01-01 We report the first results from a survey for 1665, 1667, and 1720 MHz OH emission over a small region of the Outer Galaxy centered at$l \\approx 105.0\\deg , b \\approx +1.0\\deg$. This sparse, high-sensitivity survey ($\\Delta Ta \\approx \\Delta Tmb \\approx 3.0 - 3.5$mK rms in 0.55 km/s channels), was carried out as a pilot project with the Green Bank Telescope (GBT, FWHM$\\approx 7.6'$) on a 3 X 9 grid at$0.5\\deg$spacing. The pointings chosen correspond with those of the existing$^{12}$CO(1-0) CfA survey of the Galaxy (FWHM$\\approx 8.4'$). With 2-hr integrations, 1667 MHz OH emission was detected with the GBT at$\\gtrsim 21$of the 27 survey positions ($\\geq 78\\%), confirming the ubiquity of molecular gas in the ISM as traced by this spectral line. With few exceptions, the main OH lines at 1665 and 1667 MHz appear in the ratio of 5:9 characteristic of LTE at our sensitivity levels. No OH absorption features are recorded in the area of the present survey, in agreement with the low levels of continuum bac... 6. Mesosphere Study by Wide-Field Twilight Polarization Measurements: First Results beyond the Polar Circle CERN Document Server Ugolnikov, Oleg S 2015-01-01 The paper contains the observations description and first results of mesosphere temperature and dust study based on twilight wide-field polarization analysis started in 2015 in Apatity, northern Russia (67.6 deg N, 33.4 deg E) with original all-sky camera. It is the first twilight polarization measurements set in the polar region and the first one during the winter and early spring epoch. The general polarization properties of the twilight sky and single scattering separation procedure are described. The basic results are the Boltzmann temperature decrease above 70 km and lack of mesosphere dust that is typical for this season. 7. Very Low Ohmic Contact Resistance through an AlGaN Etch-Stop in Nitrogen-Polar GaN-Based High Electron Mobility Transistors Science.gov (United States) Nidhi; Brown, David F.; Keller, Stacia; Mishra, Umesh K. 2010-02-01 Ultra-low ohmic contact resistance of 0.1 Ω mm has been obtained as a step towards a deep-recess structure using N-polar GaN-based high electron mobility transistors (HEMTs). An AlGaN etchstop layer was investigated to obtain smooth and reliable gate recess. However due to reverse polarization, AlGaN results in a polarization-induced Schottky barrier which prevents ohmic contact to the channel through the etchstop. In this work, we have proposed a novel methodology to contact the two-dimensional electron gas (2DEG) by etching through the GaN cap and the AlGaN etchstop to eliminate the barrier and angular-evaporation of metals to achieve side-alloying resulting in very low ohmic contact resistance of 0.1 Ω mm achieved to N-polar GaN 2DEG. This result is state-of-the-art for alloyed contacts achieved to GaN-based 2DEG. 8. Neutron irradiation of silicon diodes at temperatures of +20deg C and -20deg C Energy Technology Data Exchange (ETDEWEB) Anghinolfi, F.; Glaser, M.; Heijne, E.H.M.; Jarron, P.; Lemeilleur, F.; Occelli, E.; Poppleton, A. (CERN, Geneva (Switzerland)); Bardos, R.; Gorfine, G.; Moorhead, G.; Taylor, G.; Tovey, S. (School of Physics, Univ. Melbourne, Parkville (Australia)); Bates, S.J.; Munday, D.J.; Parker, M.A. (Cavendish Lab., Univ. Cambridge (United Kingdom)); Bonino, R.; Clark, A.G.; Wu, X. (DPNC, Univ. Geneva (Switzerland)); Claussen, N.; Fretwurst, E.; Lindstroem, G.; Papendick, B.; Schulz, T.; Wunstorf, R. (Inst. fuer Experimentalphysik, Univ. Hamburg (Germany)); Goessling, C.; Klingenberg, R.; Pagel, H.; Pollmann, D.; Rolf, A. (Inst. fuer Physik, Univ. Dortmund (Germany)); Scampoli, P. (Dipt. di Fisica, Univ. Perugia (Italy) INFN, Sezione Perugia (Italy)); Weidberg, A.R. (Dept. of Nuclear Physics, Oxford Univ. (United Kingdom)); RD2 Collaboration 1993-03-01 We report measurements of the behaviour of silicon diodes when exposed to integrated neutron doses of up to 5x10[sup 13] neutrons/cm[sup 2]. The measurements have been made at diode temperatures between room temperature and -20deg C. From measurements of the diode leakage current and depletion voltage, and consequent evaluations of the effective impurity concentration, the temperature dependence of these quantities is discussed in terms of the annealing behaviour of the diodes. Comments are made on the suitability of silicon as a detector medium for particle physics experiments at future accelerators. (orig.). 9. DegP Chaperone Suppresses Toxic Inner Membrane Translocation Intermediates Science.gov (United States) Braselmann, Esther; Chaney, Julie L.; Champion, Matthew M. 2016-01-01 The periplasm of Gram-negative bacteria includes a variety of molecular chaperones that shepherd the folding and targeting of secreted proteins. A central player of this quality control network is DegP, a protease also suggested to have a chaperone function. We serendipitously discovered that production of the Bordetella pertussis autotransporter virulence protein pertactin is lethal in Escherichia coli ΔdegP strains. We investigated specific contributions of DegP to secretion of pertactin as a model system to test the functions of DegP in vivo. The DegP chaperone activity was sufficient to restore growth during pertactin production. This chaperone dependency could be relieved by changing the pertactin signal sequence: an E. coli signal sequence leading to co-translational inner membrane (IM) translocation was sufficient to suppress lethality in the absence of DegP, whereas an E. coli post-translational signal sequence was sufficient to recapitulate the lethal phenotype. These results identify a novel connection between the DegP chaperone and the mechanism used to translocate a protein across the IM. Lethality coincided with loss of periplasmic proteins, soluble σE, and proteins regulated by this essential stress response. These results suggest post-translational IM translocation can lead to the formation of toxic periplasmic folding intermediates, which DegP can suppress. PMID:27626276 10. DegP Chaperone Suppresses Toxic Inner Membrane Translocation Intermediates. Science.gov (United States) Braselmann, Esther; Chaney, Julie L; Champion, Matthew M; Clark, Patricia L 2016-01-01 The periplasm of Gram-negative bacteria includes a variety of molecular chaperones that shepherd the folding and targeting of secreted proteins. A central player of this quality control network is DegP, a protease also suggested to have a chaperone function. We serendipitously discovered that production of the Bordetella pertussis autotransporter virulence protein pertactin is lethal in Escherichia coli ΔdegP strains. We investigated specific contributions of DegP to secretion of pertactin as a model system to test the functions of DegP in vivo. The DegP chaperone activity was sufficient to restore growth during pertactin production. This chaperone dependency could be relieved by changing the pertactin signal sequence: an E. coli signal sequence leading to co-translational inner membrane (IM) translocation was sufficient to suppress lethality in the absence of DegP, whereas an E. coli post-translational signal sequence was sufficient to recapitulate the lethal phenotype. These results identify a novel connection between the DegP chaperone and the mechanism used to translocate a protein across the IM. Lethality coincided with loss of periplasmic proteins, soluble σE, and proteins regulated by this essential stress response. These results suggest post-translational IM translocation can lead to the formation of toxic periplasmic folding intermediates, which DegP can suppress. 11. Millimeter and sub-millimeter heterodyne mixing based on 2DEG hot-electron bolometers Science.gov (United States) Wang, Kai; Bell, Matthew; Ramaswamy, Rahul; Sergeev, Andrei; Strasser, Gottfried; Mitin, Vladimir 2010-03-01 We investigate GHz and THz heterodyne mixer based on the electron heating effect of a two-dimensional electron gas (2DEG) by electromagnetic radiation at liquid nitrogen temperatures (77K). The devices are fabricated from AlGaAs/GaAs heterostructures with a channel width of 150 μm and lengths varying from 3-20 μm. Steady-state measurements are used to investigate electron heating in these devices and determine basic parameters, such as electron-phonon energy relaxation time and electron heat capacity. We perform mixing experiments at ˜100 GHz frequency range with two Gunn diodes as the radiation sources, and find that electron heating is the primary mixing mechanism at these frequencies. For the mixing experiments at ˜ 2 terahertz range, a quantum cascade laser (QCL) is employed as the local oscillator. To optimize our device, we also investigate electron kinetics and transport properties in the 2DEG hot-electron bolometer. 12. Involvement of DEG5 and DEG8 proteases in the turnover of the photosystem II reaction center D1 protein under heat stress in Arabidopsis thaliana Institute of Scientific and Technical Information of China (English) SUN XuWu; WANG LiYuan; ZHANG LiXin 2007-01-01 Deg5,deg8 and the double mutant,deg5deg8 of Arabidopsis thaliana were used to study the physiological role of the DEG proteases in the repair cycle of photosystem II (PSII) under heat stress. PSII activity in deg mutants showed increased sensitivity to heat stress,and the extent of this effect was greater in the double mutant,deg5deg8,than in the single mutants,deg5 and deg8. Degradation of the D1 protein was slower in the mutants than in the WT plants. Furthermore,the levels of other PSII reaction center proteins tested remained relatively stable in the mutant and WT plants following high-temperature treatment. Thus,our results indicate that DEG5 and DEG8 may have synergistic function in degradation of D1 protein under heat stress. 13. The Prevalence of the 22 deg Halo in Cirrus Clouds Science.gov (United States) Diedenhoven, vanBastiaan 2014-01-01 Halos at 22 deg from the sun attributed to randomly-orientated, pristine hexagonal crystals are frequently observed through ice clouds. These frequent sightings of halos formed by pristine crystals pose an apparent inconsistency with the dominance of distorted, nonpristine ice crystals indicated by in situ and remote sensing data. Furthermore, the 46 deg halo, which is associated with pristine hexagonal crystals as well, is observed far less frequently than the 22 deg halo. Considering that plausible mechanisms that could cause crystal distortion such as aggregation, sublimation, riming and collisions are stochastic processes that likely lead to distributions of crystals with varying distortion levels, here the presence of the 22 deg and 46 deg halo features in phase functions of mixtures of pristine and distorted hexagonal ice crystals is examined. We conclude that the 22 deg halo feature is generally present if the contribution by pristine crystals to the total scattering cross section is greater than only about 10% in the case of compact particles or columns, and greater than about 40% for plates. The 46 deg halo feature is present only if the mean distortion level is low and the contribution of pristine crystals to the total scattering cross section is above about 20%, 50% and 70%, in the case of compact crystals, plates and columns, respectively. These results indicate that frequent sightings of 22 deg halos are not inconsistent with the observed dominance of distorted, non-pristine ice crystals. Furthermore, the low mean distortion levels and large contributions by pristine crystals needed to produce the 461 halo features provide a potential explanation of the common sighting of the 22 deg halo without any detectable 46 deg halo. 14. La formazione iniziale degli insegnanti in Italia Directory of Open Access Journals (Sweden) Carlo Cappa 2013-07-01 Full Text Available L’articolo è diviso in tre parti. La prima presenta gli elementi storici e di sfondo che occorre tenere presenti per comprendere l’evoluzione della formazione iniziale degli insegnanti verso gli attuali modelli, che pur essendo oggi tutti gestiti dalle università conservano una sensibile diversità a seconda che si tratti di formare maestri per la scuola dell’infanzia e primaria oppure professori di scuola secondaria di primo e secondo grado. La seconda parte analizza il passaggio, maturato tra la fine del secolo scorso e l’inizio del XXI secolo, della formazione dei maestri dalla scuola secondaria (Istituto magistrale all’università (Corso di laurea in Scienze della formazione primaria, e l’istituzione delle Scuole di Specializzazione per l’Insegnamento Secondario (SSIS fino alla soppressione di queste ultime, avvenuta nel 2009. La terza parte presenta il quadro attuale della formazione iniziale dei docenti in Italia con riguardo soprattutto agli insegnanti della scuola secondaria, per i quali – a differenza che per i maestri - sono intervenute dal 2010 importanti innovazioni legislative. Le SSIS sono state infatti sostituite con il Tirocinio Formativo Attivo (TFA, attualmente in fase di attuazione da parte delle università. Nella parte finale dell’articolo si traccia un primo bilancio dell’esperienza del TFA e si indicano alcuni problemi aperti. Il focus rimane sostanzialmente sulla formazione iniziale, in quanto in Italia la formazione in servizio, che pure non è del tutto assente, non è mai stata oggetto di una normativa né di una azione organica, ma avviene, quando avviene, sulla base di iniziative di specifici gruppi o associazioni.The article is organised in three parts. The first one illustrates the historical features and the institutional and political background that have to be taken into account in order to understand how initial teacher education and training has developed in Italy. Presently, all teacher 15. 基于椭圆偏振光注入垂直腔表面发射激光器的正交偏振模式单周期振荡产生两路光子微波∗%Two channel photonic microwave generation based on period-one oscillations of two orthogonally polar-ized modes in a vertical-cavity surface-emitting laser subjected to an elliptically polarized optical injection Institute of Scientific and Technical Information of China (English) 周娅; 吴正茂; 樊利; 孙波; 何洋; 夏光琼 2015-01-01 Previous investigations demonstrated that a semiconductor laser subjected to optical injection can realize period-one (P1) oscillation output under suitable operational parameters, which can be used to obtain high quality photonic microwave. In this paper, we propose a scheme for simultaneously generating two channel photonic microwave based on the P1 oscillations of two orthogonally polarization modes in a vertical-cavity surface-emitting laser (VCSEL) subjected to an elliptical polarization optical injection, and the relevant characteristics of obtained photonic microwave are numerically simulated and analyzed. The results show that under suitable operational parameters, a free-running VCSEL (named master VCSEL, M-VCSEL) can output an elliptical polarization light in which both X and Y polarization components of the elliptical polarization light oscillate at the same frequency. By using the elliptical polarization light from the M-VCSEL as an injection light into another VCSEL (named slave VCSEL, S-VCSEL), both two polarization components of the S-VCSEL can be driven into P1 oscillation through selecting suitable injection strength under a fixed frequency detuning between the M-VCSEL and the S-VCSEL. Based on the P1 oscillation, two orthogonally photonic microwave signals can be obtained. With the increase of the injection strength from the M-VCSEL, the frequency of photonic microwave shows a gradually increasing trend while the power of photonic microwave displays an increasing process accompanied by slight ripples. Combining the distribution mappings of the frequency, the power, and the amplitude difference between the first sideband and the second sideband of the photonic microwave in the parameter space of the injection strength and the frequency detuning, certain regions with optimally operational parameters can be determined for acquiring high quality photonic microwave. 16. Polarization-Analyzing CMOS Image Sensor With Monolithically Embedded Polarizer for Microchemistry Systems. Science.gov (United States) Tokuda, T; Yamada, H; Sasagawa, K; Ohta, J 2009-10-01 This paper proposes and demonstrates a polarization-analyzing CMOS sensor based on image sensor architecture. The sensor was designed targeting applications for chiral analysis in a microchemistry system. The sensor features a monolithically embedded polarizer. Embedded polarizers with different angles were implemented to realize a real-time absolute measurement of the incident polarization angle. Although the pixel-level performance was confirmed to be limited, estimation schemes based on the variation of the polarizer angle provided a promising performance for real-time polarization measurements. An estimation scheme using 180 pixels in a 1deg step provided an estimation accuracy of 0.04deg. Polarimetric measurements of chiral solutions were also successfully performed to demonstrate the applicability of the sensor to optical chiral analysis. 17. Optimization of polarization lidar structure Science.gov (United States) Abramochkin, Alexander I.; Kaul, Bruno V.; Tikhomirov, Alexander A. 1999-11-01 The problems of the polarization lidar transceiver optimization are considered. The basic features and the optimization criteria of lidar polarization units are presented and the comparative analysis of polarization units is fulfilled. We have analyzed optical arrangements of the transmitter to form the desired polarization state of sounding radiation. We have also considered various types of lidar receiving systems: (1) one-channel, providing measurement of Stocks parameters at a successive change of position of polarization analyzers in the lidar receiver, and (2) multichannel, where each channel has a lens, an analyzer, and a photodetector. In the latter case measurements of Stocks parameters are carried out simultaneously. The optimization criteria of the polarization lidar considering the atmospheric state are determined with the purpose to decrease the number of polarization devices needed. 18. Barrier reduction via implementation of InGaN interlayer in wafer-bonded current aperture vertical electron transistors consisting of InGaAs channel and N-polar GaN drain Energy Technology Data Exchange (ETDEWEB) Kim, Jeonghee, E-mail: jhkim@ece.ucsb.edu; Laurent, Matthew A.; Li, Haoran; Lal, Shalini; Mishra, Umesh K. [Department of Electrical and Computer Engineering, University of California, Santa Barbara, California 93106 (United States) 2015-01-12 This letter reports the influence of the added InGaN interlayer on reducing the inherent interfacial barrier and hence improving the electrical characteristics of wafer-bonded current aperture vertical electron transistors consisting of an InGaAs channel and N-polar GaN drain. The current-voltage characteristics of the transistors show that the implementation of N-polar InGaN interlayer effectively reduces the barrier to electron transport across the wafer-bonded interface most likely due to its polarization induced downward band bending, which increases the electron tunneling probability. Fully functional wafer-bonded transistors with nearly 600 mA/mm of drain current at V{sub GS} = 0 V and L{sub go} = 2 μm have been achieved, and thus demonstrate the feasibility of using wafer-bonded heterostructures for applications that require active carrier transport through both materials. 19. Influence of polarization state, baud rate and PMD on non-linear impairments in WDM systems with mixed PM (D)QPSK and OOK channels. Science.gov (United States) Chughtai, Mohsan Niaz; Forzati, Marco; Mårtensson, Jonas; Rafique, Danish 2012-03-26 In this paper we numerically investigate nonlinear impairments in a WDM system with mixed PM (D)QPSK and OOK channels. First we analyze the dependence of XPM and XPolM on SOP and baud rate in absence of PMD. In this case we find that the nonlinear impairments are highly dependent on relative SOP between the PM (D)QPSK and neighbouring OOK channels. The dependence on relative SOP is more pronounced in differential detection than in coherent detection. However, with increasing values of PMD this dependence decreases, and non-linear tolerance improves. 20. Students' Understanding of External Representations of the Potassium Ion Channel Protein, Part I: Affordances and Limitations of Ribbon Diagrams, Vines, and Hydrophobic/Polar Representations Science.gov (United States) Harle, Marissa; Towns, Marcy H. 2012-01-01 Research on external representations in biochemistry has uncovered student difficulties in comprehending and interpreting external representations. This project focuses on students' understanding of three external representations of the potassium ion channel protein. This is part I of a two-part study, which focuses on the affordances and… 1. The family of Deg/HtrA proteases in plants Directory of Open Access Journals (Sweden) Schuhmann Holger 2012-04-01 Full Text Available Abstract Background The Deg/HtrA family of ATP-independent serine endopeptidases is present in nearly all organisms from bacteria to human and vascular plants. In recent years, multiple deg/htrA protease genes were identified in various plant genomes. During genome annotations most proteases were named according to the order of discovery, hence the same names were sometimes given to different types of Deg/HtrA enzymes in different plant species. This can easily lead to false inference of individual protease functions based solely on a shared name. Therefore, the existing names and classification of these proteolytic enzymes does not meet our current needs and a phylogeny-based standardized nomenclature is required. Results Using phylogenetic and domain arrangement analysis, we improved the nomenclature of the Deg/HtrA protease family, standardized protease names based on their well-established nomenclature in Arabidopsis thaliana, and clarified the evolutionary relationship between orthologous enzymes from various photosynthetic organisms across several divergent systematic groups, including dicots, a monocot, a moss and a green alga. Furthermore, we identified a “core set” of eight proteases shared by all organisms examined here that might provide all the proteolytic potential of Deg/HtrA proteases necessary for a hypothetical plant cell. Conclusions In our proposed nomenclature, the evolutionarily closest orthologs have the same protease name, simplifying scientific communication when comparing different plant species and allowing for more reliable inference of protease functions. Further, we proposed that the high number of Deg/HtrA proteases in plants is mainly due to gene duplications unique to the respective organism. 2. Information Content Analysis for the Multi-Viewing, Multi-Channel, Multi-Polarization Imaging (3MI) Instrument : Toward Retrieval of Vertically Resolved Cloud Properties from Passive Only Measurements. Science.gov (United States) Riedi, J.; Merlin, G.; Labonnote, L.; Cornet, C.; Ferlay, N.; Desmons, M.; Dubuisson, P.; Parol, F.; Davis, A. B.; Marbach, T. 2014-12-01 The EUMETSAT Polar System- Second Generation (EPS-SG) is currently under development to take over the current EUMETSAT Polar System at the 2020 horizon. As part of it, the Multi-Viewing Multi-Channel Multi-Polarization Imaging mission (3MI) will be dedicated to the operational monitoring of aerosols but will also provide unique observations for characterization of cloud properties building on the legacy of POLDER and particularly of its 3rd mission (PARASOL) within the A-Train. Through the synergy of POLDER3/PARASOL and MODIS/AQUA several studies have demonstrated the great interest of combining multispectral, multiangle and polarization measurements in the visible, near and shortwave infrared to better constrain retrieval of clouds microphysical and macrophysical properties. Remote-sensing of cloud thermodynamic phase (Riedi et al, 2010), liquid (Bréon and Doutriaux-Boucher, 2005) or ice clouds microphysics (Zhang et al, 2009; Cole et al, 2012), cloud radiative (Zeng et al, 2012) or macrophysical properties (Ferlay et al, 2010; Desmons et al, 2013) can unarguably benefit from the additional information content brought by polarization and multiangle measurements. At the same time, retrieval algorithms are gaining further complexity and skills. Thanks to availability of computational resources, practical implementation of optimal estimation or related optimization techniques (Delanoe & Hogan, 2008; Dubovik et al, 2013) have appeared that allow simultaneous and consistent retrieval of larger sets of parameters from constantly growing observations vectors. Therefore 3MI observations will not only allow to improve accuracy of future cloud products but also opens perspectives for the development of new retrieval algorithms. A major challenge for cloud remote-sensing from passive measurements is to obtain information on clouds properties vertical distribution and structure. Through results of a comprehensive information content analysis we will illustrate our current 3. Limiting Global Warming to 2 deg C and Beyond Science.gov (United States) Lea, D. W. 2011-12-01 This presentation addresses the question of how feasible is it to limit global warming to a specific temperature rise, whether 1.5, 2 or 3 deg C. Inherent in the idea of limiting global warming to a specific temperature level is the notion that future GHG emissions will be subject to a top-down international agreement. In the post-Copenhagen era, however, such an agreement is unlikely, and a bottoms-up approach of national pledges will likely have to serve as a surrogate for achieving emissions reduction. In this case, an additional question is what temperature targets are realistic under scenarios that are bounded by achievable national pledges as opposed to binding mandates. The question of feasibility depends largely on future emission pathways of CO2, other GHGs, black carbon and aerosols. Those pathways depend on many societal, technological and economic factors, but it is likely that the ultimate limiting factor is the maximum possible rate of absolute emission reduction. That rate is limited by how rapidly energy infrastructure can be turned over. Most studies suggest that an absolute emission reduction rate of 3.5% is the highest rate achievable. Climate sensitivity and the current cooling effect of aerosols and earth system responses such as the rate of ocean heat uptake and carbon cycle feedbacks determine how a specific emissions pathway translates into probable climate change. A useful framework for CO2 alone is provided by the newly emerging paradigm of cumulative emissions, which holds that peak temperature can be largely predicted by the total amount of carbon emitted, regardless of pathway. Most studies suggest that 1 Tt of cumulative carbon is equivalent to ~2 deg of peak warming. A consideration of these factors suggests that limiting warming to 1.5 deg C is no longer possible under any feasible economic scenario. For one, currently emitted GHGs are equivalent to a ~1.3 deg C warming commitment. This leaves very little room for future emissions 4. Athermalized channeled spectropolarimeter enhancement. Energy Technology Data Exchange (ETDEWEB) Jones, Julia Craven; Way, Brandyn Michael; Mercier, Jeffrey Alan; Hunt, Jeffery P. 2013-09-01 Channeled spectropolarimetry can measure the complete polarization state of light as a function of wavelength. Typically, a channeled spectropolarimeter uses high order retarders made of uniaxial crystal to amplitude modulate the measured spectrum with the spectrally-dependent Stokes polarization information. A primary limitation of conventional channeled spectropolarimeters is related to the thermal variability of the retarders. Thermal variation often forces frequent system recalibration, particularly for field deployed systems. However, implementing thermally stable retarders, made of biaxial crystal, results in an athermal channeled spectropolarimeter that relieves the need for frequent recalibration. This report presents experimental results for an anthermalized channeled spectropolarimeter prototype produced using potassium titanyl phosphate. The results of this prototype are compared to the current thermal stabilization state of the art. Finally, the application of the technique to the thermal infrared is studied, and the athermalization concept is applied to an infrared imaging spectropolarimeter design. 5. Tropospheric ozone over a tropical Atlantic station in the Northern Hemisphere: Paramaribo, Surinam (6 deg N, 55 deg W) Energy Technology Data Exchange (ETDEWEB) Peters, W.; Krol, M.C. [Inst. for Marine and Atmospheric Research Utrecht (Netherlands); Fortuin, J.P.F.; Kelder, H.M. [Koninklijke Nederlandse Meteorologische Dienst, De Bilt (Netherlands); Thompson, A.M. [Goddard Space Flight Center, NASA, Greenbelt, MD (United States); Becker, C.R. [Meteorologische Dienst Suriname, Paramaribo (Suriname); Lelieveld, J.; Crutzen, P.J. [Max Planck Inst. fuer Chemie, Mainz (Germany) 2004-02-01 We present an analysis of 2.5 yr of weekly ozone soundings conducted at a new monitoring station in Paramaribo, Surinam (6 deg N, 55 deg W). This is currently one of only three ozone sounding stations in the Northern Hemisphere (NH) tropics, and the only one in the equatorial Atlantic region. Paramaribo is part of the Southern Hemisphere Additional Ozone Sounding program (SHADOZ). Owing to its position close to the equator, the inter-tropical convergence zone (ITCZ) passes over Paramaribo twice per year, which results in a semi-annual seasonality of many parameters including relative humidity and ozone. The dataset from Paramaribo is used to: (1) evaluate the ozone variability relative to precipitation, atmospheric circulation patterns and biomass burning; (2) contrast ozone at the NH equatorial Atlantic with that at nearby Southern Hemisphere (SH) stations Natal (6 deg S, 35 deg W) and Ascension (8 deg S, 14 deg W); (3) compare the seasonality of tropospheric ozone with a satellite-derived ozone product: tropical tropospheric ozone columns from the modified residual method (MR-TTOC). We find that Paramaribo is a distinctly Atlantic station. Despite its position north of the equator, it resembles nearby SH stations during most of the year. Transport patterns in the lower and middle troposphere during February and March differ from SH stations, which leads to a seasonality of ozone with two maxima. MR-TTOC over Paramaribo does not match the observed seasonality of ozone due to the use of a SH ozone sonde climatology in the MR method. The Paramaribo ozone record is used to suggest an improvement for Northern Hemisphere MR-TTOC retrievals. We conclude that station Paramaribo shows unique features in the region, and clearly adds new information to the existing SHADOZ record. 6. Radio identification of decameter-wave sources. II: The 30degdeg declination interval CERN Document Server Verkhodanov, O V; Andernach, H; 10.1134/S1990341309010052 2009-01-01 This paper is dedicated to the identification of decameter-wave sources of the UTR catalog within declination interval 30degdeg. UTR sources are cross-identified with CATS database catalogs within 40'x40' error boxes. The sources are deblended using the data on the coordinates of the objects and the behavior of their continuum radio spectra. The spectra of 876 sources are derived and fitted by standard analytical functions. Of these sources, 221 objects have straight-line spectra with spectral indices alpha<-1.0. All objects are catalogued and stored in the CATS database. 7. Accuracy Assessments of Cloud Droplet Size Retrievals from Polarized Reflectance Measurements by the Research Scanning Polarimeter Science.gov (United States) Alexandrov, Mikhail Dmitrievic; Cairns, Brian; Emde, Claudia; Ackerman, Andrew S.; vanDiedenhove, Bastiaan 2012-01-01 We present an algorithm for the retrieval of cloud droplet size distribution parameters (effective radius and variance) from the Research Scanning Polarimeter (RSP) measurements. The RSP is an airborne prototype for the Aerosol Polarimetery Sensor (APS), which was on-board of the NASA Glory satellite. This instrument measures both polarized and total reflectance in 9 spectral channels with central wavelengths ranging from 410 to 2260 nm. The cloud droplet size retrievals use the polarized reflectance in the scattering angle range between 135deg and 165deg, where they exhibit the sharply defined structure known as the rain- or cloud-bow. The shape of the rainbow is determined mainly by the single scattering properties of cloud particles. This significantly simplifies both forward modeling and inversions, while also substantially reducing uncertainties caused by the aerosol loading and possible presence of undetected clouds nearby. In this study we present the accuracy evaluation of our algorithm based on the results of sensitivity tests performed using realistic simulated cloud radiation fields. 8. A 20 GHz Bright Sample for Delta > 72 deg - II. Multi-frequency Follow-up CERN Document Server Ricci, R; Verma, R; Prandoni, I; Carretti, E; Mack, K -H; Massardi, M; Procopio, P; Zanichelli, A; Gregorini, L; Mantovani, F; Gawronski, M P; Peel, M W 2013-01-01 We present follow-up observations at 5, 8 and 30 GHz of the K-band Northern Wide Survey (KNoWS) 20 GHz Bright Sample, performed with the 32-m Medicina Radio Telescope and the 32-m Torun Radio Telescope. The KNoWS sources were selected in the Northern Polar Cap (Delta > 72 deg) and have a flux density limit S(20GHz) = 115 mJy. We include NVSS 1.4 GHz measurements to derive the source radio spectra between 1.4 and 30 GHz. Based on optical identifications, 68 per cent of the sources are QSOs, and 27 per cent are radio galaxies. A redshift measurement is available for 58 per cent of the sources. The radio spectral properties of the different source populations are found to be in agreement with those of other high-frequency selected samples. 9. Embrittlement of reduced-activation ferritic/martensitic steels irradiated in HFIR at 300 deg. C and 400 deg. C Energy Technology Data Exchange (ETDEWEB) Klueh, R.L. E-mail: ku2@ornl.gov; Sokolov, M.A.; Shiba, K.; Miwa, Y.; Robertson, J.P 2000-12-01 Miniature tensile and Charpy specimens of four ferritic/martensitic steels were irradiated at 300 deg. C and 400 deg. C in the high flux isotope reactor (HFIR) to a maximum dose of {approx}12 dpa. The steels were standard F82H (F82H-Std), a modified F82H (F82H-Mod), ORNL 9Cr-2WVTa, and 9Cr-2WVTa-2Ni, the 9Cr-2WVTa containing 2% Ni to produce helium by (n,{alpha}) reactions with thermal neutrons. More helium was produced in the F82H-Std than the F82H-Mod because of the presence of boron. Irradiation embrittlement in the form of an increase in the ductile-brittle transition temperature ({delta}DBTT) and a decrease in the upper-shelf energy (USE) occurred for all the steels. The two F82H steels had similar {delta}DBTTs after irradiation at 300 deg. C, but after irradiation at 400 deg. C, the {delta}DBTT for F82H-Std was less than for F82H-Mod. Under these irradiation conditions, little effect of the extra helium in the F82H-Std could be discerned. Less embrittlement was observed for 9Cr-2WVTa steel irradiated at 400 deg. C than for the two F82H steels. The 9Cr-2WVTa-2Ni steel with {approx}115 appm He had a larger {delta}DBTT than the 9Cr-2WVTa with {approx}5 appm He, indicating a possible helium effect. 10. Modello metodologico per il monitoraggio degli incidenti stradali in Trentino Directory of Open Access Journals (Sweden) P. Fateh-Moghadam 2003-05-01 Full Text Available Obiettivi: realizzazione di un’infrastruttura informatica, per l’unificazione tempestiva dei flussi sugli incidenti stradali (ISTAT-ACI e sanitari con la georeferenziazione degli eventi a partire dall’anno 2000. Materiali e Metodi: dall’archivio di Trentino emergenza sono stati estratti gli interventi per incidente stradale selezionando la combinazione: descrizione patologica: “traumatismi”, tipologia luogo: “strada”, tipologia incidente. Dai dati di ogni Pronto soccorso è stato costruito un archivio unico contenente il totale degli accessi e sono stati estratti gli accessi per “incidente stradale” e quelli per lesioni accidentali in generale. Dall’archivio SDO si sono selezionati sia i ricoveri con il criterio “3” alla variabile mtraav (=incidente stradale che quelli per traumatismi. Nell’ambito del progetto “Metodi informatici predittivi per la mitigazione del rischio da incidenti stradali” (Mitris, finanziato dal Ministero della Salute, è stata realizzata l’immissione tramite interfaccia internet o decodifica automatica dei verbali informatizzati delle Forze dell’ordine, e la contestuale realizzazione di un interfaccia WebGIS in grado di visualizzare la localizzazione degli incidenti stradali. Risultati: tramite la combinazione “data nascita”, “data incidente”, “sesso” è stato eseguito un primo collegamento tra gli archivi. Aggiungendo alla data incidente uno o più giorni, è stato costruito un nuovo archivio PS contenente il 97,4% degli eventi raccolti dalle forze dell’Ordine e contenuti nel data base Mitris. Approccio analogo è stato seguito per il linkage con SDO e 118. Tramite interfaccia WebGIS è stata creata una mappa degli incidenti interrogabile on-line, che oltre alla semplice localizzazione riporta dinamica e esiti con possibilità di produrre statistiche e grafici. Il sistema copre attualmente 11. The Role of Potassium Channels in the Temperature Control of Stomatal Aperture. Science.gov (United States) Ilan, N.; Moran, N.; Schwartz, A. 1995-07-01 We used the patch-clamp technique to examine the effect of temperature (13-36[deg]C) on the depolarization-activated K channels (KD channels) and on the hyperpolarization-activated channels (KH channels) in the plasma membrane of Vicia faba guard-cell protoplasts. The steady-state whole-cell conductance of both K channel types increased with temperature up to 20[deg]C. However, whereas the whole-cell conductance of the KH channels increased further and saturated at 28[deg]C, that of KD channels decreased at higher temperatures. The unitary conductance of both channel types increased with temperature like the rate of diffusion in water (temperature quotient of approximately 1.5), constituting the major contribution to the conductance increase in the whole cells. The mean number of available KH channels was not affected significantly by temperature, but the mean number of available KD channels increased significantly between 13 and 20[deg]C and declined drastically above 20[deg]C. This decrease and the reduced steady-state voltage-dependent probability of opening of the KD channels above 28[deg]C (because of a shift of voltage dependence by +21 mV) account for the depression of the whole-cell KD conductance at the higher temperatures. This may be a basic mechanism by which leaves of well-watered plants keep their stomata open during heat stress to promote cooling by transpiration. 12. Molecular modeling of mechanosensory ion channel structural and functional features. Science.gov (United States) Gessmann, Renate; Kourtis, Nikos; Petratos, Kyriacos; Tavernarakis, Nektarios 2010-09-16 The DEG/ENaC (Degenerin/Epithelial Sodium Channel) protein family comprises related ion channel subunits from all metazoans, including humans. Members of this protein family play roles in several important biological processes such as transduction of mechanical stimuli, sodium re-absorption and blood pressure regulation. Several blocks of amino acid sequence are conserved in DEG/ENaC proteins, but structure/function relations in this channel class are poorly understood. Given the considerable experimental limitations associated with the crystallization of integral membrane proteins, knowledge-based modeling is often the only route towards obtaining reliable structural information. To gain insight into the structural characteristics of DEG/ENaC ion channels, we derived three-dimensional models of MEC-4 and UNC-8, based on the available crystal structures of ASIC1 (Acid Sensing Ion Channel 1). MEC-4 and UNC-8 are two DEG/ENaC family members involved in mechanosensation and proprioception respectively, in the nematode Caenorhabditis elegans. We used these models to examine the structural effects of specific mutations that alter channel function in vivo. The trimeric MEC-4 model provides insight into the mechanism by which gain-of-function mutations cause structural alterations that result in increased channel permeability, which trigger cell degeneration. Our analysis provides an introductory framework to further investigate the multimeric organization of the DEG/ENaC ion channel complex. 13. Molecular modeling of mechanosensory ion channel structural and functional features. Directory of Open Access Journals (Sweden) Renate Gessmann Full Text Available The DEG/ENaC (Degenerin/Epithelial Sodium Channel protein family comprises related ion channel subunits from all metazoans, including humans. Members of this protein family play roles in several important biological processes such as transduction of mechanical stimuli, sodium re-absorption and blood pressure regulation. Several blocks of amino acid sequence are conserved in DEG/ENaC proteins, but structure/function relations in this channel class are poorly understood. Given the considerable experimental limitations associated with the crystallization of integral membrane proteins, knowledge-based modeling is often the only route towards obtaining reliable structural information. To gain insight into the structural characteristics of DEG/ENaC ion channels, we derived three-dimensional models of MEC-4 and UNC-8, based on the available crystal structures of ASIC1 (Acid Sensing Ion Channel 1. MEC-4 and UNC-8 are two DEG/ENaC family members involved in mechanosensation and proprioception respectively, in the nematode Caenorhabditis elegans. We used these models to examine the structural effects of specific mutations that alter channel function in vivo. The trimeric MEC-4 model provides insight into the mechanism by which gain-of-function mutations cause structural alterations that result in increased channel permeability, which trigger cell degeneration. Our analysis provides an introductory framework to further investigate the multimeric organization of the DEG/ENaC ion channel complex. 14. Immagini dinamiche: appunti per un catalogo degli usi didattici Directory of Open Access Journals (Sweden) Filippo Bruni 2013-03-01 Full Text Available Le immagini dinamiche costituiscono un’importante risorsa per le attività didattiche. A partire da una riflessione storica, si evidenzia in primo luogo l’importanza di un loro uso efficace alla luce della classificazione operata da Clark e Lyons. In secondo luogo si segnalano alcune attività emergenti legate alla documentazione, al digital storytelling e alla formazione degli insegnanti. 15. Technical Note: Using DEG CPCs at upper tropospheric temperatures CERN Document Server Wimmer, D; Nieminen, T; Duplissy, J; Ehrhart, S; Almeida, J; Rondo, L; Franchin, A; Kreissl, F; Manninen, H E; Kulmala, M; Curtius, J; Petäjä, T 2014-01-01 Over the last few years, several Condensation Particle Counters (CPC) capable of measuring in the sub-3 nm size range have been developed. Here we study the performance of Diethylene glycol (DEG) based CPCs at different temperatures during Cosmics Leaving Outdoor Droplets (CLOUD) measurements at CERN. The data shown here is the first set of verification measurements for sub-3 nm CPCs under upper tropospheric temperatures using atmospherically relevant aerosol particles. To put the results in perspective we calibrated the DEG-CPC at room temperature, resulting in a cut-off diameter of 1.4 nm. All diameters refer to mobility equivalent diameters in this manuscript. At upper tropospheric temperatures between −25 °C and −65 °C, we found cut-off sizes in the range of 2.5 and 2.8 nm. Due to low number concentration after size classification, the cut-off diameters have a high uncertainty (±0.3 nm) associated with them. Operating two laminar flow DEG CPCs with different cut-off sizes together with other aeroso... 16. Book review. La forma degli animali. Adolf Portmann Directory of Open Access Journals (Sweden) Manuel Graziani 2013-09-01 Full Text Available Nel 1931 il biologo Adolf Portmann era già talmente noto a livello internazionale per le sue ricerche da guadagnarsi la cattedra in zoologia nell'università della sua città natale, Basilea, all'età di appena 34 anni. All'attività di docente universitario ha sempre affiancato un'originale riflessione sul significato delle scienze della vita, imponendosi come una delle figure chiave nel dibattito tra biologia teoretica, estetica e antropologia filosofica. La forma degli animali, la sua opera più celebre, si pone al confine tra varie discipline e conserva un grande interesse ancora oggi che il dialogo tra estetica e biologia si è fatto nuovamente intenso. Pubblicata nel 1948 e in forma ampliata nel 1960 (da cui deriva questa prima edizione italiana a cura di Pietro Conte l'opera rappresenta il frutto più maturo delle sue ricerche "interdisciplinari".Un saggio che nasce dall'insoddisfazione nei confronti dei paradigmi scientifici consolidati e che ripropone l'idea morfologica in biologia sulla scorta del pensiero di J. W. Goethe il quale affermava che "tutto ciò che è deve anche dar cenno di sé e mostrarsi". Adolf Portmann è un convinto sostenitore che dalla forma si possano dedurne le complessive caratteristiche interne ed esterne degli animali. Secondo questa prospettiva la peculiare fisionomia dell'organismo dipende dalla congiunzione delle sue parti e dalle loro reciproche funzioni. Tuttavia l'autore non vede nello studio della forma l'alternativa al funzionalismo quanto, piuttosto, il suo necessario bilanciamento come dichiara nell'introduzione: "… per giungere alla conoscenza della vita animale di strade ce ne sono molte, e tutte possono contribuire ad arricchire la nostra esperienza. Questo lavoro si occupa della forma degli animali e si propone di mettere in luce la peculiare natura dell'aspetto visibile. Ci sono persone che si dedicano allo studio degli animali, conoscono moltissime specie, hanno imparato centinaia di nomi e 17. Geology of the Delta, Escalante, Price, Richfield and Salina 1 deg x 2 deg NTMS quadrangles, Utah Science.gov (United States) Thayer, P. A. 1981-11-01 The National Uranium Resource Evaluation (NURE) program was established to evaluate domestic uranium resources in the continental United States and to identify areas favorable for uranium exploration. The Grand Junction Office of the Department of Energy is responsible for administering the program. The Savannah River Laboratory (SRL) is responsible for hydrogeochemical and stream-sediment reconnaissance (HSSR) of 3.9 million sq km (1,500,000 mi(2)) in 37 eastern and western states. This document provides geologic and mineral resources reports for the Delta, Escalante, Price, Richfield, and Salina 1 deg x 2 deg National Topographic Map Series quadrangles, Utah. The purpose of these reports is to provide background geologic and mineral resources information to aid in the interpretation of NURE geochemical reconnaissance data. Except for the Escalante Quadrangle, each report is accompanied by a geologic map and a mineral locality map (Plates 1-8, in pocket). 18. Technical Note: Using DEG-CPCs at upper tropospheric temperatures Science.gov (United States) Wimmer, D.; Lehtipalo, K.; Nieminen, T.; Duplissy, J.; Ehrhart, S.; Almeida, J.; Rondo, L.; Franchin, A.; Kreissl, F.; Bianchi, F.; Manninen, H. E.; Kulmala, M.; Curtius, J.; Petäjä, T. 2015-07-01 Over the last few years, several condensation particle counters (CPCs) capable of measuring in the sub-3 nm size range have been developed. Here we study the performance of CPCs based on diethylene glycol (DEG) at different temperatures during Cosmics Leaving OUtdoor Droplets (CLOUD) measurements at CERN. The data shown here are the first set of verification measurements for sub-3 nm CPCs under upper tropospheric temperatures using atmospherically relevant aerosol particles. To put the results in perspective we calibrated the DEG-CPC at room temperature, resulting in a cut-off diameter of 1.4 nm. All diameters refer to mobility equivalent diameters in this paper. At upper tropospheric temperatures ranging from 246.15 K to 207.15 K, we found cut-off sizes relative to a particle size magnifier in the range of 2.5 to 2.8 nm. Due to low number concentration after size classification, the cut-off diameters have a high uncertainty (±0.3 nm) associated with them. Operating two laminar flow DEG-CPCs with different cut-off sizes together with other aerosol instruments, we looked at the growth rates of aerosol population in the CLOUD chamber for particles smaller than 10 nm at different temperatures. A more consistent picture emerged when we normalized the growth rates to a fixed gas-phase sulfuric acid concentration. All of the instruments detected larger growth rates at lower temperatures, and the observed growth rates decreased as a function of temperature, showing a similar trend for all instruments. The theoretical calculations had a similar but much smaller temperature dependency. 19. Mutations suppressing the loss of DegQ function in Bacillus subtilis (natto) poly-γ-glutamate synthesis. Science.gov (United States) Do, Thi-Huyen; Suzuki, Yuki; Abe, Naoki; Kaneko, Jun; Itoh, Yoshifumi; Kimura, Keitarou 2011-12-01 The degQ gene of Bacillus subtilis (natto), encoding a small peptide of 46 amino acids, is essential for the synthesis of extracellular poly-gamma-glutamate (γPGA). To elucidate the role of DegQ in γPGA synthesis, we knocked out the degQ gene in Bacillus subtilis (natto) and screened for suppressor mutations that restored γPGA synthesis in the absence of DegQ. Suppressor mutations were found in degS, the receptor kinase gene of the DegS-DegU two-component system. Recombinant DegS-His(6) mutant proteins were expressed in Escherichia coli cells and subjected to an in vitro phosphorylation assay. Compared with the wild type, mutant DegS-His(6) proteins showed higher levels of autophosphorylation (R208Q, M195I, L248F, and D250N), reduced autodephosphorylation (D250N), reduced phosphatase activity toward DegU, or a reduced ability to stimulate the autodephosphorylation activity of DegU (R208Q, D249G, M195I, L248F, and D250N) and stabilized DegU in the phosphorylated form. These mutant DegS proteins mimic the effect of DegQ on wild-type DegSU in vitro. Interestingly, DegQ stabilizes phosphorylated DegS only in the presence of DegU, indicating a complex interaction of these three proteins. 20. Mutations Suppressing the Loss of DegQ Function in Bacillus subtilis (natto) Poly-γ-Glutamate Synthesis ▿ † Science.gov (United States) Do, Thi-Huyen; Suzuki, Yuki; Abe, Naoki; Kaneko, Jun; Itoh, Yoshifumi; Kimura, Keitarou 2011-01-01 The degQ gene of Bacillus subtilis (natto), encoding a small peptide of 46 amino acids, is essential for the synthesis of extracellular poly-gamma-glutamate (γPGA). To elucidate the role of DegQ in γPGA synthesis, we knocked out the degQ gene in Bacillus subtilis (natto) and screened for suppressor mutations that restored γPGA synthesis in the absence of DegQ. Suppressor mutations were found in degS, the receptor kinase gene of the DegS-DegU two-component system. Recombinant DegS-His6 mutant proteins were expressed in Escherichia coli cells and subjected to an in vitro phosphorylation assay. Compared with the wild type, mutant DegS-His6 proteins showed higher levels of autophosphorylation (R208Q, M195I, L248F, and D250N), reduced autodephosphorylation (D250N), reduced phosphatase activity toward DegU, or a reduced ability to stimulate the autodephosphorylation activity of DegU (R208Q, D249G, M195I, L248F, and D250N) and stabilized DegU in the phosphorylated form. These mutant DegS proteins mimic the effect of DegQ on wild-type DegSU in vitro. Interestingly, DegQ stabilizes phosphorylated DegS only in the presence of DegU, indicating a complex interaction of these three proteins. PMID:21965392 1. The Codice digitale degli archivi veronesi. A research instrument Directory of Open Access Journals (Sweden) Andrea Brugnoli 2014-04-01 Full Text Available The Codice digitale degli archivi veronesi (Verona’s archives digital code ‹http://cdavr.dtesis.univr.it› makes available online the digital reproductions of the documents produced by corporate bodies and family of Verona between the eighth and twelfth century. The framework of the site reflects the current organisation of the archives. A brief description of the circumstances around the creation of each archive, the corporate body or individual responsible for it and its structure is provided. Each archival unit is identified by its key elements: chronological date, name and qualification of the notary, original/copy, main editions. 2. The Codice digitale degli archivi veronesi. A research instrument Directory of Open Access Journals (Sweden) Andrea Brugnoli 2014-04-01 Full Text Available The Codice digitale degli archivi veronesi (Verona’s archives digital code ‹http://cdavr.dtesis.univr.it› makes available online the digital reproductions of the documents produced by corporate bodies and family of Verona between the eighth and twelfth century. The framework of the site reflects the current organisation of the archives. A brief description of the circumstances around the creation of each archive, the corporate body or individual responsible for it and its structure is provided. Each archival unit is identified by its key elements: chronological date, name and qualification of the notary, original/copy, main editions. 3. Islam, rappresentanza degli interessi religiosi e diritto comune europeo * Directory of Open Access Journals (Sweden) Gianfranco Macrì 2011-03-01 Full Text Available Contributo destinato alla pubblicazione negli Atti del Convegno: Europa e Islam. Ridiscutere i fondamenti per la disciplina delle libertà religiose, svoltosi a Salerno il 3 dicembre 2007.SOMMARIO: Premessa - 1. La società «reticolare» europea: sistema di governance e valori unificanti - 2. Europa e fenomeno religioso - 3. La sostanza del Trattato di Lisbona e il ruolo delle organizzazioni religiose - 4. Il dibattito interno all’Islam europeo - 5. La Carta dei musulmani d’Europa - 6. La rappresentanza degli interessi religiosi dell’Islam in Europa - Conclusioni. 4. Non-Local Signal in Quasi-2DEG of LAO/STO Science.gov (United States) Jin, Mi-Jin; Moon, Seon Young; Modepalli, Vijayakumar; Jo, Junhyeon; Park, Jungmin; Baek, Seung-Hyub; Yoo, Jung-Woo 2015-03-01 Electron gas arizen at the insulating oxide interfaces exhibits high electron mobility, tunable carrier densities and related unique behaviors such as coexistence of superconductivity and ferromagnetism, Kondo resistance, etc. Itinerant electrons at the oxide hetero-interface are predicted to have long spin diffusion length, while they are under the relatively strong Rashba-type spin orbit coupling due to inversion symmetry breaking. We studied non-local spin signal induced by spin orbit coupling with additional gate-controlled Rashba field in quasi-2DEG of LaAlO3/SrTiO (LAO/STO) interface. We fabricated simple hall-bar like geometry to measure non-local signal with the variation of channel length (2 ~ 10 μm). Cleaned sample was patterned using e-beam lithography and reactive ion etching followed by oxygen treatment to anneal out oxygen vacancies. When an electric current flows one line of the hall bar structure, spin orbit coupling will induce the current flow away from the source current channel via spin hall and inverse spin hall effects. The non-local signals were studied under different angles of magnetic field and the variation of applied gate voltage. This work was supported by a grant from (No. 1.140092.01) funded by the Ulsan National Institute of Science and Technology. 5. Measuring the continuum linear polarization with ESPaDOnS CERN Document Server Pereyra, A; Martioli, E 2014-01-01 Our goal is to test the feasibility to obtain accurate measurements of the continuum linear polarization from high-resolution spectra using the spectropolarimetric mode of ESPaDOnS. We used the new pipeline OPERA to reduce recent and archived ESPaDOnS data. A couple of standard polarization stars and several science objects were tested. Synthetic broad-band polarization was computed from the ESPaDOnS continuum linear polarization spectra and compared with published values to quantify the accuracy of the instrument. The continuum linear polarization measured by ESPaDOnS is consistent with the broad-band polarimetry measurements available in the literature. The polarization degree accuracy is better than 0.2% considering the full sample. The accuracy in polarization position angle using the most polarized objects is better than 5deg. Our results suggest that measurements of the continuum linear polarization using ESPaDOnS are viable. 6. Zoogeografia storica e attuale dei carnivori e degli ungulati italiani Directory of Open Access Journals (Sweden) Marco Masseti 2003-10-01 Full Text Available Come per la maggior parte degli altri paesi europei, anche l'attuale composizione delle specie a mammiferi italiane si prefigura in gran parte come il risultato della plurima e prolungata azione antropica condotta sull'ambiente naturale. Questa, avviatasi alcuni millenni or sono, condiziona oggi più che mai la ridefinizione degli equilibri ecologici del nostro Paese. All'interno dell'attuale teriofauna terrestre italiana viene segnalata la presenza di 18 specie di carnivori e di 9 artiodattili, che può rivelarsi in alcuni casi come il risultato di acclimatazioni e/o naturalizzazioni di specie esotiche avvenute in cronologie diverse, anche di epoca molto recente. All'interno dei confini biogeografici dell'Italia andrebbero anche annoverate quelle popolazioni del cervo pomellato medio-orientale, Axis axis (Erxleben, 1777, che sono state naturalizzate in epoca storica assai recente in Istria ed in alcune isole del golfo del Quarnaro (Brioni Maggiore, Cherso e Plauno. Considerazioni analoghe potrebbero forse essere condotte anche per la diffusione artificiale di Herpestes auropunctatus Hodgson, 1836, su alcune isole della Croazia. Le specie fitofaghe riferibili ai gruppi tassonomici dei lagomorfi e degli artiodattili, e che vengono convenzionalmente comprese nella categoria della cosiddetta "selvaggina", sono tra quelle che hanno più subito un'alterazione condotta in profondità dei quadri faunistici originari, proprio in virtù dell'interesse economico e culturale che ancora rappresentano. Nel caso particolare di queste specie di interesse venatorio ci troviamo quasi sempre di fronte a popolazioni che sono state sottoposte ad intensa gestione e che hanno subito frequenti estinzioni locali seguite da reiterate reintroduzioni. Attualmente, data l'espansione sia naturale che artificiale degli ecotipi indigeni e di quelli alloctoni, si osserva ormai una sovrapposizione degli areali, per cui sembra piuttosto difficile riuscire in 7. Insight toward epithelial Na+ channel mechanism revealed by the acid-sensing ion channel 1 structure. Science.gov (United States) Stockand, James D; Staruschenko, Alexander; Pochynyuk, Oleh; Booth, Rachell E; Silverthorn, Dee U 2008-09-01 The epithelial Na(+) channel/degenerin (ENaC/DEG) protein family includes a diverse group of ion channels, including nonvoltage-gated Na(+) channels of epithelia and neurons, and the acid-sensing ion channel 1 (ASIC1). In mammalian epithelia, ENaC helps regulate Na(+) and associated water transport, making it a critical determinant of systemic blood pressure and pulmonary mucosal fluidity. In the nervous system, ENaC/DEG proteins are related to sensory transduction. While the importance and physiological function of these ion channels are established, less is known about their structure. One hallmark of the ENaC/DEG channel family is that each channel subunit has only two transmembrane domains connected by an exceedingly large extracellular loop. This subunit structure was recently confirmed when Jasti and colleagues determined the crystal structure of chicken ASIC1, a neuronal acid-sensing ENaC/DEG channel. By mapping ENaC to the structural coordinates of cASIC1, as we do here, we hope to provide insight toward ENaC structure. ENaC, like ASIC1, appears to be a trimeric channel containing 1alpha, 1beta, and 1gamma subunit. Heterotrimeric ENaC and monomeric ENaC subunits within the trimer possibly contain many of the major secondary, tertiary, and quaternary features identified in cASIC1 with a few subtle but critical differences. These differences are expected to have profound effects on channel behavior. In particular, they may contribute to ENaC insensitivity to acid and to its constitutive activity in the absence of time- and ligand-dependent inactivation. Experiments resulting from this comparison of cASIC1 and ENaC may help clarify unresolved issues related to ENaC architecture, and may help identify secondary structures and residues critical to ENaC function. 8. Emission polarization study on quartz and calcite. Science.gov (United States) Vincent, R. K. 1972-01-01 Calculation of the spectral emission polarization of quartz and calcite polished plates for observation angles of 20 and 70 deg by the substitution of complex index of refraction values for each mineral into Fresnel's equations. The emission polarization is shown to be quite wavelength-dependent, demonstrating that selected narrow or medium-width spectral bands exhibit a significantly higher percentage of polarization than a broad spectral band for these two minerals. Field measurements with a broadband infrared radiometer yield polarizations on the order of 2% for a coarse-grained granite rock and beach sand (both quartz-rich). This implies that a more sensitive detector with a selected medium-width filter may be capable of measuring emission polarization accurately enough to make this parameter useful as a remote sensing tool for discrimination among rocks on the basis of texture. 9. Environmental oil spill sensitivity atlas for the West Greenland (68 deg.-72 deg. N) coastal zone, 2nd revised edition Energy Technology Data Exchange (ETDEWEB) Clausen, D.; Johansen, Kasper L.; Mosbech, A.; Boertmann, D.; Wegeberg, S. 2012-12-15 This oil spill sensitivity atlas covers the shoreline and the offshore areas of West Greenland between 68 deg. N and 72 deg. N. The coastal zone is divided into 199 shoreline segments and the offshore zone into 8 areas. A sensitivity index value is calculated for each segment/area, and each segment/area is subsequently ranked according to four degrees of sensitivity. Besides this general ranking a number of smaller areas are especially selected as they are of particular significance, they are especially vulnerable to oil spills and they have a size making oil spill response possible. The shoreline sensitivity ranking are shown on 37 maps (in scale 1:250,000), which also show the different elements included and the selected areas. Coast types, logistics and proposed response methods along the coasts are shown on another 37 maps. The sensitivities of the offshore zones are depicted on 4 maps, one for each season. Based on all the information, appropriate oil spill response methods have been assessed for each area. (Author) 10. On the rms anisotropy at 7 deg and 10 deg observed in the COBE-DMR two year sky maps Science.gov (United States) Banday, A. J.; Gorski, K. M.; Tenorio, L.; Wright, E. L.; Smoot, G. F.; Lineweaver, C. H.; Kogut, A.; Hinshaw, G.; Bennett, C. L. 1994-01-01 The frequency-independent rms temperature fluctuations determined from the Cosmic Background Explorer-Differential Microwave Radiometer (COBE-DMR) two-year sky maps are used to infer the parameter Q(sub rms-PS), which characterizes the normalization of power-law models of primordial cosmological temperature anisotropy, for a forced fit to a scale-invariant Harrison-Zel'dovich (n = 1) spectral model. Using a joint analysis of the 7 deg and 10 deg 'cross'-rms derived from both the 53 and 90 GHz sky maps, we find Q(sub rms-PS) = 17.0(sub -2.1 sup +2.5) micro Kelvin when the low quadrupole is included, and Q(sub rms-PS) = 19.4(sub -2.1 sup +2.3) micro Kelvin excluding the quadrupole. These results are consistent with the n = 1 fits from more sensitive methods. The effect of the low quadrupole derived from the COBE-DMR data on the inferred Q(sub rms-PS) normalization is investigated. A bias to lower Q(sub rms-PS) is found when the quadrupole is included. The higher normalization for a forced n = 1 fit is then favored by the cross-rms technique. 11. Polarization developments Energy Technology Data Exchange (ETDEWEB) Prescott, C.Y. 1993-07-01 Recent developments in laser-driven photoemission sources of polarized electrons have made prospects for highly polarized electron beams in a future linear collider very promising. This talk discusses the experiences with the SLC polarized electron source, the recent progress with research into gallium arsenide and strained gallium arsenide as a photocathode material, and the suitability of these cathode materials for a future linear collider based on the parameters of the several linear collider designs that exist. 12. Dislocation Majorana zero modes in perovskite oxide 2DEG Science.gov (United States) Chung, Suk Bum; Chan, Cheung; Yao, Hong 2016-05-01 Much of the current experimental efforts for detecting Majorana zero modes have been centered on probing the boundary of quantum wires with strong spin-orbit coupling. The same type of Majorana zero mode can also be realized at crystalline dislocations in 2D superconductors with the nontrivial weak topological indices. Unlike at an Abrikosov vortex, at such a dislocation, there is no other low-lying midgap state than the Majorana zero mode so that it avoids usual complications encountered in experimental detections such as scanning tunneling microscope (STM) measurements. We will show that, using the anisotropic dispersion of the t2g orbitals of Ti or Ta atoms, such a weak topological superconductivity can be realized when the surface two-dimensional electronic gas (2DEG) of SrTiO3 or KTaO3 becomes superconducting, which can occur through either intrinsic pairing or proximity to existing s-wave superconductors. 13. Giant magnetic quadrupole resonance studied with 180 deg. electron scattering CERN Document Server Neumann-Cosel, P V 1999-01-01 The nuclei sup 4 sup 8 Ca and sup 9 sup 0 Zr were investigated in 180 deg. high-resolution inelastic electron scattering for momentum transfers q approx =0.35-0.8 fm sup - sup 1. Complete M2 strength distributions could be extracted in both nuclei up to excitation energies of about 15 MeV utilizing a fluctuation analysis technique. Second-RPA calculations successfully describe the experimentally observed strong fragmentation of the M2 mode. The quenching of the spin part is found to be comparable to the M1 case, contrary to previous claims suggesting a stronger reduction. A quantitative reproduction of the data requires the presence of appreciable orbital strength which can be interpreted as a torsional elastic vibration (the so-called twist mode). 14. Laicità: finitezza degli ordini e governo delle differenze Directory of Open Access Journals (Sweden) Nicola Colaianni 2013-12-01 Full Text Available Testo della relazione al Convegno Nazionale dell’ADEC sul tema “Per una disciplina che cambia. Il diritto canonico e il diritto ecclesiastico nel tempo presente” (Bologna, 7-9 novembre 2013, destinata alla pubblicazione negli Atti del Convegno. Contributo non sottoposto a valutazioneSOMMARIO: 1. La laicità dei giudici – 2. La laicità dei giuristi – 3. Né regola né valore: un principio – 4. La finitezza degli ordini distinti: dalle materie miste alla sfera dell’indecidibile – 5. L’aconfessionalità sostanziale: a ex parte ecclesiae – 6. (segue: b ex parte status – 7. La laicità come governance delle differenze. 15. LA FORMAZIONE DEGLI ETNICI NELLA RIFLESSIONE LINGUISTICA DI FRANCESCO CHERUBINI Directory of Open Access Journals (Sweden) Federica Guerini 2016-09-01 Full Text Available Il presente contributo si propone di fornire una descrizione della struttura del Vocabolario Patronimico di Francesco Cherubini e delle fonti empiriche consultate per la sua compilazione. Si accennerà poi a due questioni ricorrenti nel dibattito sulla formazione degli etnici in italiano, ovvero, la presenza di varianti allomorfiche o suppletive, e la motivazione morfo-pragmatica sottesa all’impiego di alcuni suffissi derivativi nella formazione di etnici e aggettivi deonomastici, cercando di chiarire quale attenzione tali tematiche abbiano ricevuto nella riflessione linguistica di Francesco Cherubini. Si formuleranno infine alcune osservazioni conclusive, evidenziando luci ed ombre del Vocabolario Patronimico e sottolineando alcuni degli spunti che tale opera ancora può offrire agli studiosi contemporanei. The formation of ethnic words in Francesco Cherubini’s reflection on language The aim of this paper is to describe the structure and contents of Francesco Cherubini’s Vocabolario Patronimico, as well as the empirical sources consulted for its compilation. We will address two of the most common issues in the debate on the formation of ethnic nouns and adjectives in Italian, namely the existence of allomorphs and supplementary variants, and the morpho-pragmatic motivation displayed by some of the derivative suffixes occurring in ethnic nouns and adjectives derived from both personal and place names. We will offer a few observations on the place occupied by the above-mentioned issues in Cherubini’s thought and, by analyzing the strengths and weaknesses of the Vocabolario Patronimico, we will draw attention to a few topics which may be of some interest to contemporary scholars. 16. The Structure of Galactic Gas at High Latitudes: The Southern Polar Cap Science.gov (United States) Gosachinskii, I. V.; Il'in, G. N.; Prozorov, V. A. 2004-04-01 We analyze the angular structure of the 21-cm interstellar neutral hydrogen emission at six and seven declinations in the northern (published previously) and southern polar caps of the Galaxy (Galactic latitudes from -40 deg to -90 deg), respectively, with an extent of 90 deg in right ascension. The RATAN-600 radio telescope has a beam width averaged over these regions of 2.0' x 30'. One-dimensional power spectra for the angular distribution of interstellar neutral hydrogen emission were computed in each 6.3-km/s-wide spectral channel by using the standard Fast Fourier Transform (FFT) code and were smoothed over 1 hour in right ascension. The Galactic latitude dependence of the mean parameters for the sky distribution of H I line emission at high latitudes was found to correspond to the distribution of gas in the form of a flat layer only in the northern region, while in the southern cap, the gas distribution is much less regular. In addition, the mean H I radial velocities are negative everywhere (-3.7 +/- 3.0 km/s in the north and -6.0+/-2.4 km/s in the south). The power spectra of the angular fluctuations in the range of angular periods from 10' to 6 deg appear as power laws. However, the spectral indices change greatly over the sky: from -3 to -1.2; on average, as the Galactic latitude increases and the H I column density decreases, the fluctuation spectrum of the interstellar gas emission becomes flatter. In the northern polar region, this behavior is much more pronounced, which probably stems from the fact that the gas column density in the south is generally a factor of 2 or 3 higher than that in the north. Therefore, the spectra are, on average, also steeper in the south, but the dependence on Galactic latitude is weaker. Using simulations, we show that the observed power-law spectrum of the H I emission distribution can be obtained in terms of not only a turbulent, but also a cloud model of interstellar gas if we use our previous spectra of the diameters 17. Polarization, political NARCIS (Netherlands) M. Wojcieszak 2015-01-01 Polarization has been studied in three different forms: on a social, group, and individual level. This entry first focuses on the undisputed phenomenon of elite polarization (i.e., increasing adherence of policy positions among the elites) and also outlines different approaches to assessing mass pol 18. Polarization holography DEFF Research Database (Denmark) Nikolova, L.; Ramanujam, P.S. Current research into holography is concerned with applications in optically storing, retrieving, and processing information. Polarization holography has many unique properties compared to conventional holography. It gives results in high efficiency, achromaticity, and special polarization...... properties. This books reviews the research carried out in this field over the last 15 years. The authors provide basic concepts in polarization and the propagation of light through anisotropic materials, before presenting a sound theoretical basis for polarization holography. The fabrication...... and characterization of azobenzene based materials, which remain the most efficient for the purpose, is described in detail. This is followed by a description of other materials that are used in polarization holography. An in-depth description of various applications, including display holography and optical storage... 19. Polarization holography DEFF Research Database (Denmark) Nikolova, L.; Ramanujam, P.S. properties. This books reviews the research carried out in this field over the last 15 years. The authors provide basic concepts in polarization and the propagation of light through anisotropic materials, before presenting a sound theoretical basis for polarization holography. The fabrication......Current research into holography is concerned with applications in optically storing, retrieving, and processing information. Polarization holography has many unique properties compared to conventional holography. It gives results in high efficiency, achromaticity, and special polarization...... and characterization of azobenzene based materials, which remain the most efficient for the purpose, is described in detail. This is followed by a description of other materials that are used in polarization holography. An in-depth description of various applications, including display holography and optical storage... 20. A 360-deg Digital Image Correlation system for materials testing Science.gov (United States) Genovese, K.; Cortese, L.; Rossi, M.; Amodio, D. 2016-07-01 The increasing research interest toward natural and advanced engineered materials demands new experimental protocols capable of retrieving highly dense sets of experimental data on the full-surface of samples under multiple loading conditions. Such information, in fact, would allow to capture the possible heterogeneity and anisotropy of the material by using up-to-date inverse characterization methods. Although the development of object-specific test protocols could represent the optimal choice to address this need, it is unquestionable that universal testing machines (UTM) remain the most widespread and versatile option to test materials and components in both academic and industrial contexts. A major limitation of performing standard material tests with UTM, however, consists in the scarce information obtainable with the commonly associated sensors since they provide only global (LVDTs, extensometers, 2D-video analyzers) or local (strain gages) measures of displacement and strain. This paper presents a 3D Digital Image Correlation (DIC) system developed to perform highly accurate full-surface 360-deg measurements on either standard or custom-shaped samples under complex loading within universal testing machines. To this aim, a low cost and easy to setup video rig was specifically designed to overcome the practical limitations entailed with the integration of a multi-camera system within an already existing loading frame. In particular, the proposed system features a single SLR digital camera moved through multiple positions around the specimen by means of a large rotation stage. A proper calibration and data-processing procedure allows to automatically merge the experimental data obtained from the multiple views with an accuracy of 10-2 m m . The results of a full benchmarking of the metrological performances of the system are here reported and discussed together with illustrative examples of full-360-deg shape and deformation measurements on a Grade X65 steel 1. COSMOS Photometric Redshifts with 30-bands for 2-deg2 CERN Document Server Ilbert, O; Salvato, M; Aussel, H; McCracken, H J; Sanders, D B; Scoville, N; Kartaltepe, J; Arnouts, S; Le Floc'h, E; Mobasher, B; Taniguchi, Y; Lamareille, F; Leauthaud, A; Sasaki, S; Thompson, D; Zamojski, M; Zamorani, G; Bardelli, S; Bolzonella, M; Bongiorno, A; Brusa, M; Caputi, K I; Carollo, C M; Contini, T; Cook, R; Coppa, G; Cucciati, O; De la Torre, S; de Ravel, L; Franzetti, P; Garilli, B; Hasinger, G; Iovino, A; Kampczyk, P; Kneib, J -P; Knobel, C; Kovac, K; Le Borgne, J F; Le Brun, V; Le Fèvre, O; Lilly, S; Looper, D; Maier, C; Mainieri, V; Mellier, Y; Mignoli, M; Murayama, T; Pellò, R; Peng, Y; Pérez-Montero, E; Renzini, A; Ricciardelli, E; Schiminovich, D; Scodeggio, M; Shioya, Y; Silverman, Joseph; Surace, J; Tanaka, M; Tasca, L; Tresse, L; Vergani, D; Zucca, E 2008-01-01 We present accurate photometric redshifts in the 2-deg2 COSMOS field. The redshifts are computed with 30 broad, intermediate, and narrow bands covering the UV (GALEX), Visible-NIR (Subaru, CFHT, UKIRT and NOAO) and mid-IR (Spitzer/IRAC). A chi2 template-fitting method (Le Phare) was used and calibrated with large spectroscopic samples from VLT-VIMOS and Keck-DEIMOS. We develop and implement a new method which accounts for the contributions from emission lines (OII, Hbeta, Halpha and Ly) to the spectral energy distributions (SEDs). The treatment of emission lines improves the photo-z accuracy by a factor of 2.5. Comparison of the derived photo-z with 4148 spectroscopic redshifts (i.e. Delta z = zs - zp) indicates a dispersion of sigma_{Delta z/(1+zs)}=0.007 at i<22.5, a factor of 2-6 times more accurate than earlier photo-z in the COSMOS, CFHTLS and COMBO-17 survey fields. At fainter magnitudes i<24 and z<1.25, the accuracy is sigma_{Delta z/(1+zs)}=0.012. The deep NIR and IRAC coverage enables the ph... 2. LE ZANZARE ITALIANE: GENERALITÀ E IDENTIFICAZIONE DEGLI ADULTI (DIPTERA, CULICIDAE Directory of Open Access Journals (Sweden) Francesco Severini 2009-12-01 Full Text Available Nel presente lavoro vengono riportate le informazioni essenziali su tassonomia e biologia nonché sugli aspetti ecologici degli adulti dei Culicidi italiani. Attualmente la fauna culicidica italiana comprende 64 specie appartenenti a 2 sottofamiglie e 8 generi. Alla sottofamiglia Anophelinae appartiene soltanto il genere Anopheles, presente con 16 specie raggruppate in due sottogeneri. Alla sottofamiglia Culicinae appartengono i rimanenti 7 generi: Aedes con 6 specie raggruppate in 3 sottogeneri, Coquillettidia con 2 specie, Ochlerotatus con 20 specie raggruppate in 3 sottogeneri, Culex con 12 specie raggruppate in 4 sottogeneri, Culiseta con 6 specie raggruppate in 3 sottogeneri, Orthopodomyia e Uranotaenia con una specie ognuna. In questo contesto vengono fornite le chiavi di identificazione specifica per le zanzare adulte, in italiano e in inglese. Le chiavi sono corredate da un’ampia iconografia (figure 1-75. Alle chiavi fa seguito la diagnosi morfologica dell’adulto di ogni specie con note sulla relativa biologia e distribuzione. Per ulteriori approfondimenti viene riportata la bibliografia completa sulle zanzare della fauna italiana dal 1960 ed i precedenti lavori più autorevoli. 3. Come e cosa desidera la narrativa italiana degli anni Zero Directory of Open Access Journals (Sweden) Gianluigi Simonetti 2013-05-01 Full Text Available L'articolo analizza il trattamento del tema del desiderio - erotico e amoroso - nel romanzo italiano degli ultimi anni, impegnandosi nell'esame ravvicinato di alcuni testi esemplari. La campionatura vuole da un lato isolare alcune opere rappresentative della situazione attuale della narrativa contemporanea, dall'altro proporre un'ipotesi categoriale che seziona il campo di studio in tre parti; il sondaggio sembra infatti suggerire che le dinamiche del desiderio vengono rese in maniera specifica nei diversi ambiti della letteratura di consumo, in quella di 'nobile intrattenimento' e in quella 'forte' e letterariamente più ambiziosa. L'analisi formale risulta insomma integrata a una prospettiva di stroria dello stile, secondo un metodo che permette di utilizzare la figuralità letteraria come 'indicatore sociologico' di processi politici (e forse antropologici in atto. 4. Le caratteristiche degli acquirenti e venditori di abitazioni Directory of Open Access Journals (Sweden) Erika Ghiraldo 2011-12-01 Full Text Available L’incrocio dei dati contenuti nelle dichiarazioni dei redditi con quelli contenuti negli archivi della Pubblicità Immobiliare (ex Conservatorie rende disponibili molte informazioni sulle caratteristiche dei contraenti che hanno effettuato una compravendita di unità immobiliari. Considerando principalmente le compravendite di unità immobiliari del settore residenziale effettuate da persone fisiche sono trattate informazioni sul reddito dichiarato al fisco, l’età e l’attività di lavoro prevalente. È fornito un quadro sintetico della distribuzione delle compravendite, in termini di Numero di Transazioni Normalizzate (NTN e per dimensione delle abitazioni, per ciascuna caratteristica sia per gli acquirenti che per i venditori. La disponibilità dell’informazione sulla residenza dei soggetti consente, inoltre, di condurre un’analisi sulla provenienza degli acquirenti rispetto al luogo di ubicazione dell’immobile compravenduto. E’ possibile così analizzare la composizione del mercato distinguendo la quota di acquisti imputabile a soggetti residenti nello stesso Comune di ubicazione dell’immobile (mercato comunale dalla quota alimentata da soggetti residenti in altro Comune di una stessa provincia (mercato infraprovinciale o di altra provincia (mercato extra-provinciale. Quest’ultima indagine risulta molto interessante se effettuata su singole città. Sono, quindi, riportati i risultati dell’analisi per i mercati delle città di Milano, Roma e Napoli. 5. Properties and Construction of Polar Codes CERN Document Server Mori, Ryuhei 2010-01-01 Recently, Ar{\\i}kan introduced the method of channel polarization on which one can construct efficient capacity-achieving codes, called polar codes, for any binary discrete memoryless channel. In the thesis, we show that decoding algorithm of polar codes, called successive cancellation decoding, can be regarded as belief propagation decoding, which has been used for decoding of low-density parity-check codes, on a tree graph. On the basis of the observation, we show an efficient construction method of polar codes using density evolution, which has been used for evaluation of the error probability of belief propagation decoding on a tree graph. We further show that channel polarization phenomenon and polar codes can be generalized to non-binary discrete memoryless channels. Asymptotic performances of non-binary polar codes, which use non-binary matrices called the Reed-Solomon matrices, are better than asymptotic performances of the best explicitly known binary polar code. We also find that the Reed-Solomon ma... 6. Polarizing cues. Science.gov (United States) Nicholson, Stephen P 2012-01-01 People categorize themselves and others, creating ingroup and outgroup distinctions. In American politics, parties constitute the in- and outgroups, and party leaders hold sway in articulating party positions. A party leader's endorsement of a policy can be persuasive, inducing co-partisans to take the same position. In contrast, a party leader's endorsement may polarize opinion, inducing out-party identifiers to take a contrary position. Using survey experiments from the 2008 presidential election, I examine whether in- and out-party candidate cues—John McCain and Barack Obama—affected partisan opinion. The results indicate that in-party leader cues do not persuade but that out-party leader cues polarize. This finding holds in an experiment featuring President Bush in which his endorsement did not persuade Republicans but it polarized Democrats. Lastly, I compare the effect of party leader cues to party label cues. The results suggest that politicians, not parties, function as polarizing cues. 7. Comparisons of the Interstellar Magnetic Field Directions obtained from the IBEX Ribbon and Interstellar Polarizations CERN Document Server Frisch, Priscilla C; Berdyugin, Andrei; Funsten, Herbert O; Magalhaes, Mario; McComas, David J; Piirola, Vilppu; Schwadron, Nathan A; Slavin, Jonathan D; Wiktorowicz, Sloane J 2010-01-01 Variations in the spatial configuration of the interstellar magnetic field (ISMF) near the Sun can be constrained by comparing the ISMF direction at the heliosphere found from the Interstellar Boundary Explorer spacecraft (IBEX) observations of a 'Ribbon' of energetic neutral atoms (ENAs), with the ISMF direction derived from optical polarization data for stars within ~40 pc. Using interstellar polarization observations towards ~30 nearby stars within 90 deg of the heliosphere nose, we find that the best fits to the polarization position angles are obtained for a magnetic pole directed towards ecliptic coordinates of lambda, beta 263 deg, 37 deg (or galactic coordinates of L,B 38 deg, 23deg), with uncertainties of +/- 35 deg, based on the broad minimum of the best fits and the range of data quality. This magnetic pole is 33 deg from the magnetic pole that is defined by the center of the arc of the ENA Ribbon. The IBEX ENA ribbon is seen in sightlines that are perpendicular to the ISMF as it drapes over the he... 8. The BLAST View of the Star Forming Region in Aquila (ell=45deg,b=0deg) CERN Document Server Rivera-Ingraham, Alana; Bock, James J; Chapin, Edward L; Devlin, Mark J; Dicker, Simon R; Griffin, Matthew; Gundersen, Joshua O; Halpern, Mark; Hargrave, Peter C; Hughes, David H; Klein, Jeff; Marsden, Gaelen; Martin, Peter G; Mauskopf, Philip; Netterfield, Calvin B; Olmi, Luca; Patanchon, Guillaume; Rex, Marie; Scott, Douglas; Semisch, Christopher; Truch, Matthew D P; Tucker, Carole; Tucker, Gregory S; Viero, Marco P; Wiebe, Donald V 2010-01-01 We have carried out the first general submillimeter analysis of the field towards GRSMC 45.46+0.05, a massive star forming region in Aquila. The deconvolved 6 deg^2 (3\\degree X 2\\degree) maps provided by BLAST in 2005 at 250, 350, and 500 micron were used to perform a preliminary characterization of the clump population previously investigated in the infrared, radio, and molecular maps. Interferometric CORNISH data at 4.8 GHz have also been used to characterize the Ultracompact HII regions (UCHIIRs) within the main clumps. By means of the BLAST maps we have produced an initial census of the submillimeter structures that will be observed by Herschel, several of which are known Infrared Dark Clouds (IRDCs). Our spectral energy distributions of the main clumps in the field, located at ~7 kpc, reveal an active population with temperatures of T~35-40 K and masses of ~10^3 Msun for a dust emissivity index beta=1.5. The clump evolutionary stages range from evolved sources, with extended HII regions and prominent IR ... 9. Analytical models for the 2DEG concentration and gate leakage current in AlGaN/GaN HEMTs Science.gov (United States) Ahmed, Nadim; Dutta, Aloke K. 2017-06-01 In this paper, we present a completely analytical model for the 2DEG concentration in AlGaN/GaN HEMTs as a function of gate bias, considering the donor-like trap states present at the metal/AlGaN interface to be the primary source of 2DEG carriers. To the best of our knowledge, this is a completely new contribution of this work. The electric field in the AlGaN layer is calculated using this model, which is further used to model the gate leakage current under reverse bias. We have modified the existing TTT (Thermionic Trap-Assisted Tunneling) current model, taking into account the effect of both metal/AlGaN interface traps as well as AlGaN bulk traps. The gate current under forward bias is also modeled using the existing thermionic emission model, approximating it by its Taylor series expansion. To take into account the effect of non-zero drain-source bias (VDS), an empirical fitting parameter is introduced in order to model the channel voltage in terms of VDS. The results of our models have been compared with the experimental data reported in the literature for three different devices, and the match is found to be excellent for both forward and reverse bias as well as for zero and non-zero VDS. 10. Mercury biomagnification in polar bears ( Ursus maritimus) Science.gov (United States) Horton, T. W.; Blum, J. D.; Xie, Z.; Hren, M.; Chamberlain, C. P. 2007-12-01 Mercury biomagnification occurs in a variety of ecosystems resulting in greater potential for toxicological effects in higher-level trophic feeders. However, Hg transport pathways through different foodweb channels are not well known, particularly in high-latitude systems affected by atmospheric Hg deposition associated with snow and ice. Stable carbon and nitrogen isotope ratios and Hg concentrations determined for 26 late 19th and early 20th century polar bear hair specimens collected from cataloged museum collections elucidate relationships between high latitude marine foodweb structure and Hg transport pathways. Nitrogen and carbon isotopic compositions suggest that polar bears derive nutrition from both open water (pelagic) and ice associated (sympagic) foodweb channels. Correlation between Hg concentrations and nitrogen isotope compositions indicate mercury biomagnification occurred in most of the polar bears investigated. Interpretation of stable isotope based foodweb structure in concert with Hg concentrations further suggests that Hg biomagnification occurred to a greater degree in polar bears participating in pelagic foodweb channels. 11. Caenorhabditis elegans paraoxonase-like proteins control the functional expression of DEG/ENaC mechanosensory proteins Science.gov (United States) Chen, Yushu; Bharill, Shashank; Altun, Zeynep; O’Hagan, Robert; Coblitz, Brian; Isacoff, Ehud Y.; Chalfie, Martin 2016-01-01 Caenorhabditis elegans senses gentle touch via a mechanotransduction channel formed from the DEG/ENaC proteins MEC-4 and MEC-10. An additional protein, the paraoxonase-like protein MEC-6, is essential for transduction, and previous work suggested that MEC-6 was part of the transduction complex. We found that MEC-6 and a similar protein, POML-1, reside primarily in the endoplasmic reticulum and do not colocalize with MEC-4 on the plasma membrane in vivo. As with MEC-6, POML-1 is needed for touch sensitivity, the neurodegeneration caused by the mec-4(d) mutation, and the expression and distribution of MEC-4 in vivo. Both proteins are likely needed for the proper folding or assembly of MEC-4 channels in vivo as measured by FRET. MEC-6 detectably increases the rate of MEC-4 accumulation on the Xenopus oocyte plasma membrane. These results suggest that MEC-6 and POML-1 interact with MEC-4 to facilitate expression and localization of MEC-4 on the cell surface. Thus MEC-6 and POML-1 act more like chaperones for MEC-4 than channel components. PMID:26941331 12. Accelerated transformation of brushite to octacalcium phosphate in new biomineralization media between 36.5 deg. C and 80 deg. C Energy Technology Data Exchange (ETDEWEB) Temizel, Neslihan; Girisken, Giray; Tas, A. Cuneyt, E-mail: cuneyt-tas@ouhsc.edu 2011-07-20 This study investigated the hydrothermal transformation of brushite (dicalcium phosphate dihydrate, DCPD, CaHPO{sub 4}.2H{sub 2}O) into octacalcium phosphate (OCP, Ca{sub 8}(HPO{sub 4}){sub 2}(PO{sub 4}){sub 4}.5H{sub 2}O) in seven different newly developed biomineralization media, all inspired from the commercial DMEM solutions, over the temperature range of 36.5 deg. C to 90 deg. C with aging times varying between 1 h and 6 days. DCPD powders used in this study were synthesized in our laboratory by using a wet-chemical technique. DCPD was found to transform into OCP in the Ca{sup 2+}, Mg{sup 2+}, Na{sup +}, K{sup +}, HCO{sub 3}{sup -}, Cl{sup -} and H{sub 2}PO{sub 4}{sup -} containing aqueous biomineralization media in less than 72 h at 36.5 deg. C, without stirring. The same medium was able to convert DCPD into OCP in about 2 h at 75-80 deg. C, again without a need for stirring. Samples were characterized by using powder X-ray diffraction (XRD), Fourier-transform infrared spectroscopy (FTIR), and scanning electron microscopy (SEM). - Research highlights: {yields} New biomineralization solutions developed to convert DCPD into OCP at 36.5 deg. C to 80 deg. C. {yields} DCPD powder was the starting material. {yields} OCP was synthesized under static conditions (no need for stirring). {yields} OCP was synthesized in sealed glass media bottles in solutions free of Hepes or Tris. {yields} OCP can be synthesized at 75-80 deg. C in only 2 hours in the above solutions without stirring. 13. Flexure fatigue testing of 90 deg graphite/epoxy composites Science.gov (United States) Peck, Ann Nancy W. 1995-01-01 3-point flexure tests of 90 deg graphite/epoxy specimens. Investigations will include the volume scale effect as well as frequency and span-to-thickness ratio effects. Prior to the start of the experimental study, an analytical study using finite element modeling will be performed to investigate the span-to-thickness effect. The ratio of transverse flexure stress to shear stress will be monitored and its values predicted by the FEM analysis compared with the value obtained using a 'strength of materials' based approach. 14. Unique hue judgments as a function of test size in the fovea and at 20-deg temporal eccentricity Science.gov (United States) Nerger, Janice L.; Volbrecht, Vicki J.; Ayde, Corey J. 1995-06-01 Unique hue loci were measured for four observers in the fovea and at 20-deg temporal eccentricity as a function of test size. Eccentric measurements were made on the cone plateau following a rod bleach. The results indicate that unique yellow remains approximately invariant with respect to test size and retinal eccentricity, whereas unique blue and unique green shift to longer wavelengths with increasing test size. The locus of unique blue in the periphery reaches an asymptote at approximately the same wavelength as that from the foveal measurements, whereas unique green measured in the periphery is consistently at shorter wavelengths than in the fovea. In general, the data are best described by a model in which the short-wavelength-sensitive cone input to the two opponent-color channels decreases with decreasing test size and increasing retinal eccentricity. 15. AtDeg2 – a chloroplast protein with dual protease/chaperone activity Directory of Open Access Journals (Sweden) Przemysław Jagodzik 2014-07-01 Full Text Available Chloroplast protease AtDeg2 (an ATP-independent serine endopeptidase is cytosolically synthesized as a precursor, which is imported into the chloroplast stroma and deprived of its transit peptide. Then the mature protein undergoes routing to its functional location at the stromal side of thylakoid membrane. In its linear structure AtDeg2 molecule contains the protease domain with catalytic triad (HDS and two PDZ domains (PDZ1 and PDZ2. In vivo AtDeg2 most probably exists as a supposedly inactive haxamer, which may change its oligomeric stage to form active 12-mer, or 24-mer. AtDeg2 has recently been demonstrated to exhibit dual protease/chaperone function. This review is focused on the current awareness with regard to AtDeg2 structure and functional significance. 16. Patologie sociali, resistenze e difese degli insegnanti nell’istituzione scolastica: Considerazioni cliniche e pedagogiche Directory of Open Access Journals (Sweden) Tommaso Fratini 2014-12-01 Full Text Available L’articolo prende in esame il tema di alcune resistenze e difese degli insegnanti all’interno dell’istituzione scolastica. Partendo dall’attuale condizione di emergenza della scuola italiana e rifacendosi al concetto di patologia sociale di Giuseppe Di Chiara, viene argomentato come tali resistenze coprano le angosce persecutorie degli insegnanti nel loro lavoro scolastico quotidiano nel rapporto con gli allievi. L’articolo, tra le varie forme di patologia istituzionale, affronta principalmente il tema di quelle che presiedono alle resistenze degli insegnanti al lavoro introspettivo con il proprio mondo interno, conseguenza e ulteriore cagione di sensi di colpa nel rapporto con gli allievi e di fenomeni di burnout lavorativo degli stessi insegnanti. Tali fenomeni vanno nella direzione del rinforzo sia di un atteggiamento di chiusura verso la collaborazione con professionisti esterni all’istituzione scolastica, sia di un atteggiamento di minore empatia e vicinanza emotiva con la realtà interna degli allievi. 17. North Polar Radiative Flux Variability from 2002 Through 2014 Science.gov (United States) Rutan, David; Rose, Fred; Doelling, David; Kato, Seiji; Smith, Bill, Jr. 2017-01-01 NASA's Clouds and the Earth's Radiant Energy System (CERES) project produces the SYN1Deg data product. SYN1deg provides global, 1deg gridded, hourly estimates of Top of Atmosphere (TOA) (CERES observations and calculations) and atmospheric and surface radiative flux (calculations). Examples of 12 year North Polar averages of some variables are shown to the right. Given recent interest in polar science we focus here on TOA and Surface validation of calculated irradiant fluxes. TOA upward longwave irradiance calculations match the CERES observations well both spatially and temporally with correlations remaining strong through PC 6. Compare SYN1Deg Calculations & Meteorological Teleconnections. TOA reflected shortwave irradiance calculations match the CERES observations well both spatially and temporally with correlations remaining string through PC 7. Comparing SYN1Deg calculations to teleconnection patterns requires expanding the area to 30N for EOF analyses. Correlating the Principal Components of various variables to teleconnection time series indicates which variable is most highly correlated with which teleconnection signal. The tables indicate the Pacific North American Oscillation is most correlated to the OLR EOF 1, and the North American Oscillation is correlated most closely to surface LW flux down EOF 1. 18. Temperature dependent dynamics of DegP-trimer: A molecular dynamics study. Science.gov (United States) Rai, Nivedita; Ramaswamy, Amutha 2015-01-01 DegP is a heat shock protein from high temperature requirement protease A family, which reacts to the environmental stress conditions in an ATP independent way. The objective of the present analysis emerged from the temperature dependent functional diversity of DegP between chaperonic and protease activities at temperatures below and above 28 °C, respectively. DegP is a multimeric protein and the minimal functional unit, DegP-trimer, is of great importance in understanding the DegP pathway. The structural aspects of DegP-trimer with respect to temperature variation have been studied using molecular dynamics simulations (for 100 ns) and principal component analysis to highlight the temperature dependent dynamics facilitating its functional diversity. The DegP-trimer revealed a pronounced dynamics at both 280 and 320 K, when compared to the dynamics observed at 300 K. The LA loop is identified as the highly flexible region during dynamics and at extreme temperatures, the residues 46-80 of LA loop express a flip towards right (at 280) and left ( at 320 K) with respect to the fixed β-sheet connecting the LA loop of protease for which Phe46 acts as one of the key residues. Such dynamics of LA loop facilitates inter-monomeric interaction with the PDZ1 domain of the neighbouring monomer and explains its active participation when DegP exists as trimer. Hence, the LA loop mediated dynamics of DegP-trimer is expected to provide further insight into the temperature dependent dynamics of DegP towards the understanding of its assembly and functional diversity in the presence of substrate. 19. Temperature dependent dynamics of DegP-trimer: A molecular dynamics study Directory of Open Access Journals (Sweden) Nivedita Rai 2015-01-01 Full Text Available DegP is a heat shock protein from high temperature requirement protease A family, which reacts to the environmental stress conditions in an ATP independent way. The objective of the present analysis emerged from the temperature dependent functional diversity of DegP between chaperonic and protease activities at temperatures below and above 28 °C, respectively. DegP is a multimeric protein and the minimal functional unit, DegP-trimer, is of great importance in understanding the DegP pathway. The structural aspects of DegP-trimer with respect to temperature variation have been studied using molecular dynamics simulations (for 100 ns and principal component analysis to highlight the temperature dependent dynamics facilitating its functional diversity. The DegP-trimer revealed a pronounced dynamics at both 280 and 320 K, when compared to the dynamics observed at 300 K. The LA loop is identified as the highly flexible region during dynamics and at extreme temperatures, the residues 46–80 of LA loop express a flip towards right (at 280 and left ( at 320 K with respect to the fixed β-sheet connecting the LA loop of protease for which Phe46 acts as one of the key residues. Such dynamics of LA loop facilitates inter-monomeric interaction with the PDZ1 domain of the neighbouring monomer and explains its active participation when DegP exists as trimer. Hence, the LA loop mediated dynamics of DegP-trimer is expected to provide further insight into the temperature dependent dynamics of DegP towards the understanding of its assembly and functional diversity in the presence of substrate. 20. pi deg. and eta photoproduction on the proton at GRAAL: New measurements of beam asymmetry up to 1.5 GeV and differential cross-section up to 1.1 GeV CERN Document Server Rebreyend, D 2000-01-01 After the achievement of the first beam asymmetry (SIGMA) measurement in eta photoproduction on the proton from threshold to 1.1 GeV [1], the energy range of the GRAAL facility has been extended to 1.5 GeV. New results of SIGMA for both pi deg. and eta, covering this new domain will be presented. Also, the differential cross-section for pi deg. and eta channels will be shown for energies up to 1.1 GeV. 1. Polarization-Based Radar Detection in Sea Clutter Science.gov (United States) 2015-02-27 Cisco AP - Agilent E4438C [ESG) - WiFi channel 1 [2412 - 20MHzPi/4DQPSKat MHz,±10MHz) 2412 MHz . • Digitizer - 20dBm - GaGel44002U...polarization multiple-input multiple-output channel state information at the transmitter Defense Advanced Research Projects Agency dual-polarized...Topics that are considered in this report include the following: • Background research describing channel modeling that led to observations of PMD in RF 2. Polarized Campuses. Science.gov (United States) Parr, Susan Resneck 1991-01-01 On college campuses, the climate is polarized because of intolerance and discrimination, censorship, factionalism, and anger among students and faculty. As a result, the campus is in danger of becoming dominated by political issues and discouraging the exchange of ideas characteristic of a true liberal arts education. (MSE) 3. A simplified model of the source channel of the Leksell GammaKnife (registered) tested with PENELOPE Energy Technology Data Exchange (ETDEWEB) Al-Dweri, Feras M O [Departamento de FIsica Moderna, Universidad de Granada, E-18071 Granada (Spain); Lallena, Antonio M [Departamento de FIsica Moderna, Universidad de Granada, E-18071 Granada (Spain); Vilches, Manuel [Servicio de RadiofIsica, Hospital ClInico ' San Cecilio' , Avda. Dr Oloriz, 16, E-18012 Granada (Spain) 2004-06-21 Monte Carlo simulations using the code PENELOPE have been performed to test a simplified model of the source channel geometry of the Leksell GammaKnife (registered) . The characteristics of the radiation passing through the treatment helmets are analysed in detail. We have found that only primary particles emitted from the source with polar angles smaller than 3 deg. with respect to the beam axis are relevant for the dosimetry of the Gamma Knife. The photon trajectories reaching the output helmet collimators at (x, y, z = 236 mm) show strong correlations between {rho} = (x{sup 2} + y{sup 2}){sup 1/2} and their polar angle {theta}, on one side, and between tan{sup -1}(y/x) and their azimuthal angle {phi}, on the other. This enables us to propose a simplified model which treats the full source channel as a mathematical collimator. This simplified model produces doses in good agreement with those found for the full geometry. In the region of maximal dose, the relative differences between both calculations are within 3%, for the 18 and 14 mm helmets, and 10%, for the 8 and 4 mm ones. Besides, the simplified model permits a strong reduction (larger than a factor 15) in the computational time. 4. Polarization-Modulation Method of Measuring the Bearing of a Moving Object From Orthogonal Elliptically Polarized Signals of a Radio Beacon Science.gov (United States) Gulko, V. L.; Mescheryakov, A. A. 2017-05-01 A polarization-modulation method of estimating the bearing of a moving object using a radio beacon transmitting two mutually orthogonal elliptically polarized radio signals is considered. The signals received onboard the moving object are subject to polarization modulation. The bearing is estimated at the output from a single-channel receiver at the frequency multiple to the polarization modulation frequency. 5. The bile acid-sensitive ion channel (BASIC), the ignored cousin of ASICs and ENaC. Science.gov (United States) Wiemuth, Dominik; Assmann, Marc; Gründer, Stefan 2014-01-01 The DEG/ENaC gene family of ion channels is characterized by a high degree of structural similarity and an equally high degree of diversity concerning the physiological function. In humans and rodents, the DEG/ENaC family comprises 2 main subgroups: the subunits of the epithelial Na(+) channel (ENaC) and the subunits of the acid sensing ion channels (ASICs). The bile acid-sensitive channel (BASIC), previously known as BLINaC or INaC, represents a third subgroup within the DEG/ENaC family. Although BASIC was identified more than a decade ago, very little is known about its physiological function. Recent progress in the characterization of this neglected member of the DEG/ENaC family, which is summarized in this focused review, includes the discovery of surprising species differences, its pharmacological characterization, and the identification of bile acids as putative natural activators. 6. PAPPA: Primordial Anisotropy Polarization Pathfinder Array CERN Document Server Kogut, A; Fixsen, D; Hinshaw, G F; Limon, M; Moseley, S H; Phillips, N; Sharp, E; Wollack, E J; U-Yen, K; Cao, N; Stevenson, T; Hsieh, W; Devlin, M; Dicker, S; Semisch, C; Irwin, K 2006-01-01 The Primordial Anisotropy Polarization Pathfinder Array (PAPPA) is a balloon-based instrument to measure the polarization of the cosmic microwave background and search for the signal from gravity waves excited during an inflationary epoch in the early universe. PAPPA will survey a 20 x 20 deg patch at the North Celestial Pole using 32 pixels in 3 passbands centered at 89, 212, and 302 GHz. Each pixel uses MEMS switches in a superconducting microstrip transmission line to combine the phase modulation techniques used in radio astronomy with the sensitivity of transition-edge superconducting bolometers. Each switched circuit modulates the incident polarization on a single detector, allowing nearly instantaneous characterization of the Stokes I, Q, and U parameters. We describe the instrument design and status. 7. Using Paraffin with -10 deg C to 10 deg C Melting Point for Payload Thermal Energy Storage in SpaceX Dragon Trunk Science.gov (United States) Choi, Michael K. 2013-01-01 A concept of using paraffin wax phase change material (PCM) with a melting point between -10 deg C and 10 deg C for payload thermal energy storage in a Space Exploration Technologies (SpaceX) Dragon trunk is presented. It overcomes the problem of limited heater power available to a payload with significant radiators when the Dragon is berthed to the International Space Station (ISS). It stores adequate thermal energy to keep a payload warm without power for 6 hours during the transfer from the Dragon to an ExPRESS logistics carrier (ELC) on the ISS. 8. Far-infrared and submillimeter survey of the galactic plane from l = 11.5 deg to l = 17.5 deg Science.gov (United States) Campbell, M. F.; Niles, D. W.; Silverberg, R. F.; Hauser, M. G.; Stier, M. T.; Kelsall, T.; Hoffmann, W. F.; Thronson, H. A., Jr. 1984-01-01 Medium resolution (11 min) maps of the galactic plane are presented from l = 11.5 deg to l = 17.5 deg at wavelengths of 93 microns, 154 microns, and 190 microns. The maps are interpreted in terms of the temperature and spatial structure of diffuse far-infrared/submillimeter sources associated with evolved H II regions and a continuous ridge of galactic emission. The emission regions are found to be more extended at the longer wavelengths which implies that there must be a range of dust temperatures in the sources. The properties of the galactic ridge are similar to those of the sources. 9. Polar Diving Science.gov (United States) 2006-01-01 3 July 2006 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows layers exposed by erosion in a trough within the north polar residual cap of Mars, diving beneath a younger covering of polar materials. The layers have, since the Mariner 9 mission in 1972, been interpreted to be composed of a combination of dust and ice in unknown proportions. In this scene, a layer of solid carbon dioxide, which was deposited during the previous autumn and winter, blankets the trough as well as the adjacent terrain. Throughout northern spring, the carbon dioxide will be removed; by summer, the layers will be frost-free. Location near: 81.4oN, 352.2oW Image width: 3 km (1.9 mi) Illumination from: lower left Season: Northern Spring 10. Quantification of metallic iodides in fucus vesiculosus and serratus heated at 80 deg, 550 deg and 1 000 deg; Quantification des iodures metalliques dans des cendres d'algues. Analyse de fucus vesiculosus et serratus chauffees a 80 degres, 550 degre et 1000 degre Energy Technology Data Exchange (ETDEWEB) Aujollet, Y. [Direction Generale de la Surete Nucleaire et de la Radioprotection (DGSNR), 75 - Paris (France) 2004-02-01 Metallic iodides in aqueous phase of Fucus ashes were measured by gamma spectrometry. Before the measurements, different samples of Fucus were heated at 80 deg C (Fucus vesiculosus), 550 deg C (Fucus serratus) and 1 000 deg C (Fucus serratus). The first results gave 63% of iodide salts in Fucus vesiculosus heated at 80 deg C, 27% of iodide salts in Fucus serratus (550 deg C) and no result for ashes of Fucus serratus heated at 1 000 deg C, because there was not enough mass of product for a good analysis by gamma spectrometry. (author) 11. The unc-8 and sup-40 genes regulate ion channel function in Caenorhabditis elegans motorneurons Energy Technology Data Exchange (ETDEWEB) Shreffler, W.; Magardino, T.; Shekdar, K.; Wolinsky, E. [New York Univ. Medical School, NY (United States) 1995-03-01 Two Caenorhabditis elegans genes, unc-8 and sup-40, have been newly identified, by genetic criteria, as regulating ion channel function in motorneurons. Two dominant unc-8 alleles cause motorneuron swelling similar to that of other neuronal types in dominant mutants of the deg-1 gene family, which is homologous to a mammalian gene family encoding amiloride-sensitive sodium channel subunits. As for previously identified deg-1 family members, unc-8 dominant mutations are recessively suppressed by mutations in the mec-6 gene, which probably encodes a second type of channel component. An unusual dominant mutation, sup-41 (lb125), also co-suppresses unc-8 and deg-1, suggesting the existence of yet another common component of ion channels containing unc-8 or deg-1 subunits. Dominant, transacting, intragenic suppressor mutations have been isolated for both unc-8 and deg-1, consistent with the idea that, like their mammalian homologues, the two gene products function as multimers. The sup-40 (lb130) mutation dominantly suppresses unc-8 motorneuron swelling and produces a novel swelling phenotype in hypodermal nuclei. sup-40 may encode an ion channel component or regulator that can correct the osmotic defect caused by abnormal unc-8 channels. 37 refs., 6 figs., 3 tabs. 12. Non-Binary Polar Codes using Reed-Solomon Codes and Algebraic Geometry Codes CERN Document Server Mori, Ryuhei 2010-01-01 Polar codes, introduced by Arikan, achieve symmetric capacity of any discrete memoryless channels under low encoding and decoding complexity. Recently, non-binary polar codes have been investigated. In this paper, we calculate error probability of non-binary polar codes constructed on the basis of Reed-Solomon matrices by numerical simulations. It is confirmed that 4-ary polar codes have significantly better performance than binary polar codes on binary-input AWGN channel. We also discuss an interpretation of polar codes in terms of algebraic geometry codes, and further show that polar codes using Hermitian codes have asymptotically good performance. 13. Bioelectric modulation of macrophage polarization Science.gov (United States) Li, Chunmei; Levin, Michael; Kaplan, David L. 2016-02-01 Macrophages play a critical role in regulating wound healing and tissue regeneration by changing their polarization state in response to local microenvironmental stimuli. The native roles of polarized macrophages encompass biomaterials and tissue remodeling needs, yet harnessing or directing the polarization response has been largely absent as a potential strategy to exploit in regenerative medicine to date. Recent data have revealed that specific alteration of cells’ resting potential (Vmem) is a powerful tool to direct proliferation and differentiation in a number of complex tissues, such as limb regeneration, craniofacial patterning and tumorigenesis. In this study, we explored the bioelectric modulation of macrophage polarization by targeting ATP sensitive potassium channels (KATP). Glibenclamide (KATP blocker) and pinacidil (KATP opener) treatment not only affect macrophage polarization, but also influence the phenotype of prepolarized macrophages. Furthermore, modulation of cell membrane electrical properties can fine-tune macrophage plasticity. Glibenclamide decreased the secretion and gene expression of selected M1 markers, while pinacidil augmented M1 markers. More interestingly, glibencalmide promoted macrophage alternative activation by enhancing certain M2 markers during M2 polarization. These findings suggest that control of bioelectric properties of macrophages could offer a promising approach to regulate macrophage phenotype as a useful tool in regenerative medicine. 14. Coherent optical control of polarization with a critical metasurface CERN Document Server Kang, Ming 2015-01-01 We describe the mechanism by which a metamaterial surface can act as an ideal phase-controlled rotatable linear polarizer. With equal-power linearly polarized beams incident on each side of the surface, varying the relative phase rotates the polarization angles of the output beams, while keeping the polarization exactly linear. The explanation is based on coupled-mode theory and the idea of coherent perfect absorption into auxiliary polarization channels. The polarization-rotating behavior occurs at a critical point of the coupled-mode theory, which can be associated with the exceptional point of a parity-time (PT) symmetric effective Hamiltonian. 15. Simplified 2DEG carrier concentration model for composite barrier AlGaN/GaN HEMT Energy Technology Data Exchange (ETDEWEB) Das, Palash, E-mail: d.palash@gmail.com; Biswas, Dhrubes, E-mail: d.palash@gmail.com [Indian Institute of Technology Kharagpur, Kharagpur - 721302, West Bengal (India) 2014-04-24 The self consistent solution of Schrodinger and Poisson equations is used along with the total charge depletion model and applied with a novel approach of composite AlGaN barrier based HEMT heterostructure. The solution leaded to a completely new analytical model for Fermi energy level vs. 2DEG carrier concentration. This was eventually used to demonstrate a new analytical model for the temperature dependent 2DEG carrier concentration in AlGaN/GaN HEMT. 16. Strumentazione multisensore selettiva per il monitoraggio in continuo degli odori nel settore ambientale OpenAIRE Giuliani, Stefano 2012-01-01 2010 - 2011 L’odore indotto dall’esercizio degli impianti di ingegneria sanitaria ambientale è ritenuto la causa principale di disturbo che la popolazione residente nelle vicinanze avverte. Sebbene alle emissioni odorigene sia solo raramente associato un reale rischio tossicologico-sanitario, sia per la natura raramente pericolosa degli odoranti che per le concentrazioni generalmente molto basse, nell’immaginario collettivo, ai cattivi odori si associano spesso condizioni di “non salubrità... 17. Experimental measurement of the solubility of bismuth phases in water vapor from 220 deg. C to 300 deg. C: Implications for ore formation Energy Technology Data Exchange (ETDEWEB) Kruszewski, Jason M. [Department of Geological Sciences, University of Idaho, Moscow, ID 83844-3022 (United States); Wood, Scott A., E-mail: swood@uidaho.edu [Department of Geological Sciences, University of Idaho, Moscow, ID 83844-3022 (United States) 2009-04-15 Preliminary measurements were carried out of the solubility of the O{sub 2-}buffering assemblage bismuth + bismite (Bi{sub 2}O{sub 3}) in aqueous liquid-vapor and vapor-only systems at temperatures of 220, 250 and 300 deg. C. All experiments were carried out in Ti reaction vessels and were designed such that the Bi solids were contained in a silica tube that prevented contact with liquid water at any time during the experiment. Two blank (no Bi solids present) liquid-vapor experiments at 220 deg. C yielded Bi concentrations ({+-}1{sigma}) in the condensed liquid of 0.22 {+-} 0.02 mg/L, whereas the solubility measurements at this temperature yielded an average value of approximately 6 {+-} 9 mg/L, with replicate experiments ranging from 0.3 to 26 mg/L. Although the 6 mg/L value is associated with a considerable degree of uncertainty, the experiments do indicate transport of Bi through the vapor phase. Measured Bi concentrations in the condensed liquid at 250 deg. C were in the same range as those at 220 deg. C, whereas those at 300 deg. C were significantly lower (i.e., all below the blank value). Vapor-only experiments necessarily contained much smaller initial volumes of water, thereby making the results more susceptible to contamination. Single blank runs at 220 and 300 deg. C yielded Bi concentrations of 82 and 16 mg/L, respectively. Measured concentrations ({+-}1{sigma}) of Bi in the vapor-only solubility experiments at 220 deg. C were 235 {+-} 78 mg/L for an initial water volume of 0.5 mL, and at 300 deg. C were 56 {+-} 30 mg/L and 33 {+-} 21 for initial water volumes of 1 and 2 mL, respectively, suggesting strong preferential partitioning of Bi into the vapor. The results indicate a negative dependence of Bi solubility on temperature, but are inconclusive with respect to the dependence of Bi solubility on water density or fugacity. The experiments reported here suggest that significant Bi transport is possible in the vapor phase. Comparison of the liquid 18. Evaluation of myocardial SPECT imaging reconstructed from 270deg projection data. A study using a cardiac phantom Energy Technology Data Exchange (ETDEWEB) Kashikura, Kenichi [Japan Science and Technology Corp., Akita (Japan). Akita Lab.; Kobayashi, Hideki; Kashikura, Akemi 1997-01-01 SPECT reconstruction is commonly performed using 360deg or 180deg projection data. However, it is also possible to reconstruct SPECT images using other projection data arcs. The purpose of this study was to characterize images obtained by limiting the projection data to 270deg by discarding the projection views with severe attenuation. A series of phantom studies was performed with and without plastic chambers simulating perfusion defects using {sup 201}Tl and {sup 99m}Tc. Images using 270deg, 360deg, and 180deg projection arcs were identically reconstructed from the same data. In the absence of plastic chambers, intraslice uniformity in a given slice was assessed by computing the coefficient of variation (CV) of average counts in 8 ROIs within the slice. Interslice uniformity was assessed by computing the CV of average counts in five short axial slices. With plastic chambers in place, the variability in defect contrasts was assessed by computing the CV of defect contrasts in 4 chambers, located on the anterior, lateral, inferoposterior, and septal walls. The intraslice uniformity of the 270deg images were considerably inferior to those of the 360deg and 180deg images. The interslice uniformity was highest in the 360deg images, and lowest in the 180deg images. The variation in defect contrasts in the 270deg image was higher than those of the other two images. The 270deg images showed a high defect contrast in the septum and high counts in the anterior and anteroseptal wall. Because a large variation in defect contrasts within a segment might result in false positive or negative in diagnosis, 270deg imaging is not recommended over 360deg or 180deg imaging. (author) 19. Interfacial friction factors for air-water co-current stratified flow in inclined channels Energy Technology Data Exchange (ETDEWEB) Choi, Ki Yong; No, Hee Cheon [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of) 1997-12-31 The interfacial shear stress is experimentally investigated for co-current air-water stratified flow in inclined rectangular channels having a length of 1854mm, width of 120 mm and height of 40mm at almost atmospheric pressure. Experiments are carried out in several inclinations from 0 deg up to 10 deg. The local film thickness and the wave height are measured at three locations, i.e., L/H = 8,23, and 40. According to the inclination angle, the experimental data are categorized into two groups; nearly horizontal data group (0 deg {<=} {theta} {<=} 0.7 deg), and inclined channel data group (0.7 deg {<=} {theta} {<=} 10 deg ). Experimental observations for nearly horizontal data group show that the flow is not fully developed due to the water level gradient and the hydraulic jump within the channel. For the inclined channel data group, a dimensionless wave height, {Delta}h/h, is empirically correlated in terms of Re{sub G} and h/H. A modified root-mean-square wave height is proposed to consider the effects of the interfacial and wave propagation velocities. It is found that an equivalent roughness has a linear relationship with the modified root-mean-square wave height and its relationship is independent of the inclination. 10 refs., 6 figs., 1 tab. (Author) 20. Polarization Imaging Apparatus with Auto-Calibration Science.gov (United States) Zou, Yingyin Kevin (Inventor); Zhao, Hongzhi (Inventor); Chen, Qiushui (Inventor) 2013-01-01 A polarization imaging apparatus measures the Stokes image of a sample. The apparatus consists of an optical lens set, a first variable phase retarder (VPR) with its optical axis aligned 22.5 deg, a second variable phase retarder with its optical axis aligned 45 deg, a linear polarizer, a imaging sensor for sensing the intensity images of the sample, a controller and a computer. Two variable phase retarders were controlled independently by a computer through a controller unit which generates a sequential of voltages to control the phase retardations of the first and second variable phase retarders. A auto-calibration procedure was incorporated into the polarization imaging apparatus to correct the misalignment of first and second VPRs, as well as the half-wave voltage of the VPRs. A set of four intensity images, I(sub 0), I(sub 1), I(sub 2) and I(sub 3) of the sample were captured by imaging sensor when the phase retardations of VPRs were set at (0,0), (pi,0), (pi,pi) and (pi/2,pi), respectively. Then four Stokes components of a Stokes image, S(sub 0), S(sub 1), S(sub 2) and S(sub 3) were calculated using the four intensity images. 1. Analysis and Realization on MIMO Channel Model Directory of Open Access Journals (Sweden) Liu Hui 2014-04-01 Full Text Available In order to build the MIMO (Multiple Input Multiple Output channel model based on IEEE 802.16, the way and analysis on how to build good MIMO channel model are described in this study. By exploiting the spatial freedom of wireless channels, MIMO systems have the potential to achieve high bandwidth efficiency, promoting MIMO to be a key technique in the next generation communication systems. As a basic researching field of MIMO technologies, MIMO channel modeling significantly serve to the performance evaluation of space-time encoding algorithms as well as system level calibration and simulation. Having the superiorities of low inner-antenna correlation and small array size, multi-polarization tends to be a promising technique in future MIMO systems. However, polarization characteristics have not yet been modeled well in current MIMO channel models, so establishing meaningful multi-polarized MIMO channel models has become a hot spot in recent channel modeling investigation. In this study, I have mainly made further research on the related theories in the channel models and channel estimation and implementation algorithms on the others’ research work. 2. Magnetic field morphology in nearby molecular clouds as revealed by starlight and submillimetre polarization CERN Document Server Soler, J D; Boulanger, F; Bracco, A; Falgarone, E; Franco, G A P; Guillet, V; Hennebelle, P; Levrier, F; Martin, P G; Miville-Deschênes, M -A 2016-01-01 Within four nearby (d < 160 pc) molecular clouds, we statistically evaluate the structure of the interstellar magnetic field, projected on the plane of the sky and integrated along the line of sight, as inferred from the polarized thermal emission of Galactic dust observed by Planck at 353 GHz and from the optical and NIR polarization of background starlight. We compare the dispersion of the field orientation directly in vicinities with an area equivalent to that subtended by the Planck effective beam at 353 GHz (10') and using the second-order structure functions of the field orientation angles. We find that the average dispersion of the starlight-inferred field orientations within 10'-diameter vicinities is less than 20 deg, and that at these scales the mean field orientation is on average within 5 deg of that inferred from the submillimetre polarization observations in the considered regions. We also find that the dispersion of starlight polarization orientations and the polarization fractions within th... 3. Multiple, Distant (40 deg) in situ Observations of a Magnetic Cloud and a Corotating Interaction Region Complex Science.gov (United States) Farrugia, C. J.; Berdichevsky, D. B.; Moestl, C.; Galvin, A. B.; Leitner, M.; Popecki, M.; Simunac, K. D.; Opitz, A.; Lavraud, B.; Ogilvie, K.; Veronig, A.; Temmer, M.; Luhmann, J. G.; Sauvaud, J. 2010-12-01 We report a comprehensive analysis of in situ observations made by Wind and the STEREO probes (STA, STB) of a complex interaction between a magnetic cloud (MC) and a corotating interaction region (CIR) occurring near the heliospheric current sheet (HCS) on November 19-21, 2007. The probes were separated by 0.7 AU (~40 deg) with a spread in heliographic latitudes (4.8, 2.2, and -0.4 deg for STB, Wind and STA, respectively). We employ data from the MFI, SWE and 3DP instruments on Wind, and the PLASTIC and IMPACT suites on STEREO. STB, located east of Earth, observed a forward shock followed by signatures of a MC. The MC took the role of the HCS in that the polarity of the interplanetary magnetic field (IMF) on exit was the reverse of that on entry. A passage through a plasma sheet is observed. Along the Sun-Earth line Wind observed a stream interface (SI) between a forward and a reverse shock. A MC, compressed by the CIR, was entrained in this. STA, located 20 deg to the west of Earth, saw a MC which was not preceded by a shock. A SI trailed the transient. The shocks are examined using various methods and from this it is concluded that the forward shock at Wind - but not at STB - was driven by the MC. Examining the MC by Grad-Shafranov reconstruction, we find evidence of a double-flux rope structure at Wind and STA and possibly also at STB. The orientations are at variance with the notion of a large-scale flux tube being observed at the three spacecraft. We find consistency of this with the directional properties of the solar wind "strahl" electrons. We examine aspects of the geomagnetic response and find a double-dip storm corresponding to the two interplanetary triggers. The minimum Dst phase was prolonged and the geoffects were intensified due to the interaction. We conclude that while the formation of compound streams is a common feature of interplanetary space, understanding their components when CIRs are involved is a complicated matter needing numerical 4. Planck intermediate results. XIX. An overview of the polarized thermal emission from Galactic dust DEFF Research Database (Denmark) Cardoso, J. F.; Delabrouille, J.; Ganga, K.; 2015-01-01 This paper presents an overview of the polarized sky as seen by Planck HFI at 353 GHz, which is the most sensitive Planck channel for dust polarization. We construct and analyse maps of dust polarization fraction and polarization angle at 1° resolution, taking into account noise bias and possible... 5. Ionic Channels in Thunderclouds Science.gov (United States) Losseva, T. V.; Fomenko, A. S.; Nemtchinov, I. V. 2007-12-01 We proceed to study the formation and propagation of ionic channels in thunderclouds in the framework of the model of the corona discharge wave propagation (Fomenko A.S., Losseva T.V., Nemtchinov I.V. The corona discharge waves in thunderclouds and formation of ionic channels // 2004 Fall Meeting. EOS Trans. AGU. 2004. V. 85. ¹ 47. Suppl. Abstract AE23A-0835.). In this model we proposed a hypothesis that the structure of a thundercloud becomes nonuniform due to corona discharge on the drops and ice particles and formation of ionic channels with higher conductivity than the surrounding air. When the onset strength of corona discharge becomes smaller than the electric field strength the corona discharge increases concentrations of ions in a small part of the cloud (a hot spot). An additional charge at opposite ends of the hot spot forms due to polarization process. The increased electric field initiates corona discharge in other parts of the cloud on ice particles and water drops with smaller sizes. The corona discharge front moves as a wave with the velocity of the order of ion drift and formes a highly conductive channel. We model this non-stationary problem with Poisson equation which is solved simultaneously with a simplified set of kinetic equations for ions, small charged particles and electrons (at high electric fields), including ionization due to electronic impact, attachment and formation of positive ions. By applying 3D numerical simulations we obtain the parameters of formed ionic channels with respect to onset electric fields both from large particles (in hot spot) and from small particles (surrounding hot spot), microscopic currents from particles with different sizes and the external electric field in the cloud. The interaction of ionic channels is also investigated. This work was supported by Russian Foundation of Basic Research (Project No 07-05-00998-à). 6. Summer Mesosphere Temperature Distribution from Wide-Angle Polarization Measurements of the Twilight Sky CERN Document Server Ugolnikov, Oleg S 2012-01-01 The paper contains the results of wide-angle polarization camera (WAPC) measurements of the twilight sky background conducted in summer 2011 and 2012 at 55.2 degs.N, 37.5 degs.E, southwards from Moscow. The method of single scattering separation based on polarization data is suggested. The obtained components of scattering matrixes show the domination of Rayleigh scattering in the mesosphere for all observation days. It made possible to retrieve the altitude distribution of temperature in the mesosphere. The results are compared with the temperature data by TIMED/SABER and EOS Aura/MLS instruments for nearby dates and locations. 7. An Electromagnet for Precession of the Polarization of Fast-Neutrons Energy Technology Data Exchange (ETDEWEB) Aspesund, O.; Bjorkman, J.; Trumpy, G. 1965-05-15 The advantages of using a transverse magnetic field for precessing the polarization of fast-neutrons are discussed. Design details of a powerful electromagnet supplying a transverse field of approximately 20 kGauss are given. Precession characteristics for polarized fast neutrons obtained at 50 deg (lab. syst.) from the Li{sup 7} (p, n) Be{sup 7} reaction are reported, using elastic scattering at 42 deg (lab. syst.) off natural carbon as an analyser. Correlation of the precession data with theoretical predictions presented elsewhere is made, and good agreement is found. 8. The Primordial Inflation Polarization Explorer (PIPER) Science.gov (United States) Lazear, Justin Scott; Ade, Peter A.; Benford, Dominic J.; Bennett, Charles L.; Chuss, David T.; Dotson, Jessie L.; Eimer, Joseph R.; Fixsen, Dale J.; Halpern, Mark; Hinderks, James; Hinshaw, Gary F.; Irwin, Kent; Jhabvala, Christine; Johnson, Bradley; Kogut, Alan; Lowe, Luke; McMahon, Jeff J.; Miller, Timothy M.; Mirel, Paul; Moseley, S. Harvey; Rodriguez, Samelys; Staguhn, Johannes G.; Switzer, Eric R.; Tucker, Carole E.; Weston, Amy; Wollack, Edward 2014-01-01 The Primordial Inflation Polarization ExploreR (Piper) is a balloon-borne cosmic microwave background (CMB) polarimeter designed to search for evidence of inflation by measuring the large-angular scale CMB polarization signal. Bicep2 recently reported a detection of B-mode power corresponding to the tensor-to-scalar ratio r = 0.2 on approximately 2 degree scales. If the Bicep2 signal is caused by inflationary gravitational waves (IGWs), then there should be a corresponding increase in B-mode power on angular scales larger than 18 degrees. Piper is currently the only suborbital instrument capable of fully testing and extending the Bicep2 results by measuring the B-mode power spectrum on angular scales theta ? = approximately 0.6 deg to 90 deg, covering both the reionization bump and recombination peak, with sensitivity to measure the tensor-to-scalar ratio down to r = 0.007, and four frequency bands to distinguish foregrounds. Piper will accomplish this by mapping 85% of the sky in four frequency bands (200, 270, 350, 600 GHz) over a series of 8 conventional balloon flights from the northern and southern hemispheres. The instrument has background-limited sensitivity provided by fully cryogenic (1.5 K) optics focusing the sky signal onto four 32×40-pixel arrays of time-domain multiplexed Transition-Edge Sensor (TES) bolometers held at 140 milli-Kelvin. Polarization sensitivity and systematic control are provided by front-end Variabledelay Polarization Modulators (VPMs), which rapidly modulate only the polarized sky signal at 3 Hz and allow Piper to instantaneously measure the full Stokes vector (I,Q,U,0V) for each pointing. We describe the Piper instrument and progress towards its first flight. 9. Deletion of degQ gene enhances outer membrane vesicle production of Shewanella oneidensis cells. Science.gov (United States) Ojima, Yoshihiro; Mohanadas, Thivagaran; Kitamura, Kosei; Nunogami, Shota; Yajima, Reiki; Taya, Masahito 2017-04-01 Shewanella oneidensis is a Gram-negative facultative anaerobe that can use a wide variety of terminal electron acceptors for anaerobic respiration. In this study, S. oneidensis degQ gene, encoding a putative periplasmic serine protease, was cloned and expressed. The activity of purified DegQ was inhibited by diisopropyl fluorophosphate, a typical serine protease-specific inhibitor, indicating that DegQ is a serine protease. In-frame deletion and subsequent complementation of the degQ were carried out to examine the effect of envelope stress on the production of outer membrane vesicles (OMVs). Analysis of periplasmic proteins from the resulting S. oneidensis strain showed that deletion of degQ induced protein accumulation and resulted in a significant decrease in protease activity within the periplasmic space. OMVs from the wild-type and mutant strains were purified and observed by transmission electron microscopy. Sodium dodecyl sulfate-polyacrylamide gel electrophoresis analysis of the OMVs showed a prominent band at ~37 kDa. Nanoliquid chromatography-tandem mass spectrometry analysis identified three outer membrane porins (SO3896, SO1821, and SO3545) as dominant components of the band, suggesting that these proteins could be used as indices for comparing OMV production by S. oneidensis strains. Quantitative evaluation showed that degQ-deficient cells had a fivefold increase in OMV production compared with wild-type cells. Thus, the increased OMV production following the deletion of DegQ in S. oneidensis may be responsible for the increase in envelope stress. 10. Deep 1.4-GHz observations of diffuse polarized emission CERN Document Server Carretti, E; Reich, W; Reich, P; Fürst, E; Bernardi, G; Cortiglioni, S; Sbarra, C 2006-01-01 Polarized diffuse emission observations at 1.4-GHz in a high Galactic latitude area of the northern Celestial hemisphere are presented. The 3.2 X 3.2 deg^2 field, centred at RA = 10h 58m, Dec = +42deg 18' (B1950), has Galactic coordinates l~172deg, b~+63deg and is located in the region selected as northern target of the BaR-SPOrt experiment. Observations have been performed with the Effelsberg 100-m telescope. We find that the angular power spectra of the E- and B-modes have slopes of beta_E = -1.79 +/- 0.13 and beta_B = -1.74 +/- 0.12, respectively. Because of the very high Galactic latitude and the smooth emission, a weak Faraday rotation action is expected, which allows both a fair extrapolation to Cosmic Microwave Background Polarization (CMBP) frequencies and an estimate of the contamination by Galactic synchrotron emission. We extrapolate the E-mode spectrum up to 32-GHz and confirm the possibility to safely detect the CMBP E-mode signal in the Ka band found in another low emission region (Carretti et a... 11. Polar Shapelets CERN Document Server Massey, R; Massey, Richard; Refregier, Alexandre 2004-01-01 The shapelets method for astronomical image analysis is based around the decomposition of localised objects into a series of orthogonal components with particularly convenient mathematical properties. We extend the "Cartesian shapelet" formalism from earlier work, and construct "polar shapelet" basis functions that separate an image into components with explicit rotational symmetries. This provides a more compact representation of typical galaxy shapes, and its physical interpretation is frequently more intuitive. Linear coordinate transformations can be simply expressed using this basis set, and shape measures (including object photometry, astrometry and galaxy morphology estimators) take a naturally elegant form. Particular attention is paid to the analysis of astronomical survey images, and we test shapelet techniques with real data from the Hubble Space Telescope. We present a practical method to automatically optimise the quality of an arbitrary shapelet decomposition in the presence of noise, pixellisat... 12. Mechanosensitive Channels Science.gov (United States) Martinac, Boris Living cells are exposed to a variety of mechanical stimuli acting throughout the biosphere. The range of the stimuli extends from thermal molecular agitation to potentially destructive cell swelling caused by osmotic pressure gradients. Cellular membranes present a major target for these stimuli. To detect mechanical forces acting upon them cell membranes are equipped with mechanosensitive (MS) ion channels. Functioning as molecular mechanoelectrical transducers of mechanical forces into electrical and/or chemical intracellular signals these channels play a critical role in the physiology of mechanotransduction. Studies of prokaryotic MS channels and recent work on MS channels of eukaryotes have significantly increased our understanding of their gating mechanism, physiological functions, and evolutionary origins as well as their role in the pathology of disease. 13. A recent change in the optical and {\\gamma}-ray polarization of the Crab nebula and pulsar CERN Document Server Moran, Paul; Gouiffes, Christian; 3,; Laurent, Philipe; Hallinan, Gregg; Redfern, Michael; Shearer, Andrew 2015-01-01 We report on observations of the polarization of optical and {\\gamma}-ray photons from the Crab nebula and pulsar system using the Galway Astronomical Stokes Polarimeter (GASP), the Hubble Space Telescope/Advanced Camera for Surveys (HST/ACS) and the International Gamma-Ray Astrophysics Laboratory satellite (Integral). These, when combined with other optical polarization observations, suggest that the polarized optical emission and {\\gamma}-ray polarization changes in a similar manner. A change in the optical polarization angle has been observed by this work, from 109.5 \\pm 0.7\\deg in 2005 to 85.3 \\pm 1.4 \\deg in 2012. On the other hand, the {\\gamma}-ray polarization angle changed from 115 \\pm 11 \\deg in 2003-2007 to 80 \\pm 12 \\deg in 2012-2014. Strong flaring activities have been detected in the Crab nebula over the past few years by the high energy {\\gamma}-ray missions Agile and Fermi, and magnetic reconnection processes have been suggested to explain these observations. The change in the polarized optical... 14. Measurements of the Intensity and Polarization of the Anomalous Microwave Emission in the Perseus molecular complex with QUIJOTE CERN Document Server Génova-Santos, R; Rebolo, R; Peláez-Santos, A; López-Caraballo, C H; Harper, S; Watson, R A; Ashdown, M; Barreiro, R B; Casaponsa, B; Dickinson, C; Diego, J M; Fernández-Cobos, R; Grainge, K J B; Herranz, D; Hoyland, R; Lasenby, A; López-Caniego, M; Martínez-González, E; McCulloch, M; Melhuish, S; Piccirillo, L; Perrott, Y C; Poidevin, F; Razavi-Ghods, N; Scott, P F; Titterington, D; Tramonte, D; Vielva, P; Vignaga, R 2015-01-01 Anomalous microwave emission (AME) has been observed in numerous sky regions, in the frequency range ~10-60 GHz. One of the most scrutinized regions is G159.6-18.5, located within the Perseus molecular complex. In this paper we present further observations of this region (194 hours in total over ~250 deg^2), both in intensity and in polarization. They span four frequency channels between 10 and 20 GHz, and were gathered with QUIJOTE, a new CMB experiment with the goal of measuring the polarization of the CMB and Galactic foregrounds. When combined with other publicly-available intensity data, we achieve the most precise spectrum of the AME measured to date, with 13 independent data points being dominated by this emission. The four QUIJOTE data points provide the first independent confirmation of the downturn of the AME spectrum at low frequencies, initially unveiled by the COSMOSOMAS experiment in this region. We accomplish an accurate fit of these data using models based on electric dipole emission from spin... 15. Dependence of polar hole density on magnetic and solar conditions Science.gov (United States) Hoegy, W. R.; Grebowsky, J. M. 1991-01-01 Electron densities from the Langmuir probes on the Atmospheric Explorer C and Dynamics Explorer 2 are used for analyzing the behavior of the high-altitude night-side F region polar hole as a function of solar and magnetic activity and of universal time (UT). The polar region of invariant latitude from 70 deg to 80 deg and MLT from 22 to 03 hours is examined. The strongest dependencies are observed in F10.7 and UT; a strong hemispherical difference due to the offset of the magnetic poles from the earth's rotation axis is observed in the UT dependence of the ionization hole. A seasonal variation in the dependence of ion density on solar flux is indicated, and an overall asymmetry in the density level between hemispheres is revealed, with the winter-hole density about a factor of 10 greater in the north than in the south. 16. Study of phosphorus implanted and annealed silicon by electrical measurements and ion channeling technique CERN Document Server Hadjersi, T; Zilabdi, M; Benazzouz, C 2002-01-01 We investigated the effect of annealing temperature on the electrical activation of phosphorus implanted into silicon. The measurements performed using spreading resistance, four-point probe and ion channeling techniques have allowed us to establish the existence of two domains of variation of the electrical activation (350-700 deg. C) and (800-1100 deg. C). The presence of reverse annealing and the annihilation of defects have been put in a prominent position in the first temperature range. It has been shown that in order to achieve a complete electrical activation, the annealing temperature must belong to the second domain (800-1100 deg. C). 17. Phosphorylated DegU Manipulates Cell Fate Differentiation in the Bacillus subtilis Biofilm Science.gov (United States) Marlow, Victoria L.; Porter, Michael; Hobley, Laura; Kiley, Taryn B.; Swedlow, Jason R.; Davidson, Fordyce A. 2014-01-01 Cell differentiation is ubiquitous and facilitates division of labor and development. Bacteria are capable of multicellular behaviors that benefit the bacterial community as a whole. A striking example of bacterial differentiation occurs throughout the formation of a biofilm. During Bacillus subtilis biofilm formation, a subpopulation of cells differentiates into a specialized population that synthesizes the exopolysaccharide and the TasA amyloid components of the extracellular matrix. The differentiation process is indirectly controlled by the transcription factor Spo0A that facilitates transcription of the eps and tapA (tasA) operons. DegU is a transcription factor involved in regulating biofilm formation. Here, using a combination of genetics and live single-cell cytological techniques, we define the mechanism of biofilm inhibition at high levels of phosphorylated DegU (DegU∼P) by showing that transcription from the eps and tapA promoter regions is inhibited. Data demonstrating that this is not a direct regulatory event are presented. We demonstrate that DegU∼P controls the frequency with which cells activate transcription from the operons needed for matrix biosynthesis in favor of an off state. Subsequent experimental analysis led us to conclude that DegU∼P functions to increase the level of Spo0A∼P, driving cell fate differentiation toward the terminal developmental process of sporulation. PMID:24123822 18. Analysis of the thin layer of Galactic warm ionized gas in the range 20 < l < 30 deg, -1.5 < b < +1.5 deg CERN Document Server Paladini, R; Davies, R D; Giard, M 2005-01-01 We present an analysis of the thin layer of Galactic warm ionized gas at an angular resolution ~ 10'. This is carried out using radio continuum data at 1.4 GHz, 2.7 GHz and 5 GHz in the coordinate region 20 < l < 30 deg, -1.5 < b < +1.5 deg. For this purpose, we evaluate the zero level of the 2.7 and 5 GHz surveys using auxiliary data at 2.3 GHz and 408 MHz. The derived zero level corrections are T_{zero}(2.7 GHz)=0.15 +/- 0.06 K and T_{zero}(5 GHz)=0.1 +/- 0.05 K. We separate the thermal (free-free) and non-thermal (synchrotron) component by means of a spectral analysis performed adopting an antenna temperature spectral index -2.1 for the free-free emission, a realistic spatial distribution of indices for the synchrotron radiation and by fitting, pixel-by-pixel, the Galactic spectral index. We find that at 5 GHz, for |b| = 0 deg, the fraction of thermal emission reaches a maximum value of 82%, while at 1.4 GHz, the corresponding value is 68%. In addition, for the thermal emission, the analysis in... 19. SAS-2 observations of the diffuse gamma radiation in the galactic latitude interval 10 deg absolute b or equal to 90 deg Science.gov (United States) Fichtel, C. E.; Hartman, R. C.; Kniffen, D. A.; Thompson, D. J.; Oegelman, H. B.; Oezel, M. E.; Tuemer, T. 1977-01-01 An analysis of all of the second small astronomy satellite gamma-ray data for galactic latitudes with the absolute value of b 10 deg has shown that the intensity varies with galactic latitude, being larger near 10 deg than 90 deg. For energies above 100 MeV the gamma-ray data are consistent with a latitude distribution of the form I(b) = C sub 1 + C sub 2/sin b, with the second term being dominant. This result suggests that the radiation above 100 MeV is coming largely from local regions of the galactic disk. Between 35 and 100 MeV, a similar equation is also a good representation of the data, but here the two terms are comparable. These results indicate that the diffuse radiation above 35 MeV consists of two parts, one with a relatively hard galactic component and the other an isotropic, steep spectral component which extrapolates back well to the low energy diffuse radiation. The steepness of the diffuse isotropic component places significant constraints on possible theoretical models of this radiation. 20. Polarized Curvature Radiation in Pulsar Magnetosphere CERN Document Server Wang, P F; Han, J L 2014-01-01 The propagation of polarized emission in pulsar magnetosphere is investigated in this paper. The polarized waves are generated through curvature radiation from the relativistic particles streaming along curved magnetic field lines and co-rotating with the pulsar magnetosphere. Within the 1/{\\deg} emission cone, the waves can be divided into two natural wave mode components, the ordinary (O) mode and the extraord nary (X) mode, with comparable intensities. Both components propagate separately in magnetosphere, and are aligned within the cone by adiabatic walking. The refraction of O-mode makes the two components separated and incoherent. The detectable emission at a given height and a given rotation phase consists of incoherent X-mode and O-mode components coming from discrete emission regions. For four particle-density models in the form of uniformity, cone, core and patches, we calculate the intensities for each mode numerically within the entire pulsar beam. If the co-rotation of relativistic particles with... 1. High electron mobility recovery in AlGaN/GaN 2DEG channels regrown on etched surfaces Science.gov (United States) Chan, Silvia H.; Keller, Stacia; Tahhan, Maher; Li, Haoran; Romanczyk, Brian; DenBaars, Steven P.; Mishra, Umesh K. 2016-06-01 This paper reports high two-dimensional electron gas mobility attained from the regrowth of the AlGaN gating layer on ex situ GaN surfaces. To repair etch-damaged GaN surfaces, various pretreatments were conducted via metalorganic chemical vapor deposition, followed by a regrown AlGaN/GaN mobility test structure to evaluate the extent of recovery. The developed treatment process that was shown to significantly improve the electron mobility consisted of a N2 + NH3 pre-anneal plus an insertion of a 4 nm or thicker GaN interlayer prior to deposition of the AlGaN gating layer. Using the optimized process, a high electron mobility transistor (HEMT) device was fabricated which exhibited a high mobility of 1450 cm2 V-1 s-1 (R sh = 574 ohm/sq) and low dispersion characteristics. The additional inclusion of an in situ Al2O3 dielectric into the regrowth process for MOS-HEMTs still preserved the transport properties near etch-impacted areas. 2. Ten deg off-axis tensile test for intralaminar shear characterization of fiber composites Science.gov (United States) Chamis, C. C.; Sinclair, J. H. 1976-01-01 A combined theoretical and experimental investigation was conducted to assess the suitability of the 10 deg off-axis tensile test specimen for the intralaminar shear characterization of unidirectional composites. Composite mechanics, a combined-stress failure criterion, and a finite element analysis were used to determine theoretically the stress-strain variation across the specimen width and the relative stress and strain magnitudes at the 10 deg plane. Strain gages were used to measure the strain variation across the specimen width at specimen midlength and near the end tabs. Specimens from Mod-I/epoxy, T-300/epoxy, and S-glass/epoxy were used in the experimental program. It was found that the 10 deg off-axis tensile test specimen is suitable for intralaminar shear characterization and it is recommended that it should be considered as a possible standard test specimen for such a characterization. 3. Giovanni Degli Alessandri: i primi anni del direttorato agli Uffizi fra nuovi e vecchi ruoli Directory of Open Access Journals (Sweden) Chiara Pasquinelli 2011-11-01 Full Text Available La figura di Giovanni Degli Alessandri (1765-1830, presidente dell’Accademia di Belle Arti di Firenze e direttore degli Uffizi tra gli anni napoleonici e la Restaurazione di Ferdinando III d’Asburgo-Lorena, è quella di un personaggio chiave nella politica artistica fiorentina, e toscana più in generale. Nel saggio si esaminano i primi anni del suo direttorato alla Galleria, i rapporti con Antonio Canova, il suo ruolo all’interno dell’entourage di Elisa Baciocchi Bonaparte, oltre a considerare alcuni spunti legati al rinnovamento degli Uffizi, nonché la delicata vicenda del passaggio in città di Dominique-Vivant Denon, direttore del Louvre. L’obbiettivo è quello di introdurre elementi di approfondimento relativamente a una figura molto nota ma poco studiata. 4. A high sensitivity HI survey of the sky at delta < -25 deg Final data release CERN Document Server Bajaja, E; Larrarte, J J; Morras, R; Poppel, W G L; Kalberla, P M W 2005-01-01 We present the final data release of the high sensitivity lambda 21-cm neutral hydrogen survey of the sky south of delta < -25 degr. A total of 50980 positions lying on a galactic coordinate grid with points spaced by (Delta l, Delta b) = ((0.5 deg)/cos b, 0.5 deg) were observed with the 30-m dish of the Instituto Argentino de Radioastronomia (IAR). The angular resolution of the survey is HPBW = 0.5 deg and the velocity coverage spans the interval -450 km/s to +400 km/s (LSR). The velocity resolution is 1.27 km/s and the final rms noise of the entire database is 0.07 K. The data are corrected for stray radiation and converted to brightness temperatures. 5. The Parkes Galactic Meridian Survey (PGMS): observations and CMB polarization foreground analysis CERN Document Server Carretti, E; McConnell, D; Bernardi, G; McClure-Griffiths, N M; Cortiglioni, S; Poppi, S 2009-01-01 [abridged] We present observations, maps, polarised emission properties study, and CMB foreground analysis of the Parkes Galactic Meridian Survey (PGMS), a project to investigate the Galactic latitude behaviour of the polarized synchrotron emission at 2.3-GHz with the Parkes Radio Telescope. The survey consists of a 5-deg wide strip along the Galactic meridian l=254-deg. We identify three zones distinguished by polarized emission properties: the disc, the halo, and a transition region connecting them. The halo section lies at latitudes |b|>40-deg and is characterised by weak and smooth polarized emission with steep angular power spectra of median slope\\beta_{\\rm med} \\sim -2.6$. The disc region covers the latitudes |b|<20-deg and shows a brighter, more complex emission with inverted spectra of mean slope$\\bar{\\beta} = -1.8$. The transition region has steep spectra as in the halo, but the emission power increases toward the Galactic plane from halo to disc levels. The change at b ~ -20-deg is sudden, ind... 6. Local structures of polar wurtzites Zn1-xMgxO studied by raman and 67Zn/25Mg NMR spectroscopies and by total neutron scattering Energy Technology Data Exchange (ETDEWEB) Proffen, Thomas E [Los Alamos National Laboratory; Kim, Yiung- Il [UCSB; Cadars, Sylvian [UCSB; Shayib, Ramzy [UCSB; Feigerle, Charles S [UNIV OF TENNESSEE; Chmelka, Bradley F [UCSB; Seshadri, Ram [UCSB 2008-01-01 Research in the area of polar semiconductor heterostructures has been growing rapidly, driven in large part by interest in two-dimensional electron gas (2DEG) systems. 2DEGs are known to form at heterojunction interfaces that bear polarization gradients. They can display extremely high electron mobilities, especially at low temperatures, owing to spatial confinement of carrier motions. Recent reports of 2DEG behaviors in Ga{sub 1-x}Al{sub x}N/GaN and Zn{sub 1-x}Mg{sub x}O/ZnO heterostructures have great significance for the development of quantum Hall devices and novel high-electron-mobility transistors (HEMTs). 2DEG structures are usually designed by interfacing a polar semiconductor with its less or more polar alloys in an epitaxial manner. Since the quality of the 2DEG depends critically on interface perfection, as well as the polarization gradient at the heterojunction, understanding compositional and structural details of the parent and alloy semiconductors is an important component in 2DEG design and fabrication. Zn{sub 1-x}Mg{sub x}O/ZnO is one of the most promising heterostructure types for studies of 2DEGs, due to the large polarization of ZnO, the relatively small lattice mismatch, and the large conduction band offsets in the Zn{sub 1-x}Mg{sub x}O/ZnO heterointerface. Although 2DEG formation in Zn{sub 1-x}Mg{sub x}O/ZnO heterostructures have been researched for some time, a clear understanding of the alloy structure of Zn{sub 1-x}Mg{sub x}O is currently lacking. Here, we conduct a detailed and more precise study of the local structure of Zn{sub 1-x}Mg{sub x}O alloys using Raman and solid-state nuclear magnetic resonance (NMR), in conjunction with neutron diffraction techniques. 7. Reclutamento e formazione dei poliziotti: il caso degli ufficiali della gendarmeria francese Directory of Open Access Journals (Sweden) François Dieu 2007-04-01 Full Text Available Partendo dal caso degli ufficiali della gendarmeria francese, questo articolo illustra il modo in cui il reclutamento e la formazione possono contribuire, informalmente, alla ripartizione del potere nelle organizzazioni di polizia. Tramite la diversità delle vie di reclutamento si costituisce, di fatto, un vero e proprio sistema di "caste", con una stratificazione degli ufficiali in tre livelli gerarchici, che produce, al di là dei principi meritocratici, delle ineguaglianze manifeste nella ripartizione del potere nell'organizzazione della gendarmeria. 8. The Primordial Inflation Polarization Explorer (PIPER) CERN Document Server Lazear, Justin; Benford, Dominic; Bennett, Charles L; Chuss, David T; Dotson, Jessie L; Eimer, Joseph R; Fixsen, Dale J; Halpern, Mark; Hilton, Gene; Hinderks, James; Hinshaw, Gary F; Irwin, Kent; Jhabvala, Christine; Johnson, Bradley; Kogut, Alan; Lowe, Luke; McMahon, Jeff J; Miller, Timothy M; Mirel, Paul; Moseley, S Harvey; Rodriguez, Samelys; Sharp, Elmer; Staguhn, Johannes G; Switzer, Eric R; Tucker, Carole E; Weston, Amy; Wollack, Edward J 2014-01-01 The Primordial Inflation Polarization Explorer (PIPER) is a balloon-borne cosmic microwave background (CMB) polarimeter designed to search for evidence of inflation by measuring the large-angular scale CMB polarization signal. BICEP2 recently reported a detection of B-mode power corresponding to the tensor-to-scalar ratio r = 0.2 on ~2 degree scales. If the BICEP2 signal is caused by inflationary gravitational waves (IGWs), then there should be a corresponding increase in B-mode power on angular scales larger than 18 degrees. PIPER is currently the only suborbital instrument capable of fully testing and extending the BICEP2 results by measuring the B-mode power spectrum on angular scales$\\theta$= ~0.6 deg to 90 deg, covering both the reionization bump and recombination peak, with sensitivity to measure the tensor-to-scalar ratio down to r = 0.007, and four frequency bands to distinguish foregrounds. PIPER will accomplish this by mapping 85% of the sky in four frequency bands (200, 270, 350, 600 GHz) over a ... 9. Deterministic error correction for nonlocal spatial-polarization hyperentanglement. Science.gov (United States) Li, Tao; Wang, Guan-Yu; Deng, Fu-Guo; Long, Gui-Lu 2016-02-10 Hyperentanglement is an effective quantum source for quantum communication network due to its high capacity, low loss rate, and its unusual character in teleportation of quantum particle fully. Here we present a deterministic error-correction scheme for nonlocal spatial-polarization hyperentangled photon pairs over collective-noise channels. In our scheme, the spatial-polarization hyperentanglement is first encoded into a spatial-defined time-bin entanglement with identical polarization before it is transmitted over collective-noise channels, which leads to the error rejection of the spatial entanglement during the transmission. The polarization noise affecting the polarization entanglement can be corrected with a proper one-step decoding procedure. The two parties in quantum communication can, in principle, obtain a nonlocal maximally entangled spatial-polarization hyperentanglement in a deterministic way, which makes our protocol more convenient than others in long-distance quantum communication. 10. Reconfigurable thz polarizer DEFF Research Database (Denmark) 2016-01-01 The present invention provides a polarizer. The polarizer comprises a first membrane having a first polarization region comprising a first plurality of membrane perforations; a second membrane having a second polarization region comprising a second plurality of membrane perforations; and a support...... with one or more membrane perforations in the second plurality of perforations in a direction normal to the first polarization region or normal to the second polarization region, resulting in corresponding one or more openings in said direction.... 11. Positron Channeling CERN Document Server Badikyan, Karen 2016-01-01 The possibility of channeling the low-energy relativistic positrons around separate crystallographic axes with coaxial symmetry of negative ions in some types of crystals is shown. The process of annihilation of positrons with electrons of medium was studied in detail. 12. Brands & Channels Institute of Scientific and Technical Information of China (English) Alice Yang 2009-01-01 @@ "Brands" and "Channels" are the two most important things in Ku-Hai Chen's eyes when doing business with Main-land China. Ku-Hai Chen, Executive Director of the International Trade Institute of Taiwan External Trade Development Council (TAITRA), flies frequently between Chinese Taipei and Mainland China, and was in Beijing earlier this month for his seminar. 13. SPOrt an Experiment Aimed at Measuring the Large Scale Cosmic Microwave Background Polarization CERN Document Server Carretti, E; Bernardi, G; Cecchini, S; Macculi, C; Sbarra, C; Monari, J; Orfei, A; Poloni, M; Poppi, S; Bölla, G; Bonometto, S A; Gervasi, M; Sironi, G; Zannoni, M; Tucci, M; Baralis, M; Peverini, O A; Tascone, R; Virone, G; Fabbri, R; Nicastro, L; Ng, K W; Razin, V A; Vinyajkin, E N; Sazhin, M V; Strukov, I A 2002-01-01 SPOrt (Sky Polarization Observatory) is a space experiment to be flown on the International Space Station during Early Utilization Phase aimed at measuring the microwave polarized emission with FWHM = 7deg, in the frequency range 22-90 GHz. The Galactic polarized emission can be observed at the lower frequencies and the polarization of Cosmic Microwave Background (CMB) at 90 GHz, where contaminants are expected to be less important. The extremely low level of the CMB Polarization signal (< 1 uK) calls for intrinsically stable radiometers. The SPOrt instrument is expressly devoted to CMB polarization measurements and the whole design has been optimized for minimizing instrumental polarization effects. In this contribution we present the receiver architecture based on correlation techniques, the analysis showing its intrinsic stability and the custom hardware development carried out to detect such a low signal. 14. Degradation of PsbO by the Deg protease HhoA Is thioredoxin dependent. Directory of Open Access Journals (Sweden) Irma N Roberts Full Text Available The widely distributed members of the Deg/HtrA protease family play an important role in the proteolysis of misfolded and damaged proteins. Here we show that the Deg protease rHhoA is able to degrade PsbO, the extrinsic protein of the Photosystem II (PSII oxygen-evolving complex in Synechocystis sp. PCC 6803 and in spinach. PsbO is known to be stable in its oxidized form, but after reduction by thioredoxin it became a substrate for recombinant HhoA (rHhoA. rHhoA cleaved reduced eukaryotic (specifically, spinach PsbO at defined sites and created distinct PsbO fragments that were not further degraded. As for the corresponding prokaryotic substrate (reduced PsbO of Synechocystis sp. PCC 6803, no PsbO fragments were observed. Assembly to PSII protected PsbO from degradation. For Synechocystis sp. PCC 6803, our results show that HhoA, HhoB, and HtrA are localized in the periplasma and/or at the thylakoid membrane. In agreement with the idea that PsbO could be a physiological substrate for Deg proteases, part of the cellular fraction of the three Deg proteases of Synechocystis sp. PCC 6803 (HhoA, HhoB, and HtrA was detected in the PSII-enriched membrane fraction. 15. The air oxidation behavior of lanthanum ion implanted zirconium at 500 deg. C CERN Document Server Peng, D Q; Chen, X W; Zhou, Q G 2003-01-01 The beneficial effect of lanthanum ion implantation on the oxidation behavior of zirconium at 500 deg. C has been studied. Zirconium specimens were implanted by lanthanum ions using a MEVVA source at energy of 40 keV with a fluence range from 1x10 sup 1 sup 6 to 1x10 sup 1 sup 7 ions/cm sup 2 at maximum temperature of 130 deg. C, The weight gain curves were measured after being oxidized in air at 500 deg. C for 100 min, which showed that a significant improvement was achieved in the oxidation behavior of zirconium ion implanted with lanthanum compared with that of the as-received zirconium. The valence of the oxides in the scale was analyzed by X-ray photoemission spectroscopy; and then the depth distributions of the elements in the surface of the samples were obtained by Auger electron spectroscopy. Glancing angle X-ray diffraction at 0.3 deg. incident angles was employed to examine the modification of its phase transformation because of the lanthanum ion implantation in the oxide films. It was obviously fou... 16. Exploring a possible origin of a 14 deg y-normal spin tilt at RHIC polarimeter Energy Technology Data Exchange (ETDEWEB) Meot, F. [Brookhaven National Lab. (BNL), Upton, NY (United States); Huang, H. [Brookhaven National Lab. (BNL), Upton, NY (United States) 2015-06-15 A possible origin of a 14 deg y-normal spin n0 tilt at the polarimeter is in snake angle defects. This possible cause is investigated by scanning the snake axis angle µ, and the spin rotation angle at the snake, φ, in the vicinity of their nominal values. 17. A Byzantine chant collection from Sicily: a collaboration between Copenhagen and Piana degli Albanesi (Palermo) DEFF Research Database (Denmark) Sanfratello, Giuseppe 2016-01-01 The aim of this paper is to give an account of the collaboration between a collector of the Byzantine chant tradition of Piana degli Albanesi (Palermo) in Sicily, namely fr. Bartolomeo Di Salvo, and the editorial board of the Monumenta Musicae Byzantinae, i.e. an institution under the aegis......, Collections, Ethnomusicology, Critical edition, Monumenta Musicae Byzantinae (MMB)... 18. Spin-polarized transport in a two-dimensional electron gas with interdigital-ferromagnetic contacts DEFF Research Database (Denmark) Hu, C.-M.; Nitta, Junsaku; Jensen, Ane 2001-01-01 Ferromagnetic contacts on a high-mobility, two-dimensional electron gas (2DEG) in a narrow gap semiconductor with strong spin-orbit interaction are used to investigate spin-polarized electron transport. We demonstrate the use of magnetized contacts to preferentially inject and detect specific spin... 19. Ultra-short channel GaN high electron mobility transistor-like Gunn diode with composite contact Energy Technology Data Exchange (ETDEWEB) Wang, Ying; Yang, Lin' an, E-mail: layang@xidian.edu.cn; Wang, Zhizhe; Chen, Qing; Huang, Yonghong; Dai, Yang; Chen, Haoran; Zhao, Hongliang; Hao, Yue [The State Key Discipline Laboratory of Wide Band Gap Semiconductor Technology, School of Microelectronics, Xidian University, Xi' an 710071 (China) 2014-09-07 We present a numerical analysis on an ultra-short channel AlGaN/GaN HEMT-like planar Gunn diode based on the velocity-field dependence of two-dimensional electron gas (2-DEG) channel accounting for the ballistic electron acceleration and the inter-valley transfer. In particular, we propose a Schottky-ohmic composite contact instead of traditional ohmic contact for the Gunn diode in order to significantly suppress the impact ionization at the anode side and shorten the “dead zone” at the cathode side, which is beneficial to the formation and propagation of dipole domain in the ultra-short 2-DEG channel and the promotion of conversion efficiency. The influence of the surface donor-like traps on the electron domain in the 2-DEG channel is also included in the simulation. 20. Ultra-short channel GaN high electron mobility transistor-like Gunn diode with composite contact Science.gov (United States) Wang, Ying; Yang, Lin'an; Wang, Zhizhe; Chen, Qing; Huang, Yonghong; Dai, Yang; Chen, Haoran; Zhao, Hongliang; Hao, Yue 2014-09-01 We present a numerical analysis on an ultra-short channel AlGaN/GaN HEMT-like planar Gunn diode based on the velocity-field dependence of two-dimensional electron gas (2-DEG) channel accounting for the ballistic electron acceleration and the inter-valley transfer. In particular, we propose a Schottky-ohmic composite contact instead of traditional ohmic contact for the Gunn diode in order to significantly suppress the impact ionization at the anode side and shorten the "dead zone" at the cathode side, which is beneficial to the formation and propagation of dipole domain in the ultra-short 2-DEG channel and the promotion of conversion efficiency. The influence of the surface donor-like traps on the electron domain in the 2-DEG channel is also included in the simulation. 1. Phosphorylation of DegU is essential for activation of amyE expression in Bacillus subtilis Indian Academy of Sciences (India) Monica Gupta; K Krishnamurthy Rao 2014-12-01 Alpha ()-amylase (amyE) is one of the major exo-enzymes secreted by Bacillus subtilis during the post-exponential phase. The DegS-DegU two-component system regulates expression of majority of post-exponentially expressed genes in B. subtilis. It has been demonstrated that varying levels of the phosphorylated form of DegU (DegU-P) control different cellular processes. Exo-protease production is observed when effective concentration of DegU-P rises in the cell, whereas swarming motility is favoured at very low amounts of DegU-P. In this study we show that like other exo-proteases, expression of amyE is positively regulated by increase in DegU-P levels in the cell. We also demonstrate that residues at the DNA-binding helix-turn-helix (HTH) motif of DegU are necessary for the amyE expression. This observation is further reinforced by demonstrating the direct interaction of DegU on amyE promoter. 2. AromaDeg, a novel database for phylogenomics of aerobic bacterial degradation of aromatics. Science.gov (United States) Duarte, Márcia; Jauregui, Ruy; Vilchez-Vargas, Ramiro; Junca, Howard; Pieper, Dietmar H 2014-01-01 Understanding prokaryotic transformation of recalcitrant pollutants and the in-situ metabolic nets require the integration of massive amounts of biological data. Decades of biochemical studies together with novel next-generation sequencing data have exponentially increased information on aerobic aromatic degradation pathways. However, the majority of protein sequences in public databases have not been experimentally characterized and homology-based methods are still the most routinely used approach to assign protein function, allowing the propagation of misannotations. AromaDeg is a web-based resource targeting aerobic degradation of aromatics that comprises recently updated (September 2013) and manually curated databases constructed based on a phylogenomic approach. Grounded in phylogenetic analyses of protein sequences of key catabolic protein families and of proteins of documented function, AromaDeg allows query and data mining of novel genomic, metagenomic or metatranscriptomic data sets. Essentially, each query sequence that match a given protein family of AromaDeg is associated to a specific cluster of a given phylogenetic tree and further function annotation and/or substrate specificity may be inferred from the neighboring cluster members with experimentally validated function. This allows a detailed characterization of individual protein superfamilies as well as high-throughput functional classifications. Thus, AromaDeg addresses the deficiencies of homology-based protein function prediction, combining phylogenetic tree construction and integration of experimental data to obtain more accurate annotations of new biological data related to aerobic aromatic biodegradation pathways. We pursue in future the expansion of AromaDeg to other enzyme families involved in aromatic degradation and its regular update. Database URL: http://aromadeg.siona.helmholtz-hzi.de 3. Monitoring Polar Environmental Change Using FORMOSAT-2 Satellite Science.gov (United States) Huang, C.; Liu, C.; Chang, L.; Wang, S.; Yan, K.; Wu, F.; Wu, A. 2007-12-01 Polar ice loss to the sea currently account for virtually all of the sea-level rise that is not attributable to ocean warming. Huge section of the Ayles Ice Shelf broke off into the Arctic Ocean. Permafrost soil is losing its permanence across the Northern Hemisphere, altering ecosystems and damaging roads and buildings across Alaska, Canada, and Russia. Global warming change the polar environment significantly, especially in recent year. The National Space Organization (NSPO) of Taiwan successfully launched FORMOSAT-2 on 20 May 2004. The orbit is designed to be high-altitude,. Sun-synchronous, and daily-revisit. With high agility in attitude control, FORMOSAT-2 can cover the polar areas up to +/- 90 deg latitude. More than 72 Area of interests in Alaska, Canada, Greenland area and Ice land have imaged periodically in 2006 and 2007. The images have 2m resolution in panchromatic band and 8m in multispectral bands, with size of about 24 x 100 km or large. The ability of FORMOSAT-2 daily revisit has been extended to monitor the change of topography for the glacier and ice shelf daily, weekly and monthly. By using the FORMOSAT-2 stereo pair, we can determine the elevation profile (DEM) across the glacier surface. In this paper, we will present the mapping and topography of Greenland glaciers and ice land including Kangerdlugssuaq Glacier, Greenland, Belcher Glacier, Canada and Ayles ice island. We will demonstrate the DEM extract ability from FORMOSAT-2 polar stereo images( up to 82 deg latitude), and compared with the DEM of the popular SRTM, ASTER which can be acquired to 79 deg latitude. It is expected that FORMOSAT-2 polar images will be continuously collected for years and contribute to the research of global environmental change. 4. Heavy quarkonium production and polarization CERN Document Server Kang, Zhong-Bo; Sterman, George 2011-01-01 We present a perturbative QCD factorization formalism for the production of heavy quarkonia of large transverse momentum$p_T$at collider energies, which includes both the leading power (LP) and next-to-leading power (NLP) contributions to the cross section in the$m_Q^2/p_T^2$expansion for heavy quark mass$m_Q. We estimate fragmentation functions in the non-relativistic QCD formalism, and reproduce the bulk of the large enhancement found in explicit NLO calculations in the color singlet model. Heavy quarkonia produced from NLP channels prefer longitudinal polarization. 5. Pressure drop and mass transfer in two-pass ribbed channels Science.gov (United States) Chandra, P. R.; Han, J. C. 1989-01-01 The combined effects of the sharp 180-deg turn and of the rib configuration on the pressure drop and mass transfer characteristics in a two-pass square channel with a pair of opposite rib-roughened walls (to simulate turbine airfoil cooling passages) were determined for a Reynolds number range of 10,000-60,000. Heat transfer enhancements were compared for the first pass and for the two-pass channel with the sharp 180-deg turn. Correlations for the fully-developed friction factors and loss coefficients were obtained. 6. Channel Power in Multi-Channel Environments NARCIS (Netherlands) M.G. Dekimpe (Marnik); B. Skiera (Bernd) 2004-01-01 textabstractIn the literature, little attention has been paid to instances where companies add an Internet channel to their direct channel portfolio. However, actively managing multiple sales channels requires knowing the customers’ channel preferences and the resulting channel power. Two key compon 7. Channel Power in Multi-Channel Environments NARCIS (Netherlands) M.G. Dekimpe (Marnik); B. Skiera (Bernd) 2004-01-01 textabstractIn the literature, little attention has been paid to instances where companies add an Internet channel to their direct channel portfolio. However, actively managing multiple sales channels requires knowing the customers’ channel preferences and the resulting channel power. Two key 8. Estimation of various scattering parameters and 2-DEG mobilities from electron mobility calculations in the three conduction bands , L and X of gallium arsenide Indian Academy of Sciences (India) Sonal Singhal; A K Saxena; S Dasgupta 2007-10-01 The electron drift mobility in conduction band of GaAs has been calculated before, but for the first time, we have made attempts to estimate the electron mobilities in higher energy L and X minima. We have also calculated the value of mobility of two-dimensional electron gas needed to predict hetero-structure device characteristics using GaAs. Best scattering parameters have been derived by close comparison between experimental and theoretical mobilities. Room temperature electron mobilities in , L and X valleys are found to be nearly 9094, 945 and 247 cm2 /V-s respectively. For the above valleys, the electron masses, deformation potentials and polar phonon temperatures have been determined to be (0.067, 0.22, 0.39m 0 ), (8.5, 9.5, 6.5 eV), and (416, 382, 542 K) as best values, respectively. The 2-DEG electron mobility in minimum increases to 1.54 × 106 from 1.59 × 105 cm2 /V-s (for impurity concentration of 1014 cm-3) at 10 K. Similarly, the 2-DEG electron mobility values in L and X minima are estimated to be 2.28 × 105 and 1.44 × 105 cm2 /V-s at 10 K, which are about ∼ 4.5 and ∼ 3.9 times higher than normal value with impurity scattering present. 9. Ion channel stability and hydrogen bonding. Molecular modelling of channels formed by synthetic alamethicin analogues. Science.gov (United States) Breed, J; Kerr, I D; Molle, G; Duclohier, H; Sansom, M S 1997-12-04 Several analogues of the channel-forming peptaibol alamethicin have been demonstrated to exhibit faster switching between channel substates than does unmodified alamethicin. Molecular modelling studies are used to explore the possible molecular basis of these differences. Models of channels formed by alamethicin analogues were generated by restrained molecular dynamics in vacuo and refined by short molecular dynamics simulations with water molecules within and at either mouth of the channel. A decrease in backbone solvation was found to correlate with a decrease in open channel stability between alamethicin and an analogue in which all alpha-amino-isobutyric acid residues of alamethicin were replaced by leucine. A decrease in the extent of hydrogen-bonding at residue 7 correlates with lower open channel stabilities of analogues in which the glutamine at position 7 was replaced by smaller polar sidechains. These two observations indicate the importance of alamethicin/water H-bonds in stabilizing the open channel. 10. Hi-GAL, the Herschel infrared Galactic Plane Survey: photometric maps and compact source catalogues. First data release for Inner Milky Way: +68{\\deg}> l > -70{\\deg} CERN Document Server Molinari, S; Elia, D; Pestalozzi, M; Traficante, A; Pezzuto, S; Swinyard, B M; Noriega-Crespo, A; Bally, J; Moore, T J T; Plume, R; Zavagno, A; di Giorgio, A M; Liu, S J; Pilbratt, G L; Mottram, J C; Russeil, D; Piazzo, L; Veneziani, M; Benedettini, M; Calzoletti, L; Faustini, F; Natoli, P; Piacentini, F; Merello, M; Palmese, A; Del Grande, R; Polychroni, D; Rygl, K L J; Polenta, G; Barlow, M J; Bernard, J -P; Martin, P G; Testi, L; Ali, B; Andrè, P; Beltrán, M T; Billot, N; Brunt, C; Carey, S; Cesaroni, R; Compiègne, M; Eden, D; Fukui, Y; Garcia-Lario, P; Hoare, M G; Huang, M; Joncas, G; Lim, T L; Lord, S D; Martinavarro-Armengol, S; Motte, F; Paladini, R; Paradis, D; Peretto, N; Robitaille, T; Schilke, P; Schneider, N; Schulz, B; Sibthorpe, B; Strafella, F; Thompson, M A; Umana, G; Ward-Thompson, D; Wyrowski, F 2016-01-01 (Abridged) We present the first public release of high-quality data products (DR1) from Hi-GAL, the {\\em Herschel} infrared Galactic Plane Survey. Hi-GAL is the keystone of a suite of continuum Galactic Plane surveys from the near-IR to the radio, and covers five wavebands at 70, 160, 250, 350 and 500 micron, encompassing the peak of the spectral energy distribution of cold dust for 8 l > -70{\\deg} in a |b|<1{\\deg} latitude strip. Photometric maps have been produced with the ROMAGAL pipeline, that optimally capitalizes on the excellent sensitivity and stability of the bolometer arrays of the {\\em Herschel} PACS and SPIRE photometric cameras, to deliver images of exquisite quality and dynamical range, absolutely calibrated with {\\em Planck} and {\\em IRAS}, and recovering extended emission at all wavelengths and all spatial scales. The compact source catalogues have been generated with the CuTEx algorithm, specifically developed to optimize source detection and extraction in the extreme conditions of intens... 11. Polarized Light in Astronomy. Science.gov (United States) King, D. J. 1983-01-01 The application of very sensitive electronic detecting devices during the last decade has revolutionized and revitalized the study of polarization in celestial objects. The nature of polarization, how polaroids work, interstellar polarization, dichroic filters, polarization by scattering, and modern polarimetry are among the topics discussed. (JN) 12. Environmental fatigue behaviors of wrought and cast stainless steels in 310 .deg. C Deoxygenated Water Energy Technology Data Exchange (ETDEWEB) Cho, Pyung Yeon 2011-02-15 Environmental fatigue behaviors of wrought type 316LN stainless steel and cast CF8M stainless steel were investigated. LCF tests were performed at fixed strain rate of 0.04%/s with 0.4%, 0.6%, 0.8%, 1.0% strain amplitudes in 310 .deg. C deoxygenated water environment. In addition, to analyze microstructure effect on fatigue behavior, low cycle fatigue tests in air environment were performed at fixed strain rate of 0.4%/s, 0.04%/s with 0.4%, 0.8% strain amplitudes. It was shown that the low cycle fatigue life of CF8M in a 310 .deg. C deoxygenated water environment was slightly longer than that of 316LN. On the other hand, the low cycle fatigue life of CF8M in a 310 .deg. C air environment was slightly shorter than that of 316LN or was similar with that of 316LN. Through OM observation and phase image analysis, it was confirmed that the ferrite content of CF8M tested in a 310 .deg. C deoxygenated water environment was larger than that of CF8M tested in a 310 .deg. C air environment. It was shown that the ferrite phase fraction of CF8M tested in 310 .deg. C deoxygenated water environment was approximately 26∼28% and that of CF8M tested in air environment was approximately 10∼12%. The difference of ferrite content in CF8M results in superior tensile properties as higher ferrite content. Furthermore, the difference of ferrite content in CF8M might be the cause of different result of fatigue life between CF8M and 316LN depending on environment. In this study, focused on CF8M having 26∼28% ferrite content, to understand the causes of these differences in a 310 .deg. C deoxygenated water environment, fracture surface and crack morphology were observed. And material factors like microstructure, mechanical properties factors like stress behavior during fatigue life, factors by environmentally assisted cracking (EAC) like hydrogen induced cracking (HIC) and chemical compositions of both materials were analyzed. Mainly in a 310 .deg. C deoxygenated water environment, the 13. Wind-tunnel force and flow visualization data at Mach numbers from 1.6 to 4.63 for a series of bodies of revolution at angles of attack from minus 4 deg to 60 deg Science.gov (United States) Landrum, E. J.; Babb, C. D. 1979-01-01 Flow visualization and force data for a series of six bodies of revolution are presented without analysis. The data were obtained in the Langley Unitary Plan wind tunnel for angles of attack from -4 deg to 60 deg. The Reynolds number used for these tests was 6,600,000 per meter. 14. Fiber-Based Polarization Diversity Detection for Polarization-Sensitive Optical Coherence Tomography Directory of Open Access Journals (Sweden) Hamid Pahlevaninezhad 2014-09-01 Full Text Available We present a new fiber-based polarization diversity detection (PDD scheme for polarization sensitive optical coherence tomography (PSOCT. This implementation uses a new custom miniaturized polarization-maintaining fiber coupler with single mode (SM fiber inputs and polarization maintaining (PM fiber outputs. The SM fiber inputs obviate matching the optical lengths of the two orthogonal OCT polarization channels prior to interference while the PM fiber outputs ensure defined orthogonal axes after interference. Advantages of this detection scheme over those with bulk optics PDD include lower cost, easier miniaturization, and more relaxed alignment and handling issues. We incorporate this PDD scheme into a galvanometer-scanned OCT system to demonstrate system calibration and PSOCT imaging of an achromatic quarter-wave plate, fingernail in vivo, and chicken breast, salmon, cow leg, and basa fish muscle samples ex vivo. 15. Nonlinear channelizer Science.gov (United States) In, Visarath; Longhini, Patrick; Kho, Andy; Neff, Joseph D.; Leung, Daniel; Liu, Norman; Meadows, Brian K.; Gordon, Frank; Bulsara, Adi R.; Palacios, Antonio 2012-12-01 The nonlinear channelizer is an integrated circuit made up of large parallel arrays of analog nonlinear oscillators, which, collectively, serve as a broad-spectrum analyzer with the ability to receive complex signals containing multiple frequencies and instantaneously lock-on or respond to a received signal in a few oscillation cycles. The concept is based on the generation of internal oscillations in coupled nonlinear systems that do not normally oscillate in the absence of coupling. In particular, the system consists of unidirectionally coupled bistable nonlinear elements, where the frequency and other dynamical characteristics of the emergent oscillations depend on the system's internal parameters and the received signal. These properties and characteristics are being employed to develop a system capable of locking onto any arbitrary input radio frequency signal. The system is efficient by eliminating the need for high-speed, high-accuracy analog-to-digital converters, and compact by making use of nonlinear coupled systems to act as a channelizer (frequency binning and channeling), a low noise amplifier, and a frequency down-converter in a single step which, in turn, will reduce the size, weight, power, and cost of the entire communication system. This paper covers the theory, numerical simulations, and some engineering details that validate the concept at the frequency band of 1-4 GHz. 16. Polarization-Dependence of Coulomb Explosion of CO Irradiated with an Intense Femtosecond Laser Pulse Institute of Scientific and Technical Information of China (English) 陈建新; 马日; 任海振; 李霞; 杨宏; 龚旗煌 2003-01-01 Laser-induced Coulomb explosion of CO is studied experimentally using differently polarized femtosecond laser pulses of 2 × 1015 W/cm2 intensity at λ = 800 nm. The channels of molecular Coulomb explosion are observed to be independent of the laser polarizations. The critical distance R is deduced to be larger for the circularly polarized light in comparison with the linearly polarized light. The initial emissions of C+, C2+, O+, and O2+ions are anisotropic for linear polarization and isotropic for circular polarization. The suppression of ionization occurs for the elliptically and circularly polarized lasers. 17. Pourbaix diagrams for the system copper-chlorine at 5-100 deg C Energy Technology Data Exchange (ETDEWEB) Beverskog, B. [Studsvik Material AB, Nykoeping (Sweden); Puigdomenech, I. [Studsvik Eco and Safety AB, Nykoeping (Sweden) 1998-04-01 Pourbaix diagrams for the copper-chlorine system in the temperature interval 5-100 deg C have been revised. Predominance diagrams for dissolved copper containing species have also been calculated. Two different total concentrations of each dissolved element, 10{sup -4} and 10{sup -6} molal for copper and 0.2 and 1.5 molal for chlorine have been used in the calculations. Chloride is the predominating chlorine species in aqueous solutions. Presence of chloride increases the corrosion regions of copper at the expense of the immunity and passivity regions in the Pourbaix diagrams. CuCl{sub 2} {center_dot} 3Cu(OH){sub 2} is the only copper-chloride solid phase that forms at the concentrations of chlorine studied. However, its stability area decreases with increasing temperature. The ion CuCl{sub 2}{sup -} predominates at all temperatures at [Cl(aq)]{sub tot}=0.2 molal and this reduces the immunity and passivity areas. A corrosion region exists between the immunity and passivity regions at 100 deg C at [Cu(aq)]{sub tot}=10{sup -6} and [Cl(aq)]{sub tot}=0.2 molal. At the chlorine concentration of 1.5 molal the corrosion region exists in the whole temperature range investigated. The ion CuCl{sub 3}{sup 2-} predominates at 5-25 and 100 deg C, while CuCl{sub 2}{sup -} predominates at 50-80 deg C at [Cl(aq)]{sub tot=}1-5 molal. A copper concentration of 10{sup -4} molal reduces the corrosion areas due to expansion of the immunity and passivity areas. However, a corrosion region still exists between the immunity and passivity regions at all investigated temperatures at pH{sub {Tau}}<9.5 and 1.5 molal chloride concentration. According to our calculations the copper canisters in the deep nuclear waste repository should not corrode at the copper concentration of 10{sup -6} molal and the chloride concentration of 0.2 molal. However, at 80-100 deg C the equilibrium potentials postulated for the Swedish nuclear repository are dangerously close to a corrosion situation. According to 18. Book review, Igiene e Tecnologie degli Alimenti di Origine Animale Giampaolo Colavita (a cura di Directory of Open Access Journals (Sweden) Manuel Graziani 2008-09-01 Full Text Available Igiene e Tecnologie degli Alimenti di Origine Animale si avvale del contributo di 33 autori, tutti soci dell’Associazione Italiana Veterinari Igienisti (AIVI, che garantiscono l’appropriata trattazione di una materia estremamente vasta e dinamica. Il manuale nasce da un’iniziativa finalizzata alla realizzazione di un testo che rifletta e possa soddisfare le esigenze didattiche degli insegnamenti di un’ampia serie di materie universitarie: Igiene e Tecnologie degli Alimenti di Origine Animale della Facoltà di Medicina Veterinaria, di Agraria, nei corsi di Scienze e Tecnologie Alimentari, di Scienze e Tecnologie delle Produzioni Animali, nel corso di laurea in Tecniche della Prevenzione nell’ambiente e nei Luoghi di Lavoro, nonché in altri corsi di studio dove si insegnano le discipline relative all’igiene e alla sicurezza degli alimenti.Sono stati trattati gran parte degli alimenti di origine animale, i prodotti a base di carne, il latte e i prodotti derivati, i prodotti della pesca freschi e trasformati, i prodotti dell’alveare, le uova e gli ovoprodotti. Di particolare interesse appare il capitolo riguardante la diagnostica analitica degli alimenti, considerato che le moderne metodologie analitiche risultano fondamentali per affrontare le tematiche legate all’igiene e alla sicurezza alimentare.Il volume ha una finalità prevalentemente didattica ma è comunque rivolto a tutti coloro che operano nel campo dell’Igiene e delle Tecnologie Alimentari. Infatti, visti gli argomenti trattati come le tossinfezioni e le intossicazioni alimentari, la conservazione, il confezionamento e l’etichettatura dei prodotti alimentari, anche i professionisti del settore possono trarre dal testo elementi utili per la loro attività. Per esempio argomenti quali l’analisi del rischio, le attività di audit ed i sistemi di accreditamento e di certificazione sono particolarmente utili per chi opera nelle Aziende Sanitarie Locali e negli Istituti 19. Antenna polarization diversity for high-speed polarization multiplexing wireless signal delivery at W-band. Science.gov (United States) Li, Xinying; Yu, Jianjun; Chi, Nan; Xiao, Jiangnan 2014-03-01 We propose and experimentally demonstrate a novel architecture for a W-band integrated optical wireless system, which adopts a 2×2 multiple-input multiple-output (MIMO) wireless link based on antenna polarization diversity, and can realize 80 km single-mode fiber-28 transmission and 2 m wireless delivery for up to 39 Gbaud polarization-division-multiplexing quadrature-phase-shift-keying (PDM-QPSK) signal at 100 GHz. Classic constant-modulus-algorithm (CMA) equalization is adopted at the receiver to implement polarization demultiplexing. The 2×2 MIMO wireless link adopts one pair of horizontal-polarization (H-polarization) horn antennas (HAs) and one pair of vertical-polarization (V-polarization) HAs. Because the two pairs of HAs are fully isolated, the wireless cross talk can be effectively avoided. Thus, compared to the 2×2 MIMO wireless link at the same antenna polarization, the adoption of antenna polarization diversity cannot only make the HA adjustment easier but can also reduce the required CMA tap number. After removing 20% forward-error-correction overhead, the 39 Gbaud baud rate corresponds to a net bit rate of 130 Gb/s, which, to our best knowledge, is the highest bit rate per PDM channel demonstrated for wireless signal delivery up to now. 20. Spectral line polarimetry with a channeled polarimeter. Science.gov (United States) van Harten, Gerard; Snik, Frans; Rietjens, Jeroen H H; Martijn Smit, J; Keller, Christoph U 2014-07-01 Channeled spectropolarimetry or spectral polarization modulation is an accurate technique for measuring the continuum polarization in one shot with no moving parts. We show how a dual-beam implementation also enables spectral line polarimetry at the intrinsic resolution, as in a classic beam-splitting polarimeter. Recording redundant polarization information in the two spectrally modulated beams of a polarizing beam-splitter even provides the possibility to perform a postfacto differential transmission correction that improves the accuracy of the spectral line polarimetry. We perform an error analysis to compare the accuracy of spectral line polarimetry to continuum polarimetry, degraded by a residual dark signal and differential transmission, as well as to quantify the impact of the transmission correction. We demonstrate the new techniques with a blue sky polarization measurement around the oxygen A absorption band using the groundSPEX instrument, yielding a polarization in the deepest part of the band of 0.160±0.010, significantly different from the polarization in the continuum of 0.2284±0.0004. The presented methods are applicable to any dual-beam channeled polarimeter, including implementations for snapshot imaging polarimetry. 1. Heat transfer and pressure drop in a compact pin-fin heat exchanger with pin orientation at 18 deg to the flow direction Science.gov (United States) Olson, D. A. 1991-01-01 The heat transfer and pressure drop characteristics of a novel, compact heat exchanger in helium gas were measured at 3.5 MPa and Reynolds numbers of 450 to 12,000. The pin-fin specimen consisted of pins, 0.51 mm high and spaced 2.03 mm on centers, spanning a channel through which the helium flows; the angle of the row of pins to the flow direction was 18 deg. The specimen was radiatively heated on the top side at heat fluxes up to 74 W/sq cm and insulated on the back side. Correlations were developed for the friction factor and Nusselt number. The Nusselt number compares favorably to those of past studies of staggered pin-fins, when the measured temperatures are extrapolated to the temperature of the wall-fluid interface. 2. Polarization observables in ω photo-production Directory of Open Access Journals (Sweden) Vegna V. 2014-06-01 Full Text Available The total cross section of ω photo-production off proton shows several bumps in the incoming photon energy range 1.1–2.5 GeV, which can be ascribed to the contribution of intermediate proton excited states in the s-channel of the reaction. At the same time, differential cross sections show a diffractive behavior, which is interpreted in terms of t-channel exchange contributions. A complete understanding of the ω photo-production process requires a simultaneous investigation of both t-channel exchange terms and s-channel contributions. The measurement of the angular distributions of omega decay products allows to extract the values of the spin-density-matrix elements (SDME and to evaluate the contribution of natural/unnatural parity exchange terms. The use of polarized beam and/or target allows to measure polarization observables which can help to identify the intermediate proton excited states involved in the process. Results of SDME and polarization observables will be shown as an overview about ω photo-production. 3. Sea level variabilities in the Gulf Stream between Cape Hatteras and 50 deg W - A Geosat study Science.gov (United States) Vazquez, Jorge; Zlotnicki, Victor; Fu, Lee-Lueng 1990-01-01 Sea level variabilities in the Gulf Stream between Cape Hatteras and 50 deg W were examined by studying sea level residuals, relative to a 2-yr mean sea level, obtained from Geosat altimetry data for the period between November 1986 and December 1988. An array of sea-level time series was constructed for a region bounded by 30 deg N and 45 deg N in latitude and by 80 deg W and 50 deg W longitude. It is shown that the spectral characteristics of this time series varies with geographic location along the Gulf Stream path. Concurrent NOAA IR images are used to aid in the interpretation of sea level observations in terms of the variability of the stream's path, demonstrating the synergistic value of the combination of satellite-altimeter and IR data. 4. Creep crack growth in a reactor pressure vessel steel at 360 deg C Energy Technology Data Exchange (ETDEWEB) Rui Wu; Seitisleam, F.; Sandstroem, R. [Swedish Institute for Metals Research, Stockholm (Sweden) 1998-12-31 Plain creep (PC) and creep crack growth (CCG) tests at 360 deg C and post metallography were carried out on a low alloy reactor pressure vessel steel (ASTM A508 class 2) with different microstructures. Lives for the CCG tests were shorter than those for the PC tests and this is more pronounced for simulated heat affected zone microstructure than for the parent metal at longer lives. For the CCG tests, after initiation, the cracks grew constantly and intergranularly before they accelerated to approach rupture. The creep crack growth rate is well described by C*. The relations between reference stress, failure time and steady crack growth rate are presented for the CCG tests. It is demonstrated that the failure stress due to CCG is considerably lower than the yield stress at 360 deg C. Consequently, the CCG will control the static strength of a reactor vessel. (orig.) 17 refs. 5. The first winter solstice observed at the meridian line of Santa Maria degli Angeli in Rome CERN Document Server Sigismondi, Costantino 2014-01-01 The page written by the astronomer Francesco Bianchini (1662-1729) and containing the data of the 1701 winter solstice observed at Santa Maria degli Angeli is presented for the first time in figure 2 and widely discussed along this paper. The great meridian line in the Basilica of Santa Maria degli Angeli in Rome was built in 1701/1702 with the scope to measure the Obliquity of the Earth's orbit in the following eight centuries, upon the will of pope Clement XI. During the winter solstice of 1701 the first measurements of the obliquity have been realized by Francesco Bianchini, the astronomer who designed the meridian line, upgrading the similar instrument realized by Giandomenico Cassini in San Petronio, Bononia. In this paper the accuracy of the data observed by Francesco Bianchini is discussed and compared with up-to-date ephemerides. The modern situation of this historical instrument is also presented. 6. Isothermal section at 1400 deg. C of the Ti-Zr-Sn system Energy Technology Data Exchange (ETDEWEB) Saltykov, V.A. [I.N. Frantsevich Institute for Problems of Materials Science, Str. Krzhyzhanovsky, 3, Kiev 03142 (Ukraine)], E-mail: ssaltykov@ipms.kiev.ua; Meleshevich, K.A.; Samelyuk, A.V.; Verbytska, O.M.; Bulanova, M.V. [I.N. Frantsevich Institute for Problems of Materials Science, Str. Krzhyzhanovsky, 3, Kiev 03142 (Ukraine) 2008-07-14 By the methods of X-ray diffraction, metallography and microprobe examinations the character of phase equilibria at 1400 deg. C is studied for the Ti-(Ti,Zr){sub 5}Sn{sub 3}-Zr region of the Ti-Zr-Sn system. The isothermal section at 1400 deg. C is constructed. This is similar to the solidus surface and is characterized by two 3-phase regions: <{beta}Ti,Zr> + Ti{sub 3}Sn + (Ti,Zr){sub 5}Sn{sub 3} and Ti{sub 3}Sn + Ti{sub 2}Sn + (Ti,Zr){sub 5}Sn{sub 3}. Solubility of Sn in <{beta}Ti,Zr> solid solution is between 10 and 15 at.% Sn. Solubility of zirconium in Ti{sub 3}Sn is about 12 at.%. 7. Iron oxidation kinetics study by using infrared spectral emissivity measurements below 570deg. C Energy Technology Data Exchange (ETDEWEB) Campo, Leire del [Departamento de Fisica de la Materia Condensada, Facultad de Ciencia y Tecnologi' a, Universidad del Pai' s Vasco, Barrio Sarriena s/n, 48940 Leioa, Bizkaia (Spain); Perez-Saez, Raul B. [Departamento de Fisica de la Materia Condensada, Facultad de Ciencia y Tecnologi' a, Universidad del Pai' s Vasco, Barrio Sarriena s/n, 48940 Leioa, Bizkaia (Spain); Instituto de Sintesis y Estudio de Materiales, Universidad del Pais Vasco, Apdo. 644, 48080 Bilbao (Spain)], E-mail: raul.perez@ehu.es; Tello, Manuel J. [Departamento de Fisica de la Materia Condensada, Facultad de Ciencia y Tecnologi' a, Universidad del Pai' s Vasco, Barrio Sarriena s/n, 48940 Leioa, Bizkaia (Spain); Instituto de Sintesis y Estudio de Materiales, Universidad del Pais Vasco, Apdo. 644, 48080 Bilbao (Spain) 2008-01-15 The oxidation kinetics of iron below 570deg. C is investigated through the dependence of the spectral emissivity on the surface oxidation state. Using the theory of radiative effects of thin films, the oxide scale thickness is obtained as a function of time. A parabolic growth has been observed in all the cases, and applying Wagner's theory, the oxidation parabolic rate constants have been calculated at four temperatures. The temperature dependence of these results has additionally been used to obtain the activation energy of the oxidation process in iron. The parabolic rate constants and activation energy values are in good agreement with the theoretical predictions, and this suggests that the lattice diffusion mechanisms for the high temperature magnetite growth also occur until 400deg. C. The experimental results are also useful to test the applicability of emissivity measurements for in situ oxidation kinetics studies in the spectral range where the scales are optically thin. 8. WFPC2 Polarization Calibration Science.gov (United States) Biretta, J.; McMaster, M. 1997-12-01 We derive a detailed calibration for WFPC2 polarization data which is accurate to about 1.5%. We begin by computing polarizer flats, and show how they are applied to data. A physical model for the polarization effects of the WFPC2 optics is then created using Mueller matricies. This model includes corrections for the instrumental polarization (diattenuation and phase retardance) of the pick-off mirror, as well as the high cross-polarization transmission of the polarizer filter. We compare this model against the on-orbit observations of polarization calibrators, and show it predicts relative counts in the different polarizer/aperture settings to 1.5% RMS accuracy. We then show how this model can be used to calibrate GO data, and present two WWW tools which allow observers to easily calibrate their data. Detailed examples are given illustrationg the calibration and display of WFPC2 polarization data. In closing we describe future plans and possible improvements. 9. Metasurface polarization splitter CERN Document Server Slovick, Brian A; Yu, Zhi Gang; Kravchenckou, Ivan I; Briggs, Dayrl P; Moitra, Parikshit; Krishnamurthy, Srini; Valentine, Jason 2016-01-01 Polarization beam splitters, devices that separate the two orthogonal polarizations of light into different propagation directions, are one of the most ubiquitous optical elements. However, traditionally polarization splitters rely on bulky optical materials, while emerging optoelectronic and photonic circuits require compact, chip-scale polarization splitters. Here we show that a subwavelength rectangular lattice of cylindrical silicon Mie resonators functions as a polarization splitter, efficiently reflecting one polarization while transmitting the other. We show that the polarization splitting arises from the anisotropic permittivity and permeability of the metasurface due to the two-fold rotational symmetry of the rectangular unit cell. The high polarization efficiency, low loss, and low profile make these metasurface polarization splitters ideally suited for monolithic integration with optoelectronic and photonic circuits. 10. Subband Structure of a Two-Dimensional Electron Gas Formed at the Polar Surface of the Strong Spin-Orbit Perovskite KTaO3 Energy Technology Data Exchange (ETDEWEB) King, P.D.C. 2012-03-01 We demonstrate the formation of a two-dimensional electron gas (2DEG) at the (100) surface of the 5d transition-metal oxide KTaO{sub 3}. From angle-resolved photoemission, we find that quantum confinement lifts the orbital degeneracy of the bulk band structure and leads to a 2DEG composed of ladders of subband states of both light and heavy carriers. Despite the strong spin-orbit coupling, we find no experimental signatures of a Rashba spin splitting, which has important implications for the interpretation of transport measurements in both KTaO{sub 3}- and SrTiO{sub 3}-based 2DEGs. The polar nature of the KTaO{sub 3}(100) surface appears to help mediate formation of the 2DEG as compared to non-polar SrTiO{sub 3}(100). 11. PUMA-PUblication MAnagement: sistemi per la gestione delle pubblicazioni degli enti di ricerca OpenAIRE Biagioni, Stefania 2005-01-01 Lo scopo di questa presentazione ? quello di illustrare i) come ? stato realizzato un ciclo gestionale completo dell'informazione: dall'inserimento dei metadati e dei documenti digitali alla restituzione degli stessi all'utente finale; ii) come sono stati resi accessibili via web, a livelli diversi e secondo viste diverse l'informazione prodotta; iii) come siano stati creati servizi differenti utilizzando gli stessi oggetti. Vengono illustrati i sistemi utilizzati presso il CNR di Pisa per la... 12. Proteomica degli exosomi urinari per la ricerca di biomarcatori nella nefropatia diabetica e nelle tubulopatie ereditarie OpenAIRE Corbetta, 2015-01-01 Le urine costituiscono il fluido biologico di elezione nella ricerca di biomarcatori per le patologie renali in quanto possono essere raccolte in modo semplice e non invasivo; una strategia per la semplificazione del proteoma urinario è rappresentata dall’isolamento degli exosomi urinari (UE), nanovescicole di membrana (30-100 nm) rilasciate dalle cellule epiteliali nello spazio urinario. In questo lavoro abbiamo focalizzato l’attenzione sulla nefropatia diabetica (DN), una comune complicazio... 13. Survey of the sky at the 8. 7 and 14. 4 GHz frequencies in the 0 deg - 4 deg declination range Energy Technology Data Exchange (ETDEWEB) Amirkhanyan, V.R.; Gorshkov, A.G.; Kapustkin, A.A.; Konnikova, V.K.; Lazutkin, A.N.; Larionov, M.G.; Nikanorov, A.S.; Sidorenkov, V.N.; Ugol' kova, L.S.; Khromov, O.I. (Moskovskij Gosudarstvennyj Univ. (USSR). Gosudarstvennyj Astronomicheskij Inst. ' ' GAISh' ' ) Using the RATAN-600 radiotelescope of the USSR Academy of Sciences (from March 1979 to January 1980) the sky is observed at the 8.7 and 14.4 GHz frequencies in the 0-4 deg declination range. Lists of 82 and 24 radiosources detected at the given frequencies are presented. Six radiosources are detected for the first time. Right ascension and declination, as well as the maximum values of radio-frequency radiation fluxes are given. The problems of measuring accuracies of fluxes and coordinates and the problem of validity of detected radiosources are discussed. On the basis of comparison of the data obtained with those in other works the systematic deviation in fluxes of sources is not more than 7%. 14. Submillimeter wavelength survey of the galactic plane from l = -5 deg to l = +62 deg - Structure and energetics of the inner disk Science.gov (United States) Hauser, M. G.; Silverberg, R. F.; Stier, M. T.; Kelsall, T.; Gezari, D. Y.; Dwek, E.; Walser, D.; Mather, J. C.; Cheung, L. H. 1984-01-01 Observational results are presented from a new large-scale survey of the first quadrant of the galactic plane at wavelengths of 150, 250, and 300 microns, with a 10 x 10 arcmin beam. The emission detected in the survey arises from compact sources, most of which are identified with known peaks of 5 GHz or CO emission, or both, and from an underlying diffuse background with a typical angular width of about 0.9 deg (FWHM) which accounts for most of the emission. A total of 80 prominent discrete sources are identified and characterized, of which about half have not previously been reported at far-infrared wavelengths. The total infrared luminosity within the solar circle is about 1 to 2 x 10 to the 10th solar luminosity, and is probably emitted by dust that resides in molecular clouds. 15. Submillimeter wavelength survey of the galactic plane from l = -5 deg to l = +62 deg: Structure and energetics of the inner disk Science.gov (United States) Hauser, M. G.; Silverberg, R. F.; Stier, M. T.; Kelsall, T.; Gezari, D. Y.; Dwek, E.; Walser, D.; Mather, J. C.; Cheung, L. H. 1984-01-01 Results from a large scale survey of the first quadrant of the Milky Way galactic plane at wavelengths of 150, 250, and 300 microns with a 10x10 arcmin beam are presented. The emission detected in the survey arises from compact sources, most of which are identified with known peaks of 5 GHz and/or CO emission, and from an underlying diffuse background with a typical angular width of approximately 0.9 deg (FWHM) which accounts for most of the emission. A total of 80 prominent discrete sources were identified and characterized, of which about half were not previously reported at far infrared wavelengths. The total infrared luminosity within the solar circle is approximately 1 to 2x10 to the 10th power L sub 0, and is probably emitted by dust that resides in molecular clouds. 16. Low frequency observations of linearly polarized structures in the interstellar medium near the south Galactic pole CERN Document Server Lenc, Emil; Sun, X H; Sadler, E M; Willis, A G; Barry, N; Beardsley, A P; Bell, M E; Bernardi, G; Bowman, J D; Briggs, F; Callingham, J R; Cappallo, R J; Carroll, P; Corey, B E; de Oliveira-Costa, A; Deshpande, A A; Dillon, J S; Dwarkanath, K S; Emrich, D; Ewall-Wice, A; Feng, L; For, B -Q; Goeke, R; Greenhill, L J; Hancock, P; Hazelton, B J; Hewitt, J N; Hindson, L; Hurley-Walker, N; Johnston-Hollitt, M; Jacobs, D C; Kapinska, A D; Kaplan, D L; Kasper, J C; Kim, H -S; Kratzenberg, E; Line, J; Loeb, A; Lonsdale, C J; Lynch, M J; McKinley, B; McWhirter, S R; Mitchell, D A; Morales, M F; Morgan, E; Morgan, J; Murphy, T; Neben, A R; Oberoi, D; Offringa, A R; Ord, S M; Paul, S; Pindor, B; Pober, J C; Prabu, T; Procopio, P; Riding, J; Rogers, A E E; Roshi, A; Shankar, N Udaya; Sethi, S K; Srivani, K S; Staveley-Smith, L; Subrahmanyan, R; Sullivan, I S; Tegmark, M; Thyagarajan, Nithyanandan; Tingay, S J; Trott, C; Waterson, M; Wayth, R B; Webster, R L; Whitney, A R; Williams, A; Williams, C L; Wu, C; Wyithe, J S B; Zheng, Q 2016-01-01 We present deep polarimetric observations at 154 MHz with the Murchison Widefield Array (MWA), covering 625 deg^2 centered on RA=0 h, Dec=-27 deg. The sensitivity available in our deep observations allows an in-band, frequency-dependent analysis of polarized structure for the first time at long wavelengths. Our analysis suggests that the polarized structures are dominated by intrinsic emission but may also have a foreground Faraday screen component. At these wavelengths, the compactness of the MWA baseline distribution provides excellent snapshot sensitivity to large-scale structure. The observations are sensitive to diffuse polarized emission at ~54' resolution with a sensitivity of 5.9 mJy beam^-1 and compact polarized sources at ~2.4' resolution with a sensitivity of 2.3 mJy beam^-1 for a subset (400 deg^2) of this field. The sensitivity allows the effect of ionospheric Faraday rotation to be spatially and temporally measured directly from the diffuse polarized background. Our observations reveal large-sca... 17. Vortex lift augmentation by suction on a 60 deg swept Gothic wing Science.gov (United States) Taylor, A. H.; Jackson, L. R.; Huffman, J. K. 1982-01-01 An experimental investigation was conducted in the Langley high-speed 7- by 10-foot wind tunnel to determine the aerodynamic performance of suction applied near the wing tips above the trailing edge of a 60 deg swept Gothic wing. Moveable suction inlets were symmetrically mounted in the proximity of the trailing edge, and the amount of suction was varied to maximize wing lift. Tests were conducted at Mach 0.15, 0.30, and 0.45, and the angle of attack was varied from -4 to 50 deg. The suction augmentation increases the lift coefficient over the entire range of angle of attack. The lift improvement exceeds the unaugmented wing lift by over 20%. Moreover, the augmented lift exceeds the lift predicted by vortex lattice theory to 30 deg angle of attack. Suction augmentation is postulated to strengthen the vortex system by increasing its velocity and making it more concentrated. This causes the vortex breakdown to be delayed to a higher angle of attack 18. submitter Technical Note: Using DEG-CPCs at upper tropospheric temperatures CERN Document Server Wimmer, D; Nieminen, T; Duplissy, J; Ehrhart, S; Almeida, J; Rondo, L; Franchin, A; Kreissl, F; Bianchi, F; Manninen, H E; Kulmala, M; Curtius, J; Petäjä, T 2015-01-01 Over the last few years, several condensation particle counters (CPCs) capable of measuring in the sub-3 nm size range have been developed. Here we study the performance of CPCs based on diethylene glycol (DEG) at different temperatures during Cosmics Leaving OUtdoor Droplets (CLOUD) measurements at CERN. The data shown here are the first set of verification measurements for sub-3 nm CPCs under upper tropospheric temperatures using atmospherically relevant aerosol particles. To put the results in perspective we calibrated the DEG-CPC at room temperature, resulting in a cut-off diameter of 1.4 nm. All diameters refer to mobility equivalent diameters in this paper. At upper tropospheric temperatures ranging from 246.15 K to 207.15 K, we found cut-off sizes relative to a particle size magnifier in the range of 2.5 to 2.8 nm. Due to low number concentration after size classification, the cut-off diameters have a high uncertainty (±0.3 nm) associated with them. Operating two laminar flow DEG-CPCs with different c... 19. EDD, a novel phosphotransferase domain common to mannose transporter EIIA, dihydroxyacetone kinase, and DegV. Science.gov (United States) Kinch, Lisa N; Cheek, Sara; Grishin, Nick V 2005-02-01 Using a recently developed program (SCOPmap) designed to automatically assign new protein structures to existing evolutionary-based classification schemes, we identify a evolutionarily conserved domain (EDD) common to three different folds: mannose transporter EIIA domain (EIIA-man), dihydroxyacetone kinase (Dak), and DegV. Several lines of evidence support unification of these three folds into a single superfamily: statistically significant sequence similarity detected by PSI-BLAST; "closed structural grouping" using DALI Z-scores (each protein inside a group finds all other group members with scores higher than those to proteins outside the group) that includes only these proteins sharing a unique alpha-helical hairpin at the C-terminus and excludes all other proteins with similar topology; similar domain fusions connect Dak and DegV, and genomic neighborhood organizations connect Dak and EIIA-man. Finally, both Dak and EIIA-man perform similar phosphotransfer reactions, suggesting a phosphotransferase activity for the DegV-like family of proteins, whose function other than lipid binding revealed in the crystal structure remains unknown. 20. Tunable all electric spin polarizer Science.gov (United States) Bhandari, Nikhil K. To realize the full potential of spin-based devices, ways must be found to inject, manipulate, and detect the spin of the electron by purely electrical means. Previously, our group has shown that a quantum point contact (QPC) with lateral spin orbit coupling (LSOC) can be used to create a strongly spin-polarized current by purely electrical means. The LSOC results from the lateral in-plane electric field created by the confining potential in QPCs with in-plane side gates (SGs). Strongly spin-polarized currents can be generated by tuning the asymmetric bias voltages on the side gates. A conductance anomaly in the form of a plateau at conductance G ≅ 0.5G0 (where G 0 = 2e2/h) was observed in the ballistic conductance of a QPC based in the absence of magnetic field - which was established to be a signature of complete spin polarization. A Non-Equilibrium Green's Function (NEGF) analysis was used to model a small QPC and three ingredients were found to be essential to generate a strong spin polarization: (1) LSOC, (2) an asymmetric lateral confinement, and (3) a strong electron-electron (e-e) interaction. We have also shown that all-electric control of spin polarization can be achieved for different materials, electron mobility, heterostructure design, QPC dimensions and strength of LSOC. Our previous experimental and theoretical results have also found the presence of other conductance anomalies (i.e., at values different from 0.5 G0 ) and the main reason for these occurrences was shown to be due to the influence of surface roughness scattering. In this thesis, we address the important technological challenge to better control the location of the conductance anomalies in QPCs and create a tunable all-electric spin polarizer based on a QPC with four gates, i.e., with two in-plane SGs in series. Here, the first pair of SGs, near the source, is asymmetrically biased to create spin polarization in the QPC channel. The second set of gates, near the drain, is 1. The spatial relation between EUV cavities and linear polarization signatures Science.gov (United States) Bak-Stȩślicka, Urszula; Gibson, Sarah E.; Fan, Yuhong; Bethge, Christian; Forland, Blake; Rachmeler, Laurel A. 2014-01-01 Solar coronal cavities are regions of rarefied density and elliptical cross-section. The Coronal Multi-channel Polarimeter (CoMP) obtains daily full-Sun coronal observations in linear polarization, allowing a systematic analysis of the coronal magnetic field in polar-crown prominence cavities. These cavities commonly possess a characteristic lagomorphic'' signature in linear polarization that may be explained by a magnetic flux-rope model. We analyze the spatial relation between the EUV cavity and the CoMP linear polarization signature. 2. Polarized Electron Source Developments Energy Technology Data Exchange (ETDEWEB) Charles K. Sinclair 1990-02-23 Presently, only two methods of producing beams of polarized electrons for injection into linear accelerators are in use. Each of these methods uses optical pumping by circularly polarized light to produce electron polarization. In one case, electron polarization is established in metastable helium atoms, while in the other case, the polarized electrons are produced in the conduction band of appropriate semiconductors. The polarized electrons are liberated from the helium metastable by chemi-ionization, and from the semiconductors by lowering the work function at the surface of the material. Developments with each of these sources since the 1988 Spin Physics Conference are reviewed, and the prospects for further improvements discussed. 3. Geographical Income Polarization DEFF Research Database (Denmark) Azhar, Hussain; Jonassen, Anders Bruun In this paper we estimate the degree, composition and development of geographical income polarization based on data at the individual and municipal level in Denmark from 1984 to 2002. Rising income polarization is reconfirmed when applying new polarization measures, the driving force being greater...... inter municipal income inequality. Counter factual simulations show that rising property prices to a large part explain the rise in polarization. One side-effect of polarization is tendencies towards a parallel polarization of residence location patterns, where low skilled individuals tend to live... 4. Perfect Multi-Channel Flat Reflectors CERN Document Server Asadchy, V S; Elsakka, A; Albooyeh, M; Tretyakov, S A 2016-01-01 Recent advances in engineered gradient metasurfaces have enabled unprecedented opportunities for light manipulation using optically thin sheets, such as anomalous refraction, reflection, or focusing of an incident beam. Here we introduce a concept of multi-channel functional metasurfaces, which are able to control incoming and outgoing waves in a number of propagation directions or polarization states simultaneously and independently. In particular, we reveal a possibility to create perfect multi-channel reflectors. Under the assumption of reciprocity and energy conservation, we find that there exist three fundamental classes of multi-channel mirrors. Together they form a basis of all possible reflection functionalities achievable with flat periodically modulated reflectors. To demonstrate the potential of the introduced concept, we design and experimentally test one of the basis multi-channel reflectors, confirming the desired multi-channel response. Furthermore, by extending the concept to reflectors suppor... 5. Instantaneous polarization statistics of electromagnetic waves Institute of Scientific and Technical Information of China (English) WANG Xuesong; LI Yongzhen; DAI Dahai; XIAO Shunping; ZHUANG Zhaowen 2004-01-01 The problem of statistical description of instantaneous polarization of electromagnetic waves is studied. First, the physical meanings of instantaneous Stokes vectors' components are analyzed, which provide a short cut for solving statistical distribution functions of instantaneous Stokes vectors. Second, in the condition of Gaussian hypothesis, the analytical expressions of probability density function (PDF) of instantaneous Stokes vectors are presented. Finally, some computation results are presented in the condition of two independent polarization channels, which show the validity and simplicity of the statistical description method. 6. Polar Coding for Secure Transmission and Key Agreement CERN Document Server Koyluoglu, O Ozan 2010-01-01 Wyner's work on wiretap channels and the recent works on information theoretic security are based on random codes. Achieving information theoretical security with practical coding schemes is of definite interest. In this note, the attempt is to overcome this elusive task by employing the polar coding technique of Ar{\\i}kan. It is shown that polar codes achieve non-trivial perfect secrecy rates for binary-input degraded wiretap channels while enjoying their low encoding-decoding complexity. In the special case of symmetric main and eavesdropper channels, this coding technique achieves the secrecy capacity. Next, fading erasure wiretap channels are considered and a secret key agreement scheme is proposed, which requires only the statistical knowledge of the eavesdropper channel state information (CSI). The enabling factor is the creation of advantage over Eve, by blindly using the proposed scheme over each fading block, which is then exploited with privacy amplification techniques to generate secret keys. 7. Electric field dependence of drift velocity and electron temperature of GaAs/AlGaAs 2DEG in the low electric field region Energy Technology Data Exchange (ETDEWEB) Ari, Mehmet; Turkoglu, Orhan 2004-05-01 Experimental and theoretical results on low electric field transport of two-dimensional electron gas (2DEG) in AlGaAs/GaAs high electron mobility transistor (HEMT) channel are reported at lattice temperature T{sub L}=1.7 K under zero magnetic field. The electron temperature (T{sub e}) and the drift velocity ({upsilon}{sub d}) dependence on the electric field (F) and the electron density in the 2DEG channel are presented. In addition, the variation of the electron temperature with the drift velocity is obtained. The results are obtained for the electric field in the region of 0.01-100 V/cm and in the electron temperature range of 1.7-60 K. It is shown that the electron temperature of 2DEG is a non-monotonous function of the electric field. The results also indicate that electron heating is seen to occur for the electric field F>0.1 V/cm which corresponds to the electron temperature T{sub e}=2 K. A sharp increase in the electron temperature T{sub e} and in the drift velocity {upsilon}{sub d} with the electric field below electron temperature of 40 K is seen. The variation of electron temperature with drift velocity is very slow in the same electron temperature range where acoustic phonon emission due to deformation potential is the dominant energy loss mechanism of electronic system. When F>5 V/cm and T{sub e}>40 K, where the optic phonon emission is a dominant relaxation mechanism, the electron temperature changes linearly with electric field and the drift velocity increases very rapidly with electron temperature. Also, the drift velocity starts to saturate in this regime. The experimental results are compared with theoretical results and a good agreement is obtained at the electron temperatures of T{sub e}<50 K. Above the electron temperature of 50 K, a disagreement is observed between the experimental and the theoretical results which indicates that additional scattering mechanisms should be taken into account and the accuracy of the assumptions concerning the 8. Polarization-maintaining fiber loop with double optical length and its application to fiber optic gyroscope Institute of Scientific and Technical Information of China (English) Changsheng Li; Chunxi Zhang; Ningfang Song; Hongjie Xu 2011-01-01 @@ A novel polarization maintaining fiber (PMP) loop is proposed and used for an interferometric fiber optic gyroscope (FOG). By splicing a conventional PMF loop with two pigtailed polarization beam splitters, polarized light can be guided to propagate along the slow and fast axes of the PMF in sequence to double its effective optical length in the loop. In particular, the resultant optical length in the combined loop is partially self-compensated for some external disturbances, such as transverse strain. Primary experiments on the FOG using the proposed loop demonstrate that the average static bias deviation between -40 and +60 ℃ is less than 0.050 deg./h, and the average bias variation under conventional random vibration test is less than 0.10 deg./h.%A novel polarization maintaining fiber (PMF) loop is proposed and used for an interferometric fiber optic gyroscope (FOG). By splicing a conventional PMF loop with two pigtailed polarization beam splitters,polarized light can be guided to propagate along the slow and fast axes of the PMF in sequence to double its effective optical length in the loop. In particular, the resultant optical length in the combined loop is partially self-compensated for some external disturbances, such as transverse strain. Primary experiments on the FOG using the proposed loop demonstrate that the average static bias deviation between -40 and +60 ℃ is less than 0.050 deg./h, and the average bias variation under conventional random vibration test is less than 0.10 deg./h. 9. Dual differential polarimetry. A technique to recover polarimetric information from dual polarization observations CERN Document Server Marti-Vidal, I; Muller, S 2016-01-01 Current mm/submm interferometers, like the Atacama Large mm/submm Array (ALMA), use receivers that register the sky signal in a linear polarization basis. In the case of observations performed in full-polarization mode (where the cross-correlations are computed among all the polarization channels) it is possible to reconstruct the full-polarization brightness distribution of the observed sources, as long as a proper calibration of delay offsets and leakage among polarization channels can be performed. Observations of calibrators, preferably with some linear polarization, with a good parallactic angle coverage are usually needed for such a calibration. In principle, dual-polarization observations only allow us to recover the StokesI$intensity distribution of the sources, regardless of the parallactic angle coverage of the observations. In this paper, we present a novel technique of dual differential polarimetry that makes it possible to obtain information related to the full-polarization brightness distribu... 10. A Translational Polarization Rotator CERN Document Server Chuss, David T; Pisano, Giampaolo; Ackiss, Sheridan; U-Yen, Kongpop; Ng, Ming wah 2012-01-01 We explore a free-space polarization modulator in which a variable phase introduction between right- and left-handed circular polarization components is used to rotate the linear polarization of the outgoing beam relative to that of the incoming beam. In this device, the polarization states are separated by a circular polarizer that consists of a quarter-wave plate in combination with a wire grid. A movable mirror is positioned behind and parallel to the circular polarizer. As the polarizer-mirror distance is separated, an incident linear polarization will be rotated through an angle that is proportional to the introduced phase delay. We demonstrate a prototype device that modulates Stokes Q and U over a 20% bandwidth. 11. Polarized Light Corridor Demonstrations. Science.gov (United States) Davies, G. R. 1990-01-01 Eleven demonstrations of light polarization are presented. Each includes a brief description of the apparatus and the effect demonstrated. Illustrated are strain patterns, reflection, scattering, the Faraday Effect, interference, double refraction, the polarizing microscope, and optical activity. (CW) 12. NESDIS VIIRS Polar Winds Data.gov (United States) National Oceanic and Atmospheric Administration, Department of Commerce — This dataset contains the Level 3 Polar Winds Northern and Southern Hemisphere datasets. The Level 3 Polar Winds data from VIIRS for the Arctic and Antarctic from 65... 13. Nucleon polarization in three-body models of polarized \\bbox{^6}Li CERN Document Server Schellingerhout, N W; Coon, S A; Adam, R M 1993-01-01 Just as$^3\\roarrow{\\rm He}$can be approximately characterized as a polarized neutron target, polarized \\Li6D has been advocated as a good {\\em isoscalar} nuclear target for the extraction of the polarized gluon content of the nucleon. The original argument rests upon a presumed alpha + deuteron'' picture of \\Li6, with the polarization of the nucleus carried by the polarization of the deuteron. We have calculated the polarization of the constituents of \\Li6 as a three-body bound state of$\\alpha + n + p$interacting with local potentials fitted to the scattering data. It is necessary to include partial waves up to$j=17/2$(75 channels, or, when including the$T=1$state, 150 channels) in the Faddeev equations before the energy eigenvalue converges. The longitudinal formfactors are then described well by the wave function. Various combinations of$\\alpha$N and NN strong and Coulomb potentials yield a straight line in the charge radius {\\em vs.} energy plane which, unlike those of previous calculations, pas... 14. Three homologous subunits form a high affinity peptide-gated ion channel in Hydra DEFF Research Database (Denmark) Dürrnagel, Stefan; Kuhn, Anne; Tsiairis, Charisios D 2010-01-01 properties, like a low Na(+) selectivity and a low amiloride affinity, that are different from other channels of the DEG/ENaC gene family, suggesting that a component of the native Hydra channel might still be lacking. Here, we report the cloning of a new ion channel subunit from Hydra, HyNaC5. The new......Recently, three ion channel subunits of the degenerin (DEG)/epithelial Na(+) channel (ENaC) gene family have been cloned from the freshwater polyp Hydra magnipapillata, the Hydra Na(+) channels (HyNaCs) 2-4. Two of them, HyNaC2 and HyNaC3, co-assemble to form an ion channel that is gated...... by the neuropeptides Hydra-RFamides I and II. The HyNaC2/3 channel is so far the only cloned ionotropic receptor from cnidarians and, together with the related ionotropic receptor FMRFamide-activated Na(+) channel (FaNaC) from snails, the only known peptide-gated ionotropic receptor. The HyNaC2/3 channel has pore... 15. Inactivation of the Deg protease family in the cyanobacterium Synechocystis sp. PCC 6803 has impact on the outer cell layers. Science.gov (United States) Cheregi, Otilia; Miranda, Hélder; Gröbner, Gerhard; Funk, Christiane 2015-11-01 The serine type Deg/HtrA proteases are distributed in a wide range of organisms from Escherichia coli to humans. The cyanobacterium Synechocystis sp. PCC 6803 possesses three Deg protease orthologues: HtrA, HhoA and HhoB. Previously we compared Synechocystis 6803 wild type cells exposed to mild or severe stress conditions with a mutant lacking all three Deg proteases and demonstrated that stress had strong impact on the proteomes and metabolomes. To identify the biochemical processes, which this protease family is involved in, here we compared Synechocystis sp. PCC 6803 wild type cells with a mutant lacking all three Deg proteases grown under normal growth conditions (30°C and 40 μmol photons m(-2) s(-1)). Deletion of the Deg proteases lead to the down-regulation of proteins related to the biosynthesis of outer cell layers (e.g. the GDP mannose 4,6-dehydratase) and affected protein secretion. During the late growth phase of the culture Deg proteases were found to be secreted to the extracellular medium of the Synechocystis sp. PCC 6803 wild type strain. While cyanobacterial Deg proteases seem to act mainly in the periplasmic space, deletion of the three proteases influences the proteome and metabolome of the whole cell. Impairments in the outer cell layers of the triple mutant might explain the higher sensitivity toward light and oxidative stress, which was observed earlier by Barker and coworkers. Copyright © 2015 Elsevier B.V. All rights reserved. 16. Plasma polarization spectroscopy Energy Technology Data Exchange (ETDEWEB) Fujimoto, Takashi [Department of Engineering Physics and Mechanics, Graduate School of Engineering, Kyoto University, Kyoto (Japan) 2000-03-01 Polarization of radiation emitted from a plasma reflects the anisotropic properties of the plasma, especially the angular anisotropic distribution of electron velocities. Polarization has been observed on impurity ion lines from the WT-3 tokamak and the GAMMA-10 tandem mirror machines. The soft x-ray laser line from the neonlike germanium was also found polarized. (author) 17. Polarity at Many Levels Science.gov (United States) Flannery, Maura C. 2004-01-01 An attempt is made to find how polarity arises and is maintained, which is a central issue in development. It is a fundamental attribute of living things and cellular polarity is also important in the development of multicellular organisms and controversial new work indicates that polarization in mammals may occur much earlier than previously… 18. Geographical Income Polarization DEFF Research Database (Denmark) Azhar, Hussain; Jonassen, Anders Bruun In this paper we estimate the degree, composition and development of geographical income polarization based on data at the individual and municipal level in Denmark from 1984 to 2002. Rising income polarization is reconfirmed when applying new polarization measures, the driving force being greater... 19. Graphing Polar Curves Science.gov (United States) Lawes, Jonathan F. 2013-01-01 Graphing polar curves typically involves a combination of three traditional techniques, all of which can be time-consuming and tedious. However, an alternative method--graphing the polar function on a rectangular plane--simplifies graphing, increases student understanding of the polar coordinate system, and reinforces graphing techniques learned… 20. A Dual Polarized Quasi-Optical SIS Mixer at 550-GHz Science.gov (United States) Chattopadhyay, Goutam; Miller, David; LeDuc, Henry G.; Zmuidzinas, Jonas 2000-01-01 We describe the design, fabrication, and the performance of a low-noise dual-polarized quasi-optical superconductor insulator superconductor (SIS) mixer at 550 GHz. The mixer utilizes a novel cross-slot antenna on a hyperhemispherical substrate lens, two junction tuning circuits, niobium trilayer junctions, and an IF circuit containing a lumped element 180 deg hybrid. The antenna consists of an orthogonal pair of twin-slot antennas, and has four feed points, two for each polarization. Each feed point is coupled to a two-junction SIS mixer. The 180 deg IF hybrid is implemented using a lumped element/microstrip circuit located inside the mixer block. Fourier transform spectrometer (FTS) measurements of the mixer frequency response show good agreement with computer simulations. The measured co-polarized and cross-polarized patterns for both polarizations also agree with the theoretical predictions. The noise performance of the dual-polarized mixer is excellent, giving uncorrected receiver noise temperature of better than 115 K (DSB) at 528 GHz for both the polarizations. 1. Performance study of the gamma-ray bursts polarimeter POLAR Science.gov (United States) Sun, J. C.; Wu, B. B.; Bao, T. W.; Batsch, T.; Bernasconi, T.; Britvitch, I.; Cadoux, F.; Cernuda, I.; Chai, J. Y.; Dong, Y. W.; Gauvin, N.; Hajdas, W.; He, J. J.; Kole, M.; Kong, M. N.; Kong, S. W.; Lechanoine-Leluc, C.; Li, Lu; Liu, J. T.; Liu, X.; Marcinkowski, R.; Orsi, S.; Pohl, M.; Produit, N.; Rapin, D.; Rutczynska, A.; Rybka, D.; Shi, H. L.; Song, L. M.; Szabelski, J.; Wang, R. J.; Wen, X.; Xiao, H. L.; Xiong, S. L.; Xu, H. H.; Xu, M.; Zhang, L.; Zhang, L. Y.; Zhang, S. N.; Zhang, X. F.; Zhang, Y. J.; Zwolinska, A. 2016-07-01 The Gamma-ray Burst Polarimeter-POLAR is a highly sensitive detector which is dedicated to the measurement of GRB's polarization with a large effective detection area and a large field of view (FOV). The optimized performance of POLAR will contribute to the capture and measurement of the transient sources like GRBs and Solar Flares. The detection energy range of POLAR is 50 keV 500 keV, and mainly dominated by the Compton scattering effect. POLAR consists of 25 detector modular units (DMUs), and each DMU is composed of low Z material Plastic Scintillators (PS), multi-anode photomultipliers (MAPMT) and multi-channel ASIC Front-end Electronics (FEE). POLAR experiment is an international collaboration project involving China, Switzerland and Poland, and is expected to be launched in September in 2016 onboard the Chinese space laboratory "Tiangong-2 (TG-2)". With the efforts from the collaborations, POLAR has experienced the Demonstration Model (DM) phase, Engineering and Qualification Model (EQM) phase, Qualification Model (QM) phase, and now a full Flight Model (FM) of POLAR has been constructed. The FM of POLAR has passed the environmental acceptance tests (thermal cycling, vibration, shock and thermal vacuum tests) and experienced the calibration tests with both radioactive sources and 100% polarized Gamma-Ray beam at ESRF after its construction. The design of POLAR, Monte-Carlo simulation analysis, as well as the performance test results will all be introduced in this paper. 2. Wind-tunnel investigation of the flow correction for a model-mounted angle of attack sensor at angles of attack from -10 deg to 110 deg. [Langley 12-foot low speed wind tunnel test Science.gov (United States) Moul, T. M. 1979-01-01 A preliminary wind tunnel investigation was undertaken to determine the flow correction for a vane angle of attack sensor over an angle of attack range from -10 deg to 110 deg. The sensor was mounted ahead of the wing on a 1/5 scale model of a general aviation airplane. It was shown that the flow correction was substantial, reaching about 15 deg at an angle of attack of 90 deg. The flow correction was found to increase as the sensor was moved closer to the wing or closer to the fuselage. The experimentally determined slope of the flow correction versus the measured angle of attack below the stall angle of attack agreed closely with the slope of flight data from a similar full scale airplane. 3. Polarization of the WMAP Point Sources CERN Document Server Lopez-Caniego, M; Gonzalez-Nuevo, J; Lanz, L; Herranz, D; De Zotti, G; Sanz, J L; Argüeso, F 2009-01-01 The detection of polarized sources in the WMAP 5-year data is a very difficult task. The maps are dominated by instrumental noise and only a handful of sources show up as clear peaks in the Q and U maps. Optimal linear filters applied at the position of known bright sources detect with a high level of significance a polarized flux P from many more sources, but estimates of P are liable to biases. Using a new technique, named the "filtered fusion technique", we have detected in polarization, with a significance level greater than 99.99% in at least one WMAP channel, 22 objects, 5 of which, however, do not have a plausible low radio frequency counterpart and are therefore doubtful. Estimated polarized fluxes P < 400 mJy at 23 GHz were found to be severely affected by the Eddington bias. The corresponding polarized flux limit for Planck/LFI at 30 GHz, obtained via realistic simulations, is 300 mJy. We have also obtained statistical estimates of, or upper limits to the mean polarization degrees of bright WMAP ... 4. Coherent optical control of polarization with a critical metasurface Science.gov (United States) Kang, Ming; Chong, Y. D. 2015-10-01 We present a mechanism by which a metamaterial surface, or metasurface, can act as an ideal phase-controlled rotatable linear polarizer. Using coupled-mode theory and the idea of coherent perfect absorption into auxiliary polarization channels, we show how the losses and near-field couplings on the metasurface can be balanced so that, with equal-power linearly polarized beams incident on each side, varying the relative phase rotates the polarization angles of the output beams while maintaining zero ellipticity. The system can be described by a non-Hermitian effective Hamiltonian which is parity-time (P T ) symmetric, although there is no actual gain present; perfect polarization conversion occurs at the eigenfrequencies of this Hamiltonian, and the polarization rotating behavior occurs at the critical point of its P T -breaking transition. 5. Coherent optical communication using polarization multiple-input-multiple-output. Science.gov (United States) Han, Yan; Li, Guifang 2005-09-19 Polarization-division multiplexed (PDM) optical signals can potentially be demultiplexed by coherent detection and digital signal processing without using optical dynamic polarization control at the receiver. In this paper, we show that optical communications using PDM is analogous to wireless communications using multiple-input-multiple-output (MIMO) antennae and thus algorithms for channel estimation in wireless MIMO can be ready applied to optical polarization MIMO (PMIMO). Combined with frequency offset and phase estimation algorithms, simulations show that PDM quadrature phase-shift keying signals can be coherently detected by the proposed scheme using commercial semiconductor lasers while no optical phase locking and polarization control are required. This analogy further suggests the potential application of space-time coding in wireless communications to optical polarization MIMO systems and relates the problem of polarization-mode dispersion in fiber transmission to the multi-path propagation in wireless communications. 6. The Physics of Polarization Science.gov (United States) Landi Degl'Innocenti, Egidio 2015-10-01 The introductory lecture that has been delivered at this Symposium is a condensed version of an extended course held by the author at the XII Canary Island Winter School from November 13 to November 21, 2000. The full series of lectures can be found in Landi Degl'Innocenti (2002). The original reference is organized in 20 Sections that are here itemized: 1. Introduction, 2. Description of polarized radiation, 3. Polarization and optical devices: Jones calculus and Muller matrices, 4. The Fresnel equations, 5. Dichroism and anomalous dispersion, 6. Polarization in everyday life, 7. Polarization due to radiating charges, 8. The linear antenna, 9. Thomson scattering, 10. Rayleigh scattering, 11. A digression on Mie scattering, 12. Bremsstrahlung radiation, 13. Cyclotron radiation, 14. Synchrotron radiation, 15. Polarization in spectral lines, 16. Density matrix and atomic polarization, 17. Radiative transfer and statistical equilibrium equations, 18. The amplification condition in polarized radiative transfer, and 19. Coupling radiative transfer and statistical equilibrium equations. 7. Polarization effects. Volume 2 Energy Technology Data Exchange (ETDEWEB) Courant, E. 1981-01-01 The use of polarized proton beams in ISABELLE is important for several general reasons: (1) With a single longitudinally polarized proton beam, effects involving parity violation can be identified and hence processes involving weak interactions can be separated from those involving strong and electromagnetic interactions. (2) Spin effects are important in the strong interactions and can be useful for testing QCD. The technique for obtaining polarized proton beams in ISABELLE appears promising, particularly in view of the present development of a polarized proton beam for the AGS. Projections for the luminosity in ISABELLE for collisions of polarized protons - one or both beams polarized with longitudinal or transverse polarization - range from 1/100 to 1 times the luminosity for unpolarized protons. 8. Lampi di possibili tempeste. Arte e letteratura nel Foucault degli anni Settanta. Directory of Open Access Journals (Sweden) Diego Melegari 2012-12-01 Full Text Available Dopo avere rivestito un ruolo fondamentale negli scritti archeologici degli anni Sessanta, i riferimenti a pittura e letteratura sembrano scomparire dalla riflessione foucaultiana. Si tratta, in realtà, di uno slittamento dalle opere maggiori a brevi interventi in cui ad emergere è soprattutto il coinvolgimento soggettivo di Foucault. Questo passaggio, però, non è che un aspetto di una radicale riformulazione della funzione storico-ontologica precedentemente attribuita a letteratura e arte in favore di forme di esperienza non-strategica, dunque irriducibile al nesso potere-resistenza, e allo stesso tempo riattivabile come critica, anche politica, nel rapporto tra tempo storico e trasformazione della soggettività. 9. Il problema dei futuri contingenti e la semantica relativista degli enunciati al futuro Directory of Open Access Journals (Sweden) Diana Mazzarella 2011-11-01 Full Text Available L'articolo si propone tre obiettivi. In primo luogo, introdurre al problema dei futuri contingenti, evidenziando i limiti di un'analisi semantica standard degli enunciati al futuro. In secondo luogo, presentare le strategie di implementazione della semantica standard finalizzate ad un approccio semantico di tipo relativistico, distinguendo tra relativismo moderato e relativismo radicale. In terzo luogo, presentare il tentativo di risoluzione del problema in questione attraverso l'adozione di una prospettiva semantica relativista, con esplicito riferimento alle riflessioni di MacFarlane. 10. L’avventura del teatro granducale degli Uffizi (1586-1637 Directory of Open Access Journals (Sweden) Anna Maria Testaverde 2016-06-01 Full Text Available The essay reconstructs the chronological details of the construction and disposal of the Teatro degli Uffizi. An extensive unpublished documentation, and a newly discovered plan of the theatre in the Archivio di Stato di Modena, bring to light hitherto unknown persons and situations. The study anticipates reflections and proposals for a structural solution that would modify the model proposed in 1975 by Ludovico Zorzi. As a foundation of these new hypotheses, the essay offers a re-reading of the Vitruvius’s theories on which the florentine highly specialised technical skills were based on. 11. “Il coraggio di essere giovani”: un progetto sulla Fgci di Modena degli anni Ottanta Directory of Open Access Journals (Sweden) Claudia Capelli 2015-12-01 Full Text Available L’Istituto Storico di Modena promuove una ricerca sulla Fgci di Modena degli anni Ottanta con l'obiettivo di cominciare a riflettere sul decennio conclusivo della storia del Pci, un periodo di crisi profonda della cultura politica comunista che la storiografia non ha ancora affrontato in modo sistematico. Il caso modenese permette di osservare alcuni importanti elementi dell'esperienza della Fgci “rifondata”, come il nuovo approccio alla comunicazione politica e il rapporto con i movimenti sociali. 12. Fattori di crescita e recettori tirosin chinasici nelle neoplasie e displasie degli animali domestici OpenAIRE Muscatello, Luisa Vera 2016-01-01 La perdita della comunicazione cellulare può portare ad una crescita deregolata e dunque alla trasformazione neoplastica. Gli scopi dello studio di dottorato sono stati di individuare il rapporto funzionale di alcuni fattori di crescita (FC) e dei loro recettori (RTC) in tipi di neoplasie e displasie degli animali domestici, quali: 1. Amplificazione del proto-oncogene ERBB2 e sovra-espressione del RTC erb-b2. in tumori mammari della gatta. 2. Espressione di erb-b2, di recettori ormonal... 13. A catalogue of galaxies behind the southern Milky Way. - II. The Crux and Great Attractor regions (l = 289deg - 338deg) CERN Document Server Woudt, P A; Woudt, Patrick A.; Kraan-Korteweg, Renee C. 2001-01-01 In this second paper of the catalogue series of galaxies behind the southern Milky Way, we report on the deep optical galaxy search in the Crux region (289deg = 0.2 arcmin were identified in this ~850 square degree area: 3759 galaxies in the Crux region and 4423 galaxies in the Great Attractor region. Of the 8182 galaxies, 229 (2.8%) were catalogued before in the optical (3 in radio) and 251 galaxies have a reliable (159), or likely (92) cross-identification in the IRAS Point Source Catalogue (3.1%). A number of prominent overdensities and filaments of galaxies are identified. They are not correlated with the Galactic foreground extinction and hence indicative of extragalactic large-scale structures. Redshifts obtained at the South African Astronomical Observatory (SAAO) for 518 of the newly catalogued galaxies in the Crux and Great Attractor regions (Fairall et al. 1998; Woudt et al. 1999) confirm distinct voids and clusters in the area here surveyed. With this optical galaxy search, we have reduced the widt... 14. Polarity inversion in polar-nonpolar-polar heterostructures. Science.gov (United States) Cho, S; Youn, S J; Kim, Y; DiVenere, A; Wong, G K; Freeman, A J; Ketterson, J B 2001-09-17 We have observed an epilayer-thickness-dependent polarity inversion for the growth of CdTe on Sb(Bi)/CdTe(111)B. For films with Sb(Bi) thicknesses of less than 40 A (15 A), the CdTe layer shows a B (Te-terminated) face, but it switches to an A (Cd-terminated) face for thicker layers. On the other hand, a CdTe layer grown on Bi(Sb)/CdTe(111)A always shows the A face regardless of Sb or Bi layer thicknesses. In order to address the observations we have performed ab initio calculations, which suggest that the polarity of a polar material on a nonpolar one results from the binding energy difference between the two possible surface configurations. 15. MODIS/Terra 8-Day Clear Sky Radiance Bias Daily L3 Global 1Deg Zonal Bands V006 Data.gov (United States) National Aeronautics and Space Administration — MODIS 8-day clear-sky radiance bias (observed - calculated) statistics are provided for 1Deg latitudinal zones and selected thermal bands. Separation by day and... 16. MODIS/Aqua 8-Day Clear Sky Radiance Bias Daily L3 Global 1Deg Zonal Bands V006 Data.gov (United States) National Aeronautics and Space Administration — MODIS 8-day clear-sky radiance bias (observed - calculated) statistics are provided for 1Deg latitudinal zones and selected thermal bands. Separation by day and... 17. Polarization gating based on Mueller matrices. Science.gov (United States) Lizana, Angel; Van Eeckhout, Albert; Adamczyk, Kamil; Rodríguez, Carla; Escalera, Juan Carlos; Garcia-Caurel, Enric; Moreno, Ignacio; Campos, Juan 2017-05-01 We present mathematical formulas generalizing polarization gating (PG) techniques. PG refers to a collection of imaging methods based on the combination of different controlled polarization channels. In particular, we show how using the measured Mueller matrix (MM) of a sample, a widespread number of PG configurations can be evaluated just from analytical expressions based on the MM coefficients. We also show the interest of controlling the helicity of the states of polarization used for PG-based metrology, as this parameter has an impact in the image contrast of samples. In addition, we highlight the interest of combining PG techniques with tools of data analysis related to the MM formalism, such as the well-known MM decompositions. The method discussed in this work is illustrated with the results of polarimetric measurements done on artificial phantoms and real ex-vivo tissues. 18. Recent gluon polarization results from COMPASS CERN Document Server Quintans, C 2007-01-01 One of the main goals of the COMPASS experiment at CERN is the measurement of the gluon polarization in the nucleon,$\\Delta G$, by scattering of 160 GeV/c polarized muons on a polarized$^{6}$LiD target. This quantity is experimentally accessible via the photon-gluon fusion process, tagged either by charmed mesons production or by high$p_{T}$hadron pairs production. The status of these two analyses is presented. Preliminary results obtained from the 2002/03 data samples on the$D^{0}$and the$D^{*\\pm}$channels are shown. The high$p_{T}$hadron pairs, produced at$Q^{2}\\lessgtr$1 (GeV/c)$^{2}$, were also analysed, and the measured$\\Delta G/Gvalues are presented here. 19. Polar ocean ecosystems in a changing world Science.gov (United States) Smetacek, Victor; Nicol, Stephen 2005-09-01 Polar organisms have adapted their seasonal cycles to the dynamic interface between ice and water. This interface ranges from the micrometre-sized brine channels within sea ice to the planetary-scale advance and retreat of sea ice. Polar marine ecosystems are particularly sensitive to climate change because small temperature differences can have large effects on the extent and thickness of sea ice. Little is known about the interactions between large, long-lived organisms and their planktonic food supply. Disentangling the effects of human exploitation of upper trophic levels from basin-wide, decade-scale climate cycles to identify long-term, global trends is a daunting challenge facing polar bio-oceanography. 20. Dual-Polarized Indoor Propagation at 26 GHz DEFF Research Database (Denmark) Nielsen, Jesper Ødum; Pedersen, Gert F. 2016-01-01 This work presents results based on wideband radio channel measurements at 26 GHz. Three widely different indoor environments were measured; a cluttered laboratory, a corridor with a bend, and a large entrance hall. Power angular spectra were obtained for both vertical polarization (VP) and horiz......This work presents results based on wideband radio channel measurements at 26 GHz. Three widely different indoor environments were measured; a cluttered laboratory, a corridor with a bend, and a large entrance hall. Power angular spectra were obtained for both vertical polarization (VP......) and horizontal polarization (HP) at many different Rx locations, using both VP or HP for the fixed Tx. The results show that a quite rich channel may exist with several propagation paths. Further, coupling between the VP and HP was found in a non line of sight (NLOS) scenario.... 1. Device For Viewing Polarized Light Science.gov (United States) Noever, David A. 1995-01-01 Technique for detection of polarized light based on observation of scene through two stacked polarizing disks. No need to rotate polarizers to create flicker indicative of polarization. Implemented by relatively simple, lightweight apparatus. Polarization seen as bow-tie rainbow pattern. Advantageous for detecting polarization in variety of meteorological, geological, astronomical, and related applications. 2. Time-dependent Creep Crack Growth Behavior of Alloy 617 at 800 .deg. C Energy Technology Data Exchange (ETDEWEB) Kim, Woogon; Kim, Minhwan; Kim, Yongwan [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of); Park, Jaeyoung; Ekaputra, I. M. W. [Pukyong National Univ., Busan (Korea, Republic of) 2014-05-15 The VHTR components are designed to be used for a 60 year lifetime at a high temperature, the creep crack growth (CCG) behavior as well as creep behavior is very important for the design application due to creep damage during the long service life at elevated temperatures. Alloy 617 is a major candidate material for the IHX component. The design of the component, which will operate well into the creep range, will require a good understanding of creep crack growth deformation. Efforts are now being undertaken in the Generation IV program to provide data needed for the design and licensing of the nuclear plants, and with this goal in mind, to meet the needs of the conceptual designers of the VHTR system, 'Gen-IV Materials Handbook DB' is being established through an international collaboration program of several GIF (Gen-IV Forum) countries. CCG experimental data should be prepared to 'the Gen-IV Materials Handbook DB' website, because the CCG data for Alloy 617 are not available in the ASME design code. In this paper, experimental creep crack growth data were obtained through a series of CCG tests performed under different applied loads at 800 .deg. C. The CCG behavior was characterized in terms of the C{sup *} fracture mechanics parameter, and the CCGR equation for Alloy 617 was presented. Experimental CCG data of Alloy 617 were obtained from a series of creep crack growth tests under different applied loads at 800 .deg. C. 3. On th meridional surface profile of the Gulf Stream at 55 deg W Science.gov (United States) Hallock, Zachariah R.; Teague, William J. 1995-01-01 Nine-month records from nine inverted echo sounders (IESs) are analyzed to describe the mean baroclinic Gulf Stream at 55 deg W. IES acoustic travel times are converted to thermocline depth which is optimally interpolated. Kinematic and dynamic parameters (Gulf Stream meridional position, velocity, and vorticity) are calculated. Primary Gulf Stream variabiltiy is attributed to meandering and and changes in direction. A mean, stream-coordinate (relative to Gulf Stream instantaneous position and direction) meridional profile is derived and compared with results presented by other investigators. The mean velocity is estimated at 0.84 m/s directed 14 deg to the right eastward, and the thermocline (12 c) drops 657 m (north to south), corresponding to a baroclinic rise of the surface of 0.87 m. The effect of Gulf Stream curvature on temporal mean profiles is found to be unimportant and of minimal importance overall. The derived, downstream current profile is well represented by a Gaussian function and is about 190 km wide where it crosses zero. Surface baroclinic transport is estimated to be 8.5 x 10(exp 4) sq m/s, and maximum shear (flanking the maximum) is 1.2 x 10(exp -5). Results compare well with other in situ observational results from the same time period. On the other hand, analyses (by others) of concurrent satellite altimetry (Geosat) suggest a considerable narrower, more intense mean Gulf Stream. 4. Selecting Eco-Friendly Thermal Systems for the “Vittoriale Degli Italiani” Historic Museum Building Directory of Open Access Journals (Sweden) Davide Astiaso Garcia 2015-09-01 Full Text Available Thermal systems installed in museums should guarantee the maintenance of the optimal hygrothermal parameters ranges for the conservation of their collection materials. Considering the preservation of historic buildings, according to their historical and landscaping constraints, not all the thermal system typologies could be installed in these buildings’ typologies. Therefore, the main aim of this paper is to present some indications for the choice of the best thermal system solutions for a considered historic museum building, called Vittoriale degli Italiani, in the north of Italy, taking into account their installation feasibility and their related environmental impacts. The methodology includes a monitoring of the current hygrothermal parameters as well as the assessment of design heat and cooling loads related to the maintenance of the optimal hygrothermal parameters ranges for the conservation of collection materials. In addition, a Life Cycle Assessment (LCA of each selected system typology is considered for highlighting the most eco-friendly solution among the suitable ones. The obtained results highlights the feasible thermal system solutions able to maintain the hygrothermal parameters between the optimal ranges with a lower environmental impact in the Vittoriale degli Italiani historic museum building. 5. The segregation of starless and protostellar clumps in the Hi-GAL l=224deg region CERN Document Server Olmi, L; Elia, D; Jones, P 2016-01-01 Stars form in dense, dusty structures, which are embedded in larger clumps of molecular clouds often showing a clear filamentary structure on large scales (> 1pc). One of the best-studied regions in the Hi-GAL survey can be observed toward the l=224deg field. Here, a filamentary region has been studied and it has been found that protostellar clumps are mostly located along the main filament, whereas starless clumps are detected off this filament and are instead found on secondary, less prominent filaments. We want to investigate this segregation effect and how it may affect the clumps properties. We mapped the 12CO(1-0) line and its main three isotopologues toward the two most prominent filaments observed toward the l=224deg field using the Mopra radio telescope, in order to set observational constraints on the dynamics of these structures and the associated starless and protostellar clumps. Compared to the starless clumps, the protostellar clumps are more luminous, more turbulent and lie in regions where the... 6. Corrosion of stainless steels in lead-bismuth eutectic up to 600 deg. C Energy Technology Data Exchange (ETDEWEB) Soler, L. [Dpto. Fision Nuclear, CIEMAT, Edificio 30, Avda. Complutense 22, Madrid 28040 (Spain)]. E-mail: laura.soler@ciemat.es; Martin, F.J. [Dpto. Fision Nuclear, CIEMAT, Edificio 30, Avda. Complutense 22, Madrid 28040 (Spain); Hernandez, F. [Dpto. Fision Nuclear, CIEMAT, Edificio 30, Avda. Complutense 22, Madrid 28040 (Spain); Gomez-Briceno, D. [Dpto. Fision Nuclear, CIEMAT, Edificio 30, Avda. Complutense 22, Madrid 28040 (Spain) 2004-11-01 An experimental program has been carried out to understand the differences in the corrosion behaviour between different stainless steels: the austenitic steels 304L and 316L, the martensitic steels F82Hmod, T91 and EM10, and the low alloy steel P22. The influence of oxygen level in Pb-Bi, temperature and exposure time is studied. At 600 deg. C, the martensitic steels and the P22 steel exhibit thick oxide scales that grow with time, following a linear law for the wet environment and a parabolic law for the dry one. The austenitic stainless steels show a better corrosion behaviour, especially AISI 304L. Under reducing conditions, the steels exhibit dissolution, more severe for the austenitic stainless steels. At 450 deg. C, all the materials show an acceptable behaviour provided a sufficient oxygen level in the Pb-Bi. At reducing conditions, the martensitic steels and the P22 steel have a good corrosion resistance, while the austenitic steels exhibit already dissolution at the longer exposures. 7. Searching for dark matter halos in the Suprime-Cam 2 sq deg field CERN Document Server Miyazaki, S; Shimasaku, K; Furusawa, H; Doi, M; Hamabe, M; Imi, K; Kimura, M; Komiyama, Yu; Nakata, F; Okada, N; Okamura, S; Ouchi, M; Sekiguchi, M; Yagi, M; Yasuda, N 2002-01-01 We report the first result of weak gravitational lensing survey on a 2.1 sq deg Rc-band image taken with a wide field camera (Suprime-Cam) on the prime focus of 8.2 m Subaru Telescope. The weak lensing mass reconstruction is applied to the data to search for dark matter halos of cluster scale; M >= 10^14 solar mass. The reconstructed convergence field is divided by 1-sigma noise to obtain the signal-to-noise ratio map (S/N-map) of the detection. Local maxima and minima are searched on the S/N-map and the probability distribution function (PDF) of the peaks are created to compare with model predictions. We found excess over noise PDF created from the randomized realization on both positive and negative sides. Negative peaks imply the presence of voids in the dark matter distribution and this is the first report of the detection. Positive peaks, on the other hand, represent the dark matter halos and the number count of the halos on the 2.1 sq deg image is 4.9 +- 2.3 for S/N > 5 where the Gaussian smoothing radi... 8. La partecipazione degli enti ecclesiastici cattolici alle società di capitali Directory of Open Access Journals (Sweden) Ludovica Decimo 2015-01-01 Full Text Available SOMMARIO: 1. Valutazioni preliminari e nuove prospettive d’indagine – 2. L’attività negoziale degli enti ecclesiastici: le autorizzazioni canoniche – 3. La rilevanza dei controlli canonici nell’ordinamento italiano – 4. L’omissione delle autorizzazioni canoniche nella fase costitutiva della s.p.a. e della s.r.l. – 5. I controlli canonici e la circolazione delle azioni della s.p.a. – 6. La cessione di quote di s.r.l. in assenza delle autorizzazioni canoniche – 7. L’invalidità delle delibere peggiorative della situazione patrimoniale dell’ente ecclesiastico (l’aumento reale di capitale, la fusione, la trasformazione regressiva – 8. La partecipazione dell’ente ecclesiastico socio all’assemblea societaria: brevi cenni sulla rappresentanza delle persone giuridiche canoniche – 9. Il falsus procurator dell’ente ecclesiastico socio in assemblea ordinaria – 10. Ipotesi concrete di partecipazione degli enti ecclesiastici cattolici alle società di capitali, in particolare, alle s.r.l. – 11. L’assenza delle autorizzazioni canoniche nell’atto costitutivo della società “Tabor S.r.l.” – 12. L’errata individuazione delle autorizzazioni canoniche necessarie nell’atto costitutivo della società “G.M.G. E.R. Rinnovabili S.r.l. Unipersonale”. 9. InAs 2DEGs:What's the g-factor? Science.gov (United States) McCombe, B. D.; Pakmehr, Mehdi; Khaetskii, A.; Chiatti, Olivio; Fischer, S. F.; Buchholz, S.; Heyn, C.; Hansen, W.; Cahay, M.; Newrock, R. S.; Bandari, Nikhil 2014-03-01 Interest in spin-orbit effects in semiconductors has led us to study the electron g-factor in quasi-2DEG InAs samples. We have made magneto-transport and -photoresponse (PR) measurements on InAs QW structures in magnetic fields up to 10 T. THz cyclotron resonance (CR) is manifested in PR as a resonant envelope of the amplitude of quantum oscillations, which show clear spin-splitting (for lower mobility samples) down 4T, while direct R_xx measurements show no spin-splitting up to 9T. R_xx oscillations in a higher mobility sample show well-resolved spin-splittings over a range of fields as does the PR. We have simulated the data with a theoretical expression for 2DEG SdH oscillations (coupled with CR resonant carrier heating for the PR) and extracted g-factors from fits. We also used a different (commonly used) method, SdH oscillations vs. tilt angle of the field to extract g-factors from the angle at which the SdH frequency doubles. We find very large g-factors from fits to R_xx and PR (14 - 20), but g-factors 2-3 times smaller for these same samples from tilted field experiments (close to estimated band g-factors). These results are discussed in terms of exchange effects. Support: NSF DMR 1008138 (Buffalo); NSF ECCE 1028483(Cincinnati); DFG Fi932/4-1(Berlin). 10. Formation scenarios for the young stellar associations between galactic longitudes l = 280-360 deg CERN Document Server Sartori, M J; Dias, W S; Sartori, Marilia J.; Lepine, Jacques R. D.; Dias, Wilton S. 2003-01-01 We investigate the spatial distribution, the space velocities and age distribution of the pre-main sequence (PMS) stars belonging to Ophiuchus, Lupus and Chamaeleon star-forming regions (SFRs), and of the young early-type star members of the Scorpius-Centaurus OB association. These young stellar associations extend over the galactic longitude range from 280 deg. to 360 deg., and are at a distance interval of around 100 and 200 pc. The study is based on a compilation of distances, proper motions and radial velocities from the literature for the kinematic properties, and of basic stellar data for the construction of Hertzsprung-Russel diagrams. Although there was no well-known OB association in Chamaeleon, the distances and the proper motions of a group of 21 B- and A-type stars, taken from the Hipparcos Catalogue, lead us to propose that they form a young association. We show that the young early-type stars of the OB associations and the PMS stars of the SFRs follow a similar spatial distribution, i.e., there ... 11. L’evoluzione cerebrale degli ominidi: quando antropologia, paleontologia e psicologia convergono su una domanda Directory of Open Access Journals (Sweden) Christian Agrillo 2008-06-01 Full Text Available Lo studio dell’evoluzione cerebrale degli ominidi rappresenta uno dei punti di arrivo di diverse discipline che pongono l’essere umano al centro del proprio interesse: la paleontologia, che si serve dei reperti fossili per evincere la storia evolutiva del cranio e del cervello; l’antropologia, che utilizza utensili e tradizioni di culture differenti per accostarsi anche allo studio della cognizione umana e infine la psicologia che - attraverso il confronto con le capacità cognitive di altri primati - si propone di indagare l’unicità o meno delle potenzialità mentali di cui disponiamo, alla ricerca di elementi condivisi dai nostri parenti più prossimi evolutisi in una diversa regione del continente africano.Comprendere quali siano state le cause che hanno diversificato il cammino dell’Uomo da quello degli altri primati significa, in primo luogo, capire quali fattori costituiscano effettivamente una prerogativa della specie umana, cosa ci differenzia dalle scimmie e come questo possa essere avvenuto. Diverse teorie sono state ipotizzate al riguardo: il presente lavoro riassume le principali visioni correnti, ponendo l’una di fronte l’altra e suggerendo come la mente umana possa essersi evoluta in seguito alla compresenza di più fattori che hanno spinto verso la medesima direzione, a differenza di quanto avvenuto per le scimmie antropomorfe. 12. Interplay of Rashba and sp-d exchange couplings in magnetic 2DEGs Science.gov (United States) Mireles, Francisco; Freire, Henrique H. P.; Egues, J. Carlos 2006-03-01 In diluted magnetic semiconductor (DMS) quantum wells the sp-d exchange interaction between the itinerant conduction electrons in the well and the localized electrons in the d orbitals of the Mn impurities gives rise to interesting spin-dependent physics [1]. Recently, the interplay of the Rashba spin-orbit and the sp-d exchange interactions in Mn-based wells has been recognized via Shubnikov-de-Haas measurements [2]. While the Rashba spin-orbit has been extensively studied in non-magnetic 2DEGs, its role in DMS systems with a competing sp-d exchange interaction has not yet been addressed theoretically. In this work we present a k.p derivation of an effective Hamiltonian for a Mn-based quantum well with competing Rashba and sp-d interactions, and show numerical results for the magnetoresistance ρxx of typical magnetic 2DEGs using our effective Hamiltonian model. Our results shows interesting beating patterns of the ρxx as a function of the temperature and carrier density which suggests a significant interplay between the spin-orbit and sp-d exchange interactions, as a recent experiment observes [2]. [1] J. C. Egues, PRL 78, 4578 (1998); H. J. P. Freire and J. C. Egues, cond-mat/0412491. [2] Y. S. Gui et al. EPL. 65, 393 (2004). 13. The p-wave superconductivity in the presence of Rashba interaction in 2DEG. Science.gov (United States) Weng, Ke-Chuan; Hu, C D 2016-07-26 We investigate the effect of the Rashba interaction on two dimensional superconductivity. The presence of the Rashba interaction lifts the spin degeneracy and gives rise to the spectrum of two bands. There are intraband and interband pairs scattering which result in the coupled gap equations. We find that there are isotropic and anisotropic components in the gap function. The latter has the form of cos φk where . The former is suppressed because the intraband and the interband scatterings nearly cancel each other. Hence, -the system should exhibit the p-wave superconductivity. We perform a detailed study of electron-phonon interaction for 2DEG and find that, if only normal processes are considered, the effective coupling strength constant of this new superconductivity is about one-half of the s-wave case in the ordinary 2DEG because of the angular average of the additional in the anisotropic gap function. By taking into account of Umklapp processes, we find they are the major contribution in the electron-phonon coupling in superconductivity and enhance the transition temperature Tc. 14. The lizard celestial compass detects linearly polarized light in the blue. Science.gov (United States) Beltrami, Giulia; Parretta, Antonio; Petrucci, Ferruccio; Buttini, Paola; Bertolucci, Cristiano; Foà, Augusto 2012-09-15 The present study first examined whether ruin lizards, Podarcis sicula, are able to orientate using plane-polarized light produced by an LCD screen. Ruin lizards were trained and tested indoors, inside a hexagonal Morris water maze positioned under an LCD screen producing white polarized light with a single E-vector, which provided an axial cue. White polarized light did not include wavelengths in the UV. Lizards orientated correctly either when tested with E-vector parallel to the training axis or after 90 deg rotation of the E-vector direction, thus validating the apparatus. Further experiments examined whether there is a preferential region of the light spectrum to perceive the E-vector direction of polarized light. For this purpose, lizards reaching learning criteria under white polarized light were subdivided into four experimental groups. Each group was tested for orientation under a different spectrum of plane-polarized light (red, green, cyan and blue) with equalized photon flux density. Lizards tested under blue polarized light orientated correctly, whereas lizards tested under red polarized light were completely disoriented. Green polarized light was barely discernible by lizards, and thus insufficient for a correct functioning of their compass. When exposed to cyan polarized light, lizard orientation performances were optimal, indistinguishable from lizards detecting blue polarized light. Overall, the present results demonstrate that perception of linear polarization in the blue is necessary - and sufficient - for a proper functioning of the sky polarization compass of ruin lizards. This may be adaptively important, as detection of polarized light in the blue improves functioning of the polarization compass under cloudy skies, i.e. when the alternative celestial compass based on detection of the sun disk is rendered useless because the sun is obscured by clouds. 15. Neutron Polarization Measurements with a 3He Spin Filter for the NPDGamma Experiment Science.gov (United States) Musgrave, Matthew 2012-10-01 The Fundamental Neutron Physics Beamline (FNPB) at the Spallation Neutron Source (SNS) provides a pulsed beam of polarized cold neutrons for the NPDGamma experiment which intends to measure the parity violating asymmetry in the emitted gamma rays from the capture of polarized neutrons on protons in a para-hydrogen target. The neutrons are polarized by a multi-channel super mirror polarizer, and the polarization of each neutron pulse can be flipped with an RF spin rotator. The accuracy of the NPDGamma experiment and various commissioning experiments is dependent on the polarization of the neutron beam and the efficiency of the RF spin rotator. These parameters are measured with a polarized 3He spin filter at multiple points in the beam cross section and with multiple 3He polarizations. The measured neutron polarization is compared to a McStas model to validate our results and our beam averaging technique. The analysis methods, background effects, and results will be discussed. 16. Polar varieties revisited OpenAIRE Piene, Ragni 2016-01-01 We recall the definition of classical polar varieties, as well as those of affine and projective reciprocal polar varieties. The latter are defined with respect to a non-degenerate quadric, which gives us a notion of orthogonality. In particular we relate the reciprocal polar varieties to the "Euclidean geometry" in projective space. The Euclidean distance degree and the degree of the focal loci can be expressed in terms of the ranks, i.e., the degrees of the classical polar varieties, and he... 17. Polarization at SLC Energy Technology Data Exchange (ETDEWEB) Swartz, M.L. 1988-07-01 The SLAC Linear Collider has been designed to readily accommodate polarized electron beams. Considerable effort has been made to implement a polarized source, a spin rotation system, and a system to monitor the beam polarization. Nearly all major components have been fabricated. At the current time, several source and polarimeter components have been installed. The installation and commissioning of the entire system will take place during available machine shutdown periods as the commissioning of SLC progresses. It is expected that a beam polarization of 45% will be achieved with no loss in luminosity. 13 refs., 15 figs. 18. Polarized negative ions Energy Technology Data Exchange (ETDEWEB) Haeberli, W. 1981-04-01 This paper presents a survey of methods, commonly in use or under development, to produce beams of polarized negative ions for injection into accelerators. A short summary recalls how the hyperfine interaction is used to obtain nuclear polarization in beams of atoms. Atomic-beam sources for light ions are discussed. If the best presently known techniques are incorporated in all stages of the source, polarized H/sup -/ and D/sup -/ beams in excess of 10 ..mu..A can probably be achieved. Production of polarized ions from fast (keV) beams of polarized atoms is treated separately for atoms in the H(25) excited state (Lamb-Shift source) and atoms in the H(1S) ground state. The negative ion beam from Lamb-Shift sources has reached a plateau just above 1 ..mu..A, but this beam current is adequate for many applications and the somewhat lower beam current is compensated by other desirable characteristics. Sources using fast polarized ground state atoms are in a stage of intense development. The next sections summarize production of polarized heavy ions by the atomic beam method, which is well established, and by optical pumping, which has recently been demonstrated to yield very large nuclear polarization. A short discussion of proposed ion sources for polarized /sup 3/He/sup -/ ions is followed by some concluding remarks. 19. Performance of polar codes for quantum and private classical communication CERN Document Server Dutton, Zachary; Wilde, Mark M 2012-01-01 We analyze the practical performance of quantum polar codes, by computing rigorous bounds on block error probability and by numerically simulating them. We evaluate our bounds for quantum erasure channels with coding block lengths between 2^10 and 2^20, and we report the results of simulations for quantum erasure channels, quantum depolarizing channels, and "BB84" channels with coding block lengths up to N = 1024. For quantum erasure channels, we observe that high quantum data rates can be achieved for block error rates less than 10^(-4) and that somewhat lower quantum data rates can be achieved for quantum depolarizing and BB84 channels. Our results here also serve as bounds for and simulations of private classical data transmission over these channels, essentially due to Renes' duality bounds for privacy amplification and classical data transmission of complementary observables. Future work might be able to improve upon our numerical results for quantum depolarizing and BB84 channels by employing a polar co... 20. A candidate polar-ring galaxy in the Subaru Deep Field CERN Document Server Finkelman, Ido; Brosch, Noah 2010-01-01 We discuss the properties of an object in the Subaru Deep Field (SDF) classified as a galaxy in on-line data bases and revealed on the Subaru images as a genuine polar-ring galaxy (PRG) candidate. We analyse available photometric data and conclude that this object consists of a >5 Gyr old early-type central body surrounded by a faint, narrow inner ring tilted at a ~25 deg angle relative to the polar axis of the host galaxy. The halo surrounding the main stellar body exhibits a diversity of spatially extended stellar features of low surface brightness, including a faint asymmetric stellar cloud and two prominent loops. These faint features, together with the unperturbed morphology of the central host, are clear signs of a recent coalescence of two highly unequal mass galaxies, most likely a pre-existing early-type galaxy and a close-by gas-rich dwarf galaxy. The presumed stellar remnants observed near the edges of the ring, including possibly the surviving captured companion itself, indicate that the merger is... 1. The Q/U Imaging ExperimenT: Polarization Measurements of the Galactic Plane at 43 and 95 GHz CERN Document Server Ruud, T M; Wehus, I K; Vidal, M; Araujo, D; Bischoff, C; Buder, I; Chinone, Y; Cleary, K; Dumoulin, R N; Kusaka, A; Monsalve, R; Naess, S K; Newburgh, L B; Reeves, R A; Zwart, J T L; Bronfman, L; Davies, R D; Davis, R; Dickinson, C; Eriksen, H K; Gaier, T; Gundersen, J O; Hasegawa, M; Hazumi, M; Huffenberger, K M; Jones, M E; Lawrence, C R; Leitch, E M; Limon, M; Miller, A D; Pearson, T J; Piccirillo, L; Radford, S J E; Readhead, A C S; Samtleben, D; Seiffert, M; Shepherd, M C; Staggs, S T; Tajima, O; Thompson, K L 2015-01-01 We present polarization observations of two Galactic plane fields centered on Galactic coordinates (l,b)=(0 deg,0 deg) and (329 deg, 0 deg) at Q- (43 GHz) and W-band (95 GHz), covering between 301 and 539 square degrees depending on frequency and field. These measurements were made with the QUIET instrument between 2008 October and 2010 December, and include a total of 1263 hours of observations. The resulting maps represent the deepest large-area Galactic polarization observations published to date at the relevant frequencies with instrumental rms noise varying between 1.8 and 2.8 uK deg, 2.3-6 times deeper than corresponding WMAP and Planck maps. The angular resolution is 27.3' and 12.8' FWHM at Q- and W-band, respectively. We find excellent agreement between the QUIET and WMAP maps over the entire fields, and no compelling evidence for significant residual instrumental systematic errors in either experiment, whereas the Planck 44 GHz map deviates from these in a manner consistent with reported systematic u... 2. BD-22deg3467, a DAO-type Star Exciting the Nebula Abell 35 Science.gov (United States) Ziegler, M.; Rauch, T.; Werner, K.; Koppen, J.; Kruk, J. W. 2013-01-01 Spectral analyses of hot, compact stars with non-local thermodynamical equilibrium (NLTE) model-atmosphere techniques allow the precise determination of photospheric parameters such as the effective temperature (T(sub eff)), the surface gravity (log g), and the chemical composition. The derived photospheric metal abundances are crucial constraints for stellar evolutionary theory. Aims. Previous spectral analyses of the exciting star of the nebula A35, BD-22deg3467, were based on He+C+N+O+Si+Fe models only. For our analysis, we use state-of-the-art fully metal-line blanketed NLTE model atmospheres that consider opacities of 23 elements from hydrogen to nickel. We aim to identify all observed lines in the ultraviolet (UV) spectrum of BD-22deg3467 and to determine the abundances of the respective species precisely. Methods. For the analysis of high-resolution and high signal-to-noise ratio (S/N) far-ultraviolet (FUSE) and UV (HST/STIS) observations, we combined stellar-atmosphere models and interstellar line-absorption models to fully reproduce the entire observed UV spectrum. Results. The best agreement with the UV observation of BD-22deg3467 is achieved at T(sub eff) = 80 +/- 10 kK and log g = 7.2 +/- 0.3. While T(sub eff) of previous analyses is verified, log g is significantly lower. We re-analyzed lines of silicon and iron (1/100 and about solar abundances, respectively) and for the first time in this star identified argon, chromium, manganese, cobalt, and nickel and determined abundances of 12, 70, 35, 150, and 5 times solar, respectively. Our results partially agree with predictions of diffusion models for DA-type white dwarfs. A combination of photospheric and interstellar line-absorption models reproduces more than 90% of the observed absorption features. The stellar mass is M approx. 0.48 Solar Mass. Conclusions. BD.22.3467 may not have been massive enough to ascend the asymptotic giant branch and may have evolved directly from the extended horizontal branch 3. IL PORTFOLIO EUROPEO PER LA FORMAZIONE INIZIALE DEGLI INSEGNANTI (PEFIL COME STRUMENTO DI INSEGNAMENTO/APPRENDIMENTO Directory of Open Access Journals (Sweden) Adriana Arcuri 2013-01-01 Full Text Available Scopo di questo contributo è descrivere il modo in cui il Pefil , Portfolio europeo per la formazione iniziale degli insegnanti di lingue. Uno strumento di riflessione (ECML, 2007 è stato usato nell’ambito del “Master in didattica dell’italiano come lingua non materna” dell’Università di Palermo non solo come strumento di autovalutazione, ma anche come strumento di insegnamento/apprendimento, valorizzando cioè le potenzialità formative di questo Portfolio come auspicato dagli stessi autori.Il documento è impiegato, in una nuova prospettiva, come chiave di lettura dei contenuti della professione e ha fornito ai corsisti uno strumento per rintracciare le connessioni fra i diversi input formativi del Master. In questo modo è stato possibile per ciascuno di loro costruire un tessuto unitario di apprendimento delle competenze professionali di insegnanti di italiano L2 e LS in un’ottica di life long learning, secondo un approccio riflessivo. The Portfolio Europeo per la Formazione Iniziale degli Insegnanti (PEFIL as a teaching/learning tool The aim of this paper is to describe how the European Portfolio for Student Teachers of Languages - Portfolio Europeo per la Formazione Iniziale degli Insegnanti (PEFIL, A reflection tool for language teacher education (ECML, 2007 has been used in the Master Degree program in “Italian Foreign Language Teaching” at the University of Palermo. The PEFIL has not only been used as a tool for self-assessment, but by exploiting the educational potential of the portfolio, it has also become an important learning/teaching tool.The Portfolio was used as a way to interpret essential teaching contents. It gave students a tool for finding connections between the diverse educational elements of the Master program. Thus it was possible for each of them to create a coherent network of professional competences for teaching Italian as a second and foreign language within a life long learning 4. The phase relations in the Gd-Fe-Ga ternary system at 500 deg. C Energy Technology Data Exchange (ETDEWEB) Liu, D.C. [College of Materials Science and Engineering, Shenzhen University and Shenzhen Key Laboratory of Special Functional Materials, Shenzhen 518060 (China); Li, J.Q. [College of Materials Science and Engineering, Shenzhen University and Shenzhen Key Laboratory of Special Functional Materials, Shenzhen 518060 (China)], E-mail: junqinli@szu.edu.cn; Ouyang, M.; Liu, F.S.; Ao, W.Q. [College of Materials Science and Engineering, Shenzhen University and Shenzhen Key Laboratory of Special Functional Materials, Shenzhen 518060 (China) 2009-06-24 The isothermal section (500 deg. C) of the phase diagram of the Gd-Fe-Ga ternary system was investigated by X-ray powder diffraction analysis. Eleven binary compounds, GdGa{sub 2}, GdGa, Gd{sub 3}Ga{sub 2}, Gd{sub 5}Ga{sub 3}, GdFe{sub 2}, GdFe{sub 3}, Gd{sub 2}Fe{sub 17}, Fe{sub 3}Ga, Fe{sub 6}Ga{sub 5}, Fe{sub 3}Ga{sub 4} and FeGa{sub 3}, have been confirmed. Two ternary compounds, GdFe{sub 5.3}Ga{sub 6.7} and GdFe{sub 5}Ga{sub 7}, were found in this ternary system at 500 deg. C. The compound GdFe{sub 5.3}Ga{sub 6.7} is orthorhombic ScFe{sub 6}Ga{sub 6}-type structure (space group Immm) with a = 0.8567 (9), b = 0.86960 (9) and c = 0.50782 (5) nm, while the compound GdFe{sub 5}Ga{sub 7} is tetragonal ThMn{sub 12}-type structure (space group I4/mmm) with a = 0.8651(1) and c = 0.50934 (6) nm. The isothermal section at 500 deg. C consists of 16 single-phase regions, 31 two-phase regions and 16 three-phase regions. The maximum solid solubilities of Ga in GdFe{sub 2}, GdFe{sub 3}, Gd{sub 2}Fe{sub 17} are 9.2, 9.0, and 44.3 at.% respectively. The homogeneity range of GdGa{sub 2} is from 22 to 33.3 at.% Ga in Gd-Ga side but the solid solubility of Fe in this compound is very small. The homogeneity range of GdFe{sub 5}Ga{sub 7} is from 53.8 to 59.2 at.% Ga. Very limited solid solutions were measured in the other compounds. 5. Moderate resolution thermal mapping of Mars - The channel terrain around the Chryse basin Science.gov (United States) Christensen, P. R.; Kieffer, H. H. 1979-01-01 Moderate resolution (about 30 km) thermal inertia estimates have been made for several regions in the northern hemisphere of Mars. Examples of these maps are presented for the region 0-45 deg N, 0-90 deg W. In the region adjoining the Chryse basin there are two major channels, Kasei Vallis and Ares Vallis, whose floor materials have higher thermal inertia than the surrounding upland regions. Moreover, there are numerous craters in the region which have high inertia-low albedo features on the crater floor. 6. RHIC Polarized proton operation Energy Technology Data Exchange (ETDEWEB) Huang, H.; Ahrens, L.; Alekseev, I.G.; Aschenauer, E.; Atoian, G.; Bai, M.; Bazilevsky, A.; Blaskiewicz, M.; Brennan, J.M.; Brown, K.A.; Bruno, D.; Connolly, R.; Dion, A.; D' Ottavio, T.; Drees, K.A.; Fischer, W.; Gardner, C.; Glenn, J.W.; Gu, X.; Harvey, M.; Hayes, T.; Hoff, L.; Hulsart, R.L.; Laster, J.; Liu, C.; Luo, Y.; MacKay, W.W.; Makdisi, Y.; Marr, G.J.; Marusic, A.; Meot, F.; Mernick, K.; Michnoff, R,; Minty, M.; Montag, C.; Morris, J.; Nemesure, S.; Poblaguev, A.; Ptitsyn, V.; Ranjibar, V.; Robert-Demolaize, G.; Roser, T.; J.; Severino, F.; Schmidke, B.; Schoefer, V.; Severino, F.; Smirnov, D.; Smith, K.; Steski, D.; Svirida, D.; Tepikian, S.; Trbojevic, D.; Tsoupas, N.; Tuozzolo, J. Wang, G.; Wilinski, M.; Yip, K.; Zaltsman, A.; Zelenski, A.; Zeno, K.; Zhang, S.Y. 2011-03-28 The Relativistic Heavy Ion Collider (RHIC) operation as the polarized proton collider presents unique challenges since both luminosity(L) and spin polarization(P) are important. With longitudinally polarized beams at the experiments, the figure of merit is LP{sup 4}. A lot of upgrades and modifications have been made since last polarized proton operation. A 9 MHz rf system is installed to improve longitudinal match at injection and to increase luminosity. The beam dump was upgraded to increase bunch intensity. A vertical survey of RHIC was performed before the run to get better magnet alignment. The orbit control is also improved this year. Additional efforts are put in to improve source polarization and AGS polarization transfer efficiency. To preserve polarization on the ramp, a new working point is chosen such that the vertical tune is near a third order resonance. The overview of the changes and the operation results are presented in this paper. Siberian snakes are essential tools to preserve polarization when accelerating polarized beams to higher energy. At the same time, the higher order resonances still can cause polarization loss. As seen in RHIC, the betatron tune has to be carefully set and maintained on the ramp and during the store to avoid polarization loss. In addition, the orbit control is also critical to preserve polarization. The higher polarization during this run comes from several improvements over last run. First we have a much better orbit on the ramp. The orbit feedback brings down the vertical rms orbit error to 0.1mm, much better than the 0.5mm last run. With correct BPM offset and vertical realignment, this rms orbit error is indeed small. Second, the jump quads in the AGS improved input polarization for RHIC. Third, the vertical tune was pushed further away from 7/10 snake resonance. The tune feedback maintained the tune at the desired value through the ramp. To calibrate the analyzing power of RHIC polarimeters at any energy above 7. Gian Piero Piretto, La vita privata degli oggetti sovietici. 25 storie da un altro mondo Directory of Open Access Journals (Sweden) Enza Dammiano 2013-05-01 Full Text Available Dopo aver analizzato le “mitologie culturali” dell’era sovietica – il “radioso avvenire” che queste proiettavano (Il radioso avvenire. Mitologie culturali sovietiche, Einaudi, 2001 – e ‘illustrato’, in particolare, gli anni Trenta e Quaranta attraverso Gli occhi di Stalin (Raffaello Cortina, 2010, con La vita privata degli oggetti sovietici Gian Piero Piretto introduce il lettore nelle “storie” di venticinque «cose sovietiche» (32, disseminate lungo l’intero arco temporale di esistenza dell’URSS e oltre: «La maggior parte delle cose a cui dedicherò la mia specifica attenzione ancora circola […], talora in forme rinnovate (degenerate o adattate alla nuova realtà» (43. 8. Modeling and computation of flow in a passage with 360 deg turning and multiple airfoils Science.gov (United States) Shyy, W.; Vu, T. C. 1991-06-01 Numerical modeling of the three-dimensional flows in a spiral casing of a hydraulic turbine, containing a passage of 360-deg turning and multiple elements of airfoils (the so-called distributor), is made. The physical model is based on a novel two-level approach, comprising of (1) a global model that adequately accounts for the geometry of the spiral casing but smears out the details of the distributor and represents the multiple airfoils by a porous medium treatment; and (2) a local model that performs detailed analysis of flow in the distributor region. The global analysis supplies the inlet flow condition for the individual cascade of distributor airfoils, while the distributor analysis yields the information needed for modeling the characteristics of the porous medium. Comparisons of pressure and velocity profiles between measurement and prediction have been made to assess the validity of the present approach. Flow characteristics in the spiral casing are also discussed. 9. Effect of polarization roughness scattering (PRS) on two-dimensional electron transport of MgZnO/ZnO heterostructures Science.gov (United States) Wang, Ping; Guo, Lixin; Song, Zhenjie; Yang, Yintang; Shang, Tao; Li, Jing; Huang, Feng; Zheng, Qinghong 2013-12-01 Quantum transport properties of two-dimensional electron gas (2DEG) in undoped MgZnO/ZnO heterostructures with polarization charge effect have been investigated theoretically. Polarization roughness scattering (PRS) combining polarization charge and interface roughness scattering was proposed as a new scattering mechanism. It was found that the carriers confined in the heterostructures (HSs) would be scattered from polarization charges when they were moving along the in-plane and PRS played a very important role for the low-temperature electron mobility when the electron density Ns exceeded 1.0e11 cm-2, especially in a higher electron density region. With PRS, the experimental data on the density dependence of 2DEG mobility in the MgZnO/ZnO HSs under study can be well reproduced. The study indicates that the improved processing techniques providing a smooth interface and a good separation between the 2DEG electrons and the polarization charges should be significant for the quantum device’s performance. 10. Silica enhanced formation of hydroxyapatite nanocrystals in simulated body fluid (SBF) at 37 deg. C Energy Technology Data Exchange (ETDEWEB) Sadjadi, M.S., E-mail: m.s.sadjad@gmail.com [Department of Chemistry, Sciences and Research Branch, Islamic Azad University, Tehran (Iran, Islamic Republic of); Ebrahimi, H.R. [Department of Chemistry, Sciences and Research Branch, Islamic Azad University, Tehran (Iran, Islamic Republic of); Meskinfam, M. [Department of Chemistry, Tonekabon Branch, Islamic Azad University, Tonekabon (Iran, Islamic Republic of); Zare, K. [Department of Chemistry, University of Shahid Beheshti, Eveen Tehran (Iran, Islamic Republic of) 2011-10-17 Highlights: {yields} We report on fast formation of hexagonal nanocrystals of calcium hydroxyapatite (HA) in silica-containing simulated body fluid solution at 37 deg. C. {yields} Bioactivity and biodegradability of TCP precursor have been confirmed by the dissolution of TCP and formation of a bone like layer of new HA nanoparticles outside of the precursor after 24 h soaking in SBF solution. {yields} Successive nucleation and formation of tiny hexagonal HA nanoplates and nanorods have been confirmed by TEM results after 24 h soaking of TCP in silica-containing BSF solution. - Abstract: The chemical modification of implant (prosthesis) surfaces is being investigated worldwide for improving the fixation of orthopaedic and dental implants. The main goal in this surface modification approach is to achieve a faster bone growth and chemical bonding of the implant to the newly generated and/or remodeled bone. In this work, we report fast formation of hexagonal nanocrystals of calcium hydroxyapatite (HA) in simulated body fluid (SBF, inorganic components of human blood plasma) solutions at 37 deg. C, using calcium phosphate (TCP) and sodium silicate as precursors. Characterization and chemical analysis of the synthesized powders were performed by Fourier transform infrared spectroscopy (FT-IR), X-ray powder diffraction (XRD), scanning electron microscopy (SEM), and transmission electron microscopy (TEM). The results indicated enhanced nucleation and formation of bone like layer of HA nanocrystals at the surface of TCP nanoparticles and occurrence of HA nanocrystals during 24 h soaking of TCP in SBF solution containing silica ions. The average size of a nanoparticle, using Scherrer formula, was found to be 18.2 nm. 11. The Telemachus mission: dynamics of the polar sun and heliosphere Science.gov (United States) Roelof, E. Telemachus in Greek mythology was the faithful son of Ulysses. The Telemachus mission is envisioned as the next logical step in the exploration of the polar regions of the Sun and heliosphere so excitingly initiated by the ESA/NASA Ulysses mission. Telemachus is a polar solar-heliospheric mission described in the current NASA Sun-Earth Connections Roadmap (2003-2028) that has successfully undergone two Team X studies by NASA/JPL. The pioneering observations from Ulysses transformed our perception of the structure and dynamics of these polar regions through which flow the solar wind, magnetic fields and energetic particles that eventually populate most of the volume of the heliosphere. Ulysses carried only fields and particles detectors. Telemachus, in addition to modern versions of such essential in situ instruments, will carry imagers that will give solar astronomers a new viewpoint on coronal mass ejections and solar flares, as well as their first purely polar views of the photospheric magnetic field, thereby providing new helioseismology to probe the interior of the Sun. Unlike the RTG-powered Ulysses, the power for Telemachus will come simply from solar panels. Gravity assist encounters with Venus and Earth (twice) will yield ˜5 years of continuous in-ecliptic cruise science between 0.7 AU and 3.3 AU that will powerfully complement other contemporary solar-heliospheric missions. The Jupiter gravity assist, followed by a perihelion burn ˜8 years after launch, will place Telemachus in a permanent ˜0.2 AU by 2.5 AU heliographic polar orbit (inclination >80 deg) whose period will be 1.5 years. Telemachus will then pass over the solar poles at ˜0.4 AU (compared to 1.4 AU for Ulysses) and spend ˜2 weeks above 60 deg on each polar pass (alternating perihelions between east and west limbs as viewed from Earth). In 14 polar passes during a 10.5 year solar cycle, Telemachus would accumulate over half a year of polar science data. During the remainder of the time, it 12. NOAA Climate Data Record (CDR) of AVHRR Polar Pathfinder (APP) Cryosphere Data.gov (United States) National Oceanic and Atmospheric Administration, Department of Commerce — This NOAA Climate Data Record (CDR) contains the AVHRR Polar Pathfinder (APP) product. APP is a fundamental CDR comprised of calibrated and navigated AVHRR channel... 13. Plasma polarization spectroscopy Energy Technology Data Exchange (ETDEWEB) Iwamae, Atsushi; Inoue, Takeru; Tanaka, Akihiro; Kawakami, Kazuki; Fujimoto, Takashi [Kyoto Univ., Dept. of Engineering Physics, Kyoto (Japan) 2000-03-01 Polarization of radiation emitted from plasma reflects the anisotropic properties of the plasma, especially the angular isotropic distribution of electron velocities. Polarization has been observed on impurity ion lines from the WT-3 tokamak and GAMMA 10 tandem mirror device. (author) 14. Planetary polarization nephelometer NARCIS (Netherlands) Banfield, D.; Dissly, R.; Mishchenko, M.; Muñoz, O.; Roos-Serote, M.; Stam, D.M.; Volten, H.; Wilson, A. 2004-01-01 We have proposed to develop a polarization nephelometer for use on future planetary descent probes. It will measure both the scattered intensity and polarization phase functions of the aerosols it encounters descending through an atmosphere. These measurements will be taken at two wavelengths 15. Polar Cap Patch Dynamics Science.gov (United States) 2013-04-25 cap arcs Citation: Hosokawa, K., J. I. Moen, K. Shiokawa, and Y. Otsuka ( 2011 ), Motion of polar cap arcs , J. Geophys. Res. , 116 , A01305, doi...K., J. I. Moen, K. Shiokawa, and Y. Otsuka , (2011), Decay of polar cap patch, J. Geophys. Res., 116, A05308, doi:10.1029/2010JA016287, Abstract. We 16. Polar Code Validation Science.gov (United States) 1989-09-30 SUMMARY OF POLAR ACHIEVEMENTS ..... .......... 3 3. POLAR CODE PHYSICAL MODELS ..... ............. 5 3.1 PL- ASMA Su ^"ru5 I1LS SH A...of this problem. 1.1. The Charge-2 Rocket The Charge-2 payload was launched on a Black Brant VB from White Sands Mis- sile Range in New Mexico in 17. Polarization modulators for CMBPol Energy Technology Data Exchange (ETDEWEB) Ade, P A R; Savini, G [Cardiff University, School of Physics and Astronomy, Queens Buildings, The Parade, Cardiff, CF24 3AA (United Kingdom); Chuss, D T [NASA Goddard Space Flight Center, Code 665, Greenbelt, MD, 20771 (United States); Hanany, S [School of Physics and Astronomy, University of Minnesota/Twin Cities, Minneapolis, MN, 55455 (United States); Haynes, V; Pisano, G [University of Manchester, School of Physics and Astronomy - Alan Turing Building, Upper Brooke street, Manchester, M13 4PL (United Kingdom); Keating, B G [Department of Physics, University of California, San Diego, La Jolla, CA 92093-0424 (United States); Kogut, A [Code 665 Goddard Space Flight Center, Greenbelt, MD 20771 (United States); Ruhl, J E [Physics Department, Case Western Reserve University, Cleveland, OH, 44106 (United States); Wollack, E J [Observational Cosmology Laboratory, NASA/GSFC, Greenbelt, MD 20771 (United States) 2009-03-01 We review a number of technologies that are candidates for active polarization modulators for CMBPol. The technologies are appropriate for instruments that use bolometric detectors and include birefringent crystal-based and metal-mesh-based half-wave plates, variable phase polarization modulator, Faraday rotator, and photolithographed modulators. We also give a current account of the status of millimeter-wave orthomode transducers. 18. Polarized Light: Three Demonstrations. Science.gov (United States) Goehmann, Ruth; Welty, Scott 1984-01-01 Describes three demonstrations used in the Chicago Museum of Science and Industry polarized light show. The procedures employed are suitable for the classroom by using smaller polarizers and an overhead projector. Topic areas include properties of cellophane tape, nondisappearing arrows, and rope through a picket fence. (JN) 19. Planetary polarization nephelometer NARCIS (Netherlands) Banfield, D.; Dissly, R.; Mishchenko, M.; Muñoz, O.; Roos-Serote, M.; Stam, D.M.; Volten, H.; Wilson, A. 2004-01-01 We have proposed to develop a polarization nephelometer for use on future planetary descent probes. It will measure both the scattered intensity and polarization phase functions of the aerosols it encounters descending through an atmosphere. These measurements will be taken at two wavelengths separa 20. Our Polar Past Science.gov (United States) Clary, Renee; Wandersee, James 2009-01-01 The study of polar exploration is fascinating and offers students insights into the history, culture, and politics that affect the developing sciences at the farthest ends of Earth. Therefore, the authors think there is value in incorporating polar exploration accounts within modern science classrooms, and so they conducted research to test their… 1. Polarized Light: Three Demonstrations. Science.gov (United States) Goehmann, Ruth; Welty, Scott 1984-01-01 Describes three demonstrations used in the Chicago Museum of Science and Industry polarized light show. The procedures employed are suitable for the classroom by using smaller polarizers and an overhead projector. Topic areas include properties of cellophane tape, nondisappearing arrows, and rope through a picket fence. (JN) 2. Nomenclature of polarized light - Elliptical polarization Science.gov (United States) Clarke, D. 1974-01-01 Alternative handedness and sign conventions for relating the orientation of elliptical polarization are discussed. The discussion proceeds under two headings: (1) snapshot picture, where the emphasis for the convention is contained in the concept of handedness; and (2) angular momentum consideration, where the emphasis for the convention is strongly associated with mathematical convention and the sign of the fourth Stokes parameter. 3. Mobile radio channels CERN Document Server Pätzold, Matthias 2011-01-01 Providing a comprehensive overview of the modelling, analysis and simulation of mobile radio channels, this book gives a detailed understanding of fundamental issues and examines state-of-the-art techniques in mobile radio channel modelling. It analyses several mobile fading channels, including terrestrial and satellite flat-fading channels, various types of wideband channels and advanced MIMO channels, providing a fundamental understanding of the issues currently being investigated in the field. Important classes of narrowband, wideband, and space-time wireless channels are explored in deta 4. Parallel Polarization State Generation Science.gov (United States) She, Alan; Capasso, Federico 2016-05-01 The control of polarization, an essential property of light, is of wide scientific and technological interest. The general problem of generating arbitrary time-varying states of polarization (SOP) has always been mathematically formulated by a series of linear transformations, i.e. a product of matrices, imposing a serial architecture. Here we show a parallel architecture described by a sum of matrices. The theory is experimentally demonstrated by modulating spatially-separated polarization components of a laser using a digital micromirror device that are subsequently beam combined. This method greatly expands the parameter space for engineering devices that control polarization. Consequently, performance characteristics, such as speed, stability, and spectral range, are entirely dictated by the technologies of optical intensity modulation, including absorption, reflection, emission, and scattering. This opens up important prospects for polarization state generation (PSG) with unique performance characteristics with applications in spectroscopic ellipsometry, spectropolarimetry, communications, imaging, and security. 5. Parallel Polarization State Generation CERN Document Server She, Alan 2016-01-01 The control of polarization, an essential property of light, is of wide scientific and technological interest. The general problem of generating arbitrary time-varying states of polarization (SOP) has always been mathematically formulated by a series of linear transformations, i.e. a product of matrices, imposing a serial architecture. Here we show a parallel architecture described by a sum of matrices. The theory is experimentally demonstrated by modulating spatially-separated polarization components of a laser using a digital micromirror device that are subsequently beam combined. This method greatly expands the parameter space for engineering devices that control polarization. Consequently, performance characteristics, such as speed, stability, and spectral range, are entirely dictated by the technologies of optical intensity modulation, including absorption, reflection, emission, and scattering. This opens up important prospects for polarization state generation (PSG) with unique performance characteristi... 6. Surface channelling in grazing-incidence ion bombardment of a stepped surface Energy Technology Data Exchange (ETDEWEB) Rosandi, Yudi [Fachbereich Physik, Universitaet Kaiserslautern, Erwin-Schroedinger-Strasse, D-67663 Kaiserslautern (Germany); Urbassek, Herbert M. [Fachbereich Physik, Universitaet Kaiserslautern, Erwin-Schroedinger-Strasse, D-67663 Kaiserslautern (Germany)]. E-mail: urbassek@rhrk.uni-kl.de 2007-03-15 Using molecular-dynamics simulation, the impact of a 5keV Ar atom at 83 deg. incidence angle towards the surface normal onto a stepped Pt(111) surface is investigated. The projectile impinges with a [11-bar2] azimuth on a B step. The channelling of trajectories below the upper terrace is characterized in terms of the distribution of channelling lengths and the energy loss of channelled projectiles. The influence of target temperature is studied by simulating targets at 0K and at 550K. 7. Effect of Substrate Doping in Relaxed SiGe Buffers on Strained Si 2DEG Quantum Devices Science.gov (United States) Yao, Kun; Gaevski, Mikhail; Chernyshov, Alexander; Rokhinson, Leonid; Mike, Curtin; Park, Ji-Soo; Fiorenza, James; Lochtefeld, Anthony; Sturm, James 2009-03-01 We describe the impact of Si substrate doping on the substrate leakage in strained Si two-dimensional electron gases (2DEG) on SiGe relaxed graded buffers and on quantum devices fabricated from the 2DEG. The best commercially available high quality SiGe relaxed buffers with 30% Ge content, grown at temperature above 1000^oC, have very low threading dislocation density (heterostructures were grown at 625-700^oC in a rapid thermal chemical vapor deposition (RTCVD). However, it is shown that the substrate doping (Arsenic) contributes to leakage current origin in relaxed buffers at liquid helium temperatures if the starting Si substrate is heavily doped (˜5E17cm-2). The leakage can be attributed to enhanced dopant diffusion along misfit dislocations and high diffusion rate of As in SiGe. The leakage current makes side gating of nanostructures in the 2DEG impossible. With a lightly doped substrate, to avoid leakage, we achieved a high quality 2DEG and successful side gating of a 2DEG quantum dot for a quantum point contact. This work is supported by the NSA under ARO contract number W911NF-05-1-0437. 8. High-Throughput Design of Two-Dimensional Electron Gas Systems Based on Polar/Nonpolar Perovskite Oxide Heterostructures Science.gov (United States) Yang, Kesong; Nazir, Safdar; Behtash, Maziar; Cheng, Jianli 2016-10-01 The two-dimensional electron gas (2DEG) formed at the interface between two insulating oxides such as LaAlO3 and SrTiO3 (STO) is of fundamental and practical interest because of its novel interfacial conductivity and its promising applications in next-generation nanoelectronic devices. Here we show that a group of combinatorial descriptors that characterize the polar character, lattice mismatch, band gap, and the band alignment between the perovskite-oxide-based band insulators and the STO substrate, can be introduced to realize a high-throughput (HT) design of SrTiO3-based 2DEG systems from perovskite oxide quantum database. Equipped with these combinatorial descriptors, we have carried out a HT screening of all the polar perovskite compounds, uncovering 42 compounds of potential interests. Of these, Al-, Ga-, Sc-, and Ta-based compounds can form a 2DEG with STO, while In-based compounds exhibit a strain-induced strong polarization when deposited on STO substrate. In particular, the Ta-based compounds can form 2DEG with potentially high electron mobility at (TaO2)+/(SrO)0 interface. Our approach, by defining materials descriptors solely based on the bulk materials properties, and by relying on the perovskite-oriented quantum materials repository, opens new avenues for the discovery of perovskite-oxide-based functional interface materials in a HT fashion. 9. Polarization transfer in sup 1 H(d vector, p vector)X at 2. 1 GeV Energy Technology Data Exchange (ETDEWEB) Cheung, E.; Perdrisat, C.F.; Beard, K. (Coll. of William and Mary, Williamsburg, VA (United States)); Yonnet, J.; Boivin, M.; Beurtey, R.; Plouin, F. (Lab. National Saturne, CEN-Saclay, 91 - Gif-sur-Yvette (France)); Punjabi, V. (Norfolk State Univ., VA (United States)); Siebert, R.; Frascaria, R.; Warde, E. (Inst. de Physique Nucleaire, Univ. Paris 11, 91 - Orsay (France)); Abegg, R. (TRIUMF, Vancouver, BC (Canada) Univ. Alberta, Edmonton, AB (Canada)); Van Oers, W.T.H. (Univ. Manitoba, Winnipeg, MB (Canada)); Jacobs, W.W. (Indiana Univ., Cyclotron Facility, Bloomington, IN (United States)); Nanda, S. (CEBAF, Newport News, VA (United States)); Lippert, C. (Univ. Bonn (Germany)); Gugelot, P.C. (Univ. Virginia, Charlottesville, VA (United States)) 1992-06-25 The polarization of the proton from the inclusive breakup reaction {sup 1}H(d vector, p vector)X at 2.1 GeV was measured at 0deg. The results are expressed as the ratio of the proton polarization, P{sub p}, to the deuteron beam polarization, P{sub d}, {kappa}{sub 0}=P{sub p}/P{sub d}. The measured values of {kappa}{sub 0} range from +0.983 to -0.305 and are in general agreement with the expected behavior arising from the D state in the deuteron wave function. (orig.). 10. Circularly Polarized Light as a Communication Signal in Mantis Shrimps. Science.gov (United States) Gagnon, Yakir Luc; Templin, Rachel Marie; How, Martin John; Marshall, N Justin 2015-12-07 Animals that communicate using conspicuous body patterns face a trade-off between desired detection by intended receivers and undesired detection from eavesdropping predators, prey, rivals, or parasites. In some cases, this trade-off favors the evolution of signals that are both hidden from predators and visible to conspecifics. Animals may produce covert signals using a property of light that is invisible to those that they wish to evade, allowing them to hide in plain sight (e.g., dragonfish can see their own, otherwise rare, red bioluminescence). The use of the polarization of light is a good example of a potentially covert communication channel, as very few vertebrates are known to use polarization for object-based vision. However, even these patterns are vulnerable to eavesdroppers, as sensitivity to the linearly polarized component of light is widespread among invertebrates due to their intrinsically polarization sensitive photoreceptors. Stomatopod crustaceans appear to have gone one step further in this arms race and have evolved a sensitivity to the circular polarization of light, along with body patterns producing it. However, to date we have no direct evidence that any of these marine crustaceans use this modality to communicate with conspecifics. We therefore investigated circular polarization vision of the mantis shrimp Gonodactylaceus falcatus and demonstrate that (1) the species produces strongly circularly polarized body patterns, (2) they discriminate the circular polarization of light, and (3) that they use circular polarization information to avoid occupied burrows when seeking a refuge. Copyright © 2015 Elsevier Ltd. All rights reserved. 11. Channel nut tool Energy Technology Data Exchange (ETDEWEB) Olson, Marvin 2016-01-12 A method, system, and apparatus for installing channel nuts includes a shank, a handle formed on a first end of a shank, and an end piece with a threaded shaft configured to receive a channel nut formed on the second end of the shaft. The tool can be used to insert or remove a channel nut in a channel framing system and then removed from the channel nut. 12. 120 Gbit/s injection-locked homodyne coherent transmission of polarization-multiplexed 64 QAM signals over 150 km. Science.gov (United States) Wang, Yixin; Kasai, Keisuke; Yoshida, Masato; Nakazawa, Masataka 2014-12-15 We describe an injection-locked 64 QAM homodyne coherent transmission, which is the highest QAM multiplicity realized with an injection locking technique. The frequency locking range of the local oscillator (LO) was as wide as 1 GHz. The phase noise was only 0.2 deg, which is 1/3 of that obtained with our previous OVCO-based OPLL (0.6 deg.). As a result, a 120 Gbit/s polarization-multiplexed 64 QAM signal was successfully transmitted over 150 km with a simple receiver configuration and low DSP complexity. 13. Boiling heat transfer in horizontal and inclined rectangular channels Energy Technology Data Exchange (ETDEWEB) Morcos, S.M.; Mobarak, A.; Hilal, M.; Mohareb, M.R. (Cairo Univ. (Egypt)) 1987-05-01 The present experimental investigation is concerned with boiling heat transfer of water inside both horizontal and inclined rectangular channels under a relatively low heat flux. These configurations simulate the absorber channel of line-focus solar concentrations under boiling conditions. The experimental facility includes electrically heated aluminum rectangular channels with aspect ratios of 2.67 and 0.37. The experimental results of the two-phase Nusselt number for the two aspect ratios and for the inclination angles 0, 15, 30, and 45 deg were correlated in terms of a ratio of the two-phase to the liquid-phase Reynolds number for the forced-convection vaporization region. The proposed correlations agree well with previous investigations. In the present work, classifications of the various flow patterns were made by direct observation through a glass window at the end of the test section. 14. Polarization Ratio Determination with Two Identical Linearly Polarized Antennas Science.gov (United States) 2017-01-17 Polarization Ratio Determination with Two Identical Linearly Polarized Antennas Herbert M. Aumann1, Francis G. Willwerth2 and Kristan A. Tuttle2...maine.edu Abstract— This paper describes a method for determining the complex polarization ratio using two identical, linearly polarized antennas. By...present paper it will be shown that the later technique can also be used to determine the polarization ratio of a linearly polarized antenna. II 15. All fiber optics circular-state swept source polarization-sensitive optical coherence tomography. Science.gov (United States) Lin, Hermann; Kao, Meng-Chun; Lai, Chih-Ming; Huang, Jyun-Cin; Kuo, Wen-Chuan 2014-02-01 A swept source (SS)-based circular-state (CS) polarization-sensitive optical coherence tomography (PS-OCT) constructed entirely with polarization-maintaining fiber optics components is proposed with the experimental verification. By means of the proposed calibration scheme, bulk quarter-wave plates can be replaced by fiber optics polarization controllers to, therefore, realize an all-fiber optics CS SSPS-OCT. We also present a numerical dispersion compensation method, which can not only enhance the axial resolution, but also improve the signal-to-noise ratio of the images. We demonstrate that this compact and portable CS SSPS-OCT system with an accuracy comparable to bulk optics systems requires less stringent lens alignment and can possibly serve as a technology to realize PS-OCT instrument for clinical applications (e.g., endoscopy). The largest deviations in the phase retardation (PR) and fast-axis (FA) angle due to sample probe in the linear scanning and a rotation angle smaller than 65 deg were of the same order as those in stationary probe setups. The influence of fiber bending on the measured PR and FA is also investigated. The largest deviations of the PR were 3.5 deg and the measured FA change by ~12 to 21 deg. Finally, in vivo imaging of the human fingertip and nail was successfully demonstrated with a linear scanning probe. 16. The Galactic Plane Infrared Polarization Survey (GPIPS) Science.gov (United States) Clemens, Dan P.; Pinnick, A. F.; Pavel, M. D.; Taylor, B. W. 2012-06-01 The scientific motivation, data collection strategy, data reduction, and analysis methods are presented for the Galactic Plane Infrared Polarization Survey (GPIPS). The chief goal for the Survey was to reveal the nature of the magnetic field threading the Galactic disk, in particular through regions of low to moderate extinction (1-20 mag of AV ) and star formation in the cool interstellar medium. The Survey region spans 76 deg2 of the northern Milky Way disk, from l = 18° to 56° and b =-1° to +1°. Linear polarimetric imaging observations began in 2006 in the near-infrared H band (1.6 μm) using the Mimir instrument on the 1.8 m Perkins telescope, located outside Flagstaff, AZ. Mimir used a cold, fixed wire grid and a rotateable cold, compound half-wave plate to obtain "step-and-integrate" polarimetry over its full 10 × 10 arcmin field of view. The GPIPS bright and faint polarimetric limits are approximately 7th and 15th mag, respectively, set by saturation and photon noise. Polarimetric uncertainties track with stellar magnitude, from about 0.1% to 25%, on average, from the brightest to faintest stars. Across the 3237 field GPIPS region, approximately 0.5 million stars are estimated to show detectable linear polarization (P/σ P > 3); most of these have mH < 12. This represents many orders of magnitude improvement in the number of polarization measurements across this region. GPIPS observations are more than 90% complete and should finish in 2012. 17. Influence of polarization extinction ratio on distributed polarization coupling detection Institute of Scientific and Technical Information of China (English) XU Tian-hua; TANG Feng; JING Wen-cai; ZHANG Hong-xia; JIA Da-gong; YU Chang-song; ZHOU Ge; ZHANG Yi-mo 2008-01-01 Distributed polarization coupling in polarization-maintaining fibers can be detected by using a white light Michelsonin terferorneter. This technique usually requires that only one polarization mode is excited. However, in practical measurement,the injection polarization direction could not be exactly aligned to one of the principal axes of the PMF, so the influence of the polarization extinction ratio should be considered. Based on the polarization coupling theory, the influence of theincident polarization extinction on the measurement result is evaluated and analyzed, and a method for distributed polarization coupling detection is developed when both two orthogonal eigenmodes are excited. 18. Detailed 1 x 1 deg gravimetric Indian Ocean geoid and comparison with GEOS-3 radar altimeter geoid profiles Science.gov (United States) Kahle, H.-G.; Chapman, M.; Talwani, M. 1978-01-01 A new set of 1 x 1 deg mean free-air anomalies in the Indian Ocean is determined on the basis of previously published free-air anomaly maps (Talwani and Kahle, 1975) and the most recent Lamont surface ship gravity measurements. The data are then used to compute a (total) 1 x 1 deg gravimetric Indian Ocean geoid. The computation is carried out by combining the Goddard Space Flight Center (GSFC) GEM-6 geoid and a difference geoid that corresponds to the differences between the set of 1 x 1 deg surface gravity values and the GEM-6 gravity anomalies. The difference geoid is highest over the Madagascar Ridge (+20 m) and lowest over the Timor Trough (-30 m). The total geoid is compared with GEOS-3 radar altimeter-derived geoid profiles, and geophysical implications are discussed. 19. Results of steel corrosion tests in flowing liquid Pb/Bi at 420-600 deg. C after 2000 h Energy Technology Data Exchange (ETDEWEB) Mueller, G. E-mail: georg.mueller@ihm.fzk.de; Heinzel, A.; Konys, J.; Schumacher, G.; Weisenburger, A.; Zimmermann, F.; Engelko, V.; Rusanov, A.; Markov, V 2002-02-01 Corrosion tests were carried out on austenitic AISI 316L and 1.4970 steels and on MANET steel up to 2000 h of exposure to flowing (up to 2 m/s) Pb/Bi. The concentration of oxygen in the liquid alloy was controlled at 10{sup -6} wt%. Specimens consisted of tube and rod sections in original state and after alloying of Al into the surface. After 2000 h of exposure at 420 and 550 deg. C the specimen surfaces were covered with an intact oxide layer which provided a good protection against corrosion attack of the liquid Pb/Bi alloy. After the same time corrosion attack at 600 deg. C was severe at the original AISI 316L steel specimens. The alloyed specimens containing FeAl on the surface of the alloyed layer still maintained an intact oxide layer with good corrosion protection up to 600 deg. C. 20. Narrow multibeam satellite ground station antenna employing a linear array with a geosynchronous arc coverage of 60 deg. I - Theory Science.gov (United States) Amitay, N.; Gans, M. J. 1982-11-01 The feasibility of using an appropriately squinted linear scan in narrow multibeam satellite ground station antennas employing phased arrays is demonstrated. This linear scan has the potential of reducing the complexity of a narrow-beam planar array to that of a linear array. Calculations for such antennas placed at cities throughout the U.S. show that the peak beam pointing error in covering the 70 deg W to 130 deg W geosynchronous equatorial arc (GEA) is under 5/1000th of a degree. Communication at a 300 MBd rate in the 12/14 GHz band can be made feasible, for a grating lobe-free scan and 0.5 deg beamwidth antenna, by using a relatively simple time equalization. 1. Development of a new correlation for estimating pool boiling heat transfer coefficient of MEG/DEG/water ternary mixture Directory of Open Access Journals (Sweden) Sarafraz M.M. 2012-01-01 Full Text Available Pool boiling heat transfer coefficient of monoethylene glycol (MEG, diethylene glycol (DEG and water ternary mixtures has been experimentally measured up to heat flux 114 kW/m2 at various volumetric concentrations of MEG and DEG. As expected, heat transfer coefficient was strongly taken as a direct function of heat flux. Existing well-known correlations are shown to be unable to predict the acceptable values for the tested ternary mixtures, particularly at different concentrations of MEG and DEG. Furthermore, a new modified correlation is developed on the basis of the Stephan - Preußer correlation that predicts the values of heat transfer coefficients with absolute average error of about 7% that is reasonable and acceptable values in compare to other existing correlations. 2. PRESTO polarization transfer to quadrupolar nuclei: implications for dynamic nuclear polarization. Science.gov (United States) Perras, Frédéric A; Kobayashi, Takeshi; Pruski, Marek 2015-09-21 We show both experimentally and numerically on a series of model systems that in experiments involving transfer of magnetization from (1)H to the quadrupolar nuclei under magic-angle-spinning (MAS), the PRESTO technique consistently outperforms traditionally used cross polarization (CP), affording more quantitative intensities, improved lineshapes, better overall sensitivity, and straightforward optimization. This advantage derives from the fact that PRESTO circumvents the convoluted and uncooperative spin dynamics during the CP transfer under MAS, by replacing the spin-locking of quadrupolar nuclei with a single central transition selective 90° pulse and using a symmetry-based recoupling sequence in the (1)H channel. This is of particular importance in the context of dynamic nuclear polarization (DNP) NMR of quadrupolar nuclei, where the efficient transfer of enhanced (1)H polarization is desired to obtain the highest sensitivity. 3. Acid-sensing ion channels and migraine Directory of Open Access Journals (Sweden) Yu-qi KANG 2015-09-01 Full Text Available Acid-sensing ion channels (ASICs are ligand-gated ion channels that are activated by extracellular protons (H+, which belong to epithelial sodium channels/degenerin (ENaC/DEG superfamily. ASICs are widely distributed in central nervous system, peripheral nervous system, digestive system and some tumor tissues. Different ASIC subunits play important roles in various pathophysiological processes such as touch, sour taste, learning and memory, including inflammation, ischemic stroke, pain, learning and memory decline, epilepsy, multiple sclerosis (MS, migraine, irritable bowel syndrome and tumor. Research over the last 2 decades has achieved substantial advances in migraine pathophysiology. It is now largely accepted that inflammatory pathways play a key role and three main events seem to take place: cortical spreading depression (CSD, activation of the trigeminovascular system (i.e. dural nociceptors, peripheral and central sensitization of this pain pathway. However, the exact mechanisms that link these three events to each other and to inflammation have so far remained to be studied. This article takes an overview of newly research advances in structure, distribution and the relationship with migraine of ASICs. DOI: 10.3969/j.issn.1672-6731.2015.09.013 4. Prevalence of Deg Nala disease in eastern India and its reproduction in buffaloes by feeding Fusarium oxysporum infested rice straw Institute of Scientific and Technical Information of China (English) P Dandapat; PK Nanda; S Bandyopadhyay; Anmol Kaushal; A Sikdar 2011-01-01 Objective: To undertake a study on prevalence of Deg Nala disease in eastern states of India and to reproduce the disease in buffaloes by the Fusarium spp., isolated from the affected region.Methods:During this investigation, a survey was conducted covering four states of eastern region to identify the Deg Nala cases as well as to isolate and characterize the causative agent(s). An experimental study was carried out to reproduce the disease in healthy male buffaloes (2-3 years age) by randomly dividing them into five groups (four in each group). Each individual group was fed with rice straw artificially infested with either of the two representative isolates ofFusarium oxysporum (F. oxysporum) (F01, F02) or representative reference strains of Fusarium equiseti (F. equiseti) (ITCCF-2470) and Fusarium moniliforme (F. moniliforme) (ITCCF-4821) for 30 days, whereas the control group was fed with normal rice straw only. Results: A total of 658 Deg Nala cases were recorded and 12 Fusarium isolates were identified from the mouldy rice straw collected from these affected areas. The characterization of the isolates revealed three species viz., F. oxysporum, F. equiseti and F. moniliforme, among which F. oxysporum was predominant. The disease was artificially reproduced in three buffaloes in F01 group and one in F02 group within 20-23 days by feeding F. oxysporum infested rice straw which resembled the clinical symptoms and gross lesions of natural Deg Nala cases. Conclusions: The field investigation and laboratory studies, including experimental production of Deg Nala disease suggest the possible involvement of mycotoxins. However, further investigations needs to be done to understand nature of the toxic factors involved in production of the Deg Nala disease. 5. Polarization measurement in the COMPASS polarized target CERN Document Server Kondo, K; Baum, G; Berglund, P; Doshita, N; Gautheron, F; Görtz, S; Hasegawa, T; Horikawa, N; Ishimoto, S; Iwata, T; Kisselev, Yu V; Koivuniemi, J H; Le Goff, J M; Magnon, A; Meyer, W; Reicherz, G; Matsuda, T 2004-01-01 Continuous wave nuclear magnetic resonance (NMR) is used to determine the target polarization in the COMPASS experiment. The system is made of the so-called Liverpool Q-meters, Yale-cards, and VME modules for data taking and system controlling. In 2001 the NMR coils were embedded in the target material, while in 2002 and 2003 the coils were mounted on the outer surface of the target cells to increase the packing factor of the material. Though the error of the measurement became larger with the outer coils than with the inner coils, we have performed stable measurements throughout the COMPASS run time for 3 years. The maximum polarization was +57% and -53% as the average in the target cells. 6. Planck intermediate results. XIX. An overview of the polarized thermal emission from Galactic dust CERN Document Server Ade, P A R; Alina, D; Alves, M I R; Armitage-Caplan, C; Arnaud, M; Arzoumanian, D; Ashdown, M; Atrio-Barandela, F; Aumont, J; Baccigalupi, C; Banday, A J; Barreiro, R B; Battaner, E; Benabed, K; Benoit-Lévy, A; Bernard, J -P; Bersanelli, M; Bielewicz, P; Bock, J J; Bond, J R; Borrill, J; Bouchet, F R; Boulanger, F; Bracco, A; Burigana, C; Butler, R C; Cardoso, J -F; Catalano, A; Chamballu, A; Chary, R -R; Chiang, H C; Christensen, P R; Colombi, S; Colombo, L P L; Combet, C; Couchot, F; Coulais, A; Crill, B P; Curto, A; Cuttaia, F; Danese, L; Davies, R D; Davis, R J; de Bernardis, P; Pino, E M de Gouveia Dal; de Rosa, A; de Zotti, G; Delabrouille, J; Désert, F -X; Dickinson, C; Diego, J M; Donzelli, S; Doré, O; Douspis, M; Dunkley, J; Dupac, X; Enßlin, T A; Eriksen, H K; Falgarone, E; Ferrière, K; Finelli, F; Forni, O; Frailis, M; Fraisse, A A; Franceschi, E; Galeotta, S; Ganga, K; Ghosh, T; Giard, M; Giraud-Héraud, Y; González-Nuevo, J; Górski, K M; Gregorio, A; Gruppuso, A; Guillet, V; Hansen, F K; Harrison, D L; Helou, G; Hernández-Monteagudo, C; Hildebrandt, S R; Hivon, E; Hobson, M; Holmes, W A; Hornstrup, A; Huffenberger, K M; Jaffe, A H; Jaffe, T R; Jones, W C; Juvela, M; Keihänen, E; Keskitalo, R; Kisner, T S; Kneissl, R; Knoche, J; Kunz, M; Kurki-Suonio, H; Lagache, G; Lähteenmäki, A; Lamarre, J -M; Lasenby, A; Lawrence, C R; Leahy, J P; Leonardi, R; Levrier, F; Liguori, M; Lilje, P B; Linden-Vørnle, M; López-Caniego, M; Lubin, P M; Macías-Pérez, J F; Maffei, B; Magalhães, A M; Maino, D; Mandolesi, N; Maris, M; Marshall, D J; Martin, P G; Martínez-González, E; Masi, S; Matarrese, S; Mazzotta, P; Melchiorri, A; Mendes, L; Mennella, A; Migliaccio, M; Miville-Deschênes, M -A; Moneti, A; Montier, L; Morgante, G; Mortlock, D; Munshi, D; Murphy, J A; Naselsky, P; Nati, F; Natoli, P; Netterfield, C B; Noviello, F; Novikov, D; Novikov, I; Oxborrow, C A; Pagano, L; Pajot, F; Paladini, R; Paoletti, D; Pasian, F; Pearson, T J; Perdereau, O; Perotto, L; Perrotta, F; Piacentini, F; Piat, M; Pietrobon, D; Plaszczynski, S; Poidevin, F; Pointecouteau, E; Polenta, G; Popa, L; Pratt, G W; Prunet, S; Puget, J -L; Rachen, J P; Reach, W T; Rebolo, R; Reinecke, M; Remazeilles, M; Renault, C; Ricciardi, S; Riller, T; Ristorcelli, I; Rocha, G; Rosset, C; Roudier, G; Rubiño-Martín, J A; Rusholme, B; Sandri, M; Savini, G; Scott, D; Spencer, L D; Stolyarov, V; Stompor, R; Sudiwala, R; Sutton, D; Suur-Uski, A -S; Sygnet, J -F; Tauber, J A; Terenzi, L; Toffolatti, L; Tomasi, M; Tristram, M; Tucci, M; Umana, G; Valenziano, L; Valiviita, J; Van Tent, B; Vielva, P; Villa, F; Wade, L A; Wandelt, B D; Zacchei, A; Zonca, A 2014-01-01 This paper presents the large-scale polarized sky as seen by Planck HFI at 353 GHz, which is the most sensitive Planck channel for dust polarization. We construct and analyse large-scale maps of dust polarization fraction and polarization direction, while taking account of noise bias and possible systematic effects. We find that the maximum observed dust polarization fraction is high (pmax > 18%), in particular in some of the intermediate dust column density (AV < 1mag) regions. There is a systematic decrease in the dust polarization fraction with increasing dust column density, and we interpret the features of this correlation in light of both radiative grain alignment predictions and fluctuations in the magnetic field orientation. We also characterize the spatial structure of the polarization angle using the angle dispersion function and find that, in nearby fields at intermediate latitudes, the polarization angle is ordered over extended areas that are separated by filamentary structures, which appear a... 7. Doubling transmission capacity in optical wireless system by antenna horizontal- and vertical-polarization multiplexing. Science.gov (United States) Li, Xinying; Yu, Jianjun; Zhang, Junwen; Dong, Ze; Chi, Nan 2013-06-15 We experimentally demonstrate 2×56 Gb/s two-channel polarization-division-multiplexing quadrature-phase-shift-keying signal delivery over 80 km single-mode fiber-28 and 2 m Q-band (33-50 GHz) wireless link, adopting antenna horizontal- (H-) and vertical-polarization (V-polarization) multiplexing. At the wireless receiver, classic constant-modulus-algorithm equalization based on digital signal processing can realize polarization demultiplexing and remove the crosstalk at the same antenna polarization. By adopting antenna polarization multiplexing, the signal baud rate and performance requirements for optical and wireless devices can be reduced but at the cost of double antennas and devices, while wireless transmission capacity can also be increased but at the cost of stricter requirements for V-polarization. The isolation is only about 19 dB when V-polarization deviation approaches 10°, which will affect high-speed (>50 Gb/s) wireless delivery. 8. Convective heat-transfer rate distributions over a 140 deg blunt cone at hypersonic speeds in different gas environments Science.gov (United States) Stewart, David A.; Chen, Y. K. 1993-01-01 Experiments were conducted in air, CO2, and CO2-argon gas mixtures to obtain heating distribution data over a 140 deg blunt cone with various corner radii. The effect of corner radius on the heating distribution over the forebody of the cone was included in the investigation. These experiments provide data for validation of two-dimensional axisymmetric and three-dimensional Navier-Stokes solutions. Heating distribution data and measured bow shock wave stand-off distances for 0 deg angle of attack were compared with predicted values using a two-dimensional axisymmetric Navier-Stokes code. 9. Multi-Channel Retailing Directory of Open Access Journals (Sweden) Dirk Morschett, Dr., 2005-01-01 Full Text Available Multi-channel retailing entails the parallel use by retailing enterprises of several sales channels. The results of an online buyer survey which has been conducted to investigate the impact of multi-channel retailing (i.e. the use of several retail channels by one retail company on consumer behaviour show that the frequently expressed concern that the application of multi-channel systems in retailing would be associated with cannibalization effects, has proven unfounded. Indeed, the appropriate degree of similarity, consistency, integration and agreement achieves the exact opposite. Different channels create different advantages for consumers. Therefore the total benefit an enterprise which has a multi-channel system can offer to its consumers is larger, the greater the number of available channels. The use of multi-channel systems is associated with additional purchases in the different channels. Such systems are thus superior to those offering only one sales channel to their customers. Furthermore, multi-channel systems with integrated channels are superior to those in which the channels are essentially autonomous and independent of one another. In integrated systems, consumers can achieve synergy effects in the use of sales-channel systems. Accordingly, when appropriately formulated, multi-channel systems in retailing impact positively on consumers. They use the channels more frequently, buy more from them and there is a positive customer-loyalty impact. Multi-channel systems are strategic options for achieving customer loyalty, exploiting customer potential and for winning new customers. They are thus well suited for approaching differing and varied target groups. 10. Valutazione dell'affidabilità degli operatori per l'identificazione microscopica di peli di mammiferi Directory of Open Access Journals (Sweden) Paolo Ciucci 2003-10-01 Full Text Available La quantificazione dei resti indigesti contenuti negli escrementi è tra le tecniche più frequentemente utilizzate per studiare la dieta del lupo, dove il riconoscimento delle specie preda, nel caso dei mammiferi, si basa su caratteristiche microscopiche distintive del pelo. Tale tecnica, è tuttavia soggetta ad errori individuali nonostante l'esperienza dell'operatore e il ricorso a testi o collezioni di riferimento. Congiuntamente ad una mancata standardizzazione delle procedure di preparazione e trattamento del campione, queste fonti di errore possono alterare significativamente i risultati. Nell'ambito di un progetto UE-Life sull'ecologia del Lupo, in tre Parchi Regionali dell'Emilia-Romagna (2001-2004, abbiamo quindi applicato una procedura standardizzata per la selezione, raccolta, preparazione e trattamento dei campioni fecali di lupo ai fini dell'analisi della dieta. A tal fine è stato organizzato un corso di formazione da parte di docenti qualificati per un totale di 150 ore, suddiviso in moduli e articolato in esercitazioni e prove pratiche di autovalutazione. Al corso, e dopo un ulteriore periodo di esercitazioni individuali (ca. 300 ore/operatore, è quindi seguito un esame di identificazione che ha permesso di quantificare l'affidabilità di ciascun operatore. Il test per l'identificazione a livello di specie è stato basato su un campione di 120 peli, la cui specie di origine era ignota ai candidati (blind test, suddivisi tra ungulati selvatici (n=54: Capriolo, Cervo, Daino, Muflone, Cinghiale, ungulati domestici (n=21: bovini, ovini, caprini, equini, canidi (n= 18: lupo, cane, volpe e altre specie (n=27: lepre, marmotta, tasso, martora, faina, puzzola, gatto, scoiattolo, talpa, muridi. Un sottocampione di 65 peli è stato utilizzato per valutare l'affidabilità nel riconoscimento delle classi d'età (< 5 mesi, ≥ 5 mesi per le sole categorie degli ungulati selvatici (n=54 e degli 11. Combined study of microwave-power-dependence and linear-polarization-dependence of the microwave-radiation-induced magnetoresistance oscillations Science.gov (United States) Ye, Tianyu; Liu, Han-Chun; Mani, Ramesh; Wegscheider, Werner; Georgia State University Collaboration; ETH Zurich Collaboration 2014-03-01 Microwave radiation induced magnetoresistance oscillations (MRIMOs) represent an interesting electrical property of the high mobility two dimensional electron gas (2DEG) at low temperatures in a perpendicular magnetic field and under microwave excitation. Some questions under discussion in this topic include: (a) whether MRIMOs' amplitudes grow linearly with the microwave power and (b) how the MRIMO amplitudes change with the rotation of the microwave polarization with respect to the sample. In this study, we utilize swept microwave power and continuously changed linear polarized microwave polarization angle as two variables in four-terminal low-frequency lock-in magnetoresistance measurements of the 2DEG samples. The results show that amplitude of MRIMOs varies non-linearly with the microwave power. Also, the microwave polarization dependence measurements show that MRIMOs depend sensitively on the polarization angle of the linearly polarized microwaves, while the oscillatory magnetoresistance follows a cosine square function of the polarization angle. We provide a simple model that conveys our understanding of our observations. Basic research at Georgia State University is supported by the DOE-BES, MSE Division under DE-SC0001762. Microwave work is supported by the ARO under W911NF-07-01-0158. 12. Effects of c-Myc and TGF-Alpha on Polarized Membrane Traffic Science.gov (United States) 1999-10-01 accidental cell death due to excessive ion depletion or accumulation after loss of cell polarity. Interestingly, the CFTR chloride channel, while apical...J. Benos, and R. A. Frizzell. 1994. Polarization-dependent apical membrane CFTR targeting underlies cAMP- stimulated Cl- secretion in epithelial cells 13. Il disagio degli insegnanti tra psicologia e pedagogia: una indagine multidimensionale sul fenomeno del burnout Directory of Open Access Journals (Sweden) Francesca Botticelli 2012-06-01 Full Text Available A partire da un minuzioso esame della letteratura internazionale sui diversi versanti che costituiscono gli elementi chiave di questa ricerca (stress lavoro-correlato, burnout, formazione insegnanti il lavoro vuole analizzare il fenomeno del burnout degli insegnanti come fenomeno multi dimensionale. Si raggiunge questo obiettivo a partire dalla concezione del burnout come risultato di stress lavoro-correlato che si muove su dimensioni plurime, aventi carattere sia soggettivo che organizzativo. Per l‘apprezzamento delle prime sono stati utilizzati il Maslach Burnout Inventory (Maslach e Jackson 1986; validazione italiana Sirigatti e Stefanile, 1993; sul versante della salute organizzativa il Multidimensional Organizational Health Questionnaire (MOHQ; Avallone e Paplomatas 2005; sul versante dei principali sintomi lamentati dal campione di ricerca la Sympton Check List (SCL-90; Derogatis, 1977 e infine sulla percezione di sé Adjective Check List (ACL; Gough 1949; valid. It. Gough, Heilbrun, e Fioravanti, 1980 nella modalità di Sé reale . Il campione era costituito da 52 docenti di cui 28 maschi (53,8% e 24 femmine (46,2%. 50 anni l‘età media dei soggetti interpellati. L‘analisi dei risultati mostra la necessità di soluzioni al problema secondo più dimensioni e anche di una lettura pedagogica del fenomeno nel suo intrecciarsi con le dinamiche alla base della socialità contemporanea. Tale lettura e le soluzioni proposte si inscrivono infatti nel contesto ampio delle trasformazioni che investono a livello globale il mondo dell‘istruzione e la società nel suo complesso, generando un disagio che si coagula intorno alla perdita di senso del proprio essere nel mondo, quindi anche sul senso delle attività lavorative e dell‘educazione. Il contributo pedagogico è orientato quindi alla ricerca di senso da un lato, e al contrasto a livello istituzionale di pratiche volte a fare dell‘educazione un mercato e del suo assessment uno 14. ELABORAZIONE DI UN QUESTIONARIO PER LA RILEVAZIONE DEI BISOGNI COMUNICATIVI DEGLI ADULTI IMMIGRATI Directory of Open Access Journals (Sweden) Annamaria Aquilino 2012-02-01 Full Text Available L’intensità del fenomeno migratorio in Italia suscita una riflessione critica sui bisogni linguistici di un nuovo pubblico di apprendenti, spinti verso la conoscenza della lingua italiana da una forte esigenza di integrazione sociale. L’articolo presenta l’elaborazione di un questionario come strumento d’indagine essenziale per la rilevazione dei bisogni comunicativi degli immigrati adulti. Progettato nell’ambito di un corso di italiano L2 presso il CTP di Rozzano (Milano e sottoposto a un campione di 24 stranieri, il questionario si è rivelato molto utile per la definizione del profilo dei singoli apprendenti e dell’intera classe che, caratterizzata da una grande differenziazione, non è sempre facile da gestire. L’interpretazione finale dei dati ha messo in luce non solo gli elementi di diversità ma ha anche permesso di cogliere alcuni tratti omogenei molto interessanti, indispensabili per la programmazione del percorso didattico, che sarà tanto efficace quanto più si adatterà alla realtà psicologica e socio-culturale degli apprendenti. Questionnaire design to Survey the communicative needs of adult immigrants Widespread immigration in Italy has brought about critical reflection on the linguistic needs of a new group of learners, highly motivated to learn the Italian language because of their strong need for social integration. This article presents the designing of a questionnaire as an essential tool for surveying the communicative needs of adult immigrants. Designed for an Italian L2 course held at the CTP in Rozzano (Milano and administered to 24 foreigners, the questionnaire was very useful for defining the profile of the single learners and the whole class group, which was dissimilar, and thus not the easiest to conduct. The final interpretation of the data brought to light not only the elements of diversity but they also allowed us to recognize a few interesting common traits, essential for 15. Enhanced radiation tolerance of non-polar-terminated ZnO Science.gov (United States) Charnvanichborikarn, S.; Myers, M. T.; Shao, L.; Kucheyev, S. O. 2013-12-01 Room-temperature heavy-ion bombardment of polar (0001) ZnO leads to the formation of intermediate peak and step features in damage-depth profiles measured by ion channeling. Here, we show that these anomalous disorder effects are strongly suppressed for crystals with (112¯0) and (101¯0) non-polar surface terminations. Possible defect interaction scenarios responsible for the enhanced radiation tolerance of non-polar-terminated ZnO are discussed. 16. Processing and Analysis of Polarimetric Ship Signatures from MARSIE: Report on Results for Polar Epsilon Science.gov (United States) 2006-10-01 DRE-series trihedral corner reflectors (TCRs) mounted on tripods, two active radar calibrators (ARCs) (borrowed from CCRS) and an Ashtech GPS...polarimetry results include observations of ship target radar cross section for co-polarization and cross -polarization channels, the reduction in the...estimate the ship velocity for the case of airborne SAR geometry. The total radar cross section (RCS) as a function of linear polarization state has 17. Time Domain Induced Polarization DEFF Research Database (Denmark) Fiandaca, Gianluca; Auken, Esben; Christiansen, Anders Vest 2012-01-01 Time-domain-induced polarization has significantly broadened its field of reference during the last decade, from mineral exploration to environmental geophysics, e.g., for clay and peat identification and landfill characterization. Though, insufficient modeling tools have hitherto limited the use...... of time-domaininduced polarization for wider purposes. For these reasons, a new forward code and inversion algorithm have been developed using the full-time decay of the induced polarization response, together with an accurate description of the transmitter waveform and of the receiver transfer function......%. Furthermore, the presence of low-pass filters in time-domain-induced polarization instruments affects the early times of the acquired decays (typically up to 100 ms) and has to be modeled in the forward response to avoid significant loss of resolution. The developed forward code has been implemented in a 1D... 18. Dynamic nuclear spin polarization Energy Technology Data Exchange (ETDEWEB) Stuhrmann, H.B. [GKSS-Forschungszentrum Geesthacht GmbH (Germany) 1996-11-01 Polarized neutron scattering from dynamic polarized targets has been applied to various hydrogenous materials at different laboratories. In situ structures of macromolecular components have been determined by nuclear spin contrast variation with an unprecedented precision. The experiments of selective nuclear spin depolarisation not only opened a new dimension to structural studies but also revealed phenomena related to propagation of nuclear spin polarization and the interplay of nuclear polarisation with the electronic spin system. The observation of electron spin label dependent nuclear spin polarisation domains by NMR and polarized neutron scattering opens a way to generalize the method of nuclear spin contrast variation and most importantly it avoids precontrasting by specific deuteration. It also likely might tell us more about the mechanism of dynamic nuclear spin polarisation. (author) 4 figs., refs. 19. Invariants of polarization transformations. Science.gov (United States) Sadjadi, Firooz A 2007-05-20 The use of polarization-sensitive sensors is being explored in a variety of applications. Polarization diversity has been shown to improve the performance of the automatic target detection and recognition in a significant way. However, it also brings out the problems associated with processing and storing more data and the problem of polarization distortion during transmission. We present a technique for extracting attributes that are invariant under polarization transformations. The polarimetric signatures are represented in terms of the components of the Stokes vectors. Invariant algebra is then used to extract a set of signature-related attributes that are invariant under linear transformation of the Stokes vectors. Experimental results using polarimetric infrared signatures of a number of manmade and natural objects undergoing systematic linear transformations support the invariancy of these attributes. 20. POLARIZED LIGHT IN PHYSIOTHERAPY National Research Council Canada - National Science Library L. D. Tondiy; O. L. Tondiy; I. V. Kas; O. V. Zemlyana; O. L. Zakrevska; V. O. Zhuravliev 2015-01-01 The data on polarized light (PS) - a new promising treatment, rehabilitation and prevention, which took its deserved place among the known therapeutic physical factors and may even compete with laser radiation of low and LED therapy... 1. Cell Polarity in Yeast. Science.gov (United States) Chiou, Jian-Geng; Balasubramanian, Mohan K; Lew, Daniel J 2017-08-07 A conserved molecular machinery centered on the Cdc42 GTPase regulates cell polarity in diverse organisms. Here we review findings from budding and fission yeasts that reveal both a conserved core polarity circuit and several adaptations that each organism exploits to fulfill the needs of its lifestyle. The core circuit involves positive feedback by local activation of Cdc42 to generate a cluster of concentrated GTP-Cdc42 at the membrane. Speciesspecific pathways regulate the timing of polarization during the cell cycle, as well as the location and number of polarity sites. Expected final online publication date for the Annual Review of Cell and Developmental Biology Volume 33 is October 6, 2017. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates. 2. Coordenadas polares: curvas maravillosas OpenAIRE Norberto Jaime Chau Pérez; Roy Wil Sánchez Gutiérrez 2010-01-01 Se presenta una actividad colaborativa en la que se trabaja el tema coordenadas polares. Se presentan los objetivos de aprendizaje, el desarrollo de la actividad, los conocimientos previos necesarios y recomendaciones para una aplicación posterior. 3. Political Competition and Polarization DEFF Research Database (Denmark) Schultz, Christian This paper considers political competition and the consequences of political polarization when parties are better informed about how the economy functions than voters are. Specifically, parties know the cost producing a public good, voters do not. An incumbent's choice of policy acts like a signal...... for costs before an upcoming election. It is shown that the more polarized the political parties the more distorted the incumbent's policy choice.... 4. Hadamard quantum broadcast channels Science.gov (United States) Wang, Qingle; Das, Siddhartha; Wilde, Mark M. 2017-10-01 We consider three different communication tasks for quantum broadcast channels, and we determine the capacity region of a Hadamard broadcast channel for these various tasks. We define a Hadamard broadcast channel to be such that the channel from the sender to one of the receivers is entanglement-breaking and the channel from the sender to the other receiver is complementary to this one. As such, this channel is a quantum generalization of a degraded broadcast channel, which is well known in classical information theory. The first communication task we consider is classical communication to both receivers, the second is quantum communication to the stronger receiver and classical communication to other, and the third is entanglement-assisted classical communication to the stronger receiver and unassisted classical communication to the other. The structure of a Hadamard broadcast channel plays a critical role in our analysis: The channel to the weaker receiver can be simulated by performing a measurement channel on the stronger receiver's system, followed by a preparation channel. As such, we can incorporate the classical output of the measurement channel as an auxiliary variable and solve all three of the above capacities for Hadamard broadcast channels, in this way avoiding known difficulties associated with quantum auxiliary variables. 5. Spin Polarization of 2D Electrons in GaAs Quantum Wells at ν=1/2 from Gallium NMR Measurements Science.gov (United States) Freytag, N.; Horvatić, M.; Berthier, C.; Lévy, L.-P.; Melinte, S.; Bayot, V.; Shayegan, M. 2000-03-01 The spin polarization (\\cal P) of a two-dimensional electron gas (2DEG) in two GaAs/AlGaAs multiple-quantum-well heterostructures was probed by measurements of magnetic hyperfine shifts of gallium nuclei located in the quantum wells. The low temperature (50 mK Shankar(R. Shankar, cond-mat/9911288.). 6. Polar Warming Drivers Science.gov (United States) McDunn, T. L.; Bougher, S. W.; Mischna, M. A.; Murphy, J. R. 2012-12-01 Polar warming is a dynamically induced temperature enhancement over mid-to-high latitudes that results in a reversed (poleward) meridional temperature gradient. This phenomenon was recently characterized over the 40-90 km altitude region [1] based on nearly three martian years of Mars Climate Sounder observations [2, 3]. Here we investigate which forcing mechanisms affect the magnitude and distribution of the observed polar warming by conducting simulations with the Mars Weather Research and Forecasting General Circulation Model [4, 5]. We present simulations confirming the influence topography [6] and dust loading [e.g., 7] have upon polar warming. We then present simulations illustrating the modulating influence gravity wave momentum deposition exerts upon polar warming, consistent with previous modeling studies [e.g., 8]. The results of this investigation suggest the magnitude and distribution of polar warming in the martian middle atmosphere is modified by gravity wave activity and that the characteristics of the gravity waves that most significantly affect polar warming vary with season. References: [1] McDunn, et al., 2012 (JGR), [2]Kleinböhl, et al., 2009 (JGR), [3] Kleinböhl, et al., 2011 (JQSRT), [4] Richardson, et al., 2007 (JGR), [5] Mischna, et al., 2011 (Planet. Space Sci.), [6] Richardson and Wilson, 2002 (Nature), [7] Haberle, et al., 1982 (Icarus), [8] Barnes, 1990 (JGR). 7. Coupled-channels optical calculation of positron-hydrogen resonances Institute of Scientific and Technical Information of China (English) Yu Rong-Mei; Zhou Ya-Jun; Jiao Li-Guang; Cheng Yong-Jun 2012-01-01 An application of the coupled-channels optical method is given for the energy-dependent phenomena of positronhydrogen resonances below the n =2 excitation threshold.The equivalent local optical potential is used to account for the target polarization and positronium formation.The calculation includes 9 explicitly physical coupled channels.The lowest S-wave resonance energy position and new resonances are found.Angular dependence of the cross section in the resonance region are investigated. 8. La ballata E5 e le sue varianti nel codice degli abbozzi Directory of Open Access Journals (Sweden) Giulia Ravera 2016-07-01 Full Text Available La ballata petrarchesca Amor, che ’n cielo e ’n cor gentile alberghi (E5, composta per il musico Confortino e destinata alla definitiva esclusione dal Canzoniere, è un componimento profondamente complesso, oltre che caratterizzato da un’intrigante vicenda redazionale. E5 appare infatti imperniata sull’ambiguità tra due poli opposti, amoroso e religioso, in un gioco di contrapposizioni che rende difficile scegliere in via definitiva tra un’interpretazione sentimentale ed una lettura morale o addirittura penitenziale. La ballata è inoltre caratterizzata dall’evidente ed esteso riuso della tradizione lirica ed in particolare dei modelli stilnovistici, non solo e non tanto sul piano degli stilemi e delle immagini, quanto in termini di concezione amorosa. Il rapporto con queste fonti risulta problematico, tra ripresa e negazione, e rappresenta un ulteriore nodo significativo rispetto all’interpretazione del componimento. La graduale evoluzione della ballata, di cui possono essere identificate per lo meno tre versioni distinte, sembra accentuare gli elementi di complessità e le sovrapposizioni semantiche. Infine, l’analisi formale e contenutistica di E5 favorisce la formulazione, pur senza pretesa di certezza, di ipotesi sulle ragioni della sua sorte extravagante 9. Electrochemical characterisation of nickel-based alloys in sulphate solutions at 320 deg. C Energy Technology Data Exchange (ETDEWEB) Le Canut, J.-M.; Maximovitch, S. E-mail: suzanne.maximovitch@lepmi.inpg.fr; Dalard, F 2004-08-15 Nickel alloy steam generator tubes of pressurized water reactors (PWR) are sensitive to stress corrosion cracking (SCC) and the possibility of predicting SCC from electrochemical measurements is of considerable interest for nuclear industry. The electrochemical properties of several nickel-based alloys were studied at 320 deg. C in sulphate solutions at neutral or slightly alkaline pH from corrosion potential measurements, polarisation curves and polarisation resistance (R{sub p}) measurements by linear voltammetry and electrochemical impedance spectroscopy (EIS). The passive layers were much more stable in neutral conditions, due to the presence of chromium oxide, and alloys 600TT and 690 showed the best passivity. R{sub p} measurements confirmed that alloys 600TT and 690 have the lowest corrosion rates. At alkaline pH, the passivation currents were higher than those obtained at neutral pH, and the alloys showed a close behaviour. Reduction of sulphates to sulphides seemed to be possible. Results are in agreement with thermodynamic and surface analysis data of literature. The electrochemical stability did not appear to be directly related to SCC susceptibility since it varied inversely with the pH dependance of SCC in sulphate medium. 10. A 20 GHz bright sample for {\\delta} > +72{\\deg}: I. Catalogue CERN Document Server Righini, S; Ricci, R; Zanichelli, A; Mack, K -H; Massardi, M; Prandoni, I; Procopio, P; Verma, R; López-Caniego, M; Gregorini, L; Mantovani, F 2012-01-01 During 2010-2011, the Medicina 32-m dish hosted the 7-feed 18-26.5 GHz receiver built for the Sardinia Radio Telescope, with the goal to perform its commissioning. This opportunity was exploited to carry out a pilot survey at 20 GHz over the area for {\\delta} > + 72.3{\\deg}. This paper describes all the phases of the observations, as they were performed using new hardware and software facilities. The map-making and source extraction procedures are illustrated. A customised data reduction tool was used during the follow-up phase, which produced a list of 73 confirmed sources down to a flux density of 115 mJy. The resulting catalogue, here presented, is complete above 200 mJy. Source counts are in agreement with those provided by the AT20G survey. This pilot activity paves the way to a larger project, the K-band Northern Wide Survey (KNoWS), whose final aim is to survey the whole Northern Hemisphere down to a flux limit of 50 mJy (5{\\sigma}). 11. Effect of Cr content on the FAC of pipe material at 150 .deg. C Energy Technology Data Exchange (ETDEWEB) Park, Tae Jun; Kim, Hong Pyo [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of) 2013-06-15 Flow accelerated corrosion (FAC) of the carbon steel piping in nuclear power plants (NPPs) has been major issue in nuclear industry. During the FAC, a protective oxide layer on carbon steel dissolves into flowing water leading to a thinning of the oxide layer and accelerating corrosion of base material. As a result, severe failures may occur in the piping and equipment of NPPs. Effect of alloying elements on FAC of pipe materials was studied with rotating cylinder FAC test facility at 150 .deg. C and at flow velocity of 4m/s. The facility is equipped with on line monitoring of pH, conductivity, dissolved oxygen(DO) and temperature. Test solution was the demineralized water, and DO concentration was less than 1 ppb. Surface appearance of A 106 Gr. B which is used widely in secondary pipe in NPPs showed orange peel appearance, typical appearance of FAC. The materials with Cr content higher than 0.17wt.% showed pit. The pit is thought to early degradation mode of FAC. The corrosion product within the pit was enriched with Cr, Mo, Cu, Ni and S. But S was not detected in SA336 F22V with 2.25wt.% Cr. The enrichment of Cr and Mo seemed to be related with low, solubility of Cr and Mo compared to Fe. Measured FAC rate was compared with Ducreaux's relationship and showed slightly lower FAC rate than Ducreaux's relationship. 12. Back Pain During 6 deg Head-Down Tilt Approximates That During Actual Microgravity Science.gov (United States) Hutchinson, Karen J.; Watenpaugh, Donald E.; Murthy, Gita; Convertino, Victor A.; Hargens, Alan R. 1995-01-01 Astronauts often experience back pain during spaceflight. It was found that during spaceflight, 14 of 19 Shuttle crewmembers experienced back pain, which they described as dull (62%), localized to the lower back (500/6), and with an intensity of 2 on a 5-point scale. Further, the spine lengthens 4-7 cm in microgravity. Our objective was to compare back pain and spinal lengthening (body height increase) during simulated microgravity (6 deg head-down tilt, HDT) with the some parameters during actual microgravity. Eight male subjects completed a modified McGill pain questionnaire with intensity graded from zero (no pain) to five (intense and incapacitating gain) each day at 7.-OO pm during 2 d pre-HDT control, 16 d HDT, and I d post-HDT recovery periods. Only 2 subjects reported any pain after day 9 of HDT and during recov- ery. Heights increased 2.1 t 0.5 cm by day 3 of HDT and re- mained at that level until the end of the HDT period. Although spinal lengthening in space is greater than that during HDT, the HDT model approximates the level, type, distribution, and time course of back pain associated with actual microgrovity. In the HDT model, pain subsides in intensity when spinal lengthening stops. Therefore, back pain in actual and simulated microgravity may result from stretching of spinal andlor paraspinal tissues until a new spinal length is reached. 13. Estimating new production in the equatorial Pacific Ocean at 150 deg W Science.gov (United States) Dugdale, Richard C.; Wilkerson, Frances P.; Barber, Richard T.; Chavez, Francisco P. 1992-01-01 A major goal of the WEC88 cruise of the R/V Wecoma to the equatorial Pacific (made in February-March 1988) was to establish rates of new production along a meridional section at 150 deg W and to compare these measured rates with the relatively high values for the equatorial Pacific that had been reported previously using indirect methods and models. Production values were obtained from the traditional approach using N-15 labeled nitrate uptake, and by using C-14 fixation values multiplied by f (proportion of new production) from various sources: from N-15 data, from a C-14 fixation-versus-f relationship, or from a nitrate-versus-f relationship. The ratios of directly measured nitrate and carbon uptake and the ratios of nitrate to nitrate plus ammonium uptake, i.e., values of f, agree well; values of f calculated from carbon uptake or from nitrate concentration are overestimates for the equatorial upwelling region. Carbon-to-nitrogen uptake ratios measured with C-14 and N-15, respectively, approximate the Redfield molar ratio, 6.6 C:N. The overall mean value of f (0.17) helps confirm the view that the low primary production in the enriched eastern equatorial Pacific is due to failure of the nitrate-uptake system. 14. Novalis e Pascal. L’influsso degli “antichi maestri” nelle opere di Thomas Bernhard Directory of Open Access Journals (Sweden) Stefano Apostolo 2015-08-01 Full Text Available L’elaborato si pone come obiettivo l’analisi degli influssi che due pensatori del calibro di Novalis e Pascal esercitarono sulla poetica e sulla produzione di Thomas Bernhard (1931-1989. Partendo da citazioni ricorrenti nei testi dell’autore, si passerà ad una loro contestualizzazione e ad un esame del ruolo che le due figure ricoprirono nella cosmogonia bernhardiana. Personalità di per sé molto diverse, poeta romantico il primo e teologo il secondo, vissute in epoche e contesti differenti, costituiscono tuttavia punti di riferimento fondamentali e ineludibili per la comprensione dei testi dell’autore austriaco. Novalis, teoreta di quella filosofia della malattia che così profondamente pervade le opere di Bernhard, influenzò fortemente la sua oscura poetica della morte e della Hoffnungslosigkeit, e proprio il frammento, l’unità minima e paradigmatica della produzione novalisiana, venne erto da Bernhard a modello compositivo, sia nella prosa che nel teatro. Altro campione di questo espediente stilistico, di questo testo breve ma ricchissimo di significato, fu Blaise Pascal, che nei Pensées, formidabile apologia del Cristianesimo nonché introspezione del rapporto tra l’uomo e il Divino, mise a nudo i punti cardini della miseria e della finitezza umana, sui quali Bernhard fece leva in maniera personalissima, per consolidare la propria visione del mondo e per dare vita alla teologia negativa che pervade le sue opere. 15. On resolving the 180 deg ambiguity for a temporal sequence of vector magnetograms Science.gov (United States) Cheung, M. C. 2008-05-01 The solar coronal magnetic field evolves in response to the underlying photospheric driving. To study this connection by means of data-driven modeling, an accurate knowledge of the evolution of the photospheric vector field is essential. While there is a large body of work on attempts to resolve the 180 deg ambiguity in the component of the magnetic field transverse to the line of sight, most of these methods are applicable only to individual frames. With the imminent launch of the Solar Dynamics Observatory, it is especially timely for us to develop possible automated methods to resolve the ambiguity for temporal sequences of magnetograms. We present here the temporal acute angle method, which makes use of preceding disambiguated magnetograms as reference solutions for resolving the ambiguity in subsequent frames. To find the strengths and weaknesses of this method, we have carried out tests (1) on idealized magnetogram sequences involving simple rotating, shearing and straining flows and (2) on a synthetic magnetogram sequence from a 3D radiative MHD simulation of an buoyant magnetic flux tube emerging through granular convection. A metric for automatically picking out regions where the method is likely to fail is also presented. 16. [Physical activity: results of the German Health Interview and Examination Survey for Adults (DEGS1)]. Science.gov (United States) Krug, S; Jordan, S; Mensink, G B M; Müters, S; Finger, J; Lampert, T 2013-05-01 Regular physical activity can have a positive effect on health at any age. Today's lifestyles, however, can often be characterised as sedentary. Therefore, the promotion of physical activity and sports has become an integral part of public health measures. The representative data of adults aged 18 to 79 years in Germany obtained from the "German Health Interview and Examination Survey for Adults" (DEGS1) provide an overview of self-estimated current physical activity behaviour. The results show that one third of the adult population claims to pay close attention to reaching a sufficient level of physical activity and one fourth participates in sports for at least 2 h/week on a regular basis. Thus, the percentage of adults regularly engaged in sports has increased compared to the previous "German National Health Interview and Examination Survey 1998". Still, four out of five adults do not achieve at least 2.5 h/week of moderate-intensity physical activity as recommended by the World Health Organisation. Consequently, future individual-level and population-level interventions should focus on target group-specific measures while continuing to promote regular physical activity in all segments of the population. An English full-text version of this article is available at SpringerLink as supplemental. 17. Polarization properties of linearly polarized parabolic scaling Bessel beams Science.gov (United States) Guo, Mengwen; Zhao, Daomu 2016-10-01 The intensity profiles for the dominant polarization, cross polarization, and longitudinal components of modified parabolic scaling Bessel beams with linear polarization are investigated theoretically. The transverse intensity distributions of the three electric components are intimately connected to the topological charge. In particular, the intensity patterns of the cross polarization and longitudinal components near the apodization plane reflect the sign of the topological charge. 18. Do cephalopods communicate using polarized light reflections from their skin? Science.gov (United States) Mäthger, Lydia M; Shashar, Nadav; Hanlon, Roger T 2009-07-01 Cephalopods (squid, cuttlefish and octopus) are probably best known for their ability to change color and pattern for camouflage and communication. This is made possible by their complex skin, which contains pigmented chromatophore organs and structural light reflectors (iridophores and leucophores). Iridophores create colorful and linearly polarized reflective patterns. Equally interesting, the photoreceptors of cephalopod eyes are arranged in a way to give these animals the ability to detect the linear polarization of incoming light. The capacity to detect polarized light may have a variety of functions, such as prey detection, navigation, orientation and contrast enhancement. Because the skin of cephalopods can produce polarized reflective patterns, it has been postulated that cephalopods could communicate intraspecifically through this visual system. The term 'hidden' or 'private' communication channel has been given to this concept because many cephalopod predators may not be able to see their polarized reflective patterns. We review the evidence for polarization vision as well as polarization signaling in some cephalopod species and provide examples that tend to support the notion--currently unproven--that some cephalopods communicate using polarized light signals. 19. USACE Navigation Channels 2012 Data.gov (United States) California Department of Resources — This dataset represents both San Francisco and Los Angeles District navigation channel lines. All San Francisco District channel lines were digitized from CAD files... 20. Channelling versus inversion DEFF Research Database (Denmark) Gale, A.S.; Surlyk, Finn; Anderskouv, Kresten 2013-01-01 . Within this channel were smaller erosional structures (hardgrounds, and locally have a basal fill of granular phosphorite. The entire channel system was progressively infilled by chalk, as demonstrated by the expanded succession... 1. Effect of GaN buffer polarization on electron distribution of AlGaN/GaN heterostructure Energy Technology Data Exchange (ETDEWEB) He, Xiaoguang; Zhao, Degang, E-mail: dgzhao@red.semi.ac.cn; Liu, Wei; Yang, Jing; Li, Xiaojing; Li, Xiang 2016-06-15 The formation of 2DEG in AlGaN/GaN heterostructure is discussed in detail. A misunderstanding about the 2DEG sheet density expression is clarified. It is predicted by theoretical analysis and validated by self-consistent Schrodinger–Poisson numerical simulation that under the force of GaN polarization, large amounts of electrons will accumulate at the GaN/substrate interface in AlGaN/GaN/substrate HEMT structure. - Highlights: • The formation of 2DEG in AlGaN/GaN heterostructure is discussed in detail. • Self-consistent Schrodinger–Poisson numerical simulation is used to modulate the AlGaN/GaN/substrate structure. • It is predicted by that large amounts of electrons will accumulate at the GaN/substrate interface. 2. Relating polarization phase difference of SAR signals to scene properties Science.gov (United States) Ulaby, Fawwaz T.; Dobson, Myron C.; Mcdonald, Kyle C.; Senior, Thomas B. A.; Held, Daniel 1987-01-01 This paper examines the statistical behavior of the phase difference Delta-phi between the HH-polarized and VV-polarized backscattered signals recorded by an L-band SAR over an agricultural test site in Illinois. Polarization-phase difference distributions were generated for about 200 agricultural fields for which ground information had been acquired in conjunction with the SAR mission. For the overwhelming majority of cases, the Delta-phi distribution is symmetric and has a single major lobe centered at the mean value of the distribution Delta-phi. Whereas the mean Delta-phi was found to be close to zero degrees for bare soil, cut vegetation, alfalfa, soybeans, and clover, a different pattern was observed for the corn fields; the mean Delta-phi increased with increasing incidence angle Theta = 35 deg. The explanation proposed for this variation is that the corn canopy, most of whose mass is contained in its vertical stalks, acts like a uniaxial crystal characterized by different velocities of propagation for waves with horizontal and vertical polarization. Thus, it is hypothesized that the observed backscatter is contributed by a combination of propagation delay, forward scatter by the soil surface, and specular bistatic reflection by the stalks. Model calculations based on this assumption were found to be in general agreement with the phase observations. 3. MODIS/COMBINED MCD12C1 Land Cover Type Yearly L3 Global 0.05Deg CMG Data.gov (United States) U.S. Geological Survey, Department of the Interior — MODIS/Terra+Aqua Land Cover Type Yearly L3 Global 0.05Deg CMG The Land Cover Type Yearly Climate Modeling Grid (CMG) is a lower spatial resolution (0.05?) product,... 4. Polarized Light Microscopy Science.gov (United States) Frandsen, Athela F. 2016-01-01 Polarized light microscopy (PLM) is a technique which employs the use of polarizing filters to obtain substantial optical property information about the material which is being observed. This information can be combined with other microscopy techniques to confirm or elucidate the identity of an unknown material, determine whether a particular contaminant is present (as with asbestos analysis), or to provide important information that can be used to refine a manufacturing or chemical process. PLM was the major microscopy technique in use for identification of materials for nearly a century since its introduction in 1834 by William Fox Talbot, as other techniques such as SEM (Scanning Electron Microscopy), FTIR (Fourier Transform Infrared spectroscopy), XPD (X-ray Powder Diffraction), and TEM (Transmission Electron Microscopy) had not yet been developed. Today, it is still the only technique approved by the Environmental Protection Agency (EPA) for asbestos analysis, and is often the technique first applied for identification of unknown materials. PLM uses different configurations in order to determine different material properties. With each configuration additional clues can be gathered, leading to a conclusion of material identity. With no polarizing filter, the microscope can be used just as a stereo optical microscope, and view qualities such as morphology, size, and number of phases. With a single polarizing filter (single polars), additional properties can be established, such as pleochroism, individual refractive indices, and dispersion staining. With two polarizing filters (crossed polars), even more can be deduced: isotropy vs. anisotropy, extinction angle, birefringence/degree of birefringence, sign of elongation, and anomalous polarization colors, among others. With the use of PLM many of these properties can be determined in a matter of seconds, even for those who are not highly trained. McCrone, a leader in the field of polarized light microscopy, often 5. De novo transcriptome sequencing analysis and comparison of differentially expressed genes (DEGs in Macrobrachium rosenbergii in China. Directory of Open Access Journals (Sweden) Hai Nguyen Thanh Full Text Available Giant freshwater prawn (GFP; Macrobrachium rosenbergii is an exotic species that was introduced into China in 1976 and thereafter it became a major species in freshwater aquaculture. However the gene discovery in this species has been limited to small-scale data collection in China. We used the next generation sequencing technology for the experiment; the transcriptome was sequenced of samples of hepatopancreas organ in individuals from 4 GFP groups (A1, A2, B1 and B2. De novo transcriptome sequencing generated 66,953 isogenes. Using BLASTX to search the Non-redundant (NR, Search Tool for the Retrieval of Interacting Genes (STRING, and Kyoto Encyclopedia of Genes and Genome (KEGG databases; 21,224 unigenes were annotated, 9,552 matched unigenes with the Gene Ontology (GO classification; 5,782 matched unigenes in 25 categories of Clusters of Orthologous Groups of proteins (COG and 20,859 unigenes were consequently assigned to 312 KEGG pathways. Between the A and B groups 147 differentially expressed genes (DEGs were identified; between the A1 and A2 groups 6,860 DEGs were identified and between the B1 and B2 groups 5,229 DEGs were identified. After enrichment, the A and B groups identified 38 DEGs, but none of them were significantly enriched. The A1 and A2 groups identified 21,856 DEGs in three main categories based on functional groups: biological process, cellular_component and molecular function and the KEGG pathway defined 2,459 genes had a KEGG Ortholog-ID (KO-ID and could be categorized into 251 pathways, of those, 9 pathways were significantly enriched. The B1 and B2 groups identified 5,940 DEGs in three main categories based on functional groups: biological process, cellular_component and molecular function, and the KEGG pathway defined 1,543 genes had a KO-ID and could be categorized into 240 pathways, of those, 2 pathways were significantly enriched. We investigated 99 queries (GO which related to growth of GFP in 4 groups. After 6. De novo transcriptome sequencing analysis and comparison of differentially expressed genes (DEGs) in Macrobrachium rosenbergii in China. Science.gov (United States) Nguyen Thanh, Hai; Zhao, Liangjie; Liu, Qigen 2014-01-01 Giant freshwater prawn (GFP; Macrobrachium rosenbergii) is an exotic species that was introduced into China in 1976 and thereafter it became a major species in freshwater aquaculture. However the gene discovery in this species has been limited to small-scale data collection in China. We used the next generation sequencing technology for the experiment; the transcriptome was sequenced of samples of hepatopancreas organ in individuals from 4 GFP groups (A1, A2, B1 and B2). De novo transcriptome sequencing generated 66,953 isogenes. Using BLASTX to search the Non-redundant (NR), Search Tool for the Retrieval of Interacting Genes (STRING), and Kyoto Encyclopedia of Genes and Genome (KEGG) databases; 21,224 unigenes were annotated, 9,552 matched unigenes with the Gene Ontology (GO) classification; 5,782 matched unigenes in 25 categories of Clusters of Orthologous Groups of proteins (COG) and 20,859 unigenes were consequently assigned to 312 KEGG pathways. Between the A and B groups 147 differentially expressed genes (DEGs) were identified; between the A1 and A2 groups 6,860 DEGs were identified and between the B1 and B2 groups 5,229 DEGs were identified. After enrichment, the A and B groups identified 38 DEGs, but none of them were significantly enriched. The A1 and A2 groups identified 21,856 DEGs in three main categories based on functional groups: biological process, cellular_component and molecular function and the KEGG pathway defined 2,459 genes had a KEGG Ortholog-ID (KO-ID) and could be categorized into 251 pathways, of those, 9 pathways were significantly enriched. The B1 and B2 groups identified 5,940 DEGs in three main categories based on functional groups: biological process, cellular_component and molecular function, and the KEGG pathway defined 1,543 genes had a KO-ID and could be categorized into 240 pathways, of those, 2 pathways were significantly enriched. We investigated 99 queries (GO) which related to growth of GFP in 4 groups. After enrichment we 7. Quantum Multiple Access Channel Institute of Scientific and Technical Information of China (English) 侯广; 黄民信; 张永德 2002-01-01 We consider the transmission of classical information over a quantum channel by many senders, which is a generalization of the two-sender case. The channel capacity region is shown to be a convex hull bound by the yon Neumann entropy and the conditional yon Neumann entropies. The result allows a reasonable distribution of channel capacity over the senders. 8. [Polar and non polar notations of refraction]. Science.gov (United States) Touzeau, O; Gaujoux, T; Costantini, E; Borderie, V; Laroche, L 2010-01-01 Refraction can be expressed by four polar notations which correspond to four different combinations of spherical or cylindrical lenses. Conventional expressions of refraction (plus and minus cylinder notation) are described by sphere, cylinder, and axis. In the plus cylinder notation, the axis visualizes the most powerful meridian. The axis usually corresponds to the bow tie axis in curvature maps. Plus cylinder notation is also valuable for all relaxing procedures (i.e., selective suture ablation, arcuate keratotomy, etc.). In the cross-cylinder notation, two orthogonal cylinders can describe (without the sphere component) the actual refraction of both the principal meridians. This notation must be made before performing the vertex calculation. Using an association of a Jackson cross-cylinder and a spherical equivalent, refraction can be broken down into two pure components: astigmatism and sphere. All polar notations of refraction may perfectly characterize a single refraction but are not suitable for statistical analysis, which requires nonpolar expression. After doubling the axis, a rectangular projection breaks down the Jackson cross-cylinder, which has a polar axis, into two Jackson cross-cylinders on the 0 degrees /90 degrees and 45 degrees /135 degrees axis. This procedure results in the loss of the directional nature of the data. Refraction can be written in a nonpolar notation by three rectangular coordinates (x,y,z), which can also represent the spherocylinder by one point in a dioptric space. These three independent (orthogonal) variables have a concrete optical significance: a spherical component, a direct/inverse (WTR/ATR) component, and an oblique component of the astigmatism. Finally, nonpolar notations are useful for statistical analysis and graphical representation of refraction. 9. When measured spin polarization is not spin polarization Science.gov (United States) Dowben, P. A.; Wu, Ning; Binek, Christian 2011-05-01 Spin polarization is an unusually ambiguous scientific idiom and, as such, is rarely well defined. A given experimental methodology may allow one to quantify a spin polarization but only in its particular context. As one might expect, these ambiguities sometimes give rise to inappropriate interpretations when comparing the spin polarizations determined through different methods. The spin polarization of CrO2 and Cr2O3 illustrate some of the complications which hinders comparisons of spin polarization values. 10. Polarized nuclear target based on parahydrogen induced polarization Energy Technology Data Exchange (ETDEWEB) D. Budker, M.P. Ledbetter, S. Appelt, L.S. Bouchard, B. Wojtsekhowski 2012-12-01 We discuss a novel concept of a polarized nuclear target for accelerator fixed-target scattering experiments, which is based on parahydrogen induced polarization (PHIP). One may be able to reach a 33% free-proton polarization in the ethane molecule. The potential advantages of such a target include operation at zero magnetic field, fast ({approx}100 HZ) polarization oscillation (akin to polarization reversal), and operation with large intensity of an electron beam. 11. Bacillus subtilis response regulator DegU is a direct activator of pgsB transcription involved in gamma-poly-glutamic acid synthesis. Science.gov (United States) Ohsawa, Taku; Tsukahara, Kensuke; Ogura, Mitsuo 2009-09-01 pgsB encodes gamma-poly glutamic acid (gamma-PGA) synthetase and constitutes an operon with pgsC, pgsAA, and pgsE. Genetic analysis revealed that degQ and swrA, the known regulators of pgsB, are not required for pgsB expression when high cellular concentrations of phosphorylated form of the response regulator DegU (DegU-P) are present. However, swrA appeared still to be required for gamma-PGA synthesis under the conditions we tested. Since genetic analysis suggested that DegU-P activates pgsB directly, we performed gel retardation and footprint analyses using purified His-tagged DegU and the pgsB promoter. The in vitro experiments revealed that His-tagged DegU bound to the immediate upstream region of the -35 region of the pgsB promoter. A six-base deletion within the sequence (the -44 to -39 region) abolished DegU-binding to the pgsB promoter and pgsB transcription, confirming the importance of the sequence for DegU-dependent regulation of pgsB. Hence we conclude that DegU is a direct activator of the pgsB operon. 12. Reverse Polarity Magnetized Melt Rocks from the Cretaceous/Tertiary Chicxulub Structure, Yucatan Peninsula, Mexico Science.gov (United States) Urrutia-Fucugauchi, J.; Marin, Luis; Sharpton, Virgil L. 1994-01-01 We report paleomagnetic results for core samples of the breccia and andesitic rocks recovered from the Yucatan-6 Petrolcos Mexicanos exploratory well within the Chicxulub structure (about 60 km SSW from its center), northern Yucatan, Mexico. A previous study has shown that the rocks studied contain high iridium levels and shocked breccia clasts and an Ar/Ar date of 65.2 +/- 0.4 Ma. Andesitic rocks are characterized by stable single-component magnetizations with a mean inclination of -42.6 deg +/- 2.4 deg. Breccias present a complex paleomagnetic record characterized by multivectorial magnetizations with widely different initial NRM inclinations. However, after alternating field demagnetization, well defined characteristic components with upward inclinations are defined. IRM acquisition experiments, comparison of IRM and NRM coercivity spectra and the single component magnetization of the andesitic rocks indicate the occurrence of iron-rich titanomagnetites of single or pseudo-single domain states as the dominant magnetic carriers. Mean inclinations from the andesitic rocks and most of the breccia samples give a mean inclination of about -40 deg to -45 deg, indicating a reverse polarity for the characteristic magnetization that is consistent with geomagnetic chron 29R, which spans the Cretaceous/Tertiary (K/T) boundary. The inclination is also consistent with the expected value (and corresponding paleolatitude) for the site estimated from the reference polar wander curve for North America. We suggest that the characteristic magnetizations for the andesitic and breccia rocks are the result of shock heating at the time of formation of the impact structure and that the age, polarity and pateolatitude are consistent with a time at the K/T boundary. 13. Cylindrically Polarized Nondiffracting Optical Pulses CERN Document Server Ornigotti, Marco; Szameit, Alexander 2016-01-01 We extend the concept of radially and azimuthally polarized optical beams to the polychromatic domain by introducing cylindrically polarized nondiffracting optical pulses. In particular, we discuss in detail the case of cylindrically polarized X-waves, both in the paraxial and nonparaxial regime. The explicit expressions for the electric and magnetic fields of cylindrically polarized X-waves is also reported. 14. Sequential Polarity-Reversing Circuit Science.gov (United States) Labaw, Clayton C. 1994-01-01 Proposed circuit reverses polarity of electric power supplied to bidirectional dc motor, reversible electro-mechanical actuator, or other device operating in direction depending on polarity. Circuit reverses polarity each time power turned on, without need for additional polarity-reversing or direction signals and circuitry to process them. 15. Proteomic approaches to identify substrates of the three Deg/HtrA proteases of the cyanobacterium Synechocystis sp. PCC 6803. Science.gov (United States) Tam, Lam X; Aigner, Harald; Timmerman, Evy; Gevaert, Kris; Funk, Christiane 2015-06-15 The family of Deg/HtrA proteases plays an important role in quality control of cellular proteins in a wide range of organisms. In the genome of the cyanobacterium Synechocystis sp. PCC 6803, a model organism for photosynthetic research and renewable energy products, three Deg proteases are encoded, termed HhoA, HhoB and HtrA. In the present study, we compared wild-type (WT) Synechocystis cells with the single insertion mutants ΔhhoA, ΔhhoB and ΔhtrA. Protein expression of the remaining Deg/HtrA proteases was strongly affected in the single insertion mutants. Detailed proteomic studies using DIGE (difference gel electrophoresis) and N-terminal COFRADIC (N-terminal combined fractional diagonal chromatography) revealed that inactivation of a single Deg protease has similar impact on the proteomes of the three mutants; differences to WT were observed in enzymes involved in the major metabolic pathways. Changes in the amount of phosphate permease system Pst-1 were observed only in the insertion mutant ΔhhoB. N-terminal COFRADIC analyses on cell lysates of ΔhhoB confirmed changed amounts of many cell envelope proteins, including the phosphate permease systems, compared with WT. In vitro COFRADIC studies were performed to identify the specificity profiles of the recombinant proteases rHhoA, rHhoB or rHtrA added to the Synechocystis WT proteome. The combined in vivo and in vitro N-terminal COFRADIC datasets propose RbcS as a natural substrate for HhoA, PsbO for HhoB and HtrA and Pbp8 for HtrA. We therefore suggest that each Synechocystis Deg protease protects the cell through different, but connected mechanisms. © The Authors Journal compilation © 2015 Biochemical Society. 16. Polarization twist in perovskite ferrielectrics. Science.gov (United States) Kitanaka, Yuuki; Hirano, Kiyotaka; Ogino, Motohiro; Noguchi, Yuji; Miyayama, Masaru; Moriyoshi, Chikako; Kuroiwa, Yoshihiro 2016-09-02 Because the functions of polar materials are governed primarily by their polarization response to external stimuli, the majority of studies have focused on controlling polar lattice distortions. In some perovskite oxides, polar distortions coexist with nonpolar tilts and rotations of oxygen octahedra. The interplay between nonpolar and polar instabilities appears to play a crucial role, raising the question of how to design materials by exploiting their coupling. Here, we introduce the concept of 'polarization twist', which offers enhanced control over piezoelectric responses in polar materials. Our experimental and theoretical studies provide direct evidence that a ferrielectric perovskite exhibits a large piezoelectric response because of extended polar distortion, accompanied by nonpolar octahedral rotations, as if twisted polarization relaxes under electric fields. The concept underlying the polarization twist opens new possibilities for developing alternative materials in bulk and thin-film forms. 17. Polarization twist in perovskite ferrielectrics Science.gov (United States) Kitanaka, Yuuki; Hirano, Kiyotaka; Ogino, Motohiro; Noguchi, Yuji; Miyayama, Masaru; Moriyoshi, Chikako; Kuroiwa, Yoshihiro 2016-01-01 Because the functions of polar materials are governed primarily by their polarization response to external stimuli, the majority of studies have focused on controlling polar lattice distortions. In some perovskite oxides, polar distortions coexist with nonpolar tilts and rotations of oxygen octahedra. The interplay between nonpolar and polar instabilities appears to play a crucial role, raising the question of how to design materials by exploiting their coupling. Here, we introduce the concept of ‘polarization twist’, which offers enhanced control over piezoelectric responses in polar materials. Our experimental and theoretical studies provide direct evidence that a ferrielectric perovskite exhibits a large piezoelectric response because of extended polar distortion, accompanied by nonpolar octahedral rotations, as if twisted polarization relaxes under electric fields. The concept underlying the polarization twist opens new possibilities for developing alternative materials in bulk and thin-film forms. PMID:27586824 18. Polarization twist in perovskite ferrielectrics Science.gov (United States) Kitanaka, Yuuki; Hirano, Kiyotaka; Ogino, Motohiro; Noguchi, Yuji; Miyayama, Masaru; Moriyoshi, Chikako; Kuroiwa, Yoshihiro 2016-09-01 Because the functions of polar materials are governed primarily by their polarization response to external stimuli, the majority of studies have focused on controlling polar lattice distortions. In some perovskite oxides, polar distortions coexist with nonpolar tilts and rotations of oxygen octahedra. The interplay between nonpolar and polar instabilities appears to play a crucial role, raising the question of how to design materials by exploiting their coupling. Here, we introduce the concept of ‘polarization twist’, which offers enhanced control over piezoelectric responses in polar materials. Our experimental and theoretical studies provide direct evidence that a ferrielectric perovskite exhibits a large piezoelectric response because of extended polar distortion, accompanied by nonpolar octahedral rotations, as if twisted polarization relaxes under electric fields. The concept underlying the polarization twist opens new possibilities for developing alternative materials in bulk and thin-film forms. 19. Study of polarized-e polarized-p --> e-prime p pi0 in the Delta(1232) mass region using polarization asymmetries CERN Document Server Biselli, A; Amaryan, M J; Anciant, E; Anghinolfi, M; Asavapibhop, B; Asryan, G; Audit, G; Auger, T; Avakian, H; Barrow, S; Battaglieri, M; Beard, K; Bektasoglu, M; Bertozzi, W; Bianchi, N; Boiarinov, S; Bonner, B E; Bosted, P; Bouchigny, S; Bradford, R; Branford, D; Brooks, W K; Bültmann, S; Burkert, V D; Calarco, J R; Carman, D S; Carnahan, B; Cetina, C; Ciciani, L; Cole, P L; Coleman, A; Connelly, J; Cords, D; Corvisiero, P; Crabb, D; Crannell, H; Cummings, J; De Sanctis, E; De Vita, R; Degtyarenko, P V; Demirchyan, R A; Denizli, H; Dennis, L C; Dharmawardane, K V; Dhuga, K S; Djalali, C; Dodge, G E; Domingo, John J; Doughty, D C; Dragovitsch, P; Dugger, M; Dytman, S; Eckhause, M; Efremenko, Yu V; Egiyan, H; Egiyan, K S; Elouadrhiri, L; Empl, A; Eugenio, P; Farhi, L; Fatemi, R; Feuerbach, R J; Ficenec, J; Fissum, K; Forest, T A; Freyberger, A P; Frolov, V; Funsten, H; Gaff, S J; Gai, M; Gavalian, G; Gavrilov, V B; Gilad, S; Gilfoyle, G P; Giovanetti, K L; Girard, P; Golovatch, E; Griffioen, K A; Guidal, M; Guillo, M R; Guo, L; Gyurjyan, V; Hancock, D; Hardie, J; Heddle, D; Hersman, F W; Hicks, K; Hicks, R S; Holtrop, M; Hu, J; Hyde-Wright, C E; Ito, M M; Jenkins, D; Joo, K; Kelley, J H; Khandaker, M; Kim, K Y; Kim, K; Kim, W; Klein, A; Klein, F J; Klimenko, A V; Klusman, M; Kossov, M; Kramer, L H; Kuang, Y; Kühn, J; Kuhn, S E; Lachniet, J; Laget, J M; Lawrence, D; Leksin, G A; Longhi, A; Loukachine, K; Major, R W; Manak, J J; Marchand, C; Matthews, S K; McAleer, S; McNabb, J W C; McCarthy, J; Mecking, B A; Mestayer, M D; Meyer, C A; Minehart, R C; Mirazita, M; Miskimen, R; Mokeev, V; Muccifora, V; Müller, J; Murphy, L Y; Mutchler, G S; Napolitano, J; Nelson, S O; Niculescu, G; Niczyporuk, B B; Niyazov, R A; Nozar, M; O'Brien, J T; O'Rielly, G V; Ohandjanyan, M S; Osipenko, M; Park, K; Patois, Y; Peterson, G A; Philips, S; Pivnyuk, N; Pocanic, D; Pogorelko, O I; Polli, E; Preedom, B M; Price, J W; Qin, L M; Raue, B A; Riccardi, G; Ricco, G; Ripani, M; Ritchie, B G; Rock, S E; Ronchetti, F; Rossi, P; Rowntree, D; Rubin, P D; Sabourov, K; Salgado, C W; Sapunenko, V; Sargsyan, M; Schumacher, R A; Serov, V S; Sharabyan, Yu G; Shaw, J; Shuvalov, S M; Simionatto, S; Skabelin, A V; Smith, E S; Smith, L C; Smith, T; Sober, D I; Sorrell, L; Spraker, M; Stepanyan, S; Stoler, P; Strakovsky, I I; Taiuti, M; Taylor, S; Tedeschi, D J; Thoma, U; Thompson, R; Todor, L; Tung, T Y; Tur, C; Ungaro, M; Vineyard, M F; Vlassov, A; Wang, K; Weinstein, L B; Weller, H; Welsh, R; Weygand, D P; Whisnant, S; Witkowski, M; Wolin, E; Yegneswaran, A; Yun, J; Zhang, B; Zhao, J; Zhou, Z 2003-01-01 Measurements of the angular distributions of target and double spin asymmetries for the Delta(1232) in the exclusive channel (polarized-p polarized-e,e-prime p)pi0 obtained at Jefferson Lab in the Q2 range from 0.5 to 1.5 gev2 are presented. Results of the asymmetries are compared with the unitary isobar model, dynamical models, and the effective Lagrangian theory. Sensitivity to the different models was observed, particularly in relation to the description of background terms on which the target asymmetry depends significantly. 20. Polar low monitoring Science.gov (United States) Bobylev, Leonid; Zabolotskikh, Elizaveta; Mitnik, Leonid 2010-05-01 Polar lows are intense mesoscale atmospheric low pressure weather systems, developing poleward of the main baroclinic zone and associated with high surface wind speeds. Small size and short lifetime, sparse in-situ observations in the regions of their development complicate polar low study. Our knowledge of polar lows and mesocyclones has come almost entirely during the period of satellite remote sensing since, by virtue of their small horizontal scale, it was rarely possible to analyse these lows on conventional weather charts using only the data from the synoptic observing network. However, the effects of intense polar lows have been felt by coastal communities and seafarers since the earliest times. These weather systems are thought to be responsible for the loss of many small vessels over the centuries, although the nature of the storms was not understood and their arrival could not be predicted. The actuality of the polar low research is stipulated by their high destructive power: they are a threat to such businesses as oil and gas exploration, fisheries and shipping. They could worsen because of global warming: a shrinking of sea ice around the North Pole, which thawed to its record minimum in the summer of 2007, is likely to give rise to more powerful storms that form only over open water and can cause hurricane-strength winds. Therefore, study of polar lows, their timely detection, tracking and forecasting represents a challenge for today meteorology. Satellite passive microwave data, starting from Special Sensor Microwave Imager (SSM/I) onboard Defense Meteorological Satellite Program (DMSP) satellite, remain invaluable source of regularly available remotely sensed data to study polar lows. The sounding in this spectral range has several advantages in comparison with observations in visible and infrared ranges and Synthetic Aperture Radar (SAR) data: independence on day time and clouds, regularity and high temporal resolution in Polar Regions. Satellite 1. Polarization Curve of a Non-Uniformly Aged PEM Fuel Cell Directory of Open Access Journals (Sweden) Andrei Kulikovsky 2014-01-01 Full Text Available We develop a semi-analytical model for polarization curve of a polymer electrolyte membrane (PEM fuel cell with distributed (aged along the oxygen channel MEA transport and kinetic parameters of the membrane–electrode assembly (MEA. We show that the curve corresponding to varying along the channel parameter, in general, does not reduce to the curve for a certain constant value of this parameter. A possibility to determine the shape of the deteriorated MEA parameter along the oxygen channel by fitting the model equation to the cell polarization data is demonstrated. 2. Experimental wake survey behind Viking 75 entry vehicle at angles of attack of 0 deg, 5 deg, and 10 deg, Mach numbers from 0.20 to 1.20, and longitudinal stations from 1.50 to 11.00 body diameters Science.gov (United States) Brown, C. A., Jr.; Campbell, J. F. 1973-01-01 An investigation was conducted to obtain flow properties in the wake of a preliminary configuration of the Viking '75 Entry Vehicle at Mach numbers from 0.20 to 1.20 and at angles of attack of 0 deg, 5 deg, and 10 deg. The wake flow properties were calculated from total and static pressures measured with a pressure rake at longitudinal stations varying from 1.50 to 11.00 body diameters, and are presented in tabulated and plotted form. The wake properties were essentially symmetrical about the X-axis at alpha = 0 deg and the profiles were shifted away from the X-axis at angles of attack. An unexpected reduction in wake property ratios occurred as the Mach number increased from 0.60 to 1.00; these ratios then increased as the Mach number increased to 1.20. The reduction was present for all the longitudinal stations of the tests and decreased with increased longitudinal distance. 3. Ion channels in plants Science.gov (United States) Baluška, František; Mancuso, Stefano 2013-01-01 In his recent opus magnum review paper published in the October issue of Physiology Reviews, Rainer Hedrich summarized the field of plant ion channels.1 He started from the earliest electric recordings initiated by Charles Darwin of carnivorous Dionaea muscipula,1,2 known as Venus flytrap, and covered the topic extensively up to the most recent discoveries on Shaker-type potassium channels, anion channels of SLAC/SLAH families, and ligand-activated channels of glutamate receptor-like type (GLR) and cyclic nucleotide-gated channels (CNGC).1 PMID:23221742 4. Polarization swings in blazars Science.gov (United States) Lyutikov, Maxim; Kravchenko, Evgeniya V. 2017-06-01 We present a model of blazar variability that can both reproduce smooth large polarization angle swings and at the same time allow for the seemingly random behaviour of synchrotron fluxes, polarization fraction and, occasionally, π/2 polarization jumps. We associate the blazar flaring activity with a jet carrying helical magnetic fields and propagating along a variable direction (and possibly with a changing bulk Lorentz factor). The model predicts that for various jet trajectories (i) electric vector position angle (EVPA) can experience large smooth temporal variations, while at the same time polarization fraction (Π) can be highly variable; (ii) Π ∼ 0 near sudden EVPA jumps of 90°, but can also remain constant for large, smoother EVPA swings; (iii) the total angle of EVPA rotation can be arbitrarily large; and (iv) intensity I is usually maximal at points of fastest EVPA changes, but can have a minimum. Thus, even for a regular, deterministic motion of a steadily emitting jet, the observed properties can vary in a non-monotonic and/or seemingly stochastic way. Intrinsic fluctuations of the emissivity will further complicate the intensity profiles, but are expected to preserve the polarization structure. 5. Microstructure evolution in Zr under equal channel angular pressing Science.gov (United States) Choi, W. S.; Ryoo, H. S.; Hwang, S. K.; Kim, M. H.; Kwun, S. I.; Chae, S. W. 2002-03-01 Pure polycrystalline Zr was deformed by equal channel angular pressing (ECAP), and the microstructural characteristics were analyzed. By repeated alternating ECAP, it was possible to refine the grain size from 200 to 0.2 µm. Subsequent annealing heat treatment at 550 °C resulted in a grain growth of up to 6 µm. Mechanical twinning was an important deformation mechanism, particularly during the early stage of deformation. The most active twinning system was identified as 85.2 deg {10bar 12} tensile twinning, followed by 57.1 deg {10bar 11} compressive twinning. Crystal texture as well as grain-boundary misorientation distribution of deformed Zr were analyzed by X-ray diffraction (XRD) and electron backscattered diffraction (EBSD). The ECAP-deformed Zr showed a considerable difference in the crystallographic attributes from those of cold-rolled Zr or Ti, in that texture and boundary misorientation-angle distribution tend toward more even distribution with a slightly preferential distribution of boundaries of a 20 to 30 deg misorientation angle. Furthermore, unlike the case of cold rolling, the crystal texture was not greatly altered by subsequent annealing heat treatment. Overall, the present work suggests ECAP as a viable method to obtain significant grain refining in hexagonal close-packed (hcp) metals. 6. Letteratura tecnica e formazione degli architetti ai tempi di Antonio Mollari Directory of Open Access Journals (Sweden) Alessandro Gambuti 2014-04-01 Full Text Available Nel corso del Settecento, nella letteratura tecnica, a seguito della critica razionalista del pensiero illuminista, cominciano a comparire principî scientifici per migliorare la formazione degli architetti. Nel 1764 Girolamo Fonda, matematico, pubblica gli Elementi di Architettura civile e militare e dedica la prima parte alla “Sodezza delle fabbriche”, premettendo le regole costruttive alla convenienza e all’estetica. Francesco Milizia avvia i Principj di Architettura civile (1781 con i temi della bellezza e della comodità, ma, nella terza parte, tratta della solidità con citazioni di meccanica, fisica e ingegneria. Qualche anno dopo (1788, Girolamo Masi stampa, per la “gioventù romana”, Teoria e Pratica dell’Architettura civile; seguendo il metodo del Fonda e continuando l’opera del Milizia egli propone nozioni sui materiali e sulle “resistenze” con il sussidio di illustrazioni e tabelle. Nel 1772 era stato ristampato il Manuale… di Giovanni Branca con la revisione di Leonardo de Vegni, dilettante di architettura; una notevole utilità didattica apportarono le incisioni di Giovan Battista Cipriani, allegate ai Principj… del Milizia (1800 e le Osservazioni ed aggiunte di Giovanni Antonio Antolini alla stessa opera (1817. All’inizio dell’Ottocento, l’Architettura pratica di Giuseppe Valadier dette un incremento alla formazione professionale degli architetti per mezzo di lezioni teoriche e disegni di procedimenti ed attrezzature per i costruttori di edifici. During the XVIIIth century, in the technical treatises, owing to the rationalist criticism of the Enlightenment movement, scientific principles begin to appear in order to improve the education of the architects. In 1764 Girolamo Fonda, a mathematician, publishes Elementi di Architettura civile e militare and gives up the first part to the “Solidity of Buildings”, putting before the construction rules to the convenience and beauty. Francesco Milizia opens 7. Criteri di indagine degli spazi voltati nell’ambito dell’architettura storica e in archeologia Directory of Open Access Journals (Sweden) Luca Cipriani 2014-07-01 Full Text Available ItLo studio degli spazi voltati nell’ambito dell’architettura storica è un tema di grande interesse, che da sempre vede impegnati vari studiosi afferenti ad ambiti disciplinari diversi, dall’archeologia, alla storia dell’arte, alla conservazione. In tale contesto interdisciplinare molto spesso il ruolo di ingegneri ed architetti, che si occupano di indagare le matrici geometriche alla base della progettazione di tali spazi, viene relegato ad un ruolo accessorio rispetto a quello dei conservatori, che materialmente si occupano delle pratiche di manutenzione e di restauro. Con l’avanzare delle tecnologie di rilevamento, che spaziano con sempre maggiore affidabilità dalla documentazione dei caratteri morfologici superficiali a quelli più intrinseci alla base dei manufatti, quale può essere il ruolo attuale di chi si occupa di comprendere il progetto che generò tali ambienti? In altri termini, quel vasto patrimonio immateriale che sta alla base della concezione progettuale di un manufatto, specialmente se scaturito da una raffinata conoscenza matematica e geometrica, ha oggi un ruolo riconoscibile e sufficientemente autorevole rispetto all’ammontare di conoscenze tecniche che permettono alle “macchine” di funzionare?Con questo contributo si intende mostrare come l’integrazione di vari know-how legati sia alla modellazione reality-based che alla conoscenza dei criteri e degli strumenti di progettazione del passato, possa fornire un input sostanziale per l’intervento e per la conoscenza di manufatti caratterizzati da una evidente complessità geometrica e costruttiva. Per ricaduta si intende poi mostrare come la documentazione fine a se stessa, per quanto accurata, certificata e garantita attraverso le più avanzate tecnologie e metodologie integrate, non si configuri come base di scambio e di dialogo interdisciplinare. En The study of vaulted spaces in the context of the historic architecture is a topic of great interest 8. Survey Methods for Earthquake Damages in the "CAMERA degli SPOSI" of Mantegna (mantova) Science.gov (United States) Fratus de Balestrini, E.; Ballarin, M.; Balletti, C.; Buttolo, V.; Gottardi, C.; Guerra, F.; Mander, S.; Pilot, L.; Vernier, P. 2013-07-01 Cultural Heritage constitutes a fundamental resource for all Countries, even in economic terms, as it can be considered an extraordinary tourist attraction. This is particularly true for Italy, which is one of the Countries with the richest artistic heritage in the world. For this reason, restoration becomes an essential step towards the conservation and therefore valorisation of architecture. In this context, this paper focuses on one of the first stages that allow us to reach a complete knowledge of a building. Because of the earthquake of May 2012, the Castle of San Giorgio in Mantova (Italy) presented a series of structural damages. On the occasion of its upcoming re-opening to the public, the Soprintendenza per i Beni Architettonici e Paesaggistici per le province di Brescia, Cremona e Mantova has requested an analysis and evaluation of the damages for the development of an intervention project. In particular, a special attention was given to the "Camera degli Sposi" ("Bridal Chamber"), also known as the Camera picta ("painted chamber"). It is a frescoed room, with illusionistic paintings by Andrea Mantegna, located in the northeast tower of the Castle. It was painted between 1465 and 1474 and commissioned by Ludovico Gonzaga, and it is well-known for the use of trompe l'oeil details and for the decoration of its ceiling. The seismic shakes damaged the wall decorated with the "Scena della Corte" ("Court Scene"), above the chimney, re-opening an old crack that had to be analysed, in order to understand whether the damage was structural or just superficial. The diagnostic analyses constitute a fundamental prerequisite for the elaboration of any kind of intervention or restoration in any architectural, artistic or archaeological framework. To obtain a description of the conservation state of the Camera, non-invasive integrated survey techniques were applied. The purpose of the study presented here is the definition of a methodology able to support the necessity 9. Fast and Chaotic Fiber-Based Nonlinear Polarization Scrambler CERN Document Server Guasoni, M; Gilles, M; Picozzi, A; Fatome, J 2015-01-01 We report a simple and efficient all-optical polarization scrambler based on the nonlinear interaction in an optical fiber between a signal beam and its backward replica which is generated and amplified by a reflective loop. When the amplification factor exceeds a certain threshold, the system exhibits a chaotic regime in which the evolution of the output polarization state of the signal becomes temporally chaotic and scrambled all over the surface of the Poincar\\'e sphere. We derive some analytical estimations for the scrambling performances of our device which are well confirmed by the experimental results. The polarization scrambler has been successfully tested on a single channel 10-Gbit/s On/Off Keying Telecom signal, reaching scrambling speeds up to 250-krad/s, as well as in a wavelength division multiplexing configuration. A different configuration based on a sequent cascade of polarization scramblers is also discussed numerically, which leads to an increase of the scrambling performances. 10. Accessing the longitudinally polarized photon content of the proton Science.gov (United States) Mukherjee, A.; Pisano, C. 2004-08-01 We investigate the QED Compton process in longitudinally polarized lepton-proton scattering both in the elastic and inelastic channels and show that the cross section can be expressed in terms of the polarized equivalent photon distribution of the proton. We provide the necessary kinematical constraints to extract the polarized photon content of the proton using this process at HERMES, COMPASS, and eRHIC. We also discuss the suppression of the major background process coming from virtual Compton scattering. We point out that such an experiment can give valuable information on g1(xB,Q2) in the small xB, broad Q2 region at the future polarized collider eRHIC and especially in the lower Q2, medium xB region in fixed target experiments. 11. Measuring the influence of aerosols and albedo on sky polarization. Science.gov (United States) Kreuter, A; Emde, C; Blumthaler, M 2010-11-01 All-sky distributions of the polarized radiance are measured using an automated fish-eye camera system with a rotating polarizer. For a large range of aerosol and surface albedo situations, the influence on the degree of polarization and sky radiance is investigated. The range of aerosol optical depth and albedo is 0.05-0.5 and 0.1-0.75, respectively. For this range of parameters, a reduction of the degree of polarization from about 0.7 to 0.4 was observed. The analysis is done for 90° scattering angle in the principal plane under clear sky conditions for a broadband channel of 450 ± 25 nm and solar zenith angles between 55° and 60°. Radiative transfer calculations considering three different aerosol mixtures are performed and and agree with the measurements within the statistical error. 12. Voltage-Gated Channels as Causative Agents for Epilepsies Directory of Open Access Journals (Sweden) Mutasem Abuhamed 2008-01-01 Full Text Available Problem statement: Epilepsy is a common neurological disorder that afflicts 1-2% of the general population worldwide. It encompasses a variety of disorders with seizures. Approach: Idiopathic epilepsies were defined as a heterogeneous group of seizure disorders that show no underlying cause .Voltage-gated ion channels defect were recognized etiology of epilepsy in the central nervous system. The aim of this article was to provide an update on voltage-gated channels and their mutation as causative agents for epilepsies. We described the structures of the voltage-gated channels, discuss their current genetic studies, and then review the effects of voltage-gated channels as causative agents for epilepsies. Results: Channels control the flow of ions in and out of the cell causing depolarization and hyper polarization of the cell. Voltage-gated channels were classified into four types: Sodium, potassium calcium ands chloride. Voltage-gated channels were macromolecular protein complexes within the lipid membrane. They were divided into subunits. Each subunit had a specific function and was encoded by more than one gen. Conclusion: Current genetic studies of idiopathic epilepsies show the importance of genetic influence on Voltage-gated channels. Different genes may regulate a function in a channel; the channel defect was directly responsible for neuronal hyper excitability and seizures. 13. Rotation Measure Synthesis of Galactic Polarized Emission with the DRAO 26-m Telescope CERN Document Server Wolleben, M; Hovey, G J; Messing, R; Davison, O S; House, N L; Somaratne, K H M S; Tashev, I 2010-01-01 Radio polarimetry at decimetre wavelengths is the principal source of information on the Galactic magnetic field. The diffuse polarized emission is strongly influenced by Faraday rotation in the magneto-ionic medium and rotation measure is the prime quantity of interest, implying that all Stokes parameters must be measured over wide frequency bands with many frequency channels. The DRAO 26-m Telescope has been equipped with a wideband feed, a polarization transducer to deliver both hands of circular polarization, and a receiver, all operating from 1277 to 1762 MHz. Half-power beamwidth is between 40 and 30 arcminutes. A digital FPGA spectrometer, based on commercially available components, produces all Stokes parameters in 2048 frequency channels over a 485-MHz bandwidth. Signals are digitized to 8 bits and a Fast Fourier Transform is applied to each data stream. Stokes parameters are then generated in each frequency channel. This instrument is in use at DRAO for a Northern sky polarization survey. Observatio... 14. Indagine statistico - epidemiologica degli incidenti stradali nella cittá di Messina (1998- 2002 Directory of Open Access Journals (Sweden) S. Saffioti 2003-05-01 Full Text Available Introduzione: gli incidenti stradali rappresentano un fenomeno rilevante nell’ambito della Sanità Pubblica. Essi costituiscono non solo un’importante causa di morbosità e mortalità, ma anche una rilevante causa di handicap nella popolazione. Notevole, quindi, l’impatto sociale ed economico del fenomeno, quantificabile in termini di costi sanitari e sociali sostenuti dalla collettività, tra i quali assumono un peso particolare quelli per spese mediche, danni materiali, mancata produttività. Obiettivi: raccogliere una casistica locale finalizzata a valutare il fenomeno degli incidenti stradali e le sue conseguenze dirette ed indirette nella città di Messina. Metodi: sono stati analizzati i dati relativi agli incidenti stradali occorsi nella città di Messina dal 1 gennaio 1998 al 31 dicembre 2002. I dati derivano dalle schede compilate per ogni incidente da parte dei comandi di Forze dell’Ordine intervenuti in occasione dei sinistri. Risultati: nel territorio oggetto di analisi, nel periodo 1998-2002, sono stati rilevati 12779 incidenti che hanno coinvolto 25798 veicoli e 942 pedoni, determinando 10626 feriti e 79 morti. Il rapporto di mortalità è 6.2, il rapporto di lesività è 831.5. Conclusioni: l’indagine conferma la rilevanza del fenomeno incidenti stradali nella città di Messina. Offre, quindi, prospettive interessanti di analisi e di predisposizione di piani di prevenzione. 15. La dottrina degli avatara come prova per la datazione dell’Abhinayadarpana di Nandikesvara Directory of Open Access Journals (Sweden) Pietro Chierichetti 2012-01-01 Full Text Available Abstract - IT Come per molte opere della letteratura indiana in sanscrito, anche per l’Abhinayadarpana di Nandikesvara è difficile proporre una datazione attendibile: nel suo contributo, l’autore cerca di utilizzare un elemento interno al testo per ipotizzare il periodo nel quale il testo potrebbe collocarsi. La citazione degli avatara di Visnu, esemplificata attraverso una serie di gesti delle mani, viene vagliata criticamente al fine di un suo possibile utilizzo per collocare l’opera dal punto di vista cronologico. L’Abhinayadarpana, uno dei test fondamentali del teatro-danza in India, viene in questo modo inserito nel panorama più ampio della vicenda religiosa dell’India antica e la storia della religione hindu fornisce a sua volta uno strumento interessante per la ricostruzione della storia del testo. Abstract - EN As it often happens for many works of the Indian literature in Sanskrit, it is difficult to determine a possible dating of Nandikesvara’s iAbhinayadarpana: in his article, the author tries to assume an inner element of the text for a hypothesis about the period in which the work could be dated back to. The Visnu’s avataras, quoted in the text through a series of hand gestures, are scientifcally examined to define the work from a chronological point of view. The Abhinayadarpana, one of the most important texts of the Indian Dance-Theatre, is put in the broader landscape of the Indian ancient religion and the hindu religion history becomes an interesting tool through which the text’s history is reconstructed. 16. Endovascular treatment of splenic artery aneurysms; Trattamento endovascolare degli aneurismi dell'arteria splenica Energy Technology Data Exchange (ETDEWEB) Lagana, Domenico; Carrafiello, Gianpaolo; Mangini, Monica; Fontana, Federico; Dizonno, Massimiliano; Fugazzola, Carlo [Insubria Univ., Varese (Italy). Cattedra di radiologia; Castelli, Patrizio [Insubria Univ., Varese (Italy). Chirurgia vascolare 2005-07-15 techniques, endovascular treatment is feasible in nearly all SAAs. It ensures good immediate and long term results, and no doubt presents some advantages in comparison to surgical treatment, as it less invasive and allows the preservation of splenic function. [Italian] Scopo. Verificare l'efficacia del trattamento endovascolare degli aneurismi dell'arteria splenica (AAS). Materiale e metodi. Nel periodo compreso tra maggio 2000 e giugno 2003 sono stati trattati 11 AAS veri in 9 pazienti (7 femmine e 2 maschi; eta media 58 anni), 8 sacciformi e 3 fusiformi, 4 localizzati al tratto medio, 5 al tratto distale e 2 intrasplenici. La diagnosi e stata effettuata con eco color Doppler e/o angio-TC ed e risultata occasionate in 7 pazienti e conseguente a dolore in ipocondrio sinistro in 1 caso; un AAS e stato riscontrato in fase di fissurazione. Quattro AAS sono stati esclusi mediante embolizzazione della sacca con microspirali, con preservazione della continuita dell'asse vascolare; in 2 casi e stata associata l'iniezione transcatetere di cianoacrilato. In 4 casi e stata effettuata una legatura endovascolare, con ischemia settoriaie della milza. Un AAS fisstirato e stato trattato in urgenza con embolizzazione massiva mediante cianoacrilato dell'arteria splenica. I 2 aneurismi intrasplenici sono stati esclusi, l'uno mediante embolizzazione dell'arteria afferente con cianoacrilato e l'altro con iniezione transcatetere di trombina nella sacca aneurismatica. Risultati. E stata ottenuta la devascolarizzazione completa di tutti gli AAS (in 10/11 al termine della procedura; in 1/11 al controllo TC, effettuato dopo 3 giorni). Il follow-up (durata media 18 mesi; range 6-36 mesi) e stato espletato con eco color Doppler e/o angio-TC a 3, 6, 12 mesi e successivamente una volta all'anno; la completa esclusione degli aneurismi e stata confermata in 11/11 casi. Le complicanze riscontrate sono state: 4 casi di pleurite sinistra di modesta entita; febbre 17. Protocol channels as a new design alternative of covert channels CERN Document Server Wendzel, Steffen 2008-01-01 Covert channel techniques are used by attackers to transfer hidden data. There are two main categories of covert channels: timing channels and storage channels. This paper introduces a third category called protocol channels. A protocol channel switches one of at least two protocols to send a bit combination to a destination while sent packets include no hidden information themselves. 18. Mechanical and microstructural characterization of 6061 aluminum alloy strips severely deformed by Dissimilar Channel Angular Pressing Energy Technology Data Exchange (ETDEWEB) Tan, Evren, E-mail: etan@metu.edu.tr [Middle East Technical University, Metallurgical and Materials Eng. Dept., 06531, Ankara (Turkey); Kibar, Alp Aykut, E-mail: alpaykut@gmail.com [Scientific and Technological Research Council of Turkey, 06100, Ankara (Turkey); Guer, C. Hakan, E-mail: chgur@metu.edu.tr [Middle East Technical University, Metallurgical and Materials Eng. Dept., 06531, Ankara (Turkey) 2011-04-15 Dissimilar Channel Angular Pressing (DCAP) is a severe plastic deformation technique to improve the mechanical properties of flat products by producing ultrafine grains. In this study, the changes in the microstructure and mechanical properties of 6061 Al-alloy strips deformed by various numbers of DCAP passes were investigated. Some DCAPed samples were also held at 200 deg. C and 350 deg. C to investigate the effect of post-annealing. Mechanical properties were determined by hardness and tension tests; and microstructural changes were investigated by TEM analysis. Up to a critical level of plastic strain, remarkable improvements have been observed in the strength and hardness of the severely deformed strips; and the improvements have been explained by variations in grain size, dislocation structure, and formation of subgrains. - Research Highlights: {yields}Dissimilar Channel Angular Pressing (DCAP). {yields}Severe plastic deformation (SPD). {yields}Transmission Electron Microscopy of the 6061 Al alloy. {yields}Mechanical Properties of 6061 Al alloy. 19. Surface vacancy channels through ion channeling Energy Technology Data Exchange (ETDEWEB) Redinger, Alex; Standop, Sebastian; Michely, Thomas [II. Physikalisches Institut, Universitaet Koeln, Zuelpicher Strasse 77, 50937 Koeln (Germany); Rosandi, Yudi; Urbassek, Herbert M. [Fachbereich Physik, Technische Universitaet Kaiserslautern, Erwin-Schroedinger-Strasse, D-67663 Kaiserslautern (Germany) 2009-07-01 Damage patterns of single ion impacts on Pt(111) have been studied by scanning tunneling microscopy (STM) and molecular dynamics simulations (MD). Low temperature experiments, where surface diffusion is absent, have been performed for argon and xenon ions with energies between 1 keV and 15 keV at an angle of incidence of 86 {sup circle} measured with respect to the surface normal. Ions hitting preexisting illuminated step edges penetrate into the crystal and are guided in open crystallographic directions, one or more layers underneath the surface (subsurface channeling). In the case of argon channeling the resulting surface damage consists of adatom and vacancy pairs aligned in ion beam direction. After xenon channeling thin surface vacancy trenches along the ion trajectories - surface vacancy channels - are observed. They result from very efficient sputtering and adatom production along the ion trajectory. This phenomena is well reproduced in molecular dynamics simulations of single ion impacts at 0 K. The damage patterns of Argon and Xenon impacts can be traced back to the different energy losses of the particles in the channel. Channeling distances exceeding 1000 A for 15 keV xenon impacts are observed. 20. On polarization in biomembranes DEFF Research Database (Denmark) Zecchi, Karis Amata close to physiological conditions, making these effects biologically relevant. In this work, we consider the case of asymmetric membranes which can display spontaneous polarization in the absence of a field. Close to the phase transition, we find that the membrane displays piezoelectric, flexoelectric...... and thermoelectric behaviour. In particular, the membrane capacitance is a nonlinear function of the applied voltage. Furthermore, in the presence of spontaneous polarization, our thermodynamical description is able to explain the outward rectified current-voltage relationship measured on synthetic lipid bilayers....... Due to the nonlinear dependence of the membrane capacitance and conductance on voltage and the presence of spontaneous polarization, the traditional equivalent circuit of the membrane is not an accurate description in physiological conditions. An updated equivalent circuit of the lipid bilayer is here... 1. A lunar polar expedition Science.gov (United States) Dowling, Richard; Staehle, Robert L.; Svitek, Tomas 1992-01-01 Advanced exploration and development in harsh environments require mastery of basic human survival skill. Expeditions into the lethal climates of Earth's polar regions offer useful lessons for tommorrow's lunar pioneers. In Arctic and Antarctic exploration, 'wintering over' was a crucial milestone. The ability to establish a supply base and survive months of polar cold and darkness made extensive travel and exploration possible. Because of the possibility of near-constant solar illumination, the lunar polar regions, unlike Earth's may offer the most hospitable site for habitation. The World Space Foundation is examining a scenario for establishing a five-person expeditionary team on the lunar north pole for one year. This paper is a status report on a point design addressing site selection, transportation, power, and life support requirements. 2. Polarized Light from Jupiter Science.gov (United States) 2001-01-01 These images taken through the wide angle camera near closest approach in the deep near-infrared methane band, combined with filters which sense electromagnetic radiation of orthogonal polarization, show that the light from the poles is polarized. That is, the poles appear bright in one image, and dark in the other. Polarized light is most readily scattered by aerosols. These images indicate that the aerosol particles at Jupiter's poles are small and likely consist of aggregates of even smaller particles, whereas the particles at the equator and covering the Great Red Spot are larger. Images like these will allow scientists to ascertain the distribution, size and shape of aerosols, and consequently, the distribution of heat, in Jupiter's atmosphere. 3. No More Polarization, Please! DEFF Research Database (Denmark) Hansen, Mia Reinholt The organizational science literature on motivation has for long been polarized into two main positions; the organizational economic position focusing on extrinsic motivation and the organizational behavior position emphasizing intrinsic motivation. With the rise of the knowledge economy...... and the increasing levels of complexities it entails, such polarization is not fruitful in the attempt to explain motivation of organizational members. This paper claims that a more nuanced perspective on motivation, acknowledging the co-existence of intrinsic and extrinsic motivation, the possible interaction...... between the two as well as different types of motivations filling in the gap between the two polar types, is urgently needed in the organizational science literature. By drawing on the research on intrinsic and extrinsic motivation conducted in social psychology and combining this with contributions from... 4. [Polar body diagnosis]. Science.gov (United States) Montag, M; van der Ven, K; van der Ven, H 2009-01-01 Polar body diagnosis (PBD) is a diagnostic method for the indirect genetic analysis of oocytes. Polar bodies are by-products of the meiotic cell cycle which have no influence on further embryo development. The biopsy of polar bodies can be accomplished either by zona drilling or laser drilling within a very short time period. The paternal contribution to the genetic constitution of the developing embryo cannot be diagnosed by PBD. The major application of PBD is the detection of maternally derived chromosomal aneuploidies and translocations in oocytes. For these indications, PBD may offer a viable alternative to blastomere biopsy as the embryo's integrity remains unaffected in contrast to preimplantation genetic diagnosis by blastomere biopsy. The fast development in the field of molecular diagnostics will also influence PBD and probably allow a more general diagnosis in the future. 5.\\beta$Pictoris' inner disk in polarized light and new orbital parameters for$\\beta$Pictoris b CERN Document Server Millar-Blanchaer, Maxwell A; Pueyo, Laurent; Kalas, Paul; Dawson, Rebekah I; Wang, Jason; Perrin, Marshall; Moon, Dae-Sik; Macintosh, Bruce; Ammons, S Mark; Barman, Travis; Cardwell, Andrew; Chen, Christine H; Chiang, Eugene; Chilcote, Jeffrey; Cotten, Tara; De Rosa, Robert J; Draper, Zachary H; Dunn, Jennifer; Duchêne, Gaspard; Esposito, Thomas M; Fitzgerald, Michael P; Follette, Katherine B; Goodsell, Stephen J; Greenbaum, Alexandra Z; Hartung, Markus; Hibon, Pascale; Hinkley, Sasha; Ingraham, Patrick; Jensen-Clem, Rebecca; Konopacky, Quinn; Larkin, James E; Long, Douglas; Maire, Jérôme; Marchis, Franck; Marley, Mark S; Marois, Christian; Morzinski, Katie M; Nielsen, Eric L; Palmer, David W; Oppenheimer, Rebecca; Poyneer, Lisa; Rajan, Abhijith; Rantakyrö, Fredrik T; Ruffio, Jean-Baptiste; Sadakuni, Naru; Saddlemyer, Leslie; Schneider, Adam C; Sivaramakrishnan, Anand; Soummer, Remi; Thomas, Sandrine; Vasisht, Gautam; Vega, David; Wallace, J Kent; Ward-Duong, Kimberly; Wiktorowicz, Sloane J; Wolff, Schuyler G 2015-01-01 We present$H$-band observations of$\\beta$Pic with the Gemini Planet Imager's (GPI's) polarimetry mode that reveal the debris disk between ~0.3" (~6 AU) and ~1.7" (~33 AU), while simultaneously detecting$\\beta$Pic$b$. The polarized disk image was fit with a dust density model combined with a Henyey-Greenstein scattering phase function. The best fit model indicates a disk inclined to the line of sight ($\\phi=85.27{\\deg}^{+0.26}_{-0.19}$) with a position angle$\\theta_{PA}=30.35{\\deg}^{+0.29}_{-0.28}$(slightly offset from the main outer disk,$\\theta_{PA}\\approx29{\\deg}$), that extends from an inner disk radius of$23.6^{+0.9}_{-0.6}$AU to well outside GPI's field of view. In addition, we present an updated orbit for$\\beta$Pic$b$based on new astrometric measurements taken in GPI's spectroscopic mode spanning 14 months. The planet has a semi-major axis of$a=9.2^{+1.5}_{-0.4}$AU, with an eccentricity$e\\leq 0.26$. The position angle of the ascending node is$\\Omega=31.75{\\deg}\\pm0.15\$, offset from bot...
6. Dual differential polarimetry. A technique to recover polarimetric information from dual-polarization observations
Science.gov (United States)
Martí-Vidal, I.; Vlemmings, W. H. T.; Muller, S.
2016-09-01
Current mm/submm interferometers, like the Atacama Large mm/submm Array (ALMA), use receivers that register the sky signal in a linear polarization basis. In the case of observations performed in full-polarization mode (where the cross-correlations are computed among all the polarization channels) it is possible to reconstruct the full-polarization brightness distribution of the observed sources, as long as a proper calibration of delay offsets and leakage among polarization channels can be performed. Observations of calibrators, preferably with some linear polarization, with a good parallactic angle coverage are usually needed for such a calibration. In principle, dual-polarization observations only allow us to recover the Stokes I intensity distribution of the sources, regardless of the parallactic angle coverage of the observations. In this paper, we present a novel technique of dual differential polarimetry that makes it possible to obtain information related to the full-polarization brightness distribution of the observed sources from dual-polarization observations. This technique is inspired in the Earth-rotation polarization synthesis and can be applied even to sources with complex structures.
7. POLARIZED NEUTRONS IN RHIC
Energy Technology Data Exchange (ETDEWEB)
COURANT,E.D.
1998-04-27
There does not appear to be any obvious way to accelerate neutrons, polarized or otherwise, to high energies by themselves. To investigate the behavior of polarized neutrons the authors therefore have to obtain them by accelerating them as components of heavier nuclei, and then sorting out the contribution of the neutrons in the analysis of the reactions produced by the heavy ion beams. The best neutron carriers for this purpose are probably {sup 3}He nuclei and deuterons. A polarized deuteron is primarily a combination of a proton and a neutron with their spins pointing in the same direction; in the {sup 3}He nucleus the spins of the two protons are opposite and the net spin (and magnetic moment) is almost the same as that of a free neutron. Polarized ions other than protons may be accelerated, stored and collided in a ring such as RHIC provided the techniques proposed for polarized proton operation can be adapted (or replaced by other strategies) for these ions. To accelerate polarized particles in a ring, one must make provisions for overcoming the depolarizing resonances that occur at certain energies. These resonances arise when the spin tune (ratio of spin precession frequency to orbit frequency) resonates with a component present in the horizontal field. The horizontal field oscillates with the vertical motion of the particles (due to vertical focusing); its frequency spectrum is dominated by the vertical oscillation frequency and its modulation by the periodic structure of the accelerator ring. In addition, the magnet imperfections that distort the closed orbit vertically contain all integral Fourier harmonics of the orbit frequency.
8. Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) north polar springtime recession mapping: First Three Mars years of observations
CERN Document Server
Brown, Adrian J; Murchie, Scott L
2014-01-01
We report on mapping of the north polar region of Mars using data from the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) instrument. We have observed three Mars Years (28-30) of late-winter and spring recessions (Ls=304{\\deg}-92{\\deg}). Our investigations have led to the following observations: 1. We classify the retreat of the north polar seasonal cap into 'pre-sublimation', 'early spring', 'asymmetric' and 'stable' periods according to the prevalent H2O ice grain size distributions. 2. During the early spring, the signatures of CO2 ice at the edge of the cap are obscured by H2O ice, which increases the apparent size of the H2O ice annulus around the seasonal CO2 cap at this time. At around Ls=25{\\deg}, this process changes into an asymmetrical distribution of H2O deposition, covering CO2 signatures more rapidly in the longitude range from 90-210{\\deg}E. 3. We detect signatures of 'pure' CO2 ice in extremely limited locations (in Lomonosov Crater) even in mid winter. H2O ice signatures appear ...
9. Microwave Frequency Polarizers
Science.gov (United States)
Ha, Vien The; Mirel, Paul; Kogut, Alan J.
2013-01-01
This article describes the fabrication and analysis of microwave frequency polarizing grids. The grids are designed to measure polarization from the cosmic microwave background. It is effective in the range of 500 to 1500 micron wavelength. It is cryogenic compatible and highly robust to high load impacts. Each grid is fabricated using an array of different assembly processes which vary in the types of tension mechanisms to the shape and size of the grids. We provide a comprehensive study on the analysis of the grids' wire heights, diameters, and spacing.
10. Internal polarized targets
Energy Technology Data Exchange (ETDEWEB)
Kinney, E.R.; Coulter, K.; Gilman, R.; Holt, R.J.; Kowalczyk, R.S.; Napolitano, J.; Potterveld, D.H.; Young, L. (Argonne National Lab., IL (USA)); Mishnev, S.I.; Nikolenko, D.M.; Popov, S.G.; Rachek, I.A.; Temnykh, A.B.; Toporkov, D.K.; Tsentalovich, E.P.; Wojtsekhowski, B.B. (AN SSSR, Novosibirsk (USSR). Inst. Yadernoj Fiziki)
1989-01-01
Internal polarized targets offer a number of advantages over external targets. After a brief review of the basic motivation and principles behind internal polarized targets, the technical aspects of the atomic storage cell will be discussed in particular. Sources of depolarization and the means by which their effects can be ameliorated will be described, especially depolarization by the intense magnetic fields arising from the circulating particle beam. The experience of the Argonne Novosibirsk collaboration with the use of a storage cell in a 2 GeV electron storage ring will be the focus of this technical discussion. 17 refs., 11 figs.
11. New compact neutron polarizer
Science.gov (United States)
Krist, Th; Kennedy, S. J.; Hicks, T. J.; Mezei, F.
A new type of a neutron polarizing bender was developed in co-operation with BENSC and ANSTO. It is based upon bent thin silicon wafers coated on one side with SiFeCo polarizing supermirrors and on the other side with Gd. Initial tests at BENSC in a 300 Oe magnetic field yielded a transmission of spin-up neutrons of about 55% over an angle range of 0.75° and flipping ratios > 30. Subsequent tests at ANSTO at 1200 Oe yielded a transmission of 48% with a flipping ratio > 45.
12. First Ground-Based Infrared Solar Absorption Measurements of Free Tropospheric Methanol (CH3OH): Multidecade Infrared Time Series from Kitt Peak (31.9 deg N 111.6 deg W): Trend, Seasonal Cycle, and Comparison with Previous Measurements
Science.gov (United States)
Rinsland, Curtis P.; Mahieu, Emmanuel; Chiou, Linda; Herbin, Herve
2009-01-01
Atmospheric CH3OH (methanol) free tropospheric (2.09-14-km altitude) time series spanning 22 years has been analyzed on the basis of high-spectral resolution infrared solar absorption spectra of the strong vs band recorded from the U.S. National Solar Observatory on Kitt Peak (latitude 31.9degN, 111.6degW, 2.09-km altitude) with a 1-m Fourier transform spectrometer (FTS). The measurements span October 1981 to December 2003 and are the first long time series of CH3OH measurements obtained from the ground. The results were analyzed with SFIT2 version 3.93 and show a factor of three variations with season, a maximum at the beginning of July, a winter minimum, and no statistically significant long-term trend over the measurement time span.
13. Apparent and partial molar volumes of long-chain alkyldimethylbenzylammonium chlorides and bromides in aqueous solutions at T=15 deg. C and T=25 deg. C[Alkyldimethylbenzylammonium chlorides; Alkyldimethylbenzylammonium bromides; Micellization; Density; Apparent molar volumes
Energy Technology Data Exchange (ETDEWEB)
Gonzalez-Perez, A.; Ruso, J.M.; Nimo, J.; Rodriguez, J.R. E-mail: fmjulio@usc.es
2003-12-01
Density measurements of dodecyl- (C{sub 12}DBACl), tetradecyl- (C{sub 14}DBACl), hexadecyldimethylbenzylammonium chloride (C{sub 16}DBACl) and of decyl- (C{sub 10}DBABr) and dodecyldimethylbenzylammonium bromide (C{sub 12}DBABr) in aqueous solutions at T=15 deg. C and T=25 deg. C have been carried out. From these results, apparent and partial molar volumes were calculated. Positive deviations from the Debye-Hueckel limiting law provide evidence for limited association at concentrations below the critical micelle concentration. The change of the apparent molar volume upon micellization was calculated. The relevant parameters have been presented in function of the alkyl chain length. Apparent molar volumes of the present compounds in the micellar phase, V{sub phi}{sup m}, and the change upon micellization, {delta}V{sub phi}{sup m}, have been discussed in terms of temperature and type of counterion.
14. L’Unione degli Atei e degli Agnostici Razionalisti (UAAR, membro associato della International Humanist and Ethical Union, come soggetto stipulante un’intesa con lo Stato, ex art. 8, III Cost.
Directory of Open Access Journals (Sweden)
Domenico Bilotti
2011-07-01
Full Text Available Contributo segnalato dal Prof. Antonino Mantineo, ordinario di Diritto ecclesiastico nella Facoltà di Giurisprudenza dell’Università degli Studi Magna Graecia di Catanzaro, che ne attesta la scientificità e l’originalità.SOMMARIO: 1. I limiti dello strumento negoziale nell’esperienza giuridica italiana. una ricognizione sulle aporie evidenziatesi nella prassi politico-legislativa – 2. Verso uno statuto giuridico differenziato per le organizzazioni filosofiche non confessionali. meritevolezza degli interessi in gioco – 3. Il non-confessionismo organizzato come fenomeno associativo culturalmente orientato sul fattore religioso – 4. Permanente capacità attrattiva di una disciplina speciale e di favore: l’inevitabile ricerca di una legislazione generale in tema di libertà religiosa o l’armonizzazione dei trattamenti privilegiati?
15. German health interview and examination survey for adults (DEGS - design, objectives and implementation of the first data collection wave
Directory of Open Access Journals (Sweden)
Scheidt-Nave Christa
2012-09-01
Full Text Available Abstract Background The German Health Interview and Examination Survey for Adults (DEGS is part of the recently established national health monitoring conducted by the Robert Koch Institute. DEGS combines a nationally representative periodic health survey and a longitudinal study based on follow-up of survey participants. Funding is provided by the German Ministry of Health and supplemented for specific research topics from other sources. Methods/design The first DEGS wave of data collection (DEGS1 extended from November 2008 to December 2011. Overall, 8152 men and women participated. Of these, 3959 persons already participated in the German National Health Interview and Examination Survey 1998 (GNHIES98 at which time they were 18–79 years of age. Another 4193 persons 18–79 years of age were recruited for DEGS1 in 2008–2011 based on two-stage stratified random sampling from local population registries. Health data and context variables were collected using standardized computer assisted personal interviews, self-administered questionnaires, and standardized measurements and tests. In order to keep survey results representative for the population aged 18–79 years, results will be weighted by survey-specific weighting factors considering sampling and drop-out probabilities as well as deviations between the design-weighted net sample and German population statistics 2010. Discussion DEGS aims to establish a nationally representative data base on health of adults in Germany. This health data platform will be used for continuous health reporting and health care research. The results will help to support health policy planning and evaluation. Repeated cross-sectional surveys will permit analyses of time trends in morbidity, functional capacity levels, disability, and health risks and resources. Follow-up of study participants will provide the opportunity to study trajectories of health and disability. A special focus lies on chronic
16. Robotic Variable Polarity Plasma Arc (VPPA) Welding
Science.gov (United States)
Jaffery, Waris S.
1993-01-01
The need for automated plasma welding was identified in the early stages of the Space Station Freedom Program (SSFP) because it requires approximately 1.3 miles of welding for assembly. As a result of the Variable Polarity Plasma Arc Welding (VPPAW) process's ability to make virtually defect-free welds in aluminum, it was chosen to fulfill the welding needs. Space Station Freedom will be constructed of 2219 aluminum utilizing the computer controlled VPPAW process. The 'Node Radial Docking Port', with it's saddle shaped weld path, has a constantly changing surface angle over 360 deg of the 282 inch weld. The automated robotic VPPAW process requires eight-axes of motion (six-axes of robot and two-axes of positioner movement). The robot control system is programmed to maintain Torch Center Point (TCP) orientation perpendicular to the part while the part positioner is tilted and rotated to maintain the vertical up orientation as required by the VPPAW process. The combined speed of the robot and the positioner are integrated to maintain a constant speed between the part and the torch. A laser-based vision sensor system has also been integrated to track the seam and map the surface of the profile during welding.
17. The physics of polarization
Science.gov (United States)
Landi Degl'Innocenti, Egidio
This course is intended to give a description of the basic physical concepts which underlie the study and the interpretation of polarization phenomena. Apart from a brief historical introduction (Sect. 1), the course is organized in three parts. A first part (Sects. 2 - 6) covers the most relevant facts about the polarization phenomena that are typically encountered in laboratory applications and in everyday life. In Sect. 2, the modern description of polarization in terms of the Stokes parameters is recalled, whereas Sect. 3 is devoted to introduce the basic tools of laboratory polarimetry, such as the Jones calculus and the Mueller matrices. The polarization phenomena which are met in the reflection and refraction of a beam of radiation at the separation surface between two dielectrics, or between a dielectric and a metal, are recalled in Sect. 4. Finally, Sect. 5 gives an introduction to the phenomena of dichroism and of anomalous dispersion and Sect. 6 summarizes the polarization phenomena that are commonly encountered in everyday life. The second part of this course (Sects. 7-14) deals with the description, within the formalism of classical physics, of the spectro-polarimetric properties of the radiation emitted by accelerated charges. Such properties are derived by taking as starting point the Liénard and Wiechert equations that are recalled and discussed in Sect. 7 both in the general case and in the non-relativistic approximation. The results are developed to find the percentage polarization, the radiation diagram, the cross-section and the spectral characteristics of the radiation emitted in different phenomena particularly relevant from the astrophysical point of view. The emission of a linear antenna is derived in Sect. 8. The other Sections are devoted to Thomson scattering (Sect. 9), Rayleigh scattering (Sect. 10), Mie scattering (Sect. 11), bremsstrahlung radiation (Sect. 12), cyclotron radiation (Sect. 13), and synchrotron radiation (Sect. 14
18. Parallel and series FED microstrip array with high efficiency and low cross polarization
Science.gov (United States)
Huang, John (Inventor)
1995-01-01
A microstrip array antenna for vertically polarized fan beam (approximately 2 deg x 50 deg) for C-band SAR applications with a physical area of 1.7 m by 0.17 m comprises two rows of patch elements and employs a parallel feed to left- and right-half sections of the rows. Each section is divided into two segments that are fed in parallel with the elements in each segment fed in series through matched transmission lines for high efficiency. The inboard section has half the number of patch elements of the outboard section, and the outboard sections, which have tapered distribution with identical transmission line sections, terminated with half wavelength long open-circuit stubs so that the remaining energy is reflected and radiated in phase. The elements of the two inboard segments of the two left- and right-half sections are provided with tapered transmission lines from element to element for uniform power distribution over the central third of the entire array antenna. The two rows of array elements are excited at opposite patch feed locations with opposite (180 deg difference) phases for reduced cross-polarization.
19. Polarized Proton Collisions at RHIC
CERN Document Server
Bai, Mei; Alekseev, Igor G; Alessi, James; Beebe-Wang, Joanne; Blaskiewicz, Michael; Bravar, Alessandro; Brennan, Joseph M; Bruno, Donald; Bunce, Gerry; Butler, John J; Cameron, Peter; Connolly, Roger; De Long, Joseph; Drees, Angelika; Fischer, Wolfram; Ganetis, George; Gardner, Chris J; Glenn, Joseph; Hayes, Thomas; Hseuh Hsiao Chaun; Huang, Haixin; Ingrassia, Peter; Iriso, Ubaldo; Laster, Jonathan S; Lee, Roger C; Luccio, Alfredo U; Luo, Yun; MacKay, William W; Makdisi, Yousef; Marr, Gregory J; Marusic, Al; McIntyre, Gary; Michnoff, Robert; Montag, Christoph; Morris, John; Nicoletti, Tony; Oddo, Peter; Oerter, Brian; Osamu, Jinnouchi; Pilat, Fulvia Caterina; Ptitsyn, Vadim; Roser, Thomas; Satogata, Todd; Smith, Kevin T; Svirida, Dima; Tepikian, Steven; Tomas, Rogelio; Trbojevic, Dejan; Tsoupas, Nicholaos; Tuozzolo, Joseph; Vetter, Kurt; Wilinski, Michelle; Zaltsman, Alex; Zelenski, Anatoli; Zeno, Keith; Zhang, S Y
2005-01-01
The Relativistic Heavy Ion Collider~(RHIC) provides not only collisions of ions but also collisions of polarized protons. In a circular accelerator, the polarization of polarized proton beam can be partially or fully lost when a spin depolarizing resonance is encountered. To preserve the beam polarization during acceleration, two full Siberian snakes were employed in RHIC to avoid depolarizing resonances. In 2003, polarized proton beams were accelerated to 100~GeV and collided in RHIC. Beams were brought into collisions with longitudinal polarization at the experiments STAR and PHENIX by using spin rotators. RHIC polarized proton run experience demonstrates that optimizing polarization transmission efficiency and improving luminosity performance are significant challenges. Currently, the luminosity lifetime in RHIC is limited by the beam-beam effect. The current state of RHIC polarized proton program, including its dedicated physics run in 2005 and efforts to optimize luminosity production in beam-beam limite...
20. Fundamental limits of target detection performance in passive polarization imaging.
Science.gov (United States)
Goudail, François; Boffety, Matthieu
2017-04-01
We quantitatively determine the target detection performance of different passive polarization imaging architectures perturbed by signal-independent detection noise or signal-dependent Poisson shot noise. We compare the fully adaptive polarimetric imager and the best channel of a static polarimetric imager, and in each case, we compare the use of a polarizer and a polarizing beam splitter as the polarization analyzing device. For all these configurations, we derive a closed-form expression of the target/background separability and quantify the performance gain brought by polarization imaging compared to standard intensity imaging. We show in particular that all the considered polarimetric imaging configurations but one require a minimum value of the polarimetric contrast in order to outperform intensity imaging. The only configuration that always performs better than intensity imaging uses a polarizing beam splitter in the presence of background shot noise. These results are useful in evaluating the fundamental limits of the gain brought by polarization imaging and determining, in practice, which type of imaging architecture is preferable for a given application. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7699223160743713, "perplexity": 10395.370602174251}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891813622.87/warc/CC-MAIN-20180221123439-20180221143439-00700.warc.gz"} |
http://mathoverflow.net/questions/89505/reference-for-tensors-on-graded-spaces-needed/89524 | # Reference for Tensors on graded spaces needed
Is there a good introduction to
1.) Tensor (co)algebras on graded vector spaces ?
2.) Tensor (co)algebras on graded modules ?
In the research field of $L_\infty$-algebras there is some stuff, but nothing I know is a comprehensive introduction, including proofs.
-
One pedagogical treatment of 1) is Chapter VIII from Marco Manetti's Lectures on deformations of complex manifolds
http://lanl.arxiv.org/abs/math/0507286
Another reference is Quillen's Rational homotopy theory, Appendix B. It is published in The Annals of Math., Vol.90, No.2, 1969.
-
Thanks, on a short look on the first reference, it is indeed comprehensive. Nevertheless it says nothing about the situation on modules. (Like the tensor (co)-algebra on sections of a vector bundle) – Nevermind Feb 26 '12 at 10:51
• A very nice book wit tons of examples is "Rational homotopy theory" by Felix, Halperin and Thomas. In particular, the section on graded differential algebras begins at pag. 40.
• The book "Seminari di Geometria Algebrica" (1998-1999), Scuola Normale Superiore di Pisa (it is in English and probably available online) contains many details on tensor structures on dg vector spaces. I would start by having a look at the third chapter of the book, which is nothing but this paper by M. Grassi. Section 2 contains definitions and some results.
• If you understand French, then the first chapter of Hasegawa's thesis contains a systematic analysis of differential graded and $A_\infty$-structures.
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http://caeinfo.in2p3.fr/article304.html?lang=fr | # Laboratoire de Physique Corpusculaire de Caen
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PUBLICATIONS
### [hal-01645919] Search for Axionlike Dark Matter through Nuclear Spin Precession in Electric and Magnetic Fields
24 novembre 2017
We report on a search for ultra-low-mass axion-like dark matter by analysing the ratio of the spin-precession frequencies of stored ultracold neutrons and $^199$Hg atoms for an axion-induced oscillating electric dipole moment of the neutron and an axion-wind spin-precession effect. No signal (...)
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### [hal-01642614] Search for Axionlike Dark Matter through Nuclear Spin Precession in Electric and Magnetic Fields
22 novembre 2017
We report on a search for ultra-low-mass axion-like dark matter by analysing the ratio of the spin-precession frequencies of stored ultracold neutrons and $^199$Hg atoms for an axion-induced oscillating electric dipole moment of the neutron and an axion-wind spin-precession effect. No signal (...)
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### [hal-01642862] Highly stable atomic vector magnetometer based on free spin precession
22 novembre 2017
We present a magnetometer based on optically pumped Cs atoms that measures the magnitude and direction of a 1 $\mu$T magnetic field. Multiple circularly polarized laser beams were used to probe the free spin precession of the Cs atoms. The design was optimized for long-time stability and (...)
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### [hal-01642856] Neutron production in neutron-induced reactions at 96 MeV on $^{56}Fe$ and $^{208}Pb$
22 novembre 2017
Double-differential cross sections for neutron production were measured in 96-MeV neutron-induced reactions at The Svedberg Laboratory in Uppsala, Sweden. Measurements for Fe and Pb targets were performed using two independent setups: DECOI-DEMON, time-of-flight telescope dedicated to the (...)
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### [hal-01642836] Measurement of the $^{8}Li$ half-life
22 novembre 2017
We report a new measurement of the Li8 half-life using a plastic scintillator and an ultrafast waveform digitizing module. The result, T1/2=(838.40±0.36) ms, improves by a factor of 2.5 the most precise result obtained so far and is furthermore deduced with negligible corrections due to dead (...)
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### [hal-01642863] Measurement of transverse polarization of electrons emitted in free neutron decay
22 novembre 2017
The final analysis of the experiment determining both components of the transverse polarization of electrons ($\sigma_T_1$, $\sigma_T_2$) emitted in the $\beta$-decay of polarized, free neutrons is presented. The T-odd, P-odd correlation coefficient quantifying $\sigma_T_2$, perpendicular to (...)
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### [hal-01641066] Highly stable atomic vector magnetometer based on free spin precession
21 novembre 2017
We present a magnetometer based on optically pumped Cs atoms that measures the magnitude and direction of a 1 $\mu$T magnetic field. Multiple circularly polarized laser beams were used to probe the free spin precession of the Cs atoms. The design was optimized for long-time stability and (...)
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### [hal-01641060] Neutron production in neutron-induced reactions at 96 MeV on $^{56}Fe$ and $^{208}Pb$
21 novembre 2017
Double-differential cross sections for neutron production were measured in 96-MeV neutron-induced reactions at The Svedberg Laboratory in Uppsala, Sweden. Measurements for Fe and Pb targets were performed using two independent setups: DECOI-DEMON, time-of-flight telescope dedicated to the (...)
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### [hal-01641236] The Neutrons for Science Facility at SPIRAL-2
21 novembre 2017
The Neutrons For Science (NFS) facility is a component of SPIRAL-2 laboratory under construction at Caen (France). SPIRAL-2 is dedicated to the production of high intensity Radioactive Ions Beams (RIB). It is based on a high-power linear accelerator (LINAG) to accelerate deuterons beams in (...)
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### [hal-01641443] First high-statistics and high-resolution recoil-ion data from the WITCH retardation spectrometer
21 novembre 2017
The first high-statistics and high-resolution data set for the integrated recoil-ion energy spectrum following the $\beta^+$ decay of$^35$Ar has been collected with the WITCH retardation spectrometer located at CERN-ISOLDE. Over 25 million recoil-ion events were recorded on a large-area (...)
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### [hal-01641067] Measurement of transverse polarization of electrons emitted in free neutron decay
21 novembre 2017
The final analysis of the experiment determining both components of the transverse polarization of electrons ($\sigma_T_1$, $\sigma_T_2$) emitted in the $\beta$-decay of polarized, free neutrons is presented. The T-odd, P-odd correlation coefficient quantifying $\sigma_T_2$, perpendicular to (...)
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### [hal-01641038] Measurement of the $^{8}Li$ half-life
21 novembre 2017
We report a new measurement of the Li8 half-life using a plastic scintillator and an ultrafast waveform digitizing module. The result, T1/2=(838.40±0.36) ms, improves by a factor of 2.5 the most precise result obtained so far and is furthermore deduced with negligible corrections due to dead (...)
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### [in2p3-01597497] First tests of Li-6 doped glass scintillators for ultracold neutron detection
28 septembre 2017
[...]
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### [hal-01554897] A novel segmented-scintillator antineutrino detector
5 juillet 2017
The next generation of very-short-baseline reactor experiments will require compact detectors operating at surface level and close to a nuclear reactor. This paper presents a new detector concept based on a composite solid scintillator technology. The detector target uses cubes of (...)
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### [in2p3-01337513] Ultracold neutron detection with 6Li-doped glass scintillators, NANOSC: a fast ultracold neutron detector for the nEDM experiment at the Paul Scherrer Institute
2 novembre 2016
This paper summarizes the results from measurements aiming to characterize ultracold neutron detection with 6Li-doped glass scintillators. Single GS10 or GS20 scintillators, with a thickness of 100-200 micrometer, fulfill the ultracold neutron detection requirements with an acceptable (...)
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### [in2p3-01377559] First high-statistics and high-resolution recoil-ion data from the WITCH retardation spectrometer
7 octobre 2016
The first high-statistics and high-resolution data set for the integrated recoil-ion energy spectrum following the decay of 35Ar has been collected with the WITCH retardation spectrometer located at CERN-ISOLDE. Over 25 million recoil-ion events were recorded on a large-area multichannel plate (...)
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### [in2p3-01176181] Primary processes: from atoms to diatomic molecules and clusters
25 janvier 2016
This article presents a short review of the main progresses achieved at the GANIL facilities during the last thirty years in the field of ion-atom and ion-diatomic molecule collisions. Thanks to the wide range of projectile energies and species available on the different beam lines of the (...)
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### [in2p3-01213941] A highly stable atomic vector magnetometer based on free spin precession
15 décembre 2015
We present a magnetometer based on optically pumped Cs atoms that measures the magnitude and direction of a 1 $\mu$T magnetic field. Multiple circularly polarized laser beams were used to probe the free spin precession of the Cs atoms. The design was optimized for long-time stability and (...)
Lire la suite
### [in2p3-01140188] Measurement of a false electric dipole moment signal from $^{199}$Hg atoms exposed to an inhomogeneous magnetic field
18 novembre 2015
We report on the measurement of a Larmor frequency shift proportional to the electric-field strength for $^199\rm Hg$ atoms contained in a volume permeated with aligned magnetic and electric fields. This shift arises from the interplay between the inevitable magnetic field gradients and the (...)
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### [in2p3-01120938] A device for simultaneous spin analysis of ultracold neutrons
18 novembre 2015
We report on the design and first tests of a device allowing for measurement of ultracold neutrons polarisation by means of the simultaneous analysis of the two spin components. The device was developed in the framework of the neutron electric dipole moment experiment at the Paul Scherrer (...)
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### [in2p3-01227909] Observation of Gravitationally Induced Vertical Striation of Polarized Ultracold Neutrons by Spin-Echo Spectroscopy
13 novembre 2015
We describe a spin-echo method for ultracold neutrons (UCNs) confined in a precession chamber and exposed to a vertical bar B-0 vertical bar = 1 mu T magnetic field. We have demonstrated that the analysis of UCN spin-echo resonance signals in combination with knowledge of the ambient magnetic (...)
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### [in2p3-01199753] A revised experimental upper limit on the electric dipole moment of the neutron
6 novembre 2015
We present for the first time a detailed and comprehensive analysis of the experimental results that set the current world sensitivity limit on the magnitude of the electric dipole moment (EDM) of the neutron. We have extended and enhanced our earlier analysis to include recent developments in (...)
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### [in2p3-01159876] Observation of gravitationally induced vertical striation of polarized ultracold neutrons by spin-echo spectroscopy
19 octobre 2015
We describe a spin-echo method for ultracold neutrons (UCNs) confined in a precession chamber and exposed to a $|B_0|=1~\text\mu T$ magnetic field. We have demonstrated that the analysis of UCN spin-echo resonance signals in combination with knowledge of the ambient magnetic field provides an (...)
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### [in2p3-01169555] Gravitational depolarization of ultracold neutrons: Comparison with data
9 octobre 2015
We compare the expected effects of so-called gravitationally enhanced depolarization of ultracold neutrons to measurements carried out in a spin-precession chamber exposed to a variety of vertical magnetic-field gradients. In particular, we have investigated the dependence upon these field (...)
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### [in2p3-01177776] Experimental study of a high intensity radio-frequency cooler
23 juillet 2015
Within the framework of the DESIR/SPIRAL-2 project, a radio-frequency quadrupole cooler named SHIRaC has been studied. SHIRaC is a key device of SPIRAL-2, designed to enhance the beam quality required by DESIR. The preliminary study and development of this device has been carried out at (...)
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### [in2p3-01177675] Estimate of the reactivity of the VENUS-F subcritical configuration using a Monte Carlo MSM method
20 juillet 2015
The GUINEVERE project was launched in 2006 in order to study the feasibility of transmutation in Accelerator Driven subcritical Systems (ADS). This facility, hosted at the Belgian Nuclear Research Center SCK·CEN, couples the fast subcritical lead reactor VENUS-F with an external neutron source (...)
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### [in2p3-00089852] $\beta$-decay studies of neutron-rich K isotopes
3 juillet 2015
The beta decay of the neutron-rich nuclei $^51-53$K has been used to populate bound and unbound states in $^50-53$Ca. Measurements of gamma rays as well as beta-delayed neutrons enabled detailed decay schemes to be established and levels identified in $^50-53$Ca. A delayed one-neutron emission (...)
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### [in2p3-00134052] A telescope for monitoring fast neutron sources
1er juillet 2015
In the framework of nuclear waste management, highly radiotoxic long-lived fission products and minor actinides are planned to be transmuted in a sub-critical reactor coupled with an intense external neutron source. The latter source would be created by a high-energy proton beam hitting a high (...)
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### [in2p3-00022117] Nucleon-induced reactions at intermediate energies: New data at 96 MeV and theoretical status
1er juillet 2015
Double-differential cross sections for light charged particle production (up to A = 4) were measured in 96 MeV neutron-induced reactions, at the TSL Laboratory Cyclotron in Uppsala (Sweden). Measurements for three targets, Fe, Pb, and U, were performed using two independent devices, SCANDAL and (...)
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### [in2p3-00024846] Performance of a micro-channel plates position sensitive detector
1er juillet 2015
The absolute detection efficiency of large area micro-channel plates (MCPs) detectors has been measured with $^6$Li$^+$ and $^23$Na$^+$ ions in the 0.5–7.5 keV energy range. Two detectors of 47mm and 83mm active diameter have been tested. They consist in a pair of MCPs mounted in a chevron (...)
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### [in2p3-00113799] Spectral discrimination of Cerenkov radiation in scintillating dosimeters
1er juillet 2015
Radiation therapy accelerators require highly accurate dose deposition and the output must be monitored frequently and regularly. Ionization chambers are the primary tool for this control, but their size, their high voltage needed, and the correction needed for electrons make them unsuitable (...)
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### [in2p3-00258718] On-line monitoring of fluence distributions and imaging of scanning ion beams
1er juillet 2015
In this paper we describe the design of an ion beam monitor developed to control irradiations of biological samples with ions at GANIL (Grand Accélérateur National d'Ions Lourds). This device can be used as an on-line monitor to provide transverse fluence distributions for active scanning ion (...)
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1er juillet 2015
11 décembre 2008
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### Status of the LPCTrap facility at GANIL
10 novembre 2008
The LPCTrap is a device whose central element is a transparent Paul trap for the efficient trapping of low energy radioactive ions produced by the SPIRAL facility at GANIL. The installation comprises a linear RFQ cooler and buncher for the beam preparation, and a decay chamber where the Paul (...)
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7 novembre 2008
Future installations for radioactive ion beams aim at producing much higher intensities. Accompanying increases in unwanted (isobaric) contamination places more stringent requirements on beam purification, especially mass separation. This article describes the design, construction and first (...)
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### Paul trapping of radioactive $^{6}$He+ ions and direct observation of their beta-decay
17 octobre 2008
We demonstrate that abundant quantities of short-lived beta unstable ions can be trapped in a novel transparent Paul trap and that their decay products can directly be detected in coincidence. Low energy 6He+ (807 ms half-life) ions were extracted from the SPIRAL source at GANIL, then (...)
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25 juillet 2008
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### Studies of neutron-induced light-ion production with the MEDLEY facility
22 juillet 2008
The growing interest in applications involving high-energy neutrons (E > 20 MeV) demands high-quality experimental data on neutron-induced reactions. Such data have been measured with the MEDLEY setup at the The Svedberg Laboratory (TSL), Uppsala, Sweden. It has been used to measure (...)
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### An improved neutron electric dipole moment experiment
1er juillet 2008
A new measurement of the neutron EDM, using Ramsey's method of separated oscillatory fields, is in preparation at the new high intensity source of ultra-cold neutrons (UCN) at the Paul Scherrer Institute, Villigen, Switzerland (PSI). The existence of a non-zero nEDM would violate both parity (...)
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### A neutron beam facility at SPIRAL-2
26 juin 2008
The future SPIRAL-2 facility is mainly composed of a high-power superconducting driver LINAC, delivering a high-intensity deuteron, proton and heavy ions beams. The first two beams are particularly well suited to the construction of a neutron beam and irradiation facility called Neutrons for (...)
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### On-line monitoring of fluence distributions and imaging of scanning ion beams
25 février 2008
In this paper we describe the design of an ion beam monitor developed to control irradiations of biological samples with ions at GANIL (Grand Accélérateur National d'Ions Lourds). This device can be used as an on-line monitor to provide transverse fluence distributions for active scanning ion (...)
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### An On-line Monitor for Fluence Distributions and Imaging of Scanning Ion Beams
6 décembre 2007
Clinical applications of hadron beams have generated a wide development of radiobiology experiments, especially at GANIL (Grand Accélérateur National d'Ions Lourds), an ion accelerator in Caen. Biological samples are irradiated with ions in order to observe the induced biological effects. As (...)
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### The LPCTrap experiment: measurement of the $\beta$–ν angular correlation in $^{6}$He using a transparent Paul trap
30 novembre 2007
We report on the status of the LPCTrap experiment, devoted to measure the β–ν angular correlation in the pure Gamow–Teller decay of $^6$He. This measurement is motivated by the search for the presence of tensor type contributions to the weak interaction. The $^6$He ions are confined in a novel (...)
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### Towards a new measurement of the neutron electric dipole moment
29 octobre 2007
Precision measurements of particle electric dipole moments (EDMs) provide extremely sensitive means to search for non-standard mechanisms of T (or CP) violation. For the neutron EDM, the upper limit has been reduced by eight orders of magnitude in 50 years thereby excluding several CP violation (...)
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### The neutron EDM project at PSI
2 octobre 2007
We propose to perform a new high precision measurement of the neutron Electric Dipole Moment (nEDM). Our goal is to reach an accuracy of $5\times10^-28$ e.cm or better, i.e an improvement of nearly two orders of magnitude over the present best measurement. Our experiment will use the new (...)
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### SHIRaC : an RFQ Cooler for high-intensity beams
24 septembre 2007
Future RIB facilities like Spiral2 will push the limits of production with higher intensities and more exotic beams. However, to achieve better experimental sensitivities and accuracies, a mass resolution of m/Δm ~ few 104 is necessary to separate the ions of interest and their isobaric (...)
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### Scintillating fiber dosimeter
19 juillet 2007
Radiotherapy treatments become more and more accurate, using techniques like IMRT. Their irradiation fields and dose depositions are small and complex, and only a few dosimeters are available for real time and in vivo control for photons as well as for electrons beams. In this context, a new (...)
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### Heavy ion beams monitoring for radiobiology applications
19 juillet 2007
We describe the design and the construction of an on-line ion beam monitor. The device provides accurate measurements for radiobiology experiments currently held at GANIL (Grand Accélérateur National d'Ions Lourds) in France. A prototype named IBIS (Ion Beam Inspection System) has been tested at (...)
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### Scandal - A facility for elastic neutron scattering studies in the 50-130 MeV range
11 juillet 2007
A facility for detection of scattered neutrons in the energy interval 50−130 MeV, SCANDAL (SCAttered Nucleon Detection AssembLy), is part of the standard detection system at the 20-180 MeV neutron beam facility of the The Svedberg Laboratory, Uppsala. It has primarily been used for studies of (...)
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### A neutron beam facility at SPIRAL-2
6 juillet 2007
The SPIRAL-2 facility, dedicated to the production of radioactive beams, is expected to be operational in 2011 in GANIL, Caen (France). A high-power, superconducting driver LINAC, delivering a high-intensity deuteron as well as proton and heavy ions beams, will be built. The deuterons and (...)
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### (n,Xn) measurements at 96 MeV
5 juillet 2007
Double differential cross section for neutron production were measured in 96MeV neutrons induced reactions at the TSL laboratory in Uppsala (Sweden). Measurements for Fe and Pb targets were performed using simultaneously two independent setups: DECOI-DEMON and CLODIA-SCANDAL. The double (...)
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5 juillet 2007
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28 juin 2007
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26 juin 2007
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### Nucleon-induced reactions at intermediate energies: New data at 96 MeV and theoretical status
20 juillet 2004
Double-differential cross sections for light charged particle production (up to A = 4) were measured in 96 MeV neutron-induced reactions, at the TSL Laboratory Cyclotron in Uppsala (Sweden). Measurements for three targets, Fe, Pb, and U, were performed using two independent devices, SCANDAL and (...)
Lire la suite | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8364078998565674, "perplexity": 6649.535158492596}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655884012.26/warc/CC-MAIN-20200704042252-20200704072252-00505.warc.gz"} |
http://mathematica.stackexchange.com/users/2411/zeroth | # zeroth
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TeX - LaTeX 10,605 rep 23054 Stack Overflow 176 rep 16 Programmers 151 rep 4 Area 51 151 rep 1 Mathematica 138 rep 3 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9060418605804443, "perplexity": 25352.88013007974}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1413507442420.22/warc/CC-MAIN-20141017005722-00255-ip-10-16-133-185.ec2.internal.warc.gz"} |
http://physics.stackexchange.com/users/30181/nicolas?tab=activity | # Nicolas
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Nov21 comment Maxwell's demon - scaling down from something that seems to work correct, but this doesnt violate the 2nd law since your damper would merely transfer heat to a laeger reservoir. Nov20 revised Maxwell's demon - scaling down from something that seems to work added 125 characters in body Nov20 answered Maxwell's demon - scaling down from something that seems to work Nov9 answered Microwaves and state of matter Nov7 awarded Critic Nov7 answered How are the finite speed of light and the atomic nature of mater related to the end of Moore's law? Oct31 answered Electron in strong magnetic field Oct31 answered Spring force vs Spring Potential Energy? Oct31 comment Why does rubber ball bounce back while iron ball doesn't? They're pretty similar actually. In both cases the kinetic energy of the incoming ball is stored as an elastic (=reversible) deformation of the ball. The difference between rubber and steel is that the magnitude of the deformation required to store all the initial energy is much smaller for steel (Young's modulus of steel is about 10^4 times higher) Oct30 comment Why does rubber ball bounce back while iron ball doesn't? Well in that case it means that either the ball itself gets scratched, or it bounces back. Note however that even very small scratches or bumps amount to significant energy loss. Oct30 comment Why does rubber ball bounce back while iron ball doesn't? The velocity is not so much in question as the ability of the wall to deform and bounce back while giving all the initial energy back Oct30 answered Why does rubber ball bounce back while iron ball doesn't? Oct30 answered Why are we living in the $q$ part of the phase space? Oct30 answered Why isn't all of the dust in a nebula used in the formation of a star? Oct29 awarded Citizen Patrol Oct22 comment What is the reason of the semidiurnal pressure oscillation in the atmosphere? That seems just like it! I'll try and understand that as soon as I can! Oct21 comment Find current in a nontrivial circuit That's rather a question for electronics.stackexchange.com I suppose... Oct21 answered Behavior of gasses, ideal and otherwise Oct21 comment Behavior of gasses, ideal and otherwise Absolutely. But that's an independent question. Oct21 revised Behavior of gasses, ideal and otherwise added 15 characters in body | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6519652605056763, "perplexity": 1594.9152049806353}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657118605.64/warc/CC-MAIN-20140914011158-00107-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"} |
https://calinon.ch/paper3034.htm | ### Abstract
Research in learning from demonstration has focused on transferring movements from humans to robots. However, a need is arising for robots that do not just replicate the task on their own, but that also interact with humans in a safe and natural way to accomplish tasks cooperatively. Robots with variable impedance capabilities opens the door to new challenging applications, where the learning algorithms must be extended by encapsulating force and vision information. In this paper we propose a framework to transfer impedance-based behaviors to a torque-controlled robot by kinesthetic teaching. The proposed model encodes the exam- ples as a task-parameterized statistical dynamical system, where the robot impedance is shaped by estimating virtual stiffness matrices from the set of demonstrations. A collaborative assembly task is used as testbed. The results show that the model can be used to modify the robot impedance along task execution to facilitate the collaboration, by triggering stiff and compliant behaviors in an on-line manner to adapt to the user's actions.
### Bibtex reference
@inproceedings{Rozo13AAAI,
author="Rozo, L. and Calinon, S. and Caldwell, D. G. and Jimenez, P. and Torras, C.",
title="Learning collaborative impedance-based robot behaviors",
booktitle="{AAAI} Conference on Artificial Intelligence",
year="2013",
pages="1422--1428"
}
### Video
This video shows the result of a learning by imitation approach that allows two users to demonstrate an assembly skill requiring different levels of compliance. Each furniture item to assemble will have specific characteristic that needs that are transferred to the robot. Re-programming the robot for each new item would not be possible. Here, the robot can learn this skill by demonstration. One user is grasping the robot and moving it by hand to demonstrate how it should collaborate with another user (kinesthetic teaching). A force sensor mounted at the wrist of the robot and a marker-based vision tracking system is used to record the position and orientation of the table legs that need to be mounted at four different point on the table top. After demonstration, the robot learns that it should first be compliant to let the user re-orient the table top in a comfortable pose to screw the corresponding table leg. Once the user starts to screw the leg, the robot becomes stiff to facilitate the task. This behavior is not pre-programmed, but is instead learn by the robot by extracting the regularities of the task from multiple demonstrations.
Credits: Leonel Rozo, Sylvain Calinon
### Source codes
Training of a task-parameterized Gaussian mixture model (GMM) based on candidate frames of reference. The proposed task-parameterized GMM approach relies on the linear transformation and product properties of Gaussian distributions to derive an expectation-maximization (EM) algorithm to train the model. The proposed approach is contrasted with an implementation of the approach proposed by Wilson and Bobick in 1999, with an implementation applied to GMM (that we will call PGMM) and following the model described in "Parametric Hidden Markov Models for Gesture Recognition", IEEE Trans. on Pattern Analysis and Machine Intelligence.
In contrast to the standard PGMM approach, the new approach that we propose allows the parameterization of both the centers and covariance matrices of the Gaussians. It has been designed for targeting problems in which the task parameters can be represented in the form of coordinate systems, which is for example the case in robot manipulation problems.
#### Usage
For the Matlab version, unzip the file and run 'demo1' or 'demo2' in Matlab.
For the C++ version, unzip the file and follow the instructions in the ReadMe.txt file.
#### Reference
• Calinon, S., Li, Z., Alizadeh, T., Tsagarakis, N.G. and Caldwell, D.G. (2012) Statistical dynamical systems for skills acquisition in humanoids. Proc. of the IEEE Intl Conf. on Humanoid Robots (Humanoids).
#### Demo 1 - Simple example of task-parameterized GMM learning and comparison with standard PGMM
This example uses 3 trajectories demonstrated in a frame of reference that varies from one demonstration to the other. A model of 3 Gaussian components is used to encode the data in the different frames, by providing the parameters of the coordinate systems as inputs (transformation matrix A and offset vector b).
#### Demo 2 - Example of task-parameterized movement learning with DS-GMR (statistical dynamical systems based on Gaussian mixture regression)
This demo shows how the approach can be combined with the DS-GMR model to learn movements modulated with respect to different frames of reference. The DS-GMR model is a statistical dynamical system approach to learn and reproduce movements with a superposition of virtual spring-damper systems retrieved by Gaussian mixture regression (GMR). For more details, see the 'DMP-learned-by-GMR-v1.0' example code downloadable from the website below. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3443463146686554, "perplexity": 1805.0494556874057}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046151641.83/warc/CC-MAIN-20210725080735-20210725110735-00335.warc.gz"} |
http://crypto.stanford.edu/pbc/notes/numbertheory/crt.html | ## The Chinese Remainder Theorem
Suppose we are asked to solve
$x = 2 \pmod{5}$ $x = 3 \pmod{7}$
for $x$. If we have a solution $y$, then $y + 35$ is also a solution, and more generally $y$ plus any mulitple of $35$. So we only need to look for solutions modulo $35$. By brute force, we find the only solution is $x = 17 \pmod{35}$.
For any system of equations like this, the Chinese Remainder Theorem tells us that there is always a unique solution up to a certain modulus, and describes how to find the solution efficiently.
Theorem: Let $p, q$ be coprime. Then the system of equations
$x = a \pmod{p}$ $x = b \pmod{q}$
has a unique solution for $x$ modulo $p q$.
The reverse direction is trivial: given $x \in \mathbb{Z}_{p q}$, we can reduce $x$ modulo $p$ and $x$ modulo $q$ to obtain two equations of the above form.
Proof: Let $p_1 = p^{-1} \pmod{q}$ and $q_1 = q^{-1} \pmod{p}$. These must exist since $p, q$ are coprime. Then we claim that if $y$ is an integer such that
$y = a q q_1 + b p p_1 \pmod{p q}$
then $y$ satisfies both equations:
Modulo $p$, we have $y = a q q_1 = a \pmod{p}$ since $q q_1 = 1 \pmod{p}$. Similarly $y = b \pmod{q}$. Thus $y$ is a solution for $x$.
It remains to show no other solutions exist modulo $p q$. If $z = a \pmod{p}$ then $z - y$ is a multiple of $p$. If $z = b \pmod{q}$ as well, then $z - y$ is also a multiple of $q$. Since $p$ and $q$ are coprime, this implies $z - y$ is a multiple of $p q$, hence $z = y \pmod {p q}$. ∎
This theorem implies we can represent an element of $\mathbb{Z}_{p q}$ by one element of $\mathbb{Z}_p$ and one element of $\mathbb{Z}_q$, and vice versa. In other words, we have a bijection between $\mathbb{Z}_{p q}$ and $\mathbb{Z}_p \times \mathbb{Z}_q$.
Examples: We can write $17 \in \mathbb{Z}_{35}$ as $(2,3) \in \mathbb{Z}_5 \times \mathbb{Z}_7$. We can write $1 \in \mathbb{Z}_{p q}$ as $(1,1) \in \mathbb{Z}_p \times \mathbb{Z}_q$.
In fact, this correspondence goes further than a simple relabelling. Suppose $x, y \in \mathbb{Z}_{p q}$ correspond to $(a,b), (c,d) \in \mathbb{Z}_p \times \mathbb{Z}_q$ respectively. Then a little thought shows $x + y$ corresponds to $(a + c, b + d)$, and similarly $x y$ corresponds to $(a c, b d)$.
A practical application: if we have many computations to perform on $x \in \mathbb{Z}_{p q}$ (e.g. RSA signing and decryption), we can convert $x$ to $(a,b) \in \mathbb{Z}_p \times \mathbb{Z}_q$ and do all the computations on $a$ and $b$ instead before converting back. This is often cheaper because for many algorithms, doubling the size of the input more than doubles the running time.
Example: To compute $17 \times 17 \pmod{35}$, we can compute $(2\times 2,3\times 3) = (4,2)$ in $\mathbb{Z}_5\times\mathbb{Z}_7$, and then apply the Chinese Remainder Theorem to find that $(4,2)$ is $9 \pmod{35}$.
Let us restate the Chinese Remainder Theorem in the form it is usually presented.
## For Several Equations
Theorem: Let $m_1,...,m_n$ be pairwise coprime (that is $\gcd(m_i, m_j) = 1$ whenever $i \ne j$). Then the system of $n$ equations
$x = a_1 \pmod{m_1}$ $...$ $x = a_n \pmod{m_n}$
has a unique solution for $x$ modulo $M$ where $M = m_1...m_n$.
Proof: This is an easy induction from the previous form of the theorem, or we can write down the solution directly.
Define $b_i = M / m_i$ (the product of all the moduli except for $m_i$) and $b'_i = b_i^{-1} \pmod{m_i}$. Then by a similar argument to before,
$x = \sum_{i=1}^n a_i b_i b'_i \pmod{M}$
is the unique solution.∎
## Prime Powers First
An important consequence of the theorem is that when studying modular arithmetic in general, we can first study modular arithmetic a prime power and then appeal to the Chinese Remainder Theorem to generalize any results. For any integer $n$, we factorize $n$ into primes $n = p_1^{k_1} ... p_m^{k_m}$ and then use the Chinese Remainder Theorem to get
$\mathbb{Z}_n = \mathbb{Z}_{p_1^{k_1}} \times ... \times \mathbb{Z}_{p_m^{k_m}}$
To prove statements in $\mathbb{Z}_{p^k}$, one starts from $\mathbb{Z}_p$, and inductively works up to $\mathbb{Z}_{p^k}$. Thus the most important case to study is $\mathbb{Z}_p$. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9863961935043335, "perplexity": 85.63031703844423}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246637445.19/warc/CC-MAIN-20150417045717-00254-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/probability-of-coin-and-markov-transition-matrix.148719/ | Probability of coin and markov transition matrix
1. Dec 19, 2006
hupdy
1. Consider n flips of a fair coin. Calculate the probability:
a. n/2 < -Total number of heads
c. n/2 < total #heads < 5n/8
WHERE n = 8992
2. Consider the shopping problem
Markov transition matrix
.5 | .5
-----------------
.75 - k | .25 + k
where k = 8992 divided by 20000..
Start with initial v0 = (..5,.5) and describe the behavior of the
system for many time steps.
Does your result cycle, does one state become extinct, or does it
approach a limit value?
Any help will be nice.
2. Dec 19, 2006
cristo
Staff Emeritus
3. Dec 19, 2006
CRGreathouse
If you calculate the answer to #1a exactly, there are 2706 digits in the numerator and the same number in the denominator. :tongue2: | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8665746450424194, "perplexity": 4960.850267037231}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280128.70/warc/CC-MAIN-20170116095120-00403-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://terahertztechnology.blogspot.com/2017/06/abstract-nonlinear-spin-current.html | ## Monday, June 5, 2017
### Abstract-Nonlinear spin current generation in noncentrosymmetric spin-orbit coupled systems
###### Keita Hamamoto, Motohiko Ezawa, Kun Woo Kim, Takahiro Morimoto, and Naoto Nagaosa
https://journals.aps.org/prb/accepted/cb07bYe6Nb61e650459e1259f3e627996a7912eec
Spin current plays a central role in spintronics. In particular, finding more efficient ways to generate spin current has been an important issue and studied actively. For example, representative methods of spin current generation include spin polarized current injections from ferromagnetic metals, spin Hall effect, and spin battery. Here we theoretically propose a new mechanism of spin current generation based on nonlinear phenomena. By using Boltzmann transport theory, we show that a simple application of the electric field \bm{E} induces spin current proportional to \bm{E^2} in noncentrosymmetric spin-orbit coupled systems. We demonstrate that the nonlinear spin current of the proposed mechanism is supported in the surface state of three-dimensional topological insulators and two-dimensional semiconductors with the Rashba and/or Dresselhaus interaction. In the latter case, the angular dependence of the nonlinear spin current can be manipulated by the direction of the electric field and by the ratio of the Rashba and Dresselhaus interactions. We find that the magnitude of the spin current largely exceeds those in the previous methods for a reasonable magnitude of the electric field. Furthermore, we show that application of AC electric fields (e.g. terahertz light) leads to the rectifying effect of the spin current where DC spin current is generated. These findings will pave a new route to manipulate the spin current in noncentrosymmetric crystals. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.83973228931427, "perplexity": 1220.1831623031098}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676588972.37/warc/CC-MAIN-20180715203335-20180715223335-00388.warc.gz"} |
https://kycaqyqozyz.driftwood-dallas.com/numerical-grid-methods-and-their-application-to-schroedingers-equation-book-31415mu.php | Last edited by Samuzahn
Saturday, July 25, 2020 | History
6 edition of Numerical Grid Methods and Their Application to Schrödinger"s Equation found in the catalog.
# Numerical Grid Methods and Their Application to Schrödinger"s Equation
## by C. Cerjan
Written in English
Subjects:
• Chemical physics,
• Theoretical methods,
• Schrèodinger equation,
• Wave Mechanics,
• Science,
• Waves & Wave Mechanics,
• Science/Mathematics,
• Chemistry - Physical & Theoretical,
• Nuclear Physics,
• Science / Nuclear Physics,
• Science / Waves & Wave Mechanics,
• Science-Chemistry - Physical & Theoretical,
• Science-Nuclear Physics,
• Congresses,
• Numerical grid generation (Num,
• Numerical grid generation (Numerical analysis),
• Schrodinger equation,
• Schrèodinger equation
• Edition Notes
NATO Science Series C:
The Physical Object
FormatHardcover
Number of Pages268
ID Numbers
Open LibraryOL7807275M
ISBN 100792324234
ISBN 109780792324232
Sti problems and their numerical solution Numerical solution of the heat conduction equation II Numerical methods for boundary value problems 5 Motivation and accuracy of a chosen numerical scheme. This book is File Size: 2MB. The time-dependent Schrödinger equation is discretized in space by a sparse grid pseudospectral method. The Strang splitting for the resulting evolutionary problem features first or second order convergence in time, depending on the smoothness of the potential and of the initial by:
grid with the same spacing hbetween grid points in each direction. (Later we will discuss other coordinate systems, e.g., polar coordinates.) Fig. 1 shows a section of this grid. We label the grid points by a pair of indices i;j, which just count grid points from some reference point, say the lower left hand corner. Thus assuming the reference File Size: KB. Book Description. Numerical Methods in Astrophysics: An Introduction outlines various fundamental numerical methods that can solve gravitational dynamics, hydrodynamics, and radiation transport equations. This resource indicates which methods are most suitable for particular problems, demonstrates what the accuracy requirements are in numerical simulations, and suggests ways to .
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).Numerical analysis naturally finds application in all fields of engineering and the physical sciences, but in the 21st century also the life sciences, social sciences, medicine, business and. This is the first book devoted to the numerical solution of general problems with periodic and oscillating solutions. It encompasses all the recent research in this area and compares various techniques on the solution of the Schrödinger equation and related problems from several disciplines such as astronomy and mathematics.
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### Numerical Grid Methods and Their Application to Schrödinger"s Equation by C. Cerjan Download PDF EPUB FB2
The use of numerical grid methods to solve the Schrodinger equation has rapidly evolved in the past early attempts to demonstrate the computational viability of grid methods have been largely superseded by applications to specific problems and deeper research into more sophisticated quadrature : Hardcover.
Numerical Grid Methods and Their Application to Schroedinger's Equation by C. Cerjan,available at Book Depository with free delivery worldwide. Grid generation methods are indispensable for the numerical solution of differential equations.
Adaptive grid-mapping techniques, in particular, are the main focus and represent a promising tool to deal with systems with singularities. This 3rd edition includes three new chapters on numerical implementations (10), control of grid properties (11 Cited by: COVID Resources.
Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus.
Proceedings of the NATO Advanced Research Workshop on `Grid methods in Atomic and Molecular Quantum Calculations', Corte, Corsica, France, September October 3, The use of numerical grid methods to solve the Schrodinger equation has rapidly evolved in the past early attempts to demonstrate the computational viability of grid methods have been.
Get this from a library. Numerical grid methods and their application to schrödinger's equation. [Charles Cerjan; North Atlantic Treaty Organization. Scientific Affairs Division.;] -- This book offers a unique perspective on the rapidly growing field of numerical grid methods applied to the solution of the Schr?dinger equation.
Several articles provide comprehensive reviews of the. In: Numerical Grid Methods and Their Applications to Schrödinger’s Equation, ed. by C. Cerjan (Kluwer Academic Publishers, The Netherlands ) pp. 89– Google Scholar V.S. Melezhik, D. Baye: Phys.
Rev. C 59, () ADS CrossRef Google ScholarAuthor: K. Taylor, J. Parker, D. Dundas, K. Meharg, L. Moore, E. Smyth, J. McCann. Cerjan, Numerical Grid Methods and Their Application to Schrödinger’s Equation,Buch, Bücher schnell und portofrei.
region. (Finite volume methods are effectively a type of conservative finite difference method on these grids.) In this text, grid generation and the use thereof in numerical solutions of partial equations are both discussed. The intent was to provide the necessary basic information,File Size: 2MB.
exact or approximate numerical methods must be employed. Here we will rst discuss solutions of the Schr odinger equation (1) in one dimension, which is a problem almost identical to solving the radial wave function for spherically symmetric potentials in two or three dimensions.
We will derive and use Numerov’s method, which is a very elegantFile Size: KB. Buy Numerical Methods for Grid Equations: Direct Methods v. 1 by Samarskij, A.A., Nikolaev, E.S. (ISBN: ) from Amazon's Book Store. Author: A.A. Samarskij, E.S. Nikolaev. Numerical Methods for Partial Differential Equations Concrete examples are given in terms of Cauchy-Riemann equations and the steady-state incompressible Navier-Stokes equations.
Their multi-grid solution, based on new єdistributive” relaxation schemes, costs about seven work-units. This chapter presents some numerical methods for. He has written on numerical methods and their application in finance, with a focus on asset allocation.
His research interests include quantitative investment strategies and portfolio construction, computationally-intensive methods (in particular, optimization), and. Numerical modeling study was carried out by finite difference method (FDM). In this method, the whole domain was discretized into small two-dimensional zones (elements) that were interconnected with their grid points (nodes) (Naylor, ; Soren et al., ).
Over each zone, the differential equation of equilibrium was approximated. Numerical methods vary in their behavior, and the many different types of differ-ential equation problems affect the performanceof numerical methods in a variety of ways.
An excellent book for “real world” examples of solving differential equations is that of Shampine, Gladwell, and Thompson [74].File Size: 1MB. Chapter 1 Introduction The purpose of these lectures is to present a set of straightforward numerical methods with applicability to essentially any problem associated with a partial di erential equation (PDE) or system of PDEs inde.
Numerical solution of partial di erential equations Dr. Louise Olsen-Kettle The University of Queensland Applied Numerical Methods for Engineers using Matlab and C, R. Schilling equations which must be solved over the whole grid. Implicit methods are stable for all step by: 4.
Here we review the basic numerical techniques for dealing with such equations, including the case of semi-Lagrangian methods, discrete-velocity models and spectral methods.
In addition we give an overview of the current state of the art of numerical methods for kinetic by: Baker et al. proposed such a mapping for a radial grid for atomic & molecular electronic structure computations in It is still used in modern electronic structure codes, e.g. FHI-AIMS uses them, as described in a recent paper.
Even with such a mapping, the same problems still remains: if something interesting should happen beyound the outermost grid point, you will miss it.
Numerical methods for ordinary differential equations/J.C. Butcher. Includes bibliographical references and index. ISBN (cloth) 1. Differential equations—Numerical solutions. Title. QAB94 —dc22 British Library Cataloguing in Publication Data.
and backward (implicit) Euler method $\psi(x,t+dt)=\psi(x,t) - i*H \psi(x,t+dt)*dt$ The backward component makes Crank-Nicholson method stable. The forward component makes it more accurate, but prone to oscillations.
If you want to get rid of oscillations, use a smaller time step, or use backward (implicit) Euler method. That is all there is to it.The CPU time to solve the system of equations differs substantially from method to method.
Finite differences are usually the cheapest on a per grid point basis followed by the finite element method and spectral method. However, a per grid point basis comparison is a .PHY Computational Methods in Physics and Astrophysics II Fall An overview of numerical methods and their application to problems in physics and . | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3294006288051605, "perplexity": 2654.573490061399}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320300805.79/warc/CC-MAIN-20220118062411-20220118092411-00132.warc.gz"} |
https://undergroundmathematics.org/chain-rule/r9809 | Review question
# When do these normals to a parabola meet on the parabola? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource
Ref: R9809
## Question
Find the equation of the normal to the parabola $y^2=4ax$ at the point $(at^2,2at)$.
The parameters of the points $P$, $Q$ are $t_1$ and $t_2$ respectively. Show that, if $PQ$ passes through the point $(-2a,0)$, then $t_1t_2=2$ and the normals at $P$ and $Q$ to the parabola meet at a point $R$ on the parabola.
If $O$ is the origin, show, by considering the gradients of the sides of the quadrilateral $OPQR$ or otherwise, that the circumcircle of the triangle $PQR$ passes through $O$. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.30119559168815613, "perplexity": 195.41421611072272}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267160085.77/warc/CC-MAIN-20180924011731-20180924032131-00549.warc.gz"} |
http://forge.cbp.ens-lyon.fr/redmine/issues/2706 | ## Bug #2706
### Initial step on relaunch calculation for refinement.
Status:New Start date:12/31/2019
Priority:Normal Due date:
Assignee:Carles Marti % Done:
0%
Category:- Spent time: -
Target version:-
Description
When carrying out the calculations for refinement of the adsorbed species structure, the restart file from the former lower precision calculation is taken as input for the higher precision one. On this restart file, the initial step number is set as the successive from the lower precision calculation, this fact makes the refinement calculation start from a step number higher than one and thus more likely to arrive to the maximum step number allowed for the geometry optimization.
### Associated revisions
Revision 76cb4d88
Sets the initial step number of the refinment calculation not to be conserved from the lower precision stage (ie. it starts always at 1); Fixes #2706
Also available in: Atom PDF | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.84879469871521, "perplexity": 3397.0623312294265}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370493121.36/warc/CC-MAIN-20200328225036-20200329015036-00124.warc.gz"} |
http://mathhelpforum.com/calculus/123004-indefinite-integrals.html | # Math Help - Indefinite integrals
1. ## Indefinite integrals
Question:
$\int \sqrt[3] {3x+5}.dx$
So the equation will be $\int (3x+5)^\frac{1}{3}.dx$
$u=3x+5 \rightarrow \int u^\frac{1}{3}$
$du=3$
After this step i dont know what to do , do i divide by 3 to produce 1?
2. Originally Posted by mj.alawami
Question:
$\int \sqrt[3] {3x+5}.dx$
So the equation will be $\int (3x+5)^\frac{1}{3}.dx$
$u=3x+5 \rightarrow \int u^\frac{1}{3}$
$du=3$
Here's your problem! du is NOT equal to 3, du= 3dx.
And from that it should be easy to see that dx= (1/3)du.
After this step i dont know what to do , do i divide by 3 to produce 1?
I have no idea what you could mean by "do i divide by 3 to produce 1?". Divide what by 3? "Produce 1" where and how? The more precise you are in mathematics, the bettter. Practise being precise.
3. Originally Posted by mj.alawami
Question:
$\int \sqrt[3] {3x+5}.dx$
So the equation will be $\int (3x+5)^\frac{1}{3}.dx$
$u=3x+5 \rightarrow \int u^\frac{1}{3}$
$du=3$
After this step i dont know what to do , do i divide by 3 to produce 1?
$u=3x+5$ then
$du=3dx$
$\frac{1}{3}du=dx$.
So, we have
$\int(3x+5)^{1/3}dx=\int{u^{1/3}}\frac{1}{3}du$
4. Originally Posted by HallsofIvy
Here's your problem! du is NOT equal to 3, du= 3dx.
And from that it should be easy to see that dx= (1/3)du.
I have no idea what you could mean by "do i divide by 3 to produce 1?". Divide what by 3? "Produce 1" where and how? The more precise you are in mathematics, the bettter. Practise being precise.
$\int \frac{1}{4} (3x+5)^\frac{4}{3} +C$
5. Originally Posted by mj.alawami
Question:
$\int \sqrt[3] {3x+5}.dx$
So the equation will be $\int (3x+5)^\frac{1}{3}.dx$
$u=3x+5 \rightarrow \int u^\frac{1}{3}$
$du=3$
After this step i dont know what to do , do i divide by 3 to produce 1?
It might help to write it out like this
$u = 3x + 5$ so $\frac{du}{dx} = 3$.
Now work on the integral
$\int{(3x + 5)^{\frac{1}{3}}\,dx} = \frac{1}{3}\int{(3x + 5)^{\frac{1}{3}} \cdot 3\,dx}$
$= \frac{1}{3}\int{u^{\frac{1}{3}}\,\frac{du}{dx}\,dx }$
$= \frac{1}{3}\int{u^{\frac{1}{3}}\,du}$.
Might be an extra step but easier to avoid making mistakes...
6. Originally Posted by Prove It
It might help to write it out like this
$u = 3x + 5$ so $\frac{du}{dx} = 3$.
Now work on the integral
$\int{(3x + 5)^{\frac{1}{3}}\,dx} = \frac{1}{3}\int{(3x + 5)^{\frac{1}{3}} \cdot 3\,dx}$
$= \frac{1}{3}\int{u^{\frac{1}{3}}\,\frac{du}{dx}\,dx }$
$= \frac{1}{3}\int{u^{\frac{1}{3}}\,du}$.
Might be an extra step but easier to avoid making mistakes...
$\frac{1}{2} (3x+5)^\frac{4}{3} +C$
7. No.
$\frac{1}{3}\int{u^{\frac{1}{3}}\,du} = \frac{1}{3}\cdot\frac{3}{4}u^{\frac{4}{3}} + C$
$= \frac{1}{4}u^{\frac{4}{3}} + C$
$= \frac{1}{4}(3x + 5)^{\frac{4}{3}} + C$.
8. Originally Posted by mj.alawami
$\int \frac{1}{4} (3x+5)^\frac{4}{3} +C$
What do you get if you differentiate that? Did you even try that?
9. substitution isn't needed in this question.
If you remember this:
if you have a derivative that is in the form: (ax+b)^n
then the integral will be: [(ax+b)^n+1] / a(n+1)
so just substitute your question into that rule.
10. Originally Posted by bhuang
substitution isn't needed in this question.
If you remember this:
if you have a derivative that is in the form: (ax+b)^n
then the integral will be: [(ax+b)^n+1] / a(n+1)
so just substitute your question into that rule.
Don't try remembering lots of rules, it gets to be too much of a headache.
It's easier to remember a few basic rules and to use substitution for the rest.
Besides, the rule you speak of comes from substitution anyway. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 36, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9033272862434387, "perplexity": 1004.5530386192223}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246646036.55/warc/CC-MAIN-20150417045726-00217-ip-10-235-10-82.ec2.internal.warc.gz"} |