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3,842,182 | https://en.wikipedia.org/wiki/Cord%20%28unit%29 | The cord is a unit of measure of dry volume used to measure firewood and pulpwood in the United States and Canada.
A cord is the amount of wood that, when "racked and well stowed" (arranged so pieces are aligned, parallel, touching, and compact), occupies a volume of . This corresponds to a well-stacked woodpile high, wide, and deep; or any other arrangement of linear measurements that yields the same volume.
The name cord probably comes from the use of a cord or string to measure it.
The face cord is a unit of volume for stacked firewood, 8 feet long, 4 feet wide, and 16 inches high—equal to 1/3 of a cord. The symbol for the unit is fc - cd.
Definitions
In Canada, the cord is legally defined by Measurement Canada. The cord is one of three legal standards for the sale of firewood in Canada: stacked cubic meter (or stere), cubic foot, and cord.
In the United States, the cord is defined by statute in most states. The U.S. National Institute of Standards and Technology Handbook 130, section 2.4.1.2, defines a cord and provides uniform regulations for the sale of fireplace and stove wood. In the metric system, wood is usually measured in steres and cubic meters: 1 stere = 1 m3 ≈ 0.276 cords.
Maine appears unique among U.S. states by also defining a "loose thrown cord" or pile of cut firewood: "A cord of in length shall mean the amount of wood, bark, and air contained in a space of ; and a cord of wood in length shall mean the amount of wood, bark, and air contained in a space of . [1981, c. 219 (amd).]"
Other non-official terms for firewood volume include standing cord, kitchen cord, running cord, face cord, fencing cord, country cord, long cord, and rick, all subject to local variation. These are usually taken to mean a well-stacked pile of wood in which the logs are shorter or longer than in a legal cord, to accommodate various burners. For example, a face cord commonly consists of wood that is long. The volume of a face cord therefore is typically 1/3 of the volume of a full cord even though it is long and high. A face cord is also called a rick in the midwestern United States.
The term is used in other English-speaking countries, such as New Zealand, but may not have a legal definition.
The corde was a unit of volume used before metrication in several French-speaking countries (France, Belgium and Luxembourg). Its value varied from depending on the region, corresponding approximately to 2 to 5 steres.
Heating value
One seasoned (dry) cord of Northern red oak with a heating value of has the heating equivalent of of fuel oil with a heating value of .
Australia
Until metrication in Australia, an imperial cord was a measurement for wood and firewood. The measurements for a cord of wood were 4 feet wide by 4 feet deep by 8 feet high, or usually a stack of wood containing 128 cubic feet (cu ft). The imperial cord enclosed 128 cu ft.
See also
Board foot
Cubic ton
Forest product
Hoppus foot
Imperial units
List of unusual units of measurement
Measurement Canada
Measurement Information Division of Industry Canada
Standard (timber unit)
Units of measurement
References
External links
Nova Scotia Natural Resources Information Circular DNR - 1A: "Guide to buying and measuring stacked firewood"
Customary units of measurement in the United States
Units of volume
Logging | Cord (unit) | [
"Mathematics"
] | 729 | [
"Units of volume",
"Quantity",
"Units of measurement"
] |
3,846,249 | https://en.wikipedia.org/wiki/Beryllide | Beryllide is an intermetallic compound of beryllium with other metals, e.g. zirconium, tantalum, titanium, nickel, or cobalt. Typical chemical formulae are Be12Ti and FeBe5. These are hard, metal-like materials that display properties distinct from the constituents, especially with regards to their resilience toward oxidation.
Applications and potential applications
Beryllides of cobalt and nickel have metallurgical importance as the precipitated phase in beryllium copper alloys. These materials are nonsparking, which allows them to be used in certain hazardous environments.
In nuclear technology, beryllides are investigated as neutron multipliers. Unlike metallic Be, materials such as Be12Ti are more resistant to oxidation by water but retain the neutron-multiplying properties of the predominant isotope 9Be.
References
External links
04.03-1980A, 900704, The Development of FeBe5 Fiber Using a Dual Plasma Deposition System
Present status of beryllide R&D as neutron multiplier
Beryllium compounds
Intermetallics | Beryllide | [
"Physics",
"Chemistry",
"Materials_science"
] | 228 | [
"Inorganic compounds",
"Alloy stubs",
"Metallurgy",
"Intermetallics",
"Condensed matter physics",
"Alloys"
] |
24,421,488 | https://en.wikipedia.org/wiki/Macromolecular%20Reaction%20Engineering | Macromolecular Reaction Engineering is a peer-reviewed scientific journal published monthly by Wiley-VCH. The journal covers academic and industrial research in the field of polymer reaction engineering, which includes polymer science. It emerged from a section that was part of Macromolecular Materials and Engineering. The journal publishes reviews, feature articles, communications, and full papers in the entire field of polymer reaction engineering, including polymer reaction modeling, reactor optimization, and control. Its 2020 impact factor is 1.931.
The journal also produces special issues. The 2009 and 2010 topics included "New Frontiers in Polymer Engineering" and "Controlled Radical Polymerization".
Aims and scope
Macromolecular Reaction Engineering is intended for polymer scientists, chemists, physicists, materials scientists, theoreticians, and chemical engineers. The journal covers recent and significant results of academic and industrial research in the field of interest, encompassing all related topics - this includes polymer reaction modeling, reactor optimization and control, polyolefins, polymer production, sensors, process control, polymers, macromolecular materials, polymer reaction engineering, modelling, reactor optimization, polymeric materials, and polymer engineering.
Abstracting and indexing
The journal is abstracted and indexed in Chemical Abstracts Service, Chemistry Citation Index, Compendex, Current Contents/Engineering, Computing & Technology, Current Contents/Physical, Chemical & Earth Sciences, Inspec, Journal Citation Reports/Science Edition, Materials Science Citation Index, and the Science Citation Index Expanded.
References
External links
Chemistry journals
Materials science journals
Academic journals established in 2007
Wiley (publisher) academic journals
Monthly journals
English-language journals | Macromolecular Reaction Engineering | [
"Materials_science",
"Engineering"
] | 329 | [
"Materials science journals",
"Materials science"
] |
24,422,145 | https://en.wikipedia.org/wiki/Deuterated%20dichloromethane | Deuterated dichloromethane (CDCl or CHCl) is a form (isotopologue) of dichloromethane (DCM, CHCl) in which the hydrogen atoms (H) are deuterium (heavy hydrogen) (H or D). Deuterated DCM is not a common solvent used in NMR spectroscopy as it is expensive compared to deuterated chloroform.
Notes
References
Deuterated solvents | Deuterated dichloromethane | [
"Chemistry"
] | 100 | [
"Deuterated solvents",
"Nuclear magnetic resonance",
"Organic compounds",
"Nuclear chemistry stubs",
"Nuclear magnetic resonance stubs",
"Organic compound stubs",
"Organic chemistry stubs"
] |
24,423,385 | https://en.wikipedia.org/wiki/Jacobsen%27s%20catalyst | Jacobsen's catalyst is the common name for N,N'-bis(3,5-di-tert-butylsalicylidene)-1,2-cyclohexanediaminomanganese(III) chloride, a coordination compound of manganese and a salen-type ligand. It is used as an asymmetric catalyst in the Jacobsen epoxidation, which is renowned for its ability to enantioselectively transform prochiral alkenes into epoxides. Before its development, catalysts for the asymmetric epoxidation of alkenes required the substrate to have a directing functional group, such as an alcohol as seen in the Sharpless epoxidation. This compound has two enantiomers, which give the appropriate epoxide product from the alkene starting material.
Enantiomerically pure epoxides are desirable as building blocks for complex molecules with specific chirality. Biologically active compounds can exhibit radically different activity based on differences in chirality and therefore the ability to obtain desired stereocenters in a molecule is of great importance to the pharmaceutical industry. Jacobsen's catalyst and other asymmetric catalysts are particularly useful in this field; for example, Jacobsen's catalyst was used to synthesize phenylisoserine, a side chain to the famous anti-cancer drug Taxol, in a four-step synthesis as early as 1992.
Structure and basic properties
Jacobsen's catalyst consists of a salen ligand, tetradentate, meaning it binds to the central manganese metal through four bonds, one to each oxygen and nitrogen atom of the salen backbone. Its chirality is conferred from the diamine-derived backbone. The aryl groups are decorated with tert-butyl substituents, which amplify the asymmetry around the Mn center.
Preparation
Both enantiomers of Jacobsen's catalyst are commercially available. Jacobsen's catalyst can be prepared by separating 1,2-diaminocyclohexane into its component enantiomers and then reacting the appropriate tartrate with 3,5-di-tert-butyl-2-hydroxybenzaldehyde to form a Schiff base (see intermediate formed in the reaction scheme below). Reaction with manganese(II) acetate in the presence of air gives the manganese(III) complex, which may be isolated as the chloro derivative after the addition of lithium chloride. Shown below is the preparation of the (R,R)-enantiomer. The synthesis has been adapted for undergraduate level chemistry courses in order to stress the importance of enantiomerically pure compounds.
Reaction mechanism
In general, two mechanisms have been suggested. Because Jacobsen's catalyst epoxidizes conjugated alkenes (i.e. those in which there are multiple double bonds on alternating carbons) most effectively, the generally accepted mechanism is based on a radical intermediate which is stabilized due to the conjugated nature of the substrate. For non-conjugated alkenes, the substrate is far less able to stabilize a radical, making a radical intermediate more unlikely. In this case, a concerted mechanism in which the bond to the oxygen is simultaneously broken with metal-center while it is formed with the substrate is probable. However, more recent studies have indicated a radical intermediate is possible, challenging the assumption that non-conjugated alkenes undergo concerted mechanisms.
In the original catalytic reaction, iodosylarenes (PhIO) were used as the stoichiometric oxidant, but soon after it was found that chlorine bleach (NaClO), a cheaper alternative, works as well. While other oxidants subsequently have been used, bleach continues to be the most common.
After the addition of the oxidant to the system, O=Mn(V) is generally accepted to be the active oxidant species formed (step A). The substrate is thought to approach the metal-oxo bond from the side at a perpendicular orientation in relation to the catalyst in order to allow favorable orbital overlap. This mechanism, which was originally proposed by John Groves to explain porphyrin-catalyzed epoxidation reactions, is commonly referred to as a "side-on perpendicular approach". The approach is over the diamine bridge, where the steric bulk of the tert-butyl groups on the periphery of the ligand do not interfere with the alkene's approach (see below). However, as is the case with the overall mechanism, the pathway of alkene approach is also debated.
The ease with which Jacobsen's catalyst selectively epoxidizes cis-alkenes has been difficult to replicate with terminal and trans-alkenes. Structural changes to the ligand and adaptations to the protocol for the epoxidation reaction, however, have led to some successes in these areas. For example, derivatives of Jacobsen's catalyst with small structural changes to the salen backbone have been used in conjunction with low temperatures and the oxidant m-chloroperbenzoic acid (m-CPBA) to epoxidize the terminal alkene styrene. The low temperature of the reaction favors only one pathway, the cis pathway, while m-CPBA is used because of water's high freezing point. Little success has occurred with the epoxidation of trans alkenes by manganese compounds but other salen coordination compounds, such as oxochromium complexes, can be used.
Variations
The ligand structure of Jacobsen's catalyst is easily modified for use over a wide range of reactions, such as epoxide-ring openings, Diels-Alder reactions, and conjugate additions. For example, an analogous catalyst with an aluminum center has been used for the carbonylation of epoxides in order to obtain beta-lactones.
See also
Asymmetric catalysis
Enantiomers
Jacobsen epoxidation
Salen ligand
References
Manganese(III) compounds
Catalysis
Metal salen complexes
Tert-butyl compounds
Catalysts | Jacobsen's catalyst | [
"Chemistry"
] | 1,289 | [
"Catalysis",
"Catalysts",
"Coordination chemistry",
"Chemical kinetics",
"Metal salen complexes"
] |
24,424,135 | https://en.wikipedia.org/wiki/C15H16O5 | {{DISPLAYTITLE:C15H16O5}}
The molecular formula C15H16O5 (molar mass: 276.28 g/mol, exact mass: 276.099774 u) may refer to:
Dihydromethysticin, a kavalactone found in the kava plant
Lactucin, a bitter sesquiterpene lactone found in lettuce
Vernolepin, a sesquiterpene lactone found in Vernonia amygdalina
Molecular formulas | C15H16O5 | [
"Physics",
"Chemistry"
] | 115 | [
"Molecules",
"Set index articles on molecular formulas",
"Isomerism",
"Molecular formulas",
"Matter"
] |
24,424,496 | https://en.wikipedia.org/wiki/C12H8O4 | {{DISPLAYTITLE:C12H8O4}}
The molecular formula C12H8O4 (molar mass : 216.19 g/mol) may refer to:
Bergapten, a psoralen found in bergamot essential oil
Methoxsalen, a drug used to treat psoriasis, eczema or vitiligo
2,6-Naphthalenedicarboxylic acid
Molecular formulas | C12H8O4 | [
"Physics",
"Chemistry"
] | 96 | [
"Molecules",
"Set index articles on molecular formulas",
"Isomerism",
"Molecular formulas",
"Matter"
] |
24,425,189 | https://en.wikipedia.org/wiki/Center%20for%20Stem%20Cell%20and%20Regenerative%20Medicine | The Center for Stem Cell and Regenerative Medicine (CSCRM) is a medical research institution specializing in stem cell and other cell therapy research and treatments, located in Cleveland, Ohio. They specialize in basic and clinical research programs, biomedical and tissue engineering programs, and the development and administration of new therapies to patients.
History
The CSCRM was founded in 2003 through funding by the state of Ohio. Its parent institution is the National Center for Regenerative Medicine. They have received over $33 million in funding from the state of Ohio since their inception. As of 2009, they had conducted over 50 clinical trials, treated over 300 patients, spun off four companies, and raised $235 million in venture capital.
Stem cell bank
The center possesses a wide variety of stem cells, including ASC, CSC, CTP, ESC, HSC, HB1, iPS, MSC, MAPC, NSC, SKMB and UCB.
References
Healthcare in Cleveland
Stem cell research
2003 establishments in Ohio | Center for Stem Cell and Regenerative Medicine | [
"Chemistry",
"Biology"
] | 209 | [
"Translational medicine",
"Tissue engineering",
"Stem cell research"
] |
24,426,190 | https://en.wikipedia.org/wiki/WGAViewer | WGAViewer is a bioinformatics software tool which is designed to visualize, annotate, and help interpret the results generated from a genome wide association study (GWAS). Alongside the P values of association, WGAViewer allows a researcher to visualize and consider other supporting evidence, such as the genomic context of the SNP, linkage disequilibrium (LD) with ungenotyped SNPs, gene expression database, and the evidence from other GWAS projects, when determining the potential importance of an individual SNP.
Introduction
Functions
WGAViewer currently offers several classes of annotation of the GWAS results:
(1) Overview of WGA results allowing
zooming in/out
searching for gene/SNP
top hits sorting with individual SNP annotation
(2) Genic annotation of WGA results with explicit reference to:
align results with the latest genome build
gene/transcripts context
linkage disequilibrium context
(3) Annotation for SNPs :
LD score for all HapMap SNPs in specified region
association with specified gene expression
SNP function information
(4) Gene/SNP finding :
locating and annotating specific genes, SNPs, or LD proxies for SNPs, and aligning the results with the latest genome build.
(5) Evidence from multiple scans.
(6) Supporting/QC databases:
displaying supporting information, for example, HWE P values, effect size, effect direction, QC scores, or other user-customized data.
Language
WGAViewer is developed on the Java platform.
Authors
WGAViewer is developed and maintained by Dr. Dongliang Ge and Dr. David B. Goldstein at Duke University, Institute for Genome Sciences & Policy, Center for Human Genome Variation.
Applications
A number of GWAS projects used the WGAViewer software tool.
One of these projects leads to the identification of the genetic variant predicting the hepatitis C treatment-induced viral clearance. The finding from that project, originally reported in Nature, showed that genotype 1 hepatitis C patients carrying certain genetic variant alleles near the IL28B gene are more possibly to achieve sustained virological response after the treatment of Pegylated interferon-alpha-2a or Pegylated interferon-alpha-2b (brand names Pegasys or PEG-Intron) combined with ribavirin. A later report from Nature demonstrated that the same genetic variants are also associated with the natural clearance of the genotype 1 hepatitis C virus.
References
External links
WGAViewer Homepage
Genetics software
Genomics techniques | WGAViewer | [
"Chemistry",
"Biology"
] | 541 | [
"Genetics techniques",
"Genomics techniques",
"Molecular biology techniques"
] |
24,428,035 | https://en.wikipedia.org/wiki/Alpha%20oxidation | Alpha oxidation (α-oxidation) is a process by which certain branched-chain fatty acids are broken down by removal of a single carbon from the carboxyl end. In humans, alpha-oxidation is used in peroxisomes to break down dietary phytanic acid, which cannot undergo beta-oxidation due to its β-methyl branch, into pristanic acid. Pristanic acid can then acquire CoA and subsequently become beta oxidized, yielding propionyl-CoA.
Pathway
Alpha-oxidation of phytanic acid is believed to take place entirely within peroxisomes.
Phytanic acid is first attached to CoA to form phytanoyl-CoA.
Phytanoyl-CoA is oxidized by phytanoyl-CoA dioxygenase, in a process using Fe2+ and O2, to yield 2-hydroxyphytanoyl-CoA.
2-hydroxyphytanoyl-CoA is cleaved by 2-hydroxyphytanoyl-CoA lyase in a TPP-dependent reaction to form pristanal and formyl-CoA (in turn later broken down into formate and eventually CO2).
Pristanal is oxidized by aldehyde dehydrogenase to form pristanic acid (which can then undergo beta-oxidation).
(Propionyl-CoA is released as a result of beta oxidation when the beta carbon is substituted)
Deficiency
Enzymatic deficiency in alpha-oxidation (most frequently in phytanoyl-CoA dioxygenase) leads to Refsum's disease, in which the accumulation of phytanic acid and its derivatives leads to neurological damage. Other disorders of peroxisome biogenesis also prevent alpha-oxidation from occurring.
References
Biochemistry
Cell biology
Lipid metabolism
Metabolic pathways
Fatty acids | Alpha oxidation | [
"Chemistry",
"Biology"
] | 379 | [
"Lipid biochemistry",
"Biochemistry",
"Cell biology",
"nan",
"Metabolic pathways",
"Lipid metabolism",
"Metabolism"
] |
24,430,115 | https://en.wikipedia.org/wiki/No%20Cross%2C%20No%20Crown | No Cross, No Crown is one of the chief works of William Penn, first published in 1669. It was written during Penn's imprisonment in the Tower of London.
Summary
Penn exhorts the spirit of Primitive Christianity. The book is divided into two parts, the first dealing with the importance of self-denial in the Christian life and the second gathering a series of references to men through the ages who have written of the importance of self-denial, including "heathen," professed Christians, and "retired, aged, and dying men, being their last and serious reflections, to which no ostentation or worldly interests could induce them." Penn's view of Christianity is intensely spiritual rather than formal, and in passing he defends several practices typical of the Religious Society of Friends (Quakers) including clothing which was not fashionable and speech which addressed royal and commoner alike in the second person singular "thee" and "thou."
Scholarly editions
A 1931 scholarly edition was edited by Norman Penney.
References
External links
Philosophy books
1669 books
1669 in Christianity
17th-century Christian texts
Prison writings
Works by William Penn | No Cross, No Crown | [
"Biology"
] | 231 | [
"Behavior",
"Altruism"
] |
27,702,148 | https://en.wikipedia.org/wiki/Delta%20scale | The δ (delta) scale is a non-octave repeating musical scale. It may be regarded as the beta scale's reciprocal, since it is "as far 'down' the (0 3 6 9) circle from α as β is 'up'". As such it would split the minor second (presumably 16:15) into eight equal parts of approximately 14 cents each . This would total approximately 85.7 steps per octave.
The scale step may also precisely be derived from using 50:28 (25:14, 1003.8 cents, A, ) to approximate the interval , which equals 6:5 (E, 315.64 cents, ). Thus the step is approximately 13.946 cents, and there are 86.049 steps per octave.
()
The Bohlen–Pierce delta scale is based on the tritave and the 7:5:3 "wide" triad () and the 9:7:5 "narrow" triad () (rather than the conventional 4:5:6 triad). Notes include:
1:1
25:21
9:7
75:49
5:3
9:5
15:7
7:3
25:9
3:1
See also
Alpha scale
Beta scale
Gamma scale
References
Further reading
Bohlen, Heinz: "13 Tonstufen in der Duodezime", Acustica, vol. 39 no. 2, S. Hirzel Verlag, Stuttgart, 1978, pp. 76–86.
Equal temperaments
Non–octave-repeating scales | Delta scale | [
"Physics"
] | 315 | [
"Physical quantities",
"Musical symmetry",
"Logarithmic scales of measurement",
"Equal temperaments",
"Symmetry"
] |
27,704,246 | https://en.wikipedia.org/wiki/Iljumun | Iljumun is the first gate at the entrance to many Korean Buddhist temples. Called the "One-Pillar Gate", because when viewed from the side the gate appears to be supported by a single pillar.
Description
The Iljumun is one of the three major types of gates constructed on the path that leads to the temple and often illustrates the formality of Buddhist architecture. The other two are the Cheonwangmun (Gate of Guardians) and the Haetalmun (Gate of Deliverance). The construction of Iljumun is said to have originated from the tradition of placing four gates at the four cardinal points around the stupas of Sanchi in India since the 1st century BC.
The Iljumun symbolizes the one true path of enlightenment which supports the world. Physically, the gate serves to demarcate the temple from the outside. It is the boundary between the Buddhist temple and a human's worldly life. The gate symbolizes purification and one must leave all of their worldly desires before entering the temple.
The oneness is also a metaphor for non-duality (unity) in spirit and heart.
An image of an Iljumun appears on the obverse of the Korean Service Medal.
See also
Hongsalmun, in Korean architecture with both religious and other usage
Torana, in Hindu-Buddhist Indian-origin also found in Southeast Asia and East Asia
Toran, ceremonial Indian door decoration
Torii, in Japanese temple architecture
Paifang, in Chinese temple architecture
Tam quan, in Vietnamese temple architecture
References
Gates in Korea
Buddhism in Korea | Iljumun | [
"Engineering"
] | 318 | [
"Architecture stubs",
"Architecture"
] |
27,704,310 | https://en.wikipedia.org/wiki/Hongsalmun | In architecture, a hongsalmun is a gate for entering a sacred place in Korea. Hongsalmun, also called hongjeonmun or hongmun, are usually erected to indicate Korean Confucian sites, such as shrines, tombs, and academies such as hyanggyo and seowon. The gate indicates entry to a sacred realm.
Features
Hongsalmun literally means ‘gate with red arrows’, referring to the set of pointed spikes on its top. In the past, spikes in between columns did not exist. The color is said to be red because of the belief that the color repels ghosts. The gate is composed of two round poles set vertically and two transverse bars. These pillars are usually over nine meters in height. There is no roof and no door-gate. In the middle top gate the symbol of the trident and the taegeuk image are placed.
The hongsalmun gate opens to a path that leads toward the front of hyanggyo and the hamabi or the "memorial dismount stone". The gate can also be found inside a seowon, a privately owned complex that served as a Confucian shrine and preparatory school.
Gallery
See also
Iljumun, religious portal
Torana, a type of Hindu-Buddhist gate
Torii, in Japanese temple architecture
Paifang, in Chinese temple architecture
Tam quan, in Vietnamese temple and pagoda architecture
References
Gates in Korea
Korean Confucianism | Hongsalmun | [
"Engineering"
] | 292 | [
"Architecture stubs",
"Architecture"
] |
27,712,079 | https://en.wikipedia.org/wiki/Friedrich-Karl%20Thielemann | Friedrich-Karl "Friedel“ Thielemann (born 17 April 1951 in Mülheim an der Ruhr) is a German-Swiss theoretical astrophysicist.
Thielemann studied at the TH Darmstadt, where he in 1976 he acquired his Diplom. In 1980 he earned his PhD under Wolfgang Hillebrandt (in Garching) and E. R. Hilf in nuclear astrophysics. As a post-doc he was with David Schramm and William David Arnett at the University of Chicago, William A. Fowler at Caltech, Hans Klapdor at the Max-Planck-Institut für Kernphysik, am Max-Planck-Institut für Astrophysik in Garching (with Hillebrandt) and at the University of Illinois (with James W. Truran). Starting in 1986 he was Assistant Professor and from 1991 Associate Professor at the Center for Astrophysics Harvard & Smithsonian and at the Harvard Observatory of Harvard University. In 1994 he became a professor at the University of Basel. In 1995 he was a guest professor at the University of Turin and from 1997 to 2001 a guest scientist at Oak Ridge National Laboratory.
Besides theoretical and computer-simulated astrophysics and nuclear astrophysics (including important nuclear reactions and properties of unstable stellar cores, equations of state of quark-matter and core matter of higher density), he worked on the modeling of astrophysical plasmas for important subatomic processes. He investigated, among other things, supernovae, X-ray bursts, gamma ray bursts, fusion of neutron stars, emergence of heavy elements, and evolution of chemical elements in galaxies.
In 1979 he received the Otto Hahn Medal. In 1998 he was elected a fellow of the American Physical Society for "his work at the interface of nuclear physics and astrophysics and the applications to stellar nucleosynthesis, Type Ia and Type II Supernovae, as well as the r- and rp-process." In 2008 he received the Hans Bethe Prize "for his many outstanding theoretical contributions to the understanding of nucleosynthesis, stellar evolution and stellar explosions." Since 2004 he is a member of the Swiss Research Council.
References
External links
20th-century German physicists
Swiss astrophysicists
1951 births
Living people
Fellows of the American Physical Society
Theoretical physicists
21st-century German physicists | Friedrich-Karl Thielemann | [
"Physics"
] | 481 | [
"Theoretical physics",
"Theoretical physicists"
] |
2,864,360 | https://en.wikipedia.org/wiki/Pertussis%20toxin | Pertussis toxin (PT) is a protein-based AB5-type exotoxin produced by the bacterium Bordetella pertussis, which causes whooping cough. PT is involved in the colonization of the respiratory tract and the establishment of infection. Research suggests PT may have a therapeutic role in treating a number of common human ailments, including hypertension, viral infection, and autoimmunity.
History
PT clearly plays a central role in the pathogenesis of pertussis although this was discovered only in the early 1980s. The appearance of pertussis is quite recent, compared with other epidemic infectious diseases. The earliest mention of pertussis, or whooping cough, is of an outbreak in Paris in 1414. This was published in Moulton's The Mirror of Health, in 1640. Another epidemic of pertussis took place in Paris in 1578 and was described by a contemporary observer, Guillaume de Baillou. Pertussis was well known throughout Europe by the middle of the 18th century. Jules Bordet and Octave Gengou described in 1900 the finding of a new “ovoid bacillus” in the sputum of a 6-month-old infant with whooping cough. They were also the first to cultivate Bordetella pertussis at the Pasteur Institute in Brussels in 1906.
One difference between the different species of Bordetella is that B. pertussis produces PT and the other species do not. Bordetella parapertussis shows the most similarity to B. pertussis and was therefore used for research determining the role of PT in causing the typical symptoms of whooping cough. Rat studies showed the development of paroxysmal coughing, a characteristic for whooping cough, occurred in rats infected with B. pertussis. Rats infected with B. parapertussis or a PT-deficient mutant of B. pertussis did not show this symptom; neither of these two strains produced PT.
Structure
A large group of bacterial exotoxins are referred to as "A/B toxins", in essence because they are formed from two subunits. The "A" subunit possesses enzyme activity, and is transferred to the host cell following a conformational change in the membrane-bound transport "B" subunit. Pertussis toxin is an exotoxin with six subunits (named S1 through S5—each complex contains two copies of S4). The subunits are arranged in A-B structure: the A component is enzymatically active and is formed from the S1 subunit, while the B component is the receptor-binding portion and is made up of subunits S2–S5. The subunits are encoded by ptx genes encoded on a large PT operon that also includes additional genes that encode Ptl proteins. Together, these proteins form the PT secretion complex.
Mechanism of pathogenesis
PT is released from B. pertussis in an inactive form. Following PT binding to a cell membrane receptor, it is taken up in an endosome, after which it undergoes retrograde transport to the trans-Golgi network and endoplasmic reticulum. At some point during this transport, the A subunit (or protomer) becomes activated, perhaps through the action of glutathione and ATP. PT catalyzes the ADP-ribosylation of the αi subunits of the heterotrimeric G protein. This prevents the G proteins from interacting with G protein-coupled receptors on the cell membrane, thus interfering with intracellular communication. The Gi subunits remain locked in their GDP-bound, inactive state, thus unable to inhibit adenylate cyclase activity, leading to increased cellular concentrations of cAMP.
Increased intracellular cAMP affects normal biological signaling. The toxin causes several systemic effects, among which is an increased release of insulin, causing hypoglycemia. Whether the effects of pertussis toxin are responsible for the paroxysmal cough remains unknown.
As a result of this unique mechanism, PT has also become widely used as a biochemical tool to ADP-ribosylate GTP-binding proteins in the study of signal transduction. It has also become an essential component of new acellular vaccines.
Effects on the immune system
PT has been shown to affect the innate immune response. It inhibits the early recruitment of neutrophils and macrophages, and interferes with early chemokine production and neutrophil chemotaxis. Chemokines are signalling molecules produced by infected cells and attract neutrophils and macrophages. Neutrophil chemotaxis is thought to be disrupted by inhibiting G-protein-coupled chemokine receptors by the ADP-ribosylation of Gi proteins.
Due to the disrupted signalling pathways, synthesis of chemokines will be affected. This will prevent the infected cell from producing them and thereby inhibiting recruitment of neutrophils. Under normal circumstances, alveolar macrophages and other lung cells produce a variety of chemokines. PT has been found to inhibit the early transcription of keratinocyte-derived chemokine, macrophage inflammatory protein 2 and LPS-induced CXC chemokine. Eventually, PT causes lymphocytosis, one of the systemic manifestations of whooping cough.
PT, a decisive virulence determinant of B. pertussis, is able to cross the blood–brain barrier by increasing its permeability. As a result, PT can cause severe neurological complications; however, recently it has been found that the medicinal usage of Pertussis toxin can promote the development of regulatory T cells and prevent central nervous system autoimmune disease, such as multiple sclerosis.
Metabolism
PT is known to dissociate into two parts in the endoplasmic reticulum (ER): the enzymatically active A subunit (S1) and the cell-binding B subunit. The two subunits are separated by proteolic cleavage. The B subunit will undergo ubiquitin-dependent degradation by the 26S proteasome. However, the A subunit lacks lysine residues, which are essential for ubiquitin-dependent degradation. Therefore, PT subunit A will not be metabolized like most other proteins.
PT is heat-stable and protease-resistant, but once the A and B are separated, these properties change. The B subunit will stay heat-stable at temperatures up to 60 °C, but it is susceptible to protein degradation. PT subunit A, on the other hand, is less susceptible to ubiquitin-dependent degradation, but is unstable at temperature of 37 °C. This facilitates unfolding of the protein in the ER and tricks the cell into transporting the A subunit to the cytosol, where normally unfolded proteins will be marked for degradation. So, the unfolded conformation will stimulate the ERAD-mediated translocation of PT A into the cytosol. Once in the cytosol, it can bind to NAD and form a stable, folded protein again. Being thermally unstable is also the Achilles heel of PT subunit A. As always, there is an equilibrium between the folded and unfolded states. When the protein is unfolded, it is susceptible to degradation by the 20S proteasome, which can degrade only unfolded proteins.
PT and vaccines
Since the introduction of pertussis vaccines in the 1940s and 1950s, different genetic changes have been described surrounding the pertussis toxin.
Emergence of ptxP3
ptxP is the pertussis toxin's promoter gene. There is a well documented emergence and global spread of ptxP3 strains evolving from and replacing the native ptxP1 strains, associated with an increased production of the toxin, and thus an increased virulence. Such spread has been documented in multiple countries, and sometimes but not always linked to the resurgence of pertussis in the end of the 20th century. Countries with a documented spread of ptxP3 include Australia, Denmark, Finland, Iran, Italy, Japan, the Netherlands, and Sweden.
See also
cyaA
References
Signal transduction
AB5 toxins
Protein families
Whooping cough
Invertebrate toxins
Microbiology | Pertussis toxin | [
"Chemistry",
"Biology"
] | 1,718 | [
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2,864,595 | https://en.wikipedia.org/wiki/Shapiro%20reaction | The Shapiro reaction or tosylhydrazone decomposition is an organic reaction in which a ketone or aldehyde is converted to an alkene through an intermediate hydrazone in the presence of 2 equivalents of organolithium reagent. The reaction was discovered by Robert H. Shapiro in 1967. The Shapiro reaction was used in the Nicolaou Taxol total synthesis. This reaction is very similar to the Bamford–Stevens reaction, which also involves the basic decomposition of tosyl hydrazones.
Reaction mechanism and directionality
In a prelude to the actual Shapiro reaction, a ketone or an aldehyde (1) is reacted with p-toluenesulfonylhydrazide(2) to form a p-toluenesulfonylhydrazone (or tosylhydrazone) which is a hydrazone (3). Two equivalents of strong base such as n-butyllithium abstract the proton from the hydrazone (4) followed by the less acidic proton α to the hydrazone carbon (5), forming a carbanion. The carbanion then undergoes. an elimination reaction producing a carbon–carbon double bond and ejecting the tosyl anion, forming a diazonium anion (6). This diazonium anion is then lost as molecular nitrogen resulting in a vinyllithium species (7), which can then be reacted with various electrophiles, including simple neutralization with water or an acid (8).
The reaction's directionality is controlled by the stereochemistry of the hydrazone, with deprotonation occurring cis to the tosylamide group. This is due to coordination by the nitrogen atom.
Scope
The position of the alkene in the product is controlled by the site of deprotonation by the organolithium base. In general, the kinetically favored, less substituted site of differentially substituted tosylhydrazones is deprotonated selectively, leading to the less substituted vinyllithium intermediate. Although many secondary reactions exist for the vinyllithium functional group, in the Shapiro reaction in particular water is added, resulting in protonation to the alkene. Other reactions of vinyllithium compounds include alkylation reactions with for instance alkyl halides.
Importantly, the Shapiro reaction cannot be used to synthesize 1-lithioalkenes (and the resulting functionalized derivatives), as sulfonylhydrazones derived from aldehydes undergo exclusive addition of the organolithium base to the carbon of the C–N double bond.
Catalytic Shapiro reaction
Traditional Shapiro reactions require stoichiometric (sometimes excess) amounts of base to generate the alkenyllithium reagents. To combat this problem, Yamamoto and coworkers developed an efficient stereoselective and regioselective route to alkenes using a combination of ketone phenylaziridinylhydrazones as arenesulfonylhydrazone equivalents with a catalytic amount of lithium amides.
The required phenylaziridinylhydrazone was prepared from the condensation of undecan-6-one with 1-amino-2-phenylaziridine. Treatment of the phenylaziridinylhydrazone with 0.3 equivalents of LDA in ether resulted in the alkene shown below with a cis:trans ratio of 99.4:0.6. The ratio was determined by capillary GLC analysis after conversion to the corresponding epoxides with mCPBA. The catalyst loading can be reduced to 0.05 equivalents in the case of a 30mmol scale reaction.
The high stereoselectivity is obtained by the preferential abstraction of the α-methylene hydrogen syn to the phenylaziridine, and is also accounted for by the internal chelation of the lithiated intermediated.
A one pot in situ combined Shapiro-Suzuki reaction
The Shapiro reaction can also be combined with the Suzuki reaction to produce a variety of olefin products. Keay and coworkers have developed methodology that combines these reactions in a one pot process that does not require the isolation of the boronic acid, a setback of the traditional Suzuki coupling. This reaction has a wide scope, tolerating a slew of trisylhydrazones and aryl halides, as well as several solvents and Pd sources.
An application of the Shapiro reaction in total synthesis
The Shapiro reaction has been used to generate olefins towards to complex natural products. K. Mori and coworkers wanted to determine the absolute configuration of the phytocassane group of a class of natural products called phytoalexins. This was accomplished by preparing the naturally occurring (–)-phytocassane D from (R)-Wieland-Miescher ketone. On the way to (–)-phytocassane D, a tricyclic ketone was subjected to Shapiro reaction conditions to yield the cyclic alkene product.
See also
Hydrazone iodination
Wolff–Kishner reduction
References
Carbon-carbon bond forming reactions
Olefination reactions
Organic redox reactions
Name reactions | Shapiro reaction | [
"Chemistry"
] | 1,094 | [
"Olefination reactions",
"Carbon-carbon bond forming reactions",
"Coupling reactions",
"Organic redox reactions",
"Organic reactions",
"Name reactions"
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2,864,696 | https://en.wikipedia.org/wiki/String%20cosmology | String cosmology is a relatively new field that tries to apply equations of string theory to solve the questions of early cosmology. A related area of study is brane cosmology.
Overview
This approach can be dated back to a paper by Gabriele Veneziano that shows how an inflationary cosmological model can be obtained from string theory, thus opening the door to a description of pre-Big Bang scenarios.
The idea is related to a property of the bosonic string in a curve background, better known as nonlinear sigma model. First calculations from this model showed as the beta function, representing the running of the metric of the model as a function of an energy scale, is proportional to the Ricci tensor giving rise to a Ricci flow. As this model has conformal invariance and this must be kept to have a sensible quantum field theory, the beta function must be zero producing immediately the Einstein field equations. While Einstein equations seem to appear somewhat out of place, nevertheless this result is surely striking showing as a background two-dimensional model could produce higher-dimensional physics. An interesting point here is that such a string theory can be formulated without a requirement of criticality at 26 dimensions for consistency as happens on a flat background. This is a serious hint that the underlying physics of Einstein equations could be described by an effective two-dimensional conformal field theory. Indeed, the fact that we have evidence for an inflationary universe is an important support to string cosmology.
In the evolution of the universe, after the inflationary phase, the expansion observed today sets in that is well described by Friedmann equations. A smooth transition is expected between these two different phases. String cosmology appears to have difficulties in explaining this transition. This is known in the literature as the graceful exit problem.
An inflationary cosmology implies the presence of a scalar field that drives inflation. In string cosmology, this arises from the so-called dilaton field. This is a scalar term entering into the description of the bosonic string that produces a scalar field term into the effective theory at low energies. The corresponding equations resemble those of a Brans–Dicke theory.
Analysis has been worked out from a critical number of dimension (26) down to four. In general, one gets Friedmann equations in an arbitrary number of dimensions. The other way round is to assume that a certain number of dimensions is compactified producing an effective four-dimensional theory to work with. Such a theory is a typical Kaluza–Klein theory with a set of scalar fields arising from compactified dimensions. Such fields are called moduli.
Technical details
This section presents some of the relevant equations entering into string cosmology. The starting point is the Polyakov action, which can be written as
where is the Ricci scalar in two dimensions, the dilaton field, and the string constant. The indices range over 1,2, and over , where D the dimension of the target space. A further antisymmetric field could be added. This is generally considered when one wants this action generating a potential for inflation. Otherwise, a generic potential is inserted by hand, as well as a cosmological constant.
The above string action has a conformal invariance. This is a property of a two dimensional Riemannian manifold. At the quantum level, this property is lost due to anomalies and the theory itself is not consistent, having no unitarity. So it is necessary to require that conformal invariance is kept at any order of perturbation theory. Perturbation theory is the only known approach to manage the quantum field theory. Indeed, the beta functions at two loops are
and
The assumption that conformal invariance holds implies that
producing the corresponding equations of motion of low-energy physics. These conditions can only be satisfied perturbatively, but this has to hold at any order of perturbation theory. The first term in is just the anomaly of the bosonic string theory in a flat spacetime. But here there are further terms that can grant compensation of the anomaly also when , and from this cosmological models of a pre-big bang, scenario can be constructed. Indeed, this low energy equations can be obtained from the following action:
where is a constant that can always be changed by redefining the dilaton field. One can also rewrite this action in a more familiar form by redefining the fields (Einstein frame) as
and using one can write
where
This is the formula for the Einstein action describing a scalar field interacting with a gravitational field in D dimensions. Indeed, the following identity holds:
where is the Newton constant in D dimensions and the corresponding Planck mass. When setting in this action, the conditions for inflation are not fulfilled unless a potential or antisymmetric term is added to the string action, in which case power-law inflation is possible.
Notes
References
External links
String cosmology on arxiv.org
Maurizio Gasperini's homepage
String theory
Physical cosmology
General relativity | String cosmology | [
"Physics",
"Astronomy"
] | 1,036 | [
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"Astronomical sub-disciplines",
"Theoretical physics",
"Astrophysics",
"General relativity",
"Theory of relativity",
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2,865,100 | https://en.wikipedia.org/wiki/Conformal%20family | In theoretical physics, a conformal family is an irreducible representation of the Virasoro algebra. In most cases, it is uniquely determined by its primary field or the highest weight vector. The family contains all of its descendant fields.
References
See also
Conformal field theory
Conformal field theory | Conformal family | [
"Physics"
] | 61 | [
"Quantum mechanics",
"Quantum physics stubs"
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2,865,794 | https://en.wikipedia.org/wiki/Instituto%20Tecnol%C3%B3gico%20de%20Aeron%C3%A1utica | The Instituto Tecnológico de Aeronáutica (ITA; ) is an institution of higher education maintained by the Brazilian Air Force and is located in São José dos Campos, Brazil. ITA is consistently ranked as one of the top engineering schools in Brazil and engages in advanced research in aerospace science and technology.
ITA is one of five institutes that encompass the Brazilian General Command for Aerospace Technology (CTA), having its facilities, along with its laboratories and R&D centers, inside the campus of CTA. Despite its status as a military institution, TA accommodates civilian teachers, directors, and students.
ITA offers regular 5-year engineering undergraduate courses (Bachelor of Engineering) and graduate programs including masters and doctoral degrees.
History
Casimiro Montenegro Filho, the founder of ITA, hired renowned foreign professors and experts from various parts of the world to teach at ITA, the majority of them from MIT, influenced by Prof. Richard Smith. At a given time of its history, ITA had teachers from more than 20 different nationalities in its faculty, an impressive number, considering it had (and still has) a faculty of little more than 100 teachers. Nowadays the overwhelming majority of the teachers are Brazilians, many of whom have themselves graduated from ITA.
Undergraduate Courses
All ITA undergraduate students must complete two years of fundamental courses before entering the professional course they intend to take. The six steams of professional courses available to students for study include:
Aeronautical Engineering
Aerospace Engineering
Civil-Aeronautical Engineering
Computer Engineering
Electronic Engineering
Mechanical Engineering
Graduate programs
ITA offers masters and doctoral programs through five general streams, with 20 areas of concentration between them, including:
Aeronautical & Mechanical Engineering
Aeronautical Infrastructure Engineering
Electronic & Computer Engineering
Physics
Space Science & Technology
Student life
All undergraduate students are granted full scholarships. Complete residential facilities are offered to the students during the entire five-year period at a minimal cost. ITA students are provided with free, self-served meals four times a day.
Military career
During their first year at ITA, all students are considered to be military personnel and are required to attend a military preparation course once a week and receive monthly cost-of-living allowances for it during this period. For male students, this fulfills their obligatory military service, which all male citizens in Brazil are required to attend.
Due to ITA's position as an institute maintained by the Brazilian Air Force, undergraduate students may choose to join the military upon graduation as engineering officers or keep their status as civilians members of the reserve. After the first year, students not opting for a military career return to being civilians and stop receiving their pay.
Approximately 20% of admitted undergraduate students choose a military career during their second year and be paid as student of the Reserve Officers Training Body. These students will continue the military preparation course once every two weeks. They will begin wearing uniforms during their 3rd year at ITA until graduation. Upon graduation, they are promoted to the rank of 1st lieutenant engineer and must serve for 3 years.
Economic impact
The institution was created in 1950, being responsible and contributing in a great extent for the research and development of the aerospace and defense sectors in Brazil, including the Brazilian National Institute for Space Research - INPE, Embraer and Avibrás.
From ITA's foundation, as of 2018, 6,466 engineers had graduated from the undergraduate program and 6,134 from postgraduate courses.
EMBRAER alone, which was created by ITA's undergraduate alumni, currently employs hundreds of engineers from ITA, generating a positive net export balance of $1.529 billion in 2005, over 150 times the yearly investment made in ITA by the Brazilian Government. In that year, between aircraft and aircraft parts categories, São José Dos Campos exported $3.57B (USD) or 81.9% of the total exports of the municipality.
By the time ITA was created, its home town, São José dos Campos, had about 44,000 inhabitants and its economy was mainly rural. By 2018 the city had grown to 883,943 inhabitants, or 2,528,354 when the metropolitan area is counted, and in 2014 ranked as the 5th largest exporter, by value, of all Brazilian municipalities exporting $4.6B (USD) worth of materials.
Admissions (Undergraduate)
The school's undergraduate admission exams (called vestibular in Brazil) are considered the most competitive in the country. They take place annually in over 25 cities throughout Brazil. Students are selected exclusively on their grades in the exam. ITA accepts 110 undergraduate students per year, who are distributed into the 5 available Engineering courses according to availability and preference indicated at the time of applying.
ITA's admission exam is infamous for its difficulty, even when compared to other top universities in Brazil. Math, Physics and Chemistry are often approached beyond high-school level, thus candidates have to study undergraduate-level textbooks. Candidates often need an extra year of intense study after high-school, and many take the test multiple times before being selected.
The exam is composed of two phases: the first includes general tests in each of Mathematics, Physics, Chemistry, Portuguese and English. The English exam is only eliminatory, requiring candidates to achieve a minimum set score. The second phase includes exams in Mathematics, Physics, Chemistry and an Essay in Portuguese. In this phase, all tests have equal weight. The candidates with the highest average grades are admitted in, provided they reach a minimum qualifying grade in each of the 4 exams.
Another university in Brazil has similar admission exams: Instituto Militar de Engenharia (Military Institute of Engineering - IME), which is maintained by the Brazilian Army. Candidates usually prepare for both exams. Virtually all candidates approved at ITA are also approved at IME, but choose the former.
Course Evaluation Results
From 1996 to 2003, the Brazilian government conducted yearly evaluation exams for every undergraduate course in Brazil. Written exams, specific to every different type of college course, were given to every student at the time of their graduation and the results were used to evaluate the quality of the college courses and schools in Brazil. These exams were called Provão ("big test", in English).
Based on the average grade obtained by the students' course, every school was given a grade from 'A' to 'E' for each of its courses, with 'A' being the best. ITA was the only institution in Brazil to have obtained only 'A's in all the years of Provão, for all of its courses. The Provão results are somewhat misleading, though, as the grades are given by ordering the average grades of the schools in a list and giving the label 'A' to a certain predefined number of schools, and so on. Therefore, two schools that were given the grade 'A' can have substantially different scores, and that is usually the case. The actual grades for each school were not announced by the government, but a list with the highest average grades in 2003 "leaked" and was published by the national magazine Veja.
The published list showed that the courses of Electronic and Computer Engineering at ITA, which both took the exam of Electrical Engineering, attained the highest average grade of the whole Provão in 2003. Its students had an average grade of 79.6 of a total of 100. This average was about 5 point higher than IME's, the 2nd position for Electrical Engineering, with 75.2, about 14 points higher than the 3rd position, UFRGS, with 66.3, and about 17 point higher than renowned USP and UNICAMP with 62.7 and 62.2, respectively. It was about 24 points higher than the 10th position for this course. That is a relative difference of more than 40%. All ten schools published in the list attained an 'A' grade at Provão.
It is now known that in almost every year of Provão up to 2003 ITA's courses figured in either first or second place in its categories, usually competing with IME, both within considerable distance from the remaining schools. It is hard, though, to point references for such information, as it usually comes from unofficial sources or scattered news from journalists that had access to leaked information. INEP, the government institute which conducts these evaluations, publishes the results of all Provões at its website, but only shows the alphabetic grade and percentiles in which the students from the institution are (usually more than 90% of ITA's students figure between the top 25% grades in Provão). In 2003 94,3% of ITA's Electronic and Computer Engineering students were between the 25% top grades of the exam.
In the first edition of ENADE for Engineering in 2005, successor of Provão, which is only held about every 3 years, ITA's Computer Engineering course once again achieved the highest grade of its category. For the ENADE the government is publishing the actual average grade of each school at INEP's website. In 2008, ITA's Electronics Engineering courses scored the highest evaluation grade among all university courses from the areas evaluated in 2008, which included all engineering areas, computer science, math, architecture, among others. The course evaluation grade of ITA's Electronics Engineering was 485, out of a maximum of 500, based on the test results of the students graduated in 2008.
Notable Professors
Francis Dominic Murnaghan (mathematician) – former Albert Einstein student, founder of Department of Mathematics
Sonia Guimarães - first Black Brazilian to earn a doctorate in physics; hired as a professor before women were admitted to ITA
Notable alumni
In alphabetical order:
Carlos Cesnik, Clarence L. (Kelly) Johnson Collegiate Professor of Aerospace Engineering at University of Michigan
Carlos Henrique de Brito Cruz, former dean, UNICAMP; science director, FAPESP
Carlos Nobre, Brazilian scientist and meteorologist
Cássio Taniguchi, Brazilian congressman (as of 2006)
Dimas Lara Barbosa, Rio de Janeiro auxiliary bishop, Roman Catholic Church in Brazil
Fernando de Mendonça, founder and first director of Brazil's National Institute for Space Research (INPE)
Gilberto Câmara, director of Brazil's National Institute for Space Research (INPE) from 2006 to 2013
Jean Paul Jacob, research leader IBM
Kristo Ivanov, research leader (1984–2002) and professor emeratus of informatics, Umeå University
Marcos César Pontes, first Brazilian astronaut
Ned Kock, professor of Information Systems, Texas A&M International University
Ozires Silva, founder and former CEO, EMBRAER, former president of Petrobras, and former minister of infra-structure
Reginaldo Silva, security engineer, notable for identifying an arbitrary code execution bug at Facebook
See also
Brazilian Air Force Academy
Brazil University Rankings
Universities and Higher Education in Brazil
Institute of Aeronautics and Space
References
External links
ITA homepage in English
Aeronautical engineering schools
Brazilian Air Force
Organisations based in São José dos Campos
1950 establishments in Brazil
Universities and colleges in São Paulo (state)
Aviation organisations based in Brazil
Universities and colleges established in 1950
Undergraduate military academies of Brazil
Research institutes in Brazil | Instituto Tecnológico de Aeronáutica | [
"Engineering"
] | 2,271 | [
"Aeronautical engineering schools",
"Engineering universities and colleges",
"Aeronautics organizations"
] |
2,866,340 | https://en.wikipedia.org/wiki/Equipotential | In mathematics and physics, an equipotential or isopotential refers to a region in space where every point is at the same potential. This usually refers to a scalar potential (in that case it is a level set of the potential), although it can also be applied to vector potentials. An equipotential of a scalar potential function in -dimensional space is typically an ()-dimensional space. The del operator illustrates the relationship between a vector field and its associated scalar potential field. An equipotential region might be referred as being 'of equipotential' or simply be called 'an equipotential'.
An equipotential region of a scalar potential in three-dimensional space is often an equipotential surface (or potential isosurface), but it can also be a three-dimensional mathematical solid in space. The gradient of the scalar potential (and hence also its opposite, as in the case of a vector field with an associated potential field) is everywhere perpendicular to the equipotential surface, and zero inside a three-dimensional equipotential region.
Electrical conductors offer an intuitive example. If a and b are any two points within or at the surface of a given conductor, and given there is no flow of charge being exchanged between the two points, then the potential difference is zero between the two points. Thus, an equipotential would contain both points a and b as they have the same potential. Extending this definition, an isopotential is the locus of all points that are of the same potential.
Gravity is perpendicular to the equipotential surfaces of the gravity potential, and in electrostatics and steady electric currents, the electric field (and hence the current, if any) is perpendicular to the equipotential surfaces of the electric potential (voltage).
In gravity, a hollow sphere has a three-dimensional equipotential region inside, with no gravity from the sphere (see shell theorem). In electrostatics, a conductor is a three-dimensional equipotential region. In the case of a hollow conductor (Faraday cage), the equipotential region includes the space inside.
A ball will not be accelerated left or right by the force of gravity if it is resting on a flat, horizontal surface, because it is an equipotential surface.
For the gravity of Earth, the corresponding geopotential isosurface (the equigeopotential) that best fits mean sea level is called the geoid.
See also
Potential flow
Potential gradient
Isopotential map
Scalar potential
References
External links
Electric Field Applet
Multivariable calculus
Mathematical physics
Potentials
de:Äquipotentialfläche | Equipotential | [
"Physics",
"Mathematics"
] | 559 | [
"Calculus",
"Applied mathematics",
"Theoretical physics",
"Multivariable calculus",
"Mathematical physics"
] |
2,867,520 | https://en.wikipedia.org/wiki/M1%20protein | The M1 protein is a matrix protein of the influenza virus. It forms a coat inside the viral envelope. This is a bifunctional membrane/RNA-binding protein that mediates the encapsidation of nucleoprotein cores into the membrane envelope. It is therefore required that M1 binds both membrane and RNA simultaneously.
The M1 protein binds to the viral RNA. The binding is not specific to any RNA sequence, and is performed via a peptide sequence rich in basic amino acids.
It also has multiple regulatory functions, performed by interaction with the components of the host cell. The mechanisms regulated include a role in the export of the viral ribonucleoproteins from the host cell nucleus, inhibition of viral transcription, and a role in the virus assembly and budding. The protein was found to undergo phosphorylation in the host cell.
The M1 protein forms a layer under the patches of host cell membrane that are rich with the viral hemagglutinin, neuraminidase and M2 transmembrane proteins, and facilitates budding of the mature viruses.
M1 consists of two domains connected by a linker sequence. The N-terminal domain has a multi-helical structure that can be divided into two subdomains. The C-terminal domain also contains alpha-helical structure.
See also
H5N1 genetic structure
Sources and notes
Membrane biology
Peripheral membrane proteins
Influenza A virus
Viral structural proteins | M1 protein | [
"Chemistry"
] | 295 | [
"Membrane biology",
"Molecular biology"
] |
2,867,718 | https://en.wikipedia.org/wiki/Intrinsically%20disordered%20proteins | In molecular biology, an intrinsically disordered protein (IDP) is a protein that lacks a fixed or ordered three-dimensional structure, typically in the absence of its macromolecular interaction partners, such as other proteins or RNA. IDPs range from fully unstructured to partially structured and include random coil, molten globule-like aggregates, or flexible linkers in large multi-domain proteins. They are sometimes considered as a separate class of proteins along with globular, fibrous and membrane proteins.
IDPs are a very large and functionally important class of proteins and their discovery has disproved the idea that three-dimensional structures of proteins must be fixed to accomplish their biological functions. For example, IDPs have been identified to participate in weak multivalent interactions that are highly cooperative and dynamic, lending them importance in DNA regulation and in cell signaling. Many IDPs can also adopt a fixed three-dimensional structure after binding to other macromolecules. Overall, IDPs are different from structured proteins in many ways and tend to have distinctive function, structure, sequence, interactions, evolution and regulation.
History
In the 1930s-1950s, the first protein structures were solved by protein crystallography. These early structures suggested that a fixed three-dimensional structure might be generally required to mediate biological functions of proteins. These publications solidified the central dogma of molecular biology in that the amino acid sequence of a protein determines its structure which, in turn, determines its function. In 1950, Karush wrote about 'Configurational Adaptability' contradicting this assumption. He was convinced that proteins have more than one configuration at the same energy level and can choose one when binding to other substrates. In the 1960s, Levinthal's paradox suggested that the systematic conformational search of a long polypeptide is unlikely to yield a single folded protein structure on biologically relevant timescales (i.e. microseconds to minutes). Curiously, for many (small) proteins or protein domains, relatively rapid and efficient refolding can be observed in vitro. As stated in Anfinsen's Dogma from 1973, the fixed 3D structure of these proteins is uniquely encoded in its primary structure (the amino acid sequence), is kinetically accessible and stable under a range of (near) physiological conditions, and can therefore be considered as the native state of such "ordered" proteins.
During the subsequent decades, however, many large protein regions could not be assigned in x-ray datasets, indicating that they occupy multiple positions, which average out in electron density maps. The lack of fixed, unique positions relative to the crystal lattice suggested that these regions were "disordered". Nuclear magnetic resonance spectroscopy of proteins also demonstrated the presence of large flexible linkers and termini in many solved structural ensembles.
In 2001, Dunker questioned whether the newly found information was ignored for 50 years with more quantitative analyses becoming available in the 2000s. In the 2010s it became clear that IDPs are common among disease-related proteins, such as alpha-synuclein and tau.
Abundance
It is now generally accepted that proteins exist as an ensemble of similar structures with some regions more constrained than others. IDPs occupy the extreme end of this spectrum of flexibility and include proteins of considerable local structure tendency or flexible multidomain assemblies.
Intrinsic disorder is particularly elevated among proteins that regulate chromatin and transcription, and bioinformatic predictions indicate that is more common in genomes and proteomes than in known structures in the protein database. Based on DISOPRED2 prediction, long (>30 residue) disordered segments occur in 2.0% of archaean, 4.2% of eubacterial and 33.0% of eukaryotic proteins, including certain disease-related proteins.
Biological roles
Highly dynamic disordered regions of proteins have been linked to functionally important phenomena such as allosteric regulation and enzyme catalysis. Many disordered proteins have the binding affinity with their receptors regulated by post-translational modification, thus it has been proposed that the flexibility of disordered proteins facilitates the different conformational requirements for binding the modifying enzymes as well as their receptors. Intrinsic disorder is particularly enriched in proteins implicated in cell signaling and transcription, as well as chromatin remodeling functions. Genes that have recently been born de novo tend to have higher disorder. In animals, genes with high disorder are lost at higher rates during evolution.
Flexible linkers
Disordered regions are often found as flexible linkers or loops connecting domains. Linker sequences vary greatly in length but are typically rich in polar uncharged amino acids. Flexible linkers allow the connecting domains to freely twist and rotate to recruit their binding partners via protein domain dynamics. They also allow their binding partners to induce larger scale conformational changes by long-range allostery. The flexible linker of FBP25 which connects two domains of FKBP25 is important for the binding of FKBP25 with DNA.
Linear motifs
Linear motifs are short disordered segments of proteins that mediate functional interactions with other proteins or other biomolecules (RNA, DNA, sugars etc.). Many roles of linear motifs are associated with cell regulation, for instance in control of cell shape, subcellular localisation of individual proteins and regulated protein turnover. Often, post-translational modifications such as phosphorylation tune the affinity (not rarely by several orders of magnitude) of individual linear motifs for specific interactions. Relatively rapid evolution and a relatively small number of structural restraints for establishing novel (low-affinity) interfaces make it particularly challenging to detect linear motifs but their widespread biological roles and the fact that many viruses mimick/hijack linear motifs to efficiently recode infected cells underlines the timely urgency of research on this very challenging and exciting topic.
Pre-structured motifs
Unlike globular proteins, IDPs do not have spatially-disposed active pockets. Fascinatingly, 80% of target-unbound IDPs (~4 dozens) subjected to detailed structural characterization by NMR possess linear motifs termed PresMos (pre-structured motifs) that are transient secondary structural elements primed for target recognition. In several cases it has been demonstrated that these transient structures become full and stable secondary structures, e.g., helices, upon target binding. Hence, PresMos are the putative active sites in IDPs.
Coupled folding and binding
Many unstructured proteins undergo transitions to more ordered states upon binding to their targets (e.g. Molecular Recognition Features (MoRFs)). The coupled folding and binding may be local, involving only a few interacting residues, or it might involve an entire protein domain. It was recently shown that the coupled folding and binding allows the burial of a large surface area that would be possible only for fully structured proteins if they were much larger. Moreover, certain disordered regions might serve as "molecular switches" in regulating certain biological function by switching to ordered conformation upon molecular recognition like small molecule-binding, DNA/RNA binding, ion interactions etc.
The ability of disordered proteins to bind, and thus to exert a function, shows that stability is not a required condition. Many short functional sites, for example Short Linear Motifs are over-represented in disordered proteins. Disordered proteins and short linear motifs are particularly abundant in many RNA viruses such as Hendra virus, HCV, HIV-1 and human papillomaviruses. This enables such viruses to overcome their informationally limited genomes by facilitating binding, and manipulation of, a large number of host cell proteins.
Disorder in the bound state (fuzzy complexes)
Intrinsically disordered proteins can retain their conformational freedom even when they bind specifically to other proteins. The structural disorder in bound state can be static or dynamic. In fuzzy complexes structural multiplicity is required for function and the manipulation of the bound disordered region changes activity. The conformational ensemble of the complex is modulated via post-translational modifications or protein interactions. Specificity of DNA binding proteins often depends on the length of fuzzy regions, which is varied by alternative splicing. Some fuzzy complexes may exhibit high binding affinity, although other studies showed different affinity values for the same system in a different concentration regime.
Structural aspects
Intrinsically disordered proteins adapt many different structures in vivo according to the cell's conditions, creating a structural or conformational ensemble.
Therefore, their structures are strongly function-related. However, only few proteins are fully disordered in their native state. Disorder is mostly found in intrinsically disordered regions (IDRs) within an otherwise well-structured protein. The term intrinsically disordered protein (IDP) therefore includes proteins that contain IDRs as well as fully disordered proteins.
The existence and kind of protein disorder is encoded in its amino acid sequence. In general, IDPs are characterized by a low content of bulky hydrophobic amino acids and a high proportion of polar and charged amino acids, usually referred to as low hydrophobicity. This property leads to good interactions with water. Furthermore, high net charges promote disorder because of electrostatic repulsion resulting from equally charged residues. Thus disordered sequences cannot sufficiently bury a hydrophobic core to fold into stable globular proteins. In some cases, hydrophobic clusters in disordered sequences provide the clues for identifying the regions that undergo coupled folding and binding (refer to biological roles). Many disordered proteins reveal regions without any regular secondary structure. These regions can be termed as flexible, compared to structured loops. While the latter are rigid and contain only one set of Ramachandran angles, IDPs involve multiple sets of angles. The term flexibility is also used for well-structured proteins, but describes a different phenomenon in the context of disordered proteins. Flexibility in structured proteins is bound to an equilibrium state, while it is not so in IDPs. Many disordered proteins also reveal low complexity sequences, i.e. sequences with over-representation of a few residues. While low complexity sequences are a strong indication of disorder, the reverse is not necessarily true, that is, not all disordered proteins have low complexity sequences. Disordered proteins have a low content of predicted secondary structure.
Due to the disordered nature of these proteins, topological approaches have been developed to search for conformational patterns in their dynamics. For instance, circuit topology has been applied to track the dynamics of disordered protein domains. By employing a topological approach, one can categorize motifs according to their topological buildup and the timescale of their formation.
Experimental validation
IDPs can be validated in several contexts. Most approaches for experimental validation of IDPs are restricted to extracted or purified proteins while some new experimental strategies aim to explore in vivo conformations and structural variations of IDPs inside intact living cells and systematic comparisons between their dynamics in vivo and in vitro.
In vivo approaches
The first direct evidence for in vivo persistence of intrinsic disorder has been achieved by in-cell NMR upon electroporation of a purified IDP and recovery of cells to an intact state.
Larger-scale in vivo validation of IDR predictions is now possible using biotin 'painting'.
In vitro approaches
Intrinsically unfolded proteins, once purified, can be identified by various experimental methods. The primary method to obtain information on disordered regions of a protein is NMR spectroscopy. The lack of electron density in X-ray crystallographic studies may also be a sign of disorder.
Folded proteins have a high density (partial specific volume of 0.72-0.74 mL/g) and commensurately small radius of gyration. Hence, unfolded proteins can be detected by methods that are sensitive to molecular size, density or hydrodynamic drag, such as size exclusion chromatography, analytical ultracentrifugation, small angle X-ray scattering (SAXS), and measurements of the diffusion constant. Unfolded proteins are also characterized by their lack of secondary structure, as assessed by far-UV (170–250 nm) circular dichroism (esp. a pronounced minimum at ~200 nm) or infrared spectroscopy. Unfolded proteins also have exposed backbone peptide groups exposed to solvent, so that they are readily cleaved by proteases, undergo rapid hydrogen-deuterium exchange and exhibit a small dispersion (<1 ppm) in their 1H amide chemical shifts as measured by NMR. (Folded proteins typically show dispersions as large as 5 ppm for the amide protons.)
Recently, new methods including Fast parallel proteolysis (FASTpp) have been introduced, which allow to determine the fraction folded/disordered without the need for purification. Even subtle differences in the stability of missense mutations, protein partner binding and (self)polymerisation-induced folding of (e.g.) coiled-coils can be detected using FASTpp as recently demonstrated using the tropomyosin-troponin protein interaction. Fully unstructured protein regions can be experimentally validated by their hypersusceptibility to proteolysis using short digestion times and low protease concentrations.
Bulk methods to study IDP structure and dynamics include SAXS for ensemble shape information, NMR for atomistic ensemble refinement, Fluorescence for visualising molecular interactions and conformational transitions, x-ray crystallography to highlight more mobile regions in otherwise rigid protein crystals, cryo-EM to reveal less fixed parts of proteins, light scattering to monitor size distributions of IDPs or their aggregation kinetics, NMR chemical shift and Circular Dichroism to monitor secondary structure of IDPs.
Single-molecule methods to study IDPs include spFRET to study conformational flexibility of IDPs and the kinetics of structural transitions, optical tweezers for high-resolution insights into the ensembles of IDPs and their oligomers or aggregates, nanopores to reveal global shape distributions of IDPs, magnetic tweezers to study structural transitions for long times at low forces, high-speed AFM to visualise the spatio-temporal flexibility of IDPs directly.
Disorder annotation
Intrinsic disorder can be either annotated from experimental information or predicted with specialized software. Disorder prediction algorithms can predict Intrinsic Disorder (ID) propensity with high accuracy (approaching around 80%) based on primary sequence composition, similarity to unassigned segments in protein x-ray datasets, flexible regions in NMR studies and physico-chemical properties of amino acids.
Disorder databases
Databases have been established to annotate protein sequences with intrinsic disorder information. The DisProt database contains a collection of manually curated protein segments which have been experimentally determined to be disordered. MobiDB is a database combining experimentally curated disorder annotations (e.g. from DisProt) with data derived from missing residues in X-ray crystallographic structures and flexible regions in NMR structures.
Predicting IDPs by sequence
Separating disordered from ordered proteins is essential for disorder prediction. One of the first steps to find a factor that distinguishes IDPs from non-IDPs is to specify biases within the amino acid composition. The following hydrophilic, charged amino acids A, R, G, Q, S, P, E and K have been characterized as disorder-promoting amino acids, while order-promoting amino acids W, C, F, I, Y, V, L, and N are hydrophobic and uncharged. The remaining amino acids H, M, T and D are ambiguous, found in both ordered and unstructured regions. A more recent analysis ranked amino acids by their propensity to form disordered regions as follows (order promoting to disorder promoting): W, F, Y, I, M, L, V, N, C, T, A, G, R, D, H, Q, K, S, E, P. As it can be seen from the list, small, charged, hydrophilic residues often promote disorder, while large and hydrophobic residues promote order.
This information is the basis of most sequence-based predictors. Regions with little to no secondary structure, also known as NORS (NO Regular Secondary structure) regions, and low-complexity regions can easily be detected. However, not all disordered proteins contain such low complexity sequences.
Prediction methods
Determining disordered regions from biochemical methods is very costly and time-consuming. Due to the variable nature of IDPs, only certain aspects of their structure can be detected, so that a full characterization requires a large number of different methods and experiments. This further increases the expense of IDP determination. In order to overcome this obstacle, computer-based methods are created for predicting protein structure and function. It is one of the main goals of bioinformatics to derive knowledge by prediction. Predictors for IDP function are also being developed, but mainly use structural information such as linear motif sites. There are different approaches for predicting IDP structure, such as neural networks or matrix calculations, based on different structural and/or biophysical properties.
Many computational methods exploit sequence information to predict whether a protein is disordered. Notable examples of such software include IUPRED and Disopred. Different methods may use different definitions of disorder. Meta-predictors show a new concept, combining different primary predictors to create a more competent and exact predictor.
Due to the different approaches of predicting disordered proteins, estimating their relative accuracy is fairly difficult. For example, neural networks are often trained on different datasets. The disorder prediction category is a part of biannual CASP experiment that is designed to test methods according accuracy in finding regions with missing 3D structure (marked in PDB files as REMARK465, missing electron densities in X-ray structures).
Disorder and disease
Intrinsically unstructured proteins have been implicated in a number of diseases. Aggregation of misfolded proteins is the cause of many synucleinopathies and toxicity as those proteins start binding to each other randomly and can lead to cancer or cardiovascular diseases. Thereby, misfolding can happen spontaneously because millions of copies of proteins are made during the lifetime of an organism. The aggregation of the intrinsically unstructured protein α-synuclein is thought to be responsible. The structural flexibility of this protein together with its susceptibility to modification in the cell leads to misfolding and aggregation. Genetics, oxidative and nitrative stress as well as mitochondrial impairment impact the structural flexibility of the unstructured α-synuclein protein and associated disease mechanisms. Many key tumour suppressors have large intrinsically unstructured regions, for example p53 and BRCA1. These regions of the proteins are responsible for mediating many of their interactions. Taking the cell's native defense mechanisms as a model drugs can be developed, trying to block the place of noxious substrates and inhibiting them, and thus counteracting the disease.
Computer simulations
Owing to high structural heterogeneity, NMR/SAXS experimental parameters obtained will be an average over a large number of highly diverse and disordered states (an ensemble of disordered states). Hence, to understand the structural implications of these experimental parameters, there is a necessity for accurate representation of these ensembles by computer simulations. All-atom molecular dynamic simulations can be used for this purpose but their use is limited by the accuracy of current force-fields in representing disordered proteins. Nevertheless, some force-fields have been explicitly developed for studying disordered proteins by optimising force-field parameters using available NMR data for disordered proteins. (examples are CHARMM 22*, CHARMM 32, Amber ff03* etc.)
MD simulations restrained by experimental parameters (restrained-MD) have also been used to characterise disordered proteins. In principle, one can sample the whole conformational space given an MD simulation (with accurate Force-field) is run long enough. Because of very high structural heterogeneity, the time scales that needs to be run for this purpose are very large and are limited by computational power. However, other computational techniques such as accelerated-MD simulations, replica exchange simulations,
metadynamics, multicanonical MD simulations, or methods using coarse-grained representation with implicit and explicit solvents have been used to sample broader conformational space in smaller time scales.
Moreover, various protocols and methods of analyzing IDPs, such as studies based on quantitative analysis of GC content in genes and their respective chromosomal bands, have been used to understand functional IDP segments.
See also
IDPbyNMR
DisProt database
MobiDB database
Molten globule
Prion
Random coil
Dark proteome
References
External links
Intrinsically disordered protein at Proteopedia
MobiDB: a comprehensive database of intrinsic protein disorder annotations
IDEAL - Intrinsically Disordered proteins with Extensive Annotations and Literature
D2P2 Database of Disordered Protein Predictions
Gallery of images of intrinsically disordered proteins
First IDP journal covering all topics of IDP research
IDP Journal
Database of experimentally validated IDPs
IDP ensemble database
Proteins by structure
Protein structure | Intrinsically disordered proteins | [
"Chemistry"
] | 4,326 | [
"Protein structure",
"Structural biology"
] |
2,868,301 | https://en.wikipedia.org/wiki/Acoustic%20Doppler%20current%20profiler | An acoustic doppler current profiler (ADCP) is a hydroacoustic current meter similar to a sonar, used to measure water current velocities over a depth range using the Doppler effect of sound waves scattered back from particles within the water column. The term ADCP is a generic term for all acoustic current profilers, although the abbreviation originates from an instrument series introduced by RD Instruments in the 1980s. The working frequencies range of ADCPs range from 38 kHz to several megahertz.
A similar device is a SODAR, which works in the air and uses the same principles for wind speed profiling.
Working principle
ADCPs contain piezoelectric transducers to transmit and receive sound signals. The traveling time of sound waves gives an estimate of the distance. The frequency shift of the echo is proportional to the water velocity along the acoustic path. To measure 3D velocities, at least three beams are required. In rivers, only the 2D velocity is relevant and ADCPs typically have two beams. In recent years, more functionality has been added to ADCPs (notably wave and turbulence measurements) and systems can be found with 2,3,4,5 or even 9 beams.
Further components of an ADCP are an electronic amplifier, a receiver, a clock to measure the traveling time, a temperature sensor, a compass to know the heading, and a pitch/roll sensor to know the orientation. An analog-to-digital converter and a digital signal processor are required to sample the returning signal in order to determine the Doppler shift. A temperature sensor is used to estimate the sound velocity at the instrument position using the seawater equation of state, and uses this to estimate scale the frequency shift to water velocities. This procedure assumes that the salinity has a preconfigured constant value. Finally, the results are saved to internal memory or output online to an external display software.
Processing methods
Three common methods are used to calculate the Doppler shift and thus the water velocity along the acoustic beams. The first method uses a monochromatic transmit pulse and is referred to as "incoherent" or "narrowband". The method is robust and provides good quality mean current profiles but has limited space-time resolution. When the transmit pulse consists of coded elements that are repeated, the method is referred to as "repeat sequence coding" or "broadband". This method improves the space-time resolution by a factor of 5 (typical). Commercially, this method was protected by US patent 5615173 until 2011. The pulse-to-pulse coherent method relies on a sequence of transmit pulses where the echo from subsequent pulses are assumed not to interfere with each other. This method is only applicable for very short profiling ranges but the corresponding improvement in space time resolution is of order 1000.
Applications
Depending on the mounting, one can distinguish between side-looking, downward- and upward-looking ADCPs. A bottom-mounted ADCP can measure the speed and direction of currents at equal intervals all the way to the surface. Mounted sideways on a wall or bridge piling in rivers or canals, it can measure the current profile from bank to bank. In very deep water they can be lowered on cables from the surface.
The primary usage is for oceanography. The instruments can also be used in rivers and canals to continuously measure the discharge.
Mounted on moorings within the water column or directly at the seabed, water current and wave studies may be performed. They can stay underwater for years at a time, the limiting factor is the lifetime of the battery pack. Depending on the nature of the deployment the instrument usually has the ability to be powered from shore, using the same umbilical cable for data communication. Deployment duration can be extended by a factor of three by substituting lithium battery packs for the standard alkaline packs.
Bottom tracking
By adjusting the window where the Doppler shift is calculated, it is possible to measure the relative velocity between the instrument and the bottom. This feature is referred to as bottom-track. The process has two parts; first identify the position of the bottom from the acoustic echo, then calculating the velocity from a window centered around the bottom position. When an ADCP is mounted on a moving ship, the bottom track velocity may be subtracted from the measured water velocity. The result is the net current profile. Bottom track provides the foundation for surveys of the water currents in coastal areas. In deep water where the acoustic signals cannot reach the bottom, the ship velocity is estimated from a more complex combination of velocity and heading information from GPS, gyro, etc.
Discharge measurements
In rivers, the ADCP is used to measure the total water transport. The method requires a vessel with an ADCP mounted over the side to cross from one bank to another while measuring continuously. Using the bottom track feature, the track of the boat as well as the cross sectional area is estimated after adjustment for left and right bank areas. The discharge can then be calculated as the dot product between the vector track and the current velocity. The method is in use by hydrographic survey organisations across the world and forms an important component in the stage-discharge curves used in many places to continuously monitor river discharge.
Doppler velocity log (DVL)
For underwater vehicles, the bottom tracking feature can be used as an important component in the navigation systems. In this case the velocity of the vehicle is combined with an initial position fix, compass or gyro heading, and data from the acceleration sensor. The sensor suite is combined (typically by use of a Kalman filter) to estimate the position of the vehicle. This may help to navigate submarines, autonomous, and remotely operated underwater vehicles.
Wave measurements
Some ADCPs can be configured to measure surface wave height and direction. The wave height is estimated with a vertical beam that measures the distance to the surface using the echo from short pulses and simple peak estimation algorithms. The wave direction is found by cross correlating the along-beam velocity estimates and the wave height measurement from the vertical beam. Wave measurements are typically available for seafloor-mounted instruments but recent improvements permit the instrument to be mounted also on rotating subsurface buoys.
Turbulence
ADCPs with pulse-to-pulse coherent processing can estimate the velocity with the precision required to resolve small scale motion. As a consequence, it is possible to estimate turbulent parameters from properly configured ADCPs. A typical approach is to fit the along beam velocity to the Kolmogorov structure configuration and thereby estimate the dissipation rate. The application of ADCPs to turbulence measurement is possible from stationary deployments but can also be done from moving underwater structures like gliders or from subsurface buoys.
Advantages and disadvantages
The two major advantages of ADCPs is the absence of moving parts that are subject to biofouling and the remote sensing aspect, where a single, stationary instrument can measure the current profile over ranges exceeding 1000 m. These features allow for long term measurements of the ocean currents over a significant portion of the water column. Since the start in the mid-1980s, many thousand ADCPs have been used in the world oceans and the instrument has played a significant role in our understanding of the world ocean circulation.
The main disadvantage of the ADCPs is the loss of data close to the boundary. This mechanism, often referred to as a sidelobe interference, covers 6–12% of the water column and, for instruments looking up toward the surface, the loss of velocity information close to the surface is a real disadvantage. Cost is also a concern but is normally dwarfed by the cost of the ship required to ensure a safe and professional deployment.
As any acoustical instrument, the ADCP contributes to noise pollution in the ocean which may interfere with cetacean navigation and echolocation. The effect depends on the frequency and the power of the instrument but most ADCPs operate in a frequency range where noise pollution has not been identified to be a serious problem.
References
Sonar
Physical oceanography
Oceanographic instrumentation
Ocean currents
Watercraft components | Acoustic Doppler current profiler | [
"Physics",
"Chemistry",
"Technology",
"Engineering"
] | 1,654 | [
"Ocean currents",
"Oceanographic instrumentation",
"Applied and interdisciplinary physics",
"Measuring instruments",
"Physical oceanography",
"Fluid dynamics"
] |
2,868,583 | https://en.wikipedia.org/wiki/List%20of%20planar%20symmetry%20groups | This article summarizes the classes of discrete symmetry groups of the Euclidean plane. The symmetry groups are named here by three naming schemes: International notation, orbifold notation, and Coxeter notation.
There are three kinds of symmetry groups of the plane:
2 families of rosette groups – 2D point groups
7 frieze groups – 2D line groups
17 wallpaper groups – 2D space groups.
Rosette groups
There are two families of discrete two-dimensional point groups, and they are specified with parameter n, which is the order of the group of the rotations in the group.
Frieze groups
The 7 frieze groups, the two-dimensional line groups, with a direction of periodicity are given with five notational names. The Schönflies notation is given as infinite limits of 7 dihedral groups. The yellow regions represent the infinite fundamental domain in each.
Wallpaper groups
The 17 wallpaper groups, with finite fundamental domains, are given by International notation, orbifold notation, and Coxeter notation, classified by the 5 Bravais lattices in the plane: square, oblique (parallelogrammatic), hexagonal (equilateral triangular), rectangular (centered rhombic), and rhombic (centered rectangular).
The p1 and p2 groups, with no reflectional symmetry, are repeated in all classes. The related pure reflectional Coxeter group are given with all classes except oblique.
Wallpaper subgroup relationships
See also
List of spherical symmetry groups
Orbifold notation#Hyperbolic plane - Hyperbolic symmetry groups
Notes
References
The Symmetries of Things 2008, John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, (Orbifold notation for polyhedra, Euclidean and hyperbolic tilings)
On Quaternions and Octonions, 2003, John Horton Conway and Derek A. Smith
Kaleidoscopes: Selected Writings of H. S. M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380–407, MR 2,10]
(Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559–591]
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3–45]
N. W. Johnson: Geometries and Transformations, (2018) Chapter 12: Euclidean Symmetry Groups
External links
"Conway's manuscript" on Orbifold notation (Notation changed from this original, x is now used in place of open-dot, and o is used in place of the closed dot)
The 17 Wallpaper Groups
Euclidean symmetries
Mathematics-related lists | List of planar symmetry groups | [
"Physics",
"Mathematics"
] | 625 | [
"Functions and mappings",
"Euclidean symmetries",
"Mathematical objects",
"Mathematical relations",
"Symmetry"
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2,868,762 | https://en.wikipedia.org/wiki/Hexagonal%20lattice | The hexagonal lattice (sometimes called triangular lattice) is one of the five two-dimensional Bravais lattice types. The symmetry category of the lattice is wallpaper group p6m. The primitive translation vectors of the hexagonal lattice form an angle of 120° and are of equal lengths,
The reciprocal lattice of the hexagonal lattice is a hexagonal lattice in reciprocal space with orientation changed by 90° and primitive lattice vectors of length
Honeycomb point set
The honeycomb point set is a special case of the hexagonal lattice with a two-atom basis. The centers of the hexagons of a honeycomb form a hexagonal lattice, and the honeycomb point set can be seen as the union of two offset hexagonal lattices.
In nature, carbon atoms of the two-dimensional material graphene are arranged in a honeycomb point set.
Crystal classes
The hexagonal lattice class names, Schönflies notation, Hermann-Mauguin notation, orbifold notation, Coxeter notation, and wallpaper groups are listed in the table below.
See also
Square lattice
Hexagonal tiling
Close-packing
Centered hexagonal number
Eisenstein integer
Voronoi diagram
Hermite constant
References
Lattice points
Crystal systems | Hexagonal lattice | [
"Chemistry",
"Materials_science",
"Mathematics"
] | 256 | [
"Crystallography",
"Lattice points",
"Crystal systems",
"Number theory"
] |
2,869,000 | https://en.wikipedia.org/wiki/Atovaquone | Atovaquone, sold under the brand name Mepron, is an antimicrobial medication for the prevention and treatment of Pneumocystis jirovecii pneumonia (PCP).
Atovaquone is a chemical compound that belongs to the class of naphthoquinones. Atovaquone is a hydroxy-1,4-naphthoquinone, an analog of both ubiquinone and lawsone.
Medical uses
Atovaquone is a medication used to treat or prevent:
For pneumocystis pneumonia (PCP), it is used in mild cases, although it is not approved for treatment of severe cases.
For toxoplasmosis, the medication has antiparasitic and therapeutic effects.
For malaria, it is one of the two components (along with proguanil) in the drug Malarone. Malarone has fewer side effects and is more expensive than mefloquine. Resistance has been observed.
For babesia, it is often used in conjunction with oral azithromycin.
Trimethoprim/sulfamethoxazole (TMP-SMX, Bactrim) is generally considered first-line therapy for PCP (not to be confused with sulfadiazine and pyrimethamine, which is first line for toxoplasmosis). However, atovaquone may be used in patients who cannot tolerate, or are allergic to, sulfonamide medications such as TMP-SMX. In addition, atovaquone has the advantage of not causing myelosuppression, which is an important issue in patients who have undergone bone marrow transplantation.
Atovaquone is given prophylactically to kidney transplant patients to prevent PCP in cases where Bactrim is contraindicated for the patient.
Malaria
Atovaquone, as a combination preparation with proguanil, has been commercially available from GlaxoSmithKline since 2000 as Malarone for the treatment and prevention of malaria.
Research
COVID-19
Preliminary research found that atovaquone could inhibit the replication of SARS-CoV-2 in vitro. Clinical trials of atovaquone for the treatment of COVID-19 are planned, and ongoing in United States in December 2021.
Atovaquone has also been found to inhibit human coronavirus OC43 and feline coronavirus in vitro.
In newer researches, atovaquone did not demonstrate evidence of enhanced SARS-CoV-2 viral clearance compared with placebo.
Veterinary use
Atovaquone is used in livestock veterinary cases of babesiosis in cattle, especially if imidocarb resistance is a concern.
References
Further reading
External links
Antimalarial agents
Antiprotozoal agents
1,4-Naphthoquinones
4-Chlorophenyl compounds
Drugs developed by GSK plc
Hydroxynaphthoquinones | Atovaquone | [
"Biology"
] | 613 | [
"Antiprotozoal agents",
"Biocides"
] |
2,870,010 | https://en.wikipedia.org/wiki/Wandering%20set | In dynamical systems and ergodic theory, the concept of a wandering set formalizes a certain idea of movement and mixing. When a dynamical system has a wandering set of non-zero measure, then the system is a dissipative system. This is the opposite of a conservative system, to which the Poincaré recurrence theorem applies. Intuitively, the connection between wandering sets and dissipation is easily understood: if a portion of the phase space "wanders away" during normal time-evolution of the system, and is never visited again, then the system is dissipative. The language of wandering sets can be used to give a precise, mathematical definition to the concept of a dissipative system. The notion of wandering sets in phase space was introduced by Birkhoff in 1927.
Wandering points
A common, discrete-time definition of wandering sets starts with a map of a topological space X. A point is said to be a wandering point if there is a neighbourhood U of x and a positive integer N such that for all , the iterated map is non-intersecting:
A handier definition requires only that the intersection have measure zero. To be precise, the definition requires that X be a measure space, i.e. part of a triple of Borel sets and a measure such that
for all . Similarly, a continuous-time system will have a map defining the time evolution or flow of the system, with the time-evolution operator being a one-parameter continuous abelian group action on X:
In such a case, a wandering point will have a neighbourhood U of x and a time T such that for all times , the time-evolved map is of measure zero:
These simpler definitions may be fully generalized to the group action of a topological group. Let be a measure space, that is, a set with a measure defined on its Borel subsets. Let be a group acting on that set. Given a point , the set
is called the trajectory or orbit of the point x.
An element is called a wandering point if there exists a neighborhood U of x and a neighborhood V of the identity in such that
for all .
Non-wandering points
A non-wandering point is the opposite. In the discrete case, is non-wandering if, for every open set U containing x and every N > 0, there is some n > N such that
Similar definitions follow for the continuous-time and discrete and continuous group actions.
Wandering sets and dissipative systems
A wandering set is a collection of wandering points. More precisely, a subset W of is a wandering set under the action of a discrete group if W is measurable and if, for any the intersection
is a set of measure zero.
The concept of a wandering set is in a sense dual to the ideas expressed in the Poincaré recurrence theorem. If there exists a wandering set of positive measure, then the action of is said to be , and the dynamical system is said to be a dissipative system. If there is no such wandering set, the action is said to be , and the system is a conservative system. For example, any system for which the Poincaré recurrence theorem holds cannot have, by definition, a wandering set of positive measure; and is thus an example of a conservative system.
Define the trajectory of a wandering set W as
The action of is said to be if there exists a wandering set W of positive measure, such that the orbit is almost-everywhere equal to , that is, if
is a set of measure zero.
The Hopf decomposition states that every measure space with a non-singular transformation can be decomposed into an invariant conservative set and an invariant wandering set.
See also
No wandering domain theorem
References
Alexandre I. Danilenko and Cesar E. Silva (8 April 2009). Ergodic theory: Nonsingular transformations; See Arxiv arXiv:0803.2424.
Ergodic theory
Limit sets
Dynamical systems | Wandering set | [
"Physics",
"Mathematics"
] | 818 | [
"Limit sets",
"Ergodic theory",
"Topology",
"Mechanics",
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] |
2,870,161 | https://en.wikipedia.org/wiki/Bell%27s%20spaceship%20paradox | Bell's spaceship paradox is a thought experiment in special relativity. It was first described by E. Dewan and M. Beran in 1959 but became more widely known after John Stewart Bell elaborated the idea further in 1976. A delicate thread hangs between two spaceships initially at rest in the inertial frame S. They start accelerating in the same direction simultaneously and equally, as measured in S, thus having the same velocity at all times as viewed from S. Therefore, they are all subject to the same Lorentz contraction, so the entire assembly seems to be equally contracted in the S frame with respect to the length at the start. At first sight, it might appear that the thread will not break during acceleration.
This argument, however, is incorrect as shown by Dewan and Beran, and later Bell. The distance between the spaceships does not undergo Lorentz contraction with respect to the distance at the start, because in S, it is effectively defined to remain the same, due to the equal and simultaneous acceleration of both spaceships in S. It also turns out that the rest length between the two has increased in the frames in which they are momentarily at rest (S′), because the accelerations of the spaceships are not simultaneous here due to relativity of simultaneity. The thread, on the other hand, being a physical object held together by electrostatic forces, maintains the same rest length. Thus, in frame S, it must be Lorentz contracted, which result can also be derived when the electromagnetic fields of bodies in motion are considered. So, calculations made in both frames show that the thread will break; in S′ due to the non-simultaneous acceleration and the increasing distance between the spaceships, and in S due to length contraction of the thread.
In the following, the rest length or proper length of an object is its length measured in the object's rest frame. (This length corresponds to the proper distance between two events in the special case, when these events are measured simultaneously at the endpoints in the object's rest frame.)
Dewan and Beran
Dewan and Beran stated the thought experiment by writing:
"Consider two identically constructed rockets at rest in an inertial frame S. Let them face the same direction and be situated one behind the other. If we suppose that at a prearranged time both rockets are simultaneously (with respect to S) fired up, then their velocities with respect to S are always equal throughout the remainder of the experiment (even though they are functions of time). This means, by definition, that with respect to S the distance between the two rockets does not change even when they speed up to relativistic velocities."
Then this setup is repeated again, but this time the back of the first rocket is connected with the front of the second rocket by a silk thread. They concluded:
"According to the special theory the thread must contract with respect to S because it has a velocity with respect to S. However, since the rockets maintain a constant distance apart with respect to S, the thread (which we have assumed to be taut at the start) cannot contract: therefore a stress must form until for high enough velocities the thread finally reaches its elastic limit and breaks."
Dewan and Beran also discussed the result from the viewpoint of inertial frames momentarily comoving with the first rocket, by applying a Lorentz transformation:
"Since , (..) each frame used here has a different synchronization scheme because of the factor. It can be shown that as increases, the front rocket will not only appear to be a larger distance from the back rocket with respect to an instantaneous inertial frame, but also to have started at an earlier time."
They concluded:
"One may conclude that whenever a body is constrained to move in such a way that all parts of it have the same acceleration with respect to an inertial frame (or, alternatively, in such a way that with respect to an inertial frame its dimensions are fixed, and there is no rotation), then such a body must in general experience relativistic stresses."
Then they discussed the objection, that there should be no difference between a) the distance between two ends of a connected rod, and b) the distance between two unconnected objects which move with the same velocity with respect to an inertial frame. Dewan and Beran removed those objections by arguing:
Since the rockets are constructed exactly the same way, and starting at the same moment in S with the same acceleration, they must have the same velocity all of the time in S. Thus, they are traveling the same distances in S, so their mutual distance cannot change in this frame. Otherwise, if the distance were to contract in S, then this would imply different velocities of the rockets in this frame as well, which contradicts the initial assumption of equal construction and acceleration.
They also argued that there indeed is a difference between a) and b): Case a) is the ordinary case of length contraction, based on the concept of the rod's rest length l0 in S0, which always stays the same as long as the rod can be seen as rigid. Under those circumstances, the rod is contracted in S. But the distance cannot be seen as rigid in case b) because it is increasing due to unequal accelerations in S0, and the rockets would have to exchange information with each other and adjust their velocities in order to compensate for this – all of those complications don't arise in case a).
Bell
In Bell's version of the thought experiment, three spaceships A, B and C are initially at rest in a common inertial reference frame, B and C being equidistant to A. Then, a signal is sent from A to reach B and C simultaneously, causing B and C starting to accelerate in the vertical direction (having been pre-programmed with identical acceleration profiles), while A stays at rest in its original reference frame. According to Bell, this implies that B and C (as seen in A's rest frame) "will have at every moment the same velocity, and so remain displaced one from the other by a fixed distance." Now, if a fragile thread is tied between B and C, it's not long enough anymore due to length contractions, thus it will break. He concluded that "the artificial prevention of the natural contraction imposes intolerable stress".
Bell reported that he encountered much skepticism from "a distinguished experimentalist" when he presented the paradox. To attempt to resolve the dispute, an informal and non-systematic survey of opinion at CERN was held. According to Bell, there was "clear consensus" which asserted, incorrectly, that the string would not break. Bell goes on to add,
"Of course, many people who get the wrong answer at first get the right answer on further reflection. Usually they feel obliged to work out how things look to observers B or C. They find that B, for example, sees C drifting further and further behind, so that a given piece of thread can no longer span the distance. It is only after working this out, and perhaps only with a residual feeling of unease, that such people finally accept a conclusion which is perfectly trivial in terms of A's account of things, including the Fitzgerald contraction."
Importance of length contraction
In general, it was concluded by Dewan & Beran and Bell, that relativistic stresses arise when all parts of an object are accelerated the same way with respect to an inertial frame, and that length contraction has real physical consequences. For instance, Bell argued that the length contraction of objects as well as the lack of length contraction between objects in frame S can be explained using relativistic electromagnetism. The distorted electromagnetic intermolecular fields cause moving objects to contract, or to become stressed if hindered from doing so. In contrast, no such forces act on the space between objects. (Generally, Richard Feynman demonstrated how the Lorentz transformation can be derived from the case of the potential of a charge moving with constant velocity (as represented by the Liénard–Wiechert potential). As to the historical aspect, Feynman alluded to the circumstance that Hendrik Lorentz arrived essentially the same way at the Lorentz transformation, see also History of Lorentz transformations.)
However, Petkov (2009) and Franklin (2009) interpret this paradox differently. They agreed with the result that the string will break due to unequal accelerations in the rocket frames, which causes the rest length between them to increase (see the Minkowski diagram in the analysis section). However, they denied the idea that those stresses are caused by length contraction in S. This is because, in their opinion, length contraction has no "physical reality", but is merely the result of a Lorentz transformation, i.e. a rotation in four-dimensional space which by itself can never cause any stress at all. Thus the occurrence of such stresses in all reference frames including S and the breaking of the string is supposed to be the effect of relativistic acceleration alone.
Discussions and publications
Paul Nawrocki (1962) gives three arguments why the string should not break, while Edmond Dewan (1963) showed in a reply that his original analysis still remains valid. Many years later and after Bell's book, Matsuda and Kinoshita reported receiving much criticism after publishing an article on their independently rediscovered version of the paradox in a Japanese journal. Matsuda and Kinoshita do not cite specific papers, however, stating only that these objections were written in Japanese.
However, in most publications it is agreed that the string will break, with some reformulations, modifications and different scenarios, such as by Evett & Wangsness (1960),
Dewan (1963),
Romain (1963),
Evett (1972),
Gershtein & Logunov (1998),
Tartaglia & Ruggiero (2003),
Cornwell (2005),
Flores (2005),
Semay (2006),
Styer (2007),
Freund (2008),
Redzic (2008),
Peregoudov (2009),
Redžić (2009),
Gu (2009),
Petkov (2009),
Franklin (2009),
Miller (2010),
Fernflores (2011),
Kassner (2012),
Natario (2014),
Lewis, Barnes & Sticka (2018),
Bokor (2018).
A similar problem was also discussed in relation to angular accelerations: Grøn (1979),
MacGregor (1981),
Grøn (1982, 2003).
Immediate acceleration
Similarly, in the case of Bell's spaceship paradox the relation between the initial rest length between the ships (identical to the moving length in S after acceleration) and the new rest length in S′ after acceleration, is:
.
This length increase can be calculated in different ways. For instance, if the acceleration is finished the ships will constantly remain at the same location in the final rest frame S′, so it's only necessary to compute the distance between the x-coordinates transformed from S to S′. If and are the ships' positions in S, the positions in their new rest frame S′ are:
Another method was shown by Dewan (1963) who demonstrated the importance of relativity of simultaneity. The perspective of frame S′ is described, in which both ships will be at rest after the acceleration is finished. The ships are accelerating simultaneously at in S (assuming acceleration in infinitesimal small time), though B is accelerating and stopping in S′ before A due to relativity of simultaneity, with the time difference:
Since the ships are moving with the same velocity in S′ before acceleration, the initial rest length in S is shortened in S′ by due to length contraction. From the frame of S′, B starts accelerating before A and also stops accelerating before A. Due to this B will always have higher velocity than A up until the moment A is finished accelerating too, and both of them are at rest with respect to S′. The distance between B and A keeps on increasing till A stops accelerating. Although A's acceleration timeline is delayed by an offset of , both A and B cover the same distance in their respective accelerations. But B's timeline contains acceleration and also being at rest in S` for till A stops accelerating. Hence the extra distance covered by B during the entire course can be calculated by measuring the distance traveled by B during this phase. Dewan arrived at the relation (in different notation):
It was also noted by several authors that the constant length in S and the increased length in S′ is consistent with the length contraction formula , because the initial rest length is increased by in S′, which is contracted in S by the same factor, so it stays the same in S:
Summarizing: While the rest distance between the ships increases to in S′, the relativity principle requires that the string (whose physical constitution is unaltered) maintains its rest length in its new rest system S′. Therefore, it breaks in S′ due to the increasing distance between the ships. As explained above, the same is also obtained by only considering the start frame S using length contraction of the string (or the contraction of its moving molecular fields) while the distance between the ships stays the same due to equal acceleration.
Constant proper acceleration
Instead of instantaneous changes of direction, special relativity also allows to describe the more realistic scenario of constant proper acceleration, i.e. the acceleration indicated by a comoving accelerometer. This leads to hyperbolic motion, in which the observer continuously changes momentary inertial frames
where is the coordinate time in the external inertial frame, and the proper time in the momentary frame, and the momentary velocity is given by
The mathematical treatment of this paradox is similar to the treatment of Born rigid motion. However, rather than ask about the separation of spaceships with the same acceleration in an inertial frame, the problem of Born rigid motion asks, "What acceleration profile is required by the second spaceship so that the distance between the spaceships remains constant in their proper frame?" In order for the two spaceships, initially at rest in an inertial frame, to maintain a constant proper distance, the lead spaceship must have a lower proper acceleration.
This Born rigid frame can be described by using Rindler coordinates (Kottler-Møller coordinates)
The condition of Born rigidity requires that the proper acceleration of the spaceships differs by
and the length measured in the Rindler frame (or momentary inertial frame) by one of the observers is Lorentz contracted to in the external inertial frame by
which is the same result as above. Consequently, in the case of Born rigidity, the constancy of length L' in the momentary frame implies that L in the external frame decreases constantly, the thread doesn't break. However, in the case of Bell's spaceship paradox the condition of Born rigidity is broken, because the constancy of length L in the external frame implies that L' in the momentary frame increases, the thread breaks (in addition, the expression for the distance increase between two observers having the same proper acceleration becomes also more complicated in the momentary frame).
See also
Hyperbolic motion (relativity)
Physical paradox
Rindler coordinates
Supplee's paradox
Twin paradox
References
External links
Michael Weiss; Don Koks (1995–2017): Bell's Spaceship Paradox, USENET Relativity FAQ
Mathieu Rouaud (2022): Einstein’s Elevator: World Lines, Michelson–Morley Experiment and Relativistic Paradox. Another relativistic paradox in an accelerated reference frame with three rockets: a particle of matter seems to go faster than light.
Theory of relativity
Physical paradoxes
Thought experiments in physics
Relativistic paradoxes | Bell's spaceship paradox | [
"Physics"
] | 3,288 | [
"Theory of relativity"
] |
2,870,168 | https://en.wikipedia.org/wiki/Tensor%E2%80%93vector%E2%80%93scalar%20gravity | Tensor–vector–scalar gravity (TeVeS), developed by Jacob Bekenstein in 2004, is a relativistic generalization of Mordehai Milgrom's Modified Newtonian dynamics (MOND) paradigm.
The main features of TeVeS can be summarized as follows:
As it is derived from the action principle, TeVeS respects conservation laws;
In the weak-field approximation of the spherically symmetric, static solution, TeVeS reproduces the MOND acceleration formula;
TeVeS avoids the problems of earlier attempts to generalize MOND, such as superluminal propagation;
As it is a relativistic theory it can accommodate gravitational lensing.
The theory is based on the following ingredients:
A unit vector field;
A dynamical scalar field;
A nondynamical scalar field;
A matter Lagrangian constructed using an alternate metric;
An arbitrary dimensionless function.
These components are combined into a relativistic Lagrangian density, which forms the basis of TeVeS theory.
Details
MOND is a phenomenological modification of the Newtonian acceleration law. In Newtonian gravity theory, the gravitational acceleration in the spherically symmetric, static field of a point mass at distance from the source can be written as
where is Newton's constant of gravitation. The corresponding force acting on a test mass is
To account for the anomalous rotation curves of spiral galaxies, Milgrom proposed a modification of this force law in the form
where is an arbitrary function subject to the following conditions:
In this form, MOND is not a complete theory: for instance, it violates the law of momentum conservation.
However, such conservation laws are automatically satisfied for physical theories that are derived using an action principle. This led Bekenstein to a first, nonrelativistic generalization of MOND. This theory, called AQUAL (for A QUAdratic Lagrangian) is based on the Lagrangian
where is the Newtonian gravitational potential, is the mass density, and is a dimensionless function.
In the case of a spherically symmetric, static gravitational field, this Lagrangian reproduces the MOND acceleration law after the substitutions and are made.
Bekenstein further found that AQUAL can be obtained as the nonrelativistic limit of a relativistic field theory. This theory is written in terms of a Lagrangian that contains, in addition to the Einstein–Hilbert action for the metric field , terms pertaining to a unit vector field and two scalar fields and , of which only is dynamical. The TeVeS action, therefore, can be written as
The terms in this action include the Einstein–Hilbert Lagrangian (using a metric signature and setting the speed of light, ):
where is the Ricci scalar and is the determinant of the metric tensor.
The scalar field Lagrangian is
where is a constant length, is the dimensionless parameter and an unspecified dimensionless function; while the vector field Lagrangian is
where while is a dimensionless parameter. and are respectively called the scalar and vector coupling constants of the theory. The consistency between the Gravitoelectromagnetism of the TeVeS theory and that predicted and measured by the Gravity Probe B leads to ,
and requiring consistency between the near horizon geometry of a black hole in TeVeS and that of the Einstein theory, as observed by the Event Horizon Telescope leads to So the coupling constants read:
The function in TeVeS is unspecified.
TeVeS also introduces a "physical metric" in the form
The action of ordinary matter is defined using the physical metric:
where covariant derivatives with respect to are denoted by
TeVeS solves problems associated with earlier attempts to generalize MOND, such as superluminal propagation. In his paper, Bekenstein also investigated the consequences of TeVeS in relation to gravitational lensing and cosmology.
Problems and criticisms
In addition to its ability to account for the flat rotation curves of galaxies (which is what MOND was originally designed to address), TeVeS is claimed to be consistent with a range of other phenomena, such as gravitational lensing and cosmological observations. However, Seifert shows that with Bekenstein's proposed parameters, a TeVeS star is highly unstable, on the scale of approximately 106 seconds (two weeks). The ability of the theory to simultaneously account for galactic dynamics and lensing is also challenged. A possible resolution may be in the form of massive (around 2eV) neutrinos.
A study in August 2006 reported an observation of a pair of colliding galaxy clusters, the Bullet Cluster, whose behavior, it was reported, was not compatible with any current modified gravity theory.
A quantity probing general relativity (GR) on large scales (a hundred billion times the size of the solar system) for the first time has been measured with data from the Sloan Digital Sky Survey to be (~16%) consistent with GR, GR plus Lambda CDM and the extended form of GR known as theory, but ruling out a particular TeVeS model predicting . This estimate should improve to ~1% with the next generation of sky surveys and may put tighter constraints on the parameter space of all modified gravity theories.
TeVeS appears inconsistent with recent measurements made by LIGO of gravitational waves.
See also
Gauge vector–tensor gravity
Modified Newtonian dynamics
Nonsymmetric gravitational theory
Scalar–tensor–vector gravity
References
Further reading
Dark Matter Observed (SLAC Today)
Einstein's Theory 'Improved'? (PPARC)
Einstein Was Right: General Relativity Confirmed ' TeVeS, however, made predictions that fell outside the observational error limits', (Space.com)
Theories of gravity
Astrophysics | Tensor–vector–scalar gravity | [
"Physics",
"Astronomy"
] | 1,179 | [
"Astronomical sub-disciplines",
"Theoretical physics",
"Astrophysics",
"Theories of gravity"
] |
2,870,273 | https://en.wikipedia.org/wiki/Chiral%20auxiliary | In stereochemistry, a chiral auxiliary is a stereogenic group or unit that is temporarily incorporated into an organic compound in order to control the stereochemical outcome of the synthesis. The chirality present in the auxiliary can bias the stereoselectivity of one or more subsequent reactions. The auxiliary can then be typically recovered for future use.
Most biological molecules and pharmaceutical targets exist as one of two possible enantiomers; consequently, chemical syntheses of natural products and pharmaceutical agents are frequently designed to obtain the target in enantiomerically pure form. Chiral auxiliaries are one of many strategies available to synthetic chemists to selectively produce the desired stereoisomer of a given compound.
Chiral auxiliaries were introduced by Elias James Corey in 1975 with chiral 8-phenylmenthol and by Barry Trost in 1980 with chiral mandelic acid. The menthol compound is difficult to prepare and as an alternative trans-2-phenyl-1-cyclohexanol was introduced by J. K. Whitesell in 1985.
Asymmetric synthesis
Chiral auxiliaries are incorporated into synthetic routes to control the absolute configuration of stereogenic centers. David A. Evans' synthesis of the macrolide cytovaricin, considered a classic, utilizes oxazolidinone chiral auxiliaries for one asymmetric alkylation reaction and four asymmetric aldol reactions, setting the absolute stereochemistry of nine stereocenters.
A typical auxiliary-guided stereoselective transformation involves three steps: first, the auxiliary is covalently coupled to the substrate; second, the resulting compound undergoes one or more diastereoselective transformations; and finally, the auxiliary is removed under conditions that do not cause racemization of the desired products. The cost of employing stoichiometric auxiliary and the need to spend synthetic steps appending and removing the auxiliary make this approach appear inefficient. However, for many transformations, the only available stereoselective methodology relies on chiral auxiliaries. In addition, transformations with chiral auxiliaries tend to be versatile and very well-studied, allowing the most time-efficient access to enantiomerically pure products.
Furthermore, the products of auxiliary-directed reactions are diastereomers, which enables their facile separation by methods such as column chromatography or crystallization.
8-phenylmenthol
In an early example of the use of a chiral auxiliary in asymmetric synthesis, E. J. Corey and coworkers conducted an asymmetric Diels-Alder reaction between (−)-8-phenylmenthol acrylate ester and 5-benzyloxymethylcyclopentadiene. The cycloaddition product was carried forward to the iodolactone shown below, an intermediate in the classic Corey synthesis of the prostaglandins. It is proposed that the back face of the acrylate is blocked by the auxiliary, so that cycloaddition occurs at the front face of the alkene.
(−)-8-phenylmenthol can be prepared from either enantiomer of pulegone,
though neither route is very efficient. Because of the widespread utility of the 8-phenylmenthol auxiliary, alternative compounds that are more easily synthesized, such as trans-2-phenyl-1-cyclohexanol
and trans-2-(1-pheyl-1-methylethyl)cyclohexanol have been explored.
1,1’-Binaphthyl-2,2’-diol (BINOL)
1,1’-Binaphthyl-2,2’-diol, or BINOL, has been used as chiral auxiliary for the asymmetric synthesis since 1983.
Hisashi Yamamoto first utilized (R)-BINOL as a chiral auxiliary in the asymmetric synthesis of limonene, which is an example of cyclic mono-terpenes. (R)-BINOL mononeryl ether was prepared by the monosilylation and alkylation of (R)-BINOL as the chiral auxiliary. Followed with the reduction by organoaluminum reagent, limonene was synthesized with low yields (29% yield) and moderate enantiomeric excesses up to 64% ee.
The preparation of a variety of enantiomerically pure uncommon R-amino acids can be achieved by the alkylation of chiral glycine derivatives possessing axially chiral BINOL as an auxiliary. It has been depicted by Fuji et al. Based on different electrophile, the diastereomeric excess varied from 69% to 86.
Protected at the aldehyde function with (R)-BINOL, reacted diastereoselectively with Grignard reagents to afford protected atrolactaldehyde with moderate to excellent diastereomeric excess and high yields.
BINOL was also used as a chiral auxiliary to control the formation of a P-stereocenter in an asymmetric metal-catalyzed C-P coupling process. Mondal et al. discovered that the Pd-catalysed C-P cross-coupling reaction between axially chiral BINOL-based phosphoramidites and aryl halides or triflates proceeds with excellent stereoselectivity due to the presence of BINOL near the reacting P center.
trans-2-Phenylcyclohexanol
One type of chiral auxiliary is based on the trans-2-phenylcyclohexanol motif as introduced by James K. Whitesell and coworkers in 1985. This chiral auxiliary was used in ene reactions of the derived ester of glyoxylic acid.
In the total synthesis of (−)-heptemerone B and (−)-guanacastepene E, attached with trans-2-phenylcyclohexanol, the glyoxylate reacted with 2,4-dimethyl-pent-2-ene, in the presence of tin(IV) chloride, yielding the desired anti adduct as the major product, together with a small amount of its syn isomer with 10:1 diastereomeric ratio.
For even greater conformational control, switching from a phenyl to a trityl group gives trans-2-tritylcyclohexanol (TTC). In 2015, the Brown group published an efficient chiral permanganate-mediated oxidative cyclization with TTC.
Oxazolidinones
Oxazolidinone auxiliaries, popularized by David A. Evans, have been applied to many stereoselective transformations, including aldol reactions, alkylation reactions, and Diels-Alder reactions. The oxazolidinones are substituted at the 4 and 5 positions. Through steric hindrance, the substituents direct the direction of substitution of various groups. The auxiliary is subsequently removed e.g. through hydrolysis.
Preparation
Oxazolidinones can be prepared from amino acids or readily available amino alcohols. A large number of oxazolidinones are commercially available, including the four below.
Acylation of the oxazolidinone is achieved by deprotonation with n-butyllithium and quench with an acyl chloride.
Alkylation reactions
Deprotonation at the α-carbon of an oxazolidinone imide with a strong base such as lithium diisopropylamide selectively furnishes the (Z)-enolate, which can undergo stereoselective alkylation.
Activated electrophiles, such as allylic or benzylic halides, are very good substrates.
Aldol reactions
Chiral oxazolidinones have been employed most widely in stereoselective aldol reactions.
Soft enolization with the Lewis acid dibutylboron triflate and the base diisopropylethylamine gives the (Z)-enolate, which undergoes a diastereoselective aldol reaction with an aldehyde substrate. The transformation is particularly powerful because it establishes two contiguous stereocenters simultaneously.
A model for the observed stereoselectivity can be found below. The syn-stereo relationship between the methyl group and the new secondary alcohol results from a six-membered ring Zimmerman-Traxler transition state, wherein the enolate oxygen and the aldehyde oxygen both coordinate boron. The aldehyde is oriented such that the hydrogen is placed in a pseudo-axial orientation to minimize 1,3-diaxial interactions. The absolute stereochemistry of the two stereocenters is controlled by the chirality in the auxiliary. In the transition structure, the auxiliary carbonyl is oriented away from the enolate oxygen so as to minimize the net dipole of the molecule; one face of the enolate is blocked by the substituent on the chiral auxiliary.
Removal
A variety of transformations have been developed to facilitate removal of the oxazolidinone auxiliary to generate different synthetically useful functional groups.
Camphorsultam
Camphorsultam, or Oppolzer's sultam, is a classic chiral auxiliary.
In the total synthesis of manzacidin B, Ohfune group utilized camphorsultam to construct the core oxazoline ring asymmetrically. Comparing with oxazolidinone as the chiral auxiliary, camphorsultam had a significant (2S,3R)-selectivity.
Camphorsultam also acts as a chiral auxiliary in Michael addition. Lithium base promoted stereoselective Michael addition of thiols to N-mcthacryloylcamphorsultam produced the corresponding addition products in high diastereoselectivity.
Camphorsultam was used as a chiral auxiliary for the asymmetric Claisen rearrangement. In the presence of butylated hydroxytoluene (BHT) used as a radical scavenger, a toluene solution of the adduct between geraniol and camphorsultam was heated in a sealed tube at 140 °C, to provide mainly the (2R,3S)-isomer as the major rearrangement product in 72% yield, securing the two contiguous stereocenters including the quaternary carbon.
Pseudoephedrine and pseudoephenamine
Both (R,R)- and (S,S)-pseudoephedrine can be used as chiral auxiliaries. Pseudoephedrine is reacted with a carboxylic acid, acid anhydride, or acyl chloride to give the corresponding amide.
The α-proton of the carbonyl compound is easily deprotonated by a non-nucleophilic base to give the enolate, which can further react. The configuration of the addition compound, such as with an alkyl halide, is directed by the methyl group. Thus, any addition product will be syn with the methyl and anti to the hydroxyl group. The pseudoephedrine chiral auxiliary is subsequently removed by cleaving the amide bond with an appropriate nucleophile.
Preparation
Both enantiomers of pseudoephedrine are commercially available. Racemic pseudoephedrine has many medical uses. Because pseudoephedrine can be used to illegally make methamphetamine, the purchase of pseudoephedrine for use in academic or industrial research is rather regulated. As an alternative, Myers et al. reported the utility of pseudoephenamine chiral auxiliaries in alkylation reactions. While pseudoephenamine is not readily available from commercial sources, it can be synthesized with relative ease from benzil and cannot be used to make amphetamines.
Pseudoephedrine amides are typically prepared by acylation with an acyl chloride or anhydride.
Alkylation
Pseudoephedrine amides undergo deprotonation by a strong base such as lithium diisopropylamide (LDA) to give the corresponding (Z)-enolates. Alkylation of these lithium enolates proceeds with high facial selectivity.
The diastereoselectivity is believed to result from a configuration wherein one face of the lithium enolate is blocked by the secondary lithium alkoxide and the solvent molecules associated with that lithium cation. In accordance with this proposal, it has been observed that the diastereoselectivity of the alkylation step is highly dependent on the amount of lithium chloride present and on the solvent, tetrahydrofuran (THF). Typically, 4 to 6 equivalents of lithium chloride are sufficient to saturate a solution of enolate in THF at the reaction molarity.
One primary advantage of asymmetric alkylation with pseudoephedrine amides is that the amide enolates are typically nucleophilic enough to react with primary and even secondary halides at temperatures ranging from –78 °C to 0 °C. Construction of quaternary carbon centers by alkylation of α-branched amide enolates is also possible, though the addition of DMPU is necessary for less reactive electrophiles.
Removal
Conditions have been developed for the transformation of pseudoephedrine amides into enantiomerically enriched carboxylic acids, alcohols, aldehydes, and ketones - after cleavage, the auxiliary can be recovered and reused.
tert-Butanesulfinamide
This specific sulfinamide chiral auxiliary was initially developed by Jonathan A. Ellman, and its use has been explored extensively by his group. Thus, it is often referred to as Ellman's auxiliary or Ellman's sulfinamide.
Preparation
Either enantiomer of tert-butanesulfinamide can be reached from tert-butyl disulfide in two steps: a catalytic asymmetric oxidation reaction gives the disulfide oxidation product (thiosulfinate) in high yield and enantiomeric excess. Treatment of this compound with lithium amide in ammonia affords optically pure inverted product.
Condensation of tert-butanesulfinamide with an aldehyde or ketone proceeds in high yield and affords only the (E)-isomer of the corresponding N-sulfinyl imines.
Synthesis of chiral amines
Addition of a Grignard reagent to a tert-butanesulfinyl aldimine or ketimine results in asymmetric addition to give the branched sulfinamide. The observed stereoselectivity can be rationalized by a six-membered ring transition structure, wherein both oxygen and nitrogen of the sulfinyl imine coordinate magnesium.
Removal
The auxiliary can be removed from the desired amine by treatment with hydrochloric acid in protic solvents.
SAMP/RAMP
Alkylation reactions of chiral (S)-1-amino-2-methoxymethylpyrrolidine (SAMP) and (R)-1-amino-2-methoxymethylpyrrolidine (RAMP) hydrazones were developed by Dieter Enders and E.J. Corey.
Preparation
SAMP can be prepared in six steps from (S)-proline, and RAMP can be prepared in six steps from (R)-glutamic acid.
Alkylation reactions
Condensation of SAMP or RAMP with an aldehyde or ketone affords the (E)-hydrazine. Deprotonation with lithium diisopropylamide and addition of an alkyl halide affords the alkylated product. The auxiliary can be removed by ozonolysis or hydrolysis.
Chiral auxiliaries in industry
Chiral auxiliaries are generally reliable and versatile, enabling the synthesis of a large number of enantiomerically pure compounds in a time-efficient manner. Consequently, chiral auxiliaries are often the method of choice in the early phases of drug development.
Tipranavir
The HIV protease inhibitor Tipranavir is marketed for the treatment of AIDS. The first enantioselective medicinal chemistry route to Tipranavir included the conjugate addition of an organocuprate reagent to a chiral Michael acceptor. The chiral oxazolidinone in the Michael acceptor controlled the stereochemistry of one of two stereocenters in the molecule. The final, commercial route to Tipranavir does not feature a chiral auxiliary; instead, this stereocenter is set by an asymmetric hydrogenation reaction.
Atorvastatin
The calcium salt of atorvastatin is marketed under the trade name Lipitor for the lowering of blood cholesterol. The first enantioselective medicinal chemistry route to atorvastatin relied on a diastereoselective aldol reaction with a chiral ester to set one of the two alcohol stereocenters. In the commercial route to atorvastatin, this stereocenter is carried forward from the readily available food additive isoascorbic acid.
See also
Example of use of trans-2-phenyl-1-cyclohexanol as chiral auxiliary: Ojima lactam
Valine as a Chiral auxiliary in the Schöllkopf method
References
Stereochemistry | Chiral auxiliary | [
"Physics",
"Chemistry"
] | 3,648 | [
"Spacetime",
"Stereochemistry",
"Space",
"nan"
] |
35,740,129 | https://en.wikipedia.org/wiki/Square%20antiprismatic%20molecular%20geometry | In chemistry, the square antiprismatic molecular geometry describes the shape of compounds where eight atoms, groups of atoms, or ligands are arranged around a central atom, defining the vertices of a square antiprism. This shape has D4d symmetry and is one of the three common shapes for octacoordinate transition metal complexes, along with the dodecahedron and the bicapped trigonal prism.
Like with other high coordination numbers, eight-coordinate compounds are often distorted from idealized geometries, as illustrated by the structure of Na3TaF8. In this case, with the small Na+ ions, lattice forces are strong. With the diatomic cation NO+, the lattice forces are weaker, such as in (NO)2XeF8, which crystallizes with a more idealized square antiprismatic geometry.
Examples
Square prismatic geometry and cubic geometry
Square prismatic geometry (D4h) is much less common compared to the square antiprism. An example of a molecular species with square prismatic geometry (a slightly flattened cube) is octafluoroprotactinate(V), [PaF8]3–, as found in its sodium salt, Na3PaF8. While local cubic 8-coordination is common in ionic lattices (e.g., Ca2+ in CaF2), and some 8-coordinate actinide complexes are approximately cubic, there are no reported examples of rigorously cubic 8-coordinate molecular species. A number of other rare geometries for 8-coordination are also known.
References
Stereochemistry
Molecular geometry | Square antiprismatic molecular geometry | [
"Physics",
"Chemistry"
] | 333 | [
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"nan",
"Spacetime",
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35,740,250 | https://en.wikipedia.org/wiki/Capped%20square%20antiprismatic%20molecular%20geometry | In chemistry, the capped square antiprismatic molecular geometry describes the shape of compounds where nine atoms, groups of atoms, or ligands are arranged around a central atom, defining the vertices of a gyroelongated square pyramid. The symmetry group of the resulting object is C4v
The gyroelongated square pyramid is a square pyramid with a square antiprism connected to the square base. In this respect, it can be seen as a "capped" square antiprism (a square antiprism with a pyramid erected on one of the square faces).
It is very similar to the tricapped trigonal prismatic molecular geometry, and there is some dispute over the specific geometry exhibited by certain molecules.
Examples:
[SiCo9(CO)21]2-, defined by the Co9 framework, which encapsulates the Si atom
[Pb(phen)4(OClO3)]+, defined by the N8O framework, which encapsulates the Pb2+ ion
[Ge9]4-, a zintl ion
Th(troopolonate)4(H2O), defined by the O9 framework, which encapsulates the Th4+ ion
is sometimes described as having a capped square antiprismatic geometry, although its geometry is most often described as tricapped trigonal prismatic.
, a lanthanum(III) complex with a La–La bond.
Bicapped square antiprismatic molecular geometry
Square antiprisms can be capped on both square faces, giving bicapped square antiprismatic molecular geometry. The bicapped square antiprismatic atoms surrounding a central atom define the vertices of a gyroelongated square bipyramid. The symmetry group of this object is D4d.
Examples:
B10H12, defined by the B10 framework
[AsRh10(CO)22]3− and [SRh10(CO)22]2−, defined by the Rh10 framework, which encapsulates the main group atoms As and S
[TlSn8]3−, a zintl ion
References
Stereochemistry
Molecular geometry | Capped square antiprismatic molecular geometry | [
"Physics",
"Chemistry"
] | 455 | [
"Molecular geometry",
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"Stereochemistry",
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35,741,857 | https://en.wikipedia.org/wiki/Neosaxitoxin | Neosaxitoxin (NSTX) is included, as other saxitoxin-analogs, in a broad group of natural neurotoxic alkaloids, commonly known as the paralytic shellfish toxins (PSTs). The parent compound of PSTs, saxitoxin (STX), is a tricyclic perhydropurine alkaloid, which can be substituted at various positions, leading to more than 30 naturally occurring STX analogues. All of them are related imidazoline guanidinium derivatives.
Sources
NSTX, and other PSTs, are produced by several species of marine dinoflagellates (eukaryotes) and freshwater cyanobacteria, blue-green algae (prokaryotes), which can form extensive blooms around the world. Under special conditions, during harmful algal blooms (HAB) or red tide, all these toxins may build up in filter-feeding shellfish, such as mussels, clams and oysters, and can produce an outbreak of Paralytic Shellfish Poisoning (PSP).
Saxitoxin analogues associated to PSP can be divided into three categories:
Carbamate compounds, including saxitoxin, neosaxitoxin and gonyautoxins 1–4.
N-sulfocarbamoyl compounds, including C and B toxins.
Decarbamoyl compounds with respect to the presence or absence of 1-N-hydroxyl, 11-hydroxysulfate, and 21-N-sulfocarbamoyl substitutions as well as epimerization at the C-11 position.
Structure and properties
NSTX is quite similar to saxitoxin, like all the neurotoxins associated to PSP, the only difference is that NSTX shows one hydroxyl group bonded to nitrogen "1", where saxitoxyn contains one hydrogen.
This purine is highly hydrophilic and thermostable, it is not destroyed by cooking. Moreover, is very stable in usual storage, specially in acidic condition.
Mechanism of action
NSTX blocks the extracellular portion, the outer vestibule, of some voltage gated sodium channels in a very powerful and reversible manner, without affection of other ion channels.
"Voltage-gated", also called "voltage-sensitive" and "voltage-dependent" sodium channel also known as "VGSCs" or "Nav channel" are crucial elements of normal physiology in a variety of animals, including flies, leeches, squid and jellyfish, as well as mammalian and non-mammalian vertebrates. This large integral membrane protein plays an essential role in the initiation and propagation of action potentials in neurons, myocytes and other excitable cells.
Nav channels form the basis for electrical excitability in animals. Nav channels evolved from Ca2+ channels and were present in the common ancestor of choanoflagellates and animals, although this channel was likely permeable to both Na+ and Ca2+. Thus, like many other neuronal channels and receptors, Nav channels predated neurons. Invertebrates possess two Nav channels (Nav1 and Nav2), whereas vertebrate Nav channels are of the Nav1 family.
Sodium-channel proteins in the mammalian brain are composed of an association that include one alpha subunit and one or more auxiliary beta subunits. Nine types of alpha subunits have been described (Nav1.1 to Nav1.9), and a tenth related isoform (Nax) may also play some role as a Nav channel. Based in this information, ten Nav classes can be described: Nav1.1 to Nav1.9, and Nax.
Former five, but more recently, six neurotoxin receptor sites have been recognized between the seven receptor site located in the vertebrate sodium channel receptor alpha subunit:
Site 1 binds the sodium channel blockers tetrodotoxin and saxitoxin.
Site 2 binds lipid-soluble sodium channel activators such as veratridine.
Site 3 binds alpha-scorpion and sea anemone toxins, which slow sodium channel inactivation.
Site 4 binds beta-scorpion toxins, which affect sodium channel activation.
Site 5 binds the polyether ladder brevetoxins and ciguatoxin.
Site 6 binds delta-conotoxin.
Local anesthetic receptor site binds local anesthetics, antiarrhythmic drugs and antiepileptic drugs
NSTX and other site 1 blockers have high affinity (very low dissociation constant) and high specificity for Nav channels. The action of NSTX produces minimal effect on cardiac Nav, where it exhibits about 20–60 fold lesser affinity than in Nav channels from rat skeletal muscle and rat brain. Most data emphasize the role of "STX resistant" Nav channel 1.5 in human heart.
Toxins such as neosaxitoxin and tetrodotoxin have less affinity for most cardiac Nav channels than for most Nav channels in nerve tissue. Moreover, NSTX is so active on nerve Nav channel than is roughly a million-fold more potent than lidocaine.
Effects on humans
This mechanism of action can produce two well known kinds of effects in humans:
Toxic effect, associated to plasmatic levels of NSTX
It can be approximately described using one of the classical model of neurotoxic disease, known from ancient times as red tide, the most harmful algal bloom (HAB). This well known clinical model is the "paralytic shellfish poisoning".
Of course, there are great differences between different algal blooms, because of the mix of species included in each HAB, usually related to environmental conditions; because of the levels and quality of PSTs produced in each HAB, that may be modulated by concurrent microorganism; and, last but not least, because of the specific properties of each kind of PST, for example:
Brevetoxins are lipid-soluble (hydrophobic) polyether marine toxins; their predominant effect is excitatory (blocked by tetrodotoxin), mediated by the enhancement of cellular Na+ influx; and bind to site 5 on Nav (like ciguatoxin).
Tetrodotoxin (TTX) toxicity is associated with marked and surprising cardiovascular effects (i.e.: hypotension and bradycardia). Those effects are unexpected because of notorious TTX-resistance observed in vertebrate cardiac Nav channel. Moreover, this characteristic of the mammalian cardiac Nav channel is attributed to the cardiac predominance of the TTX-resistant Nav channel isoform (Nav1.5). On the contrary, as presumed on physiologic basis, NSTX produces just mild and transient cardiovascular abnormalities during experimental intoxication (there are no data on pure NSTX clinical toxicity).
STX has two positive charges, in contrast to TTX's single charge and GTX2/3, a naturally occurring STX congener with a net +1 charge. In view of their rather different structures, it is not surprising that STX and TTX bind in a different fashion to VGSCs. In fact, when Phe 385 near the selectivity filter of Nav1.2 is mutated to Cys, the channel's affinity for TTX is reduced 3,000-fold, whereas that for STX is reduced (only) 340-fold.
There are very limited data on the relative potency of different PSTs, and developing alternative methods to animal bioassays for marine-toxin detection is an urgent need.
In spite of its heterogeneous and poorly understood epidemiology, the clinical picture of PSP could be useful to anticipate clinical effects of systemic NSTX.
In the most frequent and benign situation, the patient suffers just mild, short-lived paresthesias of the mouth or extremities.
In moderate cases perioral tingling progressing to numbness spreading to face and neck can be observed.
In severe cases, patient can suffer apnea secondary to motor block, requiring mechanical ventilation.
Usually, the victims of mild and severe acute intoxications eliminate the toxin in urine during the first 24 hours after ingestion, and improve to full recovery in the first day of intrahospital care (when vital support is provided in a timely manner).
When outbreaks of PSP occur in remote locations, where medical assistance is limited, reported lethality is under 10% in adults, but can reach 50% in children younger than six years old. This difference could be secondary to dissimilar doses and composition of involved mixes of PSTs; delay in medical support; or some kind of susceptibility of children. More recent information suggest that lethality could be around 1% of symptomatic patients, including cases where air transportation was required from remote locations of Alaska.
Electrophysiologic observations demonstrated sub clinical abnormalities lasting for some days or weeks after clinical recovery .
Some evidence suggest the presence of metabolic pathways for the sequential oxidation and glucuronidation of PST in vitro, both being the initial detoxication reactions for the excretion of these toxins in humans.
Forensic analysis of fatalities after severe cases, conclude that PSP toxins are metabolically transformed by humans and that they are removed from the body by excretion in the urine and feces like any other xenobiotic compound.
Considering the heterogeneous nature of toxins mixes contained in contaminated bivalve molluscs, the safe limit of toxin content in shellfish adequate for human ingestion is expressed in "saxitoxin equivalents". According to the Food and Agriculture Organization of the United Nations (FAO) and European Parliament, this limit is 80 microgram of saxitoxin equivalent per 100 gram of mussel meat (each mussel weights around 23 g). The U.S. Food and Drug Administration extends the same definition to "fish" quality, but the term "fish" refers to fresh or saltwater fin fish, crustaceans, other forms of aquatic animal life other than birds or mammals, and all mollusks; and incorporate the use of "ppm" as another measure for saxitoxin equivalent concentration in mentioned foods.
Paradoxically, the chronic and/or repeated exposure to marine seafood toxins, which is a much more realistic phenomenon, has not been fully examined. One study in rats exposed to chronic (12 weeks) NSTX administration demonstrated some reduction in water and food intake, and a mild degree of transient cholestasis, probably associated to fasting, without other abnormalities.
Anesthetic effect, produced by local infiltration of NSTX
This action has been demonstrated in animals and humans.
The medical use of the NSTX anesthetic effect is supported by three reasons:
NSTX anesthetic duration:
Any current available local anesthetic hardly produces clinical effects 12 hours after a single injection. Then, in cases of severe or prolonged pain, some patients need repeated injections, catheters, pumps and opioids to feel comfortable, with different kinds of side effects, costs and risks.
On the other hand, NSTX local infiltration produces long lasting anesthesia, well over all the current available local anesthetics. Some investigations demonstrated anesthetic effect lasting over one week after single injection in rodents, using extended release formulation, without histologic or functional sequelae.
Additionally, two human reports demonstrated strong potentiation between NSTX anesthetic effect, bupivacaine and epinephrine.
NSTX local safety:
All available local anesthetic are associated with local damage in different models. This undesired effect could be enhanced by sustained release formulations.
On the contrary, several investigations show local safety of saxitoxin-related neurotoxins, including very sensitive models, and there is no reason to presume otherwise for NSTX.
NSTX systemic safety:
In spite of advances of ultrasound guided injections, acute systemic local anesthetic toxicity is still an unsolved clinical problem, and can produce devastating consequences, related to the neurologic and cardiovascular effects of all available local anesthetics.
Otherwise, clinical experience and animal models shows the relative safety of accidental and experimental NSTX intoxication (when appropriate support therapy is provided in a timely manner).
Recent investigation in sheep shows a safe limit, due to motor block, over 1 μg/kg for intravenous injection of NSTX, with full recovery after a brief course of mechanical ventilation.
Regarding systemic safety, saxitoxins diffuse through the blood–brain barrier, but, because of Nav channel specificity, acute toxicity is associated to a very low risk of seizures. This establishes an important difference with current local anesthetic toxicity.
As could be predicted from its ion channel selectivity, NSTX intoxication clinical picture is almost devoid of arrhythmias, establishing another difference with available local anesthetic's numerous cardiac effects.
And last but not least, some degree of improving in therapeutic index of NSTX can be observed when is mixed with bupivacaine and/or epinephrine.
In conclusion, NSTX is a well defined molecule with a long-lasting and sometimes dangerous relationship with human subjects. Recent investigations suggest a clinical application as a new local anesthetic that sounds "too good to be true", but more investigation is required.
See also
Canadian Reference Materials
References
Local anesthetics
Marine neurotoxins
Voltage-gated sodium channel blockers
Guanidine alkaloids
Hydroxyguanidines
Geminal diols
Purines
Pharmacology | Neosaxitoxin | [
"Chemistry"
] | 2,880 | [
"Pharmacology",
"Alkaloids by chemical classification",
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35,742,703 | https://en.wikipedia.org/wiki/3D%20bioprinting | Three dimensional (3D) bioprinting is the use of 3D printing–like techniques to combine cells, growth factors, bio-inks, and biomaterials to fabricate functional structures that were traditionally used for tissue engineering applications but in recent times have seen increased interest in other applications such as biosensing, and environmental remediation. Generally, 3D bioprinting uses a layer-by-layer method to deposit materials known as bio-inks to create tissue-like structures that are later used in various medical and tissue engineering fields. 3D bioprinting covers a broad range of bioprinting techniques and biomaterials. Currently, bioprinting can be used to print tissue and organ models to help research drugs and potential treatments. Nonetheless, translation of bioprinted living cellular constructs into clinical application is met with several issues due to the complexity and cell number necessary to create functional organs. However, innovations span from bioprinting of extracellular matrix to mixing cells with hydrogels deposited layer by layer to produce the desired tissue. In addition, 3D bioprinting has begun to incorporate the printing of scaffolds which can be used to regenerate joints and ligaments. Apart from these, 3D bioprinting has recently been used in environmental remediation applications, including the fabrication of functional biofilms that host functional microorganisms that can facilitate pollutant removal.
Process
3D bioprinting generally follows three steps: pre-bioprinting, bioprinting, and post-bioprinting.
Pre-bioprinting
Pre-bioprinting is the process of creating a model that the printer will later create and choosing the materials that will be used. One of the first steps is to obtain a biopsy of the organ, to sample cells. Common technologies used for bioprinting are computed tomography (CT) and magnetic resonance imaging (MRI). To print with a layer-by-layer approach, tomographic reconstruction is done on the images. The now-2D images are then sent to the printer to be made. Once the image is created, certain cells are isolated and multiplied. These cells are then mixed with a special liquefied material that provides oxygen and other nutrients to keep them alive. This aggregation of cells does not require a scaffold, and is required for placing in the tubular-like tissue fusion for processes such as extrusion.
Bioprinting
In the second step, the liquid mixtures of cells, matrix, and nutrients known as bioinks are placed in a printer cartridge and deposited using the patients' medical scans. When a bioprinted pre-tissue is transferred to an incubator, this cell-based pre-tissue matures into a tissue.
3D bioprinting for fabricating biological constructs typically involves dispensing cells onto a biocompatible scaffold using a successive layer-by-layer approach to generate tissue-like three-dimensional structures. Artificial organs such as livers and kidneys made by 3D bioprinting have been shown to lack crucial elements that affect the body such as working blood vessels, tubules for collecting urine, and the growth of billions of cells required for these organs. Without these components the body has no way to get the essential nutrients and oxygen deep within their interiors. Given that every tissue in the body is naturally composed of different cell types, many technologies for printing these cells vary in their ability to ensure stability and viability of the cells during the manufacturing process. Some of the methods that are used for 3D bioprinting of cells are photolithography, magnetic 3D bioprinting, stereolithography, and direct cell extrusion.
Post-bioprinting
The post-bioprinting process is necessary to create a stable structure from the biological material. If this process is not well-maintained, the mechanical integrity and function of the 3D printed object is at risk. To maintain the object, both mechanical and chemical stimulations are needed. These stimulations send signals to the cells to control the remodeling and growth of tissues. In addition, in recent development, bioreactor technologies have allowed the rapid maturation of tissues, vascularization of tissues and the ability to survive transplants.
Bioreactors work in either providing convective nutrient transport, creating microgravity environments, changing the pressure causing solution to flow through the cells, or adding compression for dynamic or static loading. Each type of bioreactor is ideal for different types of tissue, for example compression bioreactors are ideal for cartilage tissue.
Bioprinting approach
Researchers in the field have developed approaches to produce living organs that are constructed with the appropriate biological and mechanical properties. 3D bioprinting is based on three main approaches: biomimicry, autonomous self-assembly and mini-tissue building blocks.
Biomimicry
The first approach of bioprinting is called biomimicry. The main goal of this approach is to create fabricated structures that are identical to the natural structure that are found in the tissues and organs in the human body. Biomimicry requires duplication of the shape, framework, and the microenvironment of the organs and tissues. The application of biomimicry in bioprinting involves creating both identical cellular and extracellular parts of organs. For this approach to be successful, the tissues must be replicated on a micro scale. Therefore, it is necessary to understand the microenvironment, the nature of the biological forces in this microenvironment, the precise organization of functional and supporting cell types, solubility factors, and the composition of extracellular matrix.
Autonomous self-assembly
The second approach of bioprinting is autonomous self-assembly. This approach relies on the physical process of embryonic organ development as a model to replicate the tissues of interest. When cells are in their early development, they create their own extracellular matrix building block, the proper cell signaling, and independent arrangement and patterning to provide the required biological functions and micro-architecture. Autonomous self-assembly demands specific information about the developmental techniques of the tissues and organs of the embryo. There is a "scaffold-free" model that uses self-assembling spheroids that subjects to fusion and cell arrangement to resemble evolving tissues. Autonomous self-assembly depends on the cell as the fundamental driver of histogenesis, guiding the building blocks, structural and functional properties of these tissues. It demands a deeper understanding of how embryonic tissues mechanisms develop as well as the microenvironment surrounded to create the bioprinted tissues.
Mini-tissue
The third approach of bioprinting is a combination of both the biomimicry and self-assembly approaches, called mini tissues. Organs and tissues are built from very small functional components. The mini-tissue approach takes these small pieces and arrange them into larger framework.
Classification of bioprinters
Akin to ordinary ink printers, bioprinters have three major components to them. These are the hardware used, the type of bio-ink, and the material it is printed on (biomaterials). Bio-ink is a material made from living cells that behaves much like a liquid, allowing people to 'print' it in order to create the desired shape. To make bio-ink, scientists create a slurry of cells that can be loaded into a cartridge and inserted into a specially designed printer, along with another cartridge containing a gel known as bio-paper." In bioprinting, there are three major types of printers that have been used. These are inkjet, laser-assisted, and extrusion printers. Inkjet printers are mainly used in bioprinting for fast and large-scale products. One type of inkjet printer, called drop-on-demand inkjet printer, prints materials in exact amounts, minimizing cost and waste. Printers that use lasers provide high-resolution printing; however, these printers are often expensive. Extrusion printers print cells layer-by-layer, just like 3D printing to create 3D constructs. In addition to just cells, extrusion printers may also use hydrogels infused with cells.
Extrusion-based
Extrusion-based printing is a very common technique within the field of 3D printing which entails extruding, or forcing, a continuous stream of melted solid material or viscous liquid through a sort of orifice, often a nozzle or syringe. When it comes to extrusion based bioprinting, there are four main types of extrusion. These are pneumatic driven, piston driven, screw driven and eccentric screw driven (also known as progressing cavity pump). Each extrusion method has their own advantages and disadvantages. Pneumatic extrusion uses pressurized air to force liquid bioink through a depositing agent. Air filters are commonly used to sterilize the air before it is used, to ensure air pushing the bioink is not contaminated. Piston driven extrusion uses a piston connected to a guide screw. The linear motion of the piston squeezes material out of the nozzle. Screw driven extrusion uses an auger screw to extrude material using rotational motion. Screw driven devices allow for the use of higher viscosity materials and provide more volumetric control. Eccentric screw driven systems allow for a much more precise deposition of low to high viscosity materials due to the self-sealing chambers in the extruder. Once printed, many materials require a crosslinking step to achieve the desired mechanical properties for the construct, which can be achieved for example with the treatment of chemical agents or photo-crosslinkers.
Direct extrusion is one of the most common extrusion-based bioprinting techniques, wherein the pressurized force directs the bioink to flow out of the nozzle, and directly print the scaffold without any necessary casting. The bioink itself for this approach can be a blend of polymer hydrogels, naturally derived materials such as collagen, and live cells suspended in the solution. In this manner, scaffolds can be cultured post-print and without the need for further treatment for cellular seeding. Some focus in the use of direct printing techniques is based upon the use of coaxial nozzle assemblies, or coaxial extrusion. The coaxial nozzle setup enables the simultaneous extrusion of multiple material bioinks, capable of making multi-layered scaffolds in a single extrusion step. The development of tubular structures has found the layered extrusion achieved via these techniques desirable for the radial variability in material characterization that it can offer, as the coaxial nozzle provides an inner and outer tube for bioink flow. Indirect extrusion techniques for bioprinting rather require the printing of a base material of cell-laden hydrogels, but unlike direct extrusion contains a sacrificial hydrogel that can be trivially removed post-printing through thermal or chemical extraction. The remaining resin solidifies and becomes the desired 3D-printed construct.
Laser-based
Laser-based bioprinting can be split into two major classes: those based on cell transfer technologies or photo-polymerization. In cell transfer laser printing, a laser stimulates the connection between energy-absorbing material (e.g. gold, titanium, etc.) and the bioink. This 'donor layer' vaporizes under the laser's irradiation, forming a bubble from the bioink layer which gets deposited from a jet. Photo-polymerization techniques rather use photoinitiated reactions to solidify the ink, moving the beam path of a laser to induce the formation of a desired construct. Certain laser frequencies paired with photopolymerization reactions can be carried out without damaging cells in the material.
Fixed deposition modelling
In this form of printing, plastic residues are melted down and individual layered in sections to create a desired shape. Nylon and PVA are examples of biomaterials used in this method. This technique is most often used to design prototypes for prosthetics and cartilage construction.
Inkjet
Another form of bioprinting involves an inkjet printer, which is primarily used in biomedical settings. This method prints detailed proteins and nucleic acids. Hydrogels are commonly selected as the bioink. Cells can be printed on to a selected surface media to proliferate and ultimately differentiate. A drawback of this printing method is the ability of the bioinks such as hydrogels to clog the printing nozzle, due to their high viscosity. Ideal inkjet bioprinting involves using a low polymer viscosity (ideally below 10 centipoise), low cell density (<10 million cells/mL), and low structural heights (<10 million cells/mL).
Additional printing methods
There are several other bioprinting techniques which are less commonly used. Droplet-based bioprinting is a technique in which the bioink blend of cells and/or hydrogels are placed in droplets in precise positions. Most common amongst this approach are thermal and piezoelectric-drop-on-demand techniques. This method of bioprinting is often used experimentally with lung and ovarian cancer models. Thermal technologies use short duration signals to heat the bioink, inducing the formation of small bubbles which are ejected. Piezoelectric bioprinting has short duration current applied to a piezoelectric actuator, which induces a mechanical vibration capable of ejecting a small globule of bioink through the nozzle. A significant aspect of the study of droplet-based approaches to bioprinting is accounting for mechanical and thermal stress cells within the bioink experience near the nozzle-tip as they are extruded.
Significance of bioink selection
Bioinks are essential components of the bioprinting process. They are composed of living cells and enzymatic supplements to nurture an environment that supports the biological needs of the printed tissue. The environment created by the bioink allows for the cell to attach, grow, and differentiate into its adult form. Cell-encapsualting hydrogels are used in extrusion based bioprinting methods, while gelatin MethacryloylGelatin methacrylon (GelMA) and acellular comprised bioinks are most often used in tissue engineering techniques that require cross-linkage and precise structural integrity. It is essential for bioinks to help replicate the external cellular matrix environment that the cell would naturally occur in.
Applications
Tissue engineering
3D bioprinting can be used to reconstruct tissue from various regions of the body. The precursor to the adoption of 3D printing in healthcare was a series of trials conducted by researchers at Boston Children's Hospital. The team built replacement urinary bladders by hand for seven patients by constructing scaffolds, then layering the scaffolds with cells from the patients and allowing them to grow. The trials were a success as the patients remained in good health 7 years after implantation, which led a research fellow named Anthony Atala, MD, to search for ways to automate the process. Patients with end-stage bladder disease can now be treated by using bio-engineered bladder tissues to rebuild the damaged organ. This technology can also potentially be applied to bone, skin, cartilage and muscle tissue. Though one long-term goal of 3D bioprinting technology is to reconstruct an entire organ as well as minimize the problem of the lack of organs for transplantation. There has been little success in bioprinting of fully functional organs e.g. liver, skin, meniscus or pancreas. Unlike implantable stents, organs have complex shapes and are significantly harder to bioprint. A bioprinted heart, for example, must not only meet structural requirements, but also vascularization, mechanical load, and electrical signal propagation requirements. In 2022, the first success of a clinical trial for a 3D bioprinted transplant that is made from the patient's own cells, an external ear to treat microtia, was reported.
3D bioprinting contributes to significant advances in the medical field of tissue engineering by allowing for research to be done on innovative materials called biomaterials. Some of the most notable bioengineered substances are usually stronger than the average bodily materials, including soft tissue and bone. These constituents can act as future substitutes, even improvements, for the original body materials. In addition, the Defense Threat Reduction Agency aims to print mini organs such as hearts, livers, and lungs as the potential to test new drugs more accurately and perhaps eliminate the need for testing in animals.
Cultured meat
Bioprinting can also be used for cultured meat. In 2021, a steak-like cultured meat, composed of three types of bovine cell fibers was produced. The Wagyu-like beef has a structure similar to original meat. This technology provides an alternative to natural meat harvesting methods if the livestock industry is plagued by disease. In addition, it provides a possible solution to reducing the environmental impact of the livestock industry.
Bioremediation
Bioremediation uses microorganisms or in recent times, materials of biological origin, such as enzymes, biocomposites, biopolymers, or nanoparticles, to biochemically degrade contaminants into harmless substances, making it an environmentally friendly and cost-effective alternative; 3D bioprinting facilitates the fabrication of functional structures using these materials that enhance bioremediation processes leading to a significant interest in the application of 3D bioprinted constructs in improving bioremediation.
Biofilms
The bioprinting of biofilms uses the same methods as other bioprinting. Oftentimes, the biofilm begins with an extrusion of a polysaccharide to provide structure for biofilm growth. An example of one of these polysaccharides is alginate. The alginate structure can have microbes embedded within the structure. Hydrogels can also be used to assist in the formation of functional biofilms. Biofilms are difficult to analyze in a laboratory setting due to the complex structure and the time it takes for a functional biofilm to form. 3D bioprinting biofilms allows us to skip certain processes and makes it easier to analyze functional biofilms. Thickness of the biofilm being printed with change the functionality due to nutrient and oxygen diffusion. Thicker 3D printed biofilms will naturally select for anaerobes for example.
Biofilms are capable of remediation in the natural environment which suggests there is potential in regards to the use of 3D bioprinted biofilm use in environmental remediation. Microbes are able to degrade a large range of chemicals and metals and providing a structure for these microbes to flourish such as in biofilm structures is beneficial. Artificial biofilms protect the microbes from the dangers of the environment while promoting signaling and overall microbial interactions. 3D bioprinting allows functional microorganisms to be placed in structures that provide mechanical stability and protects them from environmental conditions. The larger contact area provided by 3D printed structures compared to normal environmental structures provides more efficient removal of pollutants.
Future uses
Bioprinting also has possible uses in the future in assisting in wastewater treatment and in corrosion control. When humans come in contact with environmental biofilms, it is possible for infections and long-term health hazards to occur. Antibiotic penetration and expansion within a biofilm is an area of research which can benefit from bioprinting techniques, to further explore the effect of environmental biofilms on human health. Biofilm printing requires further research due to limited published data and complex protocols.
See also
3D printing § Bio-printing
Biofabrication
Cultured meat
Ethics of bioprinting
Regenerative medicine
Bioinks
References
Further reading
Bioprinting
Biomaterials
Tissue engineering
Synthetic biology
Self-replication | 3D bioprinting | [
"Physics",
"Chemistry",
"Engineering",
"Biology"
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"Cloning",
"Chemical engineering",
"Self-replication",
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35,745,858 | https://en.wikipedia.org/wiki/Degree%20of%20reaction | In turbomachinery, degree of reaction or reaction ratio (denoted ) is defined as the ratio of the change in static pressure in the rotating blades of a compressor or turbine, to the static pressure change in the compressor or turbine stage. Alternatively it is the ratio of static enthalpy change in the rotor to the static enthalpy change in the stage.
Various definitions exist in terms of enthalpies, pressures or flow geometry of the device.
In case of turbines, both impulse and reaction machines, degree of reaction is defined as the ratio of energy transfer by the change in static head to the total energy transfer in the rotor:
For a gas turbine or compressor it is defined as the ratio of isentropic heat drop in the moving blades (the rotor) to the sum of the isentropic heat drops in both the fixed blades (the stator) and the moving blades:
In pumps, degree of reaction deals in static and dynamic head. Degree of reaction is defined as the fraction of energy transfer by change in static head to the total energy transfer in the rotor:
Relation
Most turbo machines are efficient to a certain degree and can be approximated to undergo isentropic process in the stage.
Hence from
it is easy to see that for isentropic process . Hence it can be implied
The same can be expressed mathematically as:
Where 1 to 3ss in Figure 1 represents the isentropic process beginning from stator inlet at 1 to rotor outlet at 3. And 2 to 3s is the isentropic process from rotor inlet at 2 to rotor outlet at 3. The velocity triangle (Figure 2.) for the flow process within the stage represents the change in fluid velocity as it flows first in the stator or the fixed blades and then through the rotor or the moving blades. Due to the change in velocities there is a corresponding pressure change.
Another useful definition used commonly uses stage velocities as:
is the enthalpy drop in the rotor and
is the total enthalpy drop. The degree of reaction is then expressed as
For axial machines , then
The degree of reaction can also be written in terms of the geometry of the turbomachine as obtained by
where is the vane angle of rotor outlet and is the vane angle of stator outlet. In practice is substituted as and as giving
The degree of reaction now depends only on and which again depend on geometrical parameters and i.e. the vane angles of stator outlet and rotor outlet. Using the velocity triangles degree of reaction can be derived as:
This relation is again very useful when the rotor blade angle and rotor vane angle are defined for the given geometry.
Choice of reaction (R) and effect on efficiency
The Figure 3 alongside shows the variation of total-to-static efficiency at different blade loading coefficient with the degree of reaction.
The governing equation is written as
where
is the stage loading factor. The diagram shows the optimization of total - to - static efficiency at a given stage loading factor, by a suitable choice of reaction. It is evident from the diagram that for a fixed stage loading factor that there is a relatively small change in total-to-static efficiency for a wide range of designs.
50% reaction
The degree of reaction contributes to the stage efficiency and thus used as a design parameter. Stages having 50% degree of reaction are used where the pressure drop is equally shared by the stator and the rotor for a turbine.
This reduces the tendency of boundary layer separation from the blade surface avoiding large stagnation pressure losses.
If R= then from the relation of degree of reaction,|| α2 = β3 and the velocity triangle (Figure 4.) is symmetric. The stage enthalpy gets equally distributed in the stage (Figure 5.) . In addition the whirl components are also the same at the inlet of rotor and diffuser.
Reaction less than 50%
Stage having reaction less than half suggest that pressure drop or enthalpy drop in the
rotor is less than the pressure drop in the stator for the turbine. The same follows for a pump or compressor as shown in Figure 6. From the relation for degree of reaction,
|| α2 > β3.
Reaction more than 50%
Stage having reaction more than half suggest that pressure drop or enthalpy drop in the rotor is more than the pressure drop in the stator for the turbine. The same follows for a pump or compressor. From the relation for degree of reaction,|| α2 < β3 which is also shown in corresponding Figure 7.
Reaction = zero
This is special case used for impulse turbine which suggest that entire pressure drop in the turbine is obtained in the stator.
The stator performs a nozzle action converting pressure head to velocity head. It is difficult to achieve adiabatic expansion in the impulse stage, i.e. expansion only in the nozzle, due to irreversibility involved, in actual practice. Figure 8 shows the corresponding enthalpy drop for the reaction = 0 case.
References
Further reading and works referred to
Gopalakrishnan, G. and Prithvi Raj, D., A Treatise on Turbomachines, Scitech, Chennai, India, 2012
Shepherd, D.G., Principles of Turbomachinery, Ninth Printing, Macmillan, 1969
Wisclicenus, G.F., Fluid Mechanics of Turbomachinery, McGraw-Hill, New York, 1947
Thomson, W.R., Preliminary Design of Gas Turbines, Emmott and CO. Ltd., London, 1963
Traupel, W., Thermische Turbomachinen, 3rd Edn, Springer Verlag, Berlin, 1978
Ainley, D. G. and Mathieson, G. C. R. (1951). A method of performance estimation for axial flow turbines. ARC R. and M.
Dunham, J. and Panton, J. (1973). Experiments on the design of a small axial turbine. Conference Publication 3, Instn. Mech. Engrs.
Horlock, J. H. (1960). Losses and efficiencies in axial-flow turbines. Int. J. Mech. Sci.,
Kim, T. H., Takao, M., Setoguchi, T., Kaneko, K. and Inoue, M. (2001). Performance comparison of turbines for wave power conversion. Int. J. Therm. Sci.,
http://www.physicsforums.com/archive/index.php/t-243219.html
https://www.scribd.com/doc/55453233/18/Degree-of-reaction
Turbines
Steam turbines
Pumps
Gas compressors
Ventilation fans
Hydraulic engineering | Degree of reaction | [
"Physics",
"Chemistry",
"Engineering",
"Environmental_science"
] | 1,381 | [
"Pumps",
"Hydrology",
"Turbomachinery",
"Gas compressors",
"Turbines",
"Physical systems",
"Hydraulics",
"Civil engineering",
"Hydraulic engineering"
] |
5,195,676 | https://en.wikipedia.org/wiki/Ergun%20equation | The Ergun equation, derived by the Turkish chemical engineer Sabri Ergun in 1952, expresses the friction factor in a packed column as a function of the modified Reynolds number.
Equation
where:
is the modified Reynolds number,
is the packed bed friction factor,
is the pressure drop across the bed,
is the length of the bed (not the column),
is the equivalent spherical diameter of the packing,
is the density of fluid,
is the dynamic viscosity of the fluid,
is the superficial velocity (i.e. the velocity that the fluid would have through the empty tube at the same volumetric flow rate),
is the void fraction (porosity) of the bed, and
is the particle Reynolds Number (based on superficial velocity)..
Extension
To calculate the pressure drop in a given reactor, the following equation may be deduced:
This arrangement of the Ergun equation makes clear its close relationship to the simpler Kozeny-Carman equation, which describes laminar flow of fluids across packed beds via the first term on the right hand side. On the continuum level, the second-order velocity term demonstrates that the Ergun equation also includes the pressure drop due to inertia, as described by the Darcy–Forchheimer equation. Specifically, the Ergun equation gives the following permeability and inertial permeability from the Darcy-Forchheimer law:
and
The extension of the Ergun equation to fluidized beds, where the solid particles flow with the fluid, is discussed by Akgiray and Saatçı (2001).
See also
Hagen–Poiseuille equation
Kozeny–Carman equation
References
Ergun, Sabri. "Fluid flow through packed columns." Chem. Eng. Prog. 48 (1952).
Ö. Akgiray and A. M. Saatçı, Water Science and Technology: Water Supply, Vol:1, Issue:2, pp. 65–72, 2001.
Equations
Chemical process engineering
Fluid dynamics | Ergun equation | [
"Chemistry",
"Mathematics",
"Engineering"
] | 409 | [
"Chemical engineering",
"Mathematical objects",
"Equations",
"Piping",
"Chemical process engineering",
"Fluid dynamics"
] |
21,453,848 | https://en.wikipedia.org/wiki/Lipid%20bilayer%20characterization | Lipid bilayer characterization is the use of various optical, chemical and physical probing methods to study the properties of lipid bilayers. Many of these techniques are elaborate and require expensive equipment because the fundamental nature of the lipid bilayer makes it a very difficult structure to study. An individual bilayer, since it is only a few nanometers thick, is invisible in traditional light microscopy. The bilayer is also a relatively fragile structure since it is held together entirely by non-covalent bonds and is irreversibly destroyed if removed from water. In spite of these limitations dozens of techniques have been developed over the last seventy years to allow investigations of the structure and function of bilayers. The first general approach was to utilize non-destructive in situ measurements such as x-ray diffraction and electrical resistance which measured bilayer properties but did not actually image the bilayer. Later, protocols were developed to modify the bilayer and allow its direct visualization at first in the electron microscope and, more recently, with fluorescence microscopy. Over the past two decades, a new generation of characterization tools including AFM has allowed the direct probing and imaging of membranes in situ with little to no chemical or physical modification. More recently, dual polarisation interferometry has been used to measure the optical birefringence of lipid bilayers to characterise order and disruption associated with interactions or environmental effects.
Fluorescence Microscopy
Fluorescence microscopy is a technique whereby certain molecules can be excited with one wavelength of light and will emit another longer wavelength of light. Because each fluorescent molecule has a unique spectrum of absorption and emission, the location of particular types of molecules can be determined. Natural lipids do not fluoresce, so it is always necessary to include a dye molecule in order to study lipid bilayers with fluorescence microscopy. To some extent, the addition of the dye molecule always changes the system, and in some cases it can be difficult to say whether the observed effect is due to the lipids, the dye or, most commonly, some combination of the two. The dye is usually attached either to a lipid or a molecule that closely resembles a lipid, but since the dye domain is relatively large it can alter the behavior of this other molecule. This is a particularly contentious issue when studying the diffusion or phase separation of lipids, as both processes are very sensitive to the size and shape of the molecules involved.
This potential complication has been given an argument against the use of one of fluorescence recovery after photobleaching (FRAP) to determine bilayer diffusion coefficients. In a typical FRAP experiment a small (~30 μm diameter) area is photobleached by exposure to an intense light source. This area is then monitored over time as the “dead” dye molecules diffuse out and are replaced by intact dye molecules from the surrounding bilayer. By fitting this recovery curve it is possible to calculate the diffusion coefficient of the bilayer. An argument against the use of this technique is that what is actually being studied is the diffusion of the dye, not the lipid. While correct, this distinction is not always important, since the mobility of the dye is often dominated by the mobility of the bilayer.
In traditional fluorescence microscopy the resolution has been limited to approximately half the wavelength of the light used. Through the use of confocal microscopy and image processing this limit can be extended, but typically not much below 100 nanometers, which is much smaller than a typical cell but much larger than the thickness of a lipid bilayer. More recently, advanced microscopy methods have allowed much greater resolution under certain circumstances, even down to sub-nm. One of the first of these methods to be developed was Förster resonance energy transfer (FRET). In FRET, two dye molecules are chosen such that the emission spectrum of one overlaps the absorption spectrum of the other. This energy transfer is extremely distance dependent, so it is possible to tell with angstrom resolution how far apart the two dyes are. This can be used for instance to determine when two bilayers fuse and their components mix. Another high resolution microscopy technique is fluorescence interference contrast microscopy (FLIC). This method requires that the sample be mounted on a precisely micromachined reflective surface. By studying the destructive interference patterns formed it is possible to individually resolve the two leaflets of a supported bilayer and determine the distribution of a fluorescent dye in each.
Electrical
Electrical measurements are the most straightforward way to characterize one of the more important functions of a bilayer, namely its ability to segregate and prevent the flow of ions in solution. Accordingly, electrical characterization was one of the first tools used to study the properties of model systems such as black membranes. It was already known that the cell membrane was capable of supporting an ionic gradient and that this gradient is responsible for the ability of neurons to send signals via an action potential. Demonstrating that similar phenomena could be replicated in vitro was an important verification of the utility of model systems.
Fundamentally, all electrical measurements of bilayers involve the placement of an electrode on either side of the membrane. By applying a bias across these electrodes and measuring the resulting current, it is possible to determine the resistance of the bilayer. This resistance is typically quite high for intact bilayers, often exceeding 100 GΩ since the hydrophobic core is impermeable to charged hydrated species. Because this resistance is so large, the presence of even a few nanometer-scale holes results in a dramatic increase in current and can be easily determined. The sensitivity of this system is such that even the activity of single ion channels can be resolved. In such DC measurements, it is necessary to use electrochemically active electrodes to provide the necessary positive charges on one side and negative charges on the other. The most common system is the silver/silver chloride electrode since this reaction is stable, reversible, involves a single electron transfer and can produce large currents. In addition to simple DC current measurements it is also possible to perform AC electrical characterization to extract information about the capacitance and complex impedance of a bilayer. Because capacitance is inversely proportional to thickness and bilayers are very thin they typically have a very large capacitance, on the order of 2 μF/cm2. Capacitance measurements are particularly useful when dealing with black lipid membranes, as they can be used to determine when the solvent/lipid plug thins down to a single bilayer.
Optical
Lipids are highly polar molecules which when self assembled into bilayers creates a highly birefringent layer where the optical properties parallel are very different from those perpendicular. This effect, studied by dual polarisation interferometry has been used to measure dynamic reorganisation of the layer due to temperature, ionic strength, and molecular interactions with e.g. antimicrobial peptides.
Hydrated bilayers show rich vibrational dynamics and are good media for efficient vibrational energy transfer. Vibrational properties of lipid monolayers and bilayers has been investigated by ultrafast spectroscopic techniques and recently developed computational methods.
AFM
Atomic force microscopy (AFM) has been used in recent years to image and probe the physical properties of lipid bilayers. AFM is a promising technique because it has the potential to image with nanometer resolution at room temperature and even underwater, conditions necessary for natural bilayer behavior. These capabilities have allowed direct imaging of the subtle ripple phase transition in a supported bilayer. Another AFM experiment performed in a tapping mode under aqueous buffer medium allowed (1) to determine the formation of transmembrane pores (holes) around nanoparticles of approximately 1.2 to 22 nm diameter via subtraction of AFM images from series recorded during the lipid bilayer formation and (2) to observe adsorption of single insulin molecules onto exposed nanoparticles. Another advantage is that AFM does not require fluorescent or isotopic labeling of the lipids, as the probe tip interacts mechanically with the bilayer surface. Because of this, the same scan can reveal information about both the bilayer and any associated structures, even to the extent of resolving individual membrane proteins. In addition to imaging, AFM can also probe the mechanical nature of small delicate structures such as lipid bilayers. One study demonstrated the possibility of measuring the elastic modulus of individual nano-scale membranes suspended over porous anodic alumina.
Although AFM is a powerful and versatile tool for studying lipid bilayers, there are some practical limitations and difficulties. Because of the fragile nature of the bilayer, extremely low scanning forces (typically 50pN or less) must be used to avoid damage. This consideration is particularly important when studying metastable systems such as vesicles adsorbed on a substrate, since the AFM tip can induce rupture and other structural changes. Care must also be taken to choose an appropriate material and surface preparation for the AFM tip, as hydrophobic surfaces can interact strongly with lipids and disrupt the bilayer structure.
Electron microscopy
In electron microscopy a beam of focused electrons interacts with the sample rather than a beam of light as in traditional microscopy. Electrons have a much shorter wavelength than light so electron microscopy has much higher resolution than light microscopy, potentially down to the atomic scale. Because lipid bilayers are arranged on the molecular level, this higher resolution has been invaluable. In 1960, when the structure of the bilayer was still debated, it was electron microscopy that offered the first direct visualization of the two apposing leaflets. In conjunction with rapid freezing techniques, electron microscopy has also been used to study the mechanisms of inter- and intracellular transport, for instance in demonstrating that exocytotic vesicles are the means of chemical release at synapses. Often, electron microscopy is the only probe technique with sufficient resolution to determine complex nanometer-scale morphologies.
The limitations of electron microscopy in the study of lipid structures deal primarily with sample preparation. Most electron microscopes require the sample to be under vacuum, which is incompatible with hydration at room temperature. To surmount this problem, samples can be imaged under cryogenic conditions with the associated water frozen, or a metallic negative can be made from a frozen sample. It is also typically necessary to stain the bilayer with a heavy metal compound such as osmium tetroxide or uranyl acetate because the low atomic weight constituents of lipids (carbon, nitrogen, phosphorus, etc.) offer little contrast compared to water. If a Transmission electron microscope (TEM) is being used, it is also necessary to cut or polish the sample into a very thin (<1 micrometre) sheet, which can be difficult and time-consuming. Scanning Electron Microscopy (SEM) does not require this step, but cannot offer the same resolution as TEM. Both methods are surface-sensitive techniques and cannot reveal information about deeply buried structures.
Neutron and X-ray scattering
Both X-rays and high-energy neutrons are used to probe the structure and periodicity of biological structures including bilayers because they can be tuned to interact with matter at the relevant (angstrom-nm) length scales. Often, these two classes of experiment provide complementary information because each has different advantages and disadvantages. X-rays interact only weakly with water, so bulk samples can be probed with relatively easy sample preparation. This is one of the reasons that x-ray scattering was the technique first used to systematically study inter-bilayer spacing. X-ray scattering can also yield information on the average spacing between individual lipid molecules, which has led to its use in characterizing phase transitions. One limitation of x-ray techniques is that x-rays are relatively insensitive to light elements such as hydrogen. This effect is a consequence of the fact that x-rays interact with matter by scattering off of electron density which decreases with decreasing atomic number. In contrast, neutrons scatter off of nuclear density and nuclear magnetic fields so sensitivity does not decrease monotonically with z. This mechanism also provides strong isotopic contrast in some cases, notably between hydrogen and deuterium, allowing researchers to tune the experimental baseline by mixing water and deuterated water. Using reflectometry rather than scattering with neutrons or x-rays allow experimenters to probe supported bilayers or multilayer stacks. These measurements are more complicated to perform an analysis, but allow determination of cross sectional composition, including the location and concentration of water within the bilayer. In the case of both neutron and x-ray scattering measurements, the information provided is an ensemble average of the system and is therefore subject to uncertainty based on thermal fluctuations in these highly mobile structures.
References
Membrane biology | Lipid bilayer characterization | [
"Chemistry"
] | 2,625 | [
"Membrane biology",
"Molecular biology"
] |
21,457,419 | https://en.wikipedia.org/wiki/Bacterial%20cellular%20morphologies | Bacterial cellular morphologies are the shapes that are characteristic of various types of bacteria and often key to their identification. Their direct examination under a light microscope enables the classification of these bacteria (and archaea).
Generally, the basic morphologies are spheres (coccus) and round-ended cylinders or rod shaped (bacillus). But, there are also other morphologies such as helically twisted cylinders (example Spirochetes), cylinders curved in one plane (selenomonads) and unusual morphologies (the square, flat box-shaped cells of the Archaean genus Haloquadratum). Other arrangements include pairs, tetrads, clusters, chains and palisades.
Types
Coccus
A coccus (plural cocci, from the Latin coccinus (scarlet) and derived from the Greek kokkos (berry)), is any microorganism (usually bacteria) whose overall shape is spherical or nearly spherical. Coccus refers to the shape of the bacteria and can contain multiple genera, such as staphylococci or streptococci. Cocci can grow in pairs, chains, or clusters, depending on their orientation and attachment during cell division. In contrast to many bacilli-shaped bacteria, most cocci bacteria do not have flagella and are non-motile.
Cocci is an English loanword of a modern or Neo-Latin noun, which in turn stems from the Greek masculine noun () meaning 'berry'.
Important human diseases caused by coccoid bacteria include staphylococcal infections, some types of food poisoning, some urinary tract infections, toxic shock syndrome, gonorrhea, as well as some forms of meningitis, throat infections, pneumonias, and sinusitis.
Arrangements
Coccoid bacteria often occur in characteristic arrangements and these forms have specific names as well; listed here are the basic forms as well as representative bacterial genera:
Diplococci are pairs of cocci.
Streptococci are chains of cocci such as Streptococcus pyogenes.
Staphylococci are irregular (grape-like) clusters of cocci (e.g. Staphylococcus aureus).
Tetrads are clusters of four cocci arranged within the same plane such as Micrococcus sp.).
Sarcina describes a pack-like cuboidal arrangement of eight cocci such as Sarcina ventriculi.
Gram-positive cocci
The gram-positive cocci are a large group of bacteria with similar morphology. All are spherical or nearly so, but they vary considerably in size. Members of some genera are identifiable by the way cells are attached to one another: in pockets, in chains, or grape-like clusters. These arrangements reflect patterns of cell division and that cells stick together. Sarcina cells, for example, are arranged in cubical pockets because cell division alternates regularly among the three perpendicular planes. Streptococcus spp. resemble a string of beads because division always occurs in the same plane. Some of these strings, for example, S. pneumoniae, are only two cells long. They are called diplococci. Species of Staphylococcus have no regular plane of division. They form grape-like structures.
The various gram-positive cocci differ physiologically and by habitat. Micrococcus spp. are obligate aerobes that inhabit human skin. Staphylococcus spp. also inhabit human skin, but they are facultative anaerobes. They ferment sugars, producing lactic acid as an end product. Many of these species produce carotenoid pigments, which color their colonies yellow or orange. Staphylococcus aureus is a major human pathogen. It can infect almost any tissue in the body, frequently the skin. It often causes nosocomial (hospital-acquired) infections.
Diplococci
Diplococci are pairs of cocci. Examples of gram-negative diplococci are Neisseria spp. and Moraxella catarrhalis. Examples of gram-positive diplococci are Streptococcus pneumoniae and Enterococcus spp. Presumably, diplococcus has been implicated in encephalitis lethargica. The genus Neisseria belongs to the family Neisseriaceae. This genus, Neisseria, is divided into more than ten different species, but most of them are gram negative and coccoid. The gram-negative, coccoid species include: Neisseria cinerea, N. gonorrhoeae, N. polysaccharea, N. lactamica, N. meningitidis, N. mucosa, N. oralis and N. subflava. The most common of these species are the pathogenic N. meningitidis and N. gonorrhoeae.
The genus Moraxella belongs to the family Moraxellaceae. This genus, Moraxellaceae, comprises gram-negative coccobacilli bacteria: Moraxella lacunata, M. atlantae, M. boevrei, M. bovis, M. canis, M. caprae, M. caviae, M. cuniculi, M. equi, M. lincolnii, M. nonliquefaciens, M. osloensis, M. ovis, M. saccharolytica, and M. pluranimalium. However, only one has a morphology of diplococcus, M. catarrhalis, a salient pathogen contributing to infections in the human body.
The species Streptococcus pneumoniae belongs to the genus Streptococcus and the family Streptococcaceae. The genus Streptococcus has around 129 species and 23 subspecies that benefit many microbiomes on the human body. There are many species that show non-pathogenic characteristics; however, there are some, like S. pneumoniae, that exhibit pathogenic characteristics in the human body.
The genus Enterococcus belongs to the family Enterococcaceae. This genus is divided into 58 species and two subspecies. These gram-positive, coccoid bacteria were once thought to be harmless to the human body. However, within the last ten years, there has been an influx of nosocomial pathogens originating from Enterococcus bacteria.
Bacillus
A bacillus (: bacilli), also called a bacilliform bacterium or often just a rod (when the context makes the sense clear), is a rod-shaped bacterium or archaeon. Bacilli are found in many different taxonomic groups of bacteria. However, the name Bacillus, capitalized and italicized, refers to a specific genus of bacteria. The name Bacilli, capitalized but not italicized, can also refer to a less specific taxonomic group of bacteria that includes two orders, one of which contains the genus Bacillus. When the word is formatted with lowercase and not italicized, 'bacillus', it will most likely be referring to shape and not to the genus. Bacilliform bacteria are also often simply called rods when the bacteriologic context is clear.
Bacilli usually divide in the same plane and are solitary, but can combine to form diplobacilli, streptobacilli, and palisades.
Diplobacilli: Two bacilli arranged side by side with each other.
Streptobacilli: Bacilli arranged in chains.
Coccobacillus: Oval and similar to coccus (circular shaped bacterium).
There is no connection between the shape of a bacterium and its color upon Gram staining; there are both gram-positive rods and gram-negative rods. MacConkey agar can be used to distinguish among gram-negative bacilli such as E. coli and salmonella.
Arrangements
Bacilli usually divide in the same plane and are solitary, but can combine to form diplobacilli, streptobacilli, and palisades.
Diplobacilli: Two bacilli arranged side by side with each other.
Streptobacilli: Bacilli arranged in chains.
Gram-positive examples
Actinomyces
Bacillus
Clostridium
Corynebacterium
Listeria
Propionibacterium
Gram-negative examples
Bacteroides
Citrobacter
Enterobacter
Escherichia
Klebsiella
Pseudomonas
Proteus
Salmonella
Serratia
Shigella
Vibrio
Yersinia
Coccobacillus
A coccobacillus (plural coccobacilli), or bacillococcus, is a type of bacterium with a shape intermediate between cocci (spherical bacteria) and bacilli (rod-shaped bacteria). Coccobacilli, then, are very short rods which may be mistaken for cocci. The word coccobacillus reflects an intermediate shape between coccus (spherical) and bacillus (elongated).
Haemophilus influenzae, Gardnerella vaginalis, and Chlamydia trachomatis are coccobacilli. Aggregatibacter actinomycetemcomitans is a Gram-negative coccobacillus prevalent in subgingival plaques. Acinetobacter strains may grow on solid media as coccobacilli. Bordetella pertussis is a Gram-negative coccobacillus responsible for causing whooping cough. Yersinia pestis, the bacterium that causes plague, is also coccobacillus.
Coxiella burnetti is also a coccobacillus. Bacteria from the genus Brucella are medically important coccobacilli that cause brucellosis. Haemophilus ducreyi, another medically important Gram-negative coccobacillus, is observed in sexually transmitted disease, chancroid, of Third World countries.
Spiral
Spiral bacteria are another major bacterial cell morphology. Spiral bacteria can be sub-classified as spirilla, spirochetes, or vibrios based on the number of twists per cell, cell thickness, cell flexibility, and motility.
Bacteria are known to evolve specific traits to survive in their ideal environment. Bacteria-caused illnesses hinge on the bacteria's physiology and their ability to interact with their environment, including the ability to shapeshift. Researchers discovered a protein that allows the bacterium Vibrio cholerae to morph into a corkscrew shape that likely helps it twist into — and then escape — the protective mucus that lines the inside of the gut.
Spirillum
A spirillum (plural spirilla) is a rigid spiral bacterium that is gram-negative and frequently has external amphitrichous or lophotrichous flagella. Examples include:
Members of the genus Spirillum
Campylobacter species, such as Campylobacter jejuni, a foodborne pathogen that causes campylobacteriosis
Helicobacter species, such as Helicobacter pylori, a cause of peptic ulcers
Spirochetes
A spirochete (plural spirochetes) is a very thin, elongate, flexible, spiral bacteria that is motile via internal periplasmic flagella inside the outer membrane. They comprise the phylum Spirochaetes. Owing to their morphological properties, spirochetes are difficult to Gram-stain but may be visualized using dark field microscopy or Warthin–Starry stain. Examples include:
Leptospira species, which cause leptospirosis.
Borrelia species, such as Borrelia burgdorferi, a tick-borne bacterium that causes Lyme disease
Treponema species, such as Treponema pallidum, subspecies of which causes treponematoses, including syphilis
Helical
Helicobacter species are helically shaped, the most common example of which is Helicobacter pylori. A helical shape is seen to be better suited for movement of bacteria in a viscous medium.
See also
Bacterial morphological plasticity
Ferdinand Cohn – gave first named shapes of bacteria
References
External links
Bacteria Picture Gallery
Bacteria
Morphology (biology) | Bacterial cellular morphologies | [
"Biology"
] | 2,589 | [
"Prokaryotes",
"Microorganisms",
"Bacteria",
"Morphology (biology)"
] |
2,062,754 | https://en.wikipedia.org/wiki/Homothetic%20vector%20field | In physics, a homothetic vector field (sometimes homothetic collineation or homothety) is a projective vector field which satisfies the condition:
where c is a real constant. Homothetic vector fields find application in the study of singularities in general relativity. They can also be used to generate new solutions for Einstein equations by similarity reduction.
See also
Affine vector field
Conformal Killing vector field
Curvature collineation
Killing vector field
Matter collineation
Spacetime symmetries
References
Mathematical methods in general relativity | Homothetic vector field | [
"Physics"
] | 109 | [
"Relativity stubs",
"Theory of relativity"
] |
2,062,984 | https://en.wikipedia.org/wiki/Higher-dimensional%20Einstein%20gravity | Higher-dimensional Einstein gravity is any of various physical theories that attempt to generalise to higher dimensions various results of the well established theory of standard (four-dimensional) Albert Einstein's gravitational theory, that is, general relativity. This attempt at generalisation has been strongly influenced in recent decades by string theory.
At present, this work can probably be most fairly described as extended theoretical speculation. Currently, it has no direct observational and experimental support, in contrast to four-dimensional general relativity. However, this theoretical work has led to the possibility of proving the existence of extra dimensions. This is best demonstrated by the proof of Harvey Reall and Roberto Emparan that there is a 'black ring' solution in 5 dimensions. If such a 'black ring' could be produced in a particle accelerator such as the Large Hadron Collider, this would provide the evidence that higher dimensions exist.
Exact solutions
The higher-dimensional generalization of the Kerr metric was discovered by Robert Myers and Malcolm Perry. Like the Kerr metric, the Myers–Perry metric has spherical horizon topology. The construction involves making a Kerr–Schild ansatz; by a similar method, the solution has been generalized to include a cosmological constant. The black ring is a solution of five-dimensional general relativity. It inherits its name from the fact that its event horizon is topologically S1 × S2. This is in contrast to other known black hole solutions in five dimensions which have horizon topology S3.
In 2014, Hari Kunduri and James Lucietti proved the existence of a black hole with Lens space topology of the L(2, 1) type in five dimensions, this was next extended to all L(p, 1) with positive integers p by Shinya Tomizawa and Masato Nozawa in 2016 and finally in a preprint to all L(p, q) and any dimension by Marcus Khuri and Jordan Rainone in 2022, a black lens doesn't necessarily need to rotate as a black ring but all examples so far need a matter field coming from the extra dimensions to remain stable.
Black hole uniqueness
In four dimensions, Hawking proved that the topology of the event horizon of a non-rotating black hole must be spherical. Because the proof uses the Gauss–Bonnet theorem, it does not generalize to higher dimensions. The discovery of black ring solutions in five dimensions shows that other topologies are allowed in higher dimensions, but it is unclear precisely which topologies are allowed. It has been shown that the horizon must be of positive Yamabe type, meaning that it must admit a metric of positive scalar curvature.
See also
Gauss–Bonnet gravity
General relativity
Kaluza–Klein theory
Graviton
References
Theories of gravity
Albert Einstein
Exact solutions in general relativity | Higher-dimensional Einstein gravity | [
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2,063,011 | https://en.wikipedia.org/wiki/Love%20wave | In elastodynamics, Love waves, named after Augustus Edward Hough Love, are horizontally polarized surface waves. The Love wave is a result of the interference of many shear waves (S-waves) guided by an elastic layer, which is welded to an elastic half space on one side while bordering a vacuum on the other side. In seismology, Love waves (also known as Q waves (Quer: German for lateral)) are surface seismic waves that cause horizontal shifting of the Earth during an earthquake. Augustus Edward Hough Love predicted the existence of Love waves mathematically in 1911. They form a distinct class, different from other types of seismic waves, such as P-waves and S-waves (both body waves), or Rayleigh waves (another type of surface wave). Love waves travel with a lower velocity than P- or S- waves, but faster than Rayleigh waves. These waves are observed only when there is a low velocity layer overlying a high velocity layer/sub–layers.
Description
The particle motion of a Love wave forms a horizontal line, perpendicular to the direction of propagation (i.e. are transverse waves). Moving deeper into the material, motion can decrease to a "node" and then alternately increase and decrease as one examines deeper layers of particles. The amplitude, or maximum particle motion, often decreases rapidly with depth.
Since Love waves travel on the Earth's surface, the strength (or amplitude) of the waves decrease exponentially with the depth of an earthquake. However, given their confinement to the surface, their amplitude decays only as , where represents the distance the wave has travelled from the earthquake. Surface waves therefore decay more slowly with distance than do body waves, which travel in three dimensions. Large earthquakes may generate Love waves that travel around the Earth several times before dissipating.
Since they decay so slowly, Love waves are the most destructive outside the immediate area of the focus or epicentre of an earthquake. They are what most people feel directly during an earthquake.
In the past, it was often thought that animals like cats and dogs could predict an earthquake before it happened. However, they are simply more sensitive to ground vibrations than humans and are able to detect the subtler body waves that precede Love waves, like the P-waves and the S-waves.
Basic theory
The conservation of linear momentum of a linear elastic material can be written as
where is the displacement vector and is the stiffness tensor. Love waves are a special solution () that satisfy this system of equations. We typically use a Cartesian coordinate system () to describe Love waves.
Consider an isotropic linear elastic medium in which the elastic properties are functions of only the coordinate, i.e., the Lamé parameters and the mass density can be expressed as . Displacements produced by Love waves as a function of time () have the form
These are therefore antiplane shear waves perpendicular to the plane. The function can be expressed as the superposition of harmonic waves with varying wave numbers () and frequencies (). Consider a single harmonic wave, i.e.,
where is the imaginary unit, i.e. . The stresses caused by these displacements are
If we substitute the assumed displacements into the equations for the conservation of momentum, we get a simplified equation
The boundary conditions for a Love wave are that the surface tractions at the free surface must be zero. Another requirement is that the stress component in a layer medium must be continuous at the interfaces of the layers. To convert the second order differential equation in into two first order equations, we express this stress component in the form
to get the first order conservation of momentum equations
The above equations describe an eigenvalue problem whose solution eigenfunctions can be found by a number of numerical methods. Another common, and powerful, approach is the propagator matrix method (also called the matricant approach).
See also
Longitudinal wave
Antiplane shear
References
A. E. H. Love, "Some problems of geodynamics", first published in 1911 by the Cambridge University Press and published again in 1967 by Dover, New York, USA. (Chapter 11: Theory of the propagation of seismic waves)
Geophysics
Surface waves
Seismology | Love wave | [
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"Surface waves",
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"Geophysics"
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2,063,517 | https://en.wikipedia.org/wiki/Plate-fin%20heat%20exchanger | A plate-fin heat exchanger is a type of heat exchanger design that uses plates and finned chambers to transfer heat between fluids, most commonly gases. It is often categorized as a compact heat exchanger to emphasize its relatively high heat transfer surface area to volume ratio.
The plate-fin heat exchanger is widely used in many industries, including the aerospace industry for its compact size and lightweight properties, as well as in cryogenics where its ability to facilitate heat transfer with small temperature differences is utilized.
Aluminum alloy plate-fin heat exchangers, often referred to as Brazed Aluminum Heat Exchangers, have been used in the aircraft industry for more than 75 years and adopted into the cryogenic air separation industry around the time of the second world war and shortly afterward into cryogenic processes in chemical plants such as Natural Gas Processing. They are also used in railway engines and motor cars. Stainless steel plate fins have been used in aircraft for over 35 years and are now becoming established in chemical plants.
Design of plate-fin heat exchangers
Originally conceived by an Italian mechanic, Paolo Fruncillo. A plate-fin heat exchanger is made of layers of corrugated sheets separated by flat metal plates, typically aluminium, to create a series of finned chambers. Separate hot and cold fluid streams flow through alternating layers of the heat exchanger and are enclosed at the edges by side bars. Heat is transferred from one stream through the fin interface to the separator plate and through the next set of fins into the adjacent fluid. The fins also serve to increase the structural integrity of the heat exchanger and allow it to withstand high pressures while providing an extended surface area for heat transfer.
A high degree of flexibility is present in plate-fin heat exchanger design as they can operate with any combination of gas, liquid, and two-phase fluids. Heat transfer between multiple process streams is also accommodated, with a variety of fin heights and types as different entry and exit points available for each stream.
The main four type of fins are: plain, which refer to simple straight-finned triangular or rectangular designs; herringbone, where the fins are placed sideways to provide a zig-zag path; and serrated and perforated which refer to cuts and perforations in the fins to augment flow distribution and improve heat transfer.
A disadvantage of plate-fin heat exchangers is that they are prone to fouling due to their small flow channels. They also cannot be mechanically cleaned and require other cleaning procedures and proper filtration for operation with potentially-fouling streams.
Flow arrangement
Various heat exchanger flow arrangements exist, such as parallel flow, cross-flow, and counterflow. In parallel flow, fluids enter the heat exchanger through their tubes, and the fluids flow in the same direction. In counterflow, the fluids flow in opposing directions. Counterflow provides the most efficient transfer of heat, as it is able to transfer the most heat from the heat transfer medium. Cross-flow has fluids travel perpendicular to one another through a heat exchanger. Exchangers may also employ corrugations or fins to alter their heat transfer rates through directing fluids to certain parts of heat exchangers, or increasing wall surface area.
Increasing the efficiency of heat exchangers can also be done through increasing the surface area of the wall between the two fluids. By providing more contact points for heat transfer to occur, the rate of transfer is increased. This method can be observed in household radiators which maintain a curvy, sinusoidal cross section to maximize surface contact between the heated water inside and the air of a room.
In a plate-fin heat exchanger, the fins are easily able to be rearranged. This allows for the two fluids to result in crossflow, counterflow, cross-counterflow or parallel flow. If the fins are designed well, the plate-fin heat exchanger can work in perfect countercurrent arrangement.
Cost
The cost of plate-fin heat exchangers is generally higher than conventional heat exchangers due to a higher level of detail required during manufacture. However, these costs can often be outweighed by the cost saving produced by the added heat transfer.
Plate-fin heat exchangers are generally applied in industries where the fluids have little chances of fouling. The delicate design as well as the thin channels in the plate-fin heat exchanger make cleaning difficult or impossible.
Applications of plate-fin heat exchangers include:
Natural gas liquefaction
Cryogenic air separation
Ammonia production
Offshore processing
Nuclear engineering
Syngas production
Aircraft cooling of bleed air and cabin air
See also
Plate heat exchanger
Shell and tube heat exchanger
Heat transfer
LMTD
NTU method
References
Coulson, J. and Richardson, J (1999). Chemical Engineering- Fluid Flow. Heat Transfer and Mass Transfer- Volume 1; Reed Educational & Professional Publishing LTD
Heat exchangers
Industrial gases
pt:Trocador de energia térmica#Trocador de calor de placas aletadas | Plate-fin heat exchanger | [
"Chemistry",
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] | 1,016 | [
"Chemical process engineering",
"Chemical equipment",
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2,063,558 | https://en.wikipedia.org/wiki/Symplectic%20integrator | In mathematics, a symplectic integrator (SI) is a numerical integration scheme for Hamiltonian systems. Symplectic integrators form the subclass of geometric integrators which, by definition, are canonical transformations. They are widely used in nonlinear dynamics, molecular dynamics, discrete element methods, accelerator physics, plasma physics, quantum physics, and celestial mechanics.
Introduction
Symplectic integrators are designed for the numerical solution of Hamilton's equations, which read
and ,
where denotes the position coordinates, the momentum coordinates, and is the Hamiltonian.
The set of position and momentum coordinates are called canonical coordinates.
(See Hamiltonian mechanics for more background.)
The time evolution of Hamilton's equations is a symplectomorphism, meaning that it conserves the symplectic 2-form . A numerical scheme is a symplectic integrator if it also conserves this 2-form.
Symplectic integrators possess, as a conserved quantity, a Hamiltonian which is slightly perturbed from the original one. By virtue of these advantages, the SI scheme has been widely applied to the calculations of long-term evolution of chaotic Hamiltonian systems ranging from the Kepler problem to the classical and semi-classical simulations in molecular dynamics.
Most of the usual numerical methods, such as the primitive Euler scheme and the classical Runge–Kutta scheme, are not symplectic integrators.
Methods for constructing symplectic algorithms
Splitting methods for separable Hamiltonians
A widely used class of symplectic integrators is formed by the splitting methods.
Assume that the Hamiltonian is separable, meaning that it can be written in the form
This happens frequently in Hamiltonian mechanics, with T being the kinetic energy and V the potential energy.
For the notational simplicity, let us introduce the symbol to denote the canonical coordinates including both the position and momentum coordinates. Then, the set of the Hamilton's equations given in the introduction can be expressed in a single expression as
where is a Poisson bracket. Furthermore, by introducing an operator , which returns a Poisson bracket of the operand with the Hamiltonian, the expression of the Hamilton's equation can be further simplified to
The formal solution of this set of equations is given as a matrix exponential:
Note the positivity of in the matrix exponential.
When the Hamiltonian has the form of equation (), the solution () is equivalent to
The SI scheme approximates the time-evolution operator in the formal solution () by a product of operators as
where and are real numbers, is an integer, which is called the order of the integrator, and where . Note that each of the operators and provides a symplectic map, so their product appearing in the right-hand side of () also constitutes a symplectic map.
Since for all , we can conclude that
By using a Taylor series, can be expressed as
where is an arbitrary real number. Combining () and (), and by using the same reasoning for as we have used for , we get
In concrete terms, gives the mapping
and gives
Note that both of these maps are practically computable.
Examples
The simplified form of the equations (in executed order) are:
Note that due to the definitions adopted above (in the operator version of the explanation), the index is traversed in decreasing order when going through the steps ( for a fourth-order scheme).
After converting into Lagrangian coordinates:
Where is the force vector at , is the acceleration vector at , and is the scalar quantity of mass.
Several symplectic integrators are given below. An illustrative way to use them is to consider a particle with position and momentum .
To apply a time step with values to the particle, carry out the following steps (again, as noted above, with the index in decreasing order):
Iteratively:
Update the position of the particle by adding to it its (previously updated) velocity multiplied by
Update the velocity of the particle by adding to it its acceleration (at updated position) multiplied by
A first-order example
The symplectic Euler method is the first-order integrator with and coefficients
Note that the algorithm above does not work if time-reversibility is needed. The algorithm has to be implemented in two parts, one for positive time steps, one for negative time steps.
A second-order example
The Verlet method is the second-order integrator with and coefficients
Since , the algorithm above is symmetric in time. There are 3 steps to the algorithm, and step 1 and 3 are exactly the same, so the positive time version can be used for negative time.
A third-order example
A third-order symplectic integrator (with ) was discovered by Ronald Ruth in 1983.
One of the many solutions is given by
A fourth-order example
A fourth-order integrator (with ) was also discovered by Ruth in 1983 and distributed privately to the particle-accelerator community at that time. This was described in a lively review article by Forest.
This fourth-order integrator was published in 1990 by Forest and Ruth and also independently discovered by two other groups around that same time.
To determine these coefficients, the Baker–Campbell–Hausdorff formula can be used. Yoshida, in particular, gives an elegant derivation of coefficients for higher-order integrators. Later on, Blanes and Moan further developed partitioned Runge–Kutta methods for the integration of systems with separable Hamiltonians with very small error constants.
Splitting methods for general nonseparable Hamiltonians
General nonseparable Hamiltonians can also be explicitly and symplectically integrated.
To do so, Tao introduced a restraint that binds two copies of phase space together to enable an explicit splitting of such systems.
The idea is, instead of , one simulates , whose solution agrees with that of in the sense that , .
The new Hamiltonian is advantageous for explicit symplectic integration, because it can be split into the sum of three sub-Hamiltonians, , , and . Exact solutions of all three sub-Hamiltonians can be explicitly obtained: both solutions correspond to shifts of mismatched position and momentum, and corresponds to a linear transformation. To symplectically simulate the system, one simply composes these solution maps.
Applications
In plasma physics
In recent decades symplectic integrator in plasma physics has become an active research topic, because straightforward applications of the standard symplectic methods do not suit the need of large-scale plasma simulations enabled by the peta- to exa-scale computing hardware. Special symplectic algorithms need to be customarily designed, tapping into the special structures of the physics problem under investigation. One such example is the charged particle dynamics in an electromagnetic field. With the canonical symplectic structure, the Hamiltonian of the dynamics is whose -dependence and -dependence are not separable, and standard explicit symplectic methods do not apply. For large-scale simulations on massively parallel clusters, however, explicit methods are preferred.
To overcome this difficulty, we can explore the specific way that the -dependence and -dependence are entangled in this Hamiltonian, and try to design a symplectic algorithm just for this or this type of problem. First, we note that the -dependence is quadratic, therefore the first order symplectic Euler method implicit in is actually explicit. This is what is used in the canonical symplectic particle-in-cell (PIC) algorithm. To build high order explicit methods, we further note that the -dependence and -dependence in this are product-separable, 2nd and 3rd order explicit symplectic algorithms can be constructed using generating functions, and arbitrarily high-order explicit symplectic integrators for time-dependent electromagnetic fields can also be constructed using Runge-Kutta techniques.
A more elegant and versatile alternative is to look at the following non-canonical symplectic structure of the problem, Here is a non-constant non-canonical symplectic form. General symplectic integrator for non-constant non-canonical symplectic structure, explicit or implicit, is not known to exist. However, for this specific problem, a family of high-order explicit non-canonical symplectic integrators can be constructed using the He splitting method. Splitting into 4 parts, we find serendipitously that for each subsystem, e.g., and the solution map can be written down explicitly and calculated exactly. Then explicit high-order non-canonical symplectic algorithms can be constructed using different compositions. Let and denote the exact solution maps for the 4 subsystems. A 1st-order symplectic scheme is A symmetric 2nd-order symplectic scheme is, which is a customarily modified Strang splitting. A -th order scheme can be constructed from a -th order scheme using the method of triple jump, The He splitting method is one of key techniques used in the structure-preserving geometric particle-in-cell (PIC) algorithms.
See also
Energy drift
Multisymplectic integrator
Variational integrator
Verlet integration
References
Numerical differential equations
Hamiltonian mechanics | Symplectic integrator | [
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2,063,672 | https://en.wikipedia.org/wiki/Thermodynamic%20beta | In statistical thermodynamics, thermodynamic beta, also known as coldness, is the reciprocal of the thermodynamic temperature of a system: (where is the temperature and is Boltzmann constant).
Thermodynamic beta has units reciprocal to that of energy (in SI units, reciprocal joules, ). In non-thermal units, it can also be measured in byte per joule, or more conveniently, gigabyte per nanojoule; 1 K−1 is equivalent to about 13,062 gigabytes per nanojoule; at room temperature: = 300K, β ≈ ≈ ≈ . The conversion factor is 1 GB/nJ = J−1.
Description
Thermodynamic beta is essentially the connection between the information theory and statistical mechanics interpretation of a physical system through its entropy and the thermodynamics associated with its energy. It expresses the response of entropy to an increase in energy. If a small amount of energy is added to the system, then β describes the amount the system will randomize.
Via the statistical definition of temperature as a function of entropy, the coldness function can be calculated in the microcanonical ensemble from the formula
(i.e., the partial derivative of the entropy with respect to the energy at constant volume and particle number ).
Advantages
Though completely equivalent in conceptual content to temperature, is generally considered a more fundamental quantity than temperature owing to the phenomenon of negative temperature, in which is continuous as it crosses zero whereas has a singularity.
In addition, has the advantage of being easier to understand causally: If a small amount of heat is added to a system, is the increase in entropy divided by the increase in heat. Temperature is difficult to interpret in the same sense, as it is not possible to "Add entropy" to a system except indirectly, by modifying other quantities such as temperature, volume, or number of particles.
Statistical interpretation
From the statistical point of view, β is a numerical quantity relating two macroscopic systems in equilibrium. The exact formulation is as follows. Consider two systems, 1 and 2, in thermal contact, with respective energies E1 and E2. We assume E1 + E2 = some constant E. The number of microstates of each system will be denoted by Ω1 and Ω2. Under our assumptions Ωi depends only on Ei. We also assume that any microstate of system 1 consistent with E1 can coexist with any microstate of system 2 consistent with E2. Thus, the number of microstates for the combined system is
We will derive β from the fundamental assumption of statistical mechanics:
When the combined system reaches equilibrium, the number Ω is maximized.
(In other words, the system naturally seeks the maximum number of microstates.) Therefore, at equilibrium,
But E1 + E2 = E implies
So
i.e.
The above relation motivates a definition of β:
Connection of statistical view with thermodynamic view
When two systems are in equilibrium, they have the same thermodynamic temperature T. Thus intuitively, one would expect β (as defined via microstates) to be related to T in some way. This link is provided by Boltzmann's fundamental assumption written as
where kB is the Boltzmann constant, S is the classical thermodynamic entropy, and Ω is the number of microstates. So
Substituting into the definition of β from the statistical definition above gives
Comparing with thermodynamic formula
we have
where is called the fundamental temperature of the system, and has units of energy.
History
The thermodynamic beta was originally introduced in 1971 (as "coldness function") by , one of the proponents of the rational thermodynamics school of thought, based on earlier proposals for a "reciprocal temperature" function.
See also
Boltzmann distribution
Canonical ensemble
Ising model
References
Statistical mechanics
Scalar physical quantities | Thermodynamic beta | [
"Physics",
"Mathematics"
] | 814 | [
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2,065,799 | https://en.wikipedia.org/wiki/Biopesticide | A Biopesticide is a biological substance or organism that damages, kills, or repels organisms seens as pests. Biological pest management intervention involves predatory, parasitic, or chemical relationships.
They are obtained from organisms including plants, bacteria and other microbes, fungi, nematodes, etc. They are components of integrated pest management (IPM) programmes, and have received much practical attention as substitutes to synthetic chemical plant protection products (PPPs).
Definitions
Regulatory positions can be influenced by public perceptions, thus:
the EU, defines biopesticides as "a form of pesticide based on micro-organisms or natural products".
the US EPA states that they "include naturally occurring substances that control pests (biochemical pesticides), microorganisms that control pests (microbial pesticides), and pesticidal substances produced by plants containing added genetic material (plant-incorporated protectants) or PIPs".
Types
Biopesticides usually have no known function in photosynthesis, growth or other basic aspects of plant physiology. Many chemical compounds produced by plants protect them from pests; they are called antifeedants. These materials are biodegradable and renewable, which can be economical for practical use. Organic farming systems embraces this approach to pest control.
Biopesticides can be classified thusly:
Microbial pesticides consist of bacteria, entomopathogenic fungi or viruses (and sometimes includes the metabolites that bacteria or fungi produce). Entomopathogenic nematodes may be classed as microbial pesticides, even though they are multicellular.
Bio-derived chemicals. Four groups are in commercial use: pyrethrum, rotenone, neem oil, and various essential oils are naturally occurring substances that control (or monitor in the case of pheromones) pests and microbial disease.
Plant-incorporated protectants (PIPs) incorporate genetic material from other species (i.e. GM crops). Their use is controversial, especially in European countries.
RNAi pesticides, some of which are topical and some of which are absorbed by the crop.
RNA interference
RNA interference is under study for use in spray-on insecticides (RNAi insecticides) by companies including Syngenta and Bayer. Such sprays do not modify the genome of the target plant. The RNA can be modified to maintain its effectiveness as target species evolve to tolerate the original. RNA is a relatively fragile molecule that generally degrades within days or weeks of application. Monsanto estimated costs to be on the order of $5/acre.
RNAi has been used to target weeds that tolerate Roundup. RNAi can be mixed with a silicone surfactant that lets the RNA molecules enter air-exchange holes in the plant's surface. This disrupted the gene for tolerance long enough to let the herbicide work. This strategy would allow the continued use of glyphosate-based herbicides.
They can be made with enough precision to target specific insect species. Monsanto is developing an RNA spray to kill Colorado potato beetles. One challenge is to make it stay on the plant for a week, even if it's raining. The potato beetle has become resistant to more than 60 conventional insecticides.
Monsanto lobbied the U.S. EPA to exempt RNAi pesticide products from any specific regulations (beyond those that apply to all pesticides) and be exempted from rodent toxicity, allergenicity and residual environmental testing. In 2014 an EPA advisory group found little evidence of a risk to people from eating RNA.
However, in 2012, the Australian Safe Food Foundation claimed that the RNA trigger designed to change the starch content of wheat might interfere with the gene for a human liver enzyme. Supporters countered that RNA does not appear to survive human saliva or stomach acids. The US National Honey Bee Advisory Board told EPA that using RNAi would put natural systems at "the epitome of risk". The beekeepers cautioned that pollinators could be hurt by unintended effects and that the genomes of many insects are still undetermined. Other unassessed risks include ecological (given the need for sustained presence for herbicides) and possible RNA drift across species boundaries.
Monsanto invested in multiple companies for their RNA expertise, including Beeologics (for RNA that kills a parasitic mite that infests hives and for manufacturing technology) and Preceres (nanoparticle lipidoid coatings) and licensed technology from Alnylam and Tekmira. In 2012 Syngenta acquired Devgen, a European RNA partner. Startup Forest Innovations is investigating RNAi as a solution to citrus greening disease that in 2014 caused 22 percent of oranges in Florida to fall off the trees.
Mycopesticide
Mycopesticides include fungi and fungi cell components. Propagules such as conidia, blastospores, chlamydospores, oospores, and zygospores have been evaluated, along with hydrolytic enzyme mixtures. The role of hydrolytic enzymes especially chitinases in the killing process, and the possible use of chitin synthesis inhibitors are the prime research areas.
Examples
Bacillus thuringiensis is a bacterium capable of causing disease of Lepidoptera, Coleoptera and Diptera. The toxin from B. thuringiensis (Bt toxin) has been incorporated directly into plants via genetic engineering. Bt toxin manufacturers claim it has little effect on other organisms, and is more environmentally friendly than synthetic pesticides.
Other microbial control agents include products based on:
entomopathogenic fungi (e.g. Beauveria bassiana, Isaria fumosorosea, Lecanicillium and Metarhizium spp.),
plant disease control agents: include Trichoderma spp. and Ampelomyces quisqualis (a hyperparasite of grape powdery mildew); Bacillus subtilis is also used to control plant pathogens.
beneficial nematodes attacking insects (e.g. Steinernema feltiae) or slugs (e.g. Phasmarhabditis hermaphrodita)
entomopathogenic viruses (e.g.. Cydia pomonella granulovirus).
weeds and rodents have been controlled with microbial agents.
Various animal, fungal, and plant organisms and extracts have been used as biopesticides. Products in this category include:
Insect pheromones and other semiochemicals
Fermentation products such as Spinosad (a macrocyclic lactone)
Chitosan: a plant in the presence of this product naturally induces systemic resistance (ISR) to allow the plant to defend itself against disease, pathogens and pests.
Biopesticides may include natural plant-derived products, which include alkaloids, terpenoids, phenolics and other secondary chemicals. Vegetable oils such as canola oil have pesticidal properties. Products based on plant extracts such as garlic have now been registered in the EU and elsewhere.
Applications
Microbial agents, effective control requires appropriate formulation and application.
Biopesticides have established themselves on a variety of crops for use against crop disease. For example, biopesticides help control downy mildew diseases. Their benefits include: a 0-day pre-harvest interval (see: maximum residue limit), success under moderate to severe disease pressure, and the ability to use as a tank mix or in a rotational program with other fungicides. Because some market studies estimate that as much as 20% of global fungicide sales are directed at downy mildew diseases, the integration of biofungicides into grape production has substantial benefits by extending the useful life of other fungicides, especially those in the reduced-risk category.
A major growth area for biopesticides is in the area of seed treatments and soil amendments. Fungicidal and biofungicidal seed treatments are used to control soil-borne fungal pathogens that cause seed rot, damping-off, root rot and seedling blights. They can also be used to control internal seed-borne fungal pathogens as well as fungal pathogens on the seed surface. Many biofungicidal products show capacities to stimulate plant host defense and other physiological processes that can make treated crops more resistant to stresses.
Disadvantages
High specificity: which may require an exact identification of the pest/pathogen and the use of multiple products used; although this can also be an advantage in that the biopesticide is less likely to harm non-target species
Slow action speed (thus making them unsuitable if a pest outbreak is an immediate threat)
Variable efficacy due to the influences of various factors (since some biopesticides are living organisms, which bring about pest/pathogen control by multiplying within or nearby the target pest/pathogen)
Living organisms evolve and increase their tolerance to control. If the target population is not exterminated or rendered incapable of reproduction, the surviving population can acquire tolerance of whatever pressures are brought to bear, resulting in an evolutionary arms race.
Unintended consequences: Studies have found broad spectrum biopesticides have lethal and nonlethal risks for non-target native pollinators such as Melipona quadrifasciata in Brazil.
Market research
The market for agricultural biologicals was forecast to reach $19.5 billion by 2031.
See also
Antagonism (phytopathology)
Bioherbicide
Biological pest control
Cembratrienol
Integrated Pest Management
LUBILOSA
Pest resistance management plans
Plant defense against herbivory
Use as a population control agent
References
External links
Bioinsecticides Market (Acquire Market Research)
Registered Biopesticides 04/29/02 United States Environmental Protection Agency. Updated 29 March 2002. Retrieved 25 November 2011.
International Biocontrol Manufacturers' Association (IBMA)
Biotechnology
Biological pest control | Biopesticide | [
"Biology"
] | 2,037 | [
"nan",
"Biotechnology"
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2,065,830 | https://en.wikipedia.org/wiki/Inverse%20photoemission%20spectroscopy | Inverse photoemission spectroscopy (IPES) is a surface science technique used to study the unoccupied electronic structure of surfaces, thin films, and adsorbates. A well-collimated beam of electrons of a well defined energy (< 20 eV) is directed at the sample. These electrons couple to high-lying unoccupied electronic states and decay to low-lying unoccupied states, with a subset of these transitions being radiative. The photons emitted in the decay process are detected and an energy spectrum, photon counts vs. incident electron energy, is generated. Due to the low energy of the incident electrons, their penetration depth is only a few atomic layers, making inverse photoemission a particularly surface sensitive technique. As inverse photoemission probes the electronic states above the Fermi level of the system, it is a complementary technique to photoemission spectroscopy.
Theory
The energy of photons (, where is the Planck constant) emitted when electrons incident on a substance using an electron beam with a constant energy () relax to a lower energy unoccupied state () is given by the conservation of energy as:
By measuring and , the unoccupied state () of the surface can be found.
Modes
Two modes can be used for this measurement. One is the isochromat mode, which scans the incident electron energy and keeps the detected photon energy constant. The other is the tunable photon energy mode, or spectrograph mode, which keeps the incident electron energy constant and measures the distribution of the detected photon energy. The latter can also measure the resonant inverse photoemission spectroscopy.
Isochromat mode
In isochromat mode, the incident electron energy is ramped and the emitted photons are detected at a fixed energy that is determined by the photon detector. Typically, an I2 gas filled Geiger-Müller tube with an entrance window of either SrF2 or CaF2 is used as the photon detector. The combination of window and filling gas determines the detected photon energy, and for I2 gas and either a SrF2 or CaF2 window, the photons energies are ~ 9.5 eV and ~ 9.7 eV, respectively.
Spectrograph mode
In spectrograph mode, the energy of the incident electron remains fixed and a grating spectrometer is used to the detect the emitted photons over a range of photon energies. A diffraction grating is used to disperse the emitted photons that are in turn detected with a two-dimensional position sensitive detector.
Comparison of modes
One advantage of spectrograph mode is the ability to acquire IPES spectra over a wide range of photon energies simultaneously. Additionally, the incident electron energy remains fixed which allows better focusing of the electron beam on the sample. Furthermore, by changing the incident electron energy the electronic structure can be studied in great detail. Although the grating spectrometer is very stable over time, the set-up can be very complex and its maintenance can be very expensive. The advantages of isochromat mode are its low cost, simple design and higher count rates.
See also
X-ray photoelectron spectroscopy
Photoelectric effect
References
Further reading
Emission spectroscopy
Surface science
Electron spectroscopy | Inverse photoemission spectroscopy | [
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"Materials_science"
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"Electron spectroscopy",
"Emission spectroscopy",
"Surface science",
"Condensed matter physics",
"Spectroscopy"
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2,066,262 | https://en.wikipedia.org/wiki/Multi-configurational%20self-consistent%20field | Multi-configurational self-consistent field (MCSCF) is a method in quantum chemistry used to generate qualitatively correct reference states of molecules in cases where Hartree–Fock and density functional theory are not adequate (e.g., for molecular ground states which are quasi-degenerate with low-lying excited states or in bond-breaking situations). It uses a linear combination of configuration state functions (CSF), or configuration determinants, to approximate the exact electronic wavefunction of an atom or molecule. In an MCSCF calculation, the set of coefficients of both the CSFs or determinants and the basis functions in the molecular orbitals are varied to obtain the total electronic wavefunction with the lowest possible energy. This method can be considered a combination between configuration interaction (where the molecular orbitals are not varied but the expansion of the wave function is) and Hartree–Fock (where there is only one determinant, but the molecular orbitals are varied).
MCSCF wave functions are often used as reference states for multireference configuration interaction (MRCI) or multi-reference perturbation theories like complete active space perturbation theory (CASPT2). These methods can deal with extremely complex chemical situations and, if computing power permits, may be used to reliably calculate molecular ground and excited states if all other methods fail.
Introduction
For the simplest single bond, found in the H2 molecule, molecular orbitals can always be written in terms of two functions χiA and χiB (which are atomic orbitals with small corrections) located at the two nuclei A and B:
where Ni is a normalization constant. The ground-state wavefunction for H2 at the equilibrium geometry is dominated by the configuration (φ1)2, which means that the molecular orbital φ1 is nearly doubly occupied. The Hartree–Fock (HF) model assumes that it is doubly occupied, which leads to a total wavefunction
where is the singlet (S = 0) spin function for two electrons. The molecular orbitals in this case φ1 are taken as sums of 1s atomic orbitals on both atoms, namely N1(1sA + 1sB). Expanding the above equation into atomic orbitals yields
This Hartree–Fock model gives a reasonable description of H2 around the equilibrium geometry about 0.735 Å for the bond length (compared to a 0.746 Å experimental value) and 350 kJ/mol (84 kcal/mol) for the bond energy (experimentally, 432 kJ/mol (103 kcal/mol)). This is typical for the HF model, which usually describes closed-shell systems around their equilibrium geometry quite well. At large separations, however, the terms describing both electrons located at one atom remain, which corresponds to dissociation to H+ + H−, which has a much larger energy than H· + H· (two hydrogen radicals). Therefore, the persisting presence of ionic terms leads to an unphysical solution in this case.
Consequently, the HF model cannot be used to describe dissociation processes with open-shell products. The most straightforward solution to this problem is introducing coefficients in front of the different terms in Ψ1:
which forms the basis for the valence bond description of chemical bonds. With the coefficients Cion and Ccov varying, the wave function will have the correct form, with Cion = 0 for the separated limit, and Cion comparable to Ccov at equilibrium. Such a description, however, uses non-orthogonal basis functions, which complicates its mathematical structure. Instead, multiconfiguration is achieved by using orthogonal molecular orbitals. After introducing an anti-bonding orbital
the total wave function of H2 can be written as a linear combination of configurations built from bonding and anti-bonding orbitals:
where Φ2 is the electronic configuration (φ2)2. In this multiconfigurational description of the H2 chemical bond, C1 = 1 and C2 = 0 close to equilibrium, and C1 will be comparable to C2 for large separations.
Complete active space SCF
A particularly important MCSCF approach is the complete active space SCF method (CASSCF), where the linear combination of CSFs includes all that arise from a particular number of electrons in a particular number of orbitals (also known as full-optimized reaction space (FORS-MCSCF)). For example, one might define CASSCF(11,8) for NO, where the 11 valence electrons are distributed between all configurations that can be constructed from 8 molecular orbitals.
Restricted active space SCF
Since the number of CSFs quickly increases with the number of active orbitals, along with the computational cost, it may be desirable to use a smaller set of CSFs. One way to make this selection is to restrict the number of electrons in certain subspaces, done in the restricted active space SCF method (RASSCF). One could, for instance, allow only single and double excitations from some strongly occupied subset of active orbitals, or restrict the number of electrons to at most 2 in another subset of active orbitals.
See also
Charlotte Froese Fischer
Douglas Hartree
Vladimir Fock
Yakov Frenkel
Hartree–Fock method
Quantum chemistry computer programs
References
Further reading
Electronic structure methods | Multi-configurational self-consistent field | [
"Physics",
"Chemistry"
] | 1,120 | [
"Quantum chemistry",
"Quantum mechanics",
"Computational physics",
"Electronic structure methods",
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2,067,016 | https://en.wikipedia.org/wiki/Lithium%20tantalate | Lithium tantalate is the inorganic compound with the formula LiTaO3. It is a white, diamagnetic, water-insoluble solid. The compound has the perovskite structure. It has optical, piezoelectric, and pyroelectric properties. Considerable information is available from commercial sources about this material.
Synthesis and processing
Lithium tantalate is produced by treating tantalum(V) oxide with lithium oxide. The use of excess alkali gives water-soluble polyoxotantalates. Single crystals of Lithium tantalate are pulled from the melt using the Czochralski method.
Applications
Lithium tantalate is used for nonlinear optics, passive infrared sensors such as motion detectors, terahertz generation and detection, surface acoustic wave applications, cell phones.
Lithium tantalate is a standard detector element in infrared spectrophotometers.
Research
The phenomenon of pyroelectric fusion has been demonstrated using a lithium tantalate crystal producing a large enough charge to generate and accelerate a beam of deuterium nuclei into a deuterated target resulting in the production of a small flux of helium-3 and neutrons through nuclear fusion without extreme heat or pressure.
A difference between positively and negatively charged parts of pyroelectric LiTaO3 crystals was observed when water freezes to them.
See also
Lithium tantalate (data page)
References
Lithium salts
Tantalates
Nonlinear optical materials
Piezoelectric materials
Crystals | Lithium tantalate | [
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2,067,581 | https://en.wikipedia.org/wiki/Routh%E2%80%93Hurwitz%20theorem | In mathematics, the Routh–Hurwitz theorem gives a test to determine whether all roots of a given polynomial lie in the left-half complex plane. Polynomials with this property are called Hurwitz stable polynomials. The Routh–Hurwitz theorem is important in dynamical systems and control theory, because the characteristic polynomial of the differential equations of a stable, linear system has roots limited to the left half plane (negative eigenvalues). Thus the theorem provides a mathematical test, the Routh–Hurwitz stability criterion, to determine whether a linear dynamical system is stable without solving the system. The Routh–Hurwitz theorem was proved in 1895, and it was named after Edward John Routh and Adolf Hurwitz.
Notations
Let be a polynomial (with complex coefficients) of degree with no roots on the imaginary axis (i.e. the line where is the imaginary unit and is a real number). Let us define real polynomials and by , respectively the real and imaginary parts of on the imaginary line.
Furthermore, let us denote by:
the number of roots of in the left half-plane (taking into account multiplicities);
the number of roots of in the right half-plane (taking into account multiplicities);
the variation of the argument of when runs from to ;
is the number of variations of the generalized Sturm chain obtained from and by applying the Euclidean algorithm;
is the Cauchy index of the rational function over the real line.
Statement
With the notations introduced above, the Routh–Hurwitz theorem states that:
From the first equality we can for instance conclude that when the variation of the argument of is positive, then will have more roots to the left of the imaginary axis than to its right.
The equality can be viewed as the complex counterpart of Sturm's theorem. Note the differences: in Sturm's theorem, the left member is and the from the right member is the number of variations of a Sturm chain (while refers to a generalized Sturm chain in the present theorem).
Routh–Hurwitz stability criterion
We can easily determine a stability criterion using this theorem as it is trivial that is Hurwitz-stable if and only if . We thus obtain conditions on the coefficients of by imposing and .
See also
Plastic ratio
References
Explaining the Routh–Hurwitz Criterion (2020)
External links
Mathworld entry
Eponymous theorems of physics
Theorems about polynomials
Theorems in complex analysis
Theorems in real analysis | Routh–Hurwitz theorem | [
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"Theorems in complex analysis",
"Eponymous theorems of physics",
"Theorems about polynomials",
"Physics theorems"
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28,987,440 | https://en.wikipedia.org/wiki/Photochemical%20reduction%20of%20carbon%20dioxide | Photochemical reduction of carbon dioxide harnesses solar energy to convert into higher-energy products. Environmental interest in producing artificial systems is motivated by recognition that CO2 is a greenhouse gas. The process has not been commercialized.
Overview
Photochemical reduction involves chemical reduction (redox) generated from the photoexcitation of another molecule, called a photosensitizer. To harness the sun's energy, the photosensitizer must be able to absorb light within the visible and ultraviolet spectrum.
Molecular sensitizers that meet this criterion often include a metal center, as the d-orbital splitting in organometallic species often falls within the energy range of far-UV and visible light. The reduction process begins with excitation of the photosensitizer, as mentioned. This causes the movement of an electron from the metal center into the functional ligands. This movement is termed a metal-to-ligand charge transfer (MLCT). Back-electron transfer from the ligands to the metal after the charge transfer, which yields no net result, is prevented by including an electron-donating species in solution. Successful photosensitizers have a long-lived excited state, usually due to the interconversion from singlet to triplet states, that allow time for electron donors to interact with the metal center.
Common donors in photochemical reduction include triethylamine (TEA), triethanolamine (TEOA), and 1-benzyl-1,4-dihydronicotinamide (BNAH).
After excitation, CO2 coordinates or otherwise interacts with the inner coordination sphere of the reduced metal. Common products include formic acid, carbon monoxide, and methanol. Note that light absorption and catalytic reduction may occur at the same metal center or on different metal centers. That is, a photosensitizer and catalyst may be tethered through an organic linkage that provides for electronic communication between the species. In this case, the two metal centers form a bimetallic supramolecular complex. And, the excited electron that had resided on the functional ligands of photosensitizer passes through the ancillary ligands to the catalytic center, which becomes a one-electron reduced (OER) species. The advantage of dividing the two processes among different centers is in the ability to tune each center for a particular task, whether through selecting different metals or ligands.
History
In the 1980s, Lehn observed that Co(I) species were produced in solutions containing CoCl2, 2,2'-bipyridine (bpy), a tertiary amine, and a Ru(bpy)3Cl2 photosensitizer. The high affinity of CO2 to cobalt centers led both him and Ziessel to study cobalt centers as electrocatalysts for reduction. In 1982, they reported CO and H2 as products from the irradiation of a solution containing 700ml of CO2, Ru(bpy)3 and Co(bpy).
Since the work of Lehn and Ziessel, several catalysts have been paired with the Ru(bpy)3 photosensitizer.
When paired with methylviologen, cobalt, and nickel-based catalysts, carbon monoxide and hydrogen gas are observed as products.
Paired with rhenium catalysts, carbon monoxide is observed as the major product, and with ruthenium catalysts formic acid is observed. Some product selection is attainable through tuning of the reaction environment. Other photosensitizers have also been employed as catalysts. They include FeTPP (TPP=5,10,15,20-tetraphenyl-21H,23H-porphine) and CoTPP, both of which produce CO while the latter produces formate also. Non-metal photocatalysts include pyridine and N-heterocyclic carbenes.
In August 2022, it was developed a photocatalyst based on lead–sulfur (Pb–S) bonds, with promising results.
See also
Artificial photosynthesis
Electrochemical reduction of carbon dioxide
Photoelectrochemical reduction of carbon dioxide
Photocatalytic water splitting
References
Carbon dioxide
Photochemistry | Photochemical reduction of carbon dioxide | [
"Chemistry"
] | 875 | [
"Greenhouse gases",
"Carbon dioxide",
"nan"
] |
28,989,696 | https://en.wikipedia.org/wiki/James%20Clerk%20Maxwell | James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish physicist and mathematician who was responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism and light as different manifestations of the same phenomenon. Maxwell's equations for electromagnetism achieved the second great unification in physics, where the first one had been realised by Isaac Newton. Maxwell was also key in the creation of statistical mechanics.
With the publication of "A Dynamical Theory of the Electromagnetic Field" in 1865, Maxwell demonstrated that electric and magnetic fields travel through space as waves moving at the speed of light. He proposed that light is an undulation in the same medium that is the cause of electric and magnetic phenomena. The unification of light and electrical phenomena led to his prediction of the existence of radio waves, and the paper contained his final version of his equations, which he had been working on since 1856. As a result of his equations, and other contributions such as introducing an effective method to deal with network problems and linear conductors, he is regarded as a founder of the modern field of electrical engineering. In 1871, Maxwell became the first Cavendish Professor of Physics, serving until his death in 1879.
Maxwell was the first to derive the Maxwell–Boltzmann distribution, a statistical means of describing aspects of the kinetic theory of gases, which he worked on sporadically throughout his career. He is also known for presenting the first durable colour photograph in 1861 and for his foundational work on analysing the rigidity of rod-and-joint frameworks (trusses) like those in many bridges. Maxwell helped to established the CGS system of measurement, and he is responsible for modern dimensional analysis. Maxwell is also recognized for laying the groundwork for chaos theory. Maxwell correctly predicted that the rings of Saturn were made up of many unattached small fragments. His 1863 paper On Governors serves as an important foundation for control theory and cybernetics, and was also the earliest mathematical analysis on control systems. In 1867, he proposed the thought experiment known as Maxwell's demon.
His discoveries helped usher in the era of modern physics, laying the foundations for such fields as relativity, also being the one to introduce the term into physics, and quantum mechanics. Many physicists regard Maxwell as the 19th-century scientist having the greatest influence on 20th-century physics. His contributions to the science are considered by many to be of the same magnitude as those of Isaac Newton and Albert Einstein. In the millennium poll—a survey of the 100 most prominent physicists—Maxwell was voted the third greatest physicist of all time, behind only Newton and Einstein, with another survey of rank-and-file physicists also voting him third. On the centenary of Maxwell's birthday, his work was described by Einstein as the "most profound and the most fruitful that physics has experienced since the time of Newton". When Einstein visited the University of Cambridge in 1922, he was told by his host that he had done great things because he stood on Newton's shoulders; Einstein replied: "No I don't. I stand on the shoulders of Maxwell." Tom Siegfried described Maxwell as "one of those once-in-a-century geniuses who perceived the physical world with sharper senses than those around him".
Life
Early life, 1831–1839
James Clerk Maxwell was born on 13 June 1831 at 14 India Street, Edinburgh, to John Clerk Maxwell of Middlebie, an advocate, and Frances Cay, daughter of Robert Hodshon Cay and sister of John Cay. (His birthplace now houses a museum operated by the James Clerk Maxwell Foundation.) His father was a man of comfortable means of the Clerk family of Penicuik, holders of the baronetcy of Clerk of Penicuik. His father's brother was the 6th baronet. He had been born "John Clerk", adding "Maxwell" to his own after he inherited (as an infant in 1793) the Middlebie estate, a Maxwell property in Dumfriesshire. James was a first cousin of both the artist Jemima Blackburn (the daughter of his father's sister) and the civil engineer William Dyce Cay (the son of his mother's brother). Cay and Maxwell were close friends and Cay acted as his best man when Maxwell married.
Maxwell's parents met and married when they were well into their thirties; his mother was nearly 40 when he was born. They had had one earlier child, a daughter named Elizabeth, who died in infancy.
When Maxwell was young his family moved to Glenlair, in Kirkcudbrightshire, which his parents had built on the estate which comprised . All indications suggest that Maxwell had maintained an unquenchable curiosity from an early age. By the age of three, everything that moved, shone, or made a noise drew the question: "what's the go o' that?" In a passage added to a letter from his father to his sister-in-law Jane Cay in 1834, his mother described this innate sense of inquisitiveness:
Education, 1839–1847
Recognising the boy's potential, Maxwell's mother Frances took responsibility for his early education, which in the Victorian era was largely the job of the woman of the house. At eight he could recite long passages of John Milton and the whole of the 119th psalm (176 verses). Indeed, his knowledge of scripture was already detailed; he could give chapter and verse for almost any quotation from the Psalms. His mother was taken ill with abdominal cancer and, after an unsuccessful operation, died in December 1839 when he was eight years old. His education was then overseen by his father and his father's sister-in-law Jane, both of whom played pivotal roles in his life. His formal schooling began unsuccessfully under the guidance of a 16-year-old hired tutor. Little is known about the young man hired to instruct Maxwell, except that he treated the younger boy harshly, chiding him for being slow and wayward. The tutor was dismissed in November 1841. James' father took him to Robert Davidson's demonstration of electric propulsion and magnetic force on 12 February 1842, an experience with profound implications for the boy.
Maxwell was sent to the prestigious Edinburgh Academy. He lodged during term times at the house of his aunt Isabella. During this time his passion for drawing was encouraged by his older cousin Jemima. The 10-year-old Maxwell, having been raised in isolation on his father's countryside estate, did not fit in well at school. The first year had been full, obliging him to join the second year with classmates a year his senior. His mannerisms and Galloway accent struck the other boys as rustic. Having arrived on his first day of school wearing a pair of homemade shoes and a tunic, he earned the unkind nickname of "Daftie". He never seemed to resent the epithet, bearing it without complaint for many years. Social isolation at the Academy ended when he met Lewis Campbell and Peter Guthrie Tait, two boys of a similar age who were to become notable scholars later in life. They remained lifelong friends.
Maxwell was fascinated by geometry at an early age, rediscovering the regular polyhedra before he received any formal instruction. Despite his winning the school's scripture biography prize in his second year, his academic work remained unnoticed until, at the age of 13, he won the school's mathematical medal and first prize for both English and poetry.
Maxwell's interests ranged far beyond the school syllabus and he did not pay particular attention to examination performance. He wrote his first scientific paper at the age of 14. In it, he described a mechanical means of drawing mathematical curves with a piece of twine, and the properties of ellipses, Cartesian ovals, and related curves with more than two foci. The work, of 1846, "On the description of oval curves and those having a plurality of foci" was presented to the Royal Society of Edinburgh by James Forbes, a professor of natural philosophy at the University of Edinburgh, because Maxwell was deemed too young to present the work himself. The work was not entirely original, since René Descartes had also examined the properties of such multifocal ellipses in the 17th century, but Maxwell had simplified their construction.
University of Edinburgh, 1847–1850
Maxwell left the Academy in 1847 at age 16 and began attending classes at the University of Edinburgh. He had the opportunity to attend the University of Cambridge, but decided, after his first term, to complete the full course of his undergraduate studies at Edinburgh. The academic staff of the university included some highly regarded names; his first-year tutors included Sir William Hamilton, who lectured him on logic and metaphysics, Philip Kelland on mathematics, and James Forbes on natural philosophy. He did not find his classes demanding, and was, therefore, able to immerse himself in private study during free time at the university and particularly when back home at Glenlair. There he would experiment with improvised chemical, electric, and magnetic apparatus; however, his chief concerns regarded the properties of polarised light. He constructed shaped blocks of gelatine, subjected them to various stresses, and with a pair of polarising prisms given to him by William Nicol, viewed the coloured fringes that had developed within the jelly. Through this practice he discovered photoelasticity, which is a means of determining the stress distribution within physical structures.
At age 18, Maxwell contributed two papers for the Transactions of the Royal Society of Edinburgh. One of these, "On the Equilibrium of Elastic Solids", laid the foundation for an important discovery later in his life, which was the temporary double refraction produced in viscous liquids by shear stress. His other paper was "Rolling Curves" and, just as with the paper "Oval Curves" that he had written at the Edinburgh Academy, he was again considered too young to stand at the rostrum to present it himself. The paper was delivered to the Royal Society by his tutor Kelland instead.
University of Cambridge, 1850–1856
In October 1850, already an accomplished mathematician, Maxwell left Scotland for the University of Cambridge. He initially attended Peterhouse, but before the end of his first term transferred to Trinity, where he believed it would be easier to obtain a fellowship. At Trinity he was elected to the elite secret society known as the Cambridge Apostles. Maxwell's intellectual understanding of his Christian faith and of science grew rapidly during his Cambridge years. He joined the "Apostles", an exclusive debating society of the intellectual elite, where through his essays he sought to work out this understanding.
In the summer of his third year, Maxwell spent some time at the Suffolk home of the Rev. C. B. Tayler, the uncle of a classmate, G. W. H. Tayler. The love of God shown by the family impressed Maxwell, particularly after he was nursed back from ill health by the minister and his wife.
On his return to Cambridge, Maxwell writes to his recent host a chatty and affectionate letter including the following testimony,
In November 1851, Maxwell studied under William Hopkins, whose success in nurturing mathematical genius had earned him the nickname of "senior wrangler-maker".
In 1854, Maxwell graduated from Trinity with a degree in mathematics. He scored second highest in the final examination, coming behind Edward Routh and earning himself the title of Second Wrangler. He was later declared equal with Routh in the more exacting ordeal of the Smith's Prize examination. Immediately after earning his degree, Maxwell read his paper "On the Transformation of Surfaces by Bending" to the Cambridge Philosophical Society. This is one of the few purely mathematical papers he had written, demonstrating his growing stature as a mathematician. Maxwell decided to remain at Trinity after graduating and applied for a fellowship, which was a process that he could expect to take a couple of years. Buoyed by his success as a research student, he would be free, apart from some tutoring and examining duties, to pursue scientific interests at his own leisure.
The nature and perception of colour was one such interest which he had begun at the University of Edinburgh while he was a student of Forbes. With the coloured spinning tops invented by Forbes, Maxwell was able to demonstrate that white light would result from a mixture of red, green, and blue light. His paper "Experiments on Colour" laid out the principles of colour combination and was presented to the Royal Society of Edinburgh in March 1855. Maxwell was this time able to deliver it himself.
Maxwell was made a fellow of Trinity on 10 October 1855, sooner than was the norm, and was asked to prepare lectures on hydrostatics and optics and to set examination papers. The following February he was urged by Forbes to apply for the newly vacant Chair of Natural Philosophy at Marischal College, Aberdeen. His father assisted him in the task of preparing the necessary references, but died on 2 April at Glenlair before either knew the result of Maxwell's candidacy. He accepted the professorship at Aberdeen, leaving Cambridge in November 1856.
Marischal College, Aberdeen, 1856–1860
The 25-year-old Maxwell was a good 15 years younger than any other professor at Marischal. He engaged himself with his new responsibilities as head of a department, devising the syllabus and preparing lectures. He committed himself to lecturing 15 hours a week, including a weekly pro bono lecture to the local working men's college. He lived in Aberdeen with his cousin William Dyce Cay, a Scottish civil engineer, during the six months of the academic year and spent the summers at Glenlair, which he had inherited from his father.
Later, his former student described Maxwell as follows:
In the late 1850s shortly before 9 am any winter’s morning you might well have seen the young James Clerk Maxwell, in his mid to late 20s, a man of middling height, with frame strongly knit, and a certain spring and elasticity in his gait; dressed for comfortable ease rather than elegance; a face expressive at once of sagacity and good humour, but overlaid with a deep shade of thoughtfulness; features boldly put pleasingly marked; eyes dark and glowing; hair and beard perfectly black, and forming a strong contrast to the pallor of his complexion.
He focused his attention on a problem that had eluded scientists for 200 years: the nature of Saturn's rings. It was unknown how they could remain stable without breaking up, drifting away or crashing into Saturn. The problem took on a particular resonance at that time because St John's College, Cambridge, had chosen it as the topic for the 1857 Adams Prize. Maxwell devoted two years to studying the problem, proving that a regular solid ring could not be stable, while a fluid ring would be forced by wave action to break up into blobs. Since neither was observed, he concluded that the rings must be composed of numerous small particles he called "brick-bats", each independently orbiting Saturn. Maxwell was awarded the £130 Adams Prize in 1859 for his essay "On the stability of the motion of Saturn's rings"; he was the only entrant to have made enough headway to submit an entry. His work was so detailed and convincing that when George Biddell Airy read it he commented, "It is one of the most remarkable applications of mathematics to physics that I have ever seen." It was considered the final word on the issue until direct observations by the Voyager flybys of the 1980s confirmed Maxwell's prediction that the rings were composed of particles. It is now understood, however, that the rings' particles are not totally stable, being pulled by gravity onto Saturn. The rings are expected to vanish entirely over the next 300 million years.
In 1857 Maxwell befriended the Reverend Daniel Dewar, who was then the Principal of Marischal. Through him Maxwell met Dewar's daughter, Katherine Mary Dewar. They were engaged in February 1858 and married in Aberdeen on 2 June 1858. On the marriage record, Maxwell is listed as Professor of Natural Philosophy in Marischal College, Aberdeen. Katherine was seven years Maxwell's senior. Comparatively little is known of her, although it is known that she helped in his lab and worked on experiments in viscosity. Maxwell's biographer and friend, Lewis Campbell, adopted an uncharacteristic reticence on the subject of Katherine, though describing their married life as "one of unexampled devotion".
In 1860 Marischal College merged with the neighbouring King's College to form the University of Aberdeen. There was no room for two professors of Natural Philosophy, so Maxwell, despite his scientific reputation, found himself laid off. He was unsuccessful in applying for Forbes's recently vacated chair at Edinburgh, the post instead going to Tait. Maxwell was granted the Chair of Natural Philosophy at King's College, London, instead. After recovering from a near-fatal bout of smallpox in 1860, he moved to London with his wife.
King's College, London, 1860–1865
Maxwell's time at King's was probably the most productive of his career. He was awarded the Royal Society's Rumford Medal in 1860 for his work on colour and was later elected to the Society in 1861. This period of his life would see him display the world's first light-fast colour photograph, further develop his ideas on the viscosity of gases, and propose a system of defining physical quantities—now known as dimensional analysis. Maxwell would often attend lectures at the Royal Institution, where he came into regular contact with Michael Faraday. The relationship between the two men could not be described as being close, because Faraday was 40 years Maxwell's senior and showed signs of senility. They nevertheless maintained a strong respect for each other's talents.
This time is especially noteworthy for the advances Maxwell made in the fields of electricity and magnetism. He examined the nature of both electric and magnetic fields in his two-part paper "On physical lines of force", which was published in 1861. In it, he provided a conceptual model for electromagnetic induction, consisting of tiny spinning cells of magnetic flux. Two more parts were later added to and published in that same paper in early 1862. In the first additional part, he discussed the nature of electrostatics and displacement current. In the second additional part, he dealt with the rotation of the plane of the polarisation of light in a magnetic field, a phenomenon that had been discovered by Faraday and is now known as the Faraday effect.
Later years, 1865–1879
In 1865 Maxwell resigned the chair at King's College, London, and returned to Glenlair with Katherine. In his paper "On governors" (1868) he mathematically described the behaviour of governors—devices that control the speed of steam engines—thereby establishing the theoretical basis of control engineering. In his paper "On reciprocal figures, frames and diagrams of forces" (1870) he discussed the rigidity of various designs of lattice. He wrote the textbook Theory of Heat (1871) and the treatise Matter and Motion (1876). Maxwell was also the first to make explicit use of dimensional analysis, in 1871.
In 1871 he returned to Cambridge to become the first Cavendish Professor of Physics. Maxwell was put in charge of the development of the Cavendish Laboratory, supervising every step in the progress of the building and of the purchase of the collection of apparatus. One of Maxwell's last great contributions to science was the editing (with copious original notes) of the research of Henry Cavendish, from which it appeared that Cavendish researched, amongst other things, such questions as the density of the Earth and the composition of water. He was elected as a member to the American Philosophical Society in 1876.
Death
In April 1879 Maxwell began to have difficulty in swallowing, the first symptom of his fatal illness.
Maxwell died in Cambridge of abdominal cancer on 5 November 1879 at the age of 48. His mother had died at the same age of the same type of cancer. The minister who regularly visited him in his last weeks was astonished at his lucidity and the immense power and scope of his memory, but comments more particularly,
As death approached Maxwell told a Cambridge colleague,
Maxwell is buried at Parton Kirk, near Castle Douglas in Galloway close to where he grew up. The extended biography The Life of James Clerk Maxwell, by his former schoolfellow and lifelong friend Professor Lewis Campbell, was published in 1882. His collected works were issued in two volumes by the Cambridge University Press in 1890.
The executors of Maxwell's estate were his physician George Edward Paget, G. G. Stokes, and Colin Mackenzie, who was Maxwell's cousin. Overburdened with work, Stokes passed Maxwell's papers to William Garnett, who had effective custody of the papers until about 1884.
There is a memorial inscription to him near the choir screen at Westminster Abbey.
Personal life
As a great lover of Scottish poetry, Maxwell memorised poems and wrote his own. The best known is Rigid Body Sings, closely based on "Comin' Through the Rye" by Robert Burns, which he apparently used to sing while accompanying himself on a guitar. It has the opening lines
A collection of his poems was published by his friend Lewis Campbell in 1882.
Descriptions of Maxwell remark upon his remarkable intellectual qualities being matched by social awkwardness.
Maxwell wrote the following aphorism for his own conduct as a scientist: He that would enjoy life and act with freedom must have the work of the day continually before his eyes. Not yesterday's work, lest he fall into despair, not to-morrow's, lest he become a visionary—not that which ends with the day, which is a worldly work, nor yet that only which remains to eternity, for by it he cannot shape his action. Happy is the man who can recognize in the work of to-day a connected portion of the work of life, and an embodiment of the work of eternity. The foundations of his confidence are unchangeable, for he has been made a partaker of Infinity. He strenuously works out his daily enterprises, because the present is given him for a possession.
Maxwell was an evangelical Presbyterian and in his later years became an Elder of the Church of Scotland. Maxwell's religious beliefs and related activities have been the focus of a number of papers. Attending both Church of Scotland (his father's denomination) and Episcopalian (his mother's denomination) services as a child, Maxwell underwent an evangelical conversion in April 1853. One facet of this conversion may have aligned him with an antipositivist position.
Scientific legacy
Electromagnetism
Maxwell had studied and commented on electricity and magnetism as early as 1855 when his paper "On Faraday's lines of force" was read to the Cambridge Philosophical Society. The paper presented a simplified model of Faraday's work and how electricity and magnetism are related. He reduced all of the current knowledge into a linked set of differential equations with 20 equations in 20 variables. This work was later published as "On Physical Lines of Force" in March 1861.
Around 1862, while lecturing at King's College, Maxwell calculated that the speed of propagation of an electromagnetic field is approximately that of the speed of light. He considered this to be more than just a coincidence, commenting, "We can scarcely avoid the conclusion that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena.
Working on the problem further, Maxwell showed that the equations predict the existence of waves of oscillating electric and magnetic fields that travel through empty space at a speed that could be predicted from simple electrical experiments; using the data available at the time, Maxwell obtained a velocity of . In his 1865 paper "A Dynamical Theory of the Electromagnetic Field", Maxwell wrote, "The agreement of the results seems to show that light and magnetism are affections of the same substance, and that light is an electromagnetic disturbance propagated through the field according to electromagnetic laws".
His famous twenty equations, in their modern form of partial differential equations, first appeared in fully developed form in his textbook A Treatise on Electricity and Magnetism in 1873. Most of this work was done by Maxwell at Glenlair during the period between holding his London post and his taking up the Cavendish chair. Oliver Heaviside reduced the complexity of Maxwell's theory down to four partial differential equations, known now collectively as Maxwell's Laws or Maxwell's equations. Although potentials became much less popular in the nineteenth century, the use of scalar and vector potentials is now standard in the solution of Maxwell's equations.
As Barrett and Grimes (1995) describe:
Maxwell expressed electromagnetism in the algebra of quaternions and made the electromagnetic potential the centerpiece of his theory. In 1881 Heaviside replaced the electromagnetic potential field by force fields as the centerpiece of electromagnetic theory. According to Heaviside, the electromagnetic potential field was arbitrary and needed to be "assassinated". (sic) A few years later there was a debate between Heaviside and [Peter Guthrie] Tate (sic) about the relative merits of vector analysis and quaternions. The result was the realization that there was no need for the greater physical insights provided by quaternions if the theory was purely local, and vector analysis became commonplace.
Maxwell was proved correct, and his quantitative connection between light and electromagnetism is considered one of the great accomplishments of 19th-century mathematical physics.
Maxwell also introduced the concept of the electromagnetic field in comparison to force lines that Faraday described. By understanding the propagation of electromagnetism as a field emitted by active particles, Maxwell could advance his work on light. At that time, Maxwell believed that the propagation of light required a medium for the waves, dubbed the luminiferous aether. Over time, the existence of such a medium, permeating all space and yet apparently undetectable by mechanical means, proved impossible to reconcile with experiments such as the Michelson–Morley experiment. Moreover, it seemed to require an absolute frame of reference in which the equations were valid, with the distasteful result that the equations changed form for a moving observer. These difficulties inspired Albert Einstein to formulate the theory of special relativity; in the process, Einstein dispensed with the requirement of a stationary luminiferous aether.
Einstein acknowledge the groundbreaking work of Maxwell, stating that:He also acknowledged the influence that his work had on his relativity theory:
Colour vision
Along with most physicists of the time, Maxwell had a strong interest in psychology. Following in the steps of Isaac Newton and Thomas Young, he was particularly interested in the study of colour vision. From 1855 to 1872, Maxwell published at intervals a series of investigations concerning the perception of colour, colour-blindness, and colour theory, and was awarded the Rumford Medal for "On the Theory of Colour Vision".
Isaac Newton had demonstrated, using prisms, that white light, such as sunlight, is composed of a number of monochromatic components which could then be recombined into white light. Newton also showed that an orange paint made of yellow and red could look exactly like a monochromatic orange light, although being composed of two monochromatic yellow and red lights. Hence the paradox that puzzled physicists of the time: two complex lights (composed of more than one monochromatic light) could look alike but be physically different, called metameres. Thomas Young later proposed that this paradox could be explained by colours being perceived through a limited number of channels in the eyes, which he proposed to be threefold, the trichromatic colour theory. Maxwell used the recently developed linear algebra to prove Young's theory. Any monochromatic light stimulating three receptors should be able to be equally stimulated by a set of three different monochromatic lights (in fact, by any set of three different lights). He demonstrated that to be the case, inventing colour matching experiments and Colourimetry.
Maxwell was also interested in applying his theory of colour perception, namely in colour photography. Stemming directly from his psychological work on colour perception: if a sum of any three lights could reproduce any perceivable colour, then colour photographs could be produced with a set of three coloured filters. In the course of his 1855 paper, Maxwell proposed that, if three black-and-white photographs of a scene were taken through red, green, and blue filters, and transparent prints of the images were projected onto a screen using three projectors equipped with similar filters, when superimposed on the screen the result would be perceived by the human eye as a complete reproduction of all the colours in the scene.
During an 1861 Royal Institution lecture on colour theory, Maxwell presented the world's first demonstration of colour photography by this principle of three-colour analysis and synthesis. Thomas Sutton, inventor of the single-lens reflex camera, took the picture. He photographed a tartan ribbon three times, through red, green, and blue filters, also making a fourth photograph through a yellow filter, which, according to Maxwell's account, was not used in the demonstration. Because Sutton's photographic plates were insensitive to red and barely sensitive to green, the results of this pioneering experiment were far from perfect. It was remarked in the published account of the lecture that "if the red and green images had been as fully photographed as the blue", it "would have been a truly-coloured image of the riband. By finding photographic materials more sensitive to the less refrangible rays, the representation of the colours of objects might be greatly improved." Researchers in 1961 concluded that the seemingly impossible partial success of the red-filtered exposure was due to ultraviolet light, which is strongly reflected by some red dyes, not entirely blocked by the red filter used, and within the range of sensitivity of the wet collodion process Sutton employed.
Kinetic theory and thermodynamics
Maxwell also investigated the kinetic theory of gases. Originating with Daniel Bernoulli, this theory was advanced by the successive labours of John Herapath, John James Waterston, James Joule, and particularly Rudolf Clausius, to such an extent as to put its general accuracy beyond a doubt; but it received enormous development from Maxwell, who in this field appeared as an experimenter (on the laws of gaseous friction) as well as a mathematician.
Between 1859 and 1866, he developed the theory of the distributions of velocities in particles of a gas, work later generalised by Ludwig Boltzmann. The formula, called the Maxwell–Boltzmann distribution, gives the fraction of gas molecules moving at a specified velocity at any given temperature. In the kinetic theory, temperatures and heat involve only molecular movement. This approach generalised the previously established laws of thermodynamics and explained existing observations and experiments in a better way than had been achieved previously. His work on thermodynamics led him to devise the thought experiment that came to be known as Maxwell's demon, where the second law of thermodynamics is violated by an imaginary being capable of sorting particles by energy.
In 1871, he established Maxwell's thermodynamic relations, which are statements of equality among the second derivatives of the thermodynamic potentials with respect to different thermodynamic variables. In 1874, he constructed a plaster thermodynamic visualisation as a way of exploring phase transitions, based on the American scientist Josiah Willard Gibbs's graphical thermodynamics papers.
Peter Guthrie Tait called Maxwell the "leading molecular scientist" of his time. Another person added after Maxwell's death that "only one man lived who could understand Gibbs's papers. That was Maxwell, and now he is dead."
Control theory
Maxwell published the paper "On governors" in the Proceedings of the Royal Society, vol. 16 (1867–1868). This paper is considered a central paper of the early days of control theory. Here "governors" refers to the governor or the centrifugal governor used to regulate steam engines.
Honours
Publications
Three of Maxwell's contributions to Encyclopædia Britannica appeared in the Ninth Edition (1878): Atom, Attraction, and Ether; and three in the Eleventh Edition (1911): Capillary Action, Diagram, and Faraday, Michael
Notes
References
External links
James Clerk Maxwell, "Experiments on colour as perceived by the Eye, with remarks on colour-blindness". Proceedings of the Royal Society of Edinburgh, vol. 3, no. 45, pp. 299–301. (digital facsimile from the Linda Hall Library)
Maxwell, BBC Radio 4 discussion with Simon Schaffer, Peter Harman & Joanna Haigh (In Our Time, 2 October 2003)
Scotland's Einstein: James Clerk Maxwell – The Man Who Changed the World, BBC Two documentary 2015.
1831 births
1879 deaths
19th-century Scottish mathematicians
19th-century British physicists
19th-century Scottish scientists
Academics of King's College London
Academics of the University of Aberdeen
Alumni of the University of Edinburgh
Alumni of Trinity College, Cambridge
Alumni of Peterhouse, Cambridge
Burials in Dumfries and Galloway
Color scientists
Deaths from stomach cancer in England
People educated at Edinburgh Academy
Elders of the Church of Scotland
Fellows of the Royal Society of Edinburgh
Fellows of the Royal Society
Fellows of King's College London
People associated with electricity
Scientists from Edinburgh
Optical physicists
Scottish Presbyterians
Calvinist and Reformed elders
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Magneticians
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Scottish people of English descent | James Clerk Maxwell | [
"Physics",
"Chemistry"
] | 6,910 | [
"Thermodynamics",
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28,993,982 | https://en.wikipedia.org/wiki/Quantum%20algebra | Quantum algebra is one of the top-level mathematics categories used by the arXiv. It is the study of noncommutative analogues and generalizations of commutative algebras, especially those arising in Lie theory.
Subjects include:
Quantum groups
Skein theories
Operadic algebra
Diagrammatic algebra
Quantum field theory
Racks and quandles
See also
Coherent states in mathematical physics
Glossary of areas of mathematics
Mathematics Subject Classification
Ordered type system, a substructural type system
Outline of mathematics
Quantum logic
References
External links
Quantum algebra at arxiv.org
Quantum groups | Quantum algebra | [
"Physics",
"Mathematics"
] | 115 | [
"Algebra",
"Algebra stubs",
"Quantum mechanics",
"Quantum physics stubs"
] |
38,526,503 | https://en.wikipedia.org/wiki/Chronometric%20singularity | In theoretical physics, a chronometric singularity (also called a temporal or horological singularity) is a point at which time cannot be measured or described.
An example involves a time at a coordinate singularity, e.g. a geographical pole. Since time on Earth is measured through longitudes, and no unique longitude exists at a pole, time is not defined uniquely at this point. There is a clear connection with coordinate singularities, as can be seen from this example. In relativity, similar singularities can be found in the case of Schwarzschild coordinates.
Stephen Hawking once compared by a talk-show guest's question about "before the beginning of time" to asking "what's north of the North Pole".
See also
Coordinate singularity
No-boundary proposal and imaginary time
Spacetime singularity
Time
References
Geodesy
Timekeeping | Chronometric singularity | [
"Physics",
"Mathematics"
] | 178 | [
"Physical quantities",
"Time",
"Applied mathematics",
"Timekeeping",
"Spacetime",
"Geodesy"
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38,529,941 | https://en.wikipedia.org/wiki/Personal%20safety%20app | A personal safety app or SOS app is a mobile application designed to provide individuals with additional security and assistance in various situations. These apps offer a range of features and functionalities that users can utilize to enhance their personal safety. Common features include emergency alerts, location sharing, safety tips, SOS buttons, audible alarms, and community safety reporting. Users can employ these apps to quickly send emergency alerts, share their real-time location with trusted contacts, and access safety-related information and resources.
Features
While most personal safety apps are offered as freeware, some are either distributed as a freemium app with paid features which can be unlocked through in-app purchases, supported through advertising, or marketed as paid applications. These include various features, including sending text messages, e-mails, IMs, or even Tweets to close friends (containing approximate location,) or emitting a loud intermittent "shrill whistle" in the manner of a rape alarm. Additional features include geofencing and preventive alerts. Some apps allow to customize the alert message sent and the ringtone that signals the reception of a new alert.
They normally include different triggering mechanisms to cope with different emergency situations. Common triggering mechanisms include pressing and holding the phone's switch button for a few seconds, shaking the phone vigorously, tapping on an alert button, and even loud screaming sound which the app can detect. When the alert signal is triggered, these apps automatically go to work, sending text messages and emails with exact location of the user to emergency contacts listed on the app.
In April 2016, the Indian government mandated that all cellphones sold in the country must contain a panic button function by 2017, activated through either a dedicated button or pressing the power key three times.
Security Concerns
Many users have expressed concerns about the safety of personal safety apps and have raised questions regarding how the data collected by these apps is processed and used. These concerns are often related to issues of privacy and data security. Users worry that the personal information, location data, and emergency alerts they share with these apps could be mishandled or accessed by unauthorized parties. Additionally there is a growing awareness of potential risks associated with the storage and transmission of sensitive data. As a result, some users are cautious about using personal safety apps and may choose to limit the information they share or thoroughly review the privacy policies and data handling practices of the apps the use. These concerns underscore the importance of transparent data practices and robust security measures within the personal safety app industry to address and alleviate user apprehensions.
Inbuilt SOS Features in Mobile Operating Systems
In recent years, major technology companies like Apple and Google have incorporated inbuilt SOS features directly into their mobile operating systems. These features are designed to provide users with quick and efficient methods of seeking assistance during emergencies. For instance, Apple's iOS includes an Emergency SOS feature that allows users to rapidly call emergency services and notify designated contacts by pressing a specific combination of hardware buttons or using the device's touchscreen. Similarly Google's Android operating system offers and Emergency Information feature that enables users to input vital medical and emergency contact information accessible even when the device is locked. These inbuilt SOS features offer an additional layer of safety and convenience for users, complementing standalone personal safety apps and reinforcing the importance of technology in enhancing personal security.
References
Alarms
Mobile software | Personal safety app | [
"Technology"
] | 689 | [
"Warning systems",
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38,529,942 | https://en.wikipedia.org/wiki/Volatile%20corrosion%20inhibitor | A volatile corrosion inhibitor (VCI) is a material that protects metals from corrosion. Corrosion inhibitors are chemical compounds that can decrease the corrosion rate of a material, typically a metal or an alloy. NACE International Standard TM0208 defines volatile corrosion inhibitor (VCI) as a chemical substance that acts to reduce corrosion by a combination of volatilization from a VCI material, vapor transport in the atmosphere of an enclosed environment, and condensation onto surface in the space, including absorption, dissolution, and hydrophobic effects on metal surfaces, where the rate of corrosion of metal surfaces is thereby inhibited. They are also called vapor-phase inhibitors, vapor-phase corrosion inhibitors, and vapor-transported corrosion inhibitors.
VCIs come in various formulations that are dependent on the type of system they will be used in; for example, films, oils, coatings, cleaners, etc. There are also variety of formulations that provide protection in ferrous, nonferrous, or multi-metal applications. Other variables include the amount of vapor phase compared to contact phase inhibitors. Because they are volatile at ambient temperature, VCI compounds can reach inaccessible crevices in metallic structures.
V.VCI is also called Vacuum VCI meaning they have special properties of performance in vacuum as well as corrosion protection properties.
History
The first widescale use of VCIs can be traced to Shell's patent for dicyclohexylammonium nitrite (DICHAN), which was eventually commercialized as VPI 260. DICHAN was used extensively by the US military to protect a wide variety of metallic components from corrosion via various delivery systems, VCI powder, VCI paper, VCI solution, VCI slushing compound, etc.
Safety and health concerns as well as inherent limitations has led to the abandonment of DICHAN as a VCI. At present, commercial VCI compounds are typically salts of moderately strong bases and weak volatile acids. The typical bases are amines and the acids are carbonic, nitrous and carboxylic.
VCI corrosion protection mechanism
For steel, the first step will be the volatilization of the inhibitor into the airspace. This may entail simple evolution of the molecule or the chemical may dissociate first and then volatilize. The molecules will then diffuse through the enclosed airspace until some of the molecules reach the metallic surface to be protected. There are two likely paths once the molecules reach the metallic surface. First the molecule may adsorb onto the metal surface thereby forming a barrier to aggressive ions and displacing any condensed water.
The second path involves the condensed water layer that has been shown to exist on the metallic surface. The VCI molecules will dissolve into the condensed water layer, raising the pH. An alkaline pH has been shown to have a beneficial effect on the corrosion resistance for steel.
The mechanism for copper begins the same as for steel, evolution of the inhibitor. Once at the copper surface however, the inhibitor will form a copper benzotriazole complex which is protective.
Vapor pressure is a critical parameter in VCI effectiveness. The most favorable range of pressure is 10−3 to 10−2 Pa at room temperature. Insufficient pressure leads to the slow establishment of the protective layer; if the pressure is too high, VCI effectiveness is limited to a short time.
Product uses
VCIs have been applied across a wide variety of application areas:
Packaging – One of the first widespread uses for VCIs was VCI paper which was used to wrap parts for transportation and/or storage. The technology then evolved with the development of VCI film, where the inhibitor was incorporated into Polyethylene film. This offered the advantage that parts could be stored in the VCI film without any rust-preventative (RP) oil, which would typically have to be removed before part was placed into service. In places where the VCI film is in direct contact with the metal, VCI molecules adsorb on the metal surfaces, creating an invisible molecular barrier against corrosive elements such as oxygen, moisture, and chlorides. As VCI molecules vaporize out of the film and diffuse throughout the package, they also form a protective molecular layer on metal surfaces not in direct contact with the film. When the packaging is removed, the VCI molecules simply vaporize and float away. VCI films protect metals both through direct contact and vapor action. Large Equipment/Assets are wrapped in VCI heat shrinkable film for long term outdoor storage. The use of polymer films for thorough protection of electronic equipment during shipment or storage should take into account the prevention of electrostatic discharge (ESD), corrosion, and the disposal of the film after use. A main property that makes a polymer film a viable packaging material for electronic equipment is the film's ability to eliminate electrostatic discharge. The most recent property addition to VCI film is biodegradability.
Coatings - The use of VCIs as alternative corrosion inhibitor technologies in coating is not a new concept. In the last few years, however, with growing environmental pressure to reduce the use of traditional inhibitors containing heavy metals, they have gained in popularity. Since VCI particles have a polar attraction to the metal substrate, this allows them to work in the coating without negatively impacting other components of the coating, such as defoamers, wetting agents, levelling agents, etc. VCIs are typically added to the formulation in very small amounts by weight of the overall formula. The particle size of the VCIs is very small in comparison to traditionally used inhibitors. This allows the VCIs to migrate into the smaller voids more effectively. Once the VCIs have adsorbed on the surface of the metal, they provide an effective barrier that is hydrophobic and prevents moisture from getting through to the metal surface. Consequently, this prevents the formation of a corrosion cell and renders the moisture ineffective.
Emitter – VCI in the form of a capsule, foam, cup, etc., is placed within an electrical cabinet, junction box, etc., to provide corrosion protection to the various components inside the box. VCI emitters also provide best protection against H2S, SO2, ammonia & humidity, It is mostly use in electrical components because it does not affect electrical, surface or optical properties.
Pipe casings – A mixture of VCI and a swellable gel is injected into the annular space between the pipe casing (the outer pipe) and the carrier pipe (the inner pipe) as to provide corrosion protection to the carrier pipe. This application has recently been of wider interest as it has been approved by PHMSA as a means to address a shorted casing in a CP protected pipeline. (PHMSA rules dictate that a shorted casing on a PHMSA regulated pipeline be repaired or treated). Details can also be found in NACE SP-200.
Pipeline preservation (internal) - VCIs are seeing widespread application for the mitigation of corrosion of the internal surfaces of new and/or existing out-of-service pipelines. Top-of-the-line TOL corrosion typically occurs in wet gas pipelines that have a stratified flow regime and poor thermal insulation. TOL corrosion is predominantly a problem of protection in the gas phase. Tests showed that the best potential for providing corrosion protection for TOL came from azoles, certain acetylene alcohols, and a "green" volatile aldehyde.
For new pipelines, the time period between hydrotesting and operations can be very unpredictable and may extend for months. Historical data has shown that significant corrosion issues can arise as a result of residual hydrotest water. For a piggable pipeline, an aqueous solution of VCI is pushed down the pipeline between two pigs after completion of the hydrotest operation. This provides corrosion mitigation until the line is put into service. For a non-piggable pipeline, the low sections where residual hydrotest water may collect after draining are identified and an aqueous VCI solution is added at nearby high points such that the inhibitor solution will flow into the low sections, thereby treating the residual water with inhibitor.
For pipeline sections that are being idled, the low-lying sections are identified, and an inhibitor solution is added at nearby high points as to fill the low-lying section to a predetermined depth.
Aboveground storage tanks (Soilside Bottom) - The bottoms of aboveground storage tanks are typically coated on the inside (product side) to prevent corrosion. The other side of the bottom, (soilside) is not coated and the unprotected steel rests directly on a foundation. There are various styles of foundations: a concrete ringwall with a sand bed and a liner, a hard pad, such as concrete or asphalt, a double bottom and finally simple soil. VCIs are applied via various methods depending the tank foundation.
For tanks with a concrete ringwall, a sand bed and a liner, the VCI is typically installed as an aqueous solution. The solution is either injected at minimal pressure through the leak detection ports, (distribution of the solution through the sand is primarily via capillary action) or through a preinstalled distribution system of perforated pipes. The tank can be in or out of service.
Various options are available for a tank on a hard pad depending on whether the tank is in or out of service. For a tank that is in service, a ring of perforated pipes is installed at the edge of the chime sealed via a membrane that creates an enclosed space between the tank chime and the hard pad foundation. The VCI is supplied as a powder in mesh sleeves that are threaded into the perforated pipes. Upon depletion of the VCI, the mesh sleeves are removed, and new sleeves installed. For a tank that is out of service with the floor removed, grooves are cut into the hard pad. A channel is also cut from the end of the groove to extend beyond the tank chime. Perforated pipe with a mesh cover is laid at the bottom of the cut grooves. The groove is then filled with sand. The tank bottom is then installed as normal. The VCI is supplied as a powder in mesh sleeves that are installed into the perforated pipe. The ends of the perforated pipes are sealed closed. Upon depletion of the VCI, the mesh sleeves are removed, and new sleeves installed. For a tank that is out of service without the floor removed, the typical approach is to inject the VCI as an aqueous solution through ports that have been installed through the floor which often are the helium ports that were used to verify the tank floor integrity.
There are two typical geometries for double bottom tank. In the first, the space between the two floors has a liner and a sand bed and for the second, a liner and a concrete pad with radial slots. (This style of double bottom is often called an El Segundo double bottom). For a double bottom with a liner and sand bed, the VCI is supplied as an aqueous solution which is injected through the leak detection ports. For an El Segundo bottom that is in service, the VCI is again supplied as an aqueous solution that is injected through the leak detection ports. The ports are sealed closed and the solution is allowed to stand for a short period of time. The ports are then opened and the VCI solution is drained leaving a residual amount of the VCI solution within the space. This residual VCI provides the corrosion protection for the space. For an El Segundo bottom that is out of service, perforated pipes are installed into the grooves in the concrete that have leak detection ports. Mesh sleeves containing inhibitor powder is inserted into the perforated pipes and the leak detection ports are closed.
Aboveground storage tanks (Roofs) – The environment in the headspace of an aboveground storage tank can be very aggressive especially for tanks storing crude oil. The environment is aggressive as a result of the acidic species that are typically found in crude oil, (sour crude). Corrosion protection is supplied via a system of dispensers that have been attached to ports that have been installed on the tank roof. (Ports and shut-off valves are installed when the tank is out of service). Bottles containing the VCI are placed in the dispenser and the shut off valves are opened. The VCI has a high vapor pressure such that the inhibitor will saturate the airspace within the dispenser and then will diffuse through the open port into the storage tank headspace.
Oils - The most common use of VCIs in oils is for the protection of oil containing systems like an engine or hydraulics during intermittent use or during longer-term storage (mothballing). The VCI treated oil is typically added to the existing oil and the unit is run to fully circulate the treated oil throughout the system. The system is then shut off for storage. The VCI treated oil can also be fogged into void spaces within a system or enclosed space.
Interior of large enclosed spaces – VCIs have been used to protect the interior of equipment such as tanks, vessels, boilers, piping, heat exchangers, etc., especially for voids and/or recessed areas of interior cavities during storage and/or transportation. The typical means are fogging/blowing the VCI powder into the interior space or applying the VCI powder in packet form. For smaller volumes, the packets are simply distributed within the space. For larger volumes, the packets are attached to leads that are then hung at the perimeter of the space.
Water treatment – Aqueous VCI solutions have been used to flush/rinse pipelines, pumps, manifolds, enclosed pits, heat exchangers, etc. as preparation for mothballing/storage.
Specialty covers – VCI film covers have been used to protect flanges, valves, etc. in harsh environments such as chemical processing plants, offshore platforms, etc.
See also
Corrosion engineering
Cosmoline
Desiccant
References
Further reading
Vendramini, J, Natale, T; (September 11–15, 2016), Corrosion Protection of Storage Tank Bottoms New Application Experience, EuroCorr, Montpellier France
Kaman A, Labine, P, Miksic B.A., Reviews on Corrosion Inhibitors Science and Technology, NACE, pp. 11–16, Houston, Texas
Zerust ReCast - R Inhibitor System, 2012 Materials Performance Readers' Choice Innovation of the Year Awards
Innovation Product Development - VCI Technology Applications Presentation, September 21, 2012, University of Akron NCERCAMP Corrosion Forum
Twigg, R J; (1989) Guidelines for the Mothballing of Process Plants, Materials Technology Institute of the Chemical Process Industries Inc., MTI Publication No 34
Lyublisnki, E, Natale, T; (March 9–13, 2014 ), Corrosion Protection of Mothballed Equipment NACE, San Antonio, Texas
Zerust Flange Savers, 2012 Materials Performance Readers' Choice Innovation of the Year Awards
Paper VCI Product in Turkey. vci kağıt
Corrosion inhibitors
Corrosion prevention
Packaging
Coatings
Corrosion | Volatile corrosion inhibitor | [
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38,530,507 | https://en.wikipedia.org/wiki/Pittsburgh%20Glass%20Center | The Pittsburgh Glass Center is a gallery, glass studio, and public-access school dedicated to teaching, creating and promoting studio glass art. It is located on Penn Avenue in the Friendship neighborhood of Pittsburgh. It has features works by Paul Joseph Stankard and classes taught by Dante Marioni, Davide Salvadore, and Cesare Toffolo.
The origins of the Pittsburgh Glass Center date to 1991, when David Stephens, then visual-arts officer of the Pennsylvania Council on the Arts, approached glass artists Ron Desmett and Kathleen Mulcahy, then a professor at Carnegie Mellon University, about the idea of a center for studio glass. It was originally to have been the Elizabeth Glass Center in Elizabeth, Pennsylvania. However, by 1999, the plans had changed and the center was re-oriented to Pittsburgh. It was officially opened in 2001.
The current facility in Friendship is LEED-certified. Its development has aided the growth of Garfield, especially with the adjacent Glass Lofts residential development.
In fall 2010, the Pittsburgh Glass Center entered into talks with Pittsburgh Filmmakers/Pittsburgh Center for the Arts. By May 2011, the talks had failed, with the Pittsburgh Glass Center withdrawing from negotiations.
In 2012, the Glass Center purchased residential housing adjacent to its main gallery space to be used as student and artist-in-residence housing.
By 2012, the center had a $1 million budget, with 10 full-time employees.
References
Museums in Pittsburgh
Art schools in Pennsylvania
Educational institutions established in 2001
Glassmaking schools
Glass museums and galleries
Education in Pittsburgh
Art museums and galleries in Pennsylvania
Glass museums and galleries in the United States
Museums established in 2001
2001 establishments in Pennsylvania | Pittsburgh Glass Center | [
"Materials_science",
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] | 333 | [
"Glass engineering and science",
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38,532,467 | https://en.wikipedia.org/wiki/Inherent%20viscosity | In polymer science, inherent viscosity is the ratio of the natural logarithm of the relative viscosity of a polymer to its mass concentration. Inherent viscosity scales inversely to mass density, and a common unit is dL/g.
Inherent viscosity is defined as where is the mass concentration of the polymer and is the relative viscosity, which is defined as where is the viscosity of the solution and is the viscosity of the solvent.
The definition of is a finite difference approximation to the derivative That ideal limiting value is the intrinsic viscosity, which is a good measure of the polymerization degree.
References
Viscosity | Inherent viscosity | [
"Physics"
] | 137 | [
"Physical phenomena",
"Physical quantities",
"Wikipedia categories named after physical quantities",
"Viscosity",
"Physical properties"
] |
33,064,180 | https://en.wikipedia.org/wiki/Coulson%E2%80%93Fischer%20theory | In theoretical chemistry and molecular physics, Coulson–Fischer theory provides a quantum mechanical description of the electronic structure of molecules. The 1949 seminal work of Coulson and Fischer established a theory of molecular electronic structure which combines the strengths of the two rival theories which emerged soon after the advent of quantum chemistry - valence bond theory and molecular orbital theory, whilst avoiding many of their weaknesses. For example, unlike the widely used Hartree–Fock molecular orbital method, Coulson–Fischer theory provides a qualitatively correct description of molecular dissociative processes. The Coulson–Fischer wave function has been said to provide a third way in quantum chemistry. Modern valence bond theory is often seen as an extension of the Coulson–Fischer method.
Theory
Coulson–Fischer theory is an extension of modern valence bond theory that uses localized atomic orbitals as the basis for VBT structures. In Coulson-Fischer Theory, orbitals are delocalized towards nearby atoms. This is described for H2 as follows:
where a and b are atomic 1s orbitals, that are used as the basis functions for VBT, and λ is a delocalization parameter from 0 to 1. The VB structures then use and as the basis functions to describe the total electronic wavefunction as
in obvious analogy to the Heitler-London wavefunction. However, an expansion of the Coulson-Fischer description of the wavefunction in terms of a and b gives:
A full VBT description of H2 that includes both ionic and covalent contributions is
where ε and μ are constants between 0 and 1.
As a result, the CF description gives the same description as a full valence bond description, but with just one VB structure.
References
External links
Theoretical chemistry
Molecular physics
Electronic structure methods | Coulson–Fischer theory | [
"Physics",
"Chemistry"
] | 374 | [
"Quantum chemistry stubs",
"Molecular physics",
"Quantum chemistry",
"Theoretical chemistry stubs",
"Quantum mechanics",
"Computational physics",
"Theoretical chemistry",
"Electronic structure methods",
"Computational chemistry",
" molecular",
"nan",
"Atomic",
"Molecular physics stubs",
"P... |
33,065,815 | https://en.wikipedia.org/wiki/%CE%94P | ΔP (Delta P) is a mathematical term symbolizing a change (Δ) in pressure (P).
Uses
Young–Laplace equation
Darcy–Weisbach equation
Given that the head loss hf expresses the pressure loss Δp as the height of a column of fluid,
where ρ is the density of the fluid. The Darcy–Weisbach equation can also be written in terms of pressure loss:
Lung compliance
In general, compliance is defined by the change in volume (ΔV) versus the associated change in pressure (ΔP), or ΔV/ΔP:
During mechanical ventilation, compliance is influenced by three main physiologic factors:
Lung compliance
Chest wall compliance
Airway resistance
Lung compliance is influenced by a variety of primary abnormalities of lung parenchyma, both chronic and acute. Airway resistance is typically increased by bronchospasm and airway secretions. Chest wall compliance can be decreased by fixed abnormalities (e.g. kyphoscoliosis, morbid obesity) or more variable problems driven by patient agitation while intubated.
Calculating compliance on minute volume (VE: ΔV is always defined by tidal volume (VT), but ΔP is different for the measurement of dynamic vs. static compliance.
Dynamic compliance (Cdyn)
where PIP = peak inspiratory pressure (the maximum pressure during inspiration), and PEEP = positive end expiratory pressure. Alterations in airway resistance, lung compliance and chest wall compliance influence Cdyn.
Static compliance (Cstat)
where Pplat = plateau pressure. Pplat is measured at the end of inhalation and prior to exhalation using an inspiratory hold maneuver. During this maneuver, airflow is transiently (~0.5 sec) discontinued, which eliminates the effects of airway resistance. Pplat is never > PIP and is typically < 3-5 cmH2O lower than PIP when airway resistance is normal.
See also
Pressure measurement
Pressure drop
Head loss
References
External links
Delta P, Diving Pressure Hazard
Mathematical notation
Pressure
Respiratory therapy
Mathematics in medicine | ΔP | [
"Physics",
"Mathematics"
] | 428 | [
"Scalar physical quantities",
"Mechanical quantities",
"Physical quantities",
"Applied mathematics",
"Pressure",
"nan",
"Wikipedia categories named after physical quantities",
"Mathematics in medicine"
] |
33,066,922 | https://en.wikipedia.org/wiki/Fire%20room | On a ship, the fire room, or FR or boiler room or stokehold, referred to the space, or spaces, of a vessel where water was brought to a boil. The steam was then transmitted to a separate engine room, often (but not always) located immediately aft, where it was utilized to power the vessel. To increase the safety and damage survivability of a vessel, the machinery necessary for operations may be segregated into various spaces, the fire room was one of these spaces, and was among the largest physical compartment of the machinery space. On some ships, the space comprised more than one fire room, such as forward and aft, or port or starboard fire rooms, or may be simply numbered. Each room was connected to a flue, exhausting into a stack ventilating smoke.
By their nature, fire rooms were less complex than their allied engine room and were normally supervised by less senior personnel.
On a large percentage of vessels, ships and boats, the fire room was located near the bottom, and at the rear, or aft, end of the vessel, and usually comprised few compartments. This design maximized the cargo carrying capacity of the vessel. The fire room on some ships was situated amid-ships, especially on vessels built from the 1880s to the 1990s.
Equipment
Vessels typically contained several engines for different purposes. Main, or propulsion engines are used to turn the ship's propeller and move the ship through the water. The fire room got its name from the days when ships burned coal to heat steam to drive the steam engines or turbines; the room was where the stokers spent their days shoveling coal continuously onto the grates under the boiler; poor men could sometimes pay for a trip across the Atlantic by signing on to work as a stoker for a one way trip, laboring in exchange for a temporary place on the crew. Later heavy fuel oil came into use, first combined with coal, then alone, as the petroleum industry developed, and the cleaner, easier to transport, load and burn liquid was found to be far superior once the appropriate logistical network was set up. With coal power, there was a mechanism for removing ash from the grates, as they would build up rapidly over time (the lighter fly ash would be drawn up the stack with the smoke).
On a steamship, power for both electricity and propulsion is provided by one or more large boilers giving rise to the alternate name boiler room. The latter name was preferred in the British Navy, among others. High pressure steam from the boiler is piped to the engine room to drive reciprocating engines or turbines for propulsion, and turbo generators for electricity. When cruising, it was normal for a naval vessel to damp the fires on up to two-thirds of their boilers, and use the steam from only a few boilers in one or two fire rooms to power the engines at low power. When higher speeds were required, more boilers would be brought on line (they were rarely extinguished entirely, as re-lighting a boiler was time-consuming). In rare occasions, when flank speed was called for, all boilers would be burning at once, generating a great deal of steam for high-speed operation, but at a very inefficient rate of coal consumption. Merchant vessels had much less need for high speed, so they would generally be satisfied with far fewer boilers, and much lower maximum speeds (and even then they would often save on fuel by not using all of the boilers, and traveling at a sedate 4-5 knots).
Naval ships typically were able to generate a large volume of smoke by changing the fuel mix. Prior to the heavy use of radar, a smoke screen could be used to mask the movement of ships (although smoke screens produced by smoke generators were also used). Coal in particular produced a large amount of black smoke, depending on the grade of coal; generally, the smallest amount of smoke was the most desirable, as it made the vessel harder to spot on the horizon.
Damage control
Damage control was enhanced by the separation of the fire and engine rooms. In the event of damage to its associated engine room, steam could be transmitted to another engine room. In turn, an engine room could still operate though its associated fire room had become inoperative.
Two engineering advances resulted in the disappearance of the fire room in the early 1990s. The first was the movement by naval shipbuilding to nuclear-powered vessels. If a room containing nuclear material was subjected to damage, it was assumed that the event would likely result in abandonment of the ship regardless of the separation of rooms.
The second was the adoption of gas turbines in place of oil-fired boilers for all other navy ships. These powered engines directly and needed no boilers.
Safety
Fire precautions
Fire rooms were hot, most often very dirty, and potentially dangerous. The presence of flammable fuel meant that a fire hazard existed in the fire room, which was monitored continuously by the ship's engineering staff and various monitoring systems.
Ventilation
Fire rooms employed some means of providing air for the operation of the flame to ignite the oil and associated ventilation. Only spot ventilation was practical to keep personnel cool. This would require an unrestricted hull opening of the same size as the intake area of the engine itself assuming the hull opening is in the fire room itself.
Forced draft fire rooms were used until World War II. These required that personnel enter through an air lock to maintain the pressure. These were abandoned when the forced draft occasionally failed and blowback occurred killing fire room personnel.
Commonly, screens were placed over openings reducing airflow by approximately 50% so the opening area was increased appropriately. The requirement for general ventilation and the requirement for sufficient combustion air are quite different. A typical arrangement might be to make the opening large enough to provide intake air plus per Minute (CFM) for additional ventilation. Engines pull sufficient air into the fire room for their own operation. However, additional airflow for ventilation usually requires intake and exhaust blowers.
Staffing requirements
When fired up, there were personnel assignments specified underway, as well as in port. For example, for an , in normal steaming four boilers were operated. This was sufficient to power the ships at speeds up to . For higher speeds, all eight boilers were lit. Each operating boiler required a minimum of four trained operators on watch: a boiler supervisor (BTOW), a superheater burnerman and saturated burnerman to control the steam temperature and pressure and a checkman, who monitored and controlled the water level in the steam drum. In addition, there was a fireroom messenger and a lower level pumpman on duty whenever the fireroom was steaming.
See also
Kearny incident
Engineering department
Marine propulsion
Marine fuel management
Mechanical room
Electrical room
Notes
External links
Photos of fire room in USS Minneapolis
Notes on boiler room operations
Video of fire room aboard Stettin
Ship compartments
Marine propulsion | Fire room | [
"Engineering"
] | 1,389 | [
"Marine propulsion",
"Marine engineering"
] |
33,070,822 | https://en.wikipedia.org/wiki/Sacrificial%20metal | A sacrificial metal is a metal used as a sacrificial anode in cathodic protection that corrodes to prevent a primary metal from corrosion or rusting. It may also be used for galvanization.
Equation
When two metals touch each other and water is present, electrolysis occurs. One well known example is the reaction between zinc (Zn) and iron (Fe). Zinc atoms will lose electrons in preference to the iron as they are more electropositive and therefore zinc is oxidized and corrodes.
Zn(s)→(aq) +2e (oxidation)
Capacity derivation from 1st Principles
The capacity of a sacrificial metal may be calculated from first principle as follows:
1 kg Al = 1000/27 moles Al
1 kg Al = 3 x 1000/27 moles of electrons
1 kg Al = 3 x 1000/27 x 96494 coulombs of charge (by Faraday principles)
= 10.72 x 106 Amp.seconds of charge per Kg Al (1 Coulomb = 1 Amp.Second)
= 10.72 x 106/3600 = 2978 Amp.Hours per Kg
By similar calculations Zinc and Magnesium have a capacity of 825 and 2206 Amp.Hours per Kg respectively.
Uses
Sacrificial metals are widely used to prevent other metals from corroding: for example in galvanised steel. Many steel objects are coated with a layer of zinc, which is more electronegative than iron, and thus oxidises in preference to the iron, preventing the iron from rusting. Similarly, sacrificial bars of a metal such as aluminium or aluminium alloys can be attached to an oil rig or to the hull of a ship to prevent it from rusting and breaking down. Magnesium may similarly be used on dry land for installations such as pipelines and oil refineries, where its high driving voltage is better for overcoming the resistance of soils found on dry land.
See also
Metal in electrochemical series
Corrosion engineering
References
Further reading
Brett CMA, Brett AMO, ELECTROCHEMISTRY, Principles, methods, and applications, Oxford University Press, (1993)
Electrochemistry
Corrosion prevention
Metallurgy | Sacrificial metal | [
"Chemistry",
"Materials_science",
"Engineering"
] | 453 | [
"Corrosion prevention",
"Metallurgy",
"Materials science",
"Corrosion",
"Electrochemistry",
"nan",
"Electrochemistry stubs",
"Physical chemistry stubs"
] |
33,072,764 | https://en.wikipedia.org/wiki/National%20Ganga%20River%20Basin%20Authority | National Ganga River Basin Authority (NGRBA) is a financing, planning, implementing, monitoring and coordinating authority for the Ganges River, functioning under the Ministry of Jal Shakti, of India. The mission of the organisation is to safeguard the drainage basin which feeds water into the Ganges by protecting it from pollution or overuse. In July 2014, the NGRBA was transferred from the Ministry of Environment and Forests to the Department of Water Resources, River Development & Ganga Rejuvenation, formerly the Ministry of Water Resources (India).
The Government of India, in a notification issued on 20 September 2016, announced that it has taken the decision under the River Ganga (Rejuvenation, Protection and Management) Authorities Order 2016 to establish a new body named the "National Council for River Ganga (Rejuvenation, Protection and Management)" (NCRG) to replace the existing NGRBA. The new body will act as an authority replacing the existing National Ganga River Basin Authority for overall responsibility pollution prevention and rejuvenation of the Ganges Basin
Establishment
It was established by the Government of India, on 20 February 2009 under Section 3(3) of the Environment Protection Act, 1986, which also declared the Ganges as the "National River" of India.
Overview
The Prime Minister is the chair of the Authority. Other members include the cabinet ministers of ministries that include the Ganges among their direct concerns and the chief ministers of states through which the Ganges River flows. The Chief Ministers as members are from the states through which Ganges flow viz. Uttarakhand, UP, Bihar, Jharkhand, West Bengal, among others.
The first meeting of the National Ganga River Basin Authority was held on 5 October 2009.
In the 2010 Union budget of India, the allocation for National Ganga River Basin Authority doubled to 500 crore (5,000,000,000.00).
Members of the NGRBA
There are total of 23 members of the NGRBA. 14 out of 23 come from the government sectors whereas the remaining 9 come from the NGO sector.
Government members of the Committee
Members belonging to the government sector are as follows:
Prime Minister of India, chair
Minister of Environment and Forests (Union Minister)
Minister of Finance
Minister of Urban Development
Minister of Water Resources
Minister of Power
Minister of Sciences and Technology
Chief Minister of Uttarakhand
Chief Minister of Uttar Pradesh
Chief Minister of Bihar
Chief Minister of Jharkhand
Chief Minister of West Bengal
Ministry of Environment and Forests (state minister)
Ministry of Environment and Forests, secretary
Expert members of the committee
Members belonging to the NGO sector are as follows:
Justice(Retd.) Giridhar Malviya, Patron, Ganga Mahasabha, Varanasi.
Shri Mohan Singh Rawat Gaonwasi, Ex. Minister Uttarakhand.
Shri M.A. Chitle, Maharashtra.
Dr. Bhure lal, IAS (Retd.), Delhi
Shri N.Vittal, Chennai
References
External links
National Ganga River Basin Authority, website
2009 establishments in Delhi
Ganges
Government agencies of India
Government agencies established in 2009
Environment of India
Organisations based in Delhi
Ecological restoration
Water in India
Ministry of Water Resources (India)
Environmental organisations based in India | National Ganga River Basin Authority | [
"Chemistry",
"Engineering"
] | 649 | [
"Ecological restoration",
"Environmental engineering"
] |
25,844,292 | https://en.wikipedia.org/wiki/Fundamental%20theorem%20of%20linear%20programming | In mathematical optimization, the fundamental theorem of linear programming states, in a weak formulation, that the maxima and minima of a linear function over a convex polygonal region occur at the region's corners. Further, if an extreme value occurs at two corners, then it must also occur everywhere on the line segment between them.
Statement
Consider the optimization problem
Where . If is a bounded polyhedron (and thus a polytope) and is an optimal solution to the problem, then is either an extreme point (vertex) of , or lies on a face of optimal solutions.
Proof
Suppose, for the sake of contradiction, that . Then there exists some such that the ball of radius centered at is contained in , that is . Therefore,
and
Hence is not an optimal solution, a contradiction. Therefore, must live on the boundary of . If is not a vertex itself, it must be the convex combination of vertices of , say . Then with and . Observe that
Since is an optimal solution, all terms in the sum are nonnegative. Since the sum is equal to zero, we must have that each individual term is equal to zero. Hence, for each , so every is also optimal, and therefore all points on the face whose vertices are , are optimal solutions.
References
Linear programming | Fundamental theorem of linear programming | [
"Mathematics"
] | 260 | [
"Theorems in mathematical analysis",
"Mathematical analysis",
"Mathematical problems",
"Mathematical theorems"
] |
22,917,401 | https://en.wikipedia.org/wiki/Volute%20%28pump%29 | A volute is a curved funnel that increases in area as it approaches the discharge port. The volute of a centrifugal pump is the casing that receives the fluid being pumped by the impeller, maintaining the velocity of the fluid through to the diffuser. As liquid exits the impeller it has high kinetic energy and the volute directs this flow through to the discharge. As the fluid travels along the volute it is joined by more and more fluid exiting the impeller but, as the cross sectional area of the volute increases, the velocity is maintained if the pump is running close to the design point. If the pump has a low flow rate then the velocity will decrease across the volute leading to a pressure rise causing a cross thrust across the impeller that we see as vibration. If the pump flow is higher than design the velocity will increase across the volute and the pressure will decrease according to the first law of thermodynamics. This will cause a side thrust in the opposite direction to that caused by low flow but the result is the samevibration with resultant short bearing and seal life.
The volute does not convert kinetic energy into pressurethat is done at the diffuser by reducing liquid velocity while increasing pressure.
The name "volute" is inspired by the resemblance of this kind of casing to the scroll-like part near the top of an ionic order column in classical architecture, called a volute.
Split volute
In a split volute or double volute pump, the path along the volute is partitioned, providing two distinct discharge paths. The streams start out 180 degrees from each other, and merge by the time they reach the discharge port. This arrangement helps to balance the radial force on the bearings.
See also
Roots blower
References
Fluid dynamics
Pumps | Volute (pump) | [
"Physics",
"Chemistry",
"Engineering"
] | 368 | [
"Pumps",
"Turbomachinery",
"Chemical engineering",
"Physical systems",
"Hydraulics",
"Piping",
"Fluid dynamics"
] |
22,920,002 | https://en.wikipedia.org/wiki/Determinantal%20variety | In algebraic geometry, determinantal varieties are spaces of matrices with a given upper bound on their ranks. Their significance comes from the fact that many examples in algebraic geometry are of this form, such as the Segre embedding of a product of two projective spaces.
Definition
Given m and n and r < min(m, n), the determinantal variety Y r is the set of all m × n matrices (over a field k) with rank ≤ r. This is naturally an algebraic variety as the condition that a matrix have rank ≤ r is given by the vanishing of all of its (r + 1) × (r + 1) minors. Considering the generic m × n matrix whose entries are algebraically independent variables x i,j, these minors are polynomials of degree r + 1. The ideal of k[x i,j] generated by these polynomials is a determinantal ideal. Since the equations defining minors are homogeneous, one can consider Y r either as an affine variety in mn-dimensional affine space, or as a projective variety in (mn − 1)-dimensional projective space.
Properties
The radical ideal defining the determinantal variety is generated by the (r + 1) × (r + 1) minors of the matrix (Bruns-Vetter, Theorem 2.10).
Assuming that we consider Y r as an affine variety, its dimension is r(m + n − r). One way to see this is as follows: form the product space over where is the Grassmannian of r-planes in an m-dimensional vector space, and consider the subspace , which is a desingularization of (over the open set of matrices with rank exactly r, this map is an isomorphism), and is a vector bundle over which is isomorphic to where is the tautological bundle over the Grassmannian. So since they are birationally equivalent, and since the fiber of has dimension nr.
The above shows that the matrices of rank <r contains the singular locus of , and in fact one has equality. This fact can be verified using that the radical ideal is given by the minors along with the Jacobian criterion for nonsingularity.
The variety Y r naturally has an action of , a product of general linear groups. The problem of determining the syzygies of , when the characteristic of the field is zero, was solved by Alain Lascoux, using the natural action of G.
Related topics
One can "globalize" the notion of determinantal varieties by considering the space of linear maps between two vector bundles on an algebraic variety. Then the determinantal varieties fall into the general study of degeneracy loci. An expression for the cohomology class of these degeneracy loci is given by the Thom-Porteous formula, see (Fulton-Pragacz).
References
Algebraic geometry
Algebraic varieties | Determinantal variety | [
"Mathematics"
] | 594 | [
"Fields of abstract algebra",
"Algebraic geometry"
] |
37,092,814 | https://en.wikipedia.org/wiki/Pterobranchia%20mitochondrial%20code | The pterobranchia mitochondrial code (translation table 24) is a genetic code used by the mitochondrial genome of Rhabdopleura compacta (Pterobranchia). The Pterobranchia are one of the two groups in the Hemichordata which together with the Echinodermata and Chordata form the three major lineages of deuterostomes. AUA translates to isoleucine in Rhabdopleura as it does in the Echinodermata and Enteropneusta while AUA encodes methionine in the Chordata. The assignment of AGG to lysine is not found elsewhere in deuterostome mitochondria but it occurs in some taxa of Arthropoda. This code shares with many other mitochondrial codes the reassignment of the UGA STOP to tryptophan, and AGG and AGA to an amino acid other than arginine. The initiation codons in Rhabdopleura compacta are ATG and GTG.
Code 24 is very similar to the mitochondrial code 33 for the Pterobranchia.
The code
AAs = FFLLSSSSYY**CCWWLLLLPPPPHHQQRRRRIIIMTTTTNNKKSSSKVVVVAAAADDEEGGGG
Starts = ---M---------------M---------------M---------------M------------
Base1 = TTTTTTTTTTTTTTTTCCCCCCCCCCCCCCCCAAAAAAAAAAAAAAAAGGGGGGGGGGGGGGGG
Base2 = TTTTCCCCAAAAGGGGTTTTCCCCAAAAGGGGTTTTCCCCAAAAGGGGTTTTCCCCAAAAGGGG
Base3 = TCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAG
Bases: adenine (A), cytosine (C), guanine (G) and thymine (T) or uracil (U).
Amino acids: Alanine (Ala, A), Arginine (Arg, R), Asparagine (Asn, N), Aspartic acid (Asp, D), Cysteine (Cys, C), Glutamic acid (Glu, E), Glutamine (Gln, Q), Glycine (Gly, G), Histidine (His, H), Isoleucine (Ile, I), Leucine (Leu, L), Lysine (Lys, K), Methionine (Met, M), Phenylalanine (Phe, F), Proline (Pro, P), Serine (Ser, S), Threonine (Thr, T), Tryptophan (Trp, W), Tyrosine (Tyr, Y), Valine (Val, V)
Differences from the standard code
See also
List of genetic codes
References
Molecular genetics
Gene expression
Protein biosynthesis | Pterobranchia mitochondrial code | [
"Chemistry",
"Biology"
] | 705 | [
"Protein biosynthesis",
"Gene expression",
"Molecular genetics",
"Biosynthesis",
"Cellular processes",
"Molecular biology",
"Biochemistry"
] |
37,094,071 | https://en.wikipedia.org/wiki/Station%20clock | A station clock is a clock at a railway station that provides a standard indication of time to both passengers and railway staff.
A railway station will often have several station clocks. They can be found in a clock tower, in the booking hall or office, on the concourse, inside a train shed, on or facing the station platforms, or elsewhere.
Design
The design of station clocks in Europe was formerly quite diverse. Today, the majority of them are derived from the Swiss railway clock designed by Hans Hilfiker, a Swiss engineer, in 1944 when he was an employee of the Swiss Federal Railways. In 1953, Hilfiker added a red second hand to its design in the shape of a railway guard's signaling disc. The technical implementation of the railway clock, the central synchronization by a master clock, was engineered together with Mobatime, a clock manufacturer still producing the Swiss railway clock as well as the German railway clock besides many others.
Modern European station standard station clock designs have a white clock face that is illuminated in the dark, bar shaped black coloured marks or scales, but no numbers, at the periphery of the clock face dial, and bar-shaped hour and minute hands, also coloured black. The second hand on these standard designs is a thin bar, thickened or fitted with a disc at the peripheral end, and often coloured red. Such clock designs are easily legible from a distance.
Examples
See also
Electric clock
Railway time
Standard time
References
Notes
Bibliography
External links
Railway Station Clocks - Architecture of Time
Clocks
Clock | Station clock | [
"Physics",
"Technology",
"Engineering"
] | 312 | [
"Physical systems",
"Machines",
"Clocks",
"Measuring instruments"
] |
34,554,373 | https://en.wikipedia.org/wiki/Reentrant%20superconductivity | In physics, reentrant superconductivity is an effect observed in systems that lie close to the boundary between ferromagnetic and superconducting. By its very nature (normal) superconductivity (condensation of electrons into the BCS ground state) cannot exist together with ferromagnetism (condensation of electrons into the same spin state, all pointing in the same direction). Reentrance is when while changing a continuous parameter, superconductivity is first observed, then destroyed by the ferromagnetic order, and later reappears.
An example is the changing of the thickness of the ferromagnetic layer in a bilayer of a superconductor and a ferromagnet. At a certain thickness superconductivity is destroyed by the Andreev reflected electrons in the ferromagnet, but if the thickness increases, this effect disappears again.
Another example are materials with a Curie temperature below the superconducting transition temperature. When cooling, first superconducting order appears in the electron system. Cooling further, the ferromagnetic order energetically wins over the superconducting order in the electron system. At even lower energy superconductivity reenters, and a nonuniform magnetic order appears. there is ferromagnetic order on short length scales, but superconducting order on large length scales.
Examples
Uranium ditelluride, (UTe2) a spin-triplet superconductor. Discovered to be a superconductor in 2018.
See also
Ferromagnetic superconductor
Further reading
Ferromagnetism and reentrant superconductivity 1998
Reentrant Superconductivity of CeRu2 1993
Reentrant superconductivity in Eu(Fe1−xIrx)2As2 2013
References
Superconductivity | Reentrant superconductivity | [
"Physics",
"Materials_science",
"Engineering"
] | 404 | [
"Physical quantities",
"Superconductivity",
"Materials science",
"Condensed matter physics",
"Electrical resistance and conductance"
] |
34,557,525 | https://en.wikipedia.org/wiki/NucleaRDB | The NucleaRDB is a database of nuclear receptors. It contains data about the sequences, ligand binding constants and mutations of those proteins.
See also
Nuclear receptor
References
External links
https://web.archive.org/web/20120409204749/http://www.receptors.org/nucleardb/.
Biological databases
Intracellular receptors
Protein families
Transcription factors | NucleaRDB | [
"Chemistry",
"Biology"
] | 79 | [
"Gene expression",
"Protein classification",
"Signal transduction",
"Bioinformatics",
"Induced stem cells",
"Protein families",
"Biological databases",
"Transcription factors"
] |
1,422,176 | https://en.wikipedia.org/wiki/Developmental%20robotics | Developmental robotics (DevRob), sometimes called epigenetic robotics, is a scientific field which aims at studying the developmental mechanisms, architectures and constraints that allow lifelong and open-ended learning of new skills and new knowledge in embodied machines. As in human children, learning is expected to be cumulative and of progressively increasing complexity, and to result from self-exploration of the world in combination with social interaction. The typical methodological approach consists in starting from theories of human and animal development elaborated in fields such as developmental psychology, neuroscience, developmental and evolutionary biology, and linguistics, then to formalize and implement them in robots, sometimes exploring extensions or variants of them. The experimentation of those models in robots allows researchers to confront them with reality, and as a consequence, developmental robotics also provides feedback and novel hypotheses on theories of human and animal development.
Developmental robotics is related to but differs from evolutionary robotics (ER). ER uses populations of robots that evolve over time, whereas DevRob is interested in how the organization of a single robot's control system develops through experience, over time.
DevRob is also related to work done in the domains of robotics and artificial life.
Background
Can a robot learn like a child? Can it learn a variety of new skills and new knowledge unspecified at design time and in a partially unknown and changing environment? How can it discover its body and its relationships with the physical and social environment? How can its cognitive capacities continuously develop without the intervention of an engineer once it is "out of the factory"? What can it learn through natural social interactions with humans? These are the questions at the center of developmental robotics. Alan Turing, as well as a number of other pioneers of cybernetics, already formulated those questions and the general approach in 1950,
but it is only since the end of the 20th century that they began to be investigated systematically.
Because the concept of adaptive intelligent machines is central to developmental robotics, it has relationships with fields such as artificial intelligence, machine learning, cognitive robotics or computational neuroscience. Yet, while it may reuse some of the techniques elaborated in these fields, it differs from them from many perspectives. It differs from classical artificial intelligence because it does not assume the capability of advanced symbolic reasoning and focuses on embodied and situated sensorimotor and social skills rather than on abstract symbolic problems. It differs from cognitive robotics because it focuses on the processes that allow the formation of cognitive capabilities rather than these capabilities themselves. It differs from computational neuroscience because it focuses on functional modeling of integrated architectures of development and learning. More generally, developmental robotics is uniquely characterized by the following three features:
It targets task-independent architectures and learning mechanisms, i.e. the machine/robot has to be able to learn new tasks that are unknown by the engineer;
It emphasizes open-ended development and lifelong learning, i.e. the capacity of an organism to acquire continuously novel skills. This should not be understood as a capacity for learning "anything" or even “everything”, but just that the set of skills that is acquired can be infinitely extended at least in some (not all) directions;
The complexity of acquired knowledge and skills shall increase (and the increase be controlled) progressively.
Developmental robotics emerged at the crossroads of several research communities including embodied artificial intelligence, enactive and dynamical systems cognitive science, connectionism. Starting from the essential idea that learning and development happen as the self-organized result of the dynamical interactions among brains, bodies and their physical and social environment, and trying to understand how this self-organization can be harnessed to provide task-independent lifelong learning of skills of increasing complexity, developmental robotics strongly interacts with fields such as developmental psychology, developmental and cognitive neuroscience, developmental biology (embryology), evolutionary biology, and cognitive linguistics. As many of the theories coming from these sciences are verbal and/or descriptive, this implies a crucial formalization and computational modeling activity in developmental robotics. These computational models are then not only used as ways to explore how to build more versatile and adaptive machines but also as a way to evaluate their coherence and possibly explore alternative explanations for understanding biological development.
Research directions
Skill domains
Due to the general approach and methodology, developmental robotics projects typically focus on having robots develop the same types of skills as human infants. A first category that is important being investigated is the acquisition of sensorimotor skills. These include the discovery of one's own body, including its structure and dynamics such as hand-eye coordination, locomotion, and interaction with objects as well as tool use, with a particular focus on the discovery and learning of affordances. A second category of skills targeted by developmental robots are social and linguistic skills: the acquisition of simple social behavioural games such as turn-taking, coordinated interaction, lexicons, syntax and grammar, and the grounding of these linguistic skills into sensorimotor skills (sometimes referred as symbol grounding). In parallel, the acquisition of associated cognitive skills are being investigated such as the emergence of the self/non-self distinction, the development of attentional capabilities, of categorization systems and higher-level representations of affordances or social constructs, of the emergence of values, empathy, or theories of mind.
Mechanisms and constraints
The sensorimotor and social spaces in which humans and robot live are so large and complex that only a small part of potentially learnable skills can actually be explored and learnt within a life-time. Thus, mechanisms and constraints are necessary to guide developmental organisms in their development and control of the growth of complexity. There are several important families of these guiding mechanisms and constraints which are studied in developmental robotics, all inspired by human development:
Motivational systems, generating internal reward signals that drive exploration and learning, which can be of two main types:
extrinsic motivations push robots/organisms to maintain basic specific internal properties such as food and water level, physical integrity, or light (e.g. in phototropic systems);
intrinsic motivations push robot to search for novelty, challenge, compression or learning progress per se, thus generating what is sometimes called curiosity-driven learning and exploration, or alternatively active learning and exploration;
Social guidance: as humans learn a lot by interacting with their peers, developmental robotics investigates mechanisms that can allow robots to participate to human-like social interaction. By perceiving and interpreting social cues, this may allow robots both to learn from humans (through diverse means such as imitation, emulation, stimulus enhancement, demonstration, etc. ...) and to trigger natural human pedagogy. Thus, social acceptance of developmental robots is also investigated;
Statistical inference biases and cumulative knowledge/skill reuse: biases characterizing both representations/encodings and inference mechanisms can typically allow considerable improvement of the efficiency of learning and are thus studied. Related to this, mechanisms allowing to infer new knowledge and acquire new skills by reusing previously learnt structures is also an essential field of study;
The properties of embodiment, including geometry, materials, or innate motor primitives/synergies often encoded as dynamical systems, can considerably simplify the acquisition of sensorimotor or social skills, and is sometimes referred as morphological computation. The interaction of these constraints with other constraints is an important axis of investigation;
Maturational constraints: In human infants, both the body and the neural system grow progressively, rather than being full-fledged already at birth. This implies, for example, that new degrees of freedom, as well as increases of the volume and resolution of available sensorimotor signals, may appear as learning and development unfold. Transposing these mechanisms in developmental robots, and understanding how it may hinder or on the contrary ease the acquisition of novel complex skills is a central question in developmental robotics.
From bio-mimetic development to functional inspiration.
While most developmental robotics projects interact closely with theories of animal and human development, the degrees of similarities and inspiration between identified biological mechanisms and their counterpart in robots, as well as the abstraction levels of modeling, may vary a lot. While some projects aim at modeling precisely both the function and biological implementation (neural or morphological models), such as in Neurorobotics, some other projects only focus on functional modeling of the mechanisms and constraints described above, and might for example reuse in their architectures techniques coming from applied mathematics or engineering fields.
Open questions
As developmental robotics is a relatively new research field and at the same time very ambitious, many fundamental open challenges remain to be solved.
First of all, existing techniques are far from allowing real-world high-dimensional robots to learn an open-ended repertoire of increasingly complex skills over a life-time period. High-dimensional continuous sensorimotor spaces constitute a significant obstacle to be solved. Lifelong cumulative learning is another one. Actually, no experiments lasting more than a few days have been set up so far, which contrasts severely with the time needed by human infants to learn basic sensorimotor skills while equipped with brains and morphologies which are tremendously more powerful than existing computational mechanisms.
Among the strategies to explore to progress towards this target, the interaction between the mechanisms and constraints described in the previous section shall be investigated more systematically. Indeed, they have so far mainly been studied in isolation. For example, the interaction of intrinsically motivated learning and socially guided learning, possibly constrained by maturation, is an essential issue to be investigated.
Another important challenge is to allow robots to perceive, interpret and leverage the diversity of multimodal social cues provided by non-engineer humans during human-robot interaction. These capacities are so far, mostly too limited to allow efficient general-purpose teaching from humans.
A fundamental scientific issue to be understood and resolved, which applied equally to human development, is how compositionality, functional hierarchies, primitives, and modularity, at all levels of sensorimotor and social structures, can be formed and leveraged during development. This is deeply linked with the problem of the emergence of symbols, sometimes referred to as the "symbol grounding problem" when it comes to language acquisition. Actually, the very existence and need for symbols in the brain are actively questioned, and alternative concepts, still allowing for compositionality and functional hierarchies are being investigated.
During biological epigenesis, morphology is not fixed but rather develops in constant interaction with the development of sensorimotor and social skills. The development of morphology poses obvious practical problems with robots, but it may be a crucial mechanism that should be further explored, at least in simulation, such as in morphogenetic robotics.
Another open problem is the understanding of the relation between the key phenomena investigated by developmental robotics (e.g., hierarchical and modular sensorimotor systems, intrinsic/extrinsic/social motivations, and open-ended learning) and the underlying brain mechanisms.
Similarly, in biology, developmental mechanisms (operating at the ontogenetic time scale) interact closely with evolutionary mechanisms (operating at the phylogenetic time scale) as shown in the flourishing "evo-devo" scientific literature.
However, the interaction of those mechanisms in artificial organisms, developmental robots, in particular, is still vastly understudied. The interaction of evolutionary mechanisms, unfolding morphologies and developing sensorimotor and social skills will thus be a highly stimulating topic for the future of developmental robotics.
Main journals
IEEE Transactions on Cognitive and Developmental Systems (previously known as IEEE Transactions on Autonomous Mental Development): https://cis.ieee.org/publications/t-cognitive-and-developmental-systems
Main conferences
International Conference on Development and Learning: http://www.cogsci.ucsd.edu/~triesch/icdl/
Epigenetic Robotics: https://www.lucs.lu.se/epirob/
ICDL-EpiRob: http://www.icdl-epirob.org/ (the two above joined since 2011)
Developmental Robotics: http://cs.brynmawr.edu/DevRob05/
The NSF/DARPA funded Workshop on Development and Learning was held April 5–7, 2000 at Michigan State University. It was the first international meeting devoted to computational understanding of mental development by robots and animals. The term "by" was used since the agents are active during development.
See also
Evolutionary developmental robotics
Robot learning
References
External links
Technical committees
IEEE Technical Committee on Cognitive and Developmental Systems (CDSTC), previously known as IEEE Technical Committee on Autonomous Mental Development,
IEEE Technical Committee on Cognitive Robotics, https://www.ieee-ras.org/cognitive-robotics
IEEE Technical Committee on Robot Learning, https://www.ieee-ras.org/robot-learning/
Academic institutions and researchers in the field
Lund University Cognitive Science - Robotics Group
Cognitive Development Lab, University of Indiana, US
Michigan State University – Embodied Intelligence Lab
Inria and Ensta ParisTech FLOWERS team, France: Exploration, interaction and learning in developmental robotics
University of Tokyo—Intelligent Systems and Informatics Lab
Cognitive Robotics Lab of Juergen Schmidhuber at IDSIA and Technical University of Munich
LIRA-Lab, University of Genova, Italy
CITEC at University of Bielefeld, Germany
Vision Lab, Psychology Department, Southern Illinois University Carbondale
FIAS (J. Triesch lab.)
LPP, CNRS (K. Oregan lab.)
AI Lab, SoftBank Robotics Europe, France
Departement of Computer Science, University of Aberdeen
Asada Laboratory, Department of Adaptive Machine Systems, Graduate School of Engineering, Osaka University, Japan
The University of Texas at Austin, UTCS Intelligent Robotics Lab
Bryn Mawr College's Developmental Robotics Project: research projects by faculty and students at Swarthmore and Bryn Mawr Colleges, Philadelphia, PA, USA
Jean Project: Information Sciences Institute of the University of Southern California
Cognitive Robotics (including Hide and Seek) at the Naval Research Laboratory
The Laboratory for Perceptual Robotics, University of Massachusetts Amherst Amherst, USA
Centre for Robotics and Neural Systems, Plymouth University Plymouth, United Kingdom
Laboratory of Computational Embodied Neuroscience, Institute of Cognitive Science and Technologies National Research Council, Rome, Italy
Neurocybernetic team, ETIS Lab., ENSEA – University of Cergy-Pontoise – CNRS, France
Machine Perception and Cognitive Robotics Lab, Florida Atlantic University, Boca Raton, Florida
Adaptive Systems Group, Department of Computer Science, Humboldt University of Berlin, Germany
Cognitive Developmental Robotics Lab (Nagai Lab), The University of Tokyo, Japan
Related large-scale projects
RobotDoC Project (funded by European Commission)
Italk Project (funded by European Commission)
IM-CLeVeR Project (funded by European Commission)
ERC Grant EXPLORERS Project (funded by European Research Council)
RobotCub Project (funded by European Commission)
Feelix Growing Project (funded by European Commission)
Courses
The first undergraduate courses in DevRob were offered at Bryn Mawr College and Swarthmore College in the Spring of 2003 by Douglas Blank and Lisa Meeden, respectively.
The first graduate course in DevRob was offered at Iowa State University by Alexander Stoytchev in the Fall of 2005.
Robotics
Learning
Machine learning | Developmental robotics | [
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1,422,748 | https://en.wikipedia.org/wiki/Nonlinear%20Schr%C3%B6dinger%20equation | In theoretical physics, the (one-dimensional) nonlinear Schrödinger equation (NLSE) is a nonlinear variation of the Schrödinger equation. It is a classical field equation whose principal applications are to the propagation of light in nonlinear optical fibers and planar waveguides and to Bose–Einstein condensates confined to highly anisotropic, cigar-shaped traps, in the mean-field regime. Additionally, the equation appears in the studies of small-amplitude gravity waves on the surface of deep inviscid (zero-viscosity) water; the Langmuir waves in hot plasmas; the propagation of plane-diffracted wave beams in the focusing regions of the ionosphere; the propagation of Davydov's alpha-helix solitons, which are responsible for energy transport along molecular chains; and many others. More generally, the NLSE appears as one of universal equations that describe the evolution of slowly varying packets
of quasi-monochromatic waves in weakly nonlinear media that have dispersion. Unlike the linear Schrödinger equation, the NLSE never describes the time evolution of a quantum state. The 1D NLSE is an example of an integrable model.
In quantum mechanics, the 1D NLSE is a special case of the classical nonlinear Schrödinger field, which in turn is a classical limit of a quantum Schrödinger field. Conversely, when the classical Schrödinger field is canonically quantized, it becomes a quantum field theory (which is linear, despite the fact that it is called ″quantum nonlinear Schrödinger equation″) that describes bosonic point particles with delta-function interactions — the particles either repel or attract when they are at the same point. In fact, when the number of particles is finite, this quantum field theory is equivalent to the Lieb–Liniger model. Both the quantum and the classical 1D nonlinear Schrödinger equations are integrable. Of special interest is the limit of infinite strength repulsion, in which case the Lieb–Liniger model becomes the Tonks–Girardeau gas (also called the hard-core Bose gas, or impenetrable Bose gas). In this limit, the bosons may, by a change of variables that is a continuum generalization of the Jordan–Wigner transformation, be transformed to a system one-dimensional noninteracting spinless fermions.
The nonlinear Schrödinger equation is a simplified 1+1-dimensional form of the Ginzburg–Landau equation introduced in 1950 in their work on superconductivity, and was written down explicitly by in their study of optical beams.
Multi-dimensional version replaces the second spatial derivative by the Laplacian. In more than one dimension, the equation is not integrable, it allows for a collapse and wave turbulence.
Definition
The nonlinear Schrödinger equation is a nonlinear partial differential equation, applicable to classical and quantum mechanics.
Classical equation
The classical field equation (in dimensionless form) is:
for the complex field ψ(x,t).
This equation arises from the Hamiltonian
with the Poisson brackets
Unlike its linear counterpart, it never describes the time evolution of a quantum state.
The case with negative κ is called focusing and allows for bright soliton solutions (localized in space, and having spatial attenuation towards infinity) as well as breather solutions. It can be solved exactly by use of the inverse scattering transform, as shown by (see below). The other case, with κ positive, is the defocusing NLS which has dark soliton solutions (having constant amplitude at infinity, and a local spatial dip in amplitude).
Quantum mechanics
To get the quantized version, simply replace the Poisson brackets by commutators
and normal order the Hamiltonian
The quantum version was solved by Bethe ansatz by Lieb and Liniger. Thermodynamics was described by Chen-Ning Yang. Quantum correlation functions also were evaluated by Korepin in 1993. The model has higher conservation laws - Davies and Korepin in 1989 expressed them in terms of local fields.
Solution
The nonlinear Schrödinger equation is integrable in 1d: solved it with the inverse scattering transform. The corresponding linear system of equations is known as the Zakharov–Shabat system:
where
The nonlinear Schrödinger equation arises as compatibility condition of the Zakharov–Shabat system:
By setting q = r* or q = − r* the nonlinear Schrödinger equation with attractive or repulsive interaction is obtained.
An alternative approach uses the Zakharov–Shabat system directly and employs the following Darboux transformation:
which leaves the system invariant.
Here, φ is another invertible matrix solution (different from ϕ) of the Zakharov–Shabat system with spectral parameter Ω:
Starting from the trivial solution U = 0 and iterating, one obtains the solutions with n solitons. This can be achieved via direct numerical simulation using, for example, the split-step method.
Applications
Fiber optics
In optics, the nonlinear Schrödinger equation occurs in the Manakov system, a model of wave propagation in fiber optics. The function ψ represents a wave and the nonlinear Schrödinger equation describes the propagation of the wave through a nonlinear medium. The second-order derivative represents the dispersion, while the κ term represents the nonlinearity. The equation models many nonlinearity effects in a fiber, including but not limited to self-phase modulation, four-wave mixing, second-harmonic generation, stimulated Raman scattering, optical solitons,
ultrashort pulses, etc.
Water waves
For water waves, the nonlinear Schrödinger equation describes the evolution of the envelope of modulated wave groups. In a paper in 1968, Vladimir E. Zakharov describes the Hamiltonian structure of water waves. In the same paper Zakharov shows that, for slowly modulated wave groups, the wave amplitude satisfies the nonlinear Schrödinger equation, approximately. The value of the nonlinearity parameter к depends on the relative water depth. For deep water, with the water depth large compared to the wave length of the water waves, к is negative and envelope solitons may occur. Additionally, the group velocity of these envelope solitons could be increased by an acceleration induced by an external time-dependent water flow.
For shallow water, with wavelengths longer than 4.6 times the water depth, the nonlinearity parameter к is positive and wave groups with envelope solitons do not exist. In shallow water surface-elevation solitons or waves of translation do exist, but they are not governed by the nonlinear Schrödinger equation.
The nonlinear Schrödinger equation is thought to be important for explaining the formation of rogue waves.
The complex field ψ, as appearing in the nonlinear Schrödinger equation, is related to the amplitude and phase of the water waves. Consider a slowly modulated carrier wave with water surface elevation η of the form:
where a(x0, t0) and θ(x0, t0) are the slowly modulated amplitude and phase. Further ω0 and k0 are the (constant) angular frequency and wavenumber of the carrier waves, which have to satisfy the dispersion relation ω0 = Ω(k0). Then
So its modulus |ψ| is the wave amplitude a, and its argument arg(ψ) is the phase θ.
The relation between the physical coordinates (x0, t0) and the (x, t) coordinates, as used in the nonlinear Schrödinger equation given above, is given by:
Thus (x, t) is a transformed coordinate system moving with the group velocity Ω'(k0) of the carrier waves,
The dispersion-relation curvature Ω"(k0) – representing group velocity dispersion – is always negative for water waves under the action of gravity, for any water depth.
For waves on the water surface of deep water, the coefficients of importance for the nonlinear Schrödinger equation are:
so
where g is the acceleration due to gravity at the Earth's surface.
In the original (x0, t0) coordinates the nonlinear Schrödinger equation for water waves reads:
with (i.e. the complex conjugate of ) and So for deep water waves.
Vortices
showed that the work of on vortex filaments is closely related to the nonlinear Schrödinger equation. Subsequently, used this correspondence to show that breather solutions can also arise for a vortex filament.
Galilean invariance
The nonlinear Schrödinger equation is Galilean invariant in the following sense:
Given a solution ψ(x, t) a new solution can be obtained by replacing x with x + vt everywhere in ψ(x, t) and by appending a phase factor of :
Gauge equivalent counterpart
NLSE (1) is gauge equivalent to the following isotropic Landau-Lifshitz equation (LLE) or Heisenberg ferromagnet equation
Note that this equation admits several integrable and non-integrable generalizations in 2 + 1 dimensions like the Ishimori equation and so on.
Zero-curvature formulation
The NLSE is equivalent to the curvature of a particular -connection on being equal to zero.
Explicitly, with coordinates on , the connection components are given by
where the are the Pauli matrices.
Then the zero-curvature equation
is equivalent to the NLSE . The zero-curvature equation is so named as it corresponds to the curvature being equal to zero if it is defined .
The pair of matrices and are also known as a Lax pair for the NLSE, in the sense that the zero-curvature equation recovers the PDE rather than them satisfying Lax's equation.
See also
AKNS system
Eckhaus equation
Gross–Pitaevskii equation
Quartic interaction for a related model in quantum field theory
Soliton (optics)
Logarithmic Schrödinger equation
References
Notes
Other
External links
Tutorial lecture on Nonlinear Schrodinger Equation (video).
Nonlinear Schrodinger Equation with a Cubic Nonlinearity at EqWorld: The World of Mathematical Equations.
Nonlinear Schrodinger Equation with a Power-Law Nonlinearity at EqWorld: The World of Mathematical Equations.
Nonlinear Schrodinger Equation of General Form at EqWorld: The World of Mathematical Equations.
Mathematical aspects of the nonlinear Schrödinger equation at Dispersive Wiki
Partial differential equations
Exactly solvable models
Schrödinger equation
Integrable systems | Nonlinear Schrödinger equation | [
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1,424,913 | https://en.wikipedia.org/wiki/Vis%20viva | Vis viva (from the Latin for "living force") is a historical term used to describe a quantity similar to kinetic energy in an early formulation of the principle of conservation of energy.
Overview
Proposed by Gottfried Leibniz over the period 1676–1689, the theory was controversial as it seemed to oppose the theory of conservation of quantity of motion advocated by René Descartes. Descartes' quantity of motion was different from momentum, but Newton defined the quantity of motion as the conjunction of the quantity of matter and velocity in Definition II of his Principia. In Definition III, he defined the force that resists a change in motion as the vis inertia of Descartes. Newton’s Third Law of Motion (for every action there is an equal and opposite reaction) is also equivalent to the principle of conservation of momentum. Leibniz accepted the principle of conservation of momentum, but rejected the Cartesian version of it. The difference between these ideas was whether the quantity of motion was simply related to a body's resistance to a change in velocity (vis inertia) or whether a body's amount of force due to its motion (vis viva) was related to the square of its velocity.
The theory was eventually absorbed into the modern theory of energy, though the term still survives in the context of celestial mechanics through the vis viva equation. The English equivalent "living force" was also used, for example by George William Hill.
The term is due to the German philosopher Gottfried Wilhelm Leibniz, who was the first to attempt a mathematical formulation from 1676 to 1689. Leibniz noticed that in many mechanical systems (of several masses, mi each with velocity vi) the quantity
was conserved. He called this quantity the vis viva or "living force" of the system. The principle represented an accurate statement of the conservation of kinetic energy in elastic collisions that was independent of the conservation of momentum.
However, many physicists at the time were unaware of this fact and, instead, were influenced by the prestige of Sir Isaac Newton in England and of René Descartes in France, both of whom advanced the conservation of momentum as a guiding principle. Thus the momentum:
was held by the rival camp to be the conserved vis viva. It was largely engineers such as John Smeaton, Peter Ewart, Karl Holtzmann, Gustave-Adolphe Hirn and Marc Seguin who objected that conservation of momentum alone was not adequate for practical calculation and who made use of Leibniz's principle. The principle was also championed by some chemists such as William Hyde Wollaston.
The French mathematician Émilie du Châtelet, who had a sound grasp of Newtonian mechanics, developed Leibniz's concept and, combining it with the observations of Willem 's Gravesande, showed that vis viva was dependent on the square of the velocities.
Members of the academic establishment such as John Playfair were quick to point out that kinetic energy is clearly not conserved. This is obvious to a modern analysis based on the second law of thermodynamics, but in the 18th and 19th centuries, the fate of the lost energy was still unknown. Gradually it came to be suspected that the heat inevitably generated by motion was another form of vis viva. In 1783, Antoine Lavoisier and Pierre-Simon Laplace reviewed the two competing theories of vis viva and caloric theory. Count Rumford's 1798 observations of heat generation during the boring of cannons added more weight to the view that mechanical motion could be converted into heat. Vis viva began to be known as energy after Thomas Young first used the term in 1807.
The recalibration of vis viva to include the coefficient of a half, namely:
was largely the result of the work of Gaspard-Gustave Coriolis and Jean-Victor Poncelet over the period 1819–1839, although the present-day definition can occasionally be found earlier (e.g., in Daniel Bernoulli's texts). The former called it the quantité de travail (quantity of work) and the latter, travail mécanique (mechanical work) and both championed its use in engineering calculation.
See also
Conservation of energy: Historical development
Élan vital
Kinetic energy
Orthogenesis
Potentiality and actuality
Vis-viva equation
Notes
References
George E. Smith, "The Vis Viva Dispute: A Controversy at the Dawn of Dynamics", Physics Today 59 (October 2006) Issue 10 pp 31–36. (see also erratum)
Natural philosophy
Obsolete theories in physics
Mechanics
Thermodynamics
Gottfried Wilhelm Leibniz
History of thermodynamics | Vis viva | [
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1,425,422 | https://en.wikipedia.org/wiki/Electric%20arc%20furnace | An electric arc furnace (EAF) is a furnace that heats material by means of an electric arc.
Industrial arc furnaces range in size from small units of approximately one-tonne capacity (used in foundries for producing cast iron products) up to about 400-tonne units used for secondary steelmaking. Arc furnaces used in research laboratories and by dentists may have a capacity of only a few dozen grams. Industrial electric arc furnace temperatures can reach , while laboratory units can exceed .
In electric arc furnaces, the charge material (the material entered into the furnace for heating, not to be confused with electric charge) is directly exposed to an electric arc, and the current from the electrode terminals passes through the charge material.
Arc furnaces differ from induction furnaces, in which the charge is heated instead by eddy currents.
History
In the 19th century, a number of people had employed an electric arc to melt iron. Sir Humphry Davy conducted an experimental demonstration in 1810; welding was investigated by Pepys in 1815; Pinchon attempted to create an electrothermic furnace in 1853; and, in 1878–79, Sir William Siemens took out patents for electric furnaces of the arc type.
The first successful and operational furnace was invented by James Burgess Readman in Edinburgh, Scotland, in 1888 and patented in 1889. This was specifically for the creation of phosphorus.
Further electric arc furnaces were developed by Paul Héroult, of France, with a commercial plant established in the United States in 1907. The Sanderson brothers formed The Sanderson Brothers Steel Co. in Syracuse, New York, installing the first electric arc furnace in the U.S. This furnace is now on display at Station Square, Pittsburgh, Pennsylvania.
Initially "electric steel" produced by an electric arc furnace was a specialty product for such uses as machine tools and spring steel. Arc furnaces were also used to prepare calcium carbide for use in carbide lamps. The Stassano electric furnace is an arc type furnace that usually rotates to mix the bath. The Girod furnace is similar to the Héroult furnace.
While EAFs were widely used in World War II for production of alloy steels, it was only later that electric steelmaking began to expand. The low capital cost for a mini-mill—around US$140–200 per ton of annual installed capacity, compared with US$1,000 per ton of annual installed capacity for an integrated steel mill—allowed mills to be quickly established in war-ravaged Europe, and also allowed them to successfully compete with the big United States steelmakers, such as Bethlehem Steel and U.S. Steel, for low-cost, carbon steel "long products" (structural steel, rod and bar, wire, and fasteners) in the U.S. market.
When Nucor—now one of the largest steel producers in the US — entered the market for long steel products in 1969, they used a mini-mill with an EAF as its steelmaking furnace, soon followed by other manufacturers. While Nucor expanded rapidly in the Eastern US, the companies that followed them into mini-mill operations concentrated on local markets for long products, where the EAF allowed the plants to vary production according to local demand. This pattern was followed globally, with EAF steel production primarily used for long products, while integrated mills, using blast furnaces and basic oxygen furnaces, cornered the markets for "flat products"—sheet steel and heavier steel plate. In 1987, Nucor expanded into the flat products market, still using the EAF production method.
Construction
An electric arc furnace used for steelmaking consists of a refractory-lined vessel, usually water-cooled in larger sizes, covered with a retractable roof, and through which one or more graphite electrodes enter the furnace.
The furnace is primarily split into three sections:
the shell, which consists of the sidewalls and lower steel "bowl";
the hearth, which consists of the refractory that lines the lower bowl;
the roof, which may be refractory-lined or water-cooled, and can be shaped as a section of a sphere, or as a frustum (conical section). The roof also supports the refractory delta in its centre, through which one or more graphite electrodes enter.
The hearth may be hemispherical in shape, or in an eccentric bottom tapping furnace (see below), the hearth has the shape of a halved egg. In modern meltshops, the furnace is often raised off the ground floor, so that ladles and slag pots can easily be maneuvered under either end of the furnace. Separate from the furnace structure is the electrode support and electrical system, and the tilting platform on which the furnace rests. Two configurations are possible: the electrode supports and the roof tilt with the furnace, or are fixed to the raised platform.
A typical alternating current furnace is powered by a three-phase electrical supply, and therefore has three electrodes. Electrodes are round in section, and typically in segments with threaded couplings, so that as the electrodes wear, new segments can be added. The arc forms between the charged material and the electrode; the charge is heated both by current passing through the charge and by the radiant energy evolved by the arc. The electric arc temperature reaches around , thus causing the lower sections of the electrodes to glow incandescently when in operation. The electrodes are automatically raised and lowered by a positioning system, which may use either electric winch hoists or hydraulic cylinders. The regulating system maintains approximately constant current and power input during the melting of the charge, even though scrap may move under the electrodes as it melts. The mast arms holding the electrodes can either carry heavy busbars (which may be hollow water-cooled copper pipes carrying current to the electrode clamps) or be "hot arms", where the whole arm carries the current, increasing efficiency. Hot arms can be made from copper-clad steel or aluminium. Large water-cooled cables connect the bus tubes or arms with the transformer located adjacent to the furnace. The transformer is installed in a vault and is cooled by pump-circulated transformer oil, with the oil being cooled by water via heat exchangers.
The furnace is built on a tilting platform so that the liquid steel can be poured into another vessel for transport. The operation of tilting the furnace to pour molten steel is called "tapping". Originally, all steelmaking furnaces had a tapping spout closed with refractory that washed out when the furnace was tilted, but often modern furnaces have an eccentric bottom tap-hole (EBT) to reduce inclusion of nitrogen and slag in the liquid steel. These furnaces have a taphole that passes vertically through the hearth and shell, and is set off-centre in the narrow "nose" of the egg-shaped hearth. It is filled with refractory sand, such as olivine, when it is closed off. Modern plants may have two shells with a single set of electrodes that can be transferred between the two; one shell preheats scrap while the other shell is utilised for meltdown. Other DC-based furnaces have a similar arrangement, but have electrodes for each shell and one set of electronics.
AC furnaces usually exhibit a pattern of hot and cold-spots around the hearth perimeter, with the cold-spots located between the electrodes. Modern furnaces mount oxygen-fuel burners in the sidewall and use them to provide chemical energy to the cold-spots, making the heating of the steel more uniform. Additional chemical energy is provided by injecting oxygen and carbon into the furnace; historically this was done through lances (hollow mild-steel tubes) in the slag door, but now this is mainly done through wall-mounted injection units that combine the oxygen-fuel burners and the oxygen or carbon injection systems into one unit.
A mid-sized modern steelmaking furnace would have a transformer rated about 60,000,000 volt-amperes (60 MVA), with a secondary voltage between 400 and 900 volts and a secondary current in excess of 44,000 amperes. In a modern shop such a furnace would be expected to produce a quantity of 80 tonnes of liquid steel in approximately 50 minutes from charging with cold scrap to tapping the furnace. In comparison, basic oxygen furnaces can have a capacity of 150–300 tonnes per batch, or "heat", and can produce a heat in 30–40 minutes. Enormous variations exist in furnace design details and operation, depending on the end product and local conditions, as well as ongoing research to improve furnace efficiency. The largest scrap-only furnace (in terms of tapping weight and transformer rating) is a DC furnace operated by Tokyo Steel in Japan, with a tap weight of 420 tonnes and fed by eight 32 MVA transformers for 256 MVA total power.
Energy density
To produce a ton of steel in an electric arc furnace requires approximately 400 kilowatt-hours (1.44 gigajoules) per short ton or about 440 kWh (1.6 GJ) per tonne. The theoretical minimum amount of energy required to melt a tonne of scrap steel is 300 kWh (1.09 GJ) (melting point ). Therefore, a 300-tonne, 300 MVA EAF will require approximately 132 MWh of energy to melt the steel, and a "power-on time" (the time that steel is being melted with an arc) of approximately 37 minutes.
Electric arc steelmaking is only economical where there is plentiful, reliable electricity, with a well-developed electrical grid. In many locations, mills operate during off-peak hours when utilities have surplus power generating capacity and the price of electricity is less. This compares very favourably with energy consumption of global steel production by all methods estimated at some 5,555 kWh (20 GJ) per tonne (1 gigajoule is equal to approximately 270 kWh).
Operation
Scrap metal is delivered to a scrap bay, located next to the melt shop. Scrap generally comes in two main grades: shred (whitegoods, cars and other objects made of similar light-gauge steel) and heavy melt (large slabs and beams), along with some direct reduced iron (DRI) or pig iron for chemical balance. Some furnaces melt almost 100% DRI.
The scrap is loaded into large buckets called baskets, with "clamshell" doors for a base. Care is taken to layer the scrap in the basket to ensure good furnace operation; heavy melt is placed on top of a light layer of protective shred, on top of which is placed more shred. These layers should be present in the furnace after charging. After loading, the basket may pass to a scrap pre-heater, which uses hot furnace off-gases to heat the scrap and recover energy, increasing plant efficiency.
The scrap basket is then taken to the melt shop, the roof is swung off the furnace, and the furnace is charged with scrap from the basket. Charging is one of the more dangerous operations for the EAF operators. A lot of potential energy is released by the tonnes of falling metal; any liquid metal in the furnace is often displaced upwards and outwards by the solid scrap, and the grease and dust on the scrap is ignited if the furnace is hot, resulting in a fireball erupting.
In some twin-shell furnaces, the scrap is charged into the second shell while the first is being melted down, and pre-heated with off-gas from the active shell. Other operations are continuous charging—pre-heating scrap on a conveyor belt, which then discharges the scrap into the furnace proper, or charging the scrap from a shaft set above the furnace, with off-gases directed through the shaft. Other furnaces can be charged with hot (molten) metal from other operations.
After charging, the roof is swung back over the furnace and meltdown commences. The electrodes are lowered onto the scrap, an arc is struck and the electrodes are then set to bore into the layer of shred at the top of the furnace. Lower voltages are selected for this first part of the operation to protect the roof and walls from excessive heat and damage from the arcs. Once the electrodes have reached the heavy melt at the base of the furnace and the arcs are shielded by the scrap, the voltage can be increased and the electrodes raised slightly, lengthening the arcs and increasing power to the melt. This enables a molten pool to form more rapidly, reducing tap-to-tap times. Oxygen is blown into the scrap, combusting or cutting the steel, and extra chemical heat is provided by wall-mounted oxygen-fuel burners. Both processes accelerate scrap meltdown. Supersonic nozzles enable oxygen jets to penetrate foaming slag and reach the liquid bath.
An important part of steelmaking is the formation of slag, which floats on the surface of the molten steel. Slag usually consists of metal oxides, and acts as a destination for oxidised impurities, as a thermal blanket (stopping excessive heat loss) and helping to reduce erosion of the refractory lining. For a furnace with basic refractories, which includes most carbon steel-producing furnaces, the usual slag formers are calcium oxide (CaO, in the form of burnt lime) and magnesium oxide (MgO, in the form of dolomite and magnesite).
These slag formers are either charged with the scrap, or blown into the furnace during meltdown. Another major component of EAF slag is iron oxide from steel combusting with the injected oxygen. Later in the heat, carbon (in the form of coke or coal) is injected into this slag layer, reacting with the iron oxide to form metallic iron and carbon monoxide gas, which then causes the slag to foam, allowing greater thermal efficiency, and better arc stability and electrical efficiency. The slag blanket also covers the arcs, preventing damage to the furnace roof and sidewalls from radiant heat.
Once the initial scrap charge has been melted down, another bucket of scrap can be charged into the furnace, although EAF development is moving towards single-charge designs. The scrap-charging and meltdown process can be repeated as many times as necessary to reach the required heat weight - the number of charges is dependent on the density of scrap; lower-density scrap means more charges. After all scrap charges have completely melted, refining operations take place to check and correct the steel chemistry and superheat the melt above its freezing temperature in preparation for tapping.
More slag formers are introduced and more oxygen is blown into the bath, burning out impurities such as silicon, sulfur, phosphorus, aluminium, manganese, and calcium, and removing their oxides to the slag. Removal of carbon takes place after these elements have burnt out first, as they have a greater affinity for oxygen. Metals that have a poorer affinity for oxygen than iron, such as nickel and copper, cannot be removed through oxidation and must be controlled through scrap chemistry alone, such as introducing the direct reduced iron and pig iron mentioned earlier.
A foaming slag is maintained throughout, and often overflows the furnace to pour out of the slag door into the slag pit. Temperature sampling and chemical sampling take place via automatic lances. Oxygen and carbon can be automatically measured via special probes that dip into the steel, but for all other elements, a "chill" sample — a small, solidified sample of the steel — is analysed on an arc-emission spectrometer.
Once the temperature and chemistry are correct, the steel is tapped out into a preheated ladle through tilting the furnace. For plain-carbon steel furnaces, as soon as slag is detected during tapping the furnace is rapidly tilted back towards the deslagging side, minimising slag carryover into the ladle. For some special steel grades, including stainless steel, the slag is poured into the ladle as well, to be treated at the ladle furnace to recover valuable alloying elements. During tapping some alloy additions are introduced into the metal stream, and more fluxes such as lime are added on top of the ladle to begin building a new slag layer.
Often, a few tonnes of liquid steel and slag is left in the furnace in order to form a "hot heel", which helps preheat the next charge of scrap and accelerate its meltdown. During and after tapping, the furnace is "turned around": the slag door is cleaned of solidified slag, the visible refractories are inspected and water-cooled components checked for leaks, and electrodes are inspected for damage or lengthened through the addition of new segments. The taphole is filled with sand at the completion of tapping. For a 90-tonne, medium-power furnace, the whole process will usually take about 60–70 minutes from the tapping of one heat to the tapping of the next (the tap-to-tap time).
The furnace is completely emptied of steel and slag on a regular basis so that an inspection of the refractories can be made and larger repairs made if necessary. As the refractories are often made from calcined carbonates, they are extremely susceptible to hydration from water, so any suspected leaks from water-cooled components are treated extremely seriously, beyond the immediate concern of potential steam explosions. Excessive refractory wear can lead to breakouts, where the liquid metal and slag penetrate the refractory and furnace shell and escape into the surrounding areas.
Advantages for steelmaking
The use of EAFs allows steel to be made from a 100% scrap metal feedstock. This greatly reduces the energy required to make steel when compared with primary steelmaking from ores.
Another benefit is flexibility: while blast furnaces cannot vary their production by much and can remain in operation for years at a time, EAFs can be rapidly started and stopped, allowing the steel mill to vary production according to demand.
Although steelmaking arc furnaces generally use scrap steel as their primary feedstock, if hot metal from a blast furnace or direct-reduced iron is available economically, these can also be used as furnace feed.
As EAFs require large amounts of electrical power, many companies schedule their operations to take advantage of off-peak electricity pricing.
A typical steelmaking arc furnace is the source of steel for a mini-mill, which may make bars or strip product. Mini-mills can be sited relatively near the markets for steel products, so the transport requirements are less than for an integrated mill, which would commonly be sited near a harbor for better access to shipping.
Depending on the proportions of steel scrap, DRI and pig iron used, electric arc furnace steelmaking can result in carbon dioxide emissions as low as 0.6 tons CO2 per ton of steel produced, which is significantly lower than the conventional production route via blast furnaces and the basic oxygen furnace, which produces 2.9 tons CO2 per ton of steel produced.
Issues
Although the modern electric arc furnace is a highly efficient recycler of steel scrap, operation of an arc furnace shop can have adverse environmental effects. Much of the capital cost of a new installation will be devoted to systems intended to reduce these effects, which include:
Enclosures to reduce high sound levels
Dust collector for furnace off-gas
slag production
cooling water demand
Heavy truck traffic for scrap, materials handling, and product
Environmental effects of electricity generation
Since EAF steelmaking mainly use recycled materials like scrap iron and scrap steel, as their composition varies the resulting EAF slag and EAF dust can be toxic. EAF dust is collected by air pollution control equipment. It is called collected dust and usually contains heavy metals, such as zinc, lead and dioxins, etc. It is categorized as hazardous industrial waste and disposal is regulated.
Because of the very dynamic quality of the arc furnace load, power systems may require technical measures to maintain the quality of power for other customers; flicker and harmonic distortion are common power system side-effects of arc furnace operation.
Other electric arc furnaces
For steelmaking, direct current (DC) arc furnaces are used, with a single electrode in the roof and the current return through a conductive bottom lining or conductive pins in the base. The advantage of DC is lower electrode consumption per ton of steel produced, since only one electrode is used, as well as less electrical harmonics and other similar problems. The size of DC arc furnaces is limited by the current carrying capacity of available electrodes, and the maximum allowable voltage. Maintenance of the conductive furnace hearth is a bottleneck in extended operation of a DC arc furnace.
In a steel plant, a ladle furnace (LF) is used to maintain the temperature of liquid steel during processing after tapping from EAF or to change the alloy composition. The ladle is used for the first purpose when there is a delay later in the steelmaking process. The ladle furnace consists of a refractory roof, a heating system, and, when applicable, a provision for injecting argon gas into the bottom of the melt for stirring. Unlike a scrap melting furnace, a ladle furnace does not have a tilting or scrap-charging mechanism.
Electric arc furnaces are also used for production of calcium carbide, ferroalloys, and other non-ferrous alloys, and for production of phosphorus. Furnaces for these services are physically different from steel-making furnaces and may operate on a continuous, rather than batch, basis. Continuous-process furnaces may also use paste-type, Søderberg electrodes to prevent interruptions from electrode changes.
Such a furnace is known as a submerged arc furnace, because the electrode tips are buried in the slag/charge, and arcing occurs through the slag, between the matte and the electrode. The casing and casing fins of the electrode melt the electrode paste through electrical current passing through the electrode casing and heat from the furnace. A steelmaking arc furnace, by comparison, arcs in the open. The key is the electrical resistance, which is what generates the heat required: the resistance in a steelmaking furnace is the atmosphere, while in a submerged-arc furnace, the slag (or charge) supplies the resistance. The liquid metal formed in either furnace is too conductive to form an effective heat-generating resistance.
Amateurs have constructed a variety of arc furnaces, often based on electric arc welding kits contained by silica blocks or flower pots. Though crude, these simple furnaces can melt a wide range of materials, create calcium carbide, and more.
Cooling methods
Smaller arc furnaces may be adequately cooled by circulation of air over structural elements of the shell and roof, but larger installations require intensive forced cooling to maintain the structure within safe operating limits. The furnace shell and roof may be cooled either by water circulated through pipes which form a panel, or by water sprayed on the panel elements. Tubular panels may be replaced when they become cracked or reach their thermal stress life cycle.
Spray cooling is the most economical and is the highest efficiency cooling method. A spray cooling piece of equipment can be relined almost endlessly. Equipment that lasts 20 years is the norm. While a tubular leak is immediately noticed in an operating furnace due to the pressure loss alarms on the panels, at this time there exists no immediate way of detecting a very small volume spray cooling leak. These typically hide behind slag coverage and can hydrate the refractory in the hearth, leading to a break out of molten metal or in the worst case a steam explosion.
Plasma arc furnace
A plasma arc furnace (PAF) uses plasma torches instead of graphite electrodes. Each of these torches has a casing with a nozzle and axial tubing for feeding a plasma-forming gas (either nitrogen or argon) and a burnable cylindrical graphite electrode within the tubing. Such furnaces can be called plasma arc melt (PAM) furnaces; they are used extensively in the titanium-melting industry and similar specialty metal industries.
Vacuum arc remelting
Vacuum arc remelting (VAR) is a secondary remelting process for vacuum refining and manufacturing of ingots with improved chemical and mechanical homogeneity.
In critical military and commercial aerospace applications, material engineers commonly specify VIM-VAR steels. VIM means vacuum induction melted and VAR means vacuum arc remelted. VIM-VAR steels become bearings for jet engines, rotor shafts for military helicopters, flap actuators for fighter jets, gears in jet or helicopter transmissions, mounts or fasteners for jet engines, jet tail hooks and other demanding applications.
Most grades of steel are melted once and are then cast or teemed into a solid form prior to extensive forging or rolling to a metallurgically-sound form. In contrast, VIM-VAR steels go through two more highly purifying melts under vacuum. After melting in an electric arc furnace and alloying in an argon oxygen decarburization vessel, steels destined for vacuum remelting are cast into ingot molds. The solidified ingots then head for a vacuum induction melting furnace. This vacuum remelting process rids the steel of inclusions and unwanted gases while optimizing the chemical composition.
The VIM operation returns these solid ingots to the molten state in the contaminant-free void of a vacuum. This tightly controlled melt often requires up to 24 hours. Still enveloped by the vacuum, the hot metal flows from the VIM furnace crucible into giant electrode molds. A typical electrode is about 15 feet (5 m) tall and will be in various diameters. The electrodes solidify under vacuum.
For VIM-VAR steels, the surface of the cooled electrodes must be ground to remove surface irregularities and impurities before the next vacuum remelt. Then the ground electrode is placed in a VAR furnace. In a VAR furnace, the steel gradually melts drop-by-drop in the vacuum-sealed chamber. Vacuum arc remelting further removes lingering inclusions to provide superior steel cleanliness and remove gases like oxygen, nitrogen and hydrogen. Controlling the rate at which these droplets form and solidify ensures a consistency of chemistry and microstructure throughout the entire VIM-VAR ingot, making the steel more resistant to fracture or fatigue. This refinement process is essential to meet the performance characteristics of parts like a helicopter rotor shaft, a flap actuator on a military jet, or a bearing in a jet engine.
For some commercial or military applications, steel alloys may go through only one vacuum remelt, namely the VAR. For example, steels for solid rocket cases, landing gears, or torsion bars for fighting vehicles typically involve one vacuum remelt.
Vacuum arc remelting is also used in production of titanium and other metals which are reactive or in which high purity is required.
See also
Flodin process
Vacuum arc remelting
Electrical steel
References
Further reading
J.A.T. Jones, B. Bowman, P.A. Lefrank, "Electric Furnace Steelmaking", in The Making, Shaping and Treating of Steel, R.J. Fruehan, Editor. 1998, The AISE Steel Foundation: Pittsburgh. p. 525–660.
Thomas Commerford Martin and Stephen Leidy Coles, The Story of Electricity, New York 1919, no ISBN, Chapter 13 "The Electric Furnace", available on the Internet Archive
External links
Recognition of first foundry as historical site
Home made small scale arc furnace using a welder (Caution with experiments!)
Electric Arc Furnace module at steeluniversity.org, including a fully interactive simulation
Process models demonstrate the EAF operation and control (MPC)
YouTube video of a small EAF in New Zealand
Electric arcs
Industrial furnaces
Steelmaking
1907 in science
1907 in France
French inventions
1907 in the United States
Metallurgy | Electric arc furnace | [
"Physics",
"Chemistry",
"Materials_science",
"Engineering"
] | 5,744 | [
"Electric arcs",
"Physical phenomena",
"Metallurgical processes",
"Plasma phenomena",
"Steelmaking",
"Metallurgy",
"Materials science",
"Industrial furnaces",
"nan"
] |
31,557,888 | https://en.wikipedia.org/wiki/Quasi-Frobenius%20ring | In mathematics, especially ring theory, the class of Frobenius rings and their generalizations are the extension of work done on Frobenius algebras. Perhaps the most important generalization is that of quasi-Frobenius rings (QF rings), which are in turn generalized by right pseudo-Frobenius rings (PF rings) and right finitely pseudo-Frobenius rings (FPF rings). Other diverse generalizations of quasi-Frobenius rings include QF-1, QF-2 and QF-3 rings.
These types of rings can be viewed as descendants of algebras examined by Georg Frobenius. A partial list of pioneers in quasi-Frobenius rings includes R. Brauer, K. Morita, T. Nakayama, C. J. Nesbitt, and R. M. Thrall.
Definitions
A ring R is quasi-Frobenius if and only if R satisfies any of the following equivalent conditions:
R is Noetherian on one side and self-injective on one side.
R is Artinian on a side and self-injective on a side.
All right (or all left) R modules which are projective are also injective.
All right (or all left) R modules which are injective are also projective.
A Frobenius ring R is one satisfying any of the following equivalent conditions. Let J=J(R) be the Jacobson radical of R.
R is quasi-Frobenius and the socle as right R modules.
R is quasi-Frobenius and as left R modules.
As right R modules , and as left R modules .
For a commutative ring R, the following are equivalent:
R is Frobenius
R is quasi-Frobenius
R is a finite direct sum of local artinian rings which have unique minimal ideals. (Such rings are examples of "zero-dimensional Gorenstein local rings".)
A ring R is right pseudo-Frobenius if any of the following equivalent conditions are met:
Every faithful right R module is a generator for the category of right R modules.
R is right self-injective and is a cogenerator of Mod-R.
R is right self-injective and is finitely cogenerated as a right R module.
R is right self-injective and a right Kasch ring.
R is right self-injective, semilocal and the socle soc(RR) is an essential submodule of R.
R is a cogenerator of Mod-R and is a left Kasch ring.
A ring R is right finitely pseudo-Frobenius if and only if every finitely generated faithful right R module is a generator of Mod-R.
Thrall's QF-1,2,3 generalizations
In the seminal article , R. M. Thrall focused on three specific properties of (finite-dimensional) QF algebras and studied them in isolation. With additional assumptions, these definitions can also be used to generalize QF rings. A few other mathematicians pioneering these generalizations included K. Morita and H. Tachikawa.
Following , let R be a left or right Artinian ring:
R is QF-1 if all faithful left modules and faithful right modules are balanced modules.
R is QF-2 if each indecomposable projective right module and each indecomposable projective left module has a unique minimal submodule. (I.e. they have simple socles.)
R is QF-3 if the injective hulls E(RR) and E(RR) are both projective modules.
The numbering scheme does not necessarily outline a hierarchy. Under more lax conditions, these three classes of rings may not contain each other. Under the assumption that R is left or right Artinian however, QF-2 rings are QF-3. There is even an example of a QF-1 and QF-3 ring which is not QF-2.
Examples
Every Frobenius k algebra is a Frobenius ring.
Every semisimple ring is quasi-Frobenius, since all modules are projective and injective. Even more is true however: semisimple rings are all Frobenius. This is easily verified by the definition, since for semisimple rings and J = rad(R) = 0.
The quotient ring is QF for any positive integer n>1.
Commutative Artinian serial rings are all Frobenius, and in fact have the additional property that every quotient ring R/I is also Frobenius. It turns out that among commutative Artinian rings, the serial rings are exactly the rings whose (nonzero) quotients are all Frobenius.
Many exotic PF and FPF rings can be found as examples in
See also
Quasi-Frobenius Lie algebra
Notes
The definitions for QF, PF and FPF are easily seen to be categorical properties, and so they are preserved by Morita equivalence, however being a Frobenius ring is not preserved.
For one-sided Noetherian rings the conditions of left or right PF both coincide with QF, but FPF rings are still distinct.
A finite-dimensional algebra R over a field k is a Frobenius k-algebra if and only if R is a Frobenius ring.
QF rings have the property that all of their modules can be embedded in a free R module. This can be seen in the following way. A module M embeds into its injective hull E(M), which is now also projective. As a projective module, E(M) is a summand of a free module F, and so E(M) embeds in F with the inclusion map. By composing these two maps, M is embedded in F.
Textbooks
References
For QF-1, QF-2, QF-3 rings:
Module theory
Ring theory | Quasi-Frobenius ring | [
"Mathematics"
] | 1,256 | [
"Fields of abstract algebra",
"Ring theory",
"Module theory"
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31,559,837 | https://en.wikipedia.org/wiki/Kirchhoff%27s%20diffraction%20formula | Kirchhoff's diffraction formula (also called Fresnel–Kirchhoff diffraction formula) approximates light intensity and phase in optical diffraction: light fields in the boundary regions of shadows. The approximation
can be used to model light propagation in a wide range of configurations, either analytically or using numerical modelling. It gives an expression for the wave disturbance when a monochromatic spherical wave is the incoming wave of a situation under consideration. This formula is derived by applying the Kirchhoff integral theorem, which uses the Green's second identity to derive the solution to the homogeneous scalar wave equation, to a spherical wave with some approximations.
The Huygens–Fresnel principle is derived by the Fresnel–Kirchhoff diffraction formula.
Derivation of Kirchhoff's diffraction formula
Kirchhoff's integral theorem, sometimes referred to as the Fresnel–Kirchhoff integral theorem, uses Green's second identity to derive the solution of the homogeneous scalar wave equation at an arbitrary spatial position P in terms of the solution of the wave equation and its first order derivative at all points on an arbitrary closed surface as the boundary of some volume including P.
The solution provided by the integral theorem for a monochromatic source is
where is the spatial part of the solution of the homogeneous scalar wave equation (i.e., as the homogeneous scalar wave equation solution), k is the wavenumber, and s is the distance from P to an (infinitesimally small) integral surface element, and denotes differentiation along the integral surface element normal unit vector (i.e., a normal derivative), i.e., . Note that the surface normal or the direction of is toward the inside of the enclosed volume in this integral; if the more usual outer-pointing normal is used, the integral will have the opposite sign. And also note that, in the integral theorem shown here, and P are vector quantities while other terms are scalar quantities.
For the below cases, the following basic assumptions are made.
The distance between a point source of waves and an integral area, the distance between the integral area and an observation point P, and the dimension of opening S are much greater than the wave wavelength .
and are discontinuous at the boundaries of the aperture, called Kirchhoff's boundary conditions. This may be related with another assumption that waves on an aperture (or an open area) is same to the waves that would be present if there was no obstacle for the waves.
Point source
Consider a monochromatic point source at P0, which illuminates an aperture in a screen. The intensity of the wave emitted by a point source falls off as the inverse square of the distance traveled, so the amplitude falls off as the inverse of the distance. The complex amplitude of the disturbance at a distance is given by
where represents the magnitude of the disturbance at the point source.
The disturbance at a spatial position P can be found by applying the Kirchhoff's integral theorem to the closed surface formed by the intersection of a sphere of radius R with the screen. The integration is performed over the areas A1, A2 and A3, giving
To solve the equation, it is assumed that the values of and in the aperture area A1 are the same as when the screen is not present, so at the position Q,
where is the length of the straight line P0Q, and is the angle between a straightly extended version of P0Q and the (inward) normal to the aperture. Note that so is a positive real number on A1.
At Q, we also have
where is the length of the straight line PQ, and is the angle between a straightly extended version of PQ and the (inward) normal to the aperture. Note that so is a negative real number on A1.
Two more following assumptions are made.
In the above normal derivatives, the terms and in the both square brackets are assumed to be negligible compared with the wavenumber , means and are much greater than the wavelength .
Kirchhoff assumes that the values of and on the opaque areas marked by A2 are zero. This implies that and are discontinuous at the edge of the aperture A1. This is not the case, and this is one of the approximations used in deriving the Kirchhoff's diffraction formula. These assumptions are sometimes referred to as Kirchhoff's boundary conditions.
The contribution from the hemisphere A3 to the integral is expected to be zero, and it can be justified by one of the following reasons.
Make the assumption that the source starts to radiate at a particular time, and then make R large enough, so that when the disturbance at P is being considered, no contributions from A3 will have arrived there. Such a wave is no longer monochromatic, since a monochromatic wave must exist at all times, but that assumption is not necessary, and a more formal argument avoiding its use has been derived.
A wave emanated from the aperture A1 is expected to evolve toward a spherical wave as it propagates (Water wave examples of this can be found in many pictures showing a water wave passing through a relatively narrow opening.). So, if R is large enough, then the integral on A3 becomes where and are the distance from the center of the aperture A1 to an integral surface element and the differential solid angle in the spherical coordinate system respectively.
As a result, finally, the integral above, which represents the complex amplitude at P, becomes
This is the Kirchhoff or Fresnel–Kirchhoff diffraction formula.
Equivalence to Huygens–Fresnel principle
The Huygens–Fresnel principle can be derived by integrating over a different closed surface (the boundary of some volume having an observation point P). The area A1 above is replaced by a part of a wavefront (emitted from a P0) at r0, which is the closest to the aperture, and a portion of a cone with a vertex at P0, which is labeled A4 in the right diagram. If the wavefront is positioned such that the wavefront is very close to the edges of the aperture, then the contribution from A4 can be neglected (assumed here). On this new A1, the inward (toward the volume enclosed by the closed integral surface, so toward the right side in the diagram) normal to A1 is along the radial direction from P0, i.e., the direction perpendicular to the wavefront. As a result, the angle and the angle is related with the angle (the angle as defined in Huygens–Fresnel principle) as
The complex amplitude of the wavefront at r0 is given by
So, the diffraction formula becomes
where the integral is done over the part of the wavefront at r0 which is the closest to the aperture in the diagram. This integral leads to the Huygens–Fresnel principle (with the obliquity factor ).
In the derivation of this integral, instead of the geometry depicted in the right diagram, double spheres centered at P0 with the inner sphere radius r0 and an infinite outer sphere radius can be used. In this geometry, the observation point P is located in the volume enclosed by the two spheres so the Fresnel-Kirchhoff diffraction formula is applied on the two spheres. (The surface normal on these integral surfaces are, say again, toward the enclosed volume in the diffraction formula above.) In the formula application, the integral on the outer sphere is zero by a similar reason of the integral on the hemisphere as zero above.
Extended source
Assume that the aperture is illuminated by an extended source wave. The complex amplitude at the aperture is given by U0(r).
It is assumed, as before, that the values of and in the area A1 are the same as when the screen is not present, that the values of and in A2 are zero (Kirchhoff's boundary conditions) and that the contribution from A3 to the integral are also zero. It is also assumed that 1/s is negligible compared with k. We then have
This is the most general form of the Kirchhoff diffraction formula. To solve this equation for an extended source, an additional integration would be required to sum the contributions made by the individual points in the source. If, however, we assume that the light from the source at each point in the aperture has a well-defined direction, which is the case if the distance between the source and the aperture is significantly greater than the wavelength, then we can write
where a(r) is the magnitude of the disturbance at the point r in the aperture. We then have
and thus
Fraunhofer and Fresnel diffraction equations
In spite of the various approximations that were made in arriving at the formula, it is adequate to describe the majority of problems in instrumental optics. This is mainly because the wavelength of light is much smaller than the dimensions of any obstacles encountered. Analytical solutions are not possible for most configurations, but the Fresnel diffraction equation and Fraunhofer diffraction equation, which are approximations of Kirchhoff's formula for the near field and far field, can be applied to a very wide range of optical systems.
One of the important assumptions made in arriving at the Kirchhoff diffraction formula is that r and s are significantly greater than λ. Another approximation can be made, which significantly simplifies the equation further: this is that the distances P0Q and QP are much greater than the dimensions of the aperture. This allows one to make two further approximations:
cos(n, r) − cos(n, s) is replaced with 2cos β, where β is the angle between P0P and the normal to the aperture. The factor 1/rs is replaced with 1/rs, where r and s are the distances from P0 and P to the origin, which is located in the aperture. The complex amplitude then becomes:
Assume that the aperture lies in the xy plane, and the coordinates of P0, P and Q (a general point in the aperture) are (x0, y0, z0), (x, y, z) and (x, y, 0) respectively. We then have:
We can express r and s as follows:
These can be expanded as power series:
The complex amplitude at P can now be expressed as
where f(x, y) includes all the terms in the expressions above for s and r apart from the first term in each expression and can be written in the form
where the ci are constants.
Fraunhofer diffraction
If all the terms in f(x, y) can be neglected except for the terms in x and y, we have the Fraunhofer diffraction equation. If the direction cosines of P0Q and PQ are
The Fraunhofer diffraction equation is then
where C is a constant. This can also be written in the form
where k0 and k are the wave vectors of the waves traveling from P0 to the aperture and from the aperture to P respectively, and r is a point in the aperture.
If the point source is replaced by an extended source whose complex amplitude at the aperture is given by U0(r' ), then the Fraunhofer diffraction equation is:
where a0(r') is, as before, the magnitude of the disturbance at the aperture.
In addition to the approximations made in deriving the Kirchhoff equation, it is assumed that
r and s are significantly greater than the size of the aperture,
second- and higher-order terms in the expression f(x, y) can be neglected.
Fresnel diffraction
When the quadratic terms cannot be neglected but all higher order terms can, the equation becomes the Fresnel diffraction equation. The approximations for the Kirchhoff equation are used, and additional assumptions are:
r and s are significantly greater than the size of the aperture,
third- and higher-order terms in the expression f(x, y) can be neglected.
References
Further reading
Baker, B.B.; Copson, E.T. (1939, 1950). The Mathematical Theory of Huygens' Principle. Oxford.
Waves
Physical optics
Diffraction
Gustav Kirchhoff | Kirchhoff's diffraction formula | [
"Physics",
"Chemistry",
"Materials_science"
] | 2,556 | [
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31,559,945 | https://en.wikipedia.org/wiki/Collapsible%20flow | Collapsible flow is a phenomenon that occurs in steady flow in tubes with significant distensibility, or the capability of swelling or stretching, under conditions of lower internal pressure relative to pressure outside the tube. Such conditions occur rarely in industrial applications but are very common in biological studies such as blood flow in veins and air flow in lungs.
When a flow is driven through a deformable channel or tube, interactions between fluid-mechanical and elastic forces can lead to a variety of biologically significant phenomena, including nonlinear pressure-drop/flow-rate relations, wave propagation,
and the generation of instabilities. Understanding the physical origin and nature of these phenomena remains a significant experimental, analytical, and computational challenge, involving unsteady flows at low or high Reynolds numbers, large-amplitude fluid-structure interactions, free-surface flows, and intrinsically 2D or 3D motion. Whereas frequently the internal flow involves a single fluid
phase (albeit often of a complex biological fluid such as blood), in many instances the presence of two or more distinct flowing phases is of primary importance (as is the case for air-liquid flows in peripheral lung airways, for example).
Single Phase in Collapsible Tubes
Venous collapse is important during exercise, when muscular compression of leg veins is used to pump blood against gravity up to the heart, and in therapeutic compression of leg veins for the treatment of deep-vein thrombosis
partial vessel collapse occurs in vessels which undergo conditions of higher external pressure relative to the fluid within and can be difficult to predict mathematically. As such, devices such as a Starling Resistor are often used to predict fluid flow under these conditions.
Fluid is forced through an elastically deforming tube which passes through a region of high external pressure causing a flattening of the tube depending on the relative pressures of the inside and outside of the tube.
In the absence of any flow (puD pd), an increase in pe generates a compressive stress in the tube wall causing it to buckle from a circular to an elliptic cross-section (except, of course, near its ends, where it is attached to the rigid tubes). Buckling to a shape with more than two lobes may arise in short, tethered, or inhomogeneous tubes. Once buckled, the tube becomes highly compliant so that small additional increases in pe lead to a substantial reduction in cross-sectional area ®. Further compression leads to contact of the opposite tube walls, first at a point, and then along a line (Figure 2, left); once in opposite-wall contact, the tube's compliance falls because strong bending forces in the tube wall at the bulbous end of each lobe provide an increasing resistance to area reductions. The “tube law,” the relation between transmural pressure P – Pexternal (where p is the internal pressure) and , for a long thin-walled tube can be approximated by thin-shell theory for an axially uniform elastic ring
References
Continuum mechanics
Flow regimes
Piping | Collapsible flow | [
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"Building engineering",
"Chemical engineering",
"Classical mechanics",
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"Fluid dynamics"
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31,562,046 | https://en.wikipedia.org/wiki/Synthetic%20ion%20channels | Synthetic ion channels are de novo chemical compounds that insert into lipid bilayers, form pores, and allow ions to flow from one side to the other. They are man-made analogues of natural ion channels, and are thus also known as artificial ion channels. Compared to biological channels, they usually allow fluxes of similar magnitude but are
minuscule in size (less than 5k Dalton vs. > 100k Dalton),
diverse in molecular architecture, and
may rely on diverse supramolecular interactions to pre-form the active, conducting structures.
Synthetic channels, like natural channels, are usually characterized by a combination of single-molecule (e.g., voltage-clamp of planar bilayers) and ensemble techniques (flux in vesicles). The study of synthetic ion channels can potentially lead to new single-molecule sensing technologies as well as new therapeutics.
History
While semi-synthetic ion channels, often based on modified peptidic channels like gramicidin, had been prepared since the 1970s, the first attempt to prepare a synthetic ion channel was made in 1982 using a substituted β-cyclodextrin.
Inspired by gramicidin, this molecule was designed to be a barrel-shaped entity spanning a single leaflet of a bilayer membrane, becoming "active" only when two molecules in opposite leaflets come together in an end-to-end fashion. While the compound does induce ion-fluxes in vesicles, the data does not unambiguously show channel formation (as opposed to other transport mechanisms; see Mechanism).
Na+ transport by such channels was first reported by two groups of investigators in 1989–1990.
With the adoption of voltage clamp technique to synthetic channel research in the early 1990s, researchers were able to observe quantized electrical activities from synthetic molecules, often considered the signature evidence for ion channels. This led to a sustained increase in research activity over the next two decades. In 2009, over 25 peer-reviewed papers were published on the topic, and a series of comprehensive reviews are available.
Characterization and mechanisms
Passive transport of ions across a membrane can take place by three main mechanisms: by ferrying, through defects in a disrupted membrane, or through a defined trajectory; these corresponds to ionophore, detergent, and ion channel transporters. While synthetic ion channel research attempts to prepare compounds that show conductance via a defined path, the elucidation of mechanism is difficult and seldom unambiguous. The two main methods of characterization both have their drawbacks, and as a consequence, often function is defined but mechanism presumed.
Ensemble, vesicle-based time course
One line of evidence for ion transport comes from macroscopic examination of statistical ensembles. All these techniques use intact vesicles with an entrapped volume, with ion channel activities reported by different spectroscopic methods.
In a typical case, a dye is entrapped within the population of vesicles. This dye is selected to be respond colorimetrically or fluorometrically to the presence of an ion; this ion is typically absent from the inside of the vesicle but present in the outside. Without an ion transporter, the lipid bilayer as a kinetic barrier to block ion flux, and the dye remains "dark" indefinitely.
As an ion transporter allows ions on the outside to diffuse in, its addition will affect the color/fluorescence property of the dye. By macroscopically monitoring the dye's properties over time, and controlling outside factors, the ability of a compound to act as an ion transporter can be measured.
Observing ion transport, however, does not pin down ion channel as the mechanism. Any class of transporter can lead to the same observation, and additional corroborating evidence is usually required. Sophisticated experiments intended to probe selectivity, gating, and other channel parameters have been developed over the past two decades and recently summarized.
Vesicle assay variations
Stochastic, planar bilayer-based current traces
An alternative to the ensemble-based method described above is the voltage-clamp experiment. In a voltage-clamp experiment, two compartments of electrolyte are divided by an aperture, usually between 5-250 micrometres in diameter. A lipid bilayer is painted across this aperture, thus electrically separating the compartments; the molecular nature can be ascertained by measuring its capacitance.
Upon the addition of an (ideal) ion channel, a defined path between the two compartments is formed. Through this pore, ions flow down the potential and electrochemical gradient rapidly (>106/second), the maximum flux limited by the geometry and dimensions of the pore. At some later instant the pore may close or collapse, whereupon the current returns to zero. This open-state current, originating and amplified from a single-molecule event, is typically on the order of pA to nA, with time-resolution of approx. millisecond. Ideal or close-to-ideal events is termed "square-tops" in the literature, and have been considered as signature for a channel-based mechanism.
It is notable that the events observed at this scale are truly stochastic - that is, they are the result of random molecular collision and conformation changes. As the membrane area is much larger than that of a pore, multiple copies may open and close independently of one another, giving rise to the staircase like appearance (Panel C in figure); these ideal events are often modelled as Markov processes.
By using the activity grid notation, synthetic ion channels studied with the voltage-clamp method during the period 1982-2010 have been critically reviewed. While the ideal traces are most frequently analyzed and reported in the literature, many records are decidedly non-ideal, with a subset was shown to be fractal. Developing methods for analyzing these non-ideal traces and clarifying their relationship to transport mechanism is an area of contemporary research.
Examples
A diverse and large pool of synthetic molecules have been reported to act as ion transporters in lipid membranes. A selection is described here to demonstrate the breadth of feasible structures and attainable functions. Comprehensive reviews for the literature up to 2010 are available in a tripartite series.
By chemical structure
Most (but not all; see minimalist channels) synthetic channels have chemical structures substantially larger than typical small molecules (molecular weights ~1-5kDa). This originates from the need to be amphiphilic, that is, have both sufficient hydrophobic portions to allow partitioning into lipid bilayer, as well as polar or charged "headgroups" to assert a defined orientation and geometry with respect to the membrane.
Macrocycles-based
Crown ethers-based
Calixarene-based
Ion channels containing calixarenes of ring size 3 and 4 have both been reported. For calix[4]arene, two conformations are accessible, and examples of both 1,3-alt and cone conformation have been developed.
Cyclodextrin-based
The first synthetic ion channel was constructed by partial substitution on the primary rim of β-cyclodextrin. Other substituted β-cyclodextrins have since been reported, including thiol-modified cyclodextrins, an anion-selective oligobutylene channel, and various poly-ethyleneoxide linked starburst oligomers. Structure-activity relationships for a large suite of cyclodextrin "half-channels" prepared by "click"-chemistry has been recently reported.
Rigid rods
Peptide-based
Alternating D/L peptide macrocycles are known to self-aggregate into nanotubes, and the resulting nanotubes have been shown to act as ion channels in lipid membranes.
Other architectures use peptide helices as a scaffold to attach other functionalities, such as crown ethers of different sizes. The property of these peptide-crown channels depend strongly on the identity of the capping end-groups.
Minimalist channels
Miscellaneous
G-quartet based channels
Metal-organic channels
Hybrid bio-channels
Semi-synthetic bio-hybrid channels constructed by modifications of natural ion channels had been constructed. Leveraging modern synthetic organic chemistry, these allows pinpoint modifications of existing structures to either elucidate their transport mechanisms or to graft on new functionalities.
Gramicidin and alamethicin had been popular starting points for selective modifications. The above diagram illustrates one example, where a crown-ether was fixed across the mouth of the ion-passing portal. This channel shows discrete conductance but different ion selectivity than wild type gramicidin in voltage-clamp experiments.
While modification of large protein channels using mutagenesis are generally considered out of the scope of synthetic channels, the demarcation is not sharp, as supramolecular or covalent bonding of cyclodextrins to alpha-hemolysin demonstrates.
By transport characteristics
An ion channel can be characterized by its opening characteristics, ion selectivity, and control of flux (gating). Many synthetic ion channels show unique properties in one or more of these aspects.
Opening characteristics
An "ion-channel forming" molecule can often show multiple types of conductance activities in planar bilayer membranes. Each of these modes of action can be characterized by their
open duration (sub-ms---hours), related to whether the active structure is kinetically labile,
unit conductance (pS---nS), related to the geometry of the active structure, and
open probability, a fraction related to the thermodynamic stability of that active structure relative to inactive forms.
These events are not necessarily uniform throughout their durations, and as a result a variety of shapes of conducting traces are possible.
Ion selectivity
The majority of synthetic ion channels follow an Eisenman I sequence (Cs+ > Rb+ > K+ > Na+ >> Li+) in their selectivity for alkali metal cations, suggesting that the origin of the selectivity is governed by the difference in energy required to remove water from a fully hydrated cation. A few synthetic channels show other patterns of ion selectivity, and only a single instance in which a synthetic channel following the opposite selectivity sequence (Eisenman XI; Cs+ < Rb+ < K+ < Na+ << Li+) had been reported.
Gating
Voltage response
Most synthetic channels are Ohmic in conductance, that is, the current passed (both individually and as an ensemble) is proportional to the potential across the membrane. Some rare channels, however, show current-voltage characteristics that is non-linear. Specifically, two different types of non-Ohmic conductance are known:
a rectifying behaviour, where current passes depends on the sign of the applied potential, and
an exponential potential dependence, where the current passed scales exponentially with the applied potential.
The former requires asymmetry with respect to the mid-plane of the lipid bilayer, and is realized often by introducing an overall molecular dipole. The latter, demonstrated in natural channels such as alamethicin, is rarely encountered in synthetic ion channels. They may be related to lipid ion channels, but to date their mechanism remains elusive.
Ligand response
Certain synthetic ion channels have conductances that can be modulated by additional of external chemicals. Both up-modulation (channels are turned on by ligand) and down-modulation (channels are turned off by ligands) are known: different mechanisms, including formation of supramolecular aggregates, as well as inter- and intramolecular blockage.
Others
Regulatory elements that responds to other signals are known; examples include photomodulated conductances as well as "thermal switches" constructed by isomerization of the carbamate group. To date, no mechanosensitive synthetic ion channels have been reported.
See also
Nanotechnology
Supramolecular chemistry
Macrocycles
Amphiphile
Ionophore
Membrane biophysics
Membrane protein
Voltage-gated ion channel
Pore-forming toxin
Antimicrobial peptides
Electrophysiology
References
Supramolecular chemistry
Molecular biology
Nanotechnology
Ion channels
Electrophysiology
Synthetic biology | Synthetic ion channels | [
"Chemistry",
"Materials_science",
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"Nanotechnology",
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6,828,483 | https://en.wikipedia.org/wiki/Tideline | A tideline refers to where two currents in the ocean converge. Driftwood, floating seaweed, foam, and other floating debris may accumulate, forming sinuous lines called tidelines (although they generally have nothing to do with the tide).
There are four mechanisms that can cause tidelines to form:
Where one body of water is sinking beneath or riding over top of the surface layer of another body of water (somewhat similar in mechanics to subduction and/or uprisal of the earth plates at continental margins). These types of tidelines are often found where rivers enter the ocean.
Along the margins of back-eddies.
Convergence zones associated with internal gravity waves.
Along adjacent cells formed by wind currents.
See also
Langmuir circulation
Ocean circulation
Flotsam and jetsam
References
Thomson, R.E. 1981. Oceanography of the British Columbia Coast. Department of Fisheries and Oceans. Canadian Special Publication of Fisheries and Aquatic Sciences 56. Ottawa. 291.
Tides
Physical oceanography | Tideline | [
"Physics"
] | 201 | [
"Applied and interdisciplinary physics",
"Physical oceanography"
] |
6,830,376 | https://en.wikipedia.org/wiki/Balz%E2%80%93Schiemann%20reaction | The Balz–Schiemann reaction (also called the Schiemann reaction) is a chemical reaction in which a primary aromatic amine is transformed to an aryl fluoride via a diazonium tetrafluoroborate intermediate. This reaction is a traditional route to fluorobenzene and some related derivatives, including 4-fluorobenzoic acid.
The reaction is conceptually similar to the Sandmeyer reaction, which converts diazonium salts to other aryl halides (ArCl, ArBr). However, while the Sandmeyer reaction involves a copper reagent/catalyst and radical intermediates, the thermal decomposition of the diazonium tetrafluoroborate proceeds without a promoter and is believed to generate highly unstable aryl cations (Ar+), which abstract F− from BF4− to give the fluoroarene (ArF), along with boron trifluoride and nitrogen as the byproducts.
Innovations
The traditional Balz–Schiemann reaction employs HBF4 and involves isolation of the diazonium salt. Both aspects can be profitably modified. Other counterions have been used in place of tetrafluoroborates, such as hexafluorophosphates (PF6−) and hexafluoroantimonates (SbF6−) with improved yields for some substrates. The diazotization reaction can be effected with nitrosonium salts such as [NO]SbF6 without isolation of the diazonium intermediate.
As a practical matter, the traditional Balz–Schiemann reaction consumes relatively expensive BF4− as a source of fluoride. An alternative methodology produces the fluoride salt of the diazonium compound. In this implementation, the diazotization is conducted with a solution of sodium nitrite in liquid hydrogen fluoride:
History
The reaction is named after the German chemists and Günther Balz.
Examples
4-Fluorotoluene is made in ~89% yield by Balz–Schiemann reaction on p-toluidine. This is then used as a precursor for 4-fluorobenzaldehyde,
Additional literature
References
Halogenation reactions
Substitution reactions
Name reactions | Balz–Schiemann reaction | [
"Chemistry"
] | 468 | [
"Name reactions"
] |
6,830,742 | https://en.wikipedia.org/wiki/Bioorganometallic%20chemistry | Bioorganometallic chemistry is the study of biologically active molecules that contain carbon directly bonded to metals or metalloids. The importance of main-group and transition-metal centers has long been recognized as important to the function of enzymes and other biomolecules. However, only a small subset of naturally-occurring metal complexes and synthetically prepared pharmaceuticals are organometallic; that is, they feature a direct covalent bond between the metal(loid) and a carbon atom. The first, and for a long time, the only examples of naturally occurring bioorganometallic compounds were the cobalamin cofactors (vitamin B12) in its various forms. In the 21st century, as a result of the discovery of new systems containing carbon–metal bonds in biology, bioorganometallic chemistry is rapidly emerging as a distinct subdiscipline of bioinorganic chemistry that straddles organometallic chemistry and biochemistry. Naturally occurring bioorganometallics include enzymes and sensor proteins. Also within this realm are synthetically prepared organometallic compounds that serve as new drugs and imaging agents (technetium-99m sestamibi) as well as the principles relevant to the toxicology of organometallic compounds (e.g., methylmercury). Consequently, bioorganometallic chemistry is increasingly relevant to medicine and pharmacology.
In cofactors and prosthetic groups
Vitamin B12 is the preeminent bioorganometallic species. Vitamin B12 is actually a collection of related enzyme cofactors, several of which contain cobalt–alkyl bonds, and is involved in biological methylation and 1,2-carbon rearrangement reactions. For a long time since its structure was elucidated by Hodgkin in 1955, it was believed to be the only example of a naturally occurring bioorganometallic system.
Several bioorganometallic enzymes carry out reactions involving carbon monoxide. Carbon monoxide dehydrogenase (CODH) catalyzes the water–gas shift reaction, which provides CO (through a nickelacarboxylate intermediate) for the biosynthesis of acetylcoenzyme A. The latter step is effected by the Ni–Fe enzyme CO-methylating acetyl-CoA synthase (ACS). CODH and ACS often occur together in a tetrameric complex, the CO being transported via a tunnel and the methyl group being provided by methyl cobalamin.
Hydrogenases are bioorganometallic in the sense that their active sites feature Fe–CO functionalities, although the CO ligands are only spectators. The binuclear [FeFe]-hydrogenases have a Fe2(μ-SR)2(μ-CO)(CO)2(CN)2 active site connected to a 4Fe4S cluster via a bridging thiolate. The active site of the [NiFe]-hydrogenases are described as (NC)2(OC)Fe(μ-SR)2Ni(SR)2 (where SR is cysteinyl). Mononuclear [Fe]-hydrogenases contain an Fe(CO)2(SR)(LX) active site, where LX is a 6-acylmethyl-2-pyridinol ligand, bound to the Fe center through the pyridyl nitrogen (L) and the acyl carbon (X). This class of hydrogenases thus provides examples of naturally occurring iron acyl complexes.
Methanogenesis, the biosynthesis of methane, entails as its final step, the scission of a nickel–methyl bond in cofactor F430.
The iron–molybdenum cofactor (FeMoco) of nitrogenases contains an Fe6C unit and is an example of an interstitial carbide found in biology.
The first example of a naturally-occurring arylmetal species, a pincer complex containing a nickel–aryl bond, has been reported to form the active site of lactate racemase.
In sensor proteins
Some [NiFe]-containing proteins are known to sense H2 and thus regulate transcription.
Copper-containing proteins are known to sense ethylene, which is known to be a hormone relevant to the ripening of fruit. This example illustrates the essential role of organometallic chemistry in nature, as few molecules outside of low-valent transition metal complexes reversibly bind alkenes. Cyclopropenes inhibit ripening by binding to the copper(I) center. Binding to copper is also implicated in the mammalian olfaction of olefins.
Carbon monoxide occurs naturally and is a transcription factor via its complex with a sensor protein based on ferrous porphyrins.
In medicine
Organometallic compounds containing mercury (e.g., thiomersal) and arsenic (e.g. Salvarsan) had a long history of use in medicine as nonselective antimicrobials before the advent of modern antibiotics.
Titanocene dichloride displays anti-cancer activity, and dichloridobis[(p-methoxybenzyl)cyclopentadienyl]titanium is a current anticancer drug candidate. Arene- and cyclopentadienyl complexes are kinetically inert platforms for the design of new radiopharmaceuticals.
Furthermore, there have been made studies utilizing exogenous semi-synthetic ligands; specifically to the dopamine transporter, observing increased resultant efficacy in regard to reward facilitating behavior (incentive salience) and habituation, namely with the phenyltropane compound [η6-(2β-carbomethoxy-3β-phenyl)tropane]tricarbonylchromium.
Carbon monoxide releasing organometallic compounds are also actively investigated, due to the importance of carbon monoxide as a gasotransmitter.
Toxicology
Within the realm of bioorganometallic chemistry is the study of the fates of synthetic organometallic compounds. Tetraethyllead has received considerable attention in this regard as has its successors such as methylcyclopentadienyl manganese tricarbonyl. Methylmercury is a particularly infamous case; this cation is produced by the action of vitamin B12-related enzymes on mercury.
References
Biochemistry
Inorganic chemistry
Organometallic chemistry
Medicinal inorganic chemistry
Bioinorganic chemistry | Bioorganometallic chemistry | [
"Chemistry",
"Biology"
] | 1,376 | [
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"Medicinal chemistry",
"nan",
"Biochemistry",
"Organometallic chemistry",
"Bioinorganic chemistry"
] |
6,831,289 | https://en.wikipedia.org/wiki/Swinging%20Atwood%27s%20machine | The swinging Atwood's machine (SAM) is a mechanism that resembles a simple Atwood's machine except that one of the masses is allowed to swing in a two-dimensional plane, producing a dynamical system that is chaotic for some system parameters and initial conditions.
Specifically, it comprises two masses (the pendulum, mass and counterweight, mass ) connected by an inextensible, massless string suspended on two frictionless pulleys of zero radius such that the pendulum can swing freely around its pulley without colliding with the counterweight.
The conventional Atwood's machine allows only "runaway" solutions (i.e. either the pendulum or counterweight eventually collides with its pulley), except for . However, the swinging Atwood's machine with has a large parameter space of conditions that lead to a variety of motions that can be classified as terminating or non-terminating, periodic, quasiperiodic or chaotic, bounded or unbounded, singular or non-singular due to the pendulum's reactive centrifugal force counteracting the counterweight's weight. Research on the SAM started as part of a 1982 senior thesis entitled Smiles and Teardrops (referring to the shape of some trajectories of the system) by Nicholas Tufillaro at Reed College, directed by David J. Griffiths.
Equations of motion
The swinging Atwood's machine is a system with two degrees of freedom. We may derive its equations of motion using either Hamiltonian mechanics or Lagrangian mechanics. Let the swinging mass be and the non-swinging mass be . The kinetic energy of the system, , is:
where is the distance of the swinging mass to its pivot, and is the angle of the swinging mass relative to pointing straight downwards. The potential energy is solely due to the acceleration due to gravity:
We may then write down the Lagrangian, , and the Hamiltonian, of the system:
We can then express the Hamiltonian in terms of the canonical momenta, , :
Lagrange analysis can be applied to obtain two second-order coupled ordinary differential equations in and . First, the equation:
And the equation:
We simplify the equations by defining the mass ratio . The above then becomes:
Hamiltonian analysis may also be applied to determine four first order ODEs in terms of , and their corresponding canonical momenta and :
Notice that in both of these derivations, if one sets and angular velocity to zero, the resulting special case is the regular non-swinging Atwood machine:
The swinging Atwood's machine has a four-dimensional phase space defined by , and their corresponding canonical momenta and . However, due to energy conservation, the phase space is constrained to three dimensions.
System with massive pulleys
If the pulleys in the system are taken to have moment of inertia and radius , the Hamiltonian of the SAM is then:
Where t is the effective total mass of the system,
This reduces to the version above when and become zero. The equations of motion are now:
where .
Integrability
Hamiltonian systems can be classified as integrable and nonintegrable. SAM is integrable when the mass ratio . The system also looks pretty regular for , but the case is the only known integrable mass ratio. It has been shown that the system is not integrable for . For many other values of the mass ratio (and initial conditions) SAM displays chaotic motion.
Numerical studies indicate that when the orbit is singular (initial conditions: ), the pendulum executes a single symmetrical loop and returns to the origin, regardless of the value of . When is small (near vertical), the trajectory describes a "teardrop", when it is large, it describes a "heart". These trajectories can be exactly solved algebraically, which is unusual for a system with a non-linear Hamiltonian.
Trajectories
The swinging mass of the swinging Atwood's machine undergoes interesting trajectories or orbits when subject to different initial conditions, and for different mass ratios. These include periodic orbits and collision orbits.
Nonsingular orbits
For certain conditions, system exhibits complex harmonic motion. The orbit is called nonsingular if the swinging mass does not touch the pulley.
Periodic orbits
When the different harmonic components in the system are in phase, the resulting trajectory is simple and periodic, such as the "smile" trajectory, which resembles that of an ordinary pendulum, and various loops. In general a periodic orbit exists when the following is satisfied:
The simplest case of periodic orbits is the "smile" orbit, which Tufillaro termed Type A orbits in his 1984 paper.
Singular orbits
The motion is singular if at some point, the swinging mass passes through the origin. Since the system is invariant under time reversal and translation, it is equivalent to say that the pendulum starts at the origin and is fired outwards:
The region close to the pivot is singular, since is close to zero and the equations of motion require dividing by . As such, special techniques must be used to rigorously analyze these cases.
The following are plots of arbitrarily selected singular orbits.
Collision orbits
Collision (or terminating singular) orbits are subset of singular orbits formed when the swinging mass is ejected from its pivot with an initial velocity, such that it returns to the pivot (i.e. it collides with the pivot):
The simplest case of collision orbits are the ones with a mass ratio of 3, which will always return symmetrically to the origin after being ejected from the origin, and were termed Type B orbits in Tufillaro's initial paper. They were also referred to as teardrop, heart, or rabbit-ear orbits because of their appearance.
When the swinging mass returns to the origin, the counterweight mass, must instantaneously change direction, causing an infinite tension in the connecting string. Thus we may consider the motion to terminate at this time.
Boundedness
For any initial position, it can be shown that the swinging mass is bounded by a curve that is a conic section. The pivot is always a focus of this bounding curve. The equation for this curve can be derived by analyzing the energy of the system, and using conservation of energy. Let us suppose that is released from rest at and . The total energy of the system is therefore:
However, notice that in the boundary case, the velocity of the swinging mass is zero. Hence we have:
To see that it is the equation of a conic section, we isolate for :
Note that the numerator is a constant dependent only on the initial position in this case, as we have assumed the initial condition to be at rest. However, the energy constant can also be calculated for nonzero initial velocity, and the equation still holds in all cases. The eccentricity of the conic section is . For , this is an ellipse, and the system is bounded and the swinging mass always stays within the ellipse. For , it is a parabola and for it is a hyperbola; in either of these cases, it is not bounded. As gets arbitrarily large, the bounding curve approaches a circle. The region enclosed by the curve is known as the Hill's region.
Recent three dimensional extension
A new integrable case for the problem of three dimensional Swinging Atwood Machine (3D-SAM) was announced in 2016. Like the 2D version, the problem is integrable when .
References
Further reading
Almeida, M.A., Moreira, I.C. and Santos, F.C. (1998) "On the Ziglin-Yoshida analysis for some classes of homogeneous hamiltonian systems", Brazilian Journal of Physics Vol.28 n.4 São Paulo Dec.
Barrera, Emmanuel Jan (2003) Dynamics of a Double-Swinging Atwood's machine, B.S. Thesis, National Institute of Physics, University of the Philippines.
Babelon, O, M. Talon, MC Peyranere (2010), "Kowalevski's analysis of a swinging Atwood's machine," Journal of Physics A: Mathematical and Theoretical Vol. 43 (8).
Bruhn, B. (1987) "Chaos and order in weakly coupled systems of nonlinear oscillators," Physica Scripta Vol.35(1).
Casasayas, J., N. B. Tufillaro, and A. Nunes (1989) "Infinity manifold of a swinging Atwood's machine," European Journal of Physics Vol.10(10), p173.
Casasayas, J, A. Nunes, and N. B. Tufillaro (1990) "Swinging Atwood's machine: integrability and dynamics," Journal de Physique Vol.51, p1693.
Chowdhury, A. Roy and M. Debnath (1988) "Swinging Atwood Machine. Far- and near-resonance region", International Journal of Theoretical Physics, Vol. 27(11), p1405-1410.
Griffiths D. J. and T. A. Abbott (1992) "Comment on ""A surprising mechanics demonstration,"" American Journal of Physics Vol.60(10), p951-953.
Moreira, I.C. and M.A. Almeida (1991) "Noether symmetries and the Swinging Atwood Machine", Journal of Physics II France 1, p711-715.
Nunes, A., J. Casasayas, and N. B. Tufillaro (1995) "Periodic orbits of the integrable swinging Atwood's machine," American Journal of Physics Vol.63(2), p121-126.
Ouazzani-T.H., A. and Ouzzani-Jamil, M., (1995) "Bifurcations of Liouville tori of an integrable case of swinging Atwood's machine," Il Nuovo Cimento B Vol. 110 (9).
Olivier, Pujol, JP Perez, JP Ramis, C. Simo, S. Simon, JA Weil (2010), "Swinging Atwood's Machine: Experimental and numerical results, and a theoretical study," Physica D 239, pp. 1067–1081.
Sears, R. (1995) "Comment on "A surprising mechanics demonstration," American Journal of Physics, Vol. 63(9), p854-855.
Yehia, H.M., (2006) "On the integrability of the motion of a heavy particle on a tilted cone and the swinging Atwood machine", Mechanics Research Communications Vol. 33 (5), p711–716.
External links
Imperial College Course
Oscilaciones en la máquina de Atwood
"Smiles and Teardrops" (1982)
2010 Videos of an experimental Swinging Atwood's Machine
Open source Java code for running the Swinging Atwood's Machine
Hamiltonian mechanics | Swinging Atwood's machine | [
"Physics",
"Mathematics"
] | 2,295 | [
"Hamiltonian mechanics",
"Theoretical physics",
"Classical mechanics",
"Dynamical systems"
] |
6,832,907 | https://en.wikipedia.org/wiki/Oxatomide | Oxatomide, sold under the brand name Tinset among others, is a antihistamine of the diphenylmethylpiperazine family which is marketed in Europe, Japan, and a number of other countries. It was discovered at Janssen Pharmaceutica in 1975. Oxatomide lacks any anticholinergic effects. In addition to its H1 receptor antagonism, it also possesses antiserotonergic activity similarly to hydroxyzine. Oxatomide was also found to have antiviral activity against Venezuelan equine encephalitis virus (VEEV).
It was patented in 1976 and came into medical use in 1981.
Chemistry
Synthesis
Reaction of 2-Benzimidazolinone with isopropenyl acetate leads to the singly protected imidazolone derivative (2). Alkylation of this with 3-chloro-1-bromopropane affords the functionalized derivative (3). Alkylation of the monobenzhydryl derivative of piperazine (4) with 3 gives oxatomide (5), after hydrolytic removal of the protecting group.
References
Benzimidazoles
Belgian inventions
H1 receptor antagonists
Janssen Pharmaceutica
Gamma-lactams
Cyclizines
Ureas | Oxatomide | [
"Chemistry"
] | 273 | [
"Organic compounds",
"Ureas"
] |
6,834,050 | https://en.wikipedia.org/wiki/Submucosa | The submucosa (or tela submucosa) is a thin layer of tissue in various organs of the gastrointestinal, respiratory, and genitourinary tracts. It is the layer of dense irregular connective tissue that supports the mucosa (mucous membrane) and joins it to the muscular layer, the bulk of overlying smooth muscle (fibers running circularly within layer of longitudinal muscle).
The submucosa (sub- + mucosa) is to a mucous membrane what the subserosa (sub- + serosa) is to a serous membrane.
Structure
Blood vessels, lymphatic vessels, and nerves (all supplying the mucosa) will run through here. In the intestinal wall, tiny parasympathetic ganglia are scattered around forming the submucous plexus (or "Meissner's plexus") where preganglionic parasympathetic neurons synapse with postganglionic nerve fibers that supply the muscularis mucosae. Histologically, the wall of the alimentary canal shows four distinct layers (from the lumen moving out): mucosa, submucosa, muscularis externa, and either a serous membrane or an adventitia.
In the gastrointestinal tract and the respiratory tract the submucosa contains the submucosal glands that secrete mucus.
Clinical significance
Identification of the submucosa plays an important role in diagnostic and therapeutic endoscopy, where special fibre-optic cameras are used to perform procedures on the gastrointestinal tract. Abnormalities of the submucosa, such as gastrointestinal stromal tumors, usually show integrity of the mucosal surface.
The submucosa is also identified in endoscopic ultrasound to identify the depth of tumours and to identify other abnormalities. An injection of dye, saline, or epinephrine into the submucosa is imperative in the safe removal of certain polyps.
Endoscopic mucosal resection involves removal of the mucosal layer, and in order to be done safely, a submucosal injection of dye is performed to ensure integrity at the beginning of the procedure.
Female uterine submucosal layers are liable to develop fibroids during pregnancy and are often excised upon discovery.
Small intestinal submucosa
Small intestinal submucosa (SIS) is submucosal tissue in the small intestines of vertebrates. SIS is harvested (typically from pigs) for transplanted structural material in several clinical applications, typically biologic meshes. They have low immunogenicity. Some uses under investigation include a scaffold for intervertebral disc regeneration.
Unlike other scaffold materials, the resorbable SIS extracellular matrix (SIS-ECM) scaffold is replaced by well-organized host tissues, including differentiated skeletal muscle.
History
A scientific article published in March 2018 proposed a revision of the anatomical definition of the submucosa. They first saw a non compact tissue which should be submucosa using a technology called endomicroscopy. They hypothesised that the submucosa was not compact as it was previously seen on histological analysis but form a reticular pattern. To confirm their findings, they performed fixed samples of bile duct into a freezing media in order to conserve the shape of the submucosa. They then performed a histological analysis and with several staining techniques, they described the submucosa as a network of collagenous bands separating open, formerly fluid-filled spaces. Theses spaces are bordered by fibroblast-like cells CD34 positive. However, these cells are devoid of ultrastructural features indicative of endothelial differentiation, including pinocytotic vesicles and Weibel-Palade bodies.
Additional images
References
Membrane biology
Digestive system | Submucosa | [
"Chemistry",
"Biology"
] | 825 | [
"Digestive system",
"Organ systems",
"Membrane biology",
"Molecular biology"
] |
24,435,370 | https://en.wikipedia.org/wiki/Isogeometric%20analysis | Isogeometric analysis is a computational approach that offers the possibility of integrating finite element analysis (FEA) into conventional NURBS-based CAD design tools. Currently, it is necessary to convert data between CAD and FEA packages to analyse new designs during development, a difficult task since the two computational geometric approaches are different. Isogeometric analysis employs complex NURBS geometry (the basis of most CAD packages) in the FEA application directly. This allows models to be designed, tested and adjusted in one go, using a common data set.
The pioneers of this technique are Tom Hughes and his group at The University of Texas at Austin. A reference free software implementation of some isogeometric analysis methods is GeoPDEs. Likewise, other implementations can be found online. For instance, PetIGA is an open framework for high performance isogeometric analysis heavily based on PETSc. In addition, MIGFEM is another IGA code which is implemented in Matlab and supports Partition of Unity enrichment IGA for 2D and 3D fracture. Furthermore, G+Smo is an open C++ library for isogeometric analysis. In particular, FEAP is a finite element analysis program which includes an Isogeometric analysis library FEAP IsoGeometric (Version FEAP84 & Version FEAP85).
Advantages of IGA with respect to FEA
Isogeometric analysis presents two main advantages with respect to the finite element method:
There is no geometric approximation error, due to the fact the domain is represented exactly
Wave propagation problems, arising for instance in cardiac electrophysiology, acoustics and elastodynamics, are better described, thanks to the reduction of numerical dispersion and dissipation errors.
Meshes
In the framework of IGA, the notions of both control mesh and physical mesh are defined.
A control mesh is made by the so-called control points and it is obtained by a piecewise linear interpolation of them. Control points play also the role of degrees of freedom (DOFs).
The physical mesh lays directly on the geometry and it consists of patches and knot spans. According to the number of patches that are used in a specific physical mesh, a single-patch or a multi-patch approach is effectively employed. A patch is mapped from a reference rectangle in two dimensions and from a reference cuboid in three dimensions: it can be seen as the entire computational domain or a smaller portion of it. Each patch can be decomposed into knot spans, which are points, lines and surfaces in 1D, 2D and 3D, respectively. Knots are inserted inside knot spans and define the elements. Basis functions are across the knots, with degree of the polynomial and multiplicity of a specific knot, and between a certain knot and the next or preceding one.
Knot vector
A knot vector, normally indicated as , is a set of non-descending points. is the knot, is the number of functions, refers to the basis functions order. A knot divides the knot span into elements. A knot vector is uniform or non-uniform according to the fact that its knots, once their multiplicity is not taken into account, are equidistant or not. If the first and the last knots appear times, the knot vector is said to be open.
Basis functions
Once a definition of knot vector is provided, several types of basis functions can be introduced in this context, such as B-splines, NURBS and T-splines.
B-splines
B-splines can be derived recursively from a piecewise constant function with :
Using De Boor's algorithm, it is possible to generate B-splines of arbitrary order :
valid for both uniform and non-uniform knot vectors. For the previous formula to work properly, let the division of two zeros to be equal to zero, i.e. .
B-splines that are generated in this way own both the partition of unity and positivity properties, i.e.:
So as to calculate derivatives or order of the B-splines of degree , another recursive formula can be employed:
where:
whenever the denominator of an coefficient is zero, the entire coefficient is forced to be zero as well.
A B-spline curve can be written in the following way:
where is the number of basis functions , and is the control point, with dimension of the space in which the curve is immersed.
An extension to the two dimensional case can be easily obtained from B-splines curves. In particular B-spline surfaces are introduced as:
where and are the numbers of basis functions and defined on two different knot vectors , , represents now a matrix of control points (also called control net).
Finally, B-splines solids, that need three sets of B-splines basis functions and a tensor of control points, can be defined as:
NURBS
In IGA basis functions are also employed to develop the computational domain and not only for representing the numerical solution. For this reason they should have all the properties that permit to represent the geometry in an exact way. B-splines, due to their intrinsic structure, are not able to generate properly circular shapes for instance. In order to circumvent this issue, non-uniform rational B-splines, also known as NURBS, are introduced in the following way:
where is a one dimensional B-spline, is referred to as weighting function, and finally is the weight.
Following the idea developed in the subsection about B-splines, NURBS curve are generated as follows:
with vector of control points.
The extension of NURBS basis functions to manifolds of higher dimensions (for instance 2 and 3) is given by:
hpk-refinements
There are three techniques in IGA that permit to enlarge the space of basis functions without touching the geometry and its parametrization.
The first one is known as knot insertion (or h-refinement in the FEA framework), where is obtained from with the addition of more knots, which implies an increment of both the number of basis functions and control points.
The second one is called degree elevation (or p-refinement in the FEA context), which permits to increase the polynomial order of the basis functions.
Finally the third method, known as k-refinement (without a counterpart in FEA), derives from the preceding two techniques, i.e. combines the order elevation with the insertion of a unique knot in .
References
External links
GeoPDEs: a free software tool for Isogeometric Analysis based on Octave
MIG(X)FEM: a free Matlab code for IGA (FEM and extended FEM)
PetIGA: A framework for high-performance Isogeometric Analysis based on PETSc
G+Smo (Geometry plus Simulation modules): a C++ library for isogeometric analysis, aiming at the seamless integration of Computer-aided Design (CAD) and Finite Element Analysis (FEA), maintained by an open-source community of contributors.
FEAP: a general purpose finite element analysis program which is designed for research and educational use, developed at University of California, Berkeley
Bembel: An open-source isogeometric boundary element library for Laplace, Helmholtz, and Maxwell problems written in C++
T.J.R. Hughes, J.A. Cottrell, Y. Bazilevs: "Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement", Computer Methods in Applied Mechanics and Engineering, Elsevier, 2005, 194 (39-41), pp.4135-4195.
Finite element method
Computer-aided design | Isogeometric analysis | [
"Engineering"
] | 1,580 | [
"Computer-aided design",
"Design engineering"
] |
24,436,033 | https://en.wikipedia.org/wiki/C24H33NO3 | {{DISPLAYTITLE:C24H33NO3}}
The molecular formula C24H33NO3 (molar mass: 383.52 g/mol, exact mass: 383.2460 u) may refer to:
Denaverine
Guineesine
Naftidrofuryl, also known as nafronyl
Molecular formulas | C24H33NO3 | [
"Physics",
"Chemistry"
] | 76 | [
"Molecules",
"Set index articles on molecular formulas",
"Isomerism",
"Molecular formulas",
"Matter"
] |
24,436,179 | https://en.wikipedia.org/wiki/C23H32N2O3 | {{DISPLAYTITLE:C23H32N2O3}}
The molecular formula C23H32N2O3 (molar mass: 384.512 g/mol, exact mass: 384.2413 u) may refer to:
MDMB-CHMICA
Zipeprol
Molecular formulas | C23H32N2O3 | [
"Physics",
"Chemistry"
] | 68 | [
"Molecules",
"Set index articles on molecular formulas",
"Isomerism",
"Molecular formulas",
"Matter"
] |
24,437,420 | https://en.wikipedia.org/wiki/Roller%20mill | Roller mills are mills that use cylindrical rollers, either in opposing pairs or against flat plates, to crush or grind various materials, such as grain, ore, gravel, plastic, and others. Roller grain mills are an alternative to traditional millstone arrangements in gristmills. Roller mills for rock complement other types of mills, such as ball mills and hammermills, in such industries as the mining and processing of ore and construction aggregate; cement milling; and recycling.
Types
Two-roller mills
Two-roller mills are the simplest variety, in which the material is crushed between two rollers before it continues on to its final destination. The spacing between the rollers can be adjusted by the operator. Thinner spacing usually leads to that material being crushed into smaller pieces.
Four-roller mills
Four-roller mills have two sets of rollers. in a four-roller mill, the grain first goes through rollers with a rather wide gap, which separates the seed from the husk without much damage to the husk, but leaves large grits. Flour is sieved out of the cracked grain, and then the coarse grist and husks are sent through the second set of rollers, which further crush the grist without damaging the crusts. Similarly, there are three-roller mills, in which one of the rollers is used twice.
Five- and six-roller mills
Six-roller mills have three sets of rollers. In this type of mill, the first set of rollers crush the whole kernel, and its output is divided three ways: Flour immediately is sent out the mill, grits without a husk proceed to the last roller, and husk, possibly still containing parts of the seed, go to the second set of rollers. From the second roller flour is directly output, as are husks and any possible seed still in them, and the husk-free grits are channeled into the last roller. Five-roller mills are six-roller mills in which one of the rollers performs double duty.
Gristmill conversion
In the 19th century roller mills were adapted to grist mills before replacing them. The mill used either steel or porcelain rollers. Between the years 1865 and 1872, the Hungarian milling industry upgraded and expanded the use of stone mills combined with roller mills in a process known as Hungarian high milling. Hungarian hard wheat so milled was claimed as integral to the "First in the world" success of the Vienna Bakery of the 1867 Paris Exposition.
Other applications
Specialized for the high production of superfine pyrophyllite powder making in glass fiber industry
Specialized for the high production of gangue powder making in coal industry
Specialized for the high production of various of chemical raw material powder making in the chemical industry.
Working principle
A motor or other prime mover drives the hanger of the grinding roller to rotate through a V pulley and center bearing. The roller, which is hung by a bearing and pendulum shaft, will roll along the inner circle of the roll ring while the hanger is rotating. A dust removal blower will generate negative pressure at the inlet and outlet of the grinder to prevent dust and radiating the heat in the machine.
History
Modern era roller mills were re-invented by the Hungarian engineer András Mechwart in 1874, then quickly spread to other parts of Europe and Americas.
See also
Calender
impact mill
unifine mill
stamp mill
crusher
pulverizer
Vertical roller mill
ball mill
Two roll rubber mill
References
Grinding mills
Mining equipment | Roller mill | [
"Engineering"
] | 713 | [
"Mining equipment"
] |
24,440,200 | https://en.wikipedia.org/wiki/Kotcherlakota%20Rangadhama%20Rao | Prof. Kotcherlakota Rangadhama Rao (9 September 1898 – 20 June 1972) was an Indian physicist in the field of Spectroscopy.
Rangadhama Rao is best known for his work on spectroscopy, his role in the development of Nuclear Quadrupole Resonance (NQR), and his long association with the physics laboratories of Andhra University. In his later years, he became known for his position as the Principal of all the colleges of Andhra University before their divisions into separate colleges, viz., AU College of Arts and Commerce, AU College of Engineering, AU College of Law, AU College of Pharmacy and AU College of Science and Technology.
Rangadhama Rao was known both for his scientific ability and his interpersonal relations and volatile personality
Early years
Kotcherlakota Rangadhama Rao was born in Vizianagaram, a coastal town in present-day Vizianagaram district of state of Andhra Pradesh, India, on 9 September 1898. His father, Kotcherlakota Venkata Narsing Rao was the postmaster of the present-day cities of Vizianagaram, Gajapathinagaram and Visakhapatnam, then small cities in the state of Andhra Pradesh in the Madras Presidency of British India. His mother, Ramayamma, died in 1923.
Kotcherlakota Rangadhama Rao had an arranged marriage to Vaddadi Perramma, as was the custom in the region. On 6 December 1925, when Rangadhama Rao was 27, the couple's first child, Ramakrishna Rao, was born. Rangadhama Rao and Vaddadi Perramma had seven more children, four sons and three daughters: Venkata Rao (5 February 1928); Venkata Narsing Rao (27 June 1933); Ramaleela (24 April 1938); Lakshmi Narayana (23 July 1940); Lalitha Kumari (31 July 1941); Amarnath (8 June 1944); and Vijaya Vani (19 September 1945).
Education
His elementary education was at Maharaja's High School, Vizianagaram for the 3rd, 4th and 5th grades during 1904 and 1906. He joined in different schools each year in his early education. He was shifted to London Mission High School, Vizianagaram, for the 6th grade and studied 7th and 8th grades in Hindu High School at Machilipatnam. He passed his 10th grade (SSLC) in C.B.M. High School at Visakhapatnam and 12th grade (Intermediate), from Mrs. A.V.N. College at Visakhapatnam.
Prof. K. Rangadhama Rao was in the first batch of students for the B.A. degree course in 1920 (there was no B.Sc. degree course at that time in Madras University) in the Maharajah's College in Vizianagaram. The B.A Degree course was initiated by Dr. Appadvedula Lakshmi Narayan in 1918.
Prof. K.R.Rao took his M.A. in Physics from Tiruchirappalli in 1923. His research career started in 1923 when he enrolled as a Research Scholar for D.Sc. (Doctor of Science) from Madras University. He was awarded the D.Sc. Degree from Madras University and was selected for studies abroad from the Andhra University in 1928. This was a turning point in his quest for knowledge and research of his lifetime.
Career
In 1924, Dr. K. Rangadhama Rao joined Dr. A.L.Narayan as a research scholar in University of Madras. Both of them worked tenaciously to build up a first rate spectroscopic laboratory second to none in the country. They had then with them a constant deviation spectrograph, a small quartz spectrograph and a medium quartz spectrograph. All these were of low dispersion and low resolving power. At this stage of their work, they required an instrument of high dispersion and high resolving power, which they could not afford. So, K.R.Rao went to Calcutta, where a ten-foot concave grating was available in the Indian Association for the Cultivation of Science of which C. V. Raman was Director and with the facilities provided there, they further extended their work on analysis of spectra in the visible and ultraviolet regions.
He was guided in his research career by Prof. A.Fowler at the Imperial College of Science and Technology, London in 1930 in Atomic Spectra for two years for which he was awarded the D.Sc. Degree from London University. In 1930, he had the opportunity of working under Prof. F.Paschen at the Physikalische Technische Reichsanstalt in Berlin for six months and under Prof. Manne Siegbahn in Upsala, Sweden on Vacuum Spectroscopy for another six months. His interest in the field of Spectroscopy was so much that he built a Vacuum Spectrograph of his design with his own expenses at Potsdam, Germany.
Prof. K.R.Rao's contribution towards physics has placed him in a high position even in his times. His contributions include development of Diatomic and Polyatomic Molecular Spectroscopy laboratory dealing with High Resolution Vibrational structure in electronic transitions, U.V.Absorption, Infrared Absorption, Raman scattering, Fluorescence and Phosphorescence and Crystal Spectra. He also reached the level of construction of microwave test benches and using these techniques he created different lines of investigations in dielectrics. He contributed to the development of Radio Frequency Spectroscopy which branched into Nuclear Quadrupole Resonance (NQR), Nuclear Magnetic Resonance (NMR) and Electron Spin Resonance (ESR) spectroscopy. In India, work on NQR was first initiated by Prof. K. Rangadhama Rao in the Physics laboratories of Andhra University.
Kotcherlakota Rangdhama Rao was the Principal of Andhra University Colleges from 1949 to 1957. He was appointed as Emeritus Professor of Physics at Andhra University (1966–72) and was special officer for the establishment of Sri Venkateswara University, Tirupathi (1954).
Contributions
During his early life of work in the Physics department of Andhra University, Prof. K.R.Rao, established scholarships in his father's name, Kotcherlakota Venkata Narsinga Rao.
Kotcherlakota Venkata Narsinga Rao Scholarship
While a Reader in the Physics Department of Jeypore Vikram Deo College of Science and Technology, Rao instituted a Research Scholarship in memory of his late father.
Honours, distinctions and awards
Prof. Rangadhama Rao was one of the foundation members for the AP Akademi of Sciences, nominated by the Government of Andhra Pradesh in 1963. The Indian National Science Academy frequently conducts a Memorial Lecture Award in the honour of Prof. Kotcherlakota Rangadhama Rao since its inception in 1979.
Prof Rangadhama Rao Memorial Lecture Award
Prof. Kotcherlakota Rangadhama Rao Memorial Lecture Award is given for the outstanding contributions in the subject of Spectroscopy in Physics. The award was established by the National Institute of Sciences of India, located in Calcutta in 1979.
List of Awardees
Publications
Prof. K.R.Rao's research works were published in various reputed National and International Journals. Some of his initial publications are given below
On the spectra of the metals of the aluminium sub-group, Proceedings of the Physical Society of London, Volume 37, Issue 1, pp. 259–264 (1924),
A Note on the Absorption of the Green Line of Thallium Vapour, Proc. R. Soc. Lond. 1 April 1925 107:762-765;
On the Fluorescence and Channelled Absorption of Bismuth at High Temperatures, Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, Vol. 107, No. 744 (1 April 1925), pp. 760–762.
On the Resonance Radiation from Thallium Vapour, Nature 115, 534-534, (11 April 1925) |
Proc. Indian natn. Sci. Acad., 46, A, No 5, 1980, pp. 423–434
Notes
References
ALN Biography - Biographies of Indian Institute of Astrophysics
INSA Awards - Indian National Science Academy Awards
Founding Members - Andhra Pradesh Akademi of Science Founding Members
Andhra University Annual Register
Proceedings of the Physical Society of London, Volume 37, Issue 1, pp. 259-264 (1924),
Proc. R. Soc. Lond. A 1 April 1925 107:762-765;
Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, Vol. 107, No. 744 (1 April 1925), pp. 760-762.
Nature 115, 534-534
Indian Academy of Science Awards, Current Science Journal, 1989, Vol.58, No.18
Further reading
Dr. K. Rangadhama Rao Memorial Lecture by RK Asundi - 1979
Dr. K. Rangadhama Rao Memorial Lecture by Mihir Chowdhury - 1989
Dr. K. Rangadhama Rao Memorial Lecture by VB Kartha - 1991
1898 births
1972 deaths
Andhra University alumni
Experimental physicists
20th-century Indian physicists
Scientists from Visakhapatnam
Fellows of the Indian National Science Academy
Telugu people | Kotcherlakota Rangadhama Rao | [
"Physics"
] | 1,940 | [
"Experimental physics",
"Experimental physicists"
] |
35,750,318 | https://en.wikipedia.org/wiki/Product%20operator%20formalism | In NMR spectroscopy, the product operator formalism is a method used to determine the outcome of pulse sequences in a rigorous but straightforward way. With this method it is possible to predict how the bulk magnetization evolves with time under the action of pulses applied in different directions. It is a net improvement from the semi-classical vector model which is not able to predict many of the results in NMR spectroscopy and is a simplification of the complete density matrix formalism.
In this model, for a single spin, four base operators exist: , , and which represent respectively polarization (population difference between the two spin states), single quantum coherence (magnetization on the xy plane) and the unit operator. Many other, non-classical operators exist for coupled systems. Using this approach, the evolution of the magnetization under free precession is represented by and corresponds to a rotation about the z-axis with a phase angle proportional to the chemical shift of the spin in question:
Pulses about the x and y axis can be represented by and respectively; these allow to interconvert the magnetization between planes and ultimately to observe it at the end of a sequence. Since every spin will evolve differently depending on its shift, with this formalism it is possible to calculate exactly where the magnetization will end up and hence devise pulse sequences to measure the desired signal while excluding others.
The product operator formalism is particularly useful in describing experiments in two-dimensions like COSY, HSQC and HMBC.
Motivation for sets of spin-1/2 particles
Throughout this section, the reduced Planck constant for convenience.
The product operator formalism is usually applied to sets of spin-1/2 particles, since the fact that the individual operators satisfy , where is the identity operator, makes the commutation relations of product operators particularly simple. In principle the formalism could be extended to higher spins, but in practice the general irreducible spherical tensor treatment is more often used. As such, we consider only the spin-1/2 case below.
The main idea of the formalism is to make it easier to follow the system density operator , which evolves under a Hamiltonian according to the Liouville-von Neumann equation as
For a time-independent Hamiltonian, the density operator inherits its solutions from the Schrödinger time-evolution operator as
Density operator-state duality
Suppose a single spin-1/2 is in the state , which is an eigenstate of the z-spin operator , that is . Similarly . Making use of the expansion of a Hermitian operator in terms of projections onto its eigenkets with eigenvalues as , the associated density operator is
where is the identity operator. Similarly, the density operator for the state is
Since the spin operators are all traceless and the expectation value of an operator for a system with density operator is , the terms proportional to the unit operator do not affect the expectations of the spin operators. Additionally those parts do not evolve in time, since they trivially commute with the Hamiltonian. Therefore those terms can be ignored, and the state corresponds to a density operator , while the state corresponds to a density operator . In exactly the same manner, polarisation along the positive x-axis, that is a state , corresponds to a density operator . This idea extends naturally to multiple spins, where the states and operators are direct products of single-spin states and operators. Hence operator terms in the density operator have a direct duality with states.
In the case of two spins , the terms in the density operator (ignoring the identity on its own) can be interpreted as representing
- longitudinal magnetisation
- in-phase transverse magnetisation, which is the observable quantity in NMR.
- anti-phase longitudinal magnetisation
- longitudinal two-spin order
- other coherences, which are more difficult to interpret, but may evolve into other terms
where eg is a shorthand for the Kronecker product , where is the identity operator on the spin, and similarly is a shorthand for .
The factors of two in the 'true' two-spin operators are to allow for convenient commutation relations in this specific spin-1/2 case - see below. Note also that we could instead choose to expand the density operator in the basis etc, where the transverse operators have been replaced with raising and lowering operators. With quadrature detection, the observable associated with an individual spin is effectively the non-Hermitian , so this is sometimes more convenient.
Evolution of the density operator
Consider operators that obey the cyclic commutation relations
In fact only the first two relations are necessary for the following derivation, but since we are usually working with operators associated with Cartesian directions, such as the individual angular momentum operators, the third commutator follows by a symmetry argument.
Introduce also the commutation superoperator of an operator (in our case, this is more formally related to the adjoint representation of the Lie algebra whose elements are ), which acts as
In particular, for the cyclic operators, we have
and consequently for integer
An identity for two operators is
which can be derived by putting where is a scalar parameter, differentiating both sides with respect to , and noting that both sides satisfy the same differential equation in that parameter, with the same initial condition at . In particular, for some scalar parameter , we have
where the final equality follows from recognising the Taylor series for sine and cosine. Now suppose that the density operator at time zero is , and it is allowed to freely evolve under the Hamiltonian where is some scalar. Using the results above, the density operator at some later time will be given by
The interpretation of this is that although nuclear spin angular momentum itself is not connected to rotations in three-dimensional space in the same way that angular momentum is, the evolution of the density operator can be viewed as rotations in an abstract space, in which the operators are the generators of rotations about the axes. An example of such a set of generators is just the spin operators themselves.
We now also introduce the 'arrow notation' typically used in NMR, which writes the general evolution given above as the shorthand
.
With more specific reference to the radiofrequency pulses applied during NMR experiments, a hard pulse with tip angle around a direction is written as above the arrow and corresponds to taking as the rotation generator in Equation . When there is no ambiguity, the arrow label may be omitted, or be eg text instead.
Note that a more complicated calculation has now been reduced to a simpler procedure that requires no knowledge of the underlying quantum mechanics, especially since the subspaces of cyclic operators can be tabulated in advance.
Examples
The 180°-refocussing pulse
The Hamiltonian for a single spin evolving under a chemical shift of angular frequency is
which means that in an ensemble of many such spins with slightly different chemical shifts, there is a dephasing of the magnetisation in the - plane. Consider the pulse sequence
— — —
where is a time interval. Starting in an equilibrium state with all the polarisation along the -axis, the evolution of an individual spin in the ensemble is
Hence this sequence refocuses the transverse magnetisation produced by the first pulse, independent of the value of the chemical shift.
As an indication of the utility of the formalism, suppose instead that we tried to reach the same result using states only and therefore the Schrödinger time evolution operators. This amounts to trying to simplify the unitary propagator taking the initial state to the final state as , where explicitly
Essentially we want to find the propagator in the form , that is as a single exponential of a combination of operators, because that gives the effective Hamiltonian acting during the sequence. Since the arguments of the exponentials in the original form of the propagator do not commute, this amounts to solving a specific example of the Baker–Campbell–Hausdorff (BCH) problem. In this relatively simple case we can solve the BCH problem using the fact that for unitary operator , operator and function , as well as the mathematical similarity of the spin operators with the physical rotation generators, which allow us to write
Hence and only the effect of the 180° pulse remains, which agrees with the product operator treatment. For larger sequences of pulses this state treatment quickly becomes even more unwieldy, unless more advanced methods such as exact effective Hamiltonian theory (which gives closed-form expressions for the entangled propagators via the Cayley–Hamilton theorem and eigendecompositions) are used.
The amplitude of a Hahn echo in an inhomogeneous magnetic field
As an extension of the refocussing pulse treated above, consider a set of two pulses with arbitrary flip angles and , that is sequence
— — —
where again is a time interval. Liberally dropping irrelevant terms, the evolution for a single spin with offset up to just after the second pulse is
Now consider an ensemble of spins in a magnetic field that is sufficiently inhomogeneous to completely dephase the spins in the interval between the pulses. After the second pulse, we can decompose the remaining terms into a sum of two spin populations differing only in the sign of the term, in the sense that for an individual spin we have
where we used the identities and .
It is the spins in the new population that has been generated by the second pulse, namely the one with , that will lead to the formation of an echo after evolution for the next interval. Therefore, remembering to include the introduced by the first pulse, the amplitude of the resulting Hahn echo relative to that produced by an ideal 90°—180° refocussing pulse sequence is roughly
Note that this is not an exact result, because it considers only the refocussing of polarisation that was transverse immediately before the second pulse. In reality there will be further transverse components originating from the tipping of the longitudinal magnetisation that remained after the first pulse. However, for many tip angles, this is a good rule of thumb.
To instead arrive at this result using the state formalism, we would have had to non-trivially evaluate the rotation propagator as
and then evaluate a transition probability by considering the result of applying this to a state representing polarisation in the transverse plane.
DEPT (Distortionless Enhancement by Polarisation Transfer)
DEPT (Distortionless Enhancement by Polarisation Transfer) is a pulse sequence used to distinguish between the multiplicity of hydrogen bonded to carbon, that is it can separate C, CH, CH2 and CH3 groups. It does this by exploiting the heteronuclear carbon-hydrogen -coupling and varying the tip angle of the final pulse in the sequence. The basic pulse sequence is shown below.
Under the weak coupling assumption, the chemical shift terms commute with the -coupling term in the Hamiltonian. Hence we can ignore the refocussed chemical shift (see ) in the two intervals containing -pulses, namely and , and additionally refrain from evaluating the chemical shift evolution in the last period . The pulse separation time is adjusted to the coupling strength (with associated Hamiltonian coefficient ) such that it satisfies
,
because then the first term in the evolved density operator in Equation vanishes under the pure coupling evolution between the pulses.
CH
Label the hydrogen spin as , and the carbon spin by . For illustrative purposes, we assume that the equilibrium state only has polarisation on the -spin (in reality, there will also be polarisation on the spin, with the relative populations determined by the thermal Boltzmann factors). The -coupling Hamiltonian is
which gives the following evolution
The non-trivial commutators used to identify the cyclic subspace for are
and consequently the next cyclic rotation
where we used the 'mixed-product identity' , which relates the matrix and Kronecker products for compatible dimensions of , and also the fact that since the two eigenvalues of any of the spin-1/2 operators are , any of their squares are given by by the Cayley–Hamilton theorem.
Note also that the term is invariant under the -coupling evolution. That is that the term commutes with the Hamiltonian, and in this case, that can be manually confirmed by evaluating the commutator using the matrix representations of the spin operators.
CH2
Now label the two hydrogen spins as and the carbon spin by . The -coupling Hamiltonian is now
which gives the following evolution
where 'others' denotes various terms that can safely be ignored because they will not evolve into observable transverse polarisation on the target spin . The required cyclic commutators for dealing with the -coupling evolution are the following three sets (and their versions if needed)
CH3
A similar (but more lengthy) treatment gives the final observable term as .
APT (Attached Proton Test)
Refer to for the notation used in this example.
APT is similar to DEPT in that it detects carbon multiplicity. However, it has additional degeneracies: it gives identical positive signals for C and CH2, and identical negative signals for CH and CH3. One variation on the basic pulse sequence is shown below.
The key observation is that since we can again ignore the refocussed chemical shift, the only relevant dynamics occur in the interval with no hydrogen decoupling, where we can consider solely the -coupling. By using an interval twice as long as in the DEPT case, we ensure that a density operator of at the start of the interval just has its sign inverted following the coupling (since this corresponds to in the general treatment, and ). The Hamiltonians for the couplings to each of the separate neighbouring hydrogen atoms commute, so the overall effect is to multiply by a factor . This motivates the alternating sign of the signal mentioned above.
References
Nuclear magnetic resonance | Product operator formalism | [
"Physics",
"Chemistry"
] | 2,824 | [
"Nuclear magnetic resonance",
"Nuclear physics"
] |
35,752,192 | https://en.wikipedia.org/wiki/Committed%20dose | The committed dose in radiological protection is a measure of the stochastic health risk due to an intake of radioactive material into the human body. Stochastic in this context is defined as the probability of cancer induction and genetic damage, due to low levels of radiation. The SI unit of measure is the sievert.
A committed dose from an internal source represents the same effective risk as the same amount of effective dose applied uniformly to the whole body from an external source, or the same amount of equivalent dose applied to part of the body. The committed dose is not intended as a measure for deterministic effects, such as radiation sickness, which are defined as the severity of a health effect which is certain to happen.
The radiation risk proposed by the International Commission on Radiological Protection (ICRP) predicts that an effective dose of one sievert carries a 5.5% chance of developing cancer. Such a risk is the sum of both internal and external radiation dose.
ICRP definition
The ICRP states "Radionuclides incorporated in the human body irradiate the tissues over time periods determined by their physical half-life and their biological retention
within the body. Thus they may give rise to doses to body tissues for many months or years after the intake. The need to regulate exposures to radionuclides and the
accumulation of radiation dose over extended periods of time has led to the definition of committed dose quantities".
The ICRP defines two dose quantities for individual committed dose.
Committed equivalent dose is the time integral of the equivalent dose rate in a particular tissue or organ that will be received by an individual following intake of radioactive material into the body by a Reference Person, where t is the integration time in years. This refers specifically to the dose in a specific tissue or organ, in the similar way to external equivalent dose.
Committed effective dose, is the sum of the products of the committed organ or tissue equivalent doses and the appropriate tissue weighting factors WT, where t is the integration time in years following the intake. The commitment period is taken to be 50 years for adults, and to age 70 years for children. This refers specifically to the dose to the whole body, in the similar way to external effective dose. The committed effective dose is used to demonstrate compliance with dose limits and is entered into the "dose of record" for occupational exposures used for recording, reporting and retrospective demonstration of compliance with regulatory dose limits.
The ICRP further states "For internal exposure, committed effective doses are generally determined from an assessment of the intakes of radionuclides from bioassay measurements or other quantities (e.g., activity retained in the body or in daily excreta). The radiation dose is determined from the intake using recommended dose coefficients".
Dose intake
The intake of radioactive material can occur through four pathways:
inhalation of airborne contaminants such as radon
ingestion of contaminated food or liquids
absorption of vapours such as tritium oxide through the skin
injection of medical radioisotopes such as technetium-99m
Some artificial radioisotopes such as iodine-131 are chemically identical to natural isotopes needed by the body, and may be more readily absorbed if the individual has a deficit of that element. For instance, potassium iodide (KI), administered orally immediately after exposure, may be used to protect the thyroid from ingested radioactive iodine in the event of an accident or attack at a nuclear power plant, or the detonation of a nuclear explosive which would release radioactive iodine.
Other radioisotopes have an affinity for particular tissues, such as plutonium into bone, and may be retained there for years in spite of their foreign nature.
In summary, not all radiation is harmful. The radiation can be absorbed through multiple pathways, varying due to the circumstances of the situation. If the radioactive material is necessary, it can be ingested orally via stable isotopes of specific elements. This is only suggested to those that have a lack of these elements however, because radioactive material can go from healthy to harmful with very small amounts. The most harmful way to absorb radiation is that of absorption because it is almost impossible to control how much will enter the body.
Physical factors
Since irradiation increases with proximity to the source of radiation, and as it is impossible to distance or shield an internal source, radioactive materials inside the body can deliver much higher doses to the host organs than they normally would from outside the body. This is particularly true for alpha and beta emitters that are easily shielded by skin and clothing. Some have hypothesized that alpha's high relative biological effectiveness might be attributable to cell's tendency to absorb transuranic metals into the cellular nucleus where they would be in very close proximity to the genome, though an elevated effectiveness can also be observed for external alpha radiation in cellular studies. As in the calculations for equivalent dose and effective dose, committed dose must include corrections for the relative biological effectiveness of the radiation type and weightings for tissue sensitivity.
Duration
The dose rate from a single uptake decays over time due to both radioactive decay, and biological decay (i.e. excretion from the body). The combined radioactive and biological half-life, called the effective half-life of the material, may range from hours for medical radioisotopes to decades for transuranic waste. Committed dose is the integral of this decaying dose rate over the presumed remaining lifespan of the organism. Most regulations require this integral to be taken over 50 years for uptakes during adulthood or over 70 years for uptakes during childhood. In dosimetry accounting, the entire committed dose is conservatively assigned to the year of uptake, even though it may take many years for the tissues to actually accumulate this dose.
Measurement
There is no direct way to measure committed dose. Estimates can be made by analyzing the data from whole body counting, blood samples, urine samples, fecal samples, biopsies, and measurement of intake.
Whole body counting (WBC) is the most direct approach, but has some limitations: it cannot detect beta emitters such as tritium; it provides no chemical information about any compound that the radioisotope may be bound to; it may be inconclusive regarding the nature of the radioisotope detected; and it is a complex measurement subject to many sources of measurement and calibration error.
Analysis of blood samples, urine samples, fecal samples, and biopsies can provide more exact information about the chemical and isotopic nature of the contaminant, its distribution in the body, and the rate of elimination. Urine samples are the standard way to measure tritium intake, while fecal samples are the standard way to measure transuranic intake.
If the nature and quantity of radioactive materials taken into the body is known, and a reliable biochemical model of this material is available, this can be sufficient to determine committed dose. In occupational or accident scenarios, approximate estimates can be based on measurements of the environment that people were exposed to, but this cannot take into account factors such as breathing rate and adherence to hygiene practices. Exact information about the intake and its biochemical impact is usually only available in medical situations where radiopharmaceuticals are measured in a radioisotope dose calibrator prior to injection.
Annual limit on intake (ALI) is the derived limit for the amount of radioactive material taken into the body of an adult worker by inhalation or ingestion in a year. ALI is the intake of a given radionuclide in a year that would result in:
a committed effective dose equivalent of 0.02 Sv (2 rems) for a "reference human body", or
a committed dose equivalent of 0.2 Sv (20 rems) to any individual organ or tissue,
whatever dose is the smaller.
Health effects
Intake of radioactive materials into the body tends to increase the risk of cancer, and possibly other stochastic effects. The International Commission on Radiological Protection has proposed a model whereby the incidence of cancers increases linearly with effective dose at a rate of 5.5% per sievert. This model is widely accepted for external radiation, but its application to internal contamination has been disputed. This model fails to account for the low rates of cancer in early workers at Los Alamos National Laboratory who were exposed to plutonium dust, and the high rates of thyroid cancer in children following the Chernobyl accident . The informal European Committee on Radiation Risk has questioned the ICRP model used for internal exposure. However a UK National Radiological Protection Board report endorses the ICRP approaches to the estimation of doses and risks from internal emitters and agrees with CERRIE conclusions that these should be best estimates and that associated uncertainties should receive more attention.
The true relationship between committed dose and cancer is almost certainly non-linear. For example, iodine-131 is notable in that high doses of the isotope are sometimes less dangerous than low doses, since they tend to kill thyroid tissues that would otherwise become cancerous as a result of the radiation. Most studies of very-high-dose I-131 for treatment of Graves disease have failed to find any increase in thyroid cancer, even though there is linear increase in thyroid cancer risk with I-131 absorption at moderate doses.
Internal exposure of the public is controlled by regulatory limits on the radioactive content of food and water. These limits are typically expressed in becquerel/kilogram, with different limits set for each contaminant.
Intake of very large amounts of radioactive material can cause acute radiation syndrome (ARS) in rare instances. Examples include the Alexander Litvinenko poisoning and Leide das Neves Ferreira. While there is no doubt that internal contamination was the cause of ARS in these cases, there is not enough data to establish what quantities of committed dose might cause ARS symptoms. In most scenarios where ARS is a concern, the external effective radiation dose is usually much more hazardous than the internal dose. Normally, the greatest concern with internal exposure is that the radioactive material may stay in the body for an extended period of time, "committing" the subject to accumulating dose long after the initial exposure has ceased. Over a hundred people, including Eben Byers and the radium girls, have received committed doses in excess of 10 Gy and went on to die of cancer or natural causes, whereas the same amount of acute external dose would invariably cause an earlier death by ARS.
Examples
Below are a series of examples of internal exposure.
Thorotrast
The exposure caused by Potassium-40 present within a normal person.
The exposure to the ingestion of a soluble radioactive substance, such as 89Sr in cows' milk.
A person who is being treated for cancer by means of an unsealed source radiotherapy method where a radioisotope is used as a drug (usually a liquid or pill). A review of this topic was published in 1999. Because the radioactive material becomes intimately mixed with the affected object it is often difficult to decontaminate the object or person in a case where internal exposure is occurring. While some very insoluble materials such as fission products within a uranium dioxide matrix might never be able to truly become part of an organism, it is normal to consider such particles in the lungs and digestive tract as a form of internal contamination which results in internal exposure.
Boron neutron capture therapy (BNCT) involves injecting a boron-10 tagged chemical that preferentially binds to tumor cells. Neutrons from a nuclear reactor are shaped by a neutron moderator to the neutron energy spectrum suitable for BNCT treatment. The tumor is selectively bombarded with these neutrons. The neutrons quickly slow down in the body to become low energy thermal neutrons. These thermal neutrons are captured by the injected boron-10, forming excited (boron-11) which breaks down into lithium-7 and a helium-4 alpha particle both of these produce closely spaced ionizing radiation. This concept is described as a binary system using two separate components for the therapy of cancer. Each component in itself is relatively harmless to the cells, but when combined for treatment they produce a highly cytocidal (cytotoxic) effect which is lethal (within a limited range of 5-9 micrometers or approximately one cell diameter). Clinical trials, with promising results, are currently carried out in Finland and Japan.
Related quantities
The US Nuclear Regulatory commission defines some non-SI quantities for the calculation of committed dose for use only within the US regulatory system. They carry different names to those used within the International ICRP radiation protection system, thus:
Committed dose equivalent (CDE) is the equivalent dose received by a particular organ or tissue from an internal source, without weighting for tissue sensitivity. This is essentially an intermediate calculation result that cannot be directly compared to final dosimetry quantities
Committed effective dose equivalent (CEDE) as defined in Title 10, Section 20.1003, of the Code of Federal Regulations of the USA the CEDE dose (HE,50) is the sum of the products of the committed dose equivalents for each of the body organs or tissues that are irradiated multiplied by the weighting factors (WT) applicable to each of those organs or tissues.
Confusion between US and ICRP dose quantity systems can arise because the use of the term "dose equivalent" has been used within the ICRP system since 1991 only for quantities calculated using the value of Q (Linear energy transfer - LET), which the ICRP calls "operational quantities". However within the US NRC system "dose equivalent" is still used to name quantities which are calculated with tissue and radiation weighting factors, which in the ICRP system are now known as the "protection quantities" which are called "effective dose" and "equivalent dose".
See also
Internal dosimetry
Radioactivity
Ionizing radiation
Collective dose
Total effective dose equivalent
Cumulative dose
Committed dose equivalent
References
US nuclear regulatory commission glossary
Argonne national laboratory glossary
Limitation of Exposure to Ionizing Radiation (Report No. 116). National Council on Radiation Protection and Measurements (NCRP).
External links
UK Govt COMARE website
Uk Govt CERRIE website
- "The confusing world of radiation dosimetry" - M.A. Boyd, 2009, U.S. Environmental Protection Agency. An account of chronological differences between USA and ICRP dosimetry systems.
Radioactivity
Radiation health effects
Radiation protection | Committed dose | [
"Physics",
"Chemistry",
"Materials_science"
] | 2,954 | [
"Radiation effects",
"Radiation health effects",
"Radioactivity",
"Nuclear physics"
] |
35,756,077 | https://en.wikipedia.org/wiki/Hermite%20reciprocity | In mathematics, Hermite's law of reciprocity, introduced by , states that the degree m covariants of a binary form of degree n correspond to the degree n covariants of a binary form of degree m. In terms of representation theory it states that the representations Sm Sn C2 and Sn Sm C2 of GL2 are isomorphic.
References
Invariant theory | Hermite reciprocity | [
"Physics"
] | 81 | [
"Invariant theory",
"Group actions",
"Symmetry"
] |
3,848,049 | https://en.wikipedia.org/wiki/Lattice%20energy | In chemistry, the lattice energy is the energy change upon formation of one mole of a crystalline ionic compound from its constituent ions, which are assumed to initially be in the gaseous state. It is a measure of the cohesive forces that bind ionic solids. The size of the lattice energy is connected to many other physical properties including solubility, hardness, and volatility. Since it generally cannot be measured directly, the lattice energy is usually deduced from experimental data via the Born–Haber cycle.
Lattice energy and lattice enthalpy
The concept of lattice energy was originally applied to the formation of compounds with structures like rocksalt (NaCl) and sphalerite (ZnS) where the ions occupy high-symmetry crystal lattice sites. In the case of NaCl, lattice energy is the energy change of the reaction
Na+ (g) + Cl− (g) → NaCl (s)
which amounts to −786 kJ/mol.
Some chemistry textbooks as well as the widely used CRC Handbook of Chemistry and Physics define lattice energy with the opposite sign, i.e. as the energy required to convert the crystal into infinitely separated gaseous ions in vacuum, an endothermic process. Following this convention, the lattice energy of NaCl would be +786 kJ/mol. Both sign conventions are widely used.
The relationship between the lattice energy and the lattice enthalpy at pressure is given by the following equation:
,
where is the lattice energy (i.e., the molar internal energy change), is the lattice enthalpy, and the change of molar volume due to the formation of the lattice. Since the molar volume of the solid is much smaller than that of the gases, . The formation of a crystal lattice from ions in vacuum must lower the internal energy due to the net attractive forces involved, and so . The term is positive but is relatively small at low pressures, and so the value of the lattice enthalpy is also negative (and exothermic).
Theoretical treatments
The lattice energy of an ionic compound depends strongly upon the charges of the ions that comprise the solid, which must attract or repel one another via Coulomb's Law. More subtly, the relative and absolute sizes of the ions influence . London dispersion forces also exist between ions and contribute to the lattice energy via polarization effects. For ionic compounds made of molecular cations and/or anions, there may also be ion-dipole and dipole-dipole interactions if either molecule has a molecular dipole moment. The theoretical treatments described below are focused on compounds made of atomic cations and anions, and neglect contributions to the internal energy of the lattice from thermalized lattice vibrations.
Born–Landé equation
In 1918 Born and Landé proposed that the lattice energy could be derived from the electric potential of the ionic lattice and a repulsive potential energy term.
where
NA is the Avogadro constant;
M is the Madelung constant, relating to the geometry of the crystal;
z+ is the charge number of the cation;
z− is the charge number of the anion;
e is the elementary charge, equal to ;
ε0 is the permittivity of free space, equal to ;
r0 is the nearest-neighbor distance between ions; and
n is the Born exponent (a number between 5 and 12, determined experimentally by measuring the compressibility of the solid, or derived theoretically).
The Born–Landé equation above shows that the lattice energy of a compound depends principally on two factors:
as the charges on the ions increase, the lattice energy increases (becomes more negative),
when ions are closer together the lattice energy increases (becomes more negative)
Barium oxide (BaO), for instance, which has the NaCl structure and therefore the same Madelung constant, has a bond radius of 275 picometers and a lattice energy of −3054 kJ/mol, while sodium chloride (NaCl) has a bond radius of 283 picometers and a lattice energy of −786 kJ/mol. The bond radii are similar but the charge numbers are not, with BaO having charge numbers of (+2,−2) and NaCl having (+1,−1); the Born–Landé equation predicts that the difference in charge numbers is the principal reason for the large difference in lattice energies.
Closely related to this widely used formula is the Kapustinskii equation, which can be used as a simpler way of estimating lattice energies where high precision is not required.
Effect of polarization
For certain ionic compounds, the calculation of the lattice energy requires the explicit inclusion of polarization effects. In these cases the polarization energy Epol associated with ions on polar lattice sites may be included in the Born–Haber cycle. As an example, one may consider the case of iron-pyrite FeS2. It has been shown that neglect of polarization led to a 15% difference between theory and experiment in the case of FeS2, whereas including it reduced the error to 2%.
Representative lattice energies
The following table presents a list of lattice energies for some common compounds as well as their structure type.
See also
Bond energy
Born–Haber cycle
Chemical bond
Enthalpy of melting
Enthalpy change of solution
Heat of dilution
Ionic conductivity
Kapustinskii equation
Madelung constant
Notes
References
Crystallography
Solid-state chemistry | Lattice energy | [
"Physics",
"Chemistry",
"Materials_science",
"Engineering"
] | 1,121 | [
"Materials science",
"Crystallography",
"Condensed matter physics",
"nan",
"Solid-state chemistry"
] |
3,849,994 | https://en.wikipedia.org/wiki/Computational%20electromagnetics | Computational electromagnetics (CEM), computational electrodynamics or electromagnetic modeling is the process of modeling the interaction of electromagnetic fields with physical objects and the environment using computers.
It typically involves using computer programs to compute approximate solutions to Maxwell's equations to calculate antenna performance, electromagnetic compatibility, radar cross section and electromagnetic wave propagation when not in free space. A large subfield is antenna modeling computer programs, which calculate the radiation pattern and electrical properties of radio antennas, and are widely used to design antennas for specific applications.
Background
Several real-world electromagnetic problems like electromagnetic scattering, electromagnetic radiation, modeling of waveguides etc., are not analytically calculable, for the multitude of irregular geometries found in actual devices. Computational numerical techniques can overcome the inability to derive closed form solutions of Maxwell's equations under various constitutive relations of media, and boundary conditions. This makes computational electromagnetics (CEM) important to the design, and modeling of antenna, radar, satellite and other communication systems, nanophotonic devices and high speed silicon electronics, medical imaging, cell-phone antenna design, among other applications.
CEM typically solves the problem of computing the E (electric) and H (magnetic) fields across the problem domain (e.g., to calculate antenna radiation pattern for an arbitrarily shaped antenna structure). Also calculating power flow direction (Poynting vector), a waveguide's normal modes, media-generated wave dispersion, and scattering can be computed from the E and H fields. CEM models may or may not assume symmetry, simplifying real world structures to idealized cylinders, spheres, and other regular geometrical objects. CEM models extensively make use of symmetry, and solve for reduced dimensionality from 3 spatial dimensions to 2D and even 1D.
An eigenvalue problem formulation of CEM allows us to calculate steady state normal modes in a structure. Transient response and impulse field effects are more accurately modeled by CEM in time domain, by FDTD. Curved geometrical objects are treated more accurately as finite elements FEM, or non-orthogonal grids. Beam propagation method (BPM) can solve for the power flow in waveguides. CEM is application specific, even if different techniques converge to the same field and power distributions in the modeled domain.
Overview of methods
The most common numerical approach is to discretize ("mesh") the problem space in terms of grids or regular shapes ("cells"), and solve Maxwell's equations simultaneously across all cells. Discretization consumes computer memory, and solving the relevant equations takes significant time. Large-scale CEM problems face memory and CPU limitations, and combating these limitations is an active area of research. High performance clustering, vector processing, and/or parallelism is often required to make the computation practical. Some typical methods involve: time-stepping through the equations over the whole domain for each time instant; banded matrix inversion to calculate the weights of basis functions (when modeled by finite element methods); matrix products (when using transfer matrix methods); calculating numerical integrals (when using the method of moments); using fast Fourier transforms; and time iterations (when calculating by the split-step method or by BPM).
Choice of methods
Choosing the right technique for solving a problem is important, as choosing the wrong one can either result in incorrect results, or results which take excessively long to compute. However, the name of a technique does not always tell one how it is implemented, especially for commercial tools, which will often have more than one solver.
Davidson gives two tables comparing the FEM, MoM and FDTD techniques in the way they are normally implemented. One table is for both open region (radiation and scattering problems) and another table is for guided wave problems.
Maxwell's equations in hyperbolic PDE form
Maxwell's equations can be formulated as a hyperbolic system of partial differential equations. This gives access to powerful techniques for numerical solutions.
It is assumed that the waves propagate in the (x,y)-plane and restrict the direction of the magnetic field to be parallel to the z-axis and thus the electric field to be parallel to the (x,y) plane. The wave is called a transverse magnetic (TM) wave. In 2D and no polarization terms present, Maxwell's equations can then be formulated as:
where u, A, B, and C are defined as
In this representation, is the forcing function, and is in the same space as . It can be used to express an externally applied field or to describe an optimization constraint. As formulated above:
may also be explicitly defined equal to zero to simplify certain problems, or to find a characteristic solution, which is often the first step in a method to find the particular inhomogeneous solution.
Integral equation solvers
The discrete dipole approximation
The discrete dipole approximation is a flexible technique for computing scattering and absorption by targets of arbitrary geometry. The formulation is based on integral form of Maxwell equations. The DDA is an approximation of the continuum target by a finite array of polarizable points. The points acquire dipole moments in response to the local electric field. The dipoles of course interact with one another via their electric fields, so the DDA is also sometimes referred to as the coupled dipole approximation. The resulting linear system of equations is commonly solved using conjugate gradient iterations. The discretization matrix has symmetries (the integral form of Maxwell equations has form of convolution) enabling fast Fourier transform to multiply matrix times vector during conjugate gradient iterations.
Method of moments and boundary element method
The method of moments (MoM) or boundary element method (BEM) is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations (i.e. in boundary integral form). It can be applied in many areas of engineering and science including fluid mechanics, acoustics, electromagnetics, fracture mechanics, and plasticity.
MoM has become more popular since the 1980s. Because it requires calculating only boundary values, rather than values throughout the space, it is significantly more efficient in terms of computational resources for problems with a small surface/volume ratio. Conceptually, it works by constructing a "mesh" over the modeled surface. However, for many problems, MoM are significantly computationally less efficient than volume-discretization methods (finite element method, finite difference method, finite volume method). Boundary element formulations typically give rise to fully populated matrices. This means that the storage requirements and computational time will tend to grow according to the square of the problem size. By contrast, finite element matrices are typically banded (elements are only locally connected) and the storage requirements for the system matrices typically grow linearly with the problem size. Compression techniques (e.g. multipole expansions or adaptive cross approximation/hierarchical matrices) can be used to ameliorate these problems, though at the cost of added complexity and with a success-rate that depends heavily on the nature and geometry of the problem.
MoM is applicable to problems for which Green's functions can be calculated. These usually involve fields in linear homogeneous media. This places considerable restrictions on the range and generality of problems suitable for boundary elements. Nonlinearities can be included in the formulation, although they generally introduce volume integrals which require the volume to be discretized before solution, removing an oft-cited advantage of MoM.
Fast multipole method
The fast multipole method (FMM) is an alternative to MoM or Ewald summation. It is an accurate simulation technique and requires less memory and processor power than MoM. The FMM was first introduced by Greengard and Rokhlin and is based on the multipole expansion technique. The first application of the FMM in computational electromagnetics was by Engheta et al.(1992). The FMM has also applications in computational bioelectromagnetics in the Charge based boundary element fast multipole method. FMM can also be used to accelerate MoM.
Plane wave time-domain
While the fast multipole method is useful for accelerating MoM solutions of integral equations with static or frequency-domain oscillatory kernels, the plane wave time-domain (PWTD) algorithm employs similar ideas to accelerate the MoM solution of time-domain integral equations involving the retarded potential. The PWTD algorithm was introduced in 1998 by Ergin, Shanker, and Michielssen.
Partial element equivalent circuit method
The partial element equivalent circuit (PEEC) is a 3D full-wave modeling method suitable for combined electromagnetic and circuit analysis. Unlike MoM, PEEC is a full spectrum method valid from dc to the maximum frequency determined by the meshing. In the PEEC method, the integral equation is interpreted as Kirchhoff's voltage law applied to a basic PEEC cell which results in a complete circuit solution for 3D geometries. The equivalent circuit formulation allows for additional SPICE type circuit elements to be easily included. Further, the models and the analysis apply to both the time and the frequency domains. The circuit equations resulting from the PEEC model are easily constructed using a modified loop analysis (MLA) or modified nodal analysis (MNA) formulation. Besides providing a direct current solution, it has several other advantages over a MoM analysis for this class of problems since any type of circuit element can be included in a straightforward way with appropriate matrix stamps. The PEEC method has recently been extended to include nonorthogonal geometries. This model extension, which is consistent with the classical orthogonal formulation, includes the Manhattan representation of the geometries in addition to the more general quadrilateral and hexahedral elements. This helps in keeping the number of unknowns at a minimum and thus reduces computational time for nonorthogonal geometries.
Cagniard-deHoop method of moments
The Cagniard-deHoop method of moments (CdH-MoM) is a 3-D full-wave time-domain integral-equation technique that is formulated via the Lorentz reciprocity theorem. Since the CdH-MoM heavily relies on the Cagniard-deHoop method, a joint-transform approach originally developed for the analytical analysis of seismic wave propagation in the crustal model of the Earth, this approach is well suited for the TD EM analysis of planarly-layered structures. The CdH-MoM has been originally applied to time-domain performance studies of cylindrical and planar antennas and, more recently, to the TD EM scattering analysis of transmission lines in the presence of thin sheets and electromagnetic metasurfaces, for example.
Differential equation solvers
Finite-Difference Frequency-Domain
Finite-difference frequency-domain (FDFD) provides a rigorous solution to Maxwell’s equations in the frequency-domain using the finite-difference method. FDFD is arguably the simplest numerical method that still provides a rigorous solution. It is incredibly versatile and able to solve virtually any problem in electromagnetics. The primary drawback of FDFD is poor efficiency compared to other methods. On modern computers, however, a huge array of problems are easily handled such as calculated guided modes in waveguides, calculating scattering from an object, calculating transmission and reflection from photonic crystals, calculate photonic band diagrams, simulating metamaterials, and much more.
FDFD may be the best "first" method to learn in computational electromagnetics (CEM). It involves almost all the concepts encountered with other methods, but in a much simpler framework. Concepts include boundary conditions, linear algebra, injecting sources, representing devices numerically, and post-processing field data to calculate meaningful things. This will help a person learn other techniques as well as provide a way to test and benchmark those other techniques.
FDFD is very similar to finite-difference time-domain (FDTD). Both methods represent space as an array of points and enforces Maxwell’s equations at each point. FDFD puts this large set of equations into a matrix and solves all the equations simultaneously using linear algebra techniques. In contrast, FDTD continually iterates over these equations to evolve a solution over time. Numerically, FDFD and FDTD are very similar, but their implementations are very different.
Finite-difference time-domain
Finite-difference time-domain (FDTD) is a popular CEM technique. It is easy to understand. It has an exceptionally simple implementation for a full wave solver. It is at least an order of magnitude less work to implement a basic FDTD solver than either an FEM or MoM solver. FDTD is the only technique where one person can realistically implement oneself in a reasonable time frame, but even then, this will be for a quite specific problem. Since it is a time-domain method, solutions can cover a wide frequency range with a single simulation run, provided the time step is small enough to satisfy the Nyquist–Shannon sampling theorem for the desired highest frequency.
FDTD belongs in the general class of grid-based differential time-domain numerical modeling methods. Maxwell's equations (in partial differential form) are modified to central-difference equations, discretized, and implemented in software. The equations are solved in a cyclic manner: the electric field is solved at a given instant in time, then the magnetic field is solved at the next instant in time, and the process is repeated over and over again.
The basic FDTD algorithm traces back to a seminal 1966 paper by Kane Yee in IEEE Transactions on Antennas and Propagation. Allen Taflove originated the descriptor "Finite-difference time-domain" and its corresponding "FDTD" acronym in a 1980 paper in IEEE Trans. Electromagn. Compat. Since about 1990, FDTD techniques have emerged as the primary means to model many scientific and engineering problems addressing electromagnetic wave interactions with material structures. An effective technique based on a time-domain finite-volume discretization procedure was introduced by Mohammadian et al. in 1991. Current FDTD modeling applications range from near-DC (ultralow-frequency geophysics involving the entire Earth-ionosphere waveguide) through microwaves (radar signature technology, antennas, wireless communications devices, digital interconnects, biomedical imaging/treatment) to visible light (photonic crystals, nanoplasmonics, solitons, and biophotonics). Approximately 30 commercial and university-developed software suites are available.
Discontinuous time-domain method
Among many time domain methods, discontinuous Galerkin time domain (DGTD) method has become popular recently since it integrates advantages of both the finite volume time domain (FVTD) method and the finite element time domain (FETD) method. Like FVTD, the numerical flux is used to exchange information between neighboring elements, thus all operations of DGTD are local and easily parallelizable. Similar to FETD, DGTD employs unstructured mesh and is capable of high-order accuracy if the high-order hierarchical basis function is adopted. With the above merits, DGTD method is widely implemented for the transient analysis of multiscale problems involving large number of unknowns.
Multiresolution time-domain
MRTD is an adaptive alternative to the finite difference time domain method (FDTD) based on wavelet analysis.
Finite element method
The finite element method (FEM) is used to find approximate solution of partial differential equations (PDE) and integral equations. The solution approach is based either on eliminating the time derivatives completely (steady state problems), or rendering the PDE into an equivalent ordinary differential equation, which is then solved using standard techniques such as finite differences, etc.
In solving partial differential equations, the primary challenge is to create an equation which approximates the equation to be studied, but which is numerically stable, meaning that errors in the input data and intermediate calculations do not accumulate and destroy the meaning of the resulting output. There are many ways of doing this, with various advantages and disadvantages. The finite element method is a good choice for solving partial differential equations over complex domains or when the desired precision varies over the entire domain.
Finite integration technique
The finite integration technique (FIT) is a spatial discretization scheme to numerically solve electromagnetic field problems in time and frequency domain. It preserves basic topological properties of the continuous equations such as conservation of charge and energy. FIT was proposed in 1977 by Thomas Weiland and has been enhanced continually over the years. This method covers the full range of electromagnetics (from static up to high frequency) and optic applications and is the basis for commercial simulation tools: CST Studio Suite developed by Computer Simulation Technology (CST AG) and
Electromagnetic Simulation solutions developed by Nimbic.
The basic idea of this approach is to apply the Maxwell equations in integral form to a set of staggered grids. This method stands out due to high flexibility in geometric modeling and boundary handling as well as incorporation of arbitrary material distributions and material properties such as anisotropy, non-linearity and dispersion. Furthermore, the use of a consistent dual orthogonal grid (e.g. Cartesian grid) in conjunction with an explicit time integration scheme (e.g. leap-frog-scheme) leads to compute and memory-efficient algorithms, which are especially adapted for transient field analysis in radio frequency (RF) applications.
Pseudo-spectral time domain
This class of marching-in-time computational techniques for Maxwell's equations uses either discrete Fourier or discrete Chebyshev transforms to calculate the spatial derivatives of the electric and magnetic field vector components that are arranged in either a 2-D grid or 3-D lattice of unit cells. PSTD causes negligible numerical phase velocity anisotropy errors relative to FDTD, and therefore allows problems of much greater electrical size to be modeled.
Pseudo-spectral spatial domain
PSSD solves Maxwell's equations by propagating them forward in a chosen spatial direction. The fields are therefore held as a function of time, and (possibly) any transverse spatial dimensions. The method is pseudo-spectral because temporal derivatives are calculated in the frequency domain with the aid of FFTs. Because the fields are held as functions of time, this enables arbitrary dispersion in the propagation medium to be rapidly and accurately modelled with minimal effort. However, the choice to propagate forward in space (rather than in time) brings with it some subtleties, particularly if reflections are important.
Transmission line matrix
Transmission line matrix (TLM) can be formulated in several means as a direct set of lumped elements solvable directly by a circuit solver (ala SPICE, HSPICE, et al.), as a custom network of elements or via a scattering matrix approach. TLM is a very flexible analysis strategy akin to FDTD in capabilities, though more codes tend to be available with FDTD engines.
Locally one-dimensional
This is an implicit method. In this method, in two-dimensional case, Maxwell equations are computed in two steps, whereas in three-dimensional case Maxwell equations are divided into three spatial coordinate directions. Stability and dispersion analysis of the three-dimensional LOD-FDTD method have been discussed in detail.
Other methods
Eigenmode expansion
Eigenmode expansion (EME) is a rigorous bi-directional technique to simulate electromagnetic propagation which relies on the decomposition of the electromagnetic fields into a basis set of local eigenmodes. The eigenmodes are found by solving Maxwell's equations in each local cross-section. Eigenmode expansion can solve Maxwell's equations in 2D and 3D and can provide a fully vectorial solution provided that the mode solvers are vectorial. It offers very strong benefits compared with the FDTD method for the modelling of optical waveguides, and it is a popular tool for the modelling of fiber optics and silicon photonics devices.
Physical optics
Physical optics (PO) is the name of a high frequency approximation (short-wavelength approximation) commonly used in optics, electrical engineering and applied physics. It is an intermediate method between geometric optics, which ignores wave effects, and full wave electromagnetism, which is a precise theory. The word "physical" means that it is more physical than geometrical optics and not that it is an exact physical theory.
The approximation consists of using ray optics to estimate the field on a surface and then integrating that field over the surface to calculate the transmitted or scattered field. This resembles the Born approximation, in that the details of the problem are treated as a perturbation.
Uniform theory of diffraction
The uniform theory of diffraction (UTD) is a high frequency method for solving electromagnetic scattering problems from electrically small discontinuities or discontinuities in more than one dimension at the same point.
The uniform theory of diffraction approximates near field electromagnetic fields as quasi optical and uses ray diffraction to determine diffraction coefficients for each diffracting object-source combination. These coefficients are then used to calculate the field strength and phase for each direction away from the diffracting point. These fields are then added to the incident fields and reflected fields to obtain a total solution.
Validation
Validation is one of the key issues facing electromagnetic simulation users. The user must understand and master the validity domain of its simulation. The measure is, "how far from the reality are the results?"
Answering this question involves three steps: comparison between simulation results and analytical formulation, cross-comparison between codes, and comparison of simulation results with measurement.
Comparison between simulation results and analytical formulation
For example, assessing the value of the radar cross section of a plate with the analytical formula:
where A is the surface of the plate and is the wavelength. The next curve presenting the RCS of a plate computed at 35 GHz can be used as reference example.
Cross-comparison between codes
One example is the cross comparison of results from method of moments and asymptotic methods in their validity domains.
Comparison of simulation results with measurement
The final validation step is made by comparison between measurements and simulation. For example, the RCS calculation and the measurement of a complex metallic object at 35 GHz. The computation implements GO, PO and PTD for the edges.
Validation processes can clearly reveal that some differences can be explained by the differences between the experimental setup and its reproduction in the simulation environment.
Light scattering codes
There are now many efficient codes for solving electromagnetic scattering problems. They are listed as:
discrete dipole approximation codes,
codes for electromagnetic scattering by cylinders,
codes for electromagnetic scattering by spheres.
Solutions which are analytical, such as Mie solution for scattering by spheres or cylinders, can be used to validate more involved techniques.
See also
EM simulation software
Analytical regularization
Computational physics
Electromagnetic field solver
Electromagnetic wave equation
Finite-difference time-domain method
Finite-difference frequency-domain
Mie theory
Physical optics
Rigorous coupled-wave analysis
Space mapping
Uniform theory of diffraction
Shooting and bouncing rays
List of textbooks in electromagnetism
References
Further reading
External links
Computational electromagnetics at the Open Directory Project
Computational electromagnetics: a review
Electrodynamics
Partial differential equations
Computational fields of study | Computational electromagnetics | [
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3,850,488 | https://en.wikipedia.org/wiki/Slow%20light | In optics, slow light is the propagation of an optical pulse or other modulation of an optical carrier at a very low group velocity. Slow light occurs when a propagating pulse is substantially slowed by the interaction with the medium in which the propagation takes place.
Group velocities below the speed of light in vacuum c were known to be possible as far back as 1880, but could not be realized in a useful manner until 1991, when Stephen Harris and collaborators demonstrated electromagnetically induced transparency in trapped strontium atoms. Reduction of the speed of light by a factor of 165 was reported in 1995. In 1998, Danish physicist Lene Vestergaard Hau led a combined team from Harvard University and the Rowland Institute for Science which realized much lower group velocities of light. They succeeded in slowing a beam of light to about 17 meters per second. In 2004, researchers at UC Berkeley first demonstrated slow light in a semiconductor, with a group velocity 9.6 kilometers per second. Hau and her colleagues later succeeded in stopping light completely, and developed methods by which it can be stopped and later restarted.
In 2005, IBM created a microchip that can slow light, fashioned out of fairly standard materials, potentially paving the way toward commercial adoption.
Background
When light propagates through a material, it travels slower than the vacuum speed, . This is a change in the phase velocity of the light and is manifested in physical effects such as refraction. This reduction in speed is quantified by the ratio between and the phase velocity. This ratio is called the refractive index of the material. Slow light is a dramatic reduction in the group velocity of light, not the phase velocity. Slow light effects are not due to abnormally large refractive indices, as will be explained below.
The simplest picture of light given by classical physics is of a wave or disturbance in the electromagnetic field. In a vacuum, Maxwell's equations predict that these disturbances will travel at a specific speed, denoted by the symbol . This well-known physical constant is commonly referred to as the speed of light. The postulate of the constancy of the speed of light in all inertial reference frames lies at the heart of special relativity and has given rise to a popular notion that the "speed of light is always the same". However, in many situations light is more than a disturbance in the electromagnetic field.
Light traveling within a medium is not merely a disturbance solely of the electromagnetic field, but rather a disturbance of the field and the positions and velocities of the charged particles (electrons) within the material. The motion of the electrons is determined by the field (due to the Lorentz force) but the field is determined by the positions and velocities of the electrons (due to Gauss' law and Ampère's law). The behavior of a disturbance of this combined electromagnetic-charge density field (i.e. light) is still determined by Maxwell's equations, but the solutions are complicated because of the intimate link between the medium and the field.
Understanding the behavior of light in a material is simplified by limiting the types of disturbances studied to sinusoidal functions of time. For these types of disturbances Maxwell's equations transform into algebraic equations and are easily solved. These special disturbances propagate through a material at a speed slower than called the phase velocity. The ratio between and the phase velocity is called the refractive index or index of refraction of the material (). The index of refraction is not a constant for a given material, but depends on temperature, pressure, and upon the frequency of the (sinusoidal) light wave. This latter leads to an effect called dispersion.
A human eye perceives the intensity of the sinusoidal disturbance as the brightness of the light and the frequency as the color. If a light is turned on or off at a specific time or otherwise modulated, then the amplitude of the sinusoidal disturbance is also time-dependent. The time-varying amplitude does not propagate at the phase velocity but rather at the group velocity. The group velocity depends not only on the refractive index of the material, but also on the way in which the refractive index changes with frequency (i.e. the derivative of refractive index with respect to frequency).
Slow light refers to a very low group velocity of light. If the dispersion relation of the refractive index is such that the index changes rapidly over a small range of frequencies, then the group velocity might be very low, thousands or millions of times less than , even though the index of refraction is still a typical value (between 1.5 and 3.5 for glasses and semiconductors).
Preparation
There are many mechanisms which can generate slow light, all of which create narrow spectral regions with high dispersion, i.e., peaks in the dispersion relation. Schemes are generally grouped into two categories: material dispersion and waveguide dispersion.
Material dispersion
Material dispersion mechanisms such as electromagnetically induced transparency (EIT), coherent population oscillation (CPO), and various four-wave mixing (FWM) schemes produce a rapid change in refractive index as a function of optical frequency, i.e., they modify the temporal component of a propagating wave. This is done by using a nonlinear effect to modify the dipole response of a medium to a signal or "probe" field. Dispersion mechanisms such as photonic crystals at red and blue edges, coupled resonator optical waveguides (CROW), and other micro-resonator structures modify the spatial component (k-vector) of a propagating wave.
Waveguide dispersion
Slow light can also be achieved by exploiting the dispersion properties of planar waveguides realized with single negative metamaterials (SNM) or double negative metamaterials (DNM).
A predominant figure of merit of slow light schemes is the bandwidth-delay product (BDP). Most slow light schemes can actually offer an arbitrarily long delay for a given device length (length/delay = signal velocity) at the expense of bandwidth. The product of the two is roughly constant. A related figure of merit is the fractional delay, the time a pulse is delayed divided by the total time of the pulse. Plasmon induced transparency – an analog of EIT – provides another approach based on the destructive interference between different resonance modes. Recent work has now demonstrated this effect over a broad transparency window across a frequency range greater than 0.40 THz.
Potential uses
Slowing down light has various potential practical applications in multiple technology fields from broadband internet to quantum computing:
Slowed light could improve data transmission in optical communications through reducing signal distortion and improving signal quality.
Optical switches which make use of slow light in photonic crystals could produce faster data transmission in fiber optic cables, while having significantly lower power requirements.
Slow light can also be used to control delays in optical networks, permitting more orderly traffic flow.
In addition, slow light can be used to build interferometers that are far more sensitive to frequency shift than conventional interferometers. This property can be used to build better, smaller frequency sensors and compact high resolution spectrometers.
Other potential applications include optical quantum memory.
In fiction
The description of "luminite" in Maurice Renard's novel, Le maître de la lumière (The Master of Light, 1933), might be one of the earliest mentions of slow light.
Subsequent fictional works that address slow light are noted below.
The slow light experiments are mentioned in Dave Eggers's novel You Shall Know Our Velocity (2002), in which the speed of light is described as a "Sunday crawl".
On Discworld, where Terry Pratchett's novel series takes place, light travels only a few hundred miles per hour due to Discworld's "embarrassingly strong" magic field.
"Slow glass" is a fictional material in Bob Shaw's short story "Light of Other Days" (Analog, 1966), and several subsequent stories. The glass, which delays the passage of light by years or decades, is used to construct windows, called scenedows, that enable city dwellers, submariners and prisoners to watch "live" countryside scenes. "Slow glass" is a material where the delay light takes in passing through the glass is attributed to photons passing "...through a spiral tunnel coiled outside the radius of capture of each atom in the glass." Shaw later reworked the stories into the novel Other Days, Other Eyes (1972).
"Slow Light" (2022) is a short film made by Kijek/Adamski with two animation techniques. It's a story of a boy who is born blind and suddenly at the age of seven sees a light. A medical examination reveals that his eyes are so dense that it takes seven years for the light to reach the retina and hence for the image to reach his consciousness.The consequence of the eye defect translates into the mental immaturity of the man, lack of understanding of the present and belated reflections on long-gone facts. The man is never mature enough for his age and constantly lingers on the past.
Valve's FPS title "Half Life 2" features a song by the name of "Slow Light" in the original soundtrack. Many other songs in this soundtrack are also references to physical phenomena such as "Brane Scan" and "Dark energy".
See also
Group velocities above c
Solid light
Notes
References
Lene Vestergaard Hau, S.E. Harris, Zachary Dutton, Cyrus H. Behroozi, Nature v.397, p. 594 (1999).
"IBM's new photonic wave-guide". Nature, November 2004.
J. Scheuer, G. T. Paloczi, J. K. S. Poon and A. Yariv, "Coupled Resonator Optical Waveguides: Towards Slowing and Storing of Light", Opt. Photon. News, Vol. 16 (2005) p. 36.
Nonlinear optics
Light
de:Lichtgeschwindigkeit#Lichtgeschwindigkeit in Materie | Slow light | [
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3,852,404 | https://en.wikipedia.org/wiki/Acoustic%20holography | Acoustic holography is a technique that allows three-dimensional distributions of sound waves called sound fields to be stored and reconstructed. To do this, sound passing through a surface is recorded as a two-dimensional pattern called a hologram (a type of interferogram). The hologram contains information about the phase and amplitude of the sound waves passing though. This pattern can be used to reconstruct the entire three-dimensional sound field. Acoustic holography is similar in principle to optical holography.
Forms
There are two distinct forms of acoustic holography: farfield acoustical holography (FAH) and nearfield acoustical holography (NAH). The distinction lies in the distance of the sound source to the hologram, which impacts the resolution of the reconstructed sound field.
Method
The hologram is made by measuring acoustic pressure away from the source using an array of transducers (microphones) or a single scanning transducer.
The next stage is data processing with a computer. Fourier transforms are used to convert information from the time domain into the frequency domain. A set of intermediate holograms are produced, one for each frequency bin used in the transform. Each hologram can then be deconstructed into individual waves with known propagation characteristics. These waves are back-propagated to the source surface, and the entire sound field recomposed by addition of all of the waves.
Applications
Acoustic holography is becoming increasingly popular in various fields, most notably those of transportation, vehicle and aircraft design, and noise, vibration, and harshness (NVH). The general idea of acoustic holography has led to advanced processing methods such as statistically optimal near-field acoustic holography (SONAH).
For audio rendering and production, Wave field synthesis and higher-order Ambisonics are related technologies, respectively modeling the acoustic pressure field on a plane, or in a spherical volume.
References
External links
Acoustic holography
Acoustics
Sound measurements
Holography | Acoustic holography | [
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3,852,580 | https://en.wikipedia.org/wiki/Gaussian%20fixed%20point | A Gaussian fixed point is a fixed point of the renormalization group flow which is noninteracting in the sense that it is described by a free field theory. The word Gaussian comes from the fact that the probability distribution is Gaussian at the Gaussian fixed point. This means that Gaussian fixed points are exactly solvable (trivially solvable in fact). Slight deviations from the Gaussian fixed point can be described by perturbation theory.
See also
UV fixed point
IR fixed point
Quantum triviality
References
Renormalization group
Statistical mechanics | Gaussian fixed point | [
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3,853,922 | https://en.wikipedia.org/wiki/Wave%20function%20renormalization | In quantum field theory, wave function renormalization is a rescaling (or renormalization) of quantum fields to take into account the effects of interactions. For a noninteracting or free field, the field operator creates or annihilates a single particle with probability 1. Once interactions are included, however, this probability is modified in general to Z 1. This appears when one calculates the propagator beyond leading order; e.g. for a scalar field,
(The shift of the mass from m0 to m constitutes the mass renormalization.)
One possible wave function renormalization, which happens to be scale independent, is to rescale the fields so that the Lehmann weight (Z in the formula above) of their quanta is 1. For the purposes of studying renormalization group flows, if the coefficient of the kinetic term in the action at the scale Λ is Z, then the field is rescaled by . A scale dependent wave function renormalization for a field means that that field has an anomalous scaling dimension.
See also
Renormalization
Renormalization group | Wave function renormalization | [
"Physics"
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"Quantum mechanics",
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3,854,163 | https://en.wikipedia.org/wiki/Cryogenic%20particle%20detector | Cryogenic particle detectors operate at very low temperature, typically only a few degrees above absolute zero. These sensors interact with an energetic elementary particle (such as a photon) and deliver a signal that can be related to the type of particle and the nature of the interaction. While many types of particle detectors might be operated with improved performance at cryogenic temperatures, this term generally refers to types that take advantage of special effects or properties occurring only at low temperature.
Introduction
The most commonly cited reason for operating any sensor at low temperature is the reduction in thermal noise, which is proportional to the square root of the absolute temperature. However, at very low temperature, certain material properties become very sensitive to energy deposited by particles in their passage through the sensor, and the gain from these changes may be even more than that from reduction in thermal noise. Two such commonly used properties are heat capacity and electrical resistivity, particularly superconductivity; other designs are based on superconducting tunnel junctions, quasiparticle trapping, rotons in superfluids, magnetic bolometers, and other principles.
Originally, astronomy pushed the development of cryogenic detectors for optical and infrared radiation. Later, particle physics and cosmology motivated cryogenic detector development for sensing known and predicted particles such as neutrinos, axions, and weakly interacting massive particles (WIMPs).
Types of cryogenic particle detectors
Calorimetric particle detection
A calorimeter is a device that measures the amount of heat deposited in a sample of material. A calorimeter differs from a bolometer in that a calorimeter measures energy, while a bolometer measures power.
Below the Debye temperature of a crystalline dielectric material (such as silicon), the heat capacity decreases inversely as the cube of the absolute temperature. It becomes very small, so that the sample's increase in temperature for a given heat input may be relatively large. This makes it practical to make a calorimeter that has a very large temperature excursion for a small amount of heat input, such as that deposited by a passing particle. The temperature rise can be measured with a standard type of thermistor, as in a classical calorimeter. In general, small sample size and very sensitive thermistors are required to make a sensitive particle detector by this method.
In principle, several types of resistance thermometers can be used. The limit of sensitivity to energy deposition is determined by the magnitude of resistance fluctuations, which are in turn determined by thermal fluctuations. Since all resistors exhibit voltage fluctuations that are proportional to their temperature, an effect known as Johnson noise, a reduction of temperature is often the only way to achieve the required sensitivity.
Superconducting transition-edge sensors
A very sensitive calorimetric sensor known as a transition-edge sensor (TES) takes advantage of superconductivity. Most pure superconductors have a very sharp transition from normal resistivity to superconductivity at some low temperature. By operating on the superconducting phase transition, a very small change in temperature resulting from interaction with a particle results in a significant change in resistance.
Superconducting tunnel junctions
The superconducting tunnel junction (STJ) consists of two pieces of superconducting material separated by a very thin (~nanometer) insulating layer. It is also known as a superconductor-insulator-superconductor tunnel junction (SIS) and is a type of a Josephson junction. Cooper pairs can tunnel across the insulating barrier, a phenomenon known as the Josephson effect. Quasiparticles can also tunnel across the barrier, although the quasiparticle current is suppressed for voltages less than twice the superconducting energy gap. A photon absorbed on one side of a STJ breaks Cooper pairs and creates quasiparticles. In the presence of an applied voltage across the junction, the quasiparticles tunnel across the junction, and the resulting tunneling current is proportional to the photon energy. The STJ can also be used as a heterodyne detector by exploiting the change in the nonlinear current–voltage characteristic that results from photon-assisted tunneling. STJs are the most sensitive heterodyne detectors available for the 100 GHz – 1 THz frequency range and are employed for astronomical observation at these frequencies.
Kinetic inductance detectors
The kinetic inductance detector (KID) is based on measuring the change in kinetic inductance caused by the absorption of photons in a thin strip of superconducting material. The change in inductance is typically measured as the change in the resonant frequency of a microwave resonator, and hence these detectors are also known as microwave kinetic inductance detectors (MKIDs).
Superconducting granules
The superconducting transition alone can be used to directly measure the heating caused by a passing particle. A type-I superconducting grain in a magnetic field exhibits perfect diamagnetism and excludes the field completely from its interior. If it is held slightly below the transition temperature, the superconductivity vanishes on heating by particle radiation, and the field suddenly penetrates the interior. This field change can be detected by a surrounding coil. The change is reversible when the grain cools again. In practice the grains must be very small and carefully made, and carefully coupled to the coil.
Magnetic calorimeters
Paramagnetic rare-earth ions are being used as particle sensors by sensing the spin flips of the paramagnetic atoms induced by heat absorbed in a low-heat-capacity material. The ions are used as a magnetic thermometer.
Other methods
Phonon particle detection
Calorimeters assume the sample is in thermal equilibrium or nearly so. In crystalline materials at very low temperature this is not necessarily the case. A good deal more information can be found by measuring the elementary excitations of the crystal lattice, or phonons, caused by the interacting particle. This can be done by several methods including superconducting transition edge sensors.
Superconducting nanowire single-photon detectors
The superconducting nanowire single-photon detector (SNSPD) is based on a superconducting wire cooled well below the superconducting transition temperature and biased with a dc current that is close to but less than the superconducting critical current. The SNSPD is typically made from ≈ 5 nm thick niobium nitride films which are patterned as narrow nanowires (with a typical width of 100 nm). Absorption of a photon breaks Cooper pairs and reduces the critical current below the bias current. A small non-superconducting section across the width of the nanowire is formed. This resistive non-superconducting section then leads to a detectable voltage pulse of a duration of about 1 nanosecond. The main advantages of this type of photon detector are its high speed (a maximal count rate of 2 GHz makes them the fastest available) and its low dark count rate. The main disadvantage is the lack of intrinsic energy resolution.
Roton detectors
In superfluid 4He the elementary collective excitations are phonons and rotons. A particle striking an electron or nucleus in this superfluid can produce rotons, which may be detected bolometrically or by the evaporation of helium atoms when they reach a free surface. 4He is intrinsically very pure so the rotons travel ballistically and are stable, so that large volumes of fluid can be used.
Quasiparticles in superfluid 3He
In the B phase, below 0.001 K, superfluid 3He acts similarly to a superconductor. Pairs of atoms are bound as quasiparticles similar to Cooper pairs with a very small energy gap of the order of 100 nanoelectronvolts. This allows building a detector
analogous to a superconducting tunnel detector. The advantage is that many (~109) pairs
could be produced by a single interaction, but the difficulties are that it is difficult
to measure the excess of normal 3He atoms produced and to prepare and maintain much
superfluid at such low temperature.
See also
References
particle detectors
sensors
superconducting detectors
superfluidity | Cryogenic particle detector | [
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"Chemistry",
"Materials_science",
"Technology",
"Engineering"
] | 1,702 | [
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"Phase transitions",
"Superconductivity",
"Phases of matter",
"Measuring instruments",
"Superfluidity",
"Particle detectors",
"Superconducting detectors",
"Condensed matter physics",
"Exotic matter",
"Sensors",
"Matter",
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3,854,225 | https://en.wikipedia.org/wiki/Waveguide%20%28radio%20frequency%29 | In radio-frequency engineering and communications engineering, a waveguide is a hollow metal pipe used to carry radio waves. This type of waveguide is used as a transmission line mostly at microwave frequencies, for such purposes as connecting microwave transmitters and receivers to their antennas, in equipment such as microwave ovens, radar sets, satellite communications, and microwave radio links.
The electromagnetic waves in a (metal-pipe) waveguide may be imagined as travelling down the guide in a zig-zag path, being repeatedly reflected between opposite walls of the guide. For the particular case of rectangular waveguide, it is possible to base an exact analysis on this view. Propagation in a dielectric waveguide may be viewed in the same way, with the waves confined to the dielectric by total internal reflection at its surface. Some structures, such as non-radiative dielectric waveguides and the Goubau line, use both metal walls and dielectric surfaces to confine the wave.
Principle
Depending on the frequency, waveguides can be constructed from either conductive or dielectric materials. Generally, the lower the frequency to be passed the larger the waveguide is. For example, the natural waveguide the earth forms given by the dimensions between the conductive ionosphere and the ground as well as the circumference at the median altitude of the Earth is resonant at 7.83 Hz. This is known as Schumann resonance. On the other hand, waveguides used in extremely high frequency (EHF) communications can be less than a millimeter in width.
History
During the 1890s theorists did the first analyses of electromagnetic waves in ducts. Around 1893 J. J. Thomson derived the electromagnetic modes inside a cylindrical metal cavity. In 1897 Lord Rayleigh did a definitive analysis of waveguides; he solved the boundary value problem of electromagnetic waves propagating through both conducting tubes and dielectric rods of arbitrary shape. He showed that the waves could travel without attenuation only in specific normal modes with either the electric field (TE modes) or magnetic field (TM modes), perpendicular to the direction of propagation. He also showed each mode had a cutoff frequency below which waves would not propagate. Since the cutoff wavelength for a given tube was of the same order as its width, it was clear that a hollow conducting tube could not carry radio wavelengths much larger than its diameter. In 1902 R. H. Weber observed that electromagnetic waves travel at a slower speed in tubes than in free space, and deduced the reason; that the waves travel in a "zigzag" path as they reflect from the walls.
Prior to the 1920s, practical work on radio waves concentrated on the low frequency end of the radio spectrum, as these frequencies were better for long-range communication. These were far below the frequencies that could propagate in even large waveguides, so there was little experimental work on waveguides during this period, although a few experiments were done. In a June 1, 1894 lecture, "The work of Hertz", before the Royal Society, Oliver Lodge demonstrated the transmission of 3 inch radio waves from a spark gap through a short cylindrical copper duct. In his pioneering 1894-1900 research on microwaves, Jagadish Chandra Bose used short lengths of pipe to conduct the waves, so some sources credit him with inventing the waveguide. However, after this, the concept of radio waves being carried by a tube or duct passed out of engineering knowledge.
During the 1920s the first continuous sources of high frequency radio waves were developed: the Barkhausen–Kurz tube, the first oscillator which could produce power at UHF frequencies; and the split-anode magnetron which by the 1930s had generated radio waves at up to 10 GHz. These made possible the first systematic research on microwaves in the 1930s. It was discovered that transmission lines used to carry lower frequency radio waves, parallel line and coaxial cable, had excessive power losses at microwave frequencies, creating a need for a new transmission method.
The waveguide was developed independently between 1932 and 1936 by George C. Southworth at Bell Telephone Laboratories and Wilmer L. Barrow at the Massachusetts Institute of Technology, who worked without knowledge of one another. Southworth's interest was sparked during his 1920s doctoral work in which he measured the dielectric constant of water with a radio frequency Lecher line in a long tank of water. He found that if he removed the Lecher line, the tank of water still showed resonance peaks, indicating it was acting as a dielectric waveguide. At Bell Labs in 1931 he resumed work in dielectric waveguides. By March 1932 he observed waves in water-filled copper pipes. Rayleigh's previous work had been forgotten, and Sergei A. Schelkunoff, a Bell Labs mathematician, did theoretical analyses of waveguides and rediscovered waveguide modes. In December 1933 it was realized that with a metal sheath the dielectric is superfluous and attention shifted to metal waveguides.
Barrow had become interested in high frequencies in 1930 studying under Arnold Sommerfeld in Germany. At MIT beginning in 1932 he worked on high frequency antennas to generate narrow beams of radio waves to locate aircraft in fog. He invented a horn antenna and hit on the idea of using a hollow pipe as a feedline to feed radio waves to the antenna. By March 1936 he had derived the propagation modes and cutoff frequency in a rectangular waveguide. The source he was using had a large wavelength of 40 cm, so for his first successful waveguide experiments he used a 16-foot section of air duct, 18 inches in diameter.
Barrow and Southworth became aware of each other's work a few weeks before both were scheduled to present papers on waveguides to a combined meeting of the American Physical Society and the Institute of Radio Engineers in May 1936. They amicably worked out credit sharing and patent division arrangements.
The development of centimeter radar during World War 2 and the first high power microwave tubes, the klystron (1938) and cavity magnetron (1940), resulted in the first widespread use of waveguide. Standard waveguide "plumbing" components were manufactured, with flanges on the end which could be bolted together. After the war in the 1950s and 60s waveguides became common in commercial microwave systems, such as airport radar and microwave relay networks which were built to transmit telephone calls and television programs between cities.
Description
In the microwave region of the electromagnetic spectrum, a waveguide normally consists of a hollow metallic conductor. These waveguides can take the form of single conductors with or without a dielectric coating, e.g. the Goubau line and helical waveguides. Hollow waveguides must be one-half wavelength or more in diameter in order to support one or more transverse wave modes.
Waveguides may be filled with pressurized gas to inhibit arcing and prevent multipaction, allowing higher power transmission. Conversely, waveguides may be required to be evacuated as part of evacuated systems (e.g. electron beam systems).
A slotted waveguide is generally used for radar and other similar applications. The waveguide serves as a feed path, and each slot is a separate radiator, thus forming an antenna. This structure has the capability of generating a radiation pattern to launch an electromagnetic wave in a specific relatively narrow and controllable direction.
A closed waveguide is an electromagnetic waveguide (a) that is tubular, usually with a circular or rectangular cross section, (b) that has electrically conducting walls, (c) that may be hollow or filled with a dielectric material, (d) that can support a large number of discrete propagating modes, though only a few may be practical, (e) in which each discrete mode defines the propagation constant for that mode, (f) in which the field at any point is describable in terms of the supported modes, (g) in which there is no radiation field, and (h) in which discontinuities and bends may cause mode conversion but not radiation.
The dimensions of a hollow metallic waveguide determine which wavelengths it can support, and in which modes. Typically the waveguide is operated so that only a single mode is present. The lowest order mode possible is generally selected. Frequencies below the guide's cutoff frequency will not propagate. It is possible to operate waveguides at higher order modes, or with multiple modes present, but this is usually impractical.
Waveguides are almost exclusively made of metal and mostly rigid structures. There are certain types of "corrugated" waveguides that have the ability to flex and bend but only used where essential since they degrade propagation properties. Due to propagation of energy in mostly air or space within the waveguide, it is one of the lowest loss transmission line types and highly preferred for high frequency applications where most other types of transmission structures introduce large losses. Due to the skin effect at high frequencies, electric current along the walls penetrates typically only a few micrometers into the metal of the inner surface. Since this is where most of the resistive loss occurs, it is important that the conductivity of interior surface be kept as high as possible. For this reason, most waveguide interior surfaces are plated with copper, silver, or gold.
Voltage standing wave ratio (VSWR) measurements may be taken to ensure that a waveguide is contiguous and has no leaks or sharp bends. If such bends or holes in the waveguide surface are present, this may diminish the performance of both transmitter and receiver equipment connected at either end. Poor transmission through the waveguide may also occur as a result of moisture build up which corrodes and degrades conductivity of the inner surfaces, which is crucial for low loss propagation. For this reason, waveguides are nominally fitted with microwave windows at the outer end that will not interfere with propagation but keep the elements out. Moisture can also cause fungus build up or arcing in high power systems such as radio or radar transmitters. Moisture in waveguides can typically be prevented with silica gel, a desiccant, or slight pressurization of the waveguide cavities with dry nitrogen or argon. Desiccant silica gel canisters may be attached with screw-on nibs and higher power systems will have pressurized tanks for maintaining pressure including leakage monitors. Arcing may also occur if there is a hole, tear or bump in the conducting walls, if transmitting at high power (usually 200 watts or more). Waveguide plumbing is crucial for proper waveguide performance. Voltage standing waves occur when impedance mismatches in the waveguide cause energy to reflect back in the opposite direction of propagation. In addition to limiting the effective transfer of energy, these reflections can cause higher voltages in the waveguide and damage equipment.
In practice
In practice, waveguides act as the equivalent of cables for super high frequency (SHF) systems. For such applications, it is desired to operate waveguides with only one mode propagating through the waveguide. With rectangular waveguides, it is possible to design the waveguide such that the frequency band over which only one mode propagates is as high as 2:1 (i.e. the ratio of the upper band edge to lower band edge is two). The relation between the waveguide dimensions and the lowest frequency is simple: if is the greater of its two dimensions, then the longest wavelength that will propagate is and the lowest frequency is thus
With circular waveguides, the highest possible bandwidth allowing only a single mode to propagate is only 1.3601:1.
Because rectangular waveguides have a much larger bandwidth over which only a single mode can propagate, standards exist for rectangular waveguides, but not for circular waveguides. In general (but not always), standard waveguides are designed such that
one band starts where another band ends, with another band that overlaps the two bands
the lower edge of the band is approximately 30% higher than the waveguide's cutoff frequency
the upper edge of the band is approximately 5% lower than the cutoff frequency of the next higher order mode
the waveguide height is half the waveguide width
The first condition is to allow for applications near band edges. The second condition limits dispersion, a phenomenon in which the velocity of propagation is a function of frequency. It also limits the loss per unit length. The third condition is to avoid evanescent-wave coupling via higher order modes. The fourth condition is that which allows a 2:1 operation bandwidth. Although it is possible to have a 2:1 operating bandwidth when the height is less than half the width, having the height exactly half the width maximizes the power that can propagate inside the waveguide before dielectric breakdown occurs.
Below is a table of standard waveguides. The waveguide name WR stands for waveguide rectangular, and the number is the inner dimension width of the waveguide in hundredths of an inch (0.01 inch = 0.254 mm) rounded to the nearest hundredth of an inch.
* Radio Components Standardization Committee
† For historical reasons the outside rather than the inside dimensions of these waveguides are 2:1 (with wall thickness WG6–WG10: 0.08" (2.0 mm), WG11A–WG15: 0.064" (1.6 mm), WG16–WG17: 0.05" (1.3 mm), WG18–WG28: 0.04" (1.0 mm))
For the frequencies in the table above, the main advantage of waveguides over coaxial cables is that waveguides support propagation with lower loss. For lower frequencies, the waveguide dimensions become impractically large, and for higher frequencies the dimensions become impractically small (the manufacturing tolerance becomes a significant portion of the waveguide size).
Mathematical analysis
Electromagnetic waveguides are analyzed by solving Maxwell's equations, or their reduced form, the electromagnetic wave equation, with boundary conditions determined by the properties of the materials and their interfaces. These equations have multiple solutions, or modes, which are eigenfunctions of the equation system. Each mode is characterized by a cutoff frequency below which the mode cannot exist in the guide. Waveguide propagation modes depend on the operating wavelength and polarization and the shape and size of the guide. The longitudinal mode of a waveguide is a particular standing wave pattern formed by waves confined in the cavity. The transverse modes are classified into different types:
TE modes (transverse electric) have no electric field in the direction of propagation.
TM modes (transverse magnetic) have no magnetic field in the direction of propagation.
TEM modes (transverse electromagnetic) have no electric nor magnetic field in the direction of propagation.
Hybrid modes have both electric and magnetic field components in the direction of propagation.
Waveguides with certain symmetries may be solved using the method of separation of variables. Rectangular wave guides may be solved in rectangular coordinates. Round waveguides may be solved in cylindrical coordinates.
In hollow, single conductor waveguides, TEM waves are not possible. This contrasts with two-conductor transmission lines used at lower frequencies; coaxial cable, parallel wire line and stripline, in which TEM mode is possible. Additionally, the propagating modes (i.e. TE and TM) inside the waveguide can be mathematically expressed as the superposition of two TEM waves.
The mode with the lowest cutoff frequency is termed the dominant mode of the guide. It is common to choose the size of the guide such that only this one mode can exist in the frequency band of operation. In rectangular and circular (hollow pipe) waveguides, the dominant modes are designated the TE1,0 mode and TE1,1 modes respectively.
Dielectric waveguides
A dielectric waveguide employs a solid dielectric rod rather than a hollow pipe. An optical fibre is a dielectric guide designed to work at optical frequencies. Transmission lines such as microstrip, coplanar waveguide, stripline or coaxial cable may also be considered to be waveguides.
Dielectric rod and slab waveguides are used to conduct radio waves, mostly at millimeter wave frequencies and above. These confine the radio waves by total internal reflection from the step in refractive index due to the change in dielectric constant at the material surface. At millimeter wave frequencies and above, metal is not a good conductor, so metal waveguides can have increasing attenuation. At these wavelengths dielectric waveguides can have lower losses than metal waveguides. Optical fibre is a form of dielectric waveguide used at optical wavelengths.
One difference between dielectric and metal waveguides is that at a metal surface the electromagnetic waves are tightly confined; at high frequencies the electric and magnetic fields penetrate a very short distance into the metal. In contrast, the surface of the dielectric waveguide is an interface between two dielectrics, so the fields of the wave penetrate outside the dielectric in the form of an evanescent (non-propagating) wave.
See also
Angular misalignment loss
Cantenna
Cavity resonator
Cutoff frequency
Feed horn
Filled cable
Leaky mode
Magic tee
Optical waveguide
Radiation mode
Radio propagation
Radio wave
Substrate-integrated waveguide
Transmission medium
Waveguide filter
Waveguide flange
Waveguide rotary joint
Flap attenuator
References
<references
This article is based in part on material from Federal Standard 1037C and from MIL-STD-188, and ATIS
J. J. Thomson, Recent Researches (1893).
O. J. Lodge, Proc. Roy. Inst. 14, p. 321 (1894).
Lord Rayleigh, Phil. Mag. 43, p. 125 (1897).
N. W. McLachlan, Theory and Applications of Mathieu Functions, p. 8 (1947) (reprinted by Dover: New York, 1964).
Further reading
George Clark Southworth, "Principles and applications of wave-guide transmission". New York, Van Nostrand [1950], xi, 689 p. illus. 24 cm. Bell Telephone Laboratories series. LCCN 50009834
External links
The Feynman Lectures on Physics Vol. II Ch. 24: Waveguides
Derivation of Fields Within a Rectangular Waveguide antenna-theory.com
Telecommunications engineering
Electrodynamics
Microwave technology
Wave mechanics | Waveguide (radio frequency) | [
"Physics",
"Mathematics",
"Engineering"
] | 3,835 | [
"Physical phenomena",
"Telecommunications engineering",
"Classical mechanics",
"Waves",
"Wave mechanics",
"Electrodynamics",
"Electrical engineering",
"Dynamical systems"
] |
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