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2014-02-25 | Du-Hwang Characteristic Area: Catch-22 | The paper is devoted to description of two interconnected mistakes generated
by the gap in the Du and Hwang approach to Gilbert-Pollack Steiner ratio
conjecture. | 1402.6079v1 |
2016-06-01 | Existence of arbitrarily smooth solutions of the LLG equation in 3D with natural boundary conditions | We prove that the Landau-Lifshitz-Gilbert equation in three space dimensions
with homogeneous Neumann boundary conditions admits arbitrarily smooth
solutions, given that the initial data is sufficiently close to a constant
function. | 1606.00086v1 |
2018-10-28 | Asymptotic Gilbert-Varshamov bound on Frequency Hopping Sequences | Given a $q$-ary frequency hopping sequence set of length $n$ and size $M$
with Hamming correlation $H$, one can obtain a $q$-ary (nonlinear) cyclic code
of length $n$ and size $nM$ with Hamming distance $n-H$. Thus, every upper
bound on the size of a code from coding theory gives an upper bound on the size
of a frequency hopping sequence set. Indeed, all upper bounds from coding
theory have been converted to upper bounds on frequency hopping sequence sets
(\cite{Ding09}). On the other hand, a lower bound from coding theory does not
automatically produce a lower bound for frequency hopping sequence sets. In
particular, the most important lower bound--the Gilbert-Varshamov bound in
coding theory has not been transformed to frequency hopping sequence sets. The
purpose of this paper is to convert the Gilbert-Varshamov bound in coding
theory to frequency hopping sequence sets by establishing a connection between
a special family of cyclic codes (which are called hopping cyclic codes in this
paper) and frequency hopping sequence sets. We provide two proofs of the
Gilbert-Varshamov bound. One is based on probabilistic method that requires
advanced tool--martingale. This proof covers the whole rate region. The other
proof is purely elementary but only covers part of the rate region. | 1810.11757v2 |
2020-05-26 | Reidemeister Moves in Gauss Diagrams | We provide a simple algorithm for recognizing and performing Reidemeister
moves in a Gauss diagram. | 2005.12957v1 |
2021-05-26 | Lee Weight for Nonbinary Quantum Error Correction | We propose the quantum Lee weight for quantum errors, provide a
Gilbert-Varshamov type bound, and a code construction for the proposed weight. | 2105.12354v1 |
2021-09-19 | Compactness of isospectral conformal Finslerian metrics set on a 3-manifold | Let F be a Finslerian metric on an n-dimensional closed manifold M. In this
work, we study problems about compactness of isospectral sets of conformal
Finslerian metrics when n=3. | 2110.06338v2 |
2001-05-31 | Lower bound for the quantum capacity of a discrete memoryless quantum channel | We generalize the random coding argument of stabilizer codes and derive a
lower bound on the quantum capacity of an arbitrary discrete memoryless quantum
channel. For the depolarizing channel, our lower bound coincides with that
obtained by Bennett et al. We also slightly improve the quantum
Gilbert-Varshamov bound for general stabilizer codes, and establish an analogue
of the quantum Gilbert-Varshamov bound for linear stabilizer codes. Our proof
is restricted to the binary quantum channels, but its extension of to l-adic
channels is straightforward. | 0105151v4 |
2007-08-30 | Asymptotic improvement of the Gilbert-Varshamov bound for linear codes | The Gilbert-Varshamov bound states that the maximum size A_2(n,d) of a binary
code of length n and minimum distance d satisfies A_2(n,d) >= 2^n/V(n,d-1)
where V(n,d) stands for the volume of a Hamming ball of radius d. Recently
Jiang and Vardy showed that for binary non-linear codes this bound can be
improved to A_2(n,d) >= cn2^n/V(n,d-1) for c a constant and d/n <= 0.499. In
this paper we show that certain asymptotic families of linear binary [n,n/2]
random double circulant codes satisfy the same improved Gilbert-Varshamov
bound. | 0708.4164v1 |
2007-09-26 | Finite Element Formalism for Micromagnetism | The aim of this work is to present the details of the finite element approach
we developed for solving the Landau-Lifschitz-Gilbert equations in order to be
able to treat problems involving complex geometries. There are several
possibilities to solve the complex Landau-Lifschitz-Gilbert equations
numerically. Our method is based on a Galerkin-type finite element approach. We
start with the dynamic Landau-Lifschitz-Gilbert equations, the associated
boundary condition and the constraint on the magnetization norm. We derive the
weak form required by the finite element method. This weak form is afterwards
integrated on the domain of calculus. We compared the results obtained with our
finite element approach with the ones obtained by a finite difference method.
The results being in very good agreement, we can state that our approach is
well adapted for 2D micromagnetic systems. | 0709.4153v1 |
2009-05-07 | Heat transport in stochastic energy exchange models of locally confined hard spheres | We study heat transport in a class of stochastic energy exchange systems that
characterize the interactions of networks of locally trapped hard spheres under
the assumption that neighbouring particles undergo rare binary collisions. Our
results provide an extension to three-dimensional dynamics of previous ones
applying to the dynamics of confined two-dimensional hard disks [Gaspard P &
Gilbert T On the derivation of Fourier's law in stochastic energy exchange
systems J Stat Mech (2008) P11021]. It is remarkable that the heat conductivity
is here again given by the frequency of energy exchanges. Moreover the
expression of the stochastic kernel which specifies the energy exchange
dynamics is simpler in this case and therefore allows for faster and more
extensive numerical computations. | 0905.1051v1 |
2011-08-15 | Hydrodynamics of self-alignment interactions with precession and derivation of the Landau-Lifschitz-Gilbert equation | We consider a kinetic model of self-propelled particles with alignment
interaction and with precession about the alignment direction. We derive a
hydrodynamic system for the local density and velocity orientation of the
particles. The system consists of the conservative equation for the local
density and a non-conservative equation for the orientation. First, we assume
that the alignment interaction is purely local and derive a first order system.
However, we show that this system may lose its hyperbolicity. Under the
assumption of weakly non-local interaction, we derive diffusive corrections to
the first order system which lead to the combination of a heat flow of the
harmonic map and Landau-Lifschitz-Gilbert dynamics. In the particular case of
zero self-propelling speed, the resulting model reduces to the phenomenological
Landau-Lifschitz-Gilbert equations. Therefore the present theory provides a
kinetic formulation of classical micromagnetization models and spin dynamics. | 1108.2951v1 |
2011-09-30 | Magnetization Dynamics, Gyromagnetic Relation, and Inertial Effects | The gyromagnetic relation - i.e. the proportionality between the angular
momentum $\vec L$ (defined by an inertial tensor) and the magnetization $\vec
M$ - is evidence of the intimate connections between the magnetic properties
and the inertial properties of ferromagnetic bodies. However, inertia is absent
from the dynamics of a magnetic dipole (the Landau-Lifshitz equation, the
Gilbert equation and the Bloch equation contain only the first derivative of
the magnetization with respect to time). In order to investigate this
paradoxical situation, the lagrangian approach (proposed originally by T. H.
Gilbert) is revisited keeping an arbitrary nonzero inertial tensor. A dynamic
equation generalized to the inertial regime is obtained. It is shown how both
the usual gyromagnetic relation and the well-known Landau-Lifshitz-Gilbert
equation are recovered at the kinetic limit, i.e. for time scales above the
relaxation time $\tau$ of the angular momentum. | 1109.6782v1 |
2012-08-28 | Decomposition of modified Landau-Lifshitz-Gilbert equation and corresponding analytic solutions | The Suzuki-Trotter decomposition in general allows one to divide the equation
of motion of a dynamical system into smaller parts whose integration are easier
than the original equation. In this study, we first rewrite by employing
feasible approximations the modified Landau-Lifshitz-Gilbert equation for
localized spins in a suitable form for simulations using the Suzuki-Trotter
decomposition. Next we decompose the equation into parts and demonstrate that
the parts are classified into three groups, each of which can be solved
exactly. Since the modified Landau-Lifshitz-Gilbert equation from which we
start is in rather a general form, simulations of spin dynamics in various
systems accompanying only small numerical errors are possible. | 1208.5545v1 |
2013-11-20 | Asymptotic Improvement of the Gilbert-Varshamov Bound on the Size of Permutation Codes | Given positive integers $n$ and $d$, let $M(n,d)$ denote the maximum size of
a permutation code of length $n$ and minimum Hamming distance $d$. The
Gilbert-Varshamov bound asserts that $M(n,d) \geq n!/V(n,d-1)$ where $V(n,d)$
is the volume of a Hamming sphere of radius $d$ in $\S_n$.
Recently, Gao, Yang, and Ge showed that this bound can be improved by a
factor $\Omega(\log n)$, when $d$ is fixed and $n \to \infty$. Herein, we
consider the situation where the ratio $d/n$ is fixed and improve the
Gilbert-Varshamov bound by a factor that is \emph{linear in $n$}. That is, we
show that if $d/n < 0.5$, then $$ M(n,d)\geq cn\,\frac{n!}{V(n,d-1)} $$ where
$c$ is a positive constant that depends only on $d/n$. To establish this
result, we follow the method of Jiang and Vardy. Namely, we recast the problem
of bounding $M(n,d)$ into a graph-theoretic framework and prove that the
resulting graph is locally sparse. | 1311.4925v1 |
2016-11-21 | On the List-Decodability of Random Self-Orthogonal Codes | In 2011, Guruswami-H{\aa}stad-Kopparty \cite{Gru} showed that the
list-decodability of random linear codes is as good as that of general random
codes. In the present paper, we further strengthen the result by showing that
the list-decodability of random {\it Euclidean self-orthogonal} codes is as
good as that of general random codes as well, i.e., achieves the classical
Gilbert-Varshamov bound. Specifically, we show that, for any fixed finite field
$\F_q$, error fraction $\delta\in (0,1-1/q)$ satisfying $1-H_q(\delta)\le
\frac12$ and small $\epsilon>0$, with high probability a random Euclidean
self-orthogonal code over $\F_q$ of rate $1-H_q(\delta)-\epsilon$ is $(\delta,
O(1/\epsilon))$-list-decodable. This generalizes the result of linear codes to
Euclidean self-orthogonal codes. In addition, we extend the result to list
decoding {\it symplectic dual-containing} codes by showing that the
list-decodability of random symplectic dual-containing codes achieves the
quantum Gilbert-Varshamov bound as well. This implies that list-decodability of
quantum stabilizer codes can achieve the quantum Gilbert-Varshamov bound.
The counting argument on self-orthogonal codes is an important ingredient to
prove our result. | 1611.06673v1 |
2017-11-29 | Linear second-order IMEX-type integrator for the (eddy current) Landau-Lifshitz-Gilbert equation | Combining ideas from [Alouges et al. (Numer. Math., 128, 2014)] and
[Praetorius et al. (Comput. Math. Appl., 2017)], we propose a numerical
algorithm for the integration of the nonlinear and time-dependent
Landau-Lifshitz-Gilbert (LLG) equation which is unconditionally convergent,
formally (almost) second-order in time, and requires only the solution of one
linear system per time-step. Only the exchange contribution is integrated
implicitly in time, while the lower-order contributions like the
computationally expensive stray field are treated explicitly in time. Then, we
extend the scheme to the coupled system of the Landau-Lifshitz-Gilbert equation
with the eddy current approximation of Maxwell equations (ELLG). Unlike
existing schemes for this system, the new integrator is unconditionally
convergent, (almost) second-order in time, and requires only the solution of
two linear systems per time-step. | 1711.10715v1 |
2017-12-28 | Subquadratic time encodable codes beating the Gilbert-Varshamov bound | We construct explicit algebraic geometry codes built from the
Garcia-Stichtenoth function field tower beating the Gilbert-Varshamov bound for
alphabet sizes at least 192. Messages are identied with functions in certain
Riemann-Roch spaces associated with divisors supported on multiple places.
Encoding amounts to evaluating these functions at degree one places. By
exploiting algebraic structures particular to the Garcia-Stichtenoth tower, we
devise an intricate deterministic \omega/2 < 1.19 runtime exponent encoding and
1+\omega/2 < 2.19 expected runtime exponent randomized (unique and list)
decoding algorithms. Here \omega < 2.373 is the matrix multiplication exponent.
If \omega = 2, as widely believed, the encoding and decoding runtimes are
respectively nearly linear and nearly quadratic. Prior to this work, encoding
(resp. decoding) time of code families beating the Gilbert-Varshamov bound were
quadratic (resp. cubic) or worse. | 1712.10052v2 |
2018-11-15 | Hilbert-Schmidt distance and entanglement witnessing | Gilbert proposed an algorithm for bounding the distance between a given point
and a convex set. In this article we apply the Gilbert's algorithm to get an
upper bound on the Hilbert-Schmidt distance between a given state and the set
of separable states. While Hilbert Schmidt Distance does not form a proper
entanglement measure, it can nevertheless be useful for witnessing
entanglement. We provide here a few methods based on the Gilbert's algorithm
that can reliably qualify a given state as strongly entangled or practically
separable, while being computationally efficient. The method also outputs
successively improved approximations to the Closest Separable State for the
given state. We demonstrate the efficacy of the method with examples. | 1811.06599v3 |
2020-02-13 | Age of Information with Gilbert-Elliot Servers and Samplers | We study age of information in a status updating system that consists of a
single sampler, i.e., source node, that sends time-sensitive status updates to
a single monitor node through a server node. We first consider a Gilbert-Elliot
service profile at the server node. In this model, service times at the server
node follow a finite state Markov chain with two states: ${bad}$ state $b$ and
${good}$ state $g$ where the server is faster in state $g$. We determine the
time average age experienced by the monitor node and characterize the
age-optimal state transition matrix $P$ with and without an average cost
constraint on the service operation. Next, we consider a Gilbert-Elliot
sampling profile at the source. In this model, the interarrival times follow a
finite state Markov chain with two states: ${bad}$ state $b$ and ${good}$ state
$g$ where samples are more frequent in state $g$. We find the time average age
experienced by the monitor node and characterize the age-optimal state
transition matrix $P$. | 2002.05711v1 |
2005-08-26 | Damping of MHD turbulence in Solar Flares | (Abridged) We describe the cascade of plasma waves or turbulence injected,
presumably by reconnection, at scales comparable to the size of a solar flare
loop to scales comparable to particle gyroradii, and evaluate their damping by
various mechanisms. We show that the classical viscous damping is unimportant
for magnetically dominated or low beta plasmas and the primary damping
mechanism is the collisionless damping by the background particles. We show
that the damping rate is proportional to the total random momentum density of
the particles. For solar flare conditions this means that in most flares,
except the very large ones, the damping is dominated by thermal background
electrons. For large flares one requires acceleration of essentially all
background electrons into a nonthermal distribution so that the accelerated
electrons can be important in the damping of the waves. In general, damping by
thermal or nonthermal protons is negligible compared to that of electrons
except for quasi-perpendicular propagating waves or for rare proton dominated
flares with strong nuclear gamma-ray line emission. Using the rate for damping
we determine the critical scale below which the damping becomes important and
the spectrum of the turbulence steepens. This critical scale, however, has
strong dependence on the angle of propagation with respect to the magnetic
field direction. The waves can cascade down to very small scales, such as the
gyroradii of the particles at small angles (quasi-parallel propagation) and
possibly near 90 degree (quasi-perpendicular propagation) giving rise to a
highly anisotropic spectral distribution. | 0508567v1 |
2011-07-27 | Constraint damping for the Z4c formulation of general relativity | One possibility for avoiding constraint violation in numerical relativity
simulations adopting free-evolution schemes is to modify the continuum
evolution equations so that constraint violations are damped away. Gundlach et.
al. demonstrated that such a scheme damps low amplitude, high frequency
constraint violating modes exponentially for the Z4 formulation of General
Relativity. Here we analyze the effect of the damping scheme in numerical
applications on a conformal decomposition of Z4. After reproducing the
theoretically predicted damping rates of constraint violations in the linear
regime, we explore numerical solutions not covered by the theoretical analysis.
In particular we examine the effect of the damping scheme on low-frequency and
on high-amplitude perturbations of flat spacetime as well and on the long-term
dynamics of puncture and compact star initial data in the context of spherical
symmetry. We find that the damping scheme is effective provided that the
constraint violation is resolved on the numerical grid. On grid noise the
combination of artificial dissipation and damping helps to suppress constraint
violations. We find that care must be taken in choosing the damping parameter
in simulations of puncture black holes. Otherwise the damping scheme can cause
undesirable growth of the constraints, and even qualitatively incorrect
evolutions. In the numerical evolution of a compact static star we find that
the choice of the damping parameter is even more delicate, but may lead to a
small decrease of constraint violation. For a large range of values it results
in unphysical behavior. | 1107.5539v2 |
1999-11-24 | Damped Lyman alpha absorber and the faint end of the galaxy luminosity function at high redshift | We combine predictions for several hierarchical cosmogonies with
observational evidence on damped Lyman alpha systems to establish a
correspondence between the high redshift galaxy population and the properties
of damped Lyman alpha systems. We assume that high redshift galaxies and damped
Lyman alpha systems are hosted by the same dark matter halos and require
consistency between the predicted halo space density, the rate of incidence and
the velocity width distribution of damped Lyman alpha systems, and the observed
galaxy luminosity function at the bright end. We arrive at the following
results: (1) predicted impact parameters between the damped absorption system
and the luminous part of the absorbing galaxy are expected to be very small
(0.3 - 1arcsec) for most galaxies; (2) luminosities of galaxies causing damped
absorption are generally fainter than m_R = 25 and damped Lyman alpha systems
are predicted to sample preferentially the outer regions of galaxies at the
faint end of the galaxy luminosity function at high redshift. Therefore, DLAS
should currently provide the best probe of the progenitors of normal
present-day galaxies. | 9911447v1 |
2003-03-13 | An explicit unconditionally stable numerical method for solving damped nonlinear Schrödinger equations with a focusing nonlinearity | This paper introduces an extension of the time-splitting sine-spectral (TSSP)
method for solving damped focusing nonlinear Schr\"{o}dinger equations (NLS).
The method is explicit, unconditionally stable and time transversal invariant.
Moreover, it preserves the exact decay rate for the normalization of the wave
function if linear damping terms are added to the NLS. Extensive numerical
tests are presented for cubic focusing nonlinear Schr\"{o}dinger equations in
2d with a linear, cubic or a quintic damping term. Our numerical results show
that quintic or cubic damping always arrests blowup, while linear damping can
arrest blowup only when the damping parameter $\dt$ is larger than a threshold
value $\dt_{\rm th}$. We note that our method can also be applied to solve the
3d Gross-Pitaevskii equation with a quintic damping term to model the dynamics
of a collapsing and exploding Bose-Einstein condensate (BEC). | 0303158v1 |
2004-11-03 | Quantum probability applied to the damped harmonic oscillator | In this introductory course we sketch the framework of quantum probability in
order to discuss open quantum systems, in particular the damped harmonic
oscillator. | 0411024v1 |
2006-11-23 | Path integrals and wavepacket evolution for damped mechanical systems | Damped mechanical systems with various forms of damping are quantized using
the path integral formalism. In particular, we obtain the path integral kernel
for the linearly damped harmonic oscillator and a particle in a uniform
gravitational field with linearly or quadratically damped motion. In each case,
we study the evolution of Gaussian wavepackets and discuss the characteristic
features that help us distinguish between different types of damping. For
quadratic damping, we show that the action and equation of motion of such a
system has a connection with the zero dimensional version of a currently
popular scalar field theory. Furthermore we demonstrate that the equation of
motion (for quadratic damping) can be identified as a geodesic equation in a
fictitious two-dimensional space. | 0611239v1 |
2007-07-05 | Damping of bulk excitations over an elongated BEC - the role of radial modes | We report the measurement of Beliaev damping of bulk excitations in cigar
shaped Bose Einstein condensates of atomic vapor. By using post selection,
excitation line shapes of the total population are compared with those of the
undamped excitations. We find that the damping depends on the initial
excitation energy of the decaying quasi particle, as well as on the excitation
momentum. We model the condensate as an infinite cylinder and calculate the
damping rates of the different radial modes. The derived damping rates are in
good agreement with the experimentally measured ones. The damping rates
strongly depend on the destructive interference between pathways for damping,
due to the quantum many-body nature of both excitation and damping products. | 0707.0776v1 |
2008-09-22 | Damping in 2D and 3D dilute Bose gases | Damping in 2D and 3D dilute gases is investigated using both the
hydrodynamical approach and the Hartree-Fock-Bogoliubov (HFB) approximation .
We found that the both methods are good for the Beliaev damping at zero
temperature and Landau damping at very low temperature, however, at high
temperature, the hydrodynamical approach overestimates the Landau damping and
the HFB gives a better approximation. This result shows that the comparison of
the theoretical calculation using the hydrodynamical approach and the
experimental data for high temperature done by Vincent Liu (PRL {\bf21} 4056
(1997)) is not proper. For two-dimensional systems, we show that the Beliaev
damping rate is proportional to $k^3$ and the Landau damping rate is
proportional to $ T^2$ for low temperature and to $T$ for high temperature. We
also show that in two dimensions the hydrodynamical approach gives the same
result for zero temperature and for low temperature as HFB, but overestimates
the Landau damping for high temperature. | 0809.3632v3 |
2008-12-08 | Landau Damping and Alfven Eigenmodes of Neutron Star Torsion Oscillations | Torsion oscillations of the neutron star crust are Landau damped by the
Alfven continuum in the bulk. For strong magnetic fields (in magnetars),
undamped Alfven eigenmodes appear. | 0812.1570v1 |
2010-09-24 | Spatial Damping of Propagating Kink Waves in Prominence Threads | Transverse oscillations and propagating waves are frequently observed in
threads of solar prominences/filaments and have been interpreted as kink
magnetohydrodynamic (MHD) modes. We investigate the spatial damping of
propagating kink MHD waves in transversely nonuniform and partially ionized
prominence threads. Resonant absorption and ion-neutral collisions (Cowling's
diffusion) are the damping mechanisms taken into account. The dispersion
relation of resonant kink waves in a partially ionized magnetic flux tube is
numerically solved by considering prominence conditions. Analytical expressions
of the wavelength and damping length as functions of the kink mode frequency
are obtained in the Thin Tube and Thin Boundary approximations. For typically
reported periods of thread oscillations, resonant absorption is an efficient
mechanism for the kink mode spatial damping, while ion-neutral collisions have
a minor role. Cowling's diffusion dominates both the propagation and damping
for periods much shorter than those observed. Resonant absorption may explain
the observed spatial damping of kink waves in prominence threads. The
transverse inhomogeneity length scale of the threads can be estimated by
comparing the observed wavelengths and damping lengths with the theoretically
predicted values. However, the ignorance of the form of the density profile in
the transversely nonuniform layer introduces inaccuracies in the determination
of the inhomogeneity length scale. | 1009.4871v1 |
2012-08-01 | Artificial Neural Network Based Prediction of Optimal Pseudo-Damping and Meta-Damping in Oscillatory Fractional Order Dynamical Systems | This paper investigates typical behaviors like damped oscillations in
fractional order (FO) dynamical systems. Such response occurs due to the
presence of, what is conceived as, pseudo-damping and meta-damping in some
special class of FO systems. Here, approximation of such damped oscillation in
FO systems with the conventional notion of integer order damping and time
constant has been carried out using Genetic Algorithm (GA). Next, a multilayer
feed-forward Artificial Neural Network (ANN) has been trained using the GA
based results to predict the optimal pseudo and meta-damping from knowledge of
the maximum order or number of terms in the FO dynamical system. | 1208.0318v1 |
2012-08-27 | Optimization of the damped quantum search | The damped quantum search proposed in [A. Mizel, Phys. Rev. Lett., 102 150501
(2009)] was analyzed by calculating the highest possible probability of finding
the target state in each iteration. A new damping parameter that depends on the
number of iterations was obtained, this was compared to the critical damping
parameter for different values of target to database size ratio. The result
shows that the range of the new damping parameter as a function of the target
to database size ratio increases as the number of iterations is increased.
Furthermore, application of the new damping parameter per iteration on the
damped quantum search scheme shows a significant improvement on some target to
database size ratio (i.e. greater than or equal to 50% maximum percentage
difference) over the critically damped quantum search. | 1208.5475v1 |
2013-04-03 | Damping the zero-point energy of a harmonic oscillator | The physics of quantum electromagnetism in an absorbing medium is that of a
field of damped harmonic oscillators. Yet until recently the damped harmonic
oscillator was not treated with the same kind of formalism used to describe
quantum electrodynamics in a arbitrary medium. Here we use the techniques of
macroscopic QED, based on the Huttner--Barnett reservoir, to describe the
quantum mechanics of a damped oscillator. We calculate the thermal and
zero-point energy of the oscillator for a range of damping values from zero to
infinity. While both the thermal and zero-point energies decrease with damping,
the energy stored in the oscillator at fixed temperature increases with
damping, an effect that may be experimentally observable. As the results follow
from canonical quantization, the uncertainty principle is valid for all damping
levels. | 1304.0977v2 |
2015-05-28 | Damping factors for head-tail modes at strong space charge | This paper suggests how feedback and Landau damping can be taken into account
for transverse oscillations of bunched beam at strong space charge. | 1505.07704v1 |
2015-06-18 | Damping of MHD turbulence in partially ionized plasma: implications for cosmic ray propagation | We study the damping from neutral-ion collisions of both incompressible and
compressible magnetohydrodynamic (MHD) turbulence in partially ionized medium.
We start from the linear analysis of MHD waves applying both single-fluid and
two-fluid treatments. The damping rates derived from the linear analysis are
then used in determining the damping scales of MHD turbulence. The physical
connection between the damping scale of MHD turbulence and cutoff boundary of
linear MHD waves is investigated. Our analytical results are shown to be
applicable in a variety of partially ionized interstellar medium (ISM) phases
and solar chromosphere. As a significant astrophysical utility, we introduce
damping effects to propagation of cosmic rays in partially ionized ISM. The
important role of turbulence damping in both transit-time damping and
gyroresonance is identified. | 1506.05585v1 |
2016-02-04 | Damping Evaluation for Free Vibration of Spherical Structures in Elastodynamic-Acoustic Interaction | This paper discusses the free vibration of elastic spherical structures in
the presence of an externally unbounded acoustic medium. In this vibration,
damping associated with the radiation of energy from the confined solid medium
to the surrounding acoustic medium is observed. Evaluating the coupled system
response (solid displacement and acoustic pressure) and characterizing the
acoustic radiation damping in conjunction with the media properties are the
main objectives of this research. In this work, acoustic damping is
demonstrated for two problems: the thin spherical shell and the solid sphere.
The mathematical approach followed in solving these coupled problems is based
on the Laplace transform method. The linear under-damped harmonic oscillator is
the reference model for damping estimation. The damping evaluation is performed
in frequency as well as in time domains; both investigations lead to identical
damping factor expressions. | 1604.06738v1 |
2017-09-05 | Enhancement of space-charge induced damping due to reactive impedances for head-tail modes | Landau damping of head-tail modes in bunches due to spreads in the tune shift
can be a deciding factor for beam stability. We demonstrate that the coherent
tune shifts due to reactive impedances can enhance the space-charge induced
damping and change the stability thresholds (here, a reactive impedance implies
the imaginary part of the impedance of both signs). For example, high damping
rates at strong space-charge, or damping of the $k=0$ mode, can be possible. It
is shown and explained, how the negative reactive impedances (causing negative
coherent tune shifts similarly to the effect of space-charge) can enhance the
Landau damping, while the positive coherent tune shifts have an opposite
effect. It is shown that the damping rate is a function of the coherent mode
position in the incoherent spectrum, in accordance with the concept of the
interaction of a collective mode with resonant particles. We present an
analytical model, which allows for quantitative predictions of damping
thresholds for different head-tail modes, for arbitrary space-charge and
coherent tune-shift conditions, as it is verified using particle tracking
simulations. | 1709.01425v1 |
2018-05-21 | Critical damping in nonviscously damped linear systems | In structural dynamics, energy dissipative mechanisms with non-viscous
damping are characterized by their dependence on the time-history of the
response velocity, mathematically represented by convolution integrals
involving hereditary functions. Combination of damping parameters in the
dissipative model can lead the system to be overdamped in some (or all) modes.
In the domain of the damping parameters, the thresholds between induced
oscillatory and non--oscillatory motion are called critical damping surfaces
(or manifolds, since we can have a lot of parameters). In this paper a general
method to obtain critical damping surfaces for nonviscously damped systems is
proposed. The approach is based on transforming the algebraic equations which
defined implicitly the critical curves into a system of differential equations.
The derivations are validated with three numerical methods covering single and
multiple degree of freedom systems. | 1805.08022v1 |
2018-11-01 | Hereditary effects of exponentially damped oscillators with past histories | Hereditary effects of exponentially damped oscillators with past histories
are considered in this paper. Nonviscously damped oscillators involve
hereditary damping forces which depend on time-histories of vibrating motions
via convolution integrals over exponentially decaying functions. As a result,
this kind of oscillators are said to have memory. In this work, initialization
for nonviscously damped oscillators is firstly proposed. Unlike the classical
viscously damped ones, information of the past history of response velocity is
necessary to fully determine the dynamic behaviors of nonviscously damped
oscillators. Then, initialization response of exponentially damped oscillators
is obtained to characterize the hereditary effects on the dynamic response. At
last, stability of initialization response is proved and the hereditary effects
are shown to gradually recede with increasing of time. | 1811.00216v1 |
2019-08-01 | The Temperature-dependent Damping of Propagating Slow Magnetoacoustic Waves | The rapid damping of slow magnetoacoustic waves in the solar corona has been
extensively studied in previous years. Most studies suggest that thermal
conduction is a dominant contributor to this damping, albeit with a few
exceptions. Employing extreme-ultraviolet (EUV) imaging data from SDO/AIA, we
measure the damping lengths of propagating slow magnetoacoustic waves observed
in several fan-like loop structures using two independent methods. The
dependence of the damping length on temperature has been studied for the first
time. The results do not indicate any apparent decrease in damping length with
temperature, which is in contrast to the existing viewpoint. Comparing with the
corresponding theoretical values calculated from damping due to thermal
conduction, it is inferred that thermal conduction is suppressed in hotter
loops. An alternative interpretation that suggests thermal conduction is not
the dominant damping mechanism, even for short period waves in warm active
region loops, is also presented. | 1908.00384v1 |
2019-10-14 | Decay rates for the damped wave equation with finite regularity damping | Decay rates for the energy of solutions of the damped wave equation on the
torus are studied. In particular, damping invariant in one direction and equal
to a sum of squares of nonnegative functions with a particular number of
derivatives of regularity is considered. For such damping energy decays at rate
$1/t^{2/3}$. If additional regularity is assumed the decay rate improves. When
such a damping is smooth the energy decays at $1/t^{4/5-\delta}$. The proof
uses a positive commutator argument and relies on a pseudodifferential calculus
for low regularity symbols. | 1910.06372v3 |
2022-07-01 | Seismic Response of Yielding Structures Coupled to Rocking Walls with Supplemental Damping | Given that the coupling of a framing structure to a strong, rocking wall
enforces a first-mode response, this paper investigates the dynamic response of
a yielding single-degree-of-freedom oscillator coupled to a rocking wall with
supplemental damping (hysteretic or linear viscous) along its sides. The full
nonlinear equations of motion are derived, and the study presents an earthquake
response analysis in term of inelastic spectra. The study shows that for
structures with preyielding period T1<1.0 s the effect of supplemental damping
along the sides of the rocking wall is marginal even when large values of
damping are used. The study uncovers that occasionally the damped response
matches or exceeds the undamped response; however, when this happens, the
exceedance is marginal. The paper concludes that for yielding structures with
strength less than 10% of their weight the use of supplemental damping along
the sides of a rocking wall coupled to a yielding structure is not recommended.
The paper shows that supplemental damping along the sides of the rocking wall
may have some limited beneficial effects for structures with longer preyielding
periods (say T1>1.0 s). Nevertheless, no notable further response reduction is
observed when larger values of hysteretic or viscous damping are used. | 2207.00641v1 |
2023-03-08 | Material-Geometry Interplay in Damping of Biomimetic Scale Beams | Biomimetic scale-covered substrates are architected meta-structures
exhibiting fascinating emergent nonlinearities via the geometry of collective
scales contacts. In spite of much progress in understanding their elastic
nonlinearity, their dissipative behavior arising from scales sliding is
relatively uninvestigated in the dynamic regime. Recently discovered is the
phenomena of viscous emergence, where dry Coulomb friction between scales can
lead to apparent viscous damping behavior of the overall multi-material
substrate. In contrast to this structural dissipation, material dissipation
common in many polymers has never been considered, especially synergestically
with geometrical factors. This is addressed here for the first time, where
material visco-elasticity is introduced via a simple Kelvin-Voigt model for
brevity and clarity. The results contrast the two damping sources in these
architectured systems: material viscoelasticity, and geometrical frictional
scales contact. It is discovered that although topically similar in effective
damping, viscoelsatic damping follows a different damping envelope than dry
friction, including starkly different effects on damping symmetry and specific
damping capacity. | 2303.04920v1 |
2023-04-11 | A comparison of 7 Tesla MR spectroscopic imaging and 3 Tesla MR fingerprinting for tumor localization in glioma patients | This paper investigates the correlation between magnetic resonance
spectroscopic imaging (MRSI) and magnetic resonance fingerprinting (MRF) in
glioma patients by comparing neuro-oncological markers obtained from MRSI to
T1/T2 maps from MRF.
Data from 12 consenting patients with gliomas were analyzed by defining
hotspots for T1, T2 and various metabolic ratios, and comparing them using
S{\o}rensen-Dice Similarity Coefficients (DSCs) and the distances between their
centers of intensity (COIDs).
Median DSCs between MRF and the tumor segmentation were 0.73 (T1) and 0.79
(T2). The DSCs between MRSI and MRF were highest for Gln/tNAA (T1: 0.75, T2:
0.80, tumor: 0.78), followed by Gly/tNAA (T1: 0.57, T2: 0.62, tumor: 0.54) and
tCho/tNAA (T1: 0.61, T2: 0.58, tumor: 0.45). The median values in the tumor
hotspot were T1=1724 ms, T2=86 ms, Gln/tNAA=0.61, Gly/tNAA=0.28, Ins/tNAA=1.15,
and tCho/tNAA=0.48, and, in the peritumoral region, were T1=1756 ms, T2=102ms,
Gln/tNAA=0.38, Gly/tNAA=0.20, Ins/tNAA=1.06, and tCho/tNAA=0.38, and, in the
NAWM, were T1=950 ms, T2=43 ms, Gln/tNAA=0.16, Gly/tNAA=0.07, Ins/tNAA=0.54,
and tCho/tNAA=0.20.
The results of this study constitute the first comparison of 7T MRSI and 3T
MRF, showing a good correspondence between these methods. | 2304.05254v1 |
1998-03-28 | Landau damping and the echo effect in a confined Bose-Einstein condensate | Low energy collective mode of a confined Bose-Einstein condensate should
demonstrate the echo effect in the regime of Landau damping. This echo is a
signature of reversible nature of Landau damping. General expression for the
echo profile is derived in the limit of small amplitudes of the external
pulses. Several universal features of the echo are found. The existence of echo
in other cases of reversible damping -- Fano effect and Caldeira-Leggett model
-- is emphasized. It is suggested to test reversible nature of the damping in
the atomic traps by conducting the echo experiment. | 9803351v1 |
2000-07-10 | Dephasing of Electrons on Helium by Collisions with Gas Atoms | The damping of quantum effects in the transport properties of electrons
deposited on a surface of liquid helium is studied. It is found that due to
vertical motion of the helium vapour atoms the interference of paths of
duration $t$ is damped by a factor $\exp - (t/\tau_v)^3$. An expression is
derived for the weak-localization lineshape in the case that damping occurs by
a combination of processes with this type of cubic exponential damping and
processes with a simple exponential damping factor. | 0007160v1 |
1997-10-07 | Damping rate of plasmons and photons in a degenerate nonrelativistic plasma | A calculation is presented of the plasmon and photon damping rates in a dense
nonrelativistic plasma at zero temperature, following the resummation program
of Braaten-Pisarski. At small soft momentum $k$, the damping is dominated by $3
\to 2$ scattering processes corresponding to double longitudinal Landau
damping. The dampings are proportional to $(\alpha/v_{F})^{3/2} k^2/m$, where
$v_{F}$ is the Fermi velocity. | 9710260v1 |
2002-12-16 | Influence of damping on the vanishing of the electro-optic effect in chiral isotropic media | Using first principles, it is demonstrated that radiative damping alone
cannot lead to a nonvanishing electro-optic effect in a chiral isotropic
medium. This conclusion is in contrast with that obtained by a calculation in
which damping effects are included using the standard phenomenological model.
We show that these predictions differ because the phenomenological damping
equations are valid only in regions where the frequencies of the applied
electromagnetic fields are nearly resonant with the atomic transitions. We also
show that collisional damping can lead to a nonvanishing electrooptic effect,
but with a strength sufficiently weak that it is unlikely to be observable
under realistic laboratory conditions. | 0212089v1 |
2005-08-28 | Simultaneous amplitude and phase damping of a kind of Gaussian states and their separability | We give out the time evolution solution of simultaneous amplitude and phase
damping for any continuous variable state. For the simultaneous amplitude and
phase damping of a wide class of two- mode entangled Gaussian states, two
analytical conditions of the separability are given. One is the sufficient
condition of separability. The other is the condition of PPT separability where
the Peres-Horodecki criterion is applied. Between the two conditions there may
exist bound entanglement. The simplest example is the simultaneous amplitude
and phase damping of a two-mode squeezed vacuum state. The damped state is
non-Gaussian. | 0508209v2 |
2007-05-14 | Identification of the dominant precession damping mechanism in Fe, Co, and Ni by first-principles calculations | The Landau-Lifshitz equation reliably describes magnetization dynamics using
a phenomenological treatment of damping. This paper presents first-principles
calculations of the damping parameters for Fe, Co, and Ni that quantitatively
agree with existing ferromagnetic resonance measurements. This agreement
establishes the dominant damping mechanism for these systems and takes a
significant step toward predicting and tailoring the damping constants of new
materials. | 0705.1990v1 |
2007-08-28 | Ising Dynamics with Damping | We show for the Ising model that is possible construct a discrete time
stochastic model analogous to the Langevin equation that incorporates an
arbitrary amount of damping. It is shown to give the correct equilibrium
statistics and is then used to investigate nonequilibrium phenomena, in
particular, magnetic avalanches. The value of damping can greatly alter the
shape of hysteresis loops, and for small damping and high disorder, the
morphology of large avalanches can be drastically effected. Small damping also
alters the size distribution of avalanches at criticality. | 0708.3855v1 |
2008-02-08 | On the scaling of the damping time for resonantly damped oscillations in coronal loops | There is not as yet full agreement on the mechanism that causes the rapid
damping of the oscillations observed by TRACE in coronal loops. It has been
suggested that the variation of the observed values of the damping time as
function of the corresponding observed values of the period contains
information on the possible damping mechanism. The aim of this Letter is to
show that, for resonant absorption, this is definitely not the case unless
detailed a priori information on the individual loops is available. | 0802.1143v1 |
2008-10-02 | Critically damped quantum search | Although measurement and unitary processes can accomplish any quantum
evolution in principle, thinking in terms of dissipation and damping can be
powerful. We propose a modification of Grover's algorithm in which the idea of
damping plays a natural role. Remarkably, we have found that there is a
critical damping value that divides between the quantum $O(\sqrt{N})$ and
classical O(N) search regimes. In addition, by allowing the damping to vary in
a fashion we describe, one obtains a fixed-point quantum search algorithm in
which ignorance of the number of targets increases the number of oracle queries
only by a factor of 1.5. | 0810.0470v1 |
2009-07-01 | Modal approximations to damped linear systems | We consider a finite dimensional damped second order system and obtain
spectral inclusion theorems for the related quadratic eigenvalue problem. The
inclusion sets are the 'quasi Cassini ovals' which may greatly outperform
standard Gershgorin circles. As the unperturbed system we take a modally damped
part of the system; this includes the known proportionally damped models, but
may give much sharper estimates. These inclusions are then applied to derive
some easily calculable sufficient conditions for the overdampedness of a given
damped system. | 0907.0167v1 |
2010-01-14 | Multi-Error-Correcting Amplitude Damping Codes | We construct new families of multi-error-correcting quantum codes for the
amplitude damping channel. Our key observation is that, with proper encoding,
two uses of the amplitude damping channel simulate a quantum erasure channel.
This allows us to use concatenated codes with quantum erasure-correcting codes
as outer codes for correcting multiple amplitude damping errors. Our new codes
are degenerate stabilizer codes and have parameters which are better than the
amplitude damping codes obtained by any previously known construction. | 1001.2356v1 |
2011-09-05 | Spectral theory of damped quantum chaotic systems | We investigate the spectral distribution of the damped wave equation on a
compact Riemannian manifold, especially in the case of a metric of negative
curvature, for which the geodesic flow is Anosov. The main application is to
obtain conditions (in terms of the geodesic flow on $X$ and the damping
function) for which the energy of the waves decays exponentially fast, at least
for smooth enough initial data. We review various estimates for the high
frequency spectrum in terms of dynamically defined quantities, like the value
distribution of the time-averaged damping. We also present a new condition for
a spectral gap, depending on the set of minimally damped trajectories. | 1109.0930v1 |
2012-06-07 | From resolvent estimates to damped waves | In this paper we show how to obtain decay estimates for the damped wave
equation on a compact manifold without geometric control via knowledge of the
dynamics near the un-damped set. We show that if replacing the damping term
with a higher-order \emph{complex absorbing potential} gives an operator
enjoying polynomial resolvent bounds on the real axis, then the "resolvent"
associated to our damped problem enjoys bounds of the same order. It is known
that the necessary estimates with complex absorbing potential can also be
obtained via gluing from estimates for corresponding non-compact models. | 1206.1565v1 |
2012-12-03 | Inviscid limit of stochastic damped 2D Navier-Stokes equations | We consider the inviscid limit of the stochastic damped 2D Navier- Stokes
equations. We prove that, when the viscosity vanishes, the stationary solution
of the stochastic damped Navier-Stokes equations converges to a stationary
solution of the stochastic damped Euler equation and that the rate of
dissipation of enstrophy converges to zero. In particular, this limit obeys an
enstrophy balance. The rates are computed with respect to a limit measure of
the unique invariant measure of the stochastic damped Navier-Stokes equations. | 1212.0509v3 |
2014-01-13 | NLSE for quantum plasmas with the radiation damping | We consider contribution of the radiation damping in the quantum hydrodynamic
equations for spinless particles. We discuss possibility of obtaining of
corresponding non-linear Schrodinger equation (NLSE) for the macroscopic wave
function. We compare contribution of the radiation damping with weakly (or
semi-) relativistic effects appearing in the second order by v/c. The radiation
damping appears in the third order by v/c. So it might be smaller than weakly
relativistic effects, but it gives damping of the Langmuir waves which can be
considerable. | 1401.2829v1 |
2014-09-26 | An ultimate storage ring lattice with vertical emittance generated by damping wigglers | We discuss the approach of generating round beams for ultimate storage rings
using vertical damping wigglers (with horizontal magnetic field). The vertical
damping wigglers provide damping and excite vertical emittance. This eliminates
the need to generate large linear coupling that is impractical with traditional
off-axis injection. We use a PEP-X compatible lattice to demonstrate the
approach. This lattice uses separate quadrupole and sextupole magnets with
realistic gradient strengths. Intrabeam scattering effects are calculated. The
horizontal and vertical emittances are 22.3 pm and 10.3 pm, respectively, for a
200 mA, 4.5 GeV beam, with a vertical damping wiggler of a total length of 90
meters, peak field of 1.5 T and wiggler period of 100 mm. | 1409.7452v2 |
2017-03-01 | Behaviors of the energy of solutions of two coupled wave equations with nonlinear damping on a compact manifold with boundary | In this paper we study the behaviors of the the energy of solutions of
coupled wave equations on a compact manifold with boundary in the case of
indirect nonlinear damping . Only one of the two equations is directly damped
by a localized nonlinear damping term. Under geometric conditions on both the
coupling and the damping regions we prove that the rate of decay of the energy
of smooth solutions of the system is determined from a first order differential
equation . | 1703.00172v1 |
2017-06-02 | Vanishing viscosity limit for global attractors for the damped Navier--Stokes system with stress free boundary conditions | We consider the damped and driven Navier--Stokes system with stress free
boundary conditions and the damped Euler system in a bounded domain
$\Omega\subset\mathbf{R}^2$. We show that the damped Euler system has a
(strong) global attractor in~$H^1(\Omega)$. We also show that in the vanishing
viscosity limit the global attractors of the Navier--Stokes system converge in
the non-symmetric Hausdorff distance in $H^1(\Omega)$ to the the strong global
attractor of the limiting damped Euler system (whose solutions are not
necessarily unique). | 1706.00607v1 |
2018-01-20 | Long time dynamics for weakly damped nonlinear Klein-Gordon equations | We continue our study of damped nonlinear Klein-Gordon equations. In our
previous work we considered fixed positive damping and proved a form of the
soliton resolution conjecture for radial solutions. In contrast, here we
consider damping which decreases in time to 0. In the class of radial data we
again establish soliton resolution provided the damping goes to 0 sufficiently
slowly. While our previous work relied on invariant manifold theory, here we
use the Lojasiewicz-Simon inequality applied to a suitable Lyapunov functional. | 1801.06735v1 |
2018-02-28 | Nonexistence of global solutions of wave equations with weak time-dependent damping and combined nonlinearity | In our previous two works, we studied the blow-up and lifespan estimates for
damped wave equations with a power nonlinearity of the solution or its
derivative, with scattering damping independently. In this work, we are devoted
to establishing a similar result for a combined nonlinearity. Comparing to the
result of wave equation without damping, one can say that the scattering
damping has no influence. | 1802.10273v1 |
2018-11-12 | Choking non-local magnetic damping in exchange biased ferromagnets | We investigated the temperature dependence of the magnetic damping in the
exchange biased Pt/ Fe50Mn50 /Fe20Ni80 /SiOx multilayers. In samples having a
strong exchange bias, we observed a drastic decrease of the magnetic damping of
the FeNi with increasing temperature up to the blocking temperature. The
results essentially indicate that the non-local enhancement of the magnetic
damping can be choked by the adjacent antiferromagnet and its temperature
dependent exchange bias. We also pointed out that such a strong temperature
dependent damping may be very beneficial for spintronic applications. | 1811.04821v1 |
2019-05-23 | Escaping Locally Optimal Decentralized Control Polices via Damping | We study the evolution of locally optimal decentralized controllers with the
damping of the control system. Empirically it is shown that even for instances
with an exponential number of connected components, damping merges all local
solutions to the one global solution. We characterize the evolution of locally
optimal solutions with the notion of hemi-continuity and further derive
asymptotic properties of the objective function and of the locally optimal
controllers as the damping becomes large. Especially, we prove that with enough
damping, there is no spurious locally optimal controller with favorable control
structures. The convoluted behavior of the locally optimal trajectory is
illustrated with numerical examples. | 1905.09915v1 |
2019-08-22 | Some remarks on the asymptotic profile of solutions to structurally damped $σ$-evolution equations | In this paper, we are interested in analyzing the asymptotic profiles of
solutions to the Cauchy problem for linear structurally damped
$\sigma$-evolution equations in $L^2$-sense. Depending on the parameters
$\sigma$ and $\delta$ we would like to not only indicate approximation formula
of solutions but also recognize the optimality of their decay rates as well in
the distinct cases of parabolic like damping and $\sigma$-evolution like
damping. Moreover, such results are also discussed when we mix these two kinds
of damping terms in a $\sigma$-evolution equation to investigate how each of
them affects the asymptotic profile of solutions. | 1908.08492v1 |
2019-09-18 | Global smooth solutions of the damped Boussinesq equations with a class of large initial data | The global regularity problem concerning the inviscid Boussinesq equations
remains an open problem. In an attempt to understand this problem, we examine
the damped Boussinesq equations and study how damping affects the regularity of
solutions. In this paper, we consider the global existence to the damped
Boussinesq equations with a class of large initial data, whose $B^{s}_{p,r}$ or
$\dot{B}^{s}_{p,r}$ norms can be arbitrarily large. The idea is splitting the
linear Boussinesq equations from the damped Boussinesq equations, the
exponentially decaying solution of the former equations together with the
structure of the Boussinesq equations help us to obtain the global smooth
solutions. | 1909.08360v1 |
2020-02-15 | Asymptotic profile and optimal decay of solutions of some wave equations with logarithmic damping | We introduce a new model of the nonlocal wave equations with a logarithmic
damping mechanism. We consider the Cauchy poroblem for the new model in the
whole space. We study the asymptotic profile and optimal decay and blowup rates
of solutions as time goes to infinity. The damping terms considered in this
paper is not studied so far, and in the low frequency parameters the damping is
rather weakly effective than that of well-studied fractional type of nonlocal
damping. In order to get the optimal estimates in time we meet the so-called
hypergeometric functions with special parameters. | 2002.06319v1 |
2020-05-13 | Weak Input to state estimates for 2D damped wave equations with localized and non-linear damping | In this paper, we study input-to-state (ISS) issues for damped wave equations
with Dirichlet boundary conditions on a bounded domain of dimension two. The
damping term is assumed to be non-linear and localized to an open subset of the
domain. In a first step, we handle the undisturbed case as an extension of a
previous work, where stability results are given with a damping term active on
the full domain. Then, we address the case with disturbances and provide
input-to-state types of results. | 2005.06206v3 |
2020-07-25 | Decay for the Kelvin-Voigt damped wave equation: Piecewise smooth damping | We study the energy decay rate of the Kelvin-Voigt damped wave equation with
piecewise smooth damping on the multi-dimensional domain. Under suitable
geometric assumptions on the support of the damping, we obtain the optimal
polynomial decay rate which turns out to be different from the one-dimensional
case studied in \cite{LR05}. This optimal decay rate is saturated by high
energy quasi-modes localised on geometric optics rays which hit the interface
along non orthogonal neither tangential directions. The proof uses
semi-classical analysis of boundary value problems. | 2007.12994v2 |
2020-08-12 | From Lieb-Thirring inequalities to spectral enclosures for the damped wave equation | Using a correspondence between the spectrum of the damped wave equation and
non-self-adjoint Schroedinger operators, we derive various bounds on complex
eigenvalues of the former. In particular, we establish a sharp result that the
one-dimensional damped wave operator is similar to the undamped one provided
that the L^1 norm of the (possibly complex-valued) damping is less than 2. It
follows that these small dampings are spectrally undetectable. | 2008.05176v1 |
2021-08-02 | Wide-Area Damping Control for Interarea Oscillations in Power Grids Based on PMU Measurements | In this paper, a phasor measurement unit (PMU)-based wide-area damping
control method is proposed to damp the interarea oscillations that threaten the
modern power system stability and security. Utilizing the synchronized PMU
data, the proposed almost model-free approach can achieve an effective damping
for the selected modes using a minimum number of synchronous generators.
Simulations are performed to show the validity of the proposed wide-area
damping control scheme. | 2108.01193v1 |
2021-09-05 | Regularity of the semigroups associated with some damped coupled elastic systems II: a nondegenerate fractional damping case | In this paper, we examine regularity issues for two damped abstract elastic
systems; the damping and coupling involve fractional powers $\mu, \theta$, with
$0 \leq \mu , \theta \leq 1$, of the principal operators. The matrix defining
the coupling and damping is nondegenerate. This new work is a sequel to the
degenerate case that we discussed recently in \cite{kfl}. First, we prove that
for $1/2 \leq \mu , \theta \leq 1$, the underlying semigroup is analytic. Next,
we show that for $\min(\mu,\theta) \in (0,1/2)$, the semigroup is of certain
Gevrey classes. Finally, some examples of application are provided. | 2109.02044v1 |
2021-09-28 | A robust and efficient line search for self-consistent field iterations | We propose a novel adaptive damping algorithm for the self-consistent field
(SCF) iterations of Kohn-Sham density-functional theory, using a backtracking
line search to automatically adjust the damping in each SCF step. This line
search is based on a theoretically sound, accurate and inexpensive model for
the energy as a function of the damping parameter. In contrast to usual damped
SCF schemes, the resulting algorithm is fully automatic and does not require
the user to select a damping. We successfully apply it to a wide range of
challenging systems, including elongated supercells, surfaces and
transition-metal alloys. | 2109.14018v3 |
2021-11-17 | Spectral asymptotics for the vectorial damped wave equation | The eigenfrequencies associated to a scalar damped wave equation are known to
belong to a band parallel to the real axis. In [Sj{\"o}00] J. Sj{\"o}strand
showed that up to a set of density 0, the eigenfrequencies are confined in a
thinner band determined by the Birkhoff limits of the damping term. In this
article we show that this result is still true for a vectorial damped wave
equation. In this setting the Lyapunov exponents of the cocycle given by the
damping term play the role of the Birkhoff limits of the scalar setting. | 2111.08982v1 |
2021-12-13 | Rotons and their damping in elongated dipolar Bose-Einstein condensates | We discuss finite temperature damping of rotons in elongated Bose-condensed
dipolar gases, which are in the Thomas-Fermi regime in the tightly confined
directions. The presence of many branches of excitations which can participate
in the damping process, is crucial for the Landau damping and results in
significant increase of the damping rate. It is found, however, that even
rotons with energies close to the roton gap may remain fairly stable in systems
with the roton gap as small as 1nK. | 2112.06835v2 |
2022-03-12 | Asymptotic expansion of solutions to the wave equation with space-dependent damping | We study the large time behavior of solutions to the wave equation with
space-dependent damping in an exterior domain. We show that if the damping is
effective, then the solution is asymptotically expanded in terms of solutions
of corresponding parabolic equations. The main idea to obtain the asymptotic
expansion is the decomposition of the solution of the damped wave equation into
the solution of the corresponding parabolic problem and the time derivative of
the solution of the damped wave equation with certain inhomogeneous term and
initial data. The estimate of the remainder term is an application of weighted
energy method with suitable supersolutions of the corresponding parabolic
problem. | 2203.06360v1 |
2022-10-27 | Sharp polynomial decay for polynomially singular damping on the torus | We study energy decay rates for the damped wave equation with unbounded
damping, without the geometric control condition. Our main decay result is
sharp polynomial energy decay for polynomially controlled singular damping on
the torus. We also prove that for normally $L^p$-damping on compact manifolds,
the Schr\"odinger observability gives $p$-dependent polynomial decay, and
finite time extinction cannot occur. We show that polynomially controlled
singular damping on the circle gives exponential decay. | 2210.15697v3 |
2023-09-27 | Dispersion and damping of ion-acoustic waves in the plasma with a regularized kappa-distribution | The dispersion and damping of ion-acoustic waves in the plasma with a
regularized kappa-distribution are studied. The generalized dispersion relation
and damping rate are derived, which both depend significantly on the parameters
alpha and kappa. The numerical analyses show that the wave frequency and the
damping rate of ion-acoustic waves in the plasma with the regularized
kappa-distribution are both generally less than those in the plasma with the
kappa-distribution, and if kappa is less than a value, the ion-acoustic waves
and their damping rate exist in the plasma with the regularized
kappa-distribution. | 2309.15885v1 |
2023-11-16 | Near-optimal Closed-loop Method via Lyapunov Damping for Convex Optimization | We introduce an autonomous system with closed-loop damping for first-order
convex optimization. While, to this day, optimal rates of convergence are only
achieved by non-autonomous methods via open-loop damping (e.g., Nesterov's
algorithm), we show that our system is the first one featuring a closed-loop
damping while exhibiting a rate arbitrarily close to the optimal one. We do so
by coupling the damping and the speed of convergence of the system via a
well-chosen Lyapunov function. We then derive a practical first-order algorithm
called LYDIA by discretizing our system, and present numerical experiments
supporting our theoretical findings. | 2311.10053v1 |
2024-02-05 | Fractional damping induces resonant behavior in the Duffing oscillator | The interaction between the fractional order parameter and the damping
parameter can play a relevant role for introducing different dynamical
behaviors in a physical system. Here, we study the Duffing oscillator with a
fractional damping term. Our findings show that for certain values of the
fractional order parameter, the damping parameter, and the forcing amplitude
high oscillations amplitude can be induced. This phenomenon is due to the
appearance of a resonance in the Duffing oscillator only when the damping term
is fractional. | 2402.02940v1 |
2024-03-13 | Impact of Decoherence on Average Correlation | This article presents a comprehensive study of the impact of decoherence on
the average correlation for pure quantum states. We explore two primary
mechanisms of decoherence: phase damping and amplitude damping, each having
distinct effects on quantum systems. Phase damping, which describes the loss of
quantum coherence without energy loss, primarily affects the phase
relationships between the components of a quantum system while amplitude
damping involves energy dissipation and also affects the state's occupation
probabilities. We show that the average correlation follows a predictable
decaying pattern in both scenarios. Our analysis can be understood in the
context of quantum computing, by focusing on how phase damping influences the
entanglement and correlation between qubits, key factors in quantum
computational efficiency and error correction protocols. | 2403.10551v1 |
1998-02-18 | Damping rates of hot Giant Dipole Resonances | The damping rate of hot giant dipole resonances (GDR) is investigated.
Besides Landau damping we consider collisions and density fluctuations as
contributions to the damping of GDR. Within the nonequilibrium Green's function
method we derive a non-Markovian kinetic equation. The linearization of the
latter one leads to complex dispersion relations. The complex solution provides
the centroid energy and the damping width of giant resonances. The experimental
damping widths are the full width half maximum (FWHM) and can be reproduced by
the full width of the structure function. Within simple finite size scaling we
give a relation between the minimal interaction strength which is required for
a collective oscillation and the clustersize. We investigate the damping of
giant dipole resonances within a Skyrme type of interaction. Different
collision integrals are compared with each other in order to incorporate
correlations. The inclusion of a conserving relaxation time approximation
allows to find the $T^2$-dependence of the damping rate with a temperature
known from the Fermi-liquid theory. However, memory effects turn out to be
essential for a proper treatment of the damping of collective modes. We derive
a Landau like formula for the one--particle relaxation time similar to the
damping of zero sound. | 9802052v2 |
2015-12-11 | Ultra-low magnetic damping of a metallic ferromagnet | The phenomenology of magnetic damping is of critical importance for devices
that seek to exploit the electronic spin degree of freedom since damping
strongly affects the energy required and speed at which a device can operate.
However, theory has struggled to quantitatively predict the damping, even in
common ferromagnetic materials. This presents a challenge for a broad range of
applications in spintronics and spin-orbitronics that depend on materials and
structures with ultra-low damping. Such systems enable many experimental
investigations that further our theoretical understanding of numerous magnetic
phenomena such as damping and spin-transport mediated by chirality and the
Rashba effect. Despite this requirement, it is believed that achieving
ultra-low damping in metallic ferromagnets is limited due to the scattering of
magnons by the conduction electrons. However, we report on a binary alloy of Co
and Fe that overcomes this obstacle and exhibits a damping parameter
approaching 0.0001, which is comparable to values reported only for
ferrimagnetic insulators. We explain this phenomenon by a unique feature of the
bandstructure in this system: The density of states exhibits a sharp minimum at
the Fermi level at the same alloy concentration at which the minimum in the
magnetic damping is found. This discovery provides both a significant
fundamental understanding of damping mechanisms as well as a test of
theoretical predictions. | 1512.03610v1 |
2020-05-12 | Effective Viscous Damping Enables Morphological Computation in Legged Locomotion | Muscle models and animal observations suggest that physical damping is
beneficial for stabilization. Still, only a few implementations of mechanical
damping exist in compliant robotic legged locomotion. It remains unclear how
physical damping can be exploited for locomotion tasks, while its advantages as
sensor-free, adaptive force- and negative work-producing actuators are
promising. In a simplified numerical leg model, we studied the energy
dissipation from viscous and Coulomb damping during vertical drops with
ground-level perturbations. A parallel spring-damper is engaged between
touch-down and mid-stance, and its damper auto-disengages during mid-stance and
takeoff. Our simulations indicate that an adjustable and viscous damper is
desired. In hardware we explored effective viscous damping and adjustability
and quantified the dissipated energy. We tested two mechanical, leg-mounted
damping mechanisms; a commercial hydraulic damper, and a custom-made pneumatic
damper. The pneumatic damper exploits a rolling diaphragm with an adjustable
orifice, minimizing Coulomb damping effects while permitting adjustable
resistance. Experimental results show that the leg-mounted, hydraulic damper
exhibits the most effective viscous damping. Adjusting the orifice setting did
not result in substantial changes of dissipated energy per drop, unlike
adjusting damping parameters in the numerical model. Consequently, we also
emphasize the importance of characterizing physical dampers during real legged
impacts to evaluate their effectiveness for compliant legged locomotion. | 2005.05725v2 |
2022-02-10 | Non-stationary Anderson acceleration with optimized damping | Anderson acceleration (AA) has a long history of use and a strong recent
interest due to its potential ability to dramatically improve the linear
convergence of the fixed-point iteration. Most authors are simply using and
analyzing the stationary version of Anderson acceleration (sAA) with a constant
damping factor or without damping. Little attention has been paid to
nonstationary algorithms. However, damping can be useful and is sometimes
crucial for simulations in which the underlying fixed-point operator is not
globally contractive. The role of this damping factor has not been fully
understood. In the present work, we consider the non-stationary Anderson
acceleration algorithm with optimized damping (AAoptD) in each iteration to
further speed up linear and nonlinear iterations by applying one extra
inexpensive optimization. We analyze this procedure and develop an efficient
and inexpensive implementation scheme. We also show that, compared with the
stationary Anderson acceleration with fixed window size sAA(m), optimizing the
damping factors is related to dynamically packaging sAA(m) and sAA(1) in each
iteration (alternating window size $m$ is another direction of producing
non-stationary AA). Moreover, we show by extensive numerical experiments that
the proposed non-stationary Anderson acceleration with optimized damping
procedure often converges much faster than stationary AA with constant damping
or without damping. | 2202.05295v1 |
2023-06-30 | A finite element method to compute the damping rate of oscillating fluids inside microfluidic nozzles | We introduce a finite element method for computing the damping rate of fluid
oscillations in nozzles of drop-on-demand (DoD) microfluidic devices. Accurate
knowledge of the damping rates for the least-damped oscillation modes following
droplet ejection is paramount for assessing jetting stability at higher jetting
frequencies, as ejection from a non-quiescent meniscus can result in deviations
from nominal droplet properties. Computational fluid dynamics (CFD) simulations
often struggle to accurately predict meniscus damping in the limit of low
viscosity and high surface tension. Moreover, their use in design loops aimed
at optimizing the nozzle geometry for stable jetting is slow and
computationally expensive. The faster alternative we adopt here is to compute
the damping rate directly from the eigenvalues of the linearized problem.
Starting from a variational formulation of the linearized governing equations,
we obtain a generalized eigenvalue problem for the oscillation modes, and
approximate its solutions with a finite element method that uses Taylor-Hood
elements. We solve the matrix eigenvalue problem with a sparse, parallelized
implementation of the Krylov-Schur algorithm. The spatial shape and temporal
evolution (angular frequency and damping rate) of the set of least-damped
oscillation modes are obtained in a matter of minutes, compared to days for a
CFD simulation. We verify that the method can reproduce an analytical benchmark
problem, and then determine numerical convergence rates on two examples with
axisymmetric geometry. We also prove that the method is free of spurious modes
with zero or positive damping rates. The method's ability to quickly generate
accurate estimates of fluid oscillation damping rates makes it suitable for
integration into design loops for prototyping microfluidic nozzles. | 2307.00094v1 |
2024-01-18 | Multithermal apparent damping of slow waves due to strands with a Gaussian temperature distribution | Context. Slow waves in solar coronal loops are strongly damped. The current
theory of damping by thermal conduction cannot explain some observational
features.\n Aims. We investigate the propagation of slow waves in a coronal
loop built up from strands of different temperatures. \n Methods. We consider
the loop to have a multithermal, Gaussian temperature distribution. The
different propagation speeds in different strands lead to an multithermal
apparent damping of the wave, similar to observational phase mixing. We use an
analytical model to predict the damping length and propagation speed for the
slow waves, including in imaging with filter telescopes. \n Results. We compare
the damping length due to this multithermal apparent damping with damping due
to thermal conduction and find that the multithermal apparent damping is more
important for shorter period slow waves. We have found the influence of
instrument filters on the wave's propagation speed and damping. This allows us
to compare our analytical theory to forward models of numerical simulations. \n
Conclusions. We find that our analytical model matches the numerical
simulations very well. Moreover, we offer an outlook for using the slow wave
properties to infer the loop's thermal properties. | 2401.09803v1 |
2001-03-09 | Rayleigh Scattering and Microwave Background Fluctuations | During the recombination epoch, cosmic background photons couple not only to
free electrons through Thompson scattering, but also to the neutral hydrogen
through Rayleigh scattering. This latter is ~2% effect for photons near the
peak of the photon energy distribution at z=800 and a ~0.2% effect at z=1100.
Including Rayleigh scattering in the calculation reduces Silk damping at fixed
redshift, alters the position of the surface of last scattering and alters the
propagation of acoustic waves. We estimate the amplitude of these effects. For
the Microwave Anisotropy Probe (MAP), Rayleigh scattering increases the
anisotropy spectrum by 0.1% at the most. For the highest frequencies of the
Planck Surveyor, the effects of Rayleigh scattering are much more dramatic
(decreasing the anisotropy spectrum by 3% at \nu~550GHz and l~1000). The
relative difference between the spectra of low and high frequencies is imposed
by an oscillation with a function of multipole l and the oscillation amplitude
is up to 0.5% between 100 and 550GHz. Rayleigh scattering also slows the
decoupling between radiation and matter, but the effect is undetectably small. | 0103149v3 |
2001-03-19 | Fluctuations in the Cosmic Microwave Background II: $C_\ell$ at Large and Small $\ell$ | General asymptotic formulas are given for the coefficient $C_\ell$ of the
term of multipole number $\ell$ in the temperature correlation function of the
cosmic microwave background, in terms of scalar and dipole form factors
introduced in a companion paper. The formulas apply in two overlapping limits:
for $\ell\gg 1$ and for $\ell d/d_A\ll 1$ (where $d_A$ is the angular diameter
distance of the surface of last scattering, and $d$ is a length, of the order
of the acoustic horizon at the time of last scattering, that characterizes
acoustic oscillations before this time.) The frequently used approximation that
$C_\ell$ receives its main contribution from wave numbers of order $\ell/d_A$
is found to be less accurate for the contribution of the Doppler effect than
for the Sachs--Wolfe effect and intrinsic temperature fluctuations. For $\ell
d/d_A\ll 1$ and $\ell\geq 2$, the growth of $C_\ell$ with $\ell$ is shown to be
affected by acoustic oscillation wave numbers of all scales. The asymptotic
formulas are applied to a model of acoustic oscillations before the time of
last scattering, with results in reasonable agreement with more elaborate
computer calculations. | 0103281v2 |
2003-01-22 | Propagation model for cosmic ray species in the Galaxy | In a recent paper (Moskalenko et al., 2002), it has been shown that the flux
of secondary cosmic ray (CR) antiprotons appears to be contradictory to
measurements of secondary to primary nuclei ratios in cosmic rays when
calculated in the same Galactic propagation model. The contradiction appears as
a value of the diffusion coefficient necessary to match the secondary ratios
antiproton/proton and B/C. In particlular, it was shown that the reacceleration
models designed to match secondary to primary nuclei ratios produce too few
antiprotons. It is, however, clear that some reacceleration is unavoidable in
the turbulent interstellar medium. Here we discuss an idea of how to improve
reacceleration model by allowing for the damping of interstellar turbulences on
the small scale by cosmic rays, mostly protons. This would lead to increase in
the mean free path lenghts at low energies, the well-known phenomena
empirically discovered in the Leaky Box models, thus producing less secondary
nuclei. Antiprotons will remain almost non-affected due to their high energy
threshold of production cross section. | 0301420v1 |
2005-02-28 | On the existence of three-dimensional hydrostatic and magnetostatic equilibria of self-gravitating fluid bodies | (Abridged) We develop an analytical spectral method to solve the equations of
equilibrium for a self-gravitating, magnetized fluid body, under the only
hypotheses that (a) the equation of state is isothermal, (b) the configuration
is scale-free, and (c) the body is electrically neutral. All physical variables
are represented as series of scalar and vector spherical harmonics of degree l
and order m, and the equilibrium equations are reduced to a set of coupled
quadratic algebraic equations for the expansion coefficients of the density and
the magnetic vector potential. The method is general, and allows to recover
previously known hydrostatic and magnetostatic solutions possessing axial
symmetry. A linear perturbation analysis of the equations in spectral form show
that these basic axisymmetric states, considered as a continuos sequence with
the relative amount of magnetic support as control parameter, have in general
no neighboring nonaxisymmetric equilibria. This result lends credence to a
conjecture originally made by H. Grad and extends early results obtained by E.
Parker to the case of self-gravitating magnetized bodies. The only allowed
bifurcations of this sequence of axisymmetric equilibria are represented by
distortions with dipole-like angular dependence (l=1) that can be continued
into the nonlinear regime. These new configurations are either (i) azimuthally
asymmetric (m=+-1) or (ii) azimuthally symmetric but without reflection
symmetry with respect to the equatorial plane (m=0). To the extent that
interstellar clouds can be represented as isolated magnetostatic equilibria,
the results of this study suggest that the observed triaxial shapes of
molecular cloud cores can be interpreted in terms of weakly damped Alfven
oscillations about an equilibrium state. | 0502584v1 |
2006-06-14 | Electron Acceleration in Solar Flares: Theory of Spectral Evolution | Context: Stochastic acceleration is thought to be a key mechanism in the
energization of solar flare electrons.
Aims: We study whether stochastic acceleration can reproduce the observed
soft-hard-soft evolution of the spectral features of the hard X-ray emitted by
suprathermal electron. We pay special attention to the effects of particle
trapping and escape.
Methods: The Fokker-Planck equation for the electron distribution is
integrated numerically using the coefficients derived by Miller et al. for
transit-time damping acceleration. The electron spectra are then converted to
photon spectra for comparison with RHESSI observation of looptop sources.
Results: The presence of particle escape softens the model spectra computed
in the stochastic acceleration framework. The ratio between the efficiency of
trapping and acceleration controls the spectral evolution which follows a
soft-hard-soft pattern. Furthermore, a pivot point (that is, a common crossing
point of the accelerated particle spectra at different times) is found at
around 10 keV. It can be brought into agreement with the observed value of 20
keV by enhanced trapping through an electric potential.
Conclusions: The model proposed here accounts for the key features observed
in the spectral evolution of hard X-ray emission from looptop sources. | 0606339v2 |
1996-07-04 | Continuous Elastic Phase Transitions in Pure and Disordered Crystals | We review the theory of second--order (ferro--)elastic phase transitions,
where the order parameter consists of a certain linear combination of strain
tensor components, and the accompanying soft mode is an acoustic phonon. In
three--dimensional crystals, the softening can occur in one-- or
two--dimensional soft sectors. The ensuing anisotropy reduces the effect of
fluctuations, rendering the critical behaviour of these systems classical for a
one--dimensional soft sector, and classical with logarithmic corrections in
case of a two--dimensional soft sector. The dynamical critical exponent is $z =
2$, and as a consequence the sound velocity vanishes as $c_s \propto | T - T_c
|^{1/2}$, while the phonon damping coefficient is essentially
temperature--independent. Disorder may lead to a variety of precursor effects
and modified critical behaviour. Defects that locally soften the crystal may
induce the phenomenon of local order parameter condensation. When the
correlation length of the pure system exceeds the average defect separation
$n_{\rm D}^{-1/3}$, a disorder--induced phase transition to a state with
non--zero average order parameter can occur at a temperature $T_c(n_{\rm D})$
well above the transition temperature $T_c^0$ of the pure crystal. Near
$T_c^0$, the order--parameter curve, susceptibility, and specific heat appear
rounded. For $T < T_c(n_{\rm D})$ the spatial inhomogeneity induces a static
central peak with finite $q$ width in the scattering cross section, accompanied
by a dynamical component that is confined to the very vicinity of the
disorder--induced phase transition. | 9607028v2 |
2004-03-28 | Bilayer Membrane in Confined Geometry: Interlayer Slide and Steric Repulsion | We derived free energy functional of a bilayer lipid membrane from the first
principles of elasticity theory. The model explicitly includes
position-dependent mutual slide of monolayers and bending deformation. Our free
energy functional of liquid-crystalline membrane allows for incompressibility
of the membrane and vanishing of the in-plane shear modulus and obeys
reflectional and rotational symmetries of the flat bilayer. Interlayer slide at
the mid-plane of the membrane results in local difference of surface densities
of the monolayers. The slide amplitude directly enters free energy via the
strain tensor. For small bending deformations the ratio between bending modulus
and area compression coefficient, Kb/KA, is proportional to the square of
monolayer thickness, h. Using the functional we performed self-consistent
calculation of steric potential acting on bilayer between parallel confining
walls separated by distance 2d. We found that temperature-dependent curvature
at the minimum of confining potential is enhanced four times for a bilayer with
slide as compared with a unit bilayer. We also calculate viscous modes of
bilayer membrane between confining walls. Pure bending of the membrane is
investigated, which is decoupled from area dilation at small amplitudes. Three
sources of viscous dissipation are considered: water and membrane viscosities
and interlayer drag. Dispersion has two branches. Confinement between the walls
modifies the bending mode with respect to membrane in bulk solution.
Simultaneously, inter-layer slipping mode, damped by viscous drag, remains
unchanged by confinement. | 0403676v1 |
1995-06-26 | A Stochastic Approach to Thermal Fluctuations during a First Order Electroweak Phase Transition | We investigate the role played by subcritical bubbles at the onset of the
electroweak phase transition. Treating the configuration modelling the thermal
fluctuations around the homogeneous zero configuration of the Higgs field as a
stochastic variable, we describe its dynamics by a phenomenological Langevin
equation. This approach allows to properly take into account both the effects
of the thermal bath on the system: a systematic dyssipative force, which tends
to erase out any initial subcritical configuration, and a random stochastic
force responsible for the fluctuations. We show that the contribution to the
variance $\lgh\phi^2(t)\rg_V$ in a given volume $V$ from any initial
subcritical configuration is quickly damped away and that, in the limit of long
times, $\lgh\phi^2(t)\rg_V$ approaches its equilibrium value provided by the
stochastic force and independent from the viscosity coefficient, as predicted
by the fluctuation-dissipation theorem. In agreement with some recent claims,
we conclude that thermal fluctuations do not affect the nucleation of critical
bubbles at the onset of the electroweak phase transition making electroweak
baryogenesis scenarios still a viable possibility to explain the primordial
baryon asymmetry in the Universe. | 9506419v1 |
1995-10-26 | Classical and quantum many-body description of bremsstrahlung in dense matter (Landau - Pomeranchuk - Migdal effect) | Some considerations about the importance of coherence effects for
bremsstrahlung processes in non--equilibrium dense matter (Landau - Pomeranchuk
- Migdal - effect) are presented. They are of particular relevance for the
application to photon - and di-lepton production from high energy nuclear
collisions, to gluon radiation in QCD transport, or parton kinetics and to
neutrino and axion radiation from supernova explosion and from hot neutron
stars. The soft behavior of the bremsstrahlung from a source described by
classical transport models is discussed and pocket correction formulas for the
in-matter radiation cross sections are suggested in terms of standard transport
coefficients. The radiation rates are also discussed within a non--equilibrium
quantum field theory (Schwinger - Kadanoff - Baym - Keldysh) formulation. A
classification of diagrams and corresponding resummation in physically
meaningful terms is proposed, which considers the finite damping width of all
source particles in matter. This way each diagram in this expansion is already
free from the infra--red divergences. Both, the correct quasi--particle and
quasi--classical limits are recovered from this subset of graphs. Explicit
results are given for dense matter in thermal equilibrium. The diagrammatic
description may suggest a formulation of a transport theory that includes the
propagation of off--shell particles in non--equilibrium dense matter. | 9510417v1 |
1997-10-15 | Domain Walls Out of Equilibrium | We study the non-equilibrium dynamics of domain walls in real time for
$\phi^4$ and Sine Gordon models in 1+1 dimensions in the dilute regime. The
equation of motion for the collective coordinate is obtained by integrating out
the meson excitations around the domain wall to one-loop order. The real-time
non-equilibrium relaxation is studied analytically and numerically to this
order. The constant friction coefficient vanishes but there is dynamical
friction and relaxation caused by off-shell non-Markovian effects. The validity
of a Markovian description is studied in detail. The proper Langevin equation
is obtained to this order, the noise is Gaussian and additive but colored. We
analyze the classical and hard thermal loop contributions to the self-energy
and noise kernels and show that at temperatures larger than the meson mass the
hard contributions are negligible and the finite temperature contribution to
the dynamics is governed by the classical soft modes of the meson bath. The
long time relaxational dynamics is completely dominated by classical Landau
damping resulting in that the corresponding time scales are not set by the
temperature but by the meson mass. The noise correlation function and the
dissipative kernel obey a generalized form of the Fluctuation-Dissipation
relation. | 9710359v2 |
2005-01-06 | Non-statistical fluctuations for deep inelastic processes in 27Al + 27Al | The excitation functions for different fragments produced in the 27Al + 27Al
dissipative collisions have been measured in steps of 250 keV in the energy
range 122 - 132 MeV. Deep inelastic processes have been selected by integrating
events over a total kinetic energy loss window of 12 MeV between 20 and 32 MeV.
Large fluctuations have been observed in all the studied excitation functions.
Non-satistical origin of these fluctuations is confirmed by large channel cross
correlations coefficients. Energy autocorrelation function of cross section
excitation function presents damped oscillation structure as predicted for the
case when a di-nuclear system with a lifetime similar with its revolution
period is formed. The periodicity of the energy autocorrelation function is
used to obtain information on the deformation of the 27Al + 27 Al di-nucleus. | 0501003v1 |
2004-10-14 | Cold Strongly Coupled Atoms Make a Near-perfect Liquid | Feshbach resonances of trapped ultracold alkali atoms allow to vary the
atomic scattering length a. At very large values of a the system enters an
universal strongly coupled regime in which its properties--the ground state
energy, pressure {\it etc.}--become independent of a. We discuss transport
properties of such systems. In particular, the universality arguments imply
that the shear viscosity of ultracold Fermi atoms at the Feschbach resonance is
proportional to the particle number density n, and the Plank constant \hbar
\eta=\hbar n \alpha_\eta, where \alpha_\eta is a universal constant. Using
Heisenberg uncertainty principle and Einstein's relation between diffusion and
viscosity we argue that the viscosity has the lower bound given by
\alpha_{\eta} \leq (6\pi)^{-1}. We relate the damping of low-frequency density
oscillations of ultracold optically trapped ^{6}Li atoms to viscosity and find
that the value of the coefficient \alpha_\eta is about 0.3. We also show that
such a small viscosity can not be explained by kinetic theory based on binary
scattering. We conclude that the system of ultracold atoms near the Feshbach
resonance is a near-ideal liquid. | 0410067v2 |
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