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2019-12-13
|
Distance between Bound Entangled States from Unextendible Product Bases and Separable States
|
We discuss the use of the Gilbert algorithm to tailor entanglement witnesses
for unextendibleproduct basis bound entangled states (UPB BE states). The
method relies on the fact that an optimalentanglement witness is given by a
plane perpendicular to a line between the reference state, entanglementof which
is to be witnessed, and its closest separable state (CSS). The Gilbert
algorithm finds anapproximation of CSS. In this article, we investigate if this
approximation can be good enough toyield a valid entanglement witness. We
compare witnesses found with Gilbert algorithm and those givenby
Bandyopadhyay-Ghosh-Roychowdhury (BGR) construction. This comparison allows us
to learnabout the amount of entanglement and we find a relationship between it
and a feature of the constructionof UPB BE states, namely the size of their
central tile. We show that in most studied cases, witnessesfound with the
Gilbert algorithm in this work are more optimal than ones obtained by
Bandyopadhyay,Ghosh, and Roychowdhury. This result implies the increased
tolerance to experimental imperfections ina realization of the state.
|
1912.06569v2
|
2020-10-16
|
Genome organization: experiments and modelling
|
This is an introduction to the special issue Genome organization: experiments
and simulations, published in Chromosome Research, volume 25, issue 1 (2017).
|
2010.08464v1
|
2023-10-17
|
Sparse grid approximation of stochastic parabolic PDEs: The Landau--Lifshitz--Gilbert equation
|
We show convergence rates for a sparse grid approximation of the distribution
of solutions of the stochastic Landau-Lifshitz-Gilbert equation. Beyond being a
frequently studied equation in engineering and physics, the stochastic
Landau-Lifshitz-Gilbert equation poses many interesting challenges that do not
appear simultaneously in previous works on uncertainty quantification: The
equation is strongly non-linear, time-dependent, and has a non-convex side
constraint. Moreover, the parametrization of the stochastic noise features
countably many unbounded parameters and low regularity compared to other
elliptic and parabolic problems studied in uncertainty quantification. We use a
novel technique to establish uniform holomorphic regularity of the
parameter-to-solution map based on a Gronwall-type estimate and the implicit
function theorem. This method is very general and based on a set of abstract
assumptions. Thus, it can be applied beyond the Landau-Lifshitz-Gilbert
equation as well. We demonstrate numerically the feasibility of approximating
with sparse grid and show a clear advantage of a multi-level sparse grid
scheme.
|
2310.11225v2
|
2024-04-04
|
Resolving Gilbert's Conjecture: Dimensional Dependencies in Hardy Spaces Valued in Clifford Modules
|
This article provides a thorough investigation into Gilbert's Conjecture,
pertaining to Hardy spaces in the upper half-space valued in Clifford modules.
We explore the conjecture proposed by Gilbert in 1991, which seeks to extend
the classical principle of representing real $L^p$ functions on the real line
as boundary values of Hardy holomorphic functions to higher-dimensional
Euclidean spaces valued in any Clifford module. We present a complete
resolution to this conjecture, demonstrating that its validity is contingent
upon the dimension $n$, specifically holding true when \(n \not\equiv 6, 7 \mod
8\) and failing otherwise. The pivotal discovery that Gilbert's conjecture can
be reformulated as a set of algebraic conditions is underscored in this work.
To navigate these conditions, we employ a novel strategy that leverages the
octonions, revealing their instrumental role in addressing issues related to
Clifford modules and spinors. This innovative approach not only provides
explicit realization through the generalization of the Hilbert transform to the
Riesz transform but also establishes a significant advancement in the
understanding of Hardy spaces within higher dimensions.
|
2404.03478v1
|
1998-02-23
|
Shell Effects on Rotational Damping in Superdeformed Nuclei
|
Damping of rotational motion in superdeformed Hg and Dy-region nuclei is
studied by means of cranked shell model diagonalization. It is shown that a
shell oscillation in single-particle alignments affects significantly
properties of rotational damping. Onset properties of damping and damping width
for Hg are quite different from those for Dy-region superdeformed nuclei.
|
9802065v1
|
2003-08-29
|
Influence of radiative damping on the optical-frequency susceptibility
|
Motivated by recent discussions concerning the manner in which damping
appears in the electric polarizability, we show that (a) there is a dependence
of the nonresonant contribution on the damping and that (b) the damping enters
according to the "opposite sign prescription." We also discuss the related
question of how the damping rates in the polarizability are related to
energy-level decay rates.
|
0309001v1
|
2024-03-19
|
Weakly elliptic damping gives sharp decay
|
We prove that weakly elliptic damping gives sharp energy decay for the
abstract damped wave semigroup, where the damping is not in the functional
calculus. In this case, there is no overdamping. We show applications in
linearised water waves and Kelvin--Voigt damping.
|
2403.13067v1
|
2015-05-15
|
Reliable Damping of Free Surface Waves in Numerical Simulations
|
This paper generalizes existing approaches for free-surface wave damping via
momentum sinks for flow simulations based on the Navier-Stokes equations. It is
shown in 2D flow simulations that, to obtain reliable wave damping, the
coefficients in the damping functions must be adjusted to the wave parameters.
A scaling law for selecting these damping coefficients is presented, which
enables similarity of the damping in model- and full-scale. The influence of
the thickness of the damping layer, the wave steepness, the mesh fineness and
the choice of the damping coefficients are examined. An efficient approach for
estimating the optimal damping setup is presented. Results of 3D ship
resistance computations show that the scaling laws apply to such simulations as
well, so the damping coefficients should be adjusted for every simulation to
ensure convergence of the solution in both model and full scale. Finally,
practical recommendations for the setup of reliable damping in flow simulations
with regular and irregular free surface waves are given.
|
1505.04087v2
|
2019-02-25
|
Resonant absorption as a damping mechanism for the transverse oscillations of the coronal loops observed by SDO/AIA
|
Solar coronal loops represent the variety of fast, intermediate, and slow
normal mode oscillations. In this study, the transverse oscillations of the
loops with a few-minutes period and also with damping caused by the resonant
absorption were analyzed using extreme ultraviolet (EUV) images of the Sun. We
employed the 171 $\AA$ data recorded by Solar Dynamic Observatory
(SDO)/Atmospheric Imaging Assembly (AIA) to analyze the parameters of coronal
loop oscillations such as period, damping time, loop length, and loop width.
For the loop observed on 11 October 2013, the period and the damping of this
loop are obtained to be 19 and 70 minutes, respectively. The damping quality,
the ratio of the damping time to the period, is computed about 3.6. The period
and damping time for the extracted loop recorded on 22 January 2013 are about
81 and 6.79 minutes, respectively. The damping quality is also computed as 12.
It can be concluded that the damping of the transverse oscillations of the
loops is in the strong damping regime, so resonant absorption would be the main
reason for the damping.
|
1902.09649v1
|
2013-05-21
|
Characterization and Synthesis of Rayleigh Damped Elastodynamic Networks
|
We consider damped elastodynamic networks where the damping matrix is assumed
to be a non-negative linear combination of the stiffness and mass matrices
(also known as Rayleigh or proportional damping). We give here a
characterization of the frequency response of such networks. We also answer the
synthesis question for such networks, i.e., how to construct a Rayleigh damped
elastodynamic network with a given frequency response. Our analysis shows that
not all damped elastodynamic networks can be realized when the proportionality
constants between the damping matrix and the mass and stiffness matrices are
fixed.
|
1305.4961v1
|
2016-08-08
|
Damping Functions correct over-dissipation of the Smagorinsky Model
|
This paper studies the time-averaged energy dissipation rate $\langle
\varepsilon_{SMD} (u)\rangle$ for the combination of the Smagorinsky model and
damping function. The Smagorinsky model is well known to over-damp. One common
correction is to include damping functions that reduce the effects of model
viscosity near walls. Mathematical analysis is given here that allows
evaluation of $\langle \varepsilon_{SMD} (u)\rangle $ for any damping function.
Moreover, the analysis motivates a modified van Driest damping. It is proven
that the combination of the Smagorinsky with this modified damping function
does not over dissipate and is also consistent with Kolmogorov phenomenology.
|
1608.02655v2
|
2012-01-27
|
Full and Half Gilbert Tessellations with Rectangular Cells
|
We investigate the ray-length distributions for two different rectangular
versions of Gilbert's tessellation. In the full rectangular version, lines
extend either horizontally (with east- and west-growing rays) or vertically
(north- and south-growing rays) from seed points which form a Poisson point
process, each ray stopping when another ray is met. In the half rectangular
version, east and south growing rays do not interact with west and north rays.
For the half rectangular tessellation we compute analytically, via recursion, a
series expansion for the ray-length distribution, whilst for the full
rectangular version we develop an accurate simulation technique, based in part
on the stopping-set theory of Zuyev, to accomplish the same. We demonstrate the
remarkable fact that plots of the two distributions appear to be identical when
the intensity of seeds in the half model is twice that in the full model. Our
paper explores this coincidence mindful of the fact that, for one model, our
results are from a simulation (with inherent sampling error). We go on to
develop further analytic theory for the half-Gilbert model using stopping-set
ideas once again, with some novel features. Using our theory, we obtain exact
expressions for the first and second moment of ray length in the half-Gilbert
model. For all practical purposes, these results can be applied to the
full-Gilbert model as much better approximations than those provided by
Mackissack and Miles.
|
1201.5780v1
|
2021-06-08
|
On numerical aspects of parameter identification for the Landau-Lifshitz-Gilbert equation in Magnetic Particle Imaging
|
The Landau-Lifshitz-Gilbert equation yields a mathematical model to describe
the evolution of the magnetization of a magnetic material, particularly in
response to an external applied magnetic field. It allows one to take into
account various physical effects, such as the exchange within the magnetic
material itself. In particular, the Landau-Lifshitz-Gilbert equation encodes
relaxation effects, i.e., it describes the time-delayed alignment of the
magnetization field with an external magnetic field. These relaxation effects
are an important aspect in magnetic particle imaging, particularly in the
calibration process. In this article, we address the data-driven modeling of
the system function in magnetic particle imaging, where the
Landau-Lifshitz-Gilbert equation serves as the basic tool to include relaxation
effects in the model. We formulate the respective parameter identification
problem both in the all-at-once and the reduced setting, present reconstruction
algorithms that yield a regularized solution and discuss numerical experiments.
Apart from that, we propose a practical numerical solver to the nonlinear
Landau-Lifshitz-Gilbert equation, not via the classical finite element method,
but through solving only linear PDEs in an inverse problem framework.
|
2106.07625v1
|
2000-09-11
|
Numerical Studies on Locally Damped Structures
|
In the JLC/NLC X-band linear collider, it is essential to reduce the
long-range dipole wakefields in the accelerator structure to prevent beam break
up (BBU) and emittance degradation. The two methods of reducing the long-range
wakefields are detuning and damping. Detuning reduces the wakefields rapidly as
the dipole modes de-cohere but, with a finite number of modes, the wakefield
will grow again as the modes re-cohere. In contrast, damping suppresses the
wakefields at a longer distance. There are two principal damping schemes:
synchronous damping using HOM manifolds such as that used in the RDDS1
structure and local damping similar to that used in the CLIC structure. In a
locally damped scheme, one can obtain almost any Q value, however, the damping
can have significant effects on the accelerating mode. In this paper, we
present a medium local-damping scheme where the wakefields are controlled to
meet the BBU requirement while minimizing the degradations of the fundamental
rf parameters. We will address the load design and pulse heating issues
associated with the medium damping scheme.
|
0009039v1
|
2015-03-13
|
A one-step optimal energy decay formula for indirectly nonlinearly damped hyperbolic systems coupled by velocities
|
In this paper, we consider the energy decay of a damped hyperbolic system of
wave-wave type which is coupled through the velocities. We are interested in
the asymptotic properties of the solutions of this system in the case of
indirect nonlinear damping, i.e. when only one equation is directly damped by a
nonlinear damping. We prove that the total energy of the whole system decays as
fast as the damped single equation. Moreover, we give a one-step general
explicit decay formula for arbitrary nonlinearity. Our results shows that the
damping properties are fully transferred from the damped equation to the
undamped one by the coupling in velocities, different from the case of
couplings through displacements as shown in \cite{AB01, ACK01, AB02, AL12} for
the linear damping case, and in \cite{AB07} for the nonlinear damping case. The
proofs of our results are based on multiplier techniques, weighted nonlinear
integral inequalities and the optimal-weight convexity method of \cite{AB05,
AB10}.
|
1503.04126v1
|
2015-08-21
|
Radiative damping in wave guide based FMR measured via analysis of perpendicular standing spin waves in sputtered Permalloy films
|
The damping $\alpha$ of the spinwave resonances in 75 nm, 120 nm, and 200nm
-thick Permalloy films is measured via vector-network-analyzer
ferromagnetic-resonance (VNA-FMR) in the out-of-plane geometry. Inductive
coupling between the sample and the waveguide leads to an additional radiative
damping term. The radiative contribution to the over-all damping is determined
by measuring perpendicular standing spin waves (PSSWs) in the Permalloy films,
and the results are compared to a simple analytical model. The damping of the
PSSWs can be fully explained by three contributions to the damping: The
intrinsic damping, the eddy-current damping, and the radiative damping. No
other contributions were observed. Furthermore, a method to determine the
radiative damping in FMR measurements with a single resonance is suggested.
|
1508.05265v1
|
2022-09-28
|
Tunable nonlinear damping in parametric regime
|
Nonlinear damping plays a significant role in several area of physics and it
is becoming increasingly important to understand its underlying mechanism.
However, microscopic origin of nonlinear damping is still a debatable topic.
Here, we probe and report nonlinear damping in a highly tunable MoS2 nano
mechanical drum resonator using electrical homodyne actuation and detection
technique. In our experiment, we achieve 2:1 internal resonance by tuning
resonance frequency and observe enhanced non-linear damping. We probe the
effect of non-linear damping by characterizing parametric gain. Geometry and
tunability of the device allow us to reduce the effect of other prominent
Duffing non-linearity to probe the non-linear damping effectively. The enhanced
non-linear damping in the vicinity of internal resonance is also observed in
direct drive, supporting possible origin of non-linear damping. Our experiment
demonstrates, a highly tunable 2D material based nanoresonator offers an
excellent platform to study the nonlinear physics and exploit nonlinear damping
in parametric regime.
|
2209.14120v1
|
2005-11-07
|
The Effects of Alfven Waves and Radiation Pressure in Dusty Winds of Late-Type Stars. II. Dust-Cyclotron Damping
|
There are in the literature several theories to explain the mass loss in
stellar winds. In particular, for late-type stars, some authors have proposed a
wind model driven by an outward-directed flux of damped Alfven waves. The winds
of these stars present great amounts of dust particles that, if charged, can
give rise to new wave modes or modify the pre-existing ones. In this work, we
study how the dust can affect the propagation of Alfven waves in these winds
taking into account a specific damping mechanism, dust-cyclotron damping. This
damping affects the Alfven wave propagation near the dust-cyclotron frequency.
Hence, if we assume a dust size distribution, the damping occurs over a broad
band of wave frequencies. In this work, we present a model of Alfven
wave-driven winds using the dust-cyclotron damping mechanism. On the basis of
coronal holes in the Sun, which present a superradial expansion, our model also
assumes a diverging geometry for the magnetic field. Thus, the mass, momentum,
and energy equations are obtained and then solved in a self-consistent
approach. Our results of wind velocity and temperature profiles for a typical
K5 supergiant star shows compatibility with observations. We also show that,
considering the presence of charged dust particles, the wave flux is less
damped due to the dust-cyclotron damping than it would be if we consider some
other damping mechanisms studied in the literature, such as nonlinear damping,
resonant surface damping, and turbulent damping.
|
0511192v2
|
2013-09-11
|
Initial versus tangent stiffness-based Rayleigh damping in inelastic time history seismic analyses
|
In the inelastic time history analyses of structures in seismic motion, part
of the seismic energy that is imparted to the structure is absorbed by the
inelastic structural model, and Rayleigh damping is commonly used in practice
as an additional energy dissipation source. It has been acknowledged that
Rayleigh damping models lack physical consistency and that, in turn, it must be
carefully used to avoid encountering unintended consequences as the appearance
of artificial damping. There are concerns raised by the mass proportional part
of Rayleigh damping, but they are not considered in this paper. As far as the
stiffness proportional part of Rayleigh damping is concerned, either the
initial structural stiffness or the updated tangent stiffness can be used. The
objective of this paper is to provide a comprehensive comparison of these two
types of Rayleigh damping models so that a practitioner (i) can objectively
choose the type of Rayleigh damping model that best fits her/his needs and (ii)
is provided with useful analytical tools to design Rayleigh damping model with
good control on the damping ratios throughout inelastic analysis. To that end,
a review of the literature dedicated to Rayleigh damping within these last two
decades is first presented; then, practical tools to control the modal damping
ratios throughout the time history analysis are developed; a simple example is
finally used to illustrate the differences resulting from the use of either
initial or tangent stiffness-based Rayleigh damping model.
|
1309.2741v1
|
2017-07-14
|
Damping of gravitational waves by matter
|
We develop a unified description, via the Boltzmann equation, of damping of
gravitational waves by matter, incorporating collisions. We identify two
physically distinct damping mechanisms -- collisional and Landau damping. We
first consider damping in flat spacetime, and then generalize the results to
allow for cosmological expansion. In the first regime, maximal collisional
damping of a gravitational wave, independent of the details of the collisions
in the matter is, as we show, significant only when its wavelength is
comparable to the size of the horizon. Thus damping by intergalactic or
interstellar matter for all but primordial gravitational radiation can be
neglected. Although collisions in matter lead to a shear viscosity, they also
act to erase anisotropic stresses, thus suppressing the damping of
gravitational waves. Damping of primordial gravitational waves remains
possible. We generalize Weinberg's calculation of gravitational wave damping,
now including collisions and particles of finite mass, and interpret the
collisionless limit in terms of Landau damping. While Landau damping of
gravitational waves cannot occur in flat spacetime, the expansion of the
universe allows such damping by spreading the frequency of a gravitational wave
of given wavevector.
|
1707.05192v2
|
2024-03-13
|
The q-ary Gilbert-Varshamov bound can be improved for all but finitely many positive integers q
|
For any positive integer $q\geq 2$ and any real number $\delta\in(0,1)$, let
$\alpha_q(n,\delta n)$ denote the maximum size of a subset of $\mathbb{Z}_q^n$
with minimum Hamming distance at least $\delta n$, where
$\mathbb{Z}_q=\{0,1,\dotsc,q-1\}$ and $n\in\mathbb{N}$. The asymptotic rate
function is defined by $ R_q(\delta) =
\limsup_{n\rightarrow\infty}\frac{1}{n}\log_q\alpha_q(n,\delta n).$ The famous
$q$-ary asymptotic Gilbert-Varshamov bound, obtained in the 1950s, states that
\[ R_q(\delta) \geq 1 -
\delta\log_q(q-1)-\delta\log_q\frac{1}{\delta}-(1-\delta)\log_q\frac{1}{1-\delta}
\stackrel{\mathrm{def}}{=}R_\mathrm{GV}(\delta,q) \] for all positive integers
$q\geq 2$ and $0<\delta<1-q^{-1}$. In the case that $q$ is an even power of a
prime with $q\geq 49$, the $q$-ary Gilbert-Varshamov bound was firstly improved
by using algebraic geometry codes in the works of Tsfasman, Vladut, and Zink
and of Ihara in the 1980s. These algebraic geometry codes have been modified to
improve the $q$-ary Gilbert-Varshamov bound $R_\mathrm{GV}(\delta,q)$ at a
specific tangent point $\delta=\delta_0\in (0,1)$ of the curve
$R_\mathrm{GV}(\delta,q)$ for each given integer $q\geq 46$. However, the
$q$-ary Gilbert-Varshamov bound $R_\mathrm{GV}(\delta,q)$ at $\delta=1/2$,
i.e., $R_\mathrm{GV}(1/2,q)$, remains the largest known lower bound of
$R_q(1/2)$ for infinitely many positive integers $q$ which is a generic prime
and which is a generic non-prime-power integer. In this paper, by using codes
from geometry of numbers introduced by Lenstra in the 1980s, we prove that the
$q$-ary Gilbert-Varshamov bound $R_\mathrm{GV}(\delta,q)$ with $\delta\in(0,1)$
can be improved for all but finitely many positive integers $q$. It is shown
that the growth defined by $\eta(\delta)=
\liminf_{q\rightarrow\infty}\frac{1}{\log q}\log[1-\delta-R_q(\delta)]^{-1}$
for every $\delta\in(0,1)$ has actually a nontrivial lower bound.
|
2403.08727v2
|
2002-06-27
|
Initial-amplitude dependence in weakly damped oscillators
|
A pedagogically instructive experimental procedure is suggested for
distinguishing between different damping terms in a weakly damped oscillator,
which highclights the connection between non-linear damping and
initial-amplitude dependence. The most common damping terms such as contact
friction, air resistance, viscous drag, and electromagnetic damping have
velocity dependences of the form constant, v, or v^2. The corresponding energy
dependences of the form \sqrt{E}, E, or E\sqrt{E} in the energy loss equation
give rise to characteristic dependence of the amplitude decay slope on the
initial amplitude.
|
0206086v1
|
2006-05-22
|
The entanglement of damped noon-state and its performance in phase measurement
|
The state evolution of the initial optical \textit{noon} state is
investigated. The residue entanglement of the state is calculated after it is
damped by amplitude and phase damping. The relative entropy of entanglement of
the damped state is exactly obtained. The performance of direct application of
the damped \textit{noon} state is compared with that of firstly distilling the
docoherence damped state then applying it in measurement.
|
0605184v1
|
2007-10-04
|
Channel-Adapted Quantum Error Correction for the Amplitude Damping Channel
|
We consider error correction procedures designed specifically for the
amplitude damping channel. We analyze amplitude damping errors in the
stabilizer formalism. This analysis allows a generalization of the [4,1]
`approximate' amplitude damping code of quant-ph/9704002. We present this
generalization as a class of [2(M+1),M] codes and present quantum circuits for
encoding and recovery operations. We also present a [7,3] amplitude damping
code based on the classical Hamming code. All of these are stabilizer codes
whose encoding and recovery operations can be completely described with
Clifford group operations. Finally, we describe optimization options in which
recovery operations may be further adapted according to the damping probability
gamma.
|
0710.1052v1
|
2010-03-24
|
Dynamical shift condition for unequal mass black hole binaries
|
Certain numerical frameworks used for the evolution of binary black holes
make use of a gamma driver, which includes a damping factor. Such simulations
typically use a constant value for damping. However, it has been found that
very specific values of the damping factor are needed for the calculation of
unequal mass binaries. We examine carefully the role this damping plays, and
provide two explicit, non-constant forms for the damping to be used with
mass-ratios further from one. Our analysis of the resultant waveforms compares
well against the constant damping case.
|
1003.4681v1
|
2011-11-30
|
Local phase damping of single qubits sets an upper bound on the phase damping rate of entangled states
|
I derive an inequality in which the phase damping rates of single qubits set
an upper bound for the phase damping rate of entangled states of many qubits.
The derivation is based on two assumptions: first, that the phase damping can
be described by a dissipator in Lindblad form and, second, that the phase
damping preserves the population of qubit states in a given basis.
|
1111.7152v2
|
2012-05-11
|
Quantum dynamics of the damped harmonic oscillator
|
The quantum theory of the damped harmonic oscillator has been a subject of
continual investigation since the 1930s. The obstacle to quantization created
by the dissipation of energy is usually dealt with by including a discrete set
of additional harmonic oscillators as a reservoir. But a discrete reservoir
cannot directly yield dynamics such as Ohmic damping (proportional to velocity)
of the oscillator of interest. By using a continuum of oscillators as a
reservoir, we canonically quantize the harmonic oscillator with Ohmic damping
and also with general damping behaviour. The dynamics of a damped oscillator is
determined by an arbitrary effective susceptibility that obeys Kramers-Kronig
relations. This approach offers an alternative description of nano-mechanical
oscillators and opto-mechanical systems.
|
1205.2545v1
|
2014-02-28
|
Escape rate for the power-law distribution in low-to-intermediate damping
|
Escape rate in the low-to-intermediate damping connecting the low damping
with the intermediate damping is established for the power-law distribution on
the basis of flux over population theory. We extend the escape rate in the low
damping to the low-to-intermediate damping, and get an expression for the
power-law distribution. Then we apply the escape rate for the power-law
distribution to the experimental study of the excited-state isomerization, and
show a good agreement with the experimental value. The extra current and the
improvement of the absorbing boundary condition are discussed.
|
1402.7194v2
|
2015-03-21
|
On damping created by heterogeneous yielding in the numerical analysis of nonlinear reinforced concrete frame elements
|
In the dynamic analysis of structural engineering systems, it is common
practice to introduce damping models to reproduce experimentally observed
features. These models, for instance Rayleigh damping, account for the damping
sources in the system altogether and often lack physical basis. We report on an
alternative path for reproducing damping coming from material nonlinear
response through the consideration of the heterogeneous character of material
mechanical properties. The parameterization of that heterogeneity is performed
through a stochastic model. It is shown that such a variability creates the
patterns in the concrete cyclic response that are classically regarded as
source of damping.
|
1503.07122v1
|
2016-01-20
|
Introduction to Landau Damping
|
The mechanism of Landau damping is observed in various systems from plasma
oscillations to accelerators. Despite its widespread use, some confusion has
been created, partly because of the different mechanisms producing the damping
but also due to the mathematical subtleties treating the effects. In this
article the origin of Landau damping is demonstrated for the damping of plasma
oscillations. In the second part it is applied to the damping of coherent
oscillations in particle accelerators. The physical origin, the mathematical
treatment leading to the concept of stability diagrams and the applications are
discussed.
|
1601.05227v1
|
2018-07-25
|
Regularity and asymptotic behaviour for a damped plate-membrane transmission problem
|
We consider a transmission problem where a structurally damped plate equation
is coupled with a damped or undamped wave equation by transmission conditions.
We show that exponential stability holds in the damped-damped situation and
polynomial stability (but no exponential stability) holds in the
damped-undamped case. Additionally, we show that the solutions first defined by
the weak formulation, in fact have higher Sobolev space regularity.
|
1807.09730v1
|
2021-08-04
|
Nonlinear fluid damping of elastically mounted pitching wings in quiescent water
|
We experimentally study the nonlinear fluid damping of a rigid but
elastically mounted pitching wing in the absence of a freestream flow. The
dynamics of the elastic mount are simulated using a cyber-physical system. We
perturb the wing and measure the fluid damping coefficient from damped
oscillations over a large range of pitching frequencies, pitching amplitudes,
pivot locations and sweep angles. A universal fluid damping scaling is proposed
to incorporate all these parameters. Flow fields obtained using particle image
velocimetry are analyzed to explain the nonlinear behaviors of the fluid
damping.
|
2108.02090v1
|
2002-11-03
|
Damping of coupled phonon--plasmon modes
|
The effect of free carriers on dispersion and damping of coupled
phonon-plasmon modes is considered in the long-wave approximation. The electron
and phonon scattering rate as well as Landau damping are taken into account.
|
0211040v1
|
2002-02-01
|
On "the authentic damping mechanism" of the phonon damping model
|
Some general features of the phonon damping model are presented. It is
concluded that the fits performed within this model have no physical content.
|
0202006v1
|
2010-12-20
|
Global attractors for the one dimensional wave equation with displacement dependent damping
|
We study the long-time behavior of solutions of the one dimensional wave
equation with nonlinear damping coefficient. We prove that if the damping
coefficient function is strictly positive near the origin then this equation
possesses a global attractor.
|
1012.4455v1
|
2018-01-28
|
Observations of excitation and damping of transversal oscillation in coronal loops by AIA/SDO
|
The excitation and damping of transversal coronal loop oscillations and
quantitative relation between damping time, damping quality (damping time per
period), oscillation amplitude, dissipation mechanism and the wake phenomena
are investigated. The observed time series data with the \textit{Atmospheric
Imaging Assembly} (AIA) telescope on NASA's \textit{Solar Dynamics Observatory}
(SDO) satellite on 2015 March 2, consisting of 400 consecutive images with 12
seconds cadence in the 171 $ \rm{{\AA}}$ pass band is analyzed for evidence of
transversal oscillations along the coronal loops by Lomb-Scargle periodgram. In
this analysis signatures of transversal coronal loop oscillations that are
damped rapidly were found with dominant oscillation periods in the range of
$\rm{P=12.25-15.80}$ minutes. Also, damping times and damping qualities of
transversal coronal loop oscillations at dominant oscillation periods are
estimated in the range of $ \rm{\tau_d=11.76-21.46}$ minutes and $
\rm{\tau_d/P=0.86-1.49}$, respectively. The observational results of this
analysis show that damping qualities decrease slowly with increasing the
amplitude of oscillation, but periods of oscillations are not sensitive
function of amplitude of oscillations. The order of magnitude of the damping
qualities and damping times are in good agreement with previous findings and
the theoretical prediction for damping of kink mode oscillations by dissipation
mechanism. Furthermore, oscillation of loop segments attenuate with time
roughly as $t^{-\alpha}$ that magnitude values of $\alpha$ for 30 different
segments change from 0.51 to 0.75.
|
1801.09217v1
|
1999-11-16
|
Probing supernovae ejecta by Halpha damping wings
|
It is predicted that H$\alpha$ emission line at the early nebular epoch of
type II-P supernovae may display robust observational effects of damping wings.
This is illustrated by Monte-Carlo simulations. The strength of damping wing
effects may be used to constrain parameters of the line-emitting zone. An
anomalous redshift, width and red wing of H$\alpha$ revealed by SN 1997D on day
150 are explained in terms of damping wing effects.
|
9911300v1
|
2009-01-23
|
Rheological Interpretation of Rayleigh Damping
|
Damping is defined through various terms such as energy loss per cycle (for
cyclic tests), logarithmic decrement (for vibration tests), complex modulus,
rise-time or spectrum ratio (for wave propagation analysis), etc. For numerical
modeling purposes, another type of damping is frequently used : it is called
Rayleigh damping. It is a very convenient way of accounting for damping in
numerical models, although the physical or rheological meaning of this approach
is not clear. A rheological model is proposed to be related to classical
Rayleigh damping : it is a generalized Maxwell model with three parameters. For
moderate damping (<25%), this model perfectly coincide with Rayleigh damping
approach since internal friction has the same expression in both cases and
dispersive phenomena are negligible. This is illustrated by finite element
(Rayleigh damping) and analytical (generalized Maxwell model) results in a
simple one-dimensional case.
|
0901.3717v1
|
2009-05-20
|
Eigenvalue asymptotics, inverse problems and a trace formula for the linear damped wave equation
|
We determine the general form of the asymptotics for Dirichlet eigenvalues of
the one-dimensional linear damped wave operator. As a consequence, we obtain
that given a spectrum corresponding to a constant damping term this determines
the damping term in a unique fashion. We also derive a trace formula for this
problem.
|
0905.3242v1
|
2015-05-06
|
Remarks on the asymptotic behavior of the solution of an abstract damped wave equation
|
We study an abstract damped wave equation. We prove that the solution of the
damped wave equation becomes closer to the solution of a heat type equation as
time tend to infinity. As an application of our approach, we also study the
asymptotic behavior of the damped wave equation in Euclidean space under the
geometric control condition.
|
1505.01794v2
|
2017-01-18
|
Two types of spurious damping forces potentially modeled in numerical seismic nonlinear response history analysis
|
The purpose of this paper is to provide practitioners with further insight
into spurious damping forces that can be generated in nonlinear seismic
response history analyses (RHA). The term 'spurious' is used to refer to
damping forces that are not present in an elastic system and appear as
nonlinearities develop: such damping forces are not necessarily intended and
appear as a result of modifications in the structural properties as it yields
or damages due to the seismic action. In this paper, two types of spurious
damping forces are characterized. Each type has often been treated separately
in the literature, but each has been qualified as 'spurious', somehow blurring
their differences. Consequently, in an effort to clarify the consequences of
choosing a particular viscous damping model for nonlinear RHA, this paper shows
that damping models that avoid spurious damping forces of one type do not
necessarily avoid damping forces of the other type.
|
1701.05092v1
|
2017-02-02
|
Exponential stability for a coupled system of damped-undamped plate equations
|
We consider the transmission problem for a coupled system of undamped and
structurally damped plate equations in two sufficiently smooth and bounded
subdomains. It is shown that, independently of the size of the damped part, the
damping is strong enough to produce uniform exponential decay of the energy of
the coupled system.
|
1702.00637v1
|
2017-09-11
|
Comparison of damping mechanisms for transverse waves in solar coronal loops
|
We present a method to assess the plausibility of alternative mechanisms to
explain the damping of magnetohydrodynamic (MHD) transverse waves in solar
coronal loops. The considered mechanisms are resonant absorption of kink waves
in the Alfv\'en continuum, phase-mixing of Alfv\'en waves, and wave leakage.
Our methods make use of Bayesian inference and model comparison techniques. We
first infer the values for the physical parameters that control the wave
damping, under the assumption of a particular mechanism, for typically observed
damping time-scales. Then, the computation of marginal likelihoods and Bayes
factors enable us to quantify the relative plausibility between the alternative
mechanisms. We find that, in general, the evidence is not large enough to
support a single particular damping mechanism as the most plausible one.
Resonant absorption and wave leakage offer the most probable explanations in
strong damping regimes, while phase mixing is the best candidate for
weak/moderate damping. When applied to a selection of 89 observed transverse
loop oscillations, with their corresponding measurements of damping times
scales and taking into account data uncertainties, we find that only in a few
cases positive evidence for a given damping mechanism is available.
|
1709.03347v1
|
2019-03-25
|
Distributed Inter-Area Oscillation Damping Control for Power Systems by Using Wind Generators and Load Aggregators
|
This paper investigates the potential of wind turbine generators (WTGs) and
load aggregators (LAs) to provide supplementary damping control services for
low frequency inter-area oscillations (LFOs) through the additional distributed
damping control units (DCUs) proposed in their controllers. In order to provide
a scalable methodology for the increasing number of WTGs and LAs, a novel
distributed control framework is proposed to coordinate damping controllers.
Firstly, a distributed algorithm is designed to reconstruct the system Jacobian
matrix for each damping bus (buses with damping controllers). Thus, the
critical LFO can be identified locally at each damping bus by applying
eigen-analysis to the obtained system Jacobian matrix. Then, if the damping
ratio of the critical LFO is less than a preset threshold, the control
parameters of DCUs will be tuned in a distributed and coordinated manner to
improve the damping ratio and minimize the total control cost at the same time.
The proposed control framework is tested in a modified IEEE 39-bus test system.
The simulation results with and without the proposed control framework are
compared to demonstrate the effectiveness of the proposed framework.
|
1903.10135v1
|
2019-08-19
|
Spectral determinant for the damped wave equation on an interval
|
We evaluate the spectral determinant for the damped wave equation on an
interval of length $T$ with Dirichlet boundary conditions, proving that it does
not depend on the damping. This is achieved by analysing the square of the
damped wave operator using the general result by Burghelea, Friedlander, and
Kappeler on the determinant for a differential operator with matrix
coefficients.
|
1908.06862v1
|
2020-10-12
|
Decays rates for Kelvin-Voigt damped wave equations II: the geometric control condition
|
We study in this article decay rates for Kelvin-Voigt damped wave equations
under a geometric control condition. We prove that when the damping coefficient
is sufficiently smooth ($C^1$ vanishing nicely) we show that exponential decay
follows from geometric control conditions (see~\cite{BuCh, Te12} for similar
results under stronger assumptions on the damping function).
|
2010.05614v2
|
2020-12-05
|
On Periodical Damping Ratio of a Controlled Dynamical System with Parametric Resonances
|
This report provides an interpretation on the periodically varying damping
ratio of a dynamical system with direct control of oscillation or vibration
damping. The principal parametric resonance of the system and a new type of
parametric resonance, named "zero-th order" parametric resonance, are
investigated by using the method of multiple scales to find approximate,
analytical solutions of the system, which provide an interpretation on such
damping variations.
|
2012.02932v1
|
2021-06-09
|
Grammage of cosmic rays in the proximity of supernova remnants embedded in a partially ionized medium
|
We investigate the damping of Alfv\'en waves generated by the cosmic ray
resonant streaming instability in the context of the cosmic ray escape and
propagation in the proximity of supernova remnants. We consider ion-neutral
damping, turbulent damping and non linear Landau damping in the warm ionized
and warm neutral phases of the interstellar medium. For the ion-neutral
damping, up-to-date damping coefficients are used. We investigate in particular
whether the self-confinement of cosmic rays nearby sources can appreciably
affect the grammage. We show that the ion-neutral damping and the turbulent
damping effectively limit the residence time of cosmic rays in the source
proximity, so that the grammage accumulated near sources is found to be
negligible. Contrary to previous results, this also happens in the most extreme
scenario where ion-neutral damping is less effective, namely in a medium with
only neutral helium and fully ionized hydrogen. Therefore, the standard
picture, in which CR secondaries are produced during the whole time spent by
cosmic rays throughout the Galactic disk, need not to be deeply revisited.
|
2106.04948v1
|
2021-06-22
|
Sharp decay rate for the damped wave equation with convex-shaped damping
|
We revisit the damped wave equation on two-dimensional torus where the damped
region does not satisfy the geometric control condition. We show that if the
damping vanishes as a H\"older function $|x|^{\beta}$, and in addition, the
boundary of the damped region is strictly convex, the wave is stable at rate
$t^{-1+\frac{2}{2\beta+7}}$, which is better than the known optimal decay rate
$t^{-1+\frac{1}{\beta+3}}$ for strip-shaped dampings of the same H\"older
regularity. Moreover, we show by example that the decay rate is optimal. This
illustrates the fact that the energy decay rate depends not only on the order
of vanishing of the damping, but also on the shape of the damped region. The
main ingredient of the proof is the averaging method (normal form reduction)
developed by Hitrick and Sj\"ostrand (\cite{Hi1}\cite{Sj}).
|
2106.11782v3
|
2021-08-09
|
Effect of stepwise adjustment of Damping factor upon PageRank
|
The effect of adjusting damping factor {\alpha}, from a small initial value
{\alpha}0 to the final desired {\alpha}f value, upon then iterations needed for
PageRank computation is observed. Adjustment of the damping factor is done in
one or more steps. Results show no improvement in performance over a fixed
damping factor based PageRank.
|
2108.04150v1
|
2021-08-17
|
Asymptotic behaviour of the wave equation with nonlocal weak damping, anti-damping and critical nonlinearity
|
In this paper we prove the existence of the global attractor for the wave
equation with nonlocal weak damping, nonlocal anti-damping and critical
nonlinearity.
|
2108.07395v2
|
2023-02-23
|
Buckling Metamaterials for Extreme Vibration Damping
|
Damping mechanical resonances is a formidable challenge in an increasing
number of applications. Many of the passive damping methods rely on using low
stiffness dissipative elements, complex mechanical structures or electrical
systems, while active vibration damping systems typically add an additional
layer of complexity. However, in many cases, the reduced stiffness or
additional complexity and mass render these vibration damping methods
unfeasible. Here, we introduce a method for passive vibration damping by
allowing buckling of the primary load path, which sets an upper limit for
vibration transmission: the transmitted acceleration saturates at a maximum
value, no matter what the input acceleration is. This nonlinear mechanism leads
to an extreme damping coefficient tan delta ~0.23 in our metal
metamaterial|orders of magnitude larger than the linear damping of traditional
lightweight structural materials. We demonstrate this principle experimentally
and numerically in free-standing rubber and metal mechanical metamaterials over
a range of accelerations, and show that bi-directional buckling can further
improve its performance. Buckling metamaterials pave the way towards extreme
vibration damping without mass or stiffness penalty, and as such could be
applicable in a multitude of high-tech applications, including aerospace
structures, vehicles and sensitive instruments.
|
2302.11968v1
|
1997-11-20
|
Symmetric matrices and quantum codes
|
This paper has been withdrawn since a Gilbert-Varshamov bound for general
quantum codes has already appeared in Ekert and Macchiavello, Prys. Rev. Lett.
77, p. 2585, and a Gilbert-Varshamov bound for stabilizer codes connected with
orthogonal geometry, or equivalently, with symmetric matrices as in this paper,
has been proved by Calredbank, Rains, Shor and Sloane, Phys. Rev. Lett. 78, p.
405. I would like to thank Robert Calderbank for pointing out these references
to me.
|
9711026v2
|
1994-06-09
|
Black Holes from Blue Spectra
|
Blue primordial power spectra with a spectral index $n>1$ can lead to a
significant production of primordial black holes in the very early Universe.
The evaporation of these objects leads to a number of observational
consequences and a model independent upper limit of $n \approx 1.4$. In some
cases this limit is strengthened to $n=1.3$. Such limits may be employed to
define the boundary to the region of parameter space consistent with
generalized inflationary predictions. [To appear in Proceedings of the CASE
WESTERN CMB WORKSHOP, April 22-24 1994. Figures available on request from
J.H.Gilbert@qmw.ac.uk]
|
9406028v1
|
1995-06-14
|
Inversions in astronomy and the SOLA method
|
This paper was presented at the Institute for Mathematics and its
Applications workshop "Inverse problems in wave propagation" and will appear in
the series IMA volumes (Springer). A brief overview of applications of
inversions within astronomy is presented and also an inventory of techniques
commonly in use. Most of this paper is focussed on the method of Subtractive
Optimally Localized Averages (SOLA) which is an adaptation of the Backus and
Gilbert method. This method was originally developed for use in helioseismology
where the Backus and Gilbert method is computationally too slow. Since then it
has also been applied to the problem of reverberation mapping of active
galactic nuclei and the differences between this inverse problem and the ones
of helioseismology are also discussed.
|
9506084v1
|
1997-11-11
|
No Need for MACHOS in the Halo
|
A simple interpretation of the more than dozen microlensing events seen in
the direction of the LMC is a halo population of MACHOs which accounts for
about half of the mass of the Galaxy. Such an interpretation is not without its
problems, and we show that current microlensing data can, with some advantage,
be explained by dark components of the disk and spheroid, whose total mass is
only about 10% of the mass of the Galaxy.
|
9711110v1
|
2006-02-11
|
Likelihood Functions for Galaxy Cluster Surveys
|
Galaxy cluster surveys offer great promise for measuring cosmological
parameters, but survey analysis methods have not been widely studied. Using
methods developed decades ago for galaxy clustering studies, it is shown that
nearly exact likelihood functions can be written down for galaxy cluster
surveys. The sparse sampling of the density field by galaxy clusters allows
simplifications that are not possible for galaxy surveys. An application to
counts in cells is explicitly tested using cluster catalogs from numerical
simulations and it is found that the calculated probability distributions are
very accurate at masses above several times 10^{14}h^{-1} solar masses at z=0
and lower masses at higher redshift.
|
0602251v3
|
2000-03-25
|
Thermokinetic approach of the generalized Landau-Lifshitz-Gilbert equation with spin polarized current
|
In order to describe the recently observed effect of current induced
magnetization reversal in magnetic nanostructures, the thermokinetic theory is
applied to a metallic ferromagnet in contact with a reservoir of spin polarized
conduction electrons. The spin flip relaxation of the conduction electrons is
described thermodynamically as a chemical reaction. The diffusion equation of
the chemical potential (or the giant magnetoresistance) and the usual
Landau-Lifshitz-Gilbert (LLG) equation are derived from the entropy variation.
The expression of the conservation laws of the magnetic moments, including spin
dependent scattering processes, leads then to the generalized LLG equation with
spin polarized current. The equation is applied to the measurements obtained on
single magnetic Ni nanowires.
|
0003409v1
|
2004-05-26
|
Nonequilibrium Extension of the Landau-Lifshitz-Gilbert Equation for Magnetic Systems
|
Using the invariant operator method for an effective Hamiltonian including
the radiation-spin interaction, we describe the quantum theory for
magnetization dynamics when the spin system evolves nonadiabatically and out of
equilibrium, $d \hat{\rho}/dt \neq 0$. It is shown that the vector parameter of
the invariant operator and the magnetization defined with respect to the
density operator, both satisfying the quantum Liouville equation, still obey
the Landau-Lifshitz-Gilbert equation.
|
0405599v1
|
2006-10-16
|
Properties of Codes with the Rank Metric
|
In this paper, we study properties of rank metric codes in general and
maximum rank distance (MRD) codes in particular. For codes with the rank
metric, we first establish Gilbert and sphere-packing bounds, and then obtain
the asymptotic forms of these two bounds and the Singleton bound. Based on the
asymptotic bounds, we observe that asymptotically Gilbert-Varsharmov bound is
exceeded by MRD codes and sphere-packing bound cannot be attained. We also
establish bounds on the rank covering radius of maximal codes, and show that
all MRD codes are maximal codes and all the MRD codes known so far achieve the
maximum rank covering radius.
|
0610099v2
|
1994-08-26
|
On the Dirichlet problem for harmonic maps with prescribed singularities
|
Let $\M$ be a classical Riemannian globally symmetric space of rank one and
non-compact type. We prove the existence and uniqueness of solutions to the
Dirichlet problem for harmonic maps into $\M$ with prescribed singularities
along a closed submanifold of the domain. This generalizes our previous work
where such maps into the hyperbolic plane were constructed. This problem, in
the case where $\M$ is the complex-hyperbolic plane, has applications to
equilibrium configurations of co-axially rotating charged black holes in
General Relativity.
|
9408005v1
|
1997-08-15
|
One-Loop Minimization Conditions in the Minimal Supersymmetric Standard Model
|
We study, in the Minimal Supersymmetric Standard Model, the electroweak
symmetry breaking conditions obtained from the one-loop effective potential.
Novel model-independent lower and upper bounds on $\tan \beta$, involving the
other free parameters of the model, are inferred and determined analytically.
We discuss briefly some of the related issues and give an outlook for further
applications.
|
9708368v1
|
2004-05-31
|
On a Penrose Inequality with Charge
|
We construct a time-symmetric asymptotically flat initial data set to the
Einstein-Maxwell Equations which satisfies the inequality: m - 1/2(R + Q^2/R) <
0, where m is the total mass, R=sqrt(A/4) is the area radius of the outermost
horizon and Q is the total charge. This yields a counter-example to a natural
extension of the Penrose Inequality to charged black holes.
|
0405602v3
|
2004-07-26
|
Automorphisms of free groups have asymptotically periodic dynamics
|
We show that every automorphism $\alpha$ of a free group $F_k$ of finite rank
$k$ has {\it asymptotically periodic} dynamics on $F_k$ and its boundary
$\partial F_k$: there exists a positive power $\alpha^q$ such that every
element of the compactum $F_k \cup \partial F_k$ converges to a fixed point
under iteration of $\alpha^q$.
|
0407437v2
|
2004-12-30
|
The Construction of a Partially Regular Solution to the Landau-Lifshitz-Gilbert Equation in $\mathbb{R}^2$
|
We establish a framework to construct a global solution in the space of
finite energy to a general form of the Landau-Lifshitz-Gilbert equation in
$\mathbb{R}^2$. Our characterization yields a partially regular solution,
smooth away from a 2-dimensional locally finite Hausdorff measure set. This
construction relies on approximation by discretization, using the special
geometry to express an equivalent system whose highest order terms are linear
and the translation of the machinery of linear estimates on the fundamental
solution from the continuous setting into the discrete setting. This method is
quite general and accommodates more general geometries involving targets that
are compact smooth hypersurfaces.
|
0412534v1
|
2002-01-13
|
Inverse Cascade Regime in Shell Models of 2-Dimensional Turbulence
|
We consider shell models that display an inverse energy cascade similar to
2-dimensional turbulence (together with a direct cascade of an enstrophy-like
invariant). Previous attempts to construct such models ended negatively,
stating that shell models give rise to a "quasi-equilibrium" situation with
equipartition of the energy among the shells. We show analytically that the
quasi-equilibrium state predicts its own disappearance upon changing the model
parameters in favor of the establishment of an inverse cascade regime with K41
scaling. The latter regime is found where predicted, offering a useful model to
study inverse cascades.
|
0201020v1
|
2002-04-23
|
Algebraic decay in hierarchical graphs
|
We study the algebraic decay of the survival probability in open hierarchical
graphs. We present a model of a persistent random walk on a hierarchical graph
and study the spectral properties of the Frobenius-Perron operator. Using a
perturbative scheme, we derive the exponent of the classical algebraic decay in
terms of two parameters of the model. One parameter defines the geometrical
relation between the length scales on the graph, and the other relates to the
probabilities for the random walker to go from one level of the hierarchy to
another. The scattering resonances of the corresponding hierarchical quantum
graphs are also studied. The width distribution shows the scaling behavior
$P(\Gamma) \sim 1/\Gamma$.
|
0204056v1
|
2004-03-11
|
Statistics of active vs. passive advections in magnetohydrodynamic turbulence
|
Active turbulent advection is considered in the context of
magneto-hydrodynamics. In this case, an auxiliary passive field bears no
apparent connection to the active field. The scaling properties of the two
fields are different. In the framework of a shell model, we show that the
two-point structure function of the passive field has a unique zero mode,
characterizing the scaling of this field only. In other words, the existence of
statistical invariants for the decaying passive field carries no information on
the scaling properties of the active field.
|
0403017v1
|
2006-01-19
|
Drift of particles in self-similar systems and its Liouvillian interpretation
|
We study the dynamics of classical particles in different classes of
spatially extended self-similar systems, consisting of (i) a self-similar
Lorentz billiard channel, (ii) a self-similar graph, and (iii) a master
equation. In all three systems the particles typically drift at constant
velocity and spread ballistically. These transport properties are analyzed in
terms of the spectral properties of the operator evolving the probability
densities. For systems (i) and (ii), we explain the drift from the properties
of the Pollicott-Ruelle resonance spectrum and corresponding eigenvectors
|
0601042v1
|
1997-11-20
|
Quantum self-dual codes and symmetric matrices
|
This paper has been withdrawn since a Gilbert-Varshamov bound for general
quantum codes has already appeared in Ekert and Macchiavello, Prys. Rev. Lett.
77, p. 2585, and a Gilbert-Varshamov bound for stabilizer codes connected with
orthogonal geometry, or equivalently, with symmetric matrices as in this paper,
has been proved by Calredbank, Rains, Shor and Sloane, Phys. Rev. Lett. 78, p.
405. I would like to thank Robert Calderbank for pointing out these references
to me.
|
9711047v2
|
2001-06-06
|
Constraints on Eavesdropping on the BB84 Protocol
|
An undetected eavesdropping attack must produce count rate statistics that
are indistinguishable from those that would arise in the absence of such an
attack. In principle this constraint should force a reduction in the amount of
information available to the eavesdropper. In this paper we illustrate, by
considering a particular class of eavesdropping attacks, how the general
analysis of this problem may proceed.
|
0106034v2
|
2007-09-14
|
A complete proof of The Graceful Tree Conjecture using the concept of Edge Degree
|
We show the Graceful Tree Conjecture holds.
|
0709.2201v9
|
2007-09-24
|
An extension of a result concerning convex geometric graphs
|
We show a general result known as the Erdos_Sos Conjecture: if
$E(G)>{1/2}(k-1)n$ where $G$ has order $n$ then $G$ contains every tree of
order $k+1$ as a subgraph.
|
0709.3590v5
|
2008-06-13
|
Heat conduction and Fourier's law by consecutive local mixing and thermalization
|
We present a first-principles study of heat conduction in a class of models
which exhibit a new multi-step local thermalization mechanism which gives rise
to Fourier's law. Local thermalization in our models occurs as the result of
binary collisions among locally confined gas particles. We explore the
conditions under which relaxation to local equilibrium, which involves no
energy exchange, takes place on time scales shorter than that of the binary
collisions which induce local thermalization. The role of this mechanism in
multi-phase material systems such as aerogels is discussed.
|
0806.2193v1
|
2009-08-05
|
Persistence effects in deterministic diffusion
|
In systems which exhibit deterministic diffusion, the gross parameter
dependence of the diffusion coefficient can often be understood in terms of
random walk models. Provided the decay of correlations is fast enough, one can
ignore memory effects and approximate the diffusion coefficient according to
dimensional arguments. By successively including the effects of one and two
steps of memory on this approximation, we examine the effects of
``persistence'' on the diffusion coefficients of extended two-dimensional
billiard tables and show how to properly account for these effects, using walks
in which a particle undergoes jumps in different directions with probabilities
that depend on where they came from.
|
0908.0600v1
|
2009-08-10
|
Diffusion coefficients for multi-step persistent random walks on lattices
|
We calculate the diffusion coefficients of persistent random walks on
lattices, where the direction of a walker at a given step depends on the memory
of a certain number of previous steps. In particular, we describe a simple
method which enables us to obtain explicit expressions for the diffusion
coefficients of walks with two-step memory on different classes of one-, two-
and higher-dimensional lattices.
|
0908.1271v1
|
2010-04-09
|
Strict inequalities of critical probabilities on Gilbert's continuum percolation graph
|
Any infinite graph has site and bond percolation critical probabilities
satisfying $p_c^{site}\geq p_c^{bond}$. The strict version of this inequality
holds for many, but not all, infinite graphs.
In this paper, the class of graphs for which the strict inequality holds is
extended to a continuum percolation model. In Gilbert's graph with
supercritical density on the Euclidean plane, there is almost surely a unique
infinite connected component. We show that on this component $p_c^{site} >
p_c^{bond}$. This also holds in higher dimensions.
|
1004.1596v2
|
2010-04-15
|
Rank of mapping tori and companion matrices
|
Given $f$ in $GL(d,Z)$, it is decidable whether its mapping torus (the
semi-direct product of $Z^d$ with $Z$) may be generated by two elements or not;
if so, one can classify generating pairs up to Nielsen equivalence. If $f$ has
infinite order, the mapping torus of $f^n$ cannot be generated by two elements
for $n$ large enough; equivalently, $f^n$ is not conjugate to a companion
matrix in $GL(d,Z)$ if $n$ is large.
|
1004.2649v1
|
2010-04-30
|
Limit theory for planar Gilbert tessellations
|
A Gilbert tessellation arises by letting linear segments (cracks) in the
plane unfold in time with constant speed, starting from a homogeneous Poisson
point process of germs in randomly chosen directions. Whenever a growing edge
hits an already existing one, it stops growing in this direction. The resulting
process tessellates the plane. The purpose of the present paper is to establish
law of large numbers, variance asymptotics and a central limit theorem for
geometric functionals of such tessellations. The main tool applied is the
stabilization theory for geometric functionals.
|
1005.0023v1
|
2010-06-24
|
Periodic solutions for the Landau-Lifshitz-Gilbert equation
|
Ferromagnetic materials tend to develop very complex magnetization patterns
whose time evolution is modeled by the so-called Landau-Lifshitz-Gilbert
equation (LLG). In this paper, we construct time-periodic solutions for LLG in
the regime of soft and small ferromagnetic particles which satisfy a certain
shape condition. Roughly speaking, it is assumed that the length of the
particle is greater than its hight and its width. The approach is based on a
perturbation argument and the spectral analysis of the corresponding linearized
problem as well as the theory of sectorial operators.
|
1006.4765v1
|
2010-12-19
|
A counterexample to a Penrose inequality conjectured by Gibbons
|
We show that the Brill-Lindquist initial data provides a counterexample to a
Riemannian Penrose inequality with charge conjectured by G. Gibbons. The
observation illustrates a sub-additive characteristic of the area radii for the
individual connected components of an outermost horizon as a lower bound of the
ADM mass.
|
1012.4190v2
|
2011-11-27
|
A two-stage approach to relaxation in billiard systems of locally confined hard spheres
|
We consider the three-dimensional dynamics of systems of many interacting
hard spheres, each individually confined to a dispersive environment, and show
that the macroscopic limit of such systems is characterized by a coefficient of
heat conduction whose value reduces to a dimensional formula in the limit of
vanishingly small rate of interaction. It is argued that this limit arises from
an effective loss of memory. Similarities with the diffusion of a tagged
particle in binary mixtures are emphasized.
|
1111.6272v1
|
2012-01-12
|
Coil-helix transition in poly(L-glutamic acid) : Evidence for a 3-state non-cooperative process
|
A careful analysis of measurements of circular dichroism of poly(L-glutamic
acid) (PGA) shows that the data can be very accurately described by introducing
a third state for the PGA configuration, in addition to the helix and coil
ones, and considering a simple equilibrium between these three states, without
cooperativity. The third state is more conspicuous when high molecular weight
polyethyleneglycol (PEG) is added. Excluded volume effects shown by differences
in presence of short and long PEG chains indicate a direct interaction of PEG
and PGA rather than an osmotic effect.
|
1201.2566v1
|
2012-03-20
|
Vortex dynamics in the presence of excess energy for the Landau-Lifschitz-Gilbert equation
|
We study the Landau-Lifshitz-Gilbert equation for the dynamics of a magnetic
vortex system. We present a PDE-based method for proving vortex dynamics that
does not rely on strong well-preparedness of the initial data and allows for
instantaneous changes in the strength of the gyrovector force due to bubbling
events. The main tools are estimates of the Hodge decomposition of the
supercurrent and an analysis of the defect measure of weak convergence of the
stress energy tensor. Ginzburg-Landau equations with mixed dynamics in the
presence of excess energy are also discussed.
|
1203.4426v1
|
2012-12-22
|
Cumulative Distance Enumerators of Random Codes and their Thresholds
|
Cumulative weight enumerators of random linear codes are introduced, their
asymptotic properties are studied, and very sharp thresholds are exhibited; as
a consequence, it is shown that the asymptotic Gilbert-Varshamov bound is a
very sharp threshold point for the density of the linear codes whose relative
distance is greater than a given positive number. For arbitrary random codes,
similar settings and results are exhibited; in particular, the very sharp
threshold point for the density of the codes whose relative distance is greater
than a given positive number is located at half the asymptotic
Gilbert-Varshamov bound.
|
1212.5679v1
|
2013-01-23
|
The Importance of Continuous Value Based Project Management in the Context of Requirements Engineering
|
Despite several scientific achievements in the last years, there are still a
lot of IT projects that fail. Researchers found that one out of five
IT-projects run out of time, budget or value. Major reasons for this failure
are unexpected economic risk factors that emerge during the runtime of
projects. In order to be able to identify emerging risks early and to
counteract reasonably, financial methods for a continuous IT-project-steering
are necessary, which as of today to the best of our knowledge are missing
within scientific literature.
|
1301.5438v1
|
2013-04-08
|
On Automorphisms and Subtowers of an asymptotically optimal Tower of Function Fields
|
In this article we investigate the automorphism group of an asymptotically
optimal tower of function fields introduced by Garcia and Stichtenoth. In
particular we provide a detailed description of the decomposition group of some
rational places. This group acts on the algebraic-geometric standard codes
obtained by the Garcia-Stichtenoth tower exceeding the Gilbert-Varshamov bound.
The fields fixed by the decomposition groups form an asymptotically optimal
non-Galois subtower, which has been first found by Bezerra and Garcia and
yields an improvement for computing codes above the Gilbert-Varshamov bound. In
this article we also describe its proportionality to the Garcia-Stichtenoth
tower and obtain new precise results on its rational places and their
Weierstra{\ss} semigroups.
|
1304.2145v1
|
2013-05-06
|
The Moment Generating function for ray lengths in the Half Gilbert Model with Rectangular Cells
|
In the full rectangular version of Gilbert's tessellation lines extend either
horizontally (with east- and west--growing rays) or vertically (north- and
south--growing rays) from seed points which form a Poisson point process, each
ray stopping when another ray is met. In the half rectangular version, east and
south growing rays do not interact with west and north rays. Using techniques
developed in our previous paper, we derive an exact expression for the moment
generating function for the ray length distribution in the half rectangular
model.
|
1305.1289v1
|
2013-07-15
|
Degenerate transition pathways for screw dislocations: implications for migration
|
In body-centred-cubic (bcc) metals migrating 1/2<111> screw dislocations
experience a periodic energy landscape with a triangular symmetry. Atomistic
simulations, such as those performed using the nudged-elastic-band (NEB)
method, generally predict a transition-pathway energy-barrier with a
double-hump; contradicting Ab Initio findings. Examining the trajectories
predicted by NEB for a particle in a Peierls energy landscape representative of
that obtained for a screw dislocation, reveals an unphysical anomaly caused by
the occurrence of monkey saddles in the landscape. The implications for motion
of screws with and without stress are discussed.
|
1307.3848v2
|
2013-08-17
|
The Riemannian Penrose Inequality with Charge for Multiple Black Holes
|
We present a proof of the Riemannian Penrose inequality with charge $r\leq m
+ \sqrt{m^2-q^2}$, where $A=4\pi r^2$ is the area of the outermost apparent
horizon with possibly multiple connected components, $m$ is the total ADM mass,
and $q$ the total charge of a strongly asymptotically flat initial data set for
the Einstein-Maxwell equations, satisfying the charged dominant energy
condition, with no charged matter outside the horizon.
|
1308.3771v3
|
2013-08-23
|
Quotients and subgroups of Baumslag-Solitar groups
|
We determine all generalized Baumslag-Solitar groups (finitely generated
groups acting on a tree with all stabilizers infinite cyclic) which are
quotients of a given Baumslag-Solitar group BS(m,n), and (when BS(m,n) is not
Hopfian) which of them also admit BS(m,n) as a quotient. We determine for which
values of r,s one may embed BS(r,s) into a given BS(m,n), and we characterize
finitely generated groups which embed into some BS(n,n).
|
1308.5122v2
|
2013-12-17
|
Limit theory for the Gilbert graph
|
For a given homogeneous Poisson point process in $\mathbb{R}^d$ two points
are connected by an edge if their distance is bounded by a prescribed distance
parameter. The behaviour of the resulting random graph, the Gilbert graph or
random geometric graph, is investigated as the intensity of the Poisson point
process is increased and the distance parameter goes to zero. The asymptotic
expectation and covariance structure of a class of length-power functionals are
computed. Distributional limit theorems are derived that have a Gaussian, a
stable or a compound Poisson limiting distribution. Finally, concentration
inequalities are provided using a concentration inequality for the convex
distance.
|
1312.4861v2
|
2014-03-13
|
Fibrations of ordered groupoids and the factorization of ordered functors
|
We investigate canonical factorizations of ordered functors of ordered
groupoids through star-surjective functors. Our main construction is a quotient
ordered groupoid, depending on an ordered version of the notion of normal
subgroupoid, that results is the factorization of an ordered functor as a
star-surjective functor followed by a star-injective functor. Any
star-injective functor possesses a universal factorization through a covering,
by Ehresmann's Maximum Enlargement Theorem. We also show that any ordered
functor has a canonical factorization through a functor with the ordered
homotopy lifting property.
|
1403.3254v2
|
2014-03-16
|
Interpolating local constants in families
|
We extend the theory of local constants to l-adic families of representations
of GL_n(F) where F is a p-adic field with l not equal to p. We construct zeta
integrals and gamma factors for representations coming from the conjectural
"local Langlands correspondence in families" of Emerton-Helm, proving a
rationality result and functional equation. We also construct a universal gamma
factor with coefficients in the integral Bernstein center.
|
1403.3914v2
|
2014-06-10
|
A thin-film limit in the Landau-Lifshitz-Gilbert equation relevant for the formation of Néel walls
|
We consider an asymptotic regime for two-dimensional ferromagnetic films that
is consistent with the formation of transition layers (N\'eel walls). We first
establish compactness of S2-valued magnetizations in the energetic regime of
N\'eel walls and characterize the set of accumulation points. We then prove
that N\'eel walls are asymptotically the unique energy minimizing
configurations. We finally study the corresponding dynamical issues, namely the
compactness properties of the magnetizations under the flow of the
Landau-Lifshitz-Gilbert equation.
|
1406.2709v1
|
2014-08-02
|
Machta-Zwanzig regime of anomalous diffusion in infinite-horizon billiards
|
We study diffusion on a periodic billiard table with infinite horizon in the
limit of narrow corridors. An effective trapping mechanism emerges according to
which the process can be modeled by a L\'evy walk combining
exponentially-distributed trapping times with free propagation along paths
whose precise probabilities we compute. This description yields an
approximation of the mean squared displacement of infinite-horizon billiards in
terms of two transport coefficients which generalizes to this anomalous regime
the Machta-Zwanzig approximation of normal diffusion in finite-horizon
billiards [Phys. Rev. Lett. 50, 1959 (1983)].
|
1408.0349v1
|
2014-12-11
|
Gamma factors of pairs and a local converse theorem in families
|
We prove a GL(n)xGL(n-1) local converse theorem for l-adic families of smooth
representations of GL(n,F) where F is a finite extension of Q_p and l is
different from p. To do so, we also extend the theory of Rankin-Selberg
integrals, first introduced by Jacquet, Piatetski-Shapiro, and Shalika, to the
setting of families, continuing previous work of the author.
|
1412.3500v2
|
2015-05-28
|
A Geometric Interpretation of the Boolean Gilbert-Johnson-Keerthi Algorithm
|
The Gilbert-Johnson-Keerthi (GJK) algorithm is an iterative improvement
technique for finding the minimum distance between two convex objects. It can
easily be extended to work with concave objects and return the pair of closest
points. [4] The key operation of GJK is testing whether a Voronoi region of a
simplex contains the origin or not. In this paper we show that, in the context
where one is interested only in the Boolean value of whether two convex objects
intersect, and not in the actual distance between them, the number of test
cases in GJK can be significantly reduced. This results in a simpler and more
efficient algorithm that can be used in many computational geometry
applications.
|
1505.07873v1
|
2016-01-29
|
Ordered groupoid quotients and congruences on inverse semigroups
|
We introduce a preorder on an inverse semigroup $S$ associated to any normal
inverse subsemigroup $N$, that lies between the natural partial order and
Green's ${\mathscr J}$-relation. The corresponding equivalence relation
$\simeq_N$ is not necessarily a congruence on $S$, but the quotient set does
inherit a natural ordered groupoid structure. We show that this construction
permits the factorisation of any inverse semigroup homomorphism into a
composition of a quotient map and a star-injective functor, and that this
decomposition implies a classification of congruences on $S$. We give an
application to the congruence and certain normal inverse subsemigroups
associate to an inverse monoid presentation.
|
1601.08194v1
|
2016-08-16
|
Closed inverse subsemigroups of graph inverse semigroups
|
As part of his study of representations of the polycylic monoids, M.V. Lawson
described all the closed inverse submonoids of a polycyclic monoid $P_n$ and
classified them up to conjugacy. We show that Lawson's description can be
extended to closed inverse subsemigroups of graph inverse semigroups. We then
apply B. Schein's theory of cosets in inverse semigroups to the closed inverse
subsemigroups of graph inverse semigroups: we give necessary and sufficient
conditions for a closed inverse subsemigroup of a graph inverse semigroup to
have finite index, and determine the value of the index when it is finite.
|
1608.04538v1
|
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