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2015-12-29 | Some local questions for hyperbolic systems with non-regular time dependent coefficients | In this note we investigate local properties for microlocally symmetrizable
hyperbolic systems with just time dependent coefficients. Thanks to
Paley-Wiener theorem, we establish finite propagation speed by showing precise
estimates on the evolution of the support of the solution in terms of suitable
norms of the coefficients of the operator and of the symmetrizer. From this
result, local existence and uniqueness follow by quite standard methods. Our
argument relies on the use of Fourier transform, and it cannot be extended to
operators whose coefficients depend also on the space variables. On the other
hand, it works under very mild regularity assumptions on the coefficients of
the operator and of the symmetrizer. | 1512.08745v1 |
2016-01-18 | Do thermal diffusion and Dufour coefficients satisfy Onsager's reciprocity relation? | It is commonly admitted that in liquids the thermal diffusion and Dufour
coefficients $D_{T}$\ and $D_{F}$ satisfy Onsager's reciprocity. From their
relation to the cross-coefficients of the phenomenological equations, we are
led to the conclusion that this is not the case in general. As illustrative and
physically relevant examples, we discuss micellar solutions and colloidal
suspensions, where $D_{T}$ arises from chemical reactions or viscous effects
but is not related to the Dufour coefficient $D_{F}$. The situation is less
clear for binary molecular mixtures; available experimental and simulation data
do not settle the question whether $D_{T}$\ and $D_{F}$ are reciprocal
coefficients. | 1601.04435v1 |
2016-05-31 | Small Values of Coefficients of a Half Lerch Sum | Andrews, Dyson and Hickerson proved many interesting properties of
coefficients for a Ramanujan's $q$-hypergeometric series by relating it to real
quadratic field $\Q(\sqrt{6})$ and using the arithmetic of $\Q(\sqrt{6})$,
hence solved a conjecture of Andrews on the distributions of its Fourier
coefficients. Motivated by Andrews's conjecture, we discuss an interesting
$q$-hypergeometric series which comes from a Lerch sum and rank and crank
moments for partitions and overpartitions. We give Andrews-like conjectures for
its coefficients. We obtain partial results on the distributions of small
values of its coefficients toward these conjectures. | 1605.09508v2 |
2016-12-16 | A correlation coefficient of belief functions | How to manage conflict is still an open issue in Dempster-Shafer evidence
theory. The correlation coefficient can be used to measure the similarity of
evidence in Dempster-Shafer evidence theory. However, existing correlation
coefficients of belief functions have some shortcomings. In this paper, a new
correlation coefficient is proposed with many desirable properties. One of its
applications is to measure the conflict degree among belief functions. Some
numerical examples and comparisons demonstrate the effectiveness of the
correlation coefficient. | 1612.05497v2 |
2017-04-30 | Use of difference tables at studying of properties of binomial coefficients | Some properties of diagonal binomial coefficients were studied in respect to
frequency of their units digits. An approach was formulated that led to use of
difference tables to predict if certain units digits can appear in the values
of binomial coefficients at quadratic terms of the binomial theorem. Frequency
distributions of units digits of binomial coefficients contain gaps (zero
frequency) under most common numbering systems with supposed exclusion to
systems with 2^n bases. Binomial coefficient arithmetics may be used to model
cell population dynamics in a multicellular organism, which implies that the
dynamics obeys power function laws. | 1705.00272v1 |
2017-05-29 | Several extreme coefficients of the Tutte polynomial of graphs | Let $t_{i,j}$ be the coefficient of $x^iy^j$ in the Tutte polynomial
$T(G;x,y)$ of a connected bridgeless and loopless graph $G$ with order $n$ and
size $m$. It is trivial that $t_{0,m-n+1}=1$ and $t_{n-1,0}=1$. In this paper,
we obtain expressions of another eight extreme coefficients $t_{i,j}$'s with
$(i,j)=(0,m-n)$,$(0,m-n-1)$,$(n-2,0)$,$(n-3,0)$,$(1,m-n)$,$(1,m-n-1)$,$(n-2,1)$
and $(n-3,1)$ in terms of small substructures of $G$. Among them, the former
four can be obtained by using coefficients of the highest, second highest and
third highest terms of chromatic or flow polynomials, and vice versa. We also
discuss their duality property and their specializations to extreme
coefficients of the Jones polynomial. | 1705.10023v1 |
2017-06-11 | The peculiar (monic) polynomials, the zeros of which equal their coefficients | We evaluate the number of monic polynomials (of arbitrary degree $N$) the
zeros of which equal their coefficients when these are allowed to take
arbitrary complex values. In the following, we call polynomials with this
property {\em peculiar\/} polynomials. We further show that the problem of
determining the peculiar polynomials of degree $N$ simplifies when any of the
coefficients is either 0 or 1. We proceed to estimate the numbers of peculiar
polynomials of degree $N$ having one coefficient zero, or one coefficient equal
to one, or neither. | 1706.03405v1 |
2018-02-08 | Gaussian binomial coefficients with negative arguments | Loeb showed that a natural extension of the usual binomial coefficient to
negative (integer) entries continues to satisfy many of the fundamental
properties. In particular, he gave a uniform binomial theorem as well as a
combinatorial interpretation in terms of choosing subsets of sets with a
negative number of elements. We show that all of this can be extended to the
case of Gaussian binomial coefficients. Moreover, we demonstrate that several
of the well-known arithmetic properties of binomial coefficients also hold in
the case of negative entries. In particular, we show that Lucas' Theorem on
binomial coefficients modulo $p$ not only extends naturally to the case of
negative entries, but even to the Gaussian case. | 1802.02684v1 |
2018-02-15 | Comparing Hecke Coefficients of Automorphic Representations | We prove a number of unconditional statistical results of the Hecke
coefficients for unitary cuspidal representations of $\operatorname{GL}(2)$
over number fields. Using partial bounds on the size of the Hecke coefficients,
instances of Langlands functoriality, and properties of Rankin-Selberg
$L$-functions, we obtain bounds on the set of places where linear combinations
of Hecke coefficients are negative. Under a mild functoriality assumption we
extend these methods to $\operatorname{GL}(n)$. As an application, we obtain a
result related to a question of Serre about the occurrence of large Hecke
eigenvalues of Maass forms. Furthermore, in the cases where the Ramanujan
conjecture is satisfied, we obtain distributional results of the Hecke
coefficients at places varying in certain congruence or Galois classes. | 1802.05684v2 |
2018-06-29 | Asymptotics of recurrence coefficients for the Laguerre weight with a singularity at the edge | In this paper, We study the asymptotics of the leading coefficients and the
recurrence coefficients for the orthogonal polynomials with repect to the
Laguerre weight with singularity of root type and jump type at the soft edge
via the Deift-Zhou steepest descent method. The asymptotic formulas of the
leading coefficients and the recurrence coefficients for large n are described
in terms of a class of analytic solutions to the the {\sigma}-form of the
Painlev\'e II equation and the Painlev\'e XXXIV equation. | 1807.00088v3 |
2018-07-14 | Estimating transport coefficients of interacting pion gas with K-matrix cross sections | We estimate the transport coefficients, $viz.$, shear and bulk viscosities as
well as thermal and electrical conductivities, of hot pionic matter using
relativistic Boltzmann equation in relaxation time approximation. We use
K-matrix parametrization of pion-pion cross sections to estimate the transport
coefficients which incorporate multiple heavy resonances while simultaneously
preserving the unitarity of S-matrix. We compare transport coefficients
estimated using K-matrix parametrization with existing literature on pionic
transport coefficients. We find that the K-matrix scheme estimations are in
reasonable agreement with previous results. | 1807.05370v2 |
2018-11-01 | Wellposedness of the two-sided variable coefficient Caputo flux fractional diffusion equation and error estimate of its spectral approximation | In this article a two-sided variable coefficient fractional diffusion
equation (FDE) is investigated, where the variable coefficient occurs outside
of the fractional integral operator. Under a suitable transformation the
variable coefficient equation is transformed to a constant coefficient
equation. Then, using the spectral decomposition approach with Jacobi
polynomials, we proved the wellposedness of the model and the regularity of its
solution. A spectral approximation scheme is proposed and the accuracy of its
approximation studied. Two numerical experiments are presented to demonstrate
the derived error estimates. | 1811.00582v1 |
2018-11-13 | Equilibrium Formulae for Transverse Magneto-transport of Strongly Correlated Metals | Exact formulas for the Hall coefficient, modified Nernst coefficient, and
thermal Hall coefficient of metals are derived from the Kubo formula. These
coefficients depend exclusively on equilibrium (time independent)
susceptibilities, which are significantly easier to compute than
conductivities. For weak isotropic scattering, Boltzmann theory is recovered.
For strong scattering, well controlled methods for thermodynamic functions are
available. As an example, the Hall sign reversals of lattice bosons near the
Mott insulator phases are determined. Appendices include mathematical
supplements and instructions for calculating the coefficients. | 1811.05775v3 |
2019-01-14 | Variable coefficient complex Ginzburg-Landau equation | The complex Ginzburg-Landau equation (CGLE) is a general model of spatially
extended nonequilibrium systems. In this paper, an analytical method for a
variable coefficient CGLE is presented to obtain exact solutions. Variable
transformations for space and time variables with coefficient functions yield
an imaginary time advection equation related to a complex valued characteristic
curve. The variable coefficient CGLE is transformed into the nonlinear
Schr{"\o}dinger equation (NLSE) on the complex valued characteristic curve.
This result indicates that the analytical solutions of the NLSE generate that
of the variable coefficient CGLE. | 1901.04205v1 |
2019-02-12 | Some properties of coefficients of cyclotomic polynomials | This paper investigates coefficients of cyclotomic polynomials theoretically
and experimentally. We prove the following result. {{\em If $n=p_1\ldots p_k$
where $p_i$ are odd primes and
$p_1<p_2<\ldots<p_r<p_1+p_2<p_{r+1}<\ldots<p_t$ with $t\geq 3$ odd,
then the numbers $-(r-2),-(r-3),\ldots, r-2, r-1$ are all coefficients
of the cyclotomic polynomial $\Phi_{2n}$. Furthermore, if $1+p_r<p_1+p_2$
then $1-r$ is also a coefficient of $\Phi_{2n}$.} In the experimental part, in
two instances we present computational evidence for asymptotic symmetry between
distribution of positive and negative coefficients, and state the resulting
conjectures.} | 1902.04631v1 |
2019-03-15 | On the $\mathrm{L}^p$-theory for second-order elliptic operators in divergence form with complex coefficients | Given a complex, elliptic coefficient function we investigate for which
values of $p$ the corresponding second-order divergence form operator,
complemented with Dirichlet, Neumann or mixed boundary conditions, generates a
strongly continuous semigroup on $\mathrm{L}^p(\Omega)$. Additional properties
like analyticity of the semigroup, $\mathrm{H}^\infty$-calculus and maximal
regularity are also discussed. Finally we prove a perturbation result for real
coefficients that gives the whole range of $p$'s for small imaginary parts of
the coefficients. Our results are based on the recent notion of
$p$-ellipticity, reverse H\"older inequalities and Gaussian estimates for the
real coefficients. | 1903.06692v1 |
2019-04-01 | Tree Boosted Varying Coefficient Models | This paper investigates the integration of gradient boosted decision trees
and varying coefficient models. We introduce the tree boosted varying
coefficient framework which justifies the implementation of decision tree
boosting as the nonparametric effect modifiers in varying coefficient models.
This framework requires no structural assumptions in the space containing the
varying coefficient covariates, is easy to implement, and keeps a balance
between model complexity and interpretability. To provide statistical
guarantees, we prove the asymptotic consistency of the proposed method under
the regression settings with $L^2$ loss. We further conduct a thorough
empirical study to show that the proposed method is capable of providing
accurate predictions as well as intelligible visual explanations. | 1904.01058v1 |
2019-04-13 | Virial coefficients expressed by heat kernel coefficients | In this paper, we generally expressed the virial expansion of ideal quantum
gases by the heat kernel coefficients for the corresponding Laplace type
operator. As examples, we give the virial coefficients for quantum gases in
$d$-dimensional confined space and spheres, respectively. Our results show
that, the relative correction from the boundary to the second virial
coefficient is independent of the dimension and it always enhances the quantum
exchange interaction. In $d$-dimensional spheres, however, the influence of the
curvature enhances the quantum exchange interaction in two dimensions, but
weakens it in higher dimensions ($d>3$). | 1904.06496v1 |
2019-05-23 | Shear Thickening of Dense Suspensions: The Role of Friction | Shear thickening of particle suspensions is characterized by a transition
between lubricated and frictional contacts between the particles. Using 3D
numerical simulations, we study how the inter-particle friction coefficient
influences the effective macroscopic friction coefficient and hence the
microstructure and rheology of dense shear thickening suspensions. We propose
expressions for effective friction coefficient in terms of distance to jamming
for varying shear stresses and particle friction coefficient values. We find
effective friction coefficient to be rather insensitive to interparticle
friction, which is perhaps surprising but agrees with recent theory and
experiments. | 1905.09732v1 |
2019-08-01 | Measuring the Clustering Strength of a Network via the Normalized Clustering Coefficient | In this paper, we propose a novel statistic of networks, the normalized
clustering coefficient, which is a modified version of the clustering
coefficient that is robust to network size, network density and degree
heterogeneity under different network generative models. In particular, under
the degree corrected block model (DCBM), the "in-out-ratio" could be inferred
from the normalized clustering coefficient. Asymptotic properties of the
proposed indicator are studied under three popular network generative models.
The normalized clustering coefficient can also be used for networks clustering,
network sampling as well as dynamic network analysis. Simulations and real data
analysis are carried out to demonstrate these applications. | 1908.00523v1 |
2019-08-18 | A New Approach to Determine the Coefficient of Skewness and An Alternative Form of Boxplot | To solve the problems in measuring coefficient of skewness related to extreme
value, irregular distance from the middle point and distance between two
consecutive numbers, "Rank skewness" a new measure of the coefficient of
skewness has been proposed in this paper. Comparing with other measures of the
coefficient of skewness, proposed measure of the coefficient of skewness
performs better specially for skewed distribution. An alternative of five point
summary boxplot, a four point summary graph has also been proposed which is
simpler than the traditional boxplot. It is based on all observation and give
better result than the five point summary. | 1908.06400v1 |
2019-12-10 | Variable-coefficient symbolic computation approach for finding multiple rogue wave solutions of nonlinear system with variable coefficients | In this paper, a variable-coefficient symbolic computation approach is
proposed to solve the multiple rogue wave solutions of nonlinear equation with
variable coefficients. As an application, a (2+1)-dimensional
variable-coefficient Kadomtsev-Petviashvili equation is investigated. The
multiple rogue wave solutions are obtained and their dynamics features are
shown in some 3D and contour plots. | 1912.04270v1 |
2020-01-21 | Strong solutions of forward-backward stochastic differential equations with measurable coefficients | This paper investigates solvability of fully coupled systems of
forward-backward stochastic differential equations (FBSDEs) with irregular
coefficients. In particular, we assume that the coefficients of the FBSDEs are
merely measurable and bounded in the forward process. We crucially use
compactness results from the theory of Malliavin calculus to construct strong
solutions. Despite the irregularity of the coefficients, the solutions turn out
to be differentiable, at least in the Malliavin sense and, as functions of the
initial variable, in the Sobolev sense. | 2001.07753v2 |
2020-01-31 | On Fourier coefficients of elliptic modular forms $\bmod \, \ell$ with applications to Siegel modular forms | We study several aspects of nonvanishing Fourier coefficients of elliptic
modular forms $\bmod \ell$, partially answering a question of
Bella\"iche-Soundararajan concerning the asymptotic formula for the count of
the number of Fourier coefficients upto $x$ which do not vanish $\bmod \ell$.
We also propose a precise conjecture as a possible answer to this question.
Further, we prove several results related to the nonvanishing of arithmetically
interesting (e.g., primitive or fundamental) Fourier coefficients $\bmod \ell $
of a Siegel modular form with integral algebraic Fourier coefficients provided
$\ell$ is large enough. We also make some efforts to make this "largeness" of
$\ell$ effective. | 2001.11700v1 |
2020-04-06 | Best constant for Ulam stability of first-order h-difference equations with periodic coefficient | We establish the best (minimum) constant for Ulam stability of first-order
linear $h$-difference equations with a periodic coefficient. First, we show
Ulam stability and find the Ulam stability constant for a first-order linear
equation with a period-two coefficient, and give several examples. In the last
section we prove Ulam stability for a periodic coefficient function of
arbitrary finite period. Results on the associated first-order perturbed linear
equation with periodic coefficient are also included. | 2004.03465v1 |
2020-04-20 | On the wave equation with multiplicities and space-dependent irregular coefficients | In this paper we study the well-posedness of the Cauchy problem for a wave
equation with multiplicities and space-dependent irregular coefficients. As in
\cite{GR:14} in order to give a meaningful notion of solution, we employ the
notion of very weak solution, which construction is based on a parameter
dependent regularisation of the coefficients via mollifiers. We prove that,
even with distributional coefficients, a very weak solution exists for our
Cauchy problem and it converges to the classical one when the coefficients are
smooth. The dependence on the mollifiers of very weak solutions is investigated
at the end of the paper in some instructive examples. | 2004.09657v1 |
2020-05-16 | Numerical solution of linear differential equations with discontinuous coefficients and Henstock integral | In this article we consider the problem of approximative solution of linear
differential equations $y'+p(x)y=q(x)$ with discontinuous coefficients $p$ and
$q$. We assume that coefficients of such equation are Henstock integrable
functions. To find the approximative solution we change the original Cauchy
problem to another problem with piecewise-constant coefficients. The sharp
solution of this new problems is the approximative solution of the original
Cauchy problem. We find the degree approximation in terms of modulus of
continuity $\omega_\delta (P),\ \omega_\delta (Q)$, where $P$ and $Q$ are
$f$-primitive for coefficients $p$ and $q$. | 2005.07978v1 |
2020-05-21 | The Lanczos Approximation for the $Γ$-Function with Complex Coefficients | We examined the properties of the coefficients of the \cite{lanczos1964}
approximation of the $\Gamma$-function with complex values of the free
parameter together with the convergence properties of the approximation when
using these coefficients. We report that for fixed real parts of the free
parameter that using complex coefficients both increases the computational cost
of the Lanczos approximation while drecreasing the accuracy. We conclude that
in practical applications of numerical evaluation of the $\Gamma$-function only
coefficients generated with real values of the free parameter should be used. | 2005.10449v1 |
2020-06-07 | Improved Recursive Computation of Clebsch-Gordan Coefficients | Fast, accurate, and stable computation of the Clebsch-Gordan (C-G)
coefficients is always desirable, for example, in light scattering simulations,
the translation of the multipole fields, quantum physics and chemistry. Current
recursive methods for computing the C-G coefficients are often unstable for
large quantum numbers due to numerical overflow or underflow. In this paper, we
present an improved method, the so-called sign-exponent recurrence, for the
recursive computation of C-G coefficients. The result shows that the proposed
method can significantly improve the stability of the computation without
losing its efficiency, producing accurate values for the C-G coefficients even
with very large quantum numbers. | 2006.04267v2 |
2020-09-16 | Parabolic and elliptic equations with singular or degenerate coefficients: the Dirichlet problem | We consider the Dirichlet problem for a class of elliptic and parabolic
equations in the upper-half space $\mathbb{R}^d_+$, where the coefficients are
the product of $x_d^\alpha, \alpha \in (-\infty, 1),$ and a bounded uniformly
elliptic matrix of coefficients. Thus, the coefficients are singular or
degenerate near the boundary $\{x_d =0\}$ and they may not locally integrable.
The novelty of the work is that we find proper weights under which the
existence, uniqueness, and regularity of solutions in Sobolev spaces are
established. These results appear to be the first of their kind and are new
even if the coefficients are constant. They are also readily extended to
systems of equations. | 2009.07967v1 |
2020-09-28 | Homological Filling Functions with Coefficients | How hard is it to fill a loop in a Cayley graph with an unoriented surface?
Following a comment of Gromov in "Asymptotic invariants of infinite groups", we
define homological filling functions of groups with coefficients in a group
$R$. Our main theorem is that the coefficients make a difference. That is, for
every $n \geq 1$ and every pair of coefficient groups $A, B \in
\{\mathbb{Z},\mathbb{Q}\} \cup \{\mathbb{Z}/p\mathbb{Z} : p\text{ prime}\}$,
there is a group whose filling functions for $n$-cycles with coefficients in
$A$ and $B$ have different asymptotic behavior. | 2009.13489v3 |
2020-10-05 | Transversal flexoelectric coefficient for nanostructures at finite deformations from first principles | We present a novel formulation for calculating the transversal flexoelectric
coefficient of nanostructures at finite deformations from first principles.
Specifically, we introduce the concept of \emph{radial polarization} to make
the coefficient a well-defined quantity for uniform bending deformations. We
use the framework to calculate the flexoelectric coefficient for group IV
atomic monolayers using density functional theory. We find that graphene's
coefficient is significantly larger than previously reported, with a charge
transfer mechanism that differs from other members of its group. | 2010.01747v1 |
2020-12-09 | The Relationship between Maximum Principle and Dynamic Programming Principle for Stochastic Recursive Control Problem with Random Coefficients | This paper aims to explore the relationship between maximum principle and
dynamic programming principle for stochastic recursive control problem with
random coefficients. Under certain regular conditions for the coefficients, the
relationship between the Hamilton system with random coefficients and
stochastic Hamilton-Jacobi-Bellman equation is obtained. It is very different
from the deterministic coefficients case since stochastic
Hamilton-Jacobi-Bellman equation is a backward stochastic partial differential
equation with solution being a pair of random fields rather than a
deterministic function. A linear quadratic recursive utility optimization
problem is given as an explicitly illustrated example based on this kind of
relationship. | 2012.04814v1 |
2021-01-19 | Improved Coefficients for the Karagiannidis-Lioumpas Approximations and Bounds to the Gaussian Q-Function | We revisit the Karagiannidis-Lioumpas (KL) approximation of the Q-function by
optimizing its coefficients in terms of absolute error, relative error and
total error. For minimizing the maximum absolute/relative error, we describe
the targeted uniform error functions by sets of nonlinear equations so that the
optimized coefficients are the solutions thereof. The total error is minimized
with numerical search. We also introduce an extra coefficient in the KL
approximation to achieve significantly tighter absolute and total error at the
expense of unbounded relative error. Furthermore, we extend the KL expression
to lower and upper bounds with optimized coefficients that minimize the error
measures in the same way as for the approximations. | 2101.07631v1 |
2021-06-09 | Relative Clustering Coefficient | In this paper, we relatively extend the definition of global clustering
coefficient to another clustering, which we call it relative clustering
coefficient. The idea of this definition is to ignore the edges in the network
that the probability of having an edge is 0. Here, we also consider a model as
an example that using relative clustering coefficient is better than global
clustering coefficient for comparing networks and also checking the properties
of the networks. | 2106.05145v1 |
2021-09-18 | Enumeration of self-reciprocal irreducible monic polynomials with prescribed leading coefficients over a finite field | A polynomial is called self-reciprocal (or palindromic) if the sequence of
its coefficients is palindromic. In this paper we enumerate self-reciprocal
irreducible monic polynomials over a finite field with prescribed leading
coefficients. Asymptotic expression with explicit error bound is derived, which
is used to show that such polynomials with degree $2n$ always exist provided
that the number of prescribed leading coefficients is slightly less than $n/4$.
Exact expressions are also obtained for fields with two or three elements and
up to two prescribed leading coefficients. | 2109.09006v3 |
2021-10-13 | High-Dimensional Varying Coefficient Models with Functional Random Effects | We consider a sparse high-dimensional varying coefficients model with random
effects, a flexible linear model allowing covariates and coefficients to have a
functional dependence with time. For each individual, we observe discretely
sampled responses and covariates as a function of time as well as time
invariant covariates. Under sampling times that are either fixed and common or
random and independent amongst individuals, we propose a projection procedure
for the empirical estimation of all varying coefficients. We extend this
estimator to construct confidence bands for a fixed number of varying
coefficients. | 2110.06426v1 |
2021-10-15 | Different coefficients for studying dependence | Through computer simulations, we research several different measures of
dependence, including Pearson's and Spearman's correlation coefficients, the
maximal correlation, the distance correlation, a function of the mutual
information called the information coefficient of correlation, and the maximal
information coefficient (MIC). We compare how well these coefficients fulfill
the criteria of generality, power, and equitability. Furthermore, we consider
how the exact type of dependence, the amount of noise and the number of
observations affect their performance. | 2110.07928v2 |
2022-04-13 | On Signs of Fourier Coefficients of Hecke-Maass Cusp Forms on $\mathrm{GL}_3$ | We consider sign changes of Fourier coefficients of Hecke-Maass cusp forms
for the group $\mathrm{SL}_3(\mathbb Z)$. When the underlying form is
self-dual, we show that there are $\gg_\varepsilon X^{5/6-\varepsilon}$ sign
changes among the coefficients $\{A(m,1)\}_{m\leq X}$ and that there is a
positive proportion of sign changes for many self-dual forms. Similar result
concerning the positive proportion of sign changes also hold for the
real-valued coefficients $A(m,m)$ for generic $\mathrm{GL}_3$ cusp forms, a
result which is based on a new effective Sato-Tate type theorem for a family of
$\mathrm{GL}_3$ cusp forms we establish. In addition, non-vanishing of the
Fourier coefficients is studied under the Ramanujan-Petersson conjecture. | 2204.06261v1 |
2022-06-07 | On Binomial coefficients of real arguments | As is well-known, a generalization of the classical concept of the factorial
$n!$ for a real number $x\in {\mathbb R}$ is the value of Euler's gamma
function $\Gamma(1+x)$. In this connection, the notion of a binomial
coefficient naturally arose for admissible values of the real arguments.
By elementary means, it is proved a number of properties of binomial
coefficients $\binom{r}{\alpha}$ of real arguments $r,\,\alpha\in {\mathbb R}$
such as analogs of unimodality, symmetry, Pascal's triangle, etc. for classical
binomial coefficients. The asymptotic behavior of such generalized binomial
coefficients of a special form is established. | 2206.03007v1 |
2022-09-19 | Fock expansion for two-electron atoms. High order angular coefficients | The Fock expansion, which describes the properties of two-electron atoms near
the nucleus, is studied. The angular Fock coefficients
$\psi_{k,p}(\alpha,\theta)$ with the maximum possible value of subscript $p$
are calculated on examples of the coefficients with $5\leq k \leq 10$. The
presented technique makes it possible to calculate such angular coefficients
for any arbitrarily large $k$. The mentioned coefficients being leading in the
logarithmic power series representing the Fock expansion may be indispensable
for the development of simple methods for calculating the helium-like
electronic structure. The theoretical results obtained are verified by other
suitable methods. The Wolfram Mathematica is used extensively. | 2209.09053v2 |
2022-09-23 | Harmonic weak Maass forms and periods II | In this paper we investigate the Fourier coefficients of harmonic Maass forms
of negative half-integral weight. We relate the algebraicity of these
coefficients to the algebraicity of the coefficients of certain canonical
meromorphic modular forms of positive even weight with poles at Heegner
divisors. Moreover, we give an explicit formula for the coefficients of
harmonic Maass forms in terms of periods of certain meromorphic modular forms
with algebraic coefficients. | 2209.11454v1 |
2023-03-03 | Time fractional parabolic equations with partially SMO coefficients | We present the unique solvability in Sobolev spaces of time fractional
parabolic equations in divergence and non-divergence forms. The leading
coefficients are merely measurable in $(t,x_1)$ for $a^{ij}$, $1 \leq i,j \leq
d$, $(i,j) \neq (1,1)$. The coefficient $a^{11}$ is merely measurable locally
either in $t$ or $x_1$. As functions of the remaining variables, the
coefficients have small mean oscillations. We consider mixed norm Sobolev
spaces with Muckenhoupt weights. Our results generalize previous work on
parabolic equations with time fractional derivatives to a much larger class of
coefficients and solution spaces. | 2303.01688v1 |
2023-03-22 | Determining coefficients of thermoelastic system from boundary information | Given a compact Riemannian manifold $(M,g)$ with smooth boundary $\partial
M$, we give an explicit expression for full symbol of the thermoelastic
Dirichlet-to-Neumann map $\Lambda_g$ with variable coefficients
$\lambda,\mu,\alpha,\beta \in C^{\infty}(\bar{M})$. We prove that $\Lambda_g$
uniquely determines partial derivatives of all orders of the coefficients on
the boundary. Moreover, for a nonempty open subset $\Gamma\subset\partial M$,
suppose that the manifold and the coefficients are real analytic up to
$\Gamma$, we show that $\Lambda_g$ uniquely determines the coefficients on the
whole manifold $\bar{M}$. | 2303.12288v1 |
2023-03-29 | Unpredictable solutions of Duffing type equations with Markov coefficients | The paper considers a stochastic differential equation of Duffing type with
Markov coefficients. The existence of unpredictable solutions is considered.
The unpredictability is a property of bounded functions characterized by
unbounded sequences of moments of divergence and convergence in Bebutov
dynamics. Markov components of the equation coefficients admit the
unpredictability property. The components of the equation coefficients are
derived from a Markov chain. The existence, uniqueness and exponential
stability of an unpredictable solution are proved. The sequences of divergence
and convergence of the coefficients and the solution are synchronized.
Numerical example that support the theoretical results are provided. | 2303.17336v1 |
2023-06-04 | Sharp coefficients bounds for Starlike functions associated with Gregory coefficients | In this paper we introduced the class $\mathcal{S}_{G}^{\ast }$ of analytic
functions which is related with starlike functions and generating function of
Gregory coefficients. By using bounds on some coefficient functionals for the
family of functions with positive real part, we obtain for functions in the
class $\mathcal{S}_{G}^{\ast }$ several sharp coefficient bounds on the first
six coeffcients and also further sharp bounds on the corresponding Hankel
determinants. | 2306.02431v1 |
2023-11-07 | Guts determine the leading coefficients of $L^2$-Alexander torsions | For 3-manifolds, the leading coefficient of the $L^2$-Alexander torsion is a
numerical invariant of a real first cohomology class. We show that the leading
coefficient equals the relative $L^2$-torsion of the manifold cut up along a
norm-minimizing surface dual to the cohomology class. Furthermore, the leading
coefficient equals the relative $L^2$-torsion of the guts associated to the
cohomology class. Finally, we prove that the leading coefficient is constant on
any open Thurston cone. The main ingredients are a new criterion for the
convergence of Fuglede-Kadison determinants and the work of Agol and Zhang on
guts of 3-manifolds. | 2311.04115v1 |
2023-12-18 | Asymptotic products of binomial and multinomial coefficients revisited | In this note, we consider asymptotic products of binomial and multinomial
coefficients and determine their asymptotic constants and formulas. Among them,
special cases are the central binomial coefficients, the related Catalan
numbers, and binomial coefficients in a row of Pascal's triangle. For the
latter case, we show that it can also be derived from a limiting case of
products of binomial coefficients over the rows. The asymptotic constants are
expressed by known constants, for example, the Glaisher--Kinkelin constant. In
addition, the constants lie in certain intervals that we determine precisely.
Subsequently, we revisit a related result of Hirschhorn and clarify the given
numerical constant by showing the exact expression. | 2312.11369v1 |
2024-03-27 | Orthogonal Polynomials with a Singularly Perturbed Airy Weight | We study the monic orthogonal polynomials with respect to a singularly
perturbed Airy weight. By using Chen and Ismail's ladder operator approach, we
derive a discrete system satisfied by the recurrence coefficients for the
orthogonal polynomials. We find that the orthogonal polynomials satisfy a
second-order linear ordinary differential equation, whose coefficients are all
expressed in terms of the recurrence coefficients. By considering the time
evolution, we obtain a system of differential-difference equations satisfied by
the recurrence coefficients. Finally, we study the asymptotics of the
recurrence coefficients when the degrees of the orthogonal polynomials tend to
infinity. | 2403.18669v1 |
2012-10-01 | Measurements of Antenna Surface for a Millimeter-Wave Space Radio Telescope II; Metal Mesh Surface for Large Deployable Reflector | Large deployable antennas with a mesh surface woven by fine metal wires are
an important technology for communications satellites and space radio
telescopes. However, it is difficult to make metal mesh surfaces with
sufficient radio-frequency (RF) performance for frequencies higher than
millimeter waves. In this paper, we present the RF performance of metal mesh
surfaces at 43 GHz. For this purpose, we developed an apparatus to measure the
reflection coefficient, transmission coefficient, and radiative coefficient of
the mesh surface. The reflection coefficient increases as a function of metal
mesh surface tension, whereas the radiative coefficient decreases. The
anisotropic aspects of the reflection coefficient and the radiative coefficient
are also clearly seen. They depend on the front and back sides of the metal
mesh surface and the rotation angle. The transmission coefficient was measured
to be almost constant. The measured radiative coefficients and transmission
coefficients would cause significant degradation of the system noise
temperature. In addition, we carried out an astronomical observation of a
well-known SiO maser source, R Cas, by using a metal mesh mirror on the NRO
45-m radio telescope Coude system. The metal mesh mirror considerably increases
the system noise temperature and slightly decreases the peak antenna
temperature. These results are consistent with laboratory measurements. | 1210.0335v1 |
2018-11-14 | A reduction principle for Fourier coefficients of automorphic forms | We consider a general class of Fourier coefficients for an automorphic form
on a finite cover of a reductive adelic group ${\bf
G}(\mathbb{A}_{\mathbb{K}})$, associated to the data of a `Whittaker pair'. We
describe a quasi-order on Fourier coefficients, and an algorithm that gives an
explicit formula for any coefficient in terms of integrals and sums involving
higher coefficients. The maximal elements for the quasi-order are
`Levi-distinguished' Fourier coefficients, which correspond to taking the
constant term along the unipotent radical of a parabolic subgroup, and then
further taking a Fourier coefficient with respect to a
$\mathbb{K}$-distinguished nilpotent orbit in the Levi quotient. Thus one can
express any Fourier coefficient, including the form itself, in terms of higher
Levi-distinguished coefficients. In follow-up papers we use this result to
determine explicit Fourier expansions of minimal and next-to-minimal
automorphic forms on split simply-laced reductive groups, and to obtain Euler
product decompositions of their top Fourier coefficients. | 1811.05966v5 |
2020-07-04 | Representations of coefficients of power series in classical statistical mechanics. Their classification and complexity criteria | It is declared that the aim of simplifying representations of coefficients of
power series of classical statistical mechanics is to simplify a process of
obtaining estimates of the coefficients using their simplified representations.
The aim of the article is: to formulate criteria for the complexity (from the
above point of view) of representations of coefficients of the power series of
classical statistical mechanics and to demonstrate their application by
examples of comparing the Ree-Hoover representations of virial coefficients
(briefly -- the RH representations) with such representations of power series
coefficients that are based on the conception of the frame classification of
labeled graphs (the abbreviation -- FC). To solve these problems, mathematical
notions were introduced (such as a basic product, a basic integral, a basic
linear combination, a basic linear combination with coefficients of
insignificant complexity(the abbreviation -- BLC with CIC) and the
classification of representations of the coefficients of power series of
classical statistical mechanics is proposed. In the classification, the class
of BLC's with CIC is the most important. It includes all the above
representations of the coefficients of power series of classical statistical
mechanics. Three criteria are formulated for estimate the comparative
complexity of BLC's with CIC. These criteria are ordered by their accuracy.
Based on each of these criteria, a criterion for the comparative complexity of
finite sets of BLC's with CIC is constructed. The constructed criteria are
ordered by their accuracy. The application of all the constructed criteria is
demonstrated by examples of comparing RH representations with the
representations of the power series coefficients based on the concept FC. The
obtained results are presented in the tables and commented. | 2007.02146v1 |
2021-11-12 | Histogram lies about distribution shape and Pearson's coefficient of variation lies about variability | Background and Objective: Histograms and Pearson's coefficient of variation
are among the most popular summary statistics. Researchers use histograms to
judge the shape of quantitative data distribution by visual inspection. The
coefficient of variation is taken as an estimator of relative variability of
these data. We explore properties of histograms and coefficient of variation by
examples in R, thus offering better alternatives: density plots and
Eisenhauer's relative dispersion coefficient. Methods: Hypothetical examples
developed in R are applied to create histograms and density plots, and to
compute coefficient of variation and relative dispersion coefficient. Results:
These hypothetical examples clearly show that these two traditional approaches
are flawed. Histograms do not necessarily reflect the distribution of
probabilities and the Pearson's coefficient of variation is not invariant with
linear transformations and is not a measure of relative variability, for it is
a ratio between a measure of absolute variability (standard deviation) and a
measure of central position (mean). Potential alternatives are explained and
applied for contrast. Conclusions: With the use of modern computers and R
language it is easy to apply density plots, which are able to approximate the
theoretical probability distribution. In addition, Eisenhauer's relative
dispersion coefficient is suggested as a suitable estimator of relative
variability, including sample size correction for lower and upper bounds. | 2111.06822v3 |
2023-02-19 | Russel and Rao Coefficient is a Suitable Substitute for Dice Coefficient in Studying Restriction Mapped Genetic Distances of Escherichia coli | Escherichia coli is one of many bacterial inhabitants found in human
intestines and any adaptation as a result of mutations may affect its host. A
commonly used technique employed to study these mutations is Restriction
Fragment Length Polymorphism (RFLP) and is proceeded with a suitable distance
coefficient to quantify genetic differences between 2 samples. Dice is
considered a suitable distance coefficient in RFLP analyses, while others were
left unstudied in its suitability for use. Hence, this study aims to identify
substitutes for Dice. Experimental data was obtained by subculturing E. coli
for 72 passages in 8 different adaptation media and RFLP profiles analyzed
using 20 distance coefficients. Our results suggest that Dennis, Fossum,
Matching and Russel and Rao to work as well or better than Dice. Dennis,
Matching and Fossum coefficients had highest discriminatory abilities but are
limited by the lack of upper or lower boundaries. Russel and Rao coefficient is
highly correlated with Dice coefficient (r2 = 0.998), with both higher and
lower boundaries, suggesting that Russel and Rao coefficient can be used to
substitute Dice coefficient in studying genetic distances in E. coli. | 2302.12714v1 |
2023-11-27 | turbo-RANS: Straightforward and Efficient Bayesian Optimization of Turbulence Model Coefficients | Industrial simulations of turbulent flows often rely on Reynolds-averaged
Navier-Stokes (RANS) turbulence models, which contain numerous closure
coefficients that need to be calibrated. Although tuning these coefficients can
produce significantly improved predictive accuracy, their default values are
often used. We believe users do not calibrate RANS models for several reasons:
there is no clearly recommended framework to optimize these coefficients; the
average user does not have the expertise to implement such a framework; and,
the optimization of the values of these coefficients can be a computationally
expensive process. In this work, we address these issues by proposing a
semi-automated calibration of these coefficients using a new framework based on
Bayesian optimization. We introduce the generalized error and default
coefficient preference (GEDCP) objective function, which can be used with
integral, sparse, or dense reference data. We demonstrate the computationally
efficient performance of turbo-RANS for three example cases: predicting the
lift coefficient of an airfoil; predicting the velocity and turbulent kinetic
energy fields for a separated flow; and, predicting the wall pressure
coefficient distribution for flow through a converging-diverging channel. In
the first two examples, we calibrate the $k$-$\omega$ shear stress transport
(SST) turbulence model and, in the last example, we calibrate user-specified
coefficients for the Generalized $k$-$\omega$ (GEKO) model in Ansys Fluent. An
in-depth hyperparameter tuning study is conducted to recommend efficient
settings for the turbo-RANS optimization procedure. Towards the goal of
facilitating RANS turbulence closure model calibration, we provide an
open-source implementation of the turbo-RANS framework that includes OpenFOAM,
Ansys Fluent, and solver-agnostic templates for user application. | 2311.15840v1 |
1994-10-06 | Damped Lyman Alpha Systems vs. Cold + Hot Dark Matter | Damped Ly$\alpha$ systems provide possibly the most significant evidence for
early structure formation, and thus a stringent constraint on the Cold + Hot
Dark Matter (CHDM) cosmology. Using the numbers of halos in N-body simulations
to normalize Press-Schechter (PS) estimates of the number densities of
protogalaxies as a function of redshift, we find that CHDM with
$\Omega_c/\Omega_\nu/\Omega_b = 0.6/0.3/0.1$ is compatible with the damped
Ly$\alpha$ data only at $z<2.5$, but that it is probably incompatible with data
at $z>3$. The predictions of CHDM are quite sensitive to the neutrino fraction.
We find that $\Omega_c/\Omega_\nu/\Omega_b = 0.725/0.20/0.075$ is compatible
with the $z>3$ data. With one massive neutrino species, this corresponds to
lowering the neutrino mass from 7.0 to 4.7 eV, for $H_0=50\kmsMpc$ and
$T=2.726$ K. By analysing our numerical simulations with different resolutions
and box sizes as well as those of Ma \& Bertchinger (1994), we show that for
the CHDM models with $\Omega_\nu$=0.2--0.3 the PS approximation should be used
with Gaussian filter with $\delta_c=1.3-1.4$ if one tries to recover the total
mass of a collapsed halo and to include nonlinear effects, due to waves both
longer and shorter than those within the simulation box. | 9410022v1 |
1995-12-05 | Small Scale Structure and High Redshift HI | Cosmological simulations with gas dynamics suggest that the Lyman-alpha
forest is produced mainly by "small scale structure" --- filaments and sheets
that are the high redshift analog of today's galaxy superclusters. There is no
sharp distinction between Lyman-alpha clouds and "Gunn-Peterson" absorption
produced by the fluctuating IGM -- the Lyman-alpha forest {\it is} the
Gunn-Peterson effect. Lyman limit and damped Lyman-alpha absorption arises in
the radiatively cooled gas of forming galaxies. At $z~2-3$, most of the gas is
in the photoionized, diffuse medium associated with the Lyman-alpha forest, but
most of the {\it neutral} gas is in damped Lyman-alpha systems. We discuss
generic evolution of cosmic gas in a hierarchical scenario of structure
formation, with particular attention to the prospects for detecting 21cm
emission from high redshift HI. A scaling argument based on the present-day
cluster mass function suggests that objects with $M_{HI} >~ 5e11 h^{-1} \msun$
should be extremely rare at $z~3$, so detections with existing instruments will
be difficult. An instrument like the proposed Square Kilometer Array could
detect individual damped Lyman-alpha systems at high redshift, making it
possible to map structure in the high redshift universe in much the same way
that today's galaxy redshift surveys map the local large scale structure. | 9512016v1 |
1996-04-03 | APM z>4 QSO Survey: Spectra and Intervening Absorption Systems | The APM multicolor survey for bright z > 4 objects, covering 2500 deg^2 of
sky to m(R)~19, resulted in the discovery of thirty-one quasars with z > 4.
High signal-to-noise optical spectrophotometry at 5A resolution has been
obtained for the twenty-eight quasars easily accessible from the northern
hemisphere. These spectra have been surveyed to create new samples of high
redshift Lyman-limit systems, damped Lyman-alpha absorbers, and metal
absorption systems (e.g. CIV and MgII). In this paper we present the spectra,
together with line lists of the detected absorption systems. The QSOs display a
wide variety of emission and absorption line characteristics, with 5 exhibiting
broad absorption lines and one with extremely strong emission lines
(BR2248-1242). Eleven candidate damped Ly-alpha absorption systems have been
identified covering the redshift range 2.8<z<4.4 (8 with z>3.5). An analysis of
the measured redshifts of the high ionization emission lines with the low
ionization lines shows them to be blueshifted by 430+/-60 km/s. In a previous
paper (Storrie-Lombardi et. al. 1994) we discussed the redshift evolution of
the Lyman limit systems catalogued here. In subsequent papers we will discuss
the properties of the Ly-alpha forest absorbers and the redshift and column
density evolution of the damped Ly-alpha absorbers. | 9604021v1 |
1996-04-10 | A Keck HIRES Investigation of the Metal Abundances and Kinematics of the z=2.46 Damped Lya System Toward Q0201+365 | We present high resolution ($\approx 8$ \kms) spectra of the QSO Q0201+365
obtained with HIRES, the echelle spectrograph on the 10m W.M. Keck Telescope.
Although we identify over $80\%$ of the absorption features and analyze several
of the more complex metal-line systems, we focus our analysis on the damped
\Lya system at $z=2.462$. Ionization simulations suggest the hydrogen in this
system is significantly neutral and all of the observed metals are
predominantly singly ionized. We measure accurate abundances for Fe, Cr, Si, Ni
and place a lower limit on the abundance of Zn: [Fe/H] = $-0.830 \pm 0.051$,
[Cr/H] = $-0.902 \pm 0.064$, [Si/H] = $-0.376 \pm 0.052$, [Ni/H] = $-1.002 \pm
0.054$ and [Zn/H] $> -0.562 \pm 0.064$. We give evidence suggesting the actual
Zn abundance is [Zn/H] $\approx -0.262$, implying the highest metallicity
observed at a redshift $z \geq 2$. The relative abundances of these elements
remains constant over essentially the entire system ($\approx 150$ \kms in
velocity space), suggesting it is well mixed. Furthermore, we use the lack of
abundance variations to infer properties of the dust responsible for element
depletion. Finally, we discuss the kinematic characteristics of this damped
\Lya system, comparing and contrasting it with other systems. The low-ion line
profiles span $\approx 200$ \kms in velocity space and have an asymmetric shape
with the strongest feature on the red edge. These kinematic characteristics are
consistent with a rotating disk model. | 9604042v1 |
1996-06-13 | Damping of Cosmic Magnetic Fields | We examine the evolution of magnetic fields in an expanding fluid composed of
matter and radiation with particular interest in the evolution of cosmic
magnetic fields. We derive the propagation velocities and damping rates for
relativistic and non-relativistic fast and slow magnetosonic, and Alfv\'en
waves in the presence of viscous and heat conducting processes. The analysis
covers all MHD modes in the radiation diffusion and the free-streaming regimes.
When our results are applied to the evolution of magnetic fields in the early
universe, we find that cosmic magnetic fields are damped from prior to the
epoch of neutrino decoupling up to recombination. Our findings have multifold
implications for cosmology. The dissipation of magnetic field energy into heat
during the epoch of neutrino decoupling ensures that most magnetic field
configurations generated in the very early universe satisfy big bang
nucleosynthesis constraints. Further dissipation before recombination
constrains models in which primordial magnetic fields give rise to galactic
magnetic fields or density perturbations. Finally, the survival of Alfv\'en and
slow magnetosonic modes on scales well below the Silk mass may be of
significance for the formation of structure on small scales (abridged). | 9606080v2 |
1997-01-09 | Molecular Hydrogen Absorption in the z= 1.97 Damped Lyman alpha Absorption system toward QSO 0013-004 | We present a new ultra-violet spectrum of the QSO 0013-004 with 0.9 \AA
resolution obtained with the MMT Blue spectrograph. The \upsilon = 0 - 0, 1 -
0, 2 - 0 and 3 - 0 Lyman bands of H_2 associated with the z = 1.9731 damped Ly
alpah absorption line system have been detected. The H_2 column density is
N(H_2) = 6.9 (\pm 1.6)\times 10^{19} cm^{-2}, and the Doppler parameter b =
15\pm 2 km/s. The populations of different rotational levels are measured and
used to derive the excitation temperatures. The estimated kinetic temperature
T_K\sim 70 K, and the total particle number density n(H) \sim 300 cm^{-3}. The
UV photoabsorption rate $\beta_0 \sim 6.7\times 10^{-9}$ s^{-1}, about a factor
of few times greater than that in a typical diffuse Milky Way interstellar
cloud. The total hydrogen column density is $N(H) = 6.4(\pm 0.5)\times 10^{20}
cm^{-2}$. The fractional H_2 abundance f = 2N(H_2)/(2N(H_2) + N(H I)) \sim 0.22
\pm 0.05 is the highest among all observed damped Ly\al absorbers. The high
fractional H_2 abundance is consistent with the inferred presence of dust and
strong C I absorption in this absorber. | 9701041v1 |
1997-02-06 | Abundance Patterns of Heavy Elements in Damped Lyman-Alpha Galaxies | We present a quantitative analysis of the abundances of heavy elements in
damped Ly-alpha galaxies in the sample of Lu et al. (1996). In particular, we
compare the observed gas-phase abundances with those expected when the
intrinsic (i.e., nucleosynthetic) pattern is the same as that in either the Sun
or in Galactic halo stars and when the depletion pattern is the same as that in
the warm Galactic interstellar medium, but with various values of the
dust-to-metals ratio. We find that the observations are equally consistent with
the solar and halo-star intrinsic patterns and that they favor some depletion,
the typical dust-to-metals ratio being 40%-90% of that in the Milky Way today.
However, neither intrinsic pattern matches the observations perfectly. For the
solar pattern, the discrepancy is mainly with [Mn/Fe], while for the halo-star
pattern, the discrepancy is with [Zn/Fe], [Ni/Fe], and possibly [Al/Fe]. Our
analysis does not support the claim by Lu et al. that the damped Ly-alpha
galaxies have halo-star abundance patterns and no dust depletion. | 9702066v2 |
1997-08-04 | Violent Relaxation, Phase Mixing, and Gravitational Landau Damping | This paper proposes a geometric interpretation of flows generated by the
collisionless Boltzmann equation (CBE), focusing on the coarse-grained approach
towards equilibrium. The CBE is a noncanonical Hamiltonian system with the
distribution function f the fundamental dynamical variable, the mean field
energy H[f] playing the role of the Hamiltonian and the natural arena of
physics being the infinite-dimensional phase space of distribution functions.
Every time-independent equilibrium f_0 is an energy extremal with respect to
all perturbations that preserve the constraints associated with Liouville's
Theorem, local energy minima corresponding to linearly stable equilibria. If an
initial f(t=0) is sufficiently close to some linearly stable lower energy f_0,
its evolution involves linear phase space oscillations about f_0 which, in many
cases, would be expected to exhibit linear Landau damping. If f(t=0) is far
from any stable extremal, the flow will be more complicated but, in general,
one would anticipate that the evolution involves nonlinear oscillations about
some lower energy f_0. In this picture, the coarse-grained approach towards
equilibrium usually termed violent relaxation is interpreted as nonlinear
Landau damping. The evolution of a generic initial f(t=0) involves a coherent
initial excitation, not necessarily small, being converted into incoherent
motion associated with nonlinear oscillations about some equilibrium f_0 which,
in general, will exhibit destructive interference. | 9708026v1 |
1998-11-23 | The Physical Nature of the Lyman Limit Systems | We analyze Keck HIRES observations of a Lyman limit system at z=2.652 toward
Q2231-00. These observations afford the most comprehensive study of the
physical properties of a LL system to date. By comparing the ionic column
densities for Fe^+, Fe^{++}, Si^+, and Si^{3+} against calculations derived
from the CLOUDY software package, we have strictly constrained the ionization
state of this system. This has enabled us to calculate accurate abundances of a
Lyman limit system for the first time at z > 2, e.g., [Fe/H] = -0.5 \pm 0.1. We
also derive a total hydrogen column density, log N(H) = 20.73 \pm 0.2, which is
comparable to values observed for the damped lya systems.
The system is special for exhibiting CII* 1335 absorption, allowing an
estimate of the electron density, n_e = 6.5 \pm 1.3 x 10^{-2} cm^{-3}. Coupling
this measurement with our knowledge of the ionization state, we derive the
following physical properties: (1) hydrogen volume density, n_H = 5.9 \pm 1.2 x
10^{-2} cm^{-3}, (2) path length, l = 3 \pm 1.6 kpc, and (3) ionizing
intensity, log J_{912} = -20.22 \pm 0.21. We point out that a number of the
physical properties (e.g. [Fe/H], N(H), n_H) resemble those observed for the
damped lya systems, which suggests this system may be the photoionized analog
of a damped system. The techniques introduced in this Letter should be
applicable to a number of Lyman limit systems and therefore enable a survey of
their chemical abundances and other physical properties. | 9811357v1 |
1998-12-03 | Gravity-Modes in ZZ Ceti Stars III. Eigenvalues and Eigenfuctions | We report on numerical calculations of nonadiabatic eigenvalues and
eigenfunctions for g-modes in ZZ Ceti variables. The spectrum of overstable
$l=1$ modes delineates the instability strip. Its blue edge occurs where
$\omega \tau_c \approx 1$ for the $n=1$ mode. Here $\omega$ is radian frequency
and $\tau_c$ is about four times the thermal timescale at the bottom of the
surface convection zone. As a ZZ Ceti cools, its convection zone deepens,
longer period modes become overstable, but the critical value of $\omega\tau_c$
separating overstable and damped modes rises. The latter is a consequence of
enhanced radiative damping for modes which propagate immediately below the
convection zone. The critical value of $\omega\tau_c$ is of observational
significance because modes with the smallest value of $\omega\tau_c$ are most
observable photometrically. Maximum periods for overstable modes predicted for
our cooler model envelopes are about a factor two longer than the observational
upper limit of $1,200\s$. We assess a number of plausible resolutions for this
discrepancy among which convective overshoot and nonlinear saturation look
promising. The nonadiabatic eigenfunctions enable us to predict relative
amplitudes and phases of photospheric variations of flux and velocity,
quantities made accessible by recent observations. We also present asymptotic
formula for damping rates of high order modes, a result of consequence for
future investigations of nonlinear saturation of the amplidues of overstable
modes. | 9812085v1 |
1999-01-19 | Collisionless Dissipative Nonlinear Alfven Waves: Nonlinear Steepening, Compressible Turbulence, and Particle Trapping | The magnetic energy of nonlinear Alfven waves in compressible plasmas may be
ponderomotively coupled only to ion-acoustic quasi-modes which modulate the
wave phase velocity and cause wave-front steepening. In the collisionless
plasma with $\beta\not=0$, the dynamics of nonlinear Alfven wave is also
affected by the resonant particle-wave interactions. Upon relatively rapid
evolution (compared to the particle bounce time), the quasi-stationary wave
structures, identical to the so called (Alfvenic) Rotational Discontinuities,
form, the emergence and dynamics of which has not been previously understood.
Collisionless (Landau) dissipation of nonlinear Alfven waves is also a
plausible and natural mechanism of the solar wind heating. Considering a
strong, compressible, Alfvenic turbulence as an ensemble of randomly
interacting Alfvenic discontinuities and nonlinear waves, it is shown that
there exist two distinct phases of turbulence. What phase realizes depends on
whether this collisionless damping is strong enough to provide adequate energy
sink at all scales and, thus, to support a steady-state cascade of the wave
energy. In long-time asymptotics, however, the particle distribution function
is affected by the wave magnetic fields. In this regime of nonlinear Landau
damping, resonant particles are trapped in the quasi-stationary Alfvenic
discontinuities, giving rise to a formation of a plateau on the distribution
function and quenching collisionless damping. Using the virial theorem for
trapped particles, it is analytically demonstrated that their effect on the
nonlinear dynamics of such discontinuities is non-trivial and forces a
significant departure of the theory from the conventional paradigm. | 9901257v1 |
2000-06-06 | A Model of Metallicity Evolution in the Early Universe | We apply the phenomenological model used to explain the abundances of Fe and
r-process elements in very metal-poor stars in the Galaxy to [Fe/H] of damped
Ly alpha systems. It is assumed that the first stars formed after the Big Bang
were very massive and promptly enriched the interstellar medium to [Fe/H] ~ -3,
at which metallicity formation of normal stars took over. Subsequent Fe
enrichment was provided by Type II supernovae. The range of [Fe/H] at a given
redshift z for damped Ly alpha systems is explained by the time t* after the
Big Bang at which normal star formation started in an individual protogalactic
system. The average t* is approx 80% the age of the universe for damped Ly
alpha systems at z approx 1.5 to 4.5, indicating a long delay between the Big
Bang and the turn-on of protogalaxies. It is inferred that a substantial
fraction of the total baryonic matter may not have been aggregated into
protogalaxies where normal star formation had occurred down to z ~ 1.5. The
data near z = 2.2 suggest that the rate of turn-on of protogalaxies was
initially very low and slowly reached a maximum at ~ 3 Gyr after the Big Bang.
This may be important in understanding the rate of formation of quasars. | 0006082v2 |
2000-09-27 | Lensing properties of 7 damped Lyman-alpha absorbing galaxy-QSO pairs | Le Brun et al. (1997) presented the first identifications of the galaxies
giving rise to 7 intermediate redshift damped Ly-alpha (DLA) absorption
systems. Here, we study the gravitational lensing properties of these
foreground galaxies based on their observed optical appearance and on the
absence of any secondary lensed quasar image. We consider the possibility that
any secondary image be hidden due to extinction by dust, but find it unlikely.
We derive upper limits on the amplification factor affecting the luminosity of
the background quasars; in each case, this factor is found to be less than 0.3
mag. We also obtain upper limits on the total mass of the damped Ly-alpha
galaxies, within radii equal to the quasar impact parameters. Mass-to-light
ratios are found to be consistent with existing estimates based on X-ray
emission or on motion of dwarf satellites. Although we show that lensing is not
important in this sample, we note that existing DLA surveys used to determine
the cosmological density of gas at z<1 are based on samples of quasars brighter
than the ones considered here and for which the amplification bias is likely to
be stronger. | 0009433v1 |
2000-11-14 | Sharp HI edges at high z: the gas distribution from Damped Lyman-alpha to Lyman-limit absorption systems | We derive the distribution of neutral and ionized gas in high redshift clouds
which are optically thick to hydrogen ionizing radiation, using published data
on Lyman-limit and Damped Lyman-alpha absorption systems in the redshift range
1.75 < z < 3.25. We assume that the distribution of the hydrogen total (HI+HII)
column density in the absorbers follows a power law K N_H^{-alpha}, whereas the
observed HI column density distribution deviates from a pure power law as a
result of ionization from a background radiation field. Comparison of the
models and observations give Maximum Likelihood solutions for the exponent
alpha and for X, the value of log(N_H/N_HI) when the Lyman-limit optical depth
is unity: alpha=2.7^{+1.0}_{-0.7} and X=2.75\pm0.35. X is much lower than what
would be obtained for a gaseous distribution in equilibrium under its own
gravity but the ratio of dark matter to gas density is not well constrained
being log(eta_0)=1.1\pm 0.8. An extrapolation of our derived power law
distribution towards systems of lower column density, the Lyman-alpha forest,
favours models with log(eta_0) < 1.1 and alpha=2.7-3.3. With alpha appreciably
larger than 2, Lyman-limit systems contain more gas than Damped Lyman-alpha
systems and Lyman-alpha forest clouds even more. Estimates of the cosmological
gas and dark matter density due to absorbers of different column density around
z=2.5 are also given. | 0011268v1 |
2000-11-29 | Implications of 21cm observations for damped Ly-$α$ systems | We present Giant Metrewave Radio Telescope HI 21cm absorption observations,
of candidate and confirmed damped Lyman-$\alpha$ systems (DLAS). The derived
spin temperatures (T_s) are in all cases $\sim 1000$ K or higher. We have also
collated from the literature a list of DLAS for which 21cm observations exist,
and discuss their implications for the nature of the absorbers.
A cross-comparison of the 21cm profiles with low ionization metal profiles
shows that the 21cm absorption coincides in velocity with the deepest metal
line feature. This is consistent with models in which the deep metal line
features arise from discrete clouds but not with models where the deepest
features are the result of velocity crowding.
We also find that the typical derived spin temperatures of DLAS are
considerably higher than those in the Galaxy or nearby spirals. The only
exceptions are DLAS which are known to be associated with the disks of spirals;
these do, in fact, show low spin temperatures. In a multi-phase medium,the
derived T_s is a weighted average of the temperatures of the individual phases.
High derived T_s values are hence to be expected from small, low metallicity
objects, since these objects should have a lower fraction of the cold phase in
their ISM as compared to large galaxies. The high T_s in DLAS is hence
consistent with their observed low metallicities as well as with recent
observations that DLAS are also associated with dwarf/LSB galaxies. Finally, we
suggest that the following trend may be identified: at low redshift, damped
absorption arises from a range of systems, including spiral galaxy disks,
while, at high redshift, absorption occurs predominantly in smaller systems.
(Abridged) | 0011540v1 |
2001-01-18 | A Comprehensive Statistical Analysis of the Gas Distribution in Lyman-limit and Damped Lyman-alpha Absorption Systems | In this paper we show how to use data on Lyman-limit and Damped Lyman-alpha
absorption systems to derive the hydrogen ionization fractions and the
distribution of the face-on total gas column density. We consider axially
symmetric, randomly oriented absorbers, ionized by an external background
radiation field in order to relate the face-on total gas distribution to that
of the neutral hydrogen observed along the line of sight. We devise a
statistical procedure based on the Maximum Likelihood criterion, that is able
to treat simultaneously data coming from different surveys and statistically
recovers the "true" column densities in the presence of large uncertainties:
this is especially important for Lyman-limit systems which leave an
unmeasurable residual flux at wavelengths shorter than the Lyman break. We make
use of simulated data to look for possible observational biases and extensively
test our procedure. For a large statistical sample of real data in the redshift
range [1.75,3.25] (collected from all published surveys) our Maximum Likelihood
procedure gives a power-law slope for the total hydrogen distribution of -2.7.
All together Lyman-limit systems therefore contain more gas than Damped
Lyman-alpha systems. Analysis of data at other redshifts shows that more
observations are needed to reach a compelling evidence for a cosmological
evolution of the slope of the gas distribution. | 0101335v1 |
2001-04-29 | The First Detection of Co in a Damped Lyman Alpha System | The study of elemental abundances in Damped Lyman Alpha systems (DLAs) at
high redshift represents one of our best opportunities to probe galaxy
formation and chemical evolution at early times. By coupling measurements made
in high z DLAs with our knowledge of abundances determined locally and with
nucleosynthetic models, we can start to piece together the star formation
histories of these galaxies. Here, we discuss the clues to galactic chemical
evolution that may be gleaned from studying the abundance of Co in DLAs. We
present high resolution echelle spectra of two QSOs, Q2206-199 and Q1223+17,
both already known to exhibit intervening damped systems. These observations
have resulted in the first ever detection of Co at high redshift, associated
with the z= 1.92 DLA in the sightline towards Q2206-199. We find that the
abundance of Co is approximately 1/4 solar and that there is a clear
overabundance relative to iron, [Co/Fe] = +0.31 +/- 0.05. From the abundance of
Zn, we determine that this is a relatively metal-rich DLA, with a metallicity
approximately 1/3 solar. Therefore, this first detection of Co is similar to
the marked overabundance relative to Fe seen in Galactic bulge and thick disk
stars. | 0104466v1 |
2001-06-22 | Self-Absorption of Ionizing Radiation and Extended Lyman Alpha Emission in High- Redshift QSOs | We calculate the neutral hydrogen column density of self-absorption in QSOs
predicted in a model where the QSOs are located in the same halos that contain
the gas in damped Lya absorption systems. The model is parameterized by the
probability P_0 that any halo has an active QSO. We assume that the QSOs ionize
the gas, but do not expel or heat it. The derived HI column densities produce
negligible Lyman limit absorption, even in the lowest luminosity QSOs, with an
optical depth of only ~ 10% for luminosity L=0.01 L_*, when P_0=10^{-2}. We
also compute the HeII Lyman limit self-absorption, which is slightly higher but
still negligible. The self-absorption can be higher if the gas is highly
clumped; only in this case the overall emissivity from QSOs could be
significantly reduced due to absorption by the known damped Lya systems, to
affect the predicted intensity of the ionizing background or the epoch of HeII
reionization. The presence of the gas associated with damped absorption systems
around QSOs could also be detected from the narrow Lya emission line, which
should have and angular extent of 0.1 to 1'' in typical high-redshift QSOs. | 0106424v2 |
2001-06-22 | Compressible MHD Turbulence in Interstellar Plasmas | Radio-wave scintillation observations reveal a nearly Kolmogorov spectrum of
density fluctuations in the ionized interstellar medium. Although this density
spectrum is suggestive of turbulence, no theory relevant to its interpretation
exists. We calculate the density spectrum in turbulent magnetized plasmas by
extending the theory of incompressible MHD turbulence given by Goldreich &
Sridhar to include the effects of compressibility and particle transport. Our
most important results are as follows. (1) Density fluctuations are due to the
slow mode and the entropy mode. Both modes are passively mixed by the cascade
of shear Alfven waves. Since the shear Alfven waves have a Kolmogorov spectrum,
so do the density fluctuations. (2) Observed density fluctuation amplitudes
imply either that the magnetic and gas pressures are comparable, or that the
outer scale of the turbulence is very small. (3) A high degree of ionization is
required for the cascade to survive damping by neutrals and thereby to extend
to small lengthscales. Regions that are insufficiently ionized produce density
fluctuations only on lengthscales larger than the neutral damping scale. These
regions may account for the excess of power that is found on large scales. (4)
Both the entropy mode and the slow mode are damped on lengthscales below that
at which protons can diffuse across an eddy during the eddy's turnover time.
Consequently, eddies whose extents along the magnetic field are smaller than
the proton collisional mean free path do not contribute to the density
spectrum. However, in MHD turbulence eddies are highly elongated along the
magnetic field. From an observational perspective, the relevant lengthscale is
that transverse to the magnetic field. Thus the cut-off lengthscale for density
fluctuations is significantly smaller than the proton mean free path. | 0106425v1 |
2001-11-20 | Collisional Cascades in Planetesimal Disks I. Stellar Flybys | We use a new multiannulus planetesimal accretion code to investigate the
evolution of a planetesimal disk following a moderately close encounter with a
passing star. The calculations include fragmentation, gas and
Poynting-Robertson drag, and velocity evolution from dynamical friction and
viscous stirring. We assume that the stellar encounter increases planetesimal
velocities to the shattering velocity, initiating a collisional cascade in the
disk. During the early stages of our calculations, erosive collisions damp
particle velocities and produce substantial amounts of dust. For a wide range
of initial conditions and input parameters, the time evolution of the dust
luminosity follows a simple relation, L_d/L_{\star} = L_0 / [alpha +
(t/t_d)^{beta}]. The maximum dust luminosity L_0 and the damping time t_d
depend on the disk mass, with L_0 proportional to M_d and t_d proportional to
M_d^{-1}. For disks with dust masses of 1% to 100% of the `minimum mass solar
nebula' (1--100 earth masses at 30--150 AU), our calculations yield t_d approx
1--10 Myr, alpha approx 1--2, beta = 1, and dust luminosities similar to the
range observed in known `debris disk' systems, L_0 approx 10^{-3} to 10^{-5}.
Less massive disks produce smaller dust luminosities and damp on longer
timescales. Because encounters with field stars are rare, these results imply
that moderately close stellar flybys cannot explain collisional cascades in
debris disk systems with stellar ages of 100 Myr or longer. | 0111384v1 |
2002-02-11 | The Contribution of HI-rich Galaxies to the Damped Lyman-alpha Absorber Population at z=0 | We present a study of the expected properties of the low redshift damped
Lyman-alpha absorber population determined from a sample of HI-selected
galaxies in the local universe. Because of a tight correlation between the HI
mass and HI cross-section, which we demonstrate spans all galaxy types, we can
use our HI-selected sample to predict the properties of the absorption line
systems. We use measurements of the number density and HI cross-section of
galaxies to show that the total HI cross-section at column densities sufficient
to produce damped Lyman-alpha absorption is consistent with no evolution of the
absorber population. We also find that the dN/dz distribution is dominated by
galaxies with HI masses near 10^9 Msolar. However, because of the large
dispersion in the correlation between HI mass and stellar luminosity, we find
that the distribution of dN/dz as a function of L_J is fairly flat.
Additionally, we examine the line widths of the HI-selected galaxies and show
that there may be evolution in the kinematics of HI-rich galaxies, but it is
not necessary for the higher redshift population to contain a greater
proportion of high mass galaxies than we find locally. | 0202216v2 |
2002-03-18 | Monte Carlo Simulation of Lyman Alpha Scattering and Application to Damped Lyman Alpha Systems | A Monte Carlo code to solve the transfer of Lyman alpha (Lya) photons is
developed, which can predict the Lya image and two-dimensional Lya spectra of a
hydrogen cloud with any given geometry, Lya emissivity, neutral hydrogen
density distribution, and bulk velocity field. We apply the code to several
simple cases of a uniform cloud to show how the Lya image and emitted line
spectrum are affected by the column density, internal velocity gradients, and
emissivity distribution. We then apply the code to two models for damped Lya
absorption systems: a spherical, static, isothermal cloud, and a flattened,
axially symmetric, rotating cloud. If the emission is due to fluorescence of
the external background radiation, the Lya image should have a core
corresponding to the region where hydrogen is self-shielded. The emission line
profile has the characteristic double peak with a deep central trough. We show
how rotation of the cloud causes the two peaks to shift in wavelength as the
slit is perpendicular to the rotation axis, and how the relative amplitude of
the two peaks is changed. In reality, damped Lya systems are likely to have a
clumpy gas distribution with turbulent velocity fields, which should smooth the
line emission profile, but should still leave the rotation signature of the
wavelength shift across the system. | 0203287v2 |
2002-04-09 | The Non-Damped Nature of Twelve Low-Redshift Damped Lyman Alpha Candidate Systems | Hubble Space Telescope (HST) UV spectroscopy of 12 candidate low-redshift
damped Lyman alpha (DLA) systems in 11 QSOs (z=0.103 in Q0054+144, z=0.969 and
z=0.987 in Q0302-223, z=0.478 in Q0454-220, z=1.476 in Q1047+550, z=1.070 in
Q1206+459, z=1.228 in Q1247+267, z=0.399 in Q1318+290B, z=0.519 in Q1329+412,
z=0.276 in Q1451-375, z=0.204 in Q2112+059, z=0.263 in Q2251+113) are
presented; the observations demonstrate that they are not DLAs with
$N(HI)\ge2\times10^{20}$ atoms cm$^{-2}$. In all cases except two the systems
either do not exist or are well below the DLA threshold column density; the
exceptions are a z=0.474 system in Q0454-220 which has $N(HI)=3\times10^{19}$
atoms cm$^{-2}$ and a z=1.223 system in Q1247+267 which has
$N(HI)=8\times10^{19}$ atoms cm$^{-2}$. Despite the availability of data in the
HST archives demonstrating that these are not suitable targets, many have
unfortunately been approved for observation with Chandra, Gemini, and/or HST
with the intent of doing followup work on low-redshift DLAs. Furthermore, these
results indicate that the low-redshift DLA statistics derived from IUE spectra
and presented by Lanzetta, Wolfe, & Turnshek (1995) and Wolfe et al. (1995) are
invalid. | 0204155v1 |
2002-05-17 | High matter density peaks from UVES observations of QSO pairs: correlation properties and chemical abundances | We study the transverse clustering properties of high matter density peaks as
traced by high column density absorption systems (either Lyman limit systems
characterized by N(HI)> 2 x 10^{17} cm^{-2} or CIV systems with W_{r}> 0.5 A)
at redshifts between 2 and 3 with UVES spectra of two QSO pairs (UM680/UM681 at
56 arcsec angular separation and Q2344+1228/Q2343+1232 at 5 arcmin angular
separation) and a QSO triplet (Q2139-4433/Q2139-4434/Q2138-4427 at 1, 7 and 8
arcmin angular separation). We find 3 damped Ly-alpha systems (N(HI)> 2 x
10^{20} cm^{-2}): 2 coinciding with strong metal systems in the nearby line of
sight and 1 matching the emission redshift of the paired QSO; plus 7 Lyman
limit systems: 4 forming two matching couples and 3 without a corresponding
metal system within ~3000 km/s in the coupled line of sight. In summary, we
detect five out of ten matching systems within 1000 km/s, indicating a highly
significant overdensity of strong absorption systems over separation lengths
from ~1 to 8 h^{-1} Mpc. The observed coincidences could arise in gas due to
starburst-driven superwinds associated with a quasar or a galaxy, or gas
belonging to large scale structures like filaments or sheets. We also determine
chemical abundance ratios for three damped Ly-alpha systems. In particular, for
the damped system at z ~ 2.53788 in the spectrum of Q2344+1228, new estimates
of the ratios O/Fe, C/Fe are obtained: [C/Fe]<0.06, [O/Fe]<0.2. They indicate
that O and C are not over-solar in this system. | 0205299v1 |
2002-08-28 | Complex rotation with internal dissipation. Applications to cosmic-dust alignment and to wobbling comets and asteroids | Neutron stars, asteroids, comets, cosmic-dust granules, spacecraft, as well
as whatever other freely spinning body dissipate energy when they rotate about
any axis different from principal. We discuss the internal-dissipation-caused
relaxation of a freely precessing rotator towards its minimal-energy mode (mode
that corresponds to the spin about the maximal-inertia axis). While the body
nutates at some rate, the internal stresses and strains within the body
oscillate at frequencies both higher and lower than this rate. The internal
dissipation takes place mostly the second and higher harmonics. We discuss the
application of our findings to asteroids. Regarding the comets, estimates show
that the currently available angular resolution of spacecraft-based instruments
makes it possible to observe wobble damping within year- or maybe even
month-long spans of time. We also discuss cosmic-dust astrophysics; in
particular, the role played by precession damping in the dust alignment. We
show that this damping provides coupling of the grain's rotational and
vibrational degrees of freedom; this entails occasional flipping of dust grains
due to thermal fluctuations. During such a flip, grain preserves its angular
momentum, but the direction of torques arising from H2 formation reverses. As a
result, flipping grain will not rotate fast in spite of the action of
uncompensated H2 formation torques. The grains get ``thermally trapped,'' and
their alignment is marginal. | 0208489v1 |
2003-06-16 | Damping of Tensor Modes in Cosmology | An analytic formula is given for the traceless transverse part of the
anisotropic stress tensor due to free streaming neutrinos, and used to derive
an integro-differential equation for the propagation of cosmological
gravitational waves. The solution shows that anisotropic stress reduces the
squared amplitude by 35.6 % for wavelengths that enter the horizon during the
radiation-dominated phase, independent of any cosmological parameters. This
decreases the tensor temperature and polarization correlation functions for
these wavelengths by the same amount. The effect is less for wavelengths that
enter the horizon at later times. At the longest wavelengths the decrease in
the tensor correlation functions due to neutrino free streaming ranges from
10.7% for $\Omega_Mh^2=0.1$ to 9.0% for $\Omega_Mh^2=0.15$. An Appendix gives a
general proof that tensor as well as scalar modes satisfy a conservation law
for perturbations outside the horizon, even when the anisotropic stress tensor
is not negligible. | 0306304v2 |
2003-12-30 | Nonlinear Pulsations in Differentially Rotating Neutron Stars: Mass-Shedding-Induced Damping and Splitting of the Fundamental Mode | We study small-amplitude, nonlinear pulsations of uniformly and
differentially rotating neutron stars employing a two-dimensional evolution
code for general-relativistic hydrodynamics. Using Fourier transforms at
several points inside the star, both the eigenfrequencies and two-dimensional
eigenfunctions of pulsations are extracted. The centrifugal forces and the
degree of differential rotation have significant effects on the
mode-eigenfunction. We find that near the mass-shedding limit, the pulsations
are damped due to shocks forming at the surface of the star. This new damping
mechanism may set a small saturation amplitude for modes that are unstable to
the emission of gravitational waves. After correcting for the assumption of the
Cowling approximation (used in our numerical code), we construct empirical
relations that predict the range of gravitational-wave frequencies from
quasi-periodic post-bounce oscillations in the core collapse of massive stars.
We also find that the fundamental quasi-radial mode is split, at least in the
Cowling approximation and mainly in differentially rotating stars, into two
different sequences. | 0312648v2 |
2004-01-16 | Simulating stochastically excited oscillations. The mode lifetime of xi Hya | The discovery of solar-like oscillations in the giant star xy Hya (G7III) was
reported by Frandsen et al. (2002). Their frequency analysis was very limited
due to alias problems in the data set (caused by single-site observations). The
extent to which the aliasing affected their analysis was unclear due to the
unknown damping time of the stellar oscillation modes. In this paper we
describe a simulator created to generate time series of stochastically excited
oscillations, which takes as input an arbitrary window function and includes
both white and non-white noise. We also outline a new method to compare a large
number of simulated time series with an observed time series to determine the
damping time, amplitude, and limited information on the degree of the
stochastically excited modes. For xi Hya we find the most likely amplitude to
be ~ 2 m/s, in good agreement with theory (Houdek & Gough, 2002), and the most
likely damping time to be ~ 2 days, which is much shorter than the theoretical
value of 15-20 days calculated by Houdek & Gough (2002). | 0401331v1 |
2004-10-13 | On the Importance of Local Sources of Radiation in Cosmological Absorption Systems | An upper limit to the importance of local sources of radiation compared to
the cosmic background in cosmological absorption systems is derived, as a
simple consequence of the conservation of surface brightness. The limit depends
only on the rate of incidence of the absorbers and the mean free path of the
radiation. It is found that, on average, the ionizing radiation intensity from
local sources in Lyman limit systems at z>2 must be less than half of the
intensity of the cosmic background. In absorbers with column densities much
lower than Lyman limit systems, the local source contribution must be
negligible. The limit on the ratio of local source to background intensities is
then applied to the class of damped Lya absorption systems with detectable
excited CII lines. A cooling rate of the gas in these systems has been measured
by Wolfe et al., who assumed that the balancing heating source is photoelectric
heating on dust by light at ~ 1500 A . The intensity from local star formation
at this wavelength in this class of damped Lya systems is found to be at most ~
3 times the background intensity. If the heating source is indeed photoelectric
heating of dust, the background created by sources associated with damped Lya
systems can then be estimated from the average cooling rates measured in the
absorbers. Current results yield a background intensity higher than previous
estimates based on observed galaxy and quasar luminosity functions, although
with a large uncertainty. The possibility of other sources of heating, such as
shock-heating in a turbulent medium, should be explored. | 0410315v1 |
2005-04-04 | Relativistic r-modes and Shear viscosity: regularizing the continuous spectrum | Within a fully relativistic framework, we derive and solve numerically the
perturbation equations of relativistic stars, including the stresses produced
by a non-vanishing shear viscosity in the stress-energy tensor. With this
approach, the real and imaginary parts of the frequency of the modes are
consistently obtained. We find that, approaching the inviscid limit from the
finite viscosity case, the continuous spectrum is regularized and we can
calculate the quasi-normal modes for stellar models that do not admit solutions
at first order in perturbation theory when the coupling between the polar and
axial perturbations is neglected. The viscous damping time is found to agree
within factor 2 with the usual estimate obtained by using the eigenfunctions of
the inviscid limit and some approximation for the energy dissipation integrals.
We find that the frequencies and viscous damping times for relativistic
$r-$modes lie between the Newtonian and Cowling results. We compare the results
obtained with homogeneous, polytropic and realistic equations of state and find
that the frequencies depend only on the rotation rate and on the compactness
parameter (M/R), being almost independent of the equation of state. Our
numerical results for realistic neutron stars give viscous damping times with
the same dependence on mass and radius as previously estimated, but
systematically larger of about 60%. | 0504062v1 |
2005-04-29 | Evidence for a magnitude-dependent bias in the Hamburg/ESO Survey for Damped Lyman-alpha Systems | We present preliminary results from the Hamburg/ESO survey for Damped
Ly-alpha (hereafter, DLA) Systems. This survey is characterized by (i) the good
knowledge of the biases affecting the parent QSO survey, (ii) the brightness
and (iii) the relatively wide magnitude distribution of the background QSOs.
Therefore, it is well-suited to study possible magnitude-dependent biases in
DLA surveys, such as the one expected from dust obscuration. We have
systematically searched for damped Lyman-alpha line candidates in 5 A
resolution spectra of the 188 QSOs that constitute our statistical sample.
These candidates have later been reobserved with UVES at the ESO--Very Large
Telescope (VLT) for confirmation and accurate N(HI) measurements. In the
redshift range covered by the survey, 19 DLA systems have been discovered. Over
the whole survey, we find that the number density, n(z), and cosmological
density of gas, Omega_gas, have comparable values to the ones obtained by
CORALS (Ellison et al. 2001). However, the number densities of DLA systems n(z)
in two sub-samples of equal absorption distance path defined by the magnitude
of the background QSOs differ by a factor of about 5. We estimate that the
probability that n(z) is equal in the two sub-samples is < 0.003. A similar,
only slightly less significant difference is found for Omega_gas. | 0504657v1 |
2005-07-06 | The free precession and libration of Mercury | An analysis based on the direct torque equations including tidal dissipation
and a viscous core-mantle coupling is used to determine the damping time scales
of O(10^5) years for free precession of the spin about the Cassini state and
free libration in longitude for Mercury. The core-mantle coupling dominates the
damping over the tides by one to two orders of magnitude for the plausible
parameters chosen. The short damping times compared with the age of the solar
system means we must find recent or on-going excitation mechanisms if such free
motions are found by the current radar experiments or the future measurement by
the MESSENGER and BepiColombo spacecraft that will orbit Mercury. We also show
that the average precession rate is increased by about 30% over that obtained
from the traditional precession constant because of a spin-orbit resonance
induced contribution by the C_{22} term in the expansion of the gravitational
field. The C_{22} contribution also causes the path of the spin during the
precession to be slightly elliptical with a variation in the precession rate
that is a maximum when the obliquity is a minimum. An observable free
precession will compromise the determination of obliquity of the Cassini state
and hence of C/MR^2 for Mercury, but a detected free libration will not
compromise the determination of the forced libration amplitude and thus the
verification of a liquid core | 0507117v1 |
2005-10-12 | Ly-alpha Radiative Transfer in Cosmological Simulations and Application to a z~8 Emitter | We develop a Ly-alpha radiative transfer (RT) Monte Carlo code for
cosmological simulations.High resolution,along with appropriately treated
cooling can result in simulated environments with very high optical
depths.Thus,solving the Ly-alpha RT problem in cosmological simulations can
take an unrealistically long time.For this reason,we develop methods to speed
up the Ly-alpha RT.With these accelerating methods,along with the
parallelization of the code,we make the problem of Ly-alpha RT in the complex
environments of cosmological simulations tractable.We test the RT code against
simple Ly-alpha emitter models,and then we apply it to the brightest Ly-alpha
emitter of a gasdynamics+N-body Adaptive Refinement Tree (ART) simulation at
z~8.We find that recombination rather than cooling radiation Ly-alpha photons
is the dominant contribution to the intrinsic Ly-alpha luminosity of the
emitter,which is ~4.8x10e43 ergs/s.The size of the emitter is pretty
small,making it unresolved for currently available instruments.Its spectrum
before adding the Ly-alpha Gunn-Peterson absorption (GP) resembles that of
static media,despite some net inward radial peculiar motion.This is because for
such high optical depths as those in ART simulations,velocities of order some
hundreds km/s are not important.We add the GP in two ways.First we assume no
damping wing,corresponding to the situation where the emitter lies within the
HII region of a very bright quasar,and second we allow for the damping
wing.Including the damping wing leads to a maximum line brightness suppression
by roughly a factor of ~62.The line fluxes,even though quite faint for current
ground-based telescopes,should be within reach for JWST. | 0510347v2 |
2005-12-05 | Kinematics and star formation activity in the z=2.03954 damped Lyman-alpha system towards PKS 0458-020 | We present UVES observations of the log N(HI)= 21.7 damped Lyman-alpha system
at z=2.03954 towards the quasar PKS 0458-020. HI Lyman-alpha emission is
detected in the center of the damped Lyman-alpha absorption trough.
Metallicities are derived for MgII, SiII, PII, CrII, MnII, FeII and ZnII and
are found to be -1.21\pm0.12, -1.28\pm0.20, -1.54\pm0.11, -1.66\pm0.10,
-2.05\pm0.11, -1.87\pm0.11, -1.22\pm0.10, respectively, relative to solar. The
depletion factor is therefore of the order of [Zn/Fe]=0.65. We observe metal
absorption lines to be blueshifted compared to the Lyman-alpha emission up to a
maximum of 100 and 200 km/s for low and high-ionization species respectively.
This can be interpreted either as the consequence of rotation in a large
(~7kpc) disk or as the imprint of a galactic wind. The star formation rate
(SFR) derived from the Lyman-alpha emission, 1.6 solar masses/yr, is compared
with that estimated from the observed CII* absorption. No molecular hydrogen is
detected in our data, yielding a molecular fraction f<-6.52. This absence of H2
can be explained as the consequence of a high ambient UV flux which is one
order of magnitude larger than the radiation field in the ISM of our Galaxy and
originates in the observed emitting region. | 0512118v1 |
2006-02-14 | On the magnetic structure and wind parameter profiles of Alfven wave driven winds in late-type supergiant stars | Cool stars at giant and supergiant evolutionary phases present low velocity
and high density winds, responsible for the observed high mass-loss rates.
Although presenting high luminosities, radiation pressure on dust particles is
not sufficient to explain the wind acceleration process. Among the possible
solutions to this still unsolved problem, Alfven waves are, probably, the most
interesting for their high efficiency in transfering energy and momentum to the
wind. Typically, models of Alfven wave driven winds result in high velocity
winds if they are not highly damped. In this work we determine
self-consistently the magnetic field geometry and solve the momentum, energy
and mass conservation equations, to demonstrate that even a low damped Alfven
wave flux is able to reproduce the low velocity wind. We show that the magnetic
fluxtubes expand with a super-radial factor S>30 near the stellar surface,
larger than that used in previous semi-empirical models. The rapid expansion
results in a strong spatial dilution of the wave flux. We obtained the wind
parameter profiles for a typical supergiant star of 16 M_sun. The wind is
accelerated in a narrow region, coincident with the region of high divergence
of the magnetic field lines, up to 100 km/s. For the temperature, we obtained a
slight decrease near the surface for low damped waves, because the wave heating
mechanism is less effective than the radiative losses. The peak temperature
occurs at 1.5 r_0 reaching 6000 K. Propagating outwards, the wind cools down
mainly due to adiabatic expansion. | 0602305v1 |
2006-03-17 | Electron impact excitation of Helium-like ions up to n=4 levels including radiation damping | Helium-like ions provide the most important X-ray spectral diagnostics in
high temperature fusion and astrophysical plasmas. We previously presented
computed collision strengths for O~VII including relativistic fine structure,
levels up to the $n=4$ complex and radiation damping of autoionizing
resonances. We have extended this work to other He-like ions (N, Ne, Mg, Al,
Si, S, Ca). The calculations are carried out using the Breit-Pauli R-matrix
(BPRM) method with a 31-level eigenfunction expansion. Collision strengths for
the principal lines important in X-ray plasma diagnostics, w, x, y and z,
corresponding to the 4 transitions to the ground level 1s^2(^1S_0) <-
1s2p(^1P^o_1), 1s2p(^3P^o_2), 1s2p(^3P^o_1), 1s2s(^3S_1), are explicitly shown.
We find the effect of radiation damping to be significant for the forbidden
transitions in heavier He-like ions, which should affect the diagnostic line
ratios. We extrapolated the collision strengths to their values at infinite
energy using the Burgess-Tully extrapolation technique. This is required to
calculate the Maxwellian average collision strengths at high temperature. We
show that the coupling between dipole allowed and inter-combination transitions
affects increasingly the effective collision strengths for the n ^1S_0 - n'
^3P_1 transition as the charge of the ion increases. This clearly affects the
treatment of the extrapolation toward the infinite energy point of the
collision strength. This work is carried out as part of the Iron Project-RmaX
Network. | 0603482v1 |
2006-07-25 | Metal-rich Damped/sub-Damped Lyman-alpha Quasar Absorbers at z<1 | Damped Lyman-alpha absorbers (DLAs), seen in absorption against a background
quasar, provide the most detailed probes available of element abundances in the
Universe over > 90 % of its age. DLAs can be used to observationally measure
the global mean metallicity in the Universe and its evolution with time.
Paradoxically, these observations are more difficult at lower redshifts, where
the absorber rest-frame UV spectra are cut-off due to the atmospheric
absorption. We present here high-resolution VLT/UVES observations of several
elements contained in three DLAs and one sub-DLA with 0.6<z_abs<0.9. We detect
Mg I, Mg II, Fe II, Zn II, Cr II, Mn II, Ti II and Ca II. Our observations more
than double the high-resolution sample of [Zn/H] at z<1. We also report the
discovery of three metal-rich systems, whereas most previous measurements show
low N(HI)-weighted mean metallicity projecting to about 1/6th solar level at
z=0. We derive [Zn/H]=-0.11+/-0.04 at z_abs=0.725, [Zn/H]=-0.54+/-0.20 at
z_abs=0.740 and [Zn/H]=-0.49+/-0.22 at z_abs=0.652, plus one additional upper
limit ([Zn/H]<-0.36 at z_abs=0.842). These measurements confirm the existence
of quasar absorbers with relatively high metallicities based on abundance
estimates free from the effect of dust depletion. Possible implications of
these results for the metallicity of neutral gas phase in the past ~ 8 Gyr are
presented and compared with models. | 0607561v1 |
1994-09-29 | Avalanches in the Weakly Driven Frenkel-Kontorova Model | A damped chain of particles with harmonic nearest-neighbor interactions in a
spatially periodic, piecewise harmonic potential (Frenkel-Kontorova model) is
studied numerically. One end of the chain is pulled slowly which acts as a weak
driving mechanism. The numerical study was performed in the limit of infinitely
weak driving. The model exhibits avalanches starting at the pulled end of the
chain. The dynamics of the avalanches and their size and strength distributions
are studied in detail. The behavior depends on the value of the damping
constant. For moderate values a erratic sequence of avalanches of all sizes
occurs. The avalanche distributions are power-laws which is a key feature of
self-organized criticality (SOC). It will be shown that the system selects a
state where perturbations are just able to propagate through the whole system.
For strong damping a regular behavior occurs where a sequence of states
reappears periodically but shifted by an integer multiple of the period of the
external potential. There is a broad transition regime between regular and
irregular behavior, which is characterized by multistability between regular
and irregular behavior. The avalanches are build up by sound waves and shock
waves. Shock waves can turn their direction of propagation, or they can split
into two pulses propagating in opposite directions leading to transient
spatio-temporal chaos. PACS numbers: 05.70.Ln,05.50.+q,46.10.+z | 9409006v1 |
1998-06-21 | Collective intersubband transitions in quantum wells: a comparative density-functional study | We use time-dependent (current) density functional theory to study collective
transitions between the two lowest subbands in GaAs/AlGaAs quantum wells. We
focus on two systems where experimental results are available: a wide single
and a narrow asymmetric double well. The aim is to calculate frequency and
linewidth of collective electronic modes damped via electron-electron
interaction only. Since Landau damping is not effective here, the dominant
damping mechanism involves dynamical exchange-correlation effects such as
multipair production. To capture these effects, one has to go beyond the widely
used adiabatic local density approximation (ALDA) and include retardation. We
perform a comparative study of two approaches which fall in this category: the
dynamical extension of the ALDA by Gross and Kohn, and a more recent method
which treats exchange and correlation beyond the ALDA as viscoelastic stresses
in the electron liquid. We find that the former method is more robust: it
performs similarly for strongly different degrees of collectivity of the
electronic motion. Results for quantum wells compare reasonably to experiment,
with a tendency towards overdamping. By contrast, the viscoelastic approach is
superior for systems where the electron dynamics is predominantly collective,
but breaks down if the local velocity field is too rapidly varying, as in the
case of a single-electron-like behavior such as tunneling through a potential
barrier. | 9806252v1 |
1998-11-27 | Renormalization group analysis of the quantum non-linear sigma model with a damping term | We investigate the behavior of the zero-temperature quantum non-linear sigma
model in d dimensions in the presence of a damping term of the form f(w)~
|w|^alpha, with 1 \le alpha <2. We find two fixed points: a spin-wave fixed
point FP1 showing a dynamic scaling exponent z=1 and a dissipative fixed point
FP2 with z>1. In the framework of the \epsilon-expansion it is seen that there
is a range of values alpha_*(d) \le alpha \le 2 where the point FP1 is stable
with respect to FP2, so that the system realizes a z=1 quantum critical
behavior even in the presence of a dissipative term. However, reasonable
arguments suggest that in d=2 this range is very narrow. In the broken symmetry
phase we discuss a phenomenological scaling approach, treating damping as a
perturbation of the ordered ground state. The relation of these results with
the pseudogap effect observed in underdoped layered cuprates is discussed. | 9811392v2 |
1999-12-14 | Spinwave damping in the two-dimensional ferromagnetic XY model | The effect of damping of spinwaves in a two-dimensional classical
ferromagnetic XY model is considered. The damping rate $\Gamma_{q}$ is
calculated using the leading diagrams due to the quartic-order deviations from
the harmonic spin Hamiltonian. The resulting four-dimensional integrals are
evaluated by extending the techniques developed by Gilat and others for
spectral density types of integrals. $\Gamma_{q}$ is included into the memory
function formalism due to Reiter and Solander, and Menezes, to determine the
dynamic structure function $S(q,\omega)$. For the infinite sized system, the
memory function approach is found to give non-divergent spinwave peaks, and a
smooth nonzero background intensity (``plateau'' or distributed intensity) for
the whole range of frequencies below the spinwave peak. The background
amplitude relative to the spinwave peak rises with temperature, and eventually
becomes higher than the spinwave peak, where it appears as a central peak. For
finite-sized systems, there are multiple sequences of weak peaks on both sides
of the spinwave peaks whose number and positions depend on the system size and
wavevector in integer units of $2\pi/L$. These dynamical finite size effects
are explained in the memory function analysis as due to either spinwave
difference processes below the spinwave peak or sum processes above the
spinwave peak. These features are also found in classical Monte Carlo --
Spin-Dynamics simulations. | 9912241v1 |
2002-01-25 | Time-dependent current density functional theory for the linear response of weakly disordered systems | This paper develops a quantitatively accurate first-principles description
for the frequency and the linewidth of collective electronic excitations in
inhomogeneous weakly disordered systems. A finite linewidth in general has
intrinsic and extrinsic sources. At low temperatures and outside the region
where electron-phonon interaction occurs, the only intrinsic damping mechanism
is provided by electron-electron interaction. This kind of intrinsic damping
can be described within time-dependent density-functional theory (TDFT), but
one needs to go beyond the adiabatic approximation and include retardation
effects. It was shown previously that a density-functional response theory that
is local in space but nonlocal in time has to be constructed in terms of the
currents, rather than the density. This theory will be reviewed in the first
part of this paper. For quantitatively accurate linewidths, extrinsic
dissipation mechanisms, such as impurities or disorder, have to be included. In
the second part of this paper, we discuss how extrinsic dissipation can be
described within the memory function formalism. We first review this formalism
for homogeneous systems, and then present a synthesis of TDFT with the memory
function formalism for inhomogeneous systems, to account simultaneously for
intrinsic and extrinsic damping of collective excitations. As example, we
calculate frequencies and linewidths of intersubband plasmons in a 40 nm wide
GaAs/AlGaAs quantum well. | 0201483v1 |
2004-05-14 | Thermoelastic relaxation in elastic structures with applications to thin plates | A new result enables direct calculation of thermoelastic damping in vibrating
elastic solids. The mechanism for energy loss is thermal diffusion caused by
inhomogeneous deformation, flexure in thin plates. The general result is
combined with the Kirchhoff assumption to obtain a new equation for the
flexural vibration of thin plates incorporating thermoelastic loss as a damping
term. The thermal relaxation loss is inhomogeneous and depends upon the local
state of vibrating flexure, specifically, the principal curvatures at a given
point on the plate. Thermal loss is zero at points where the principal
curvatures are equal and opposite, that is, saddle shaped or pure anticlastic
deformation. Conversely, loss is maximum at points where the curvatures are
equal, that is, synclastic or spherical flexure. The influence of modal
urvature on the thermoelastic damping is described through a modal
pparticipation factor. The effect of transverse thermal diffusion on plane wave
propagation is also examined. It is shown that transverse diffusion effects are
always small provided the plate thickness is far greater than the thermal
phonon mean free path, a requirement for the validity of the classical theory
of heat transport. These results generalize Zener's theory of thermoelastic
loss in beams and are useful in predicting mode widths in MEMS and NEMS
oscillators. | 0405323v2 |
2005-04-21 | Ultrafast dynamics of coherent optical phonons and nonequilibrium electrons in transition metals | The femtosecond optical pump-probe technique was used to study dynamics of
photoexcited electrons and coherent optical phonons in transition metals Zn and
Cd as a function of temperature and excitation level. The optical response in
time domain is well fitted by linear combination of a damped harmonic
oscillation because of excitation of coherent $E_{2g}$ phonon and a
subpicosecond transient response due to electron-phonon thermalization. The
electron-phonon thermalization time monotonically increases with temperature,
consistent with the thermomodulation scenario, where at high temperatures the
system can be well explained by the two-temperature model, while below
$\approx$ 50 K the nonthermal electron model needs to be applied. As the
lattice temperature increases, the damping of the coherent $E_{2g}$ phonon
increases, while the amplitudes of both fast electronic response and the
coherent $E_{2g}$ phonon decrease. The temperature dependence of the damping of
the $E_{2g}$ phonon indicates that population decay of the coherent optical
phonon due to anharmonic phonon-phonon coupling dominates the decay process. We
present a model that accounts for the observed temperature dependence of the
amplitude assuming the photoinduced absorption mechanism, where the signal
amplitude is proportional to the photoinduced change in the quasiparticle
density. The result that the amplitude of the $E_{2g}$ phonon follows the
temperature dependence of the amplitude of the fast electronic transient
indicates that under the resonant condition both electronic and phononic
responses are proportional to the change in the dielectric function. | 0504540v1 |
2005-10-10 | Quantum master equation descriptions of a nanomechanical resonator coupled to a single-electron transistor | We analyse the quantum dynamics of a nanomechanical resonator coupled to a
normal-state single-electron transistor (SET). Starting from a microscopic
description of the system, we derive a master equation for the SET island
charge and resonator which is valid in the limit of weak electro-mechanical
coupling. Using this master equation we show that, apart from brief transients,
the resonator always behaves like a damped harmonic oscillator with a shifted
frequency and relaxes into a thermal-like steady state. Although the behaviour
remains qualitatively the same, we find that the magnitude of the resonator
damping rate and frequency shift depend very sensitively on the relative
magnitudes of the resonator period and the electron tunnelling time. Maximum
damping occurs when the electrical and mechanical time-scales are the same, but
the frequency shift is greatest when the resonator moves much more slowly than
the island charge. We then derive reduced master equations which describe just
the resonator dynamics. By making slightly different approximations, we obtain
two different reduced master equations for the resonator. Apart from minor
differences, the two reduced master equations give rise to a consistent picture
of the resonator dynamics which matches that obtained from the master equation
including the SET island charge. | 0510236v1 |
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