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2023-11-11 | On asymptotic properties of solutions to $σ$-evolution equations with general double damping | In this paper, we would like to consider the Cauchy problem for semi-linear
$\sigma$-evolution equations with double structural damping for any $\sigma\ge
1$. The main purpose of the present work is to not only study the asymptotic
profiles of solutions to the corresponding linear equations but also describe
large-time behaviors of globally obtained solutions to the semi-linear
equations. We want to emphasize that the new contribution is to find out the
sharp interplay of ``parabolic like models" corresponding to $\sigma_1 \in
[0,\sigma/2)$ and ``$\sigma$-evolution like models" corresponding to $\sigma_2
\in (\sigma/2,\sigma]$, which together appear in an equation. In this
connection, we understand clearly how each damping term influences the
asymptotic properties of solutions. | 2311.06660v1 |
2023-11-14 | Enhanced classical radiation damping of electronic cyclotron motion in the vicinity of the Van Hove singularity in a waveguide | We study the damping process of electron cyclotron motion and the resulting
emission in a waveguide using the classical Friedrichs model without relying on
perturbation analysis such as Fermi's golden rule. A classical Van Hove
singularity appears at the lower bound (or cut-off frequency) of the dispersion
associated with each of the electromagnetic field modes in the waveguide. In
the vicinity of the Van Hove singularity, we found that not only is the decay
process associated with the resonance pole enhanced (amplification factor ~
$10^4$) but the branch-point effect is also comparably enhanced. As a result,
the timescale on which most of the decay occurs is dramatically shortened.
Further, this suggests that the non-Markovian branch point effect should be
experimentally observable in the vicinity of the Van Hove singularity. Our
treatment yields a physically-acceptable solution without the problematic
runaway solution that is well known to appear in the traditional treatment of
classical radiation damping based on the Abraham-Lorentz equation. | 2311.08121v3 |
2023-11-18 | The temperature dependent Boltzmann equation beyond local equilibrium assumption | In this manuscript, we present a temperature dependent Boltzmann equation for
the particles transport through a environmental reservoir, where the
temperature refers to the equilibrium temperature of reservoir, a new damping
force and a inverse damping relaxation time are derived based on the classical
Boltzmann equation, which have obvious influence on the external force and the
relaxation time of transport particles. For comparison, we also define a
non-equilibrium temperature for the transport particle by its distribution
function out of equilibrium, which is different from the equilibrium
temperature of reservoir. There exist heat transfer between the transport
particle and the reservoir, because the whole transport particles are in
non-equilibrium state. Finally, we illustrate them by an example of
one-dimensional transport procedure, the damping force and the non-equilibrium
temperature defined by us are shown numerically. | 2311.11028v1 |
2023-12-13 | Integrating Superregenerative Principles in a Compact, Power-Efficient NMR/NQR Spectrometer: A Novel Approach with Pulsed Excitation | We present a new approach to Nuclear Quadrupole Resonance (NQR)/Nuclear
Magnetic Resonance (NMR) spectroscopy, the Damp-Enhanced Superregenerative
Nuclear Spin Analyser (DESSA). This system integrates Superregenerative
principles with pulsed sample excitation and detection, offering significant
advancements over traditional Super-Regenerative Receivers (SRRs). Our approach
overcomes certain limitations associated with traditional Super-Regenerative
Receivers (SRRs) by integrating direct digital processing of the oscillator
response delay time (T$_d$) and an electronic damp unit to regulate the
excitation pulse decay time (T$_e$). The essence is combining pulsed excitation
with a reception inspired by, but distinct from, conventional SRRs. The damp
unit allows a rapid termination of the oscillation pulse and the initiation of
detection within microseconds, and direct digital processing avoids the need
for a second lower frequency which is used for quenching in a traditional SRRs,
thereby avoiding the formation of sidebands. We demonstrate the effectiveness
of DESSA on a \ch{NaClO3} sample containing the isotope Chlorine-35 where it
accurately detects the NQR signal with sub-kHz resolution. | 2312.08491v1 |
2023-12-26 | Dynamical polarization function, plasmons, their damping and collective effects in semi-Dirac bands | We have calculated the dynamical polarization, plasmons and damping rates in
semi-Dirac bands (SDB's) with zero band gap and half-linear, half-parabolic
low-energy spectrum. The obtained plasmon dispersions are strongly anisotropic
and demonstrate some crucial features of both two-dimensional electron gas and
graphene. Such gapless energy dispersions lead to a localized area of undamped
and low-damped plasmons in a limited range of the frequencies and wave vectors.
The calculated plasmon branches demonstrate an increase of their energies for a
finite tilting of the band structure and a fixed Fermi level which could be
used as a signature of a specific tilted spectrum in a semi-Dirac band. | 2312.16117v1 |
2024-01-09 | Coherent errors in stabilizer codes caused by quasistatic phase damping | Quantum error correction is a key challenge for the development of practical
quantum computers, a direction in which significant experimental progress has
been made in recent years. In solid-state qubits, one of the leading
information loss mechanisms is dephasing, usually modelled by phase flip
errors. Here, we introduce quasistatic phase damping, a more subtle error model
which describes the effect of Larmor frequency fluctuations due to 1/f noise.
We show how this model is different from a simple phase flip error model, in
terms of multi-cycle error correction. Considering the surface code, we provide
numerical evidence for an error threshold, in the presence of quasistatic phase
damping and readout errors. We discuss the implications of our results for spin
qubits and superconducting qubits. | 2401.04530v2 |
2024-01-19 | Composite learning backstepping control with guaranteed exponential stability and robustness | Adaptive backstepping control provides a feasible solution to achieve
asymptotic tracking for mismatched uncertain nonlinear systems. However,
input-to-state stability depends on high-gain feedback generated by nonlinear
damping terms, and closed-loop exponential stability with parameter convergence
involves a stringent condition named persistent excitation (PE). This paper
proposes a composite learning backstepping control (CLBC) strategy based on
modular backstepping and high-order tuners to compensate for the transient
process of parameter estimation and achieve closed-loop exponential stability
without the nonlinear damping terms and the PE condition. A novel composite
learning mechanism that maximizes the staged exciting strength is designed for
parameter estimation, such that parameter convergence can be achieved under a
condition of interval excitation (IE) or even partial IE that is strictly
weaker than PE. An extra prediction error is employed in the adaptive law to
ensure the transient performance without nonlinear damping terms. The
exponential stability of the closed-loop system is proved rigorously under the
partial IE or IE condition. Simulations have demonstrated the effectiveness and
superiority of the proposed method in both parameter estimation and control
compared to state-of-the-art methods. | 2401.10785v1 |
2024-01-23 | Model-Free $δ$-Policy Iteration Based on Damped Newton Method for Nonlinear Continuous-Time H$\infty$ Tracking Control | This paper presents a {\delta}-PI algorithm which is based on damped Newton
method for the H{\infty} tracking control problem of unknown continuous-time
nonlinear system. A discounted performance function and an augmented system are
used to get the tracking Hamilton-Jacobi-Isaac (HJI) equation. Tracking HJI
equation is a nonlinear partial differential equation, traditional
reinforcement learning methods for solving the tracking HJI equation are mostly
based on the Newton method, which usually only satisfies local convergence and
needs a good initial guess. Based upon the damped Newton iteration operator
equation, a generalized tracking Bellman equation is derived firstly. The
{\delta}-PI algorithm can seek the optimal solution of the tracking HJI
equation by iteratively solving the generalized tracking Bellman equation.
On-policy learning and off-policy learning {\delta}-PI reinforcement learning
methods are provided, respectively. Off-policy version {\delta}-PI algorithm is
a model-free algorithm which can be performed without making use of a priori
knowledge of the system dynamics. NN-based implementation scheme for the
off-policy {\delta}-PI algorithms is shown. The suitability of the model-free
{\delta}-PI algorithm is illustrated with a nonlinear system simulation. | 2401.12882v1 |
2024-01-30 | The nonlinear dynamic behavior of a Rubber-Layer Roller Bearing (RLRB) for vibration isolation | In this paper, we study the dynamic behavior of a Rubber-Layer Roller Bearing
(RLRB) interposed between a spring-mass elemental superstructure and a
vibrating base. Thanks to the viscoelastic rolling contact between the rigid
rollers and the rubber layers, the RLRB is able to provide a nonlinear damping
behavior. The effect of the RLRB geometric and material parameters is
investigated under periodic base excitation, showing that both periodic and
aperiodic responses can be achieved. Specifically, since the viscoelastic
damping is non-monotonic (bell shaped), there exist systemdynamic conditions
involving the decreasing portion of the damping curve in which a strongly
nonlinear behavior is experienced. In the second part of the paper, we
investigate the effectiveness of the nonlinear device in terms of seismic
isolation. Focusing on the mean shock of the Central Italy 2016 earthquake, we
opportunely tune the material and geometrical RLRB parameters, showing that a
significant reduction of both the peak and root-mean-square value of the
inertial force acting on the superstructure is achieved, compared to the best
performance of a linear base isolation system. | 2401.16880v1 |
2024-01-30 | Poynting-Robertson damping of laser beam driven lightsails | Lightsails using Earth-based lasers for propulsion require passive
stabilization to stay within the beam. This can be achieved through the sail's
scattering properties, creating optical restoring forces and torques. Undamped
restoring forces produce uncontrolled oscillations, which could jeopardize the
mission, but it is not obvious how to achieve damping in the vacuum of space.
Using a simple two-dimensional model we show that the Doppler effect and
relativistic aberration of the propelling laser beam create damping terms in
the optical forces and torques. The effect is similar to the Poynting-Robertson
effect causing loss of orbital momentum of dust particles around stars, but can
be enhanced by design of the sail's geometry. | 2401.16924v1 |
2024-02-29 | The Equation of Motion for Taut-Line Buzzers | Equations of motion are developed for the oscillatory rotation of a disk
suspended between twisted strings kept under tension by a hanging mass, to
which additional forces may be applied. In the absence of forcing, damped
harmonic oscillations are observed to decay with an exponential time envelope
for two different string types. This is consistent with damping caused by
string viscosity, rather than air turbulence, and may be quantified in terms of
a quality factor. To test the proposed equation of motion and model for viscous
damping within the string, we measure both the natural oscillation frequency
and the quality factor for widely varied values of string length, string
radius, disk moment of inertia, and hanging mass. The data are found to scale
in good accord with predictions. A variation where rotational kinetic energy is
converted back and forth to spring potential energy is also discussed. | 2402.19285v1 |
2024-03-08 | A design methodology for nonlinear oscillator chains enabling energy localization tuning and soliton stability enhancement with optimal damping | In this paper, the vibration energy localization in coupled nonlinear
oscillators is investigated, based on the creation of standing solitons. The
main objective is to establish a design methodology for mechanical lattices
using the Nonlinear Schr\"odinger Equation (NLSE) as a guide strategy, even in
the presence of damping. A three-dimensional diagram is used to illustrate
stable parameter regions for damped stationary solitons. Moreover, an analysis
of the influence of the number of oscillators in the system, and a numerical
investigation regarding the stability of solitonic behavior is done. Through
numerical analyses, it is observed that the developed algorithm not only has
the capability to locate the highest amplitudes in the chain of oscillators,
but also to control the intensity at which these amplitudes are located
according to design requirements. The outcomes of the proposed methodology
elucidate the impact that the coupling stiffness has on the stabilization of
the NLSE, as well as the influence of the number of oscillators on the
continuity hypothesis. The developed algorithm holds potential for practical
applications in mechanical engineering since the NLSE is used as a design line
rather than as a consequence of the phenomenon description. | 2403.05176v1 |
2024-03-08 | Damping Obliquities of Hot Jupiter Hosts by Resonance Locking | When orbiting hotter stars, hot Jupiters are often highly inclined relative
to their host star equator planes. By contrast, hot Jupiters orbiting cooler
stars are more aligned. Prior attempts to explain this correlation between
stellar obliquity and effective temperature have proven problematic. We show
how resonance locking -- the coupling of the planet's orbit to a stellar
gravity mode (g mode) -- can solve this mystery. Cooler stars with their
radiative cores are more likely to be found with g-mode frequencies increased
substantially by core hydrogen burning. Strong frequency evolution in resonance
lock drives strong tidal evolution; locking to an axisymmetric g mode damps
semi-major axes, eccentricities, and as we show for the first time,
obliquities. Around cooler stars, hot Jupiters evolve into spin-orbit alignment
and avoid engulfment. Hotter stars lack radiative cores, and therefore preserve
congenital spin-orbit misalignments. We focus on resonance locks with
axisymmetric modes, supplementing our technical results with simple physical
interpretations, and show that non-axisymmetric modes also damp obliquity. | 2403.05616v1 |
2002-03-16 | Rolling as a continuing collision | We show that two basic mechanical processes, the collision of particles and
rolling motion of a sphere on a plane, are intimately related. According to our
recent findings, the restitution coefficient for colliding spherical particles
\epsilon, which characterizes the energy loss upon collision, is directly
related to the rolling friction coefficient \mu_{roll} for a viscous sphere on
a hard plane. We quantify both coefficients in terms of material constants
which allow to determine either of them provided the other is known. This
relation between the coefficients may give rise to a novel experimental
technique to determine alternatively the coefficient of restitution or the
coefficient of rolling friction. | 0203343v1 |
2003-11-21 | Quiver coefficients are Schubert structure constants | We give an explicit natural identification between the quiver coefficients of
Buch and Fulton, decomposition coefficients for Schubert polynomials, and the
Schubert structure constants for flag manifolds. This is also achieved in
K-theory where we give a direct argument that the decomposition coefficients
have alternating signs, based on a theorem of Brion, which then implies that
the quiver coefficients have alternating signs. Our identification shows that
known combinatorial formulas for the latter two numbers give formulas for the
quiver coefficients. | 0311390v1 |
2005-01-28 | Wilson function transforms related to Racah coefficients | The irreducible $*$-representations of the Lie algebra $su(1,1)$ consist of
discrete series representations, principal unitary series and complementary
series. We calculate Racah coefficients for tensor product representations that
consist of at least two discrete series representations. We use the explicit
expressions for the Clebsch-Gordan coefficients as hypergeometric functions to
find explicit expressions for the Racah coefficients. The Racah coefficients
are Wilson polynomials and Wilson functions. This leads to natural
interpretations of the Wilson function transforms. As an application several
sum and integral identities are obtained involving Wilson polynomials and
Wilson functions. We also compute Racah coefficients for $U_q(\su(1,1))$, which
turn out to be Askey-Wilson functions and Askey-Wilson polynomials. | 0501511v1 |
2009-09-02 | A method for creating materials with a desired refraction coefficient | It is proposed to create materials with a desired refraction coefficient in a
bounded domain $D\subset \R^3$ by embedding many small balls with constant
refraction coefficients into a given material. The number of small balls per
unit volume around every point $x\in D$, i.e., their density distribution, is
calculated, as well as the constant refraction coefficients in these balls.
Embedding into $D$ small balls with these refraction coefficients according to
the calculated density distribution creates in $D$ a material with a desired
refraction coefficient. | 0909.0510v1 |
2010-11-16 | On spectral properties of the fourth order differential operator with singular coefficients | A formal fourth order differential operator with a singular coefficient that
is a linear combination of the Dirac delta-function and its derivatives is
considered. The asymptotic behavior of spectra and eigenfunctions of a family
of differential operators with smooth coefficients approximating the singular
coefficients is studied. We explore how behavior of eigenvalues and
eigenfunctions is influenced by singular coefficients. The limit operator is
constructed and is shown to depend on a type of approximation of singular
coefficients. | 1011.3675v1 |
2012-03-12 | Operator Coefficient Methods for Linear Equations | New iterative methods for solving linear equations are presented that are
easy to use, generalize good existing methods, and appear to be faster. The new
algorithms mix two kinds of linear recurrence formulas. Older methods have
either high order recurrence formulas with scalars for coefficients, as in
truncated orthomin, or have 1st order recurrence formulas with matrix
polynomials for coefficients, as in restarted gcr/gmres. The new methods
include both: high order recurrence formulas and matrix polynomials for
coefficients. These methods provide a trade-off between recurrence order and
polynomial degree that can be exploited to achieve greater efficiency.
Convergence results are obtained for both constant coefficient and varying
coefficient methods. | 1203.2390v1 |
2012-05-24 | Stability of the inverse resonance problem for Jacobi operators | When the coefficients of a Jacobi operator are finitely supported
perturbations of the 1 and 0 sequences, respectively, the left reflection
coefficient is a rational function whose poles inside, respectively outside,
the unit disk correspond to eigenvalues and resonances. By including the zeros
of the reflection coefficient, we have a set of data that determines the Jacobi
coefficients up to a translation as long as there is at most one half-bound
state. We prove that the coefficients of two Jacobi operators are pointwise
close assuming that the zeros and poles of their left reflection coefficients
are $\eps$-close in some disk centered at the origin. | 1205.5321v1 |
2013-03-20 | Beyond two criteria for supersingularity: coefficients of division polynomials | Let E: y^2 = x^3 + Ax + B be an elliptic curve defined over a finite field of
characteristic p\geq 3. In this paper we prove that the coefficient at
x^{p(p-1)/2} in the p-th division polynomial \psi_p(x) of E equals the
coefficient at x^{p-1} in (x^3 + Ax + B)^{(p-1)/2}. The first coefficient is
zero if and only if the division polynomial has no roots, which is equivalent
to E being supersingular. Deuring (1941) proved that this supersingularity is
also equivalent to the vanishing of the second coefficient. So the zero loci of
the coefficients (as functions of A and B) are equal; the main result in this
paper is clearly stronger than this last statement. | 1303.5002v1 |
2014-10-26 | Bounds on Kronecker and $q$-binomial coefficients | We present a lower bound on the Kronecker coefficients for tensor squares of
the symmetric group via the characters of~$S_n$, which we apply to obtain
various explicit estimates. Notably, we extend Sylvester's unimodality of
$q$-binomial coefficients $\binom{n}{k}_q$ as polynomials in~$q$ to derive
sharp bounds on the differences of their consecutive coefficients. We then
derive effective asymptotic lower bounds for a wider class of Kronecker
coefficients. | 1410.7087v3 |
2015-11-13 | Relating the optical absorption coefficient of nanosheet dispersions to the intrinsic monolayer absorption | The concentration of nanosheet suspensions is an important technological
parameter which is commonly measured by optical spectroscopy using the
absorption coefficient to transform absorbance into concentration. However for
all 2D materials, the absorption coefficient is poorly known, resulting in
potentially large errors in measured concentration. Here we derive an
expression relating the optical absorption coefficient of an isotropic ensemble
of nanosheets to the intrinsic monolayer absorption. This has allowed us to
calculate the absorption coefficients for suspensions of graphene, MoS2 and
other 2D materials and allows estimation of the monolayer absorption for new
materials from careful measurement of the suspension absorption coefficient. | 1511.04410v1 |
2016-02-22 | Fourier Coefficients for Theta Representations on Covers of General Linear Groups | We show that the theta representations on certain covers of general linear
groups support certain types of unique functionals. The proof involves two
types of Fourier coefficients. The first are semi-Whittaker coefficients, which
generalize coefficients introduced by Bump and Ginzburg for the double cover.
The covers for which these coefficients vanish identically (resp. do not vanish
for some choice of data) are determined in full. The second are the Fourier
coefficients associated with general unipotent orbits. In particular, we
determine the unipotent orbit attached, in the sense of Ginzburg, to the theta
representations. | 1602.06614v2 |
2016-08-05 | Quantile Regression for Partially Linear Varying Coefficient Spatial Autoregressive Models | This paper considers the quantile regression approach for partially linear
spatial autoregressive models with possibly varying coefficients. B-spline is
employed for the approximation of varying coefficients. The instrumental
variable quantile regression approach is employed for parameter estimation. The
rank score tests are developed for hypotheses on the coefficients, including
the hypotheses on the non-varying coefficients and the constancy of the varying
coefficients. The asymptotic properties of the proposed estimators and test
statistics are both established. Monte Carlo simulations are conducted to study
the finite sample performance of the proposed method. Analysis of a real data
example is presented for illustration. | 1608.01739v1 |
2017-02-05 | Jacobi-Type Continued Fractions and Congruences for Binomial Coefficients Modulo Integers $h \geq 2$ | We prove two new forms of Jacobi-type J-fraction expansions generating the
binomial coefficients, $\binom{x+n}{n}$ and $\binom{x}{n}$, over all $n \geq
0$. Within the article we establish new forms of integer congruences for these
binomial coefficient variations modulo any (prime or composite) $h \geq 2$ and
compare our results with existing known congruences for the binomial
coefficients modulo primes $p$ and prime powers $p^k$. We also prove new exact
formulas for these binomial coefficient cases from the expansions of the
$h^{th}$ convergent functions to the infinite J-fraction series generating
these coefficients for all $n$. | 1702.01374v1 |
2017-03-24 | On the coefficients of symmetric power $L$-functions | We study the signs of the Fourier coefficients of a newform. Let $f$ be a
normalized newform of weight $k$ for $\Gamma_0(N)$. Let $a_f(n)$ be the $n$th
Fourier coefficient of $f$. For any fixed positive integer $m$, we study the
distribution of the signs of $\{a_f(p^m)\}_p$, where $p$ runs over all prime
numbers. We also find out the abscissas of absolute convergence of two
Dirichlet series with coefficients involving the Fourier coefficients of cusp
forms and the coefficients of symmetric power $L$-functions. | 1703.08344v3 |
2017-08-05 | A causation coefficient and taxonomy of correlation/causation relationships | This paper introduces a causation coefficient which is defined in terms of
probabilistic causal models. This coefficient is suggested as the natural
causal analogue of the Pearson correlation coefficient and permits comparing
causation and correlation to each other in a simple, yet rigorous manner.
Together, these coefficients provide a natural way to classify the possible
correlation/causation relationships that can occur in practice and examples of
each relationship are provided. In addition, the typical relationship between
correlation and causation is analyzed to provide insight into why correlation
and causation are often conflated. Finally, example calculations of the
causation coefficient are shown on a real data set. | 1708.05069v1 |
2017-09-21 | On the Global Continuity of the Roots of Families of Monic Polynomials (in Russian) | We raise a question on the existence of continuous roots of families of monic
polynomials (by the root of a family of polynomials we mean a function of the
coefficients of polynomials of a given family that maps each tuple of
coefficients to a root of the polynomial with these coefficients). We prove
that the family of monic second-degree polynomials with complex coefficients
and the families of monic fourth-degree and fifth-degree polynomials with real
coefficients have no continuous root. We also prove that the family of monic
second-degree polynomials with real coefficients has continuous roots and we
describe the set of all such roots. | 1710.00640v1 |
2018-06-27 | Using a kinetic BGK model to determine transport coefficients of gas mixtures | We consider a non reactive two component gas mixture. In a macroscopic
description of a gas mixture we expect four physical coefficients
characterizing the physical behaviour of the gases to appear. These are the
diffusion coefficient, the viscosity coefficient, the heat conductivity and the
thermal diffusion parameter in the Navier-Stokes equations. We present a
Chapman-Enskog expansion of a kinetic model for gas mixtures by Klingenberg,
Pirner and Puppo, 2017 that has three free parameters in order to capture three
of these four physical coefficients. In addition, we propose several possible
extensions to an ellipsoidal statistical model for gas mixtures in order to
capture the fourth coefficient. | 1806.11483v1 |
2019-07-01 | Efficient computation of collisional $\ell$-mixing rate coefficients in astrophysical plasmas | We present analytical expressions for direct evaluation of $\ell$-mixing rate
coefficients in proton-excited hydrogen atom collisions and describe a software
package for efficient numerical evaluation of the collisional rate
coefficients. Comparisons between rate coefficients calculated with various
levels of approximation are discussed, highlighting their range of validity.
These rate coefficients are benchmarked via radio recombination lines for
hydrogen, evaluating the corresponding departure coefficients from local
thermal equilibrium. | 1907.00972v1 |
2019-12-30 | The Concordance coefficient: An alternative to the Kruskal-Wallis test | Kendall rank correlation coefficient is used to measure the ordinal
association between two measurements. In this paper, we introduce the
Concordance coefficient as a generalization of the Kendall rank correlation,
and illustrate its use to measure the ordinal association between quantity and
quality measures when two or more samples are considered. In this sense, the
Concordance coefficient can be seen as a generalization of the Kendall rank
correlation coefficient and an alternative to the non-parametric mean
rank-based methods to compare two or more samples. A comparison of the proposed
Concordance coefficient and the classical Kruskal-Wallis statistic is presented
through a comparison of exact distributions of both statistics. | 1912.12880v2 |
2020-10-13 | Arithmetic properties of Fourier coefficients of meromorphic modular forms | We investigate integrality and divisibility properties of Fourier
coefficients of meromorphic modular forms of weight $2k$ associated to positive
definite integral binary quadratic forms. For example, we show that if there
are no non-trivial cusp forms of weight $2k$, then the $n$-th coefficients of
these meromorphic modular forms are divisible by $n^{k-1}$ for every natural
number $n$. Moreover, we prove that their coefficients are non-vanishing and
have either constant or alternating signs. Finally, we obtain a relation
between the Fourier coefficients of meromorphic modular forms, the coefficients
of the $j$-function, and the partition function. | 2010.06297v1 |
2022-02-18 | Strichartz estimates for equations with structured Lipschitz coefficients | Sharp Strichartz estimates are proved for Schr\"odinger and wave equations
with Lipschitz coefficients satisfying additional structural assumptions. We
use Phillips functional calculus as a substitute for Fourier inversion, which
shows how dispersive properties are inherited from the constant coefficient
case. Global Strichartz estimates follow provided that the derivatives of the
coefficients are integrable. The estimates extend to structured coefficients of
bounded variations. As applications we derive Strichartz estimates with
additional derivative loss for wave equations with H\"older-continuous
coefficients and solve nonlinear Schr\"odinger equations. Finally, we record
spectral multiplier estimates, which follow from the Strichartz estimates by
well-known means. | 2202.09260v2 |
2023-06-07 | Machine-Learning Kronecker Coefficients | The Kronecker coefficients are the decomposition multiplicities of the tensor
product of two irreducible representations of the symmetric group. Unlike the
Littlewood--Richardson coefficients, which are the analogues for the general
linear group, there is no known combinatorial description of the Kronecker
coefficients, and it is an NP-hard problem to decide whether a given Kronecker
coefficient is zero or not. In this paper, we show that standard
machine-learning algorithms such as Nearest Neighbors, Convolutional Neural
Networks and Gradient Boosting Decision Trees may be trained to predict whether
a given Kronecker coefficient is zero or not. Our results show that a trained
machine can efficiently perform this binary classification with high accuracy
($\approx 0.98$). | 2306.04734v1 |
2023-10-13 | Attacking The Assortativity Coefficient Under A Rewiring Strategy | Degree correlation is an important characteristic of networks, which is
usually quantified by the assortativity coefficient. However, concerns arise
about changing the assortativity coefficient of a network when networks suffer
from adversarial attacks. In this paper, we analyze the factors that affect the
assortativity coefficient and study the optimization problem of maximizing or
minimizing the assortativity coefficient (r) in rewired networks with $k$ pairs
of edges. We propose a greedy algorithm and formulate the optimization problem
using integer programming to obtain the optimal solution for this problem.
Through experiments, we demonstrate the reasonableness and effectiveness of our
proposed algorithm. For example, rewired edges 10% in the ER network, the
assortativity coefficient improved by 60%. | 2310.08924v1 |
2024-01-04 | On Clustering Coefficients in Complex Networks | The clustering coefficient is a valuable tool for understanding the structure
of complex networks. It is widely used to analyze social networks, biological
networks, and other complex systems. While there is generally a single common
definition for the local clustering coefficient, there are two different ways
to calculate the global clustering coefficient. The first approach takes the
average of the local clustering coefficients for each node in the network. The
second one is based on the ratio of closed triplets to all triplets. It is
shown that these two definitions of the global clustering coefficients are
strongly inequivalent and may significantly impact the accuracy of the outcome. | 2401.02999v1 |
2024-02-17 | Clebsch-Gordan coefficients, hypergeometric functions and the binomial distribution | A particular case of degenerate Clebsch-Gordan coefficient can be expressed
with three binomial coefficients. Such a formula, which may be obtained using
the standard ladder operator procedure, can also be derived from the
Racah-Shimpuku formula or from expressions of Clebsch-Gordan coefficients in
terms of $_3F_2$ hypergeometric functions. The O'Hara interesting
interpretation of this Clebsch-Gordan coefficient by binomial random variables
can also be related to hypergeometric functions ($_2F_1$), in the case where
one of the parameters tends to infinity. This emphasizes the links between
Clebsch-Gordan coefficients, hypergeometric functions and, what has been less
exploited until now, the notion of probability within the framework of the
quantum theory of angular momentum. | 2402.11298v1 |
1998-10-25 | A New Approximation Of ECM Frequencies | We investigate wave amplification through the Electron Cyclotron Maser
mechanism.
We derive a semi-analytic approximation formula giving the frequencies at
which the absorption coefficient is negative. The coefficients still need to be
computed to obtain the largest, and therefore the dominant, coefficient. | 9810404v1 |
1997-08-28 | Index-free Heat Kernel Coefficients | Using index-free notation, we present the diagonal values of the first five
heat kernel coefficients associated with a general Laplace-type operator on a
compact Riemannian space without boundary. The fifth coefficient appears here
for the first time. For a flat space with a gauge connection, the sixth
coefficient is given too. Also provided are the leading terms for any
coefficient, both in ascending and descending powers of the Yang-Mills and
Riemann curvatures, to the same order as required for the fourth coefficient.
These results are obtained by directly solving the relevant recursion
relations, working in Fock-Schwinger gauge and Riemann normal coordinates. Our
procedure is thus noncovariant, but we show that for any coefficient the
`gauged' respectively `curved' version is found from the corresponding
`non-gauged' respectively `flat' coefficient by making some simple covariant
substitutions. These substitutions being understood, the coefficients retain
their `flat' form and size. In this sense the fifth and sixth coefficient have
only 26 and 75 terms respectively, allowing us to write them down. Using
index-free notation also clarifies the general structure of the heat kernel
coefficients. In particular, in flat space we find that from the fifth
coefficient onward, certain scalars are absent. This may be relevant for the
anomalies of quantum field theories in ten or more dimensions. | 9708152v1 |
2001-10-16 | On the coefficients of a Fibonacci power series | We give an explicit description of the coefficients of the formal power
series (1-x)(1-x^2)(1-x^3)(1-x^5)(1-x^8)(1-x^13)... In particular, we show that
all the coefficients are equal to -1, 0 or 1. | 0110160v1 |
2002-04-24 | On diffusion approximation with discontinuous coefficients | Convergence of stochastic processes with jumps to diffusion processes is
investigated in the case when the limit process has discontinuous coefficients.
An example is given in which the diffusion approximation of a queueing model
yields a diffusion process with discontinuous diffusion and drift coefficients. | 0204289v1 |
2004-02-09 | Backward uniqueness for parabolic operators with non-Lipscitz coefficients | We investigate the relation between the backward uniqueness and the
regularity of the coefficients for a parabolic operator. A necessary and
sufficient condition for uniqueness is given in terms of the modulus of
continuity of the coefficients. | 0402138v1 |
2006-12-02 | K-Nomial Coefficients | In this paper one extends the binomial and trinomial coefficients to the
concept of 'k-nomial' coefficients, and one obtains some properties of these.
As an application one generalizes Pascal's triangle. | 0612062v1 |
2007-03-09 | Binomial identities related to Calabi-Yau differential equations | When searching for Calabi.Yau differential equations, often different
formulas for the coefficients give the same differential equation. The
coefficients are usually sums (simple, double or triple) of products of
binomial coefficients. This results in numerous binomial identities. | 0703255v1 |
2007-10-08 | Number of binomial coefficients divided by a fixed power of a prime | We state a general formula for the number of binomial coefficients $n$ choose
$k$ that are divided by a fixed power of a prime $p$, i.e., the number of
binomial coefficients divided by $p^j$ and not divided by $p^{j+1}$. | 0710.1468v1 |
2008-12-17 | A uniqueness result on ordinary differential equations with singular coefficients | We consider the uniqueness of solutions of ordinary differential equations
where the coefficients may have singularities. We derive upper bounds on the
the order of singularities of the coefficients and provide examples to
illustrate the results. | 0812.3427v1 |
2008-12-21 | Bounds on ternary cyclotomic coefficients | We present a new bound on $A = \max_n |a_{pqr}(n)|$, where $a_{pqr}(n)$ are
the coefficients of a ternary cyclotomic polynomial. We also prove that two
consecutive coefficients of such a polynomial differ by at most one. | 0812.4024v1 |
2009-01-01 | Adjustment coefficient for risk processes in some dependent contexts | Following an article by Muller and Pflug, we study the adjustment coefficient
of ruin theory in a context of temporal dependency. We provide a consistent
estimator of this coefficient, and perform some simulations. | 0901.0182v1 |
2010-06-14 | Multivariate linear recursions with Markov-dependent coefficients | We study a linear recursion with random Markov-dependent coefficients. In a
"regular variation in, regular variation out" setup we show that its stationary
solution has a multivariate regularly varying distribution. This extends
results previously established for i.i.d. coefficients. | 1006.2694v1 |
2011-01-17 | Turán Inequalities for Three Term Recurrences with Monotonic Coefficients | We establish some new Tur\'an's type inequalities for orthogonal polynomials
defined by a three-term recurrence with monotonic coefficients. As a corollary
we deduce asymptotic bounds on the extreme zeros of orthogonal polynomials with
polynomially growing coefficients of the three-term recurrence. | 1101.3204v1 |
2011-02-07 | Two binomial coefficient conjectures | Much is known about binomial coefficients where primes are concerned, but
considerably less is known regarding prime powers and composites. This paper
provides two conjectures in these directions, one about counting binomial
coefficients modulo 16 and one about the value of Binomial[n, 2p] modulo n. | 1102.1464v1 |
2011-08-16 | Topological expansion of the coefficients of zonal polynomials in genus one | We use a combinatorial interpretation of the coefficients of zonal Kerov
polynomials as a number of unoriented maps to derive an explicit formula for
the coefficients in genus one. | 1108.3173v1 |
2012-02-15 | New extensions to the sumsets with polynomial restrictions | By taking the leading and the second leading coefficients of the Morris
identity, we get new polynomial coefficients. These coefficients lead to new
results in the sumsets with polynomial restrictions by the polynomial method of
N. Alon. | 1202.3190v1 |
2012-05-18 | Characterizing Hilbert modular cusp forms by coefficient size | Associated to an (adelic) Hilbert modular form is a sequence of `Fourier
coefficients' which uniquely determine the form. In this paper we characterize
Hilbert modular cusp forms by the size of their Fourier coefficients. This
answers in the affirmative a question posed by Winfried Kohnen. | 1205.4063v1 |
2014-07-28 | A Note on Extended Binomial Coefficients | We study the distribution of the extended binomial coefficients by deriving a
complete asymptotic expansion with uniform error terms. We obtain the expansion
from a local central limit theorem and we state all coefficients explicitly as
sums of Hermite polynomials and Bernoulli numbers. | 1407.7429v1 |
2014-08-05 | Coefficient Bounds for Level 2 Cusp Forms and Modular Functions | We give explicit upper bounds for the coefficients of arbitrary weight $k$,
level 2 cusp forms, making Deligne's well-known $O(n^{\frac{k-1}{2}+\epsilon})$
bound precise. We also derive asymptotic formulas and explicit upper bounds for
the coefficients of certain level 2 modular functions. | 1408.1083v1 |
2014-10-05 | A note on the Vilenkin-Fourier coefficients | The main aim of this paper is to find the estimation for Vilenkin-Fourier
coefficients. | 1410.7075v1 |
2015-03-18 | Methods for Accurate Free Flight Measurement of Drag Coefficients | This paper describes experimental methods for free flight measurement of drag
coefficients to an accuracy of approximately 1%. There are two main methods of
determining free flight drag coefficients, or equivalent ballistic
coefficients: 1) measuring near and far velocities over a known distance and 2)
measuring a near velocity and time of flight over a known distance. Atmospheric
conditions must also be known and nearly constant over the flight path. A
number of tradeoffs are important when designing experiments to accurately
determine drag coefficients. The flight distance must be large enough so that
the projectile's loss of velocity is significant compared with its initial
velocity and much larger than the uncertainty in the near and/or far velocity
measurements. On the other hand, since drag coefficients and ballistic
coefficients both depend on velocity, the change in velocity over the flight
path should be small enough that the average drag coefficient over the path
(which is what is really determined) is a reasonable approximation to the value
of drag coefficient at the near and far velocity. This paper considers these
tradeoffs as well as practical considerations for obtaining accurate near and
far velocity measurements and the impact of different sources of error
(velocity, distance, time, atmospheric conditions, etc.) on the resulting
accuracy of drag coefficients and ballistic coefficients. For a given level of
accuracy of various quantities, the method of using near and far velocities
usually produces drag coefficients with about half the uncertainty of the
method using a near velocity and time of flight. | 1503.05504v1 |
2016-07-11 | On the growth of the Kronecker coefficients | We study the rate of growth experienced by the Kronecker coefficients as we
add cells to the rows and columns indexing partitions. We do this by moving to
the setting of the reduced Kronecker coefficients. | 1607.02887v1 |
2018-05-15 | Strong Uniqueness of Degenerate SDEs with Hölder diffusion coefficients | In this paper we prove a new strong uniqueness result and a weak existence
result for possibly {\it degenerate} multidimensional stochastic differential
equations with Sobolev diffusion coefficients and rough drifts. In particular,
examples with H\"older diffusion coefficients are provided to show our results. | 1805.05526v1 |
2018-06-08 | Sums of series involving central binomial coefficients & harmonic numbers | This paper contains a number of series whose coefficients are products of
central binomial coefficients & harmonic numbers. An elegant sum involving
$\zeta(2)$ and two other nice sums appear in the last section. | 1806.03998v2 |
2018-07-13 | Extending the D-Wave with support for Higher Precision Coefficients | D-Wave only guarantees to support coefficients with 4 to 5 bits of resolution
or precision. This paper describes a method to extend the functionality of the
D-Wave to solve problems that require the support of higher precision
coefficients. | 1807.05244v1 |
2019-05-23 | Linear Statistics with Random Coefficients and Characterization of Hyperbolic Secant Distribution | There is given a characterization of hyperbolic secant distribution by the
independence of linear forms with random coefficients. We provide a
characterization by the identic distribution property. Keywords: hyperbolic
secant distribution; characterization of distributions; linear forms; random
coefficients. | 1905.09910v1 |
2019-05-27 | Noncommutative LR coefficients and crystal reflection operators | We relate noncommutative Littlewood-Richardson coefficients of
Bessenrodt-Luoto-van Willigenburg to classical Littlewood-Richardson
coefficients via crystal reflection operators. A key role is played by the
combinatorics of frank words. | 1905.10942v1 |
2020-01-29 | Rough differential equations with path-dependent coefficients | We establish the existence of solutions to path-dependent rough differential
equations with non-anticipative coefficients. Regularity assumptions on the
coefficients are formulated in terms of horizontal and vertical derivatives. | 2001.10688v1 |
2020-05-04 | Boundary value problem for high order equation with discontinuous coefficients | The article considers the Dirichlet problem for a high-order mixed-type
equation that splits into factors, each of which is a Lavrentiev-Bitsadze
equation with its own excellent coefficient. Sufficient conditions are found
for the coefficients under which the problem has a classical solution. | 2005.01283v1 |
2021-06-25 | On the divisibility of $q$-trinomial coefficients | We establish a congruence on sums of central $q$-binomial coefficients. From
this $q$-congruence, we derive the divisibility of the $q$-trinomial
coefficients introduced by Andrews and Baxter. | 2106.13613v2 |
2022-02-20 | Some new results about $q$-trinomial coefficients | In this paper, we present several new congruences on the $q$-trinomial
coefficients introduced by Andrews and Baxter. A new congruence on sums of
central $q$-binomial coefficients is also established. | 2202.09781v2 |
2022-04-21 | On analytical formulas for the Virial coefficients | In many fields of statistical physics, for instance in the study of the
liquid-gas phase transition in finite nuclear matter, the Virial coefficients
of the Fermi gas play a major role. In this note, we provide relations, sum
rules, analytical formulas and numerical values for such coefficients. | 2204.13600v1 |
2023-06-05 | On some conjectural series containing binomial coefficients and harmonic numbers | Binomial coefficients and harmonic numbers are important in many branches of
number theory. With the help of the operator method and several summation and
transformation formulas for hypergeometric series, we prove eight conjectural
series of Z.-W. Sun containing binomial coefficients and harmonic numbers in
this paper. | 2306.02641v1 |
2023-07-27 | Congruences concerning quadrinomial coefficients | In this paper, we establish congruences (mod $p^2$) involving the
quadrinomial coefficients $\dbinom{np-1}{p-1}_{3}$ and
$\dbinom{np-1}{\frac{p-1}{2}}_{3}$. This is an analogue of congruences
involving the trinomial coefficients $\dbinom{np-1}{p-1}_{2}$ and
$\dbinom{np-1}{\frac{p-1}{2}}_{2}$ due to Elkhiri and Mihoubi. | 2307.16768v1 |
2024-02-27 | Partition-Theoretic Results and Recurrence Relations for the Coefficients of Some Mock Theta Functions | In the paper, we give partition-theoretic results for the coefficients of
some mock theta functions and prove their congruence properties. Some
recurrence relations connecting the coefficients of the mock theta functions
with certain restricted partition functions are also established. | 2402.17551v1 |
1995-10-04 | Microlensing By a Prolate All-Macho Halo | It is widely believed that dark matter halos are flattened, that is closer to
oblate than prolate. The evidence cited is based largely on observations of
galaxies which do not look anything like our own and on numerical simulations
which use ad hoc initial conditions. Given what we believe to be a ``reasonable
doubt'' concerning the shape of dark Galactic halo we calculate the optical
depth and event rate for microlensing of stars in the LMC assuming a wide range
of models that include both prolate and oblate halos. We find, in agreement
with previous analysis, that the optical depth for a spherical (E0) halo and
for an oblate (E6) halo are roughly the same, essentially because two competing
effects cancel approximately. However the optical depth for an E6 prolate halo
is reduced by ~35%. This means that an all-Macho prolate halo with reasonable
parameters for the Galaxy is consistent with the published microlensing event
rate. | 9510023v1 |
1997-04-25 | Constraints on the density perturbation spectrum from primordial black holes | We re-examine the constraints on the density perturbation spectrum, including
its spectral index $n$, from the production of primordial black holes. The
standard cosmology, where the Universe is radiation dominated from the end of
inflation up until the recent past, was studied by Carr, Gilbert and Lidsey; we
correct two errors in their derivation and find a significantly stronger
constraint than they did, $n \lesssim 1.25$ rather than their 1.5. We then
consider an alternative cosmology in which a second period of inflation, known
as thermal inflation and designed to solve additional relic over-density
problems, occurs at a lower energy scale than the main inflationary period. In
that case, the constraint weakens to $n \lesssim 1.3$, and thermal inflation
also leads to a `missing mass' range, $10^{18} g \lesssim M \lesssim 10^{26}
g$, in which primordial black holes cannot form. Finally, we discuss the effect
of allowing for the expected non-gaussianity in the density perturbations
predicted by Bullock and Primack, which can weaken the constraints further by
up to 0.05. | 9704251v1 |
1998-02-26 | Inversion of polarimetric data from eclipsing binaries | We describe a method for determining the limb polarization and limb darkening
of stars in eclipsing binary systems, by inverting photometric and polarimetric
light curves.
Because of the ill-conditioning of the problem, we use the Backus-Gilbert
method to control the resolution and stability of the recovered solution, and
to make quantitative estimates of the maximum accuracy possible. Using this
method we confirm that the limb polarization can indeed be recovered, and
demonstrate this with simulated data, thus determining the level of
observational accuracy required to achieve a given accuracy of reconstruction.
This allows us to set out an optimal observational strategy, and to critcally
assess the claimed detection of limb polarization in the Algol system.
The use of polarization in stars has been proposed as a diagnostic tool in
microlensing surveys by Simmons et al. (1995), and we discuss the extension of
this work to the case of microlensing of extended sources. | 9802334v1 |
1998-09-04 | Cluster-Cluster Strong Lensing: Expectations and Detection Methods | We calculate the all-sky number of galaxy clusters that are expected to be
gravitationally lensed by foreground massive clusters. We describe the redshift
and number distributions of clusters using a Press-Schechter analysis, and
model the foreground lensing clusters as singular isothermal spheres. If
Omega_m=0.3 and Omega_Lambda=0.7, we expect ~ 30 cluster-cluster strong lensing
events that involve foreground X-ray luminous clusters with total mass greater
than 7.5 x 10^14 h^-1 M_sun, or X-ray luminosity L_x (2-10 keV) 8 x 10^44 h^-2
ergs s^-1, and background clusters with total mass greater than 10^14 h^-1
M_sun. The number expected in an open universe with Omega_m = 0.3 is less than
\~ 4. Because of uncertainty in sigma_8, the root-mean-square density
fluctuations in spheres of radius 8 h^-1 Mpc, the exact number of such lensing
events is uncertain by a factor of about 5. We examine methods to detect
cluster-cluster lensing events based on optical, X-ray, and Sunyaev-Zel'dovich
effect observations. | 9809062v3 |
2000-04-14 | Source Reconstruction as an Inverse Problem | Inverse Problem techniques offer powerful tools which deal naturally with
marginal data and asymmetric or strongly smoothing kernels, in cases where
parameter-fitting methods may be used only with some caution. Although they are
typically subject to some bias, they can invert data without requiring one to
assume a particular model for the source. The Backus-Gilbert method in
particular concentrates on the tradeoff between resolution and stability, and
allows one to select an optimal compromise between them. We use these tools to
analyse the problem of reconstructing features of the source star in a
microlensing event, show that it should be possible to obtain useful
information about the star with reasonably obtainable data, and note that the
quality of the reconstruction is more sensitive to the number of data points
than to the quality of individual ones. | 0004200v1 |
2000-04-18 | Galaxy Cluster Baryon Fractions, Cluster Surveys and Cosmology | The properties of nearby galaxy clusters limit the range of cosmological
parameters consistent with our universe. We describe the limits which arise
from studies of the intracluster medium (ICM) mass fraction fICM and
consideration of the possible sources of systematic error:
Omega_M<0.44h_{50}^{-1/2} at 95% confidence. We emphasize that independent of
Type Ia supernovae (SNe Ia) observations, this cluster study, taken together
with published cosmic microwave background (CMB) anisotropy studies, indicates
a non-zero quintessence or dark energy component Omega_Q>0.
We then discuss future galaxy cluster surveys which will probe the abundance
of galaxy clusters to intermediate and high redshift. We investigate the
sensitivity of these surveys to the cosmological density parameter Omega_M and
the equation of state parameter w of any quintessence component. In particular,
we show that cluster survey constraints from a proposed large solid angle X-ray
survey are comparable in precision and complementary in nature to constraints
expected from future CMB anisotropy and SNe Ia studies. | 0004244v1 |
2000-05-11 | Measurement of [OIII] Emission in Lyman Break Galaxies | Measurements of [OIII] emission in Lyman Break galaxies (LBGs) at z>3 are
presented. Four galaxies were observed with narrow-band filters using the
Near-IR Camera on the Keck I 10-m telescope. A fifth galaxy was observed
spectroscopically during the commissioning of NIRSPEC, the new infrared
spectrometer on Keck II. The emission-line spectrum is used to place limits on
the metallicity. Comparing these new measurements with others available from
the literature, we find that strong oxygen emission in LBGs may suggest
sub-solar metallicity for these objects. The [OIII]5007 line is also used to
estimate the star formation rate (SFR) of the LBGs. The inferred SFRs are
higher than those estimated from the UV continuum, and may be evidence for dust
extinction. | 0005254v1 |
2001-03-02 | Clusters in the Precision Cosmology Era | Over the coming decade, the observational samples available for studies of
cluster abundance evolution will increase from tens to hundreds, or possibly to
thousands, of clusters. Here we assess the power of future surveys to determine
cosmological parameters. We quantify the statistical differences among
cosmologies, including the effects of the cosmic equation of state parameter w,
in mock cluster catalogs simulating a 12 sq. deg Sunyaev-Zeldovich Effect
survey and a deep 10^4 sq. deg X-ray survey. The constraints from clusters are
complementary to those from studies of high-redshift Supernovae (SNe), CMB
anisotropies, or counts of high-redshift galaxies. Our results indicate that a
statistical uncertainty of a few percent on both Omega_m and w can be reached
when cluster surveys are used in combination with any of these other datasets. | 0103049v1 |
2002-07-05 | New Tests of the Cluster Entropy Floor Hypothesis | Recent efforts to account for the observed X-ray luminosity - temperature
relation of galaxy clusters has led to suggestions that the ICM has an apparent
``entropy floor'' at or above the level of 300 keV cm^2. Here, we propose new
tests based on the thermal Sunyaev-Zeldovich effect and on the cluster gas mass
- temperature trend (from X-ray data) to probe the level of excess entropy in
the ICM. We show that these new tests lend further support to the case for a
high entropy floor in massive clusters. | 0207147v1 |
2003-06-18 | Kinematic Masses of Super Star Clusters in M82 from High-Resolution Near-Infrared Spectroscopy | Using high-resolution (R~22,000) near-infrared (1.51 -- 1.75 microns) spectra
from Keck Observatory, we measure the kinematic masses of two super star
clusters in M82. Cross-correlation of the spectra with template spectra of cool
evolved stars gives stellar velocity dispersions of sigma_r=15.9 +/- 0.8 km/s
for MGG-9 and sigma_r=11.4 +/- 0.8 km/s for MGG-11. The cluster spectra are
dominated by the light of red supergiants, and correlate most closely with
template supergiants of spectral types M0 and M4.5. We fit King models to the
observed profiles of the clusters in archival HST/NICMOS images to measure the
half-light radii. Applying the virial theorem, we determine masses of 1.5 +/-
0.3 x 10^6 M_sun for MGG-9 and 3.5 +/- 0.7 x 10^5 M_sun for MGG-11. Population
synthesis modelling suggests that MGG-9 is consistent with a standard initial
mass function, whereas MGG-11 appears to be deficient in low-mass stars
relative to a standard IMF. There is, however, evidence of mass segregation in
the clusters, in which case the virial mass estimates would represent lower
limits. | 0306373v1 |
2003-09-10 | The CMB Quadrupole in a Polarized Light | The low quadrupole of the cosmic microwave background (CMB), measured by COBE
and confirmed by WMAP, has generated much discussion recently. We point out
that the well-known correlation between temperature and polarization
anisotropies of the CMB further constrains the low multipole anisotropy data.
This correlation originates from the fact that the low-multipole polarization
signal is sourced by the CMB quadrupole as seen by free electrons during the
relatively recent cosmic history. Consequently, the large-angle temperature
anisotropy data make restrictive predictions for the large-angle polarization
anisotropy, which depend primarily on the optical depth for electron scattering
after cosmological recombination, tau. We show that if current cosmological
models for the generation of large angle anisotropy are correct and the
COBE/WMAP data are not significantly contaminated by non-CMB signals, then the
observed C_te amplitude on the largest scales is discrepant at the 99.8% level
with the observed C_tt for the concordance LCDM model with tau=0.10. Using
tau=0.17, the preferred WMAP model-independent value, the discrepancy is at the
level of 98.5%. | 0309281v2 |
2003-10-11 | Statistics of Giant Arcs in Galaxy Clusters | We study the expected properties and statistics of giant arcs produced by
galaxy clusters in a LambdaCDM universe and investigate how the characteristics
of CDM clusters determine the properties of the arcs they generate. Due to the
triaxiality and substructure of CDM halos, the giant arc cross section for
individual clusters varies by more than an order of magnitude as a function of
viewing angle. In addition, the shallow density cusps and triaxiality of CDM
clusters cause systematic alignments of giant arcs which should be testable
with larger samples from forthcoming lensing surveys. We compute the predicted
statistics of giant arcs for the LambdaCDM model and compare to results from
previous surveys. The predicted arc statistics are in excellent agreement with
the numbers of giant arcs observed around low redshift (0.2 < z < 0.6) clusters
from the EMSS sample, however there are hints of a possible excess of arcs
observed around high redshift z > 0.6 clusters. This excess, if real, appears
to be due to the presence of highly massive or concentrated clusters at high
redshifts. | 0310306v1 |
2004-01-23 | Gravitational Lensing of the Microwave Background by Galaxy Clusters | Galaxy clusters will distort the pattern of temperature anisotropies in the
microwave background via gravitational lensing. We create lensed microwave
background maps using clusters drawn from numerical cosmological simulations. A
distinctive dipole-like temperature fluctuation pattern is formed aligned with
the underlying microwave temperature gradient. For a massive cluster, the
characteristic angular size of the temperature distortion is a few arcminutes
and the characteristic amplitude a few micro-Kelvin. We demonstrate a simple
technique for estimating the lensing deflection induced by the cluster;
microwave background lensing measurements have the potential to determine the
mass distribution for some clusters with good accuracy on angular scales up to
a few arcminutes. Future high-resolution and high-sensitivity microwave
background maps will have the capability to detect lensing by clusters; we
discuss various systematic limitations on probing cluster masses using this
technique. | 0401519v2 |
2004-04-15 | Is the slope of the intrinsic Baldwin effect constant? | We investigate the relationship between emission-line strength and continuum
luminosity in the best-studied nearby Seyfert 1 galaxy NGC5548. Our analysis of
13 years of ground-based optical monitoring data reveals significant
year-to-year variations in the observed H-beta emission-line response in this
source. More specifically, we confirm the result of Gilbert and Peterson (2003)
of a non-linear relationship between the continuum and H-beta emission-line
fluxes. Furthermore, we show that the slope of this relation is not constant,
but rather decreases as the continuum flux increases. Both effects are
consistent with photoionisation model predictions of a luminosity-dependent
response in this line. | 0404296v1 |
2005-08-04 | Gravitino, Axino, Kaluza-Klein Graviton Warm and Mixed Dark Matter and Reionisation | Stable particle dark matter may well originate during the decay of long-lived
relic particles, as recently extensively examined in the cases of the axino,
gravitino, and higher-dimensional Kaluza-Klein (KK) graviton. It is shown that
in much of the viable parameter space such dark matter emerges naturally
warm/hot or mixed. In particular, decay produced gravitinos (KK-gravitons) may
only be considered cold for the mass of the decaying particle in the several
TeV range, unless the decaying particle and the dark matter particle are almost
degenerate. Such dark matter candidates are thus subject to a host of
cosmological constraints on warm and mixed dark matter, such as limits from a
proper reionisation of the Universe, the Lyman-alpha forest, and the abundance
of clusters of galaxies.. It is shown that constraints from an early
reionsation epoch, such as indicated by recent observations, may potentially
limit such warm/hot components to contribute only a very small fraction to the
dark matter. | 0508141v2 |
1999-08-10 | Magnetic relaxation in a classical spin chain as model for nanowires | With decreasing particle size, different mechanisms dominate the thermally
activated magnetization reversal in ferromagnetic particles. We investigate
some of these mechanisms for the case of elongated, single-domain nanoparticles
which we describe by a classical Heisenberg spin chain driven by an external
magnetic field. For sufficiently small system size the magnetic moments rotate
coherently. With increasing size a crossover to a reversal due to
soliton-antisoliton nucleation sets in. For even larger systems many of these
soliton-antisoliton pairs nucleate at the same time. These effects give rise to
a complex size dependence of the energy barriers and characteristic time scales
of the relaxation. We study these quantities using Monte Carlo simulations as
well as a direct integration of the Landau-Lifshitz-Gilbert equation of motion
with Langevin dynamics and we compare our results with asymptotic solutions for
the escape rate following from the Fokker-Planck equation. Also, we investigate
the crossover from coherent rotation to soliton-antisoliton nucleation and
multi-droplet nucleation, especially its dependence on the system size, the
external field and the anisotropy of the system. | 9908150v1 |
2000-07-17 | Fine-grid Simulations of Thermally Activated Switching in Nanoscale Magets | Numerical integration of the Landau-Lifshitz-Gilbert equation with thermal
fluctuations is used to study the dynamic response of single-domain nanomagnets
to rapid changes in the applied magnetic field. The simulation can resolve
magnetization patterns within nanomagnets and uses the Fast Multipole method to
calculate dipole-dipole interactions efficiently. The thermal fluctuations play
an essential part in the reversal process whenever the applied field is less
than the zero-temperature coercive field. In this situation pillar-shaped
nanomagnets are found to reverse through a local curling mode that involves the
formation and propagation of a domain wall. Tapering the ends of the pillars to
reduce pole-avoidance effects changes the energies involved but not the
fundamental process. The statistical distribution of switching times is well
described by the independent nucleation and subsequent growth of regions of
reversed magnetization at both ends of the pillar. | 0007279v1 |
2001-01-31 | Langevin Simulation of Thermally Activated Magnetization Reversal in Nanoscale Pillars | Numerical solutions of the Landau-Lifshitz-Gilbert micromagnetic model
incorporating thermal fluctuations and dipole-dipole interactions (calculated
by the Fast Multipole Method) are presented for systems composed of nanoscale
iron pillars of dimension 9 nm x 9 nm x 150 nm. Hysteresis loops generated
under sinusoidally varying fields are obtained, while the coercive field is
estimated to be 1979 $\pm$ 14 Oe using linear field sweeps at T=0 K. Thermal
effects are essential to the relaxation of magnetization trapped in a
metastable orientation, such as happens after a rapid reversal of an external
magnetic field less than the coercive value. The distribution of switching
times is compared to a simple analytic theory that describes reversal with
nucleation at the ends of the nanomagnets. Results are also presented for
arrays of nanomagnets oriented perpendicular to a flat substrate. Even at a
separation of 300 nm, where the field from neighboring pillars is only $\sim$ 1
Oe, the interactions have a significant effect on the switching of the magnets. | 0101477v2 |
2001-05-04 | On a common circle: natural scenes and Gestalt rules | To understand how the human visual system analyzes images, it is essential to
know the structure of the visual environment. In particular, natural images
display consistent statistical properties that distinguish them from random
luminance distributions. We have studied the geometric regularities of oriented
elements (edges or line segments) present in an ensemble of visual scenes,
asking how much information the presence of a segment in a particular location
of the visual scene carries about the presence of a second segment at different
relative positions and orientations. We observed strong long-range correlations
in the distribution of oriented segments that extend over the whole visual
field. We further show that a very simple geometric rule, cocircularity,
predicts the arrangement of segments in natural scenes, and that different
geometrical arrangements show relevant differences in their scaling properties.
Our results show similarities to geometric features of previous physiological
and psychophysical studies. We discuss the implications of these findings for
theories of early vision. | 0105097v1 |
2002-10-11 | Fluctuations and Dissipation of Coherent Magnetization | A quantum mechanical model is used to derive a generalized Landau-Lifshitz
equation for a magnetic moment, including fluctuations and dissipation. The
model reproduces the Gilbert-Brown form of the equation in the classical limit.
The magnetic moment is linearly coupled to a reservoir of bosonic degrees of
freedom. Use of generalized coherent states makes the semiclassical limit more
transparent within a path-integral formulation. A general
fluctuation-dissipation theorem is derived. The magnitude of the magnetic
moment also fluctuates beyond the Gaussian approximation. We discuss how the
approximate stochastic description of the thermal field follows from our
result. As an example, we go beyond the linear-response method and show how the
thermal fluctuations become anisotropy-dependent even in the uniaxial case. | 0210273v2 |
2002-11-18 | Field dependence of magnetization reversal by spin transfer | We analyse the effect of the applied field (Happl) on the current-driven
magnetization reversal in pillar-shaped Co/Cu/Co trilayers, where we observe
two different types of transition between the parallel (P) and antiparallel
(AP) magnetic configurations of the Co layers. If Happl is weaker than a rather
small threshold value, the transitions between P and AP are irreversible and
relatively sharp. For Happl exceding the threshold value, the same transitions
are progressive and reversible. We show that the criteria for the stability of
the P and AP states and the experimentally observed behavior can be precisely
accounted for by introducing the current-induced torque of the spin transfer
models in a Landau-Lifschitz-Gilbert equation. This approach also provides a
good description for the field dependence of the critical currents. | 0211371v1 |
2003-10-18 | NMR Investigation of the Organic Conductor lambda-(BETS)2FeCl4 | The two-dimensional organic conductor lambda-(BETS)2FeCl4 has an unusual
phase diagram as a function of temperature and magnetic field that includes a
paramagnetic metal (PM) phase, an antiferromagnetic insulating (AFI) phase, and
a field-induced superconducting phase [S. Uji, H. Kobayashi, L. Balicas, and
James S. Brooks, Adv. Mater. 14, 243 (2002), and cited references]. Here, we
report a preliminary investigation of the PM and AFI phases at 9.0 T over the
temperature range 2.0-180 K that uses proton NMR measurements of the spectrum,
the spin-lattice relaxation rate (1/T1), and the spin echo decay rate (1/T2).
The sample is asmall single crystal whose mass is approximately 3 micrograms
(approximately 2E16 protons). Its small size creates several challenges that
include detecting small signals and excluding parasitic proton signals that are
not from the sample [H. N. Bachman and I. F. Silvera, J. Mag. Res. 162, 417
(2003)]. These strategies and other techniques used to obtain viable signals
are described. | 0310433v1 |
2004-04-22 | Non-collinear magnetic structures: a possible cause for current induced switching | Current induced switching in Co/Cu/Co trilayers is described in terms of
ab-initio determined magnetic twisting energies and corresponding sheet
resistances. In viewing the twisting energy as an energy flux the
characteristic time thereof is evaluated by means of the
Landau-Lifshitz-Gilbert equation using ab-initio parameters. The obtained
switching times are in very good agreement with available experimental data. In
terms of the calculated currents, scalar quantities since a classical Ohm's law
is applied, critical currents needed to switch magnetic configurations from
parallel to antiparallel and vice versa can unambiguously be defined. It is
found that the magnetoresistance viewed as a function of the current is
essentially determined by the twisting energy as a function of the relative
angle between the orientations of the magnetization in the magnetic slabs,
which in turn can also explain in particular cases the fact that after having
switched off the current the system remains in the switched magnetic
configuration. For all ab-initio type calculations the fully relativistic
Screened Korringa-Kohn-Rostoker method and the corresponding Kubo-Greenwood
equation in the context of density functional theory are applied. | 0404534v1 |
2004-06-21 | Basic considerations for magnetization dynamics in the combined presence of spin-transfer torques and thermal fluctuations | This article reviews basic theoretical features of Gilbert magnetization
dynamics of a single domain magnetic film in the presence of Slonczewski
spin-transfer torques, with and without thermal fluctuations taken into
account. Rather than showing results of detailed numerical calculations, the
discussion here is restricted to basic analytical results and conclusions which
can mostly be derived from simply the form of the equations of motion, as well
as elementary considerations based on classical stability analysis and the
fluctuation-dissipation theorem. The presents work describes how interesting
features of spin-transfer may be viewed as arising from non-equilibrium
thermodynamics that are a direct consequence of the nonreciprocal nature of
spin-transfer torques. The present article discusses fairly general results for
spin-torque induced instability without thermal fluctuations, as well as the
case of thermally activated magnetization reversal in uniaxial devices in the
combined presence of external fields, thermal fluctuations, and spin-transfer
torques. The results will be discussed and briefly compared and contrasted with
that of prior work. | 0406486v1 |
2004-06-24 | Thermal Effects on the Magnetic Field Dependence of Spin Transfer Induced Magnetization Reversal | We have developed a self-aligned, high-yield process to fabricate CPP
(current perpendicular to the plane) magnetic sensors of sub 100 nm dimensions.
A pinned synthetic antiferromagnet (SAF) is used as the reference layer which
minimizes dipole coupling to the free layer and field induced rotation of the
reference layer. We find that the critical currents for spin transfer induced
magnetization reversal of the free layer vary dramatically with relatively
small changes the in-plane magnetic field, in contrast to theoretical
predictions based on stability analysis of the Gilbert equations of
magnetization dynamics including Slonczewski-type spin-torque terms. The
discrepancy is believed due to thermal fluctuations over the time scale of the
measurements. Once thermal fluctuations are taken into account, we find good
quantitative agreement between our experimental results and numerical
simulations. | 0406574v1 |
2004-07-23 | Micromagnetic understanding of current-driven domain wall motion in patterned nanowires | In order to explain recent experiments reporting a motion of magnetic domain
walls (DW) in nanowires carrying a current, we propose a modification of the
spin transfer torque term in the Landau-Lifchitz-Gilbert equation. We show that
it explains, with reasonable parameters, the measured DW velocities as well as
the variation of DW propagation field under current. We also introduce
coercivity by considering rough wires. This leads to a finite DW propagation
field and finite threshold current for DW propagation, hence we conclude that
threshold currents are extrinsic. Some possible models that support this new
term are discussed. | 0407628v2 |
2004-08-07 | Hysteresis multicycles in nanomagnet arrays | We predict two new physical effects in arrays of single-domain nanomagnets by
performing simulations using a realistic model Hamiltonian and physical
parameters. First, we find hysteretic multicycles for such nanomagnets. The
simulation uses continuous spin dynamics through the Landau-Lifshitz-Gilbert
(LLG) equation. In some regions of parameter space, the probability of finding
a multicycle is as high as ~0.6. We find that systems with larger and more
anisotropic nanomagnets tend to display more multicycles. This result
demonstrates the importance of disorder and frustration for multicycle
behavior. We also show that there is a fundamental difference between the more
realistic vector LLG equation and scalar models of hysteresis, such as Ising
models. In the latter case, spin and external field inversion symmetry is
obeyed but in the former it is destroyed by the dynamics, with important
experimental implications. | 0408158v1 |
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