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2016-07-06
|
Damping of Alfven waves by Turbulence and its Consequences: from Cosmic-Rays Streaming to Launching Winds
|
This paper considers turbulent damping of Alfven waves in magnetized plasmas.
We identify two cases of damping, one related to damping of cosmic rays
streaming instability, the other related to damping of Alfven waves emitted by
a macroscopic wave source, e.g. stellar atmosphere. The physical difference
between the two cases is that in the former case the generated waves are
emitted in respect to the local direction of magnetic field, in the latter in
respect to the mean field. The scaling of damping is different in the two
cases. We the regimes of turbulence ranging from subAlfvenic to superAlfvenic
we obtain analytical expressions for the damping rates and define the ranges of
applicability of these expressions. Describing the damping of the streaming
instability, we find that for subAlfvenic turbulence the range of cosmic ray
energies influenced by weak turbulence is unproportionally large compared to
the range of scales that the weak turbulence is present. On the contrary, the
range of cosmic ray energies affected by strong Alfvenic turbulence is rather
limited. A number of astrophysical applications of the process ranging from
launching of stellar and galactic winds to propagation of cosmic rays in
galaxies and clusters of galaxies is considered. In particular, we discuss how
to reconcile the process of turbulent damping with the observed isotropy of the
Milky Way cosmic rays.
|
1607.02042v1
|
2018-01-18
|
Quantum Landau damping in dipolar Bose-Einstein condensates
|
We consider Landau damping of elementary excitations in Bose-Einstein
condensates (BECs) with dipolar interactions. We discuss quantum and
quasi-classical regimes of Landau damping. We use a generalized wave-kinetic
description of BECs which, apart from the long range dipolar interactions, also
takes into account the quantum fluctuations and the finite energy corrections
to short-range interactions. Such a description is therefore more general than
the usual mean field approximation. The present wave-kinetic approach is well
suited for the study of kinetic effects in BECs, such as those associated with
Landau damping, atom trapping and turbulent diffusion. The inclusion of quantum
fluctuations and energy corrections change the dispersion relation and the
damping rates, leading to possible experimental signatures of these effects.
Quantum Landau damping is described with generality, and particular examples
of dipole condensates in two and three dimensions are studied. The occurrence
of roton-maxon configurations, and their relevance to Landau damping is also
considered in detail, as well as the changes introduced by the three different
processes, associated with dipolar interactions, quantum fluctuations and
finite energy range collisions. The present approach is mainly based on a
linear perturbative procedure, but the nonlinear regime of Landau damping,
which includes atom trapping and atom diffusion, is also briefly discussed.
|
1801.06256v1
|
2020-05-31
|
Optimal decay rates of the compressible Euler equations with time-dependent damping in $\mathbb R^n$: (I) under-damping case
|
This paper is concerned with the multi-dimensional compressible Euler
equations with time-dependent damping of the form
$-\frac{\mu}{(1+t)^\lambda}\rho\boldsymbol u$ in $\mathbb R^n$, where $n\ge2$,
$\mu>0$, and $\lambda\in[0,1)$. When $\lambda>0$ is bigger, the damping effect
time-asymptotically gets weaker, which is called under-damping. We show the
optimal decay estimates of the solutions such that $\|\partial_x^\alpha
(\rho-1)\|_{L^2(\mathbb R^n)}\approx
(1+t)^{-\frac{1+\lambda}{2}(\frac{n}{2}+|\alpha|)}$, and $\|\partial_x^\alpha
\boldsymbol u\|_{L^2(\mathbb R^n)}\approx
(1+t)^{-\frac{1+\lambda}{2}(\frac{n}{2}+|\alpha|)-\frac{1-\lambda}{2}}$, and
see how the under-damping effect influences the structure of the Euler system.
Different from the traditional view that the stronger damping usually makes the
solutions decaying faster, here surprisingly we recognize that the weaker
damping with $0\le\lambda<1$ enhances the faster decay for the solutions. The
adopted approach is the technical Fourier analysis and the Green function
method. The main difficulties caused by the time-dependent damping lie in
twofold: non-commutativity of the Fourier transform of the linearized operator
precludes explicit expression of the fundamental solution; time-dependent
evolution implies that the Green matrix $G(t,s)$ is not translation invariant,
i.e., $G(t,s)\ne G(t-s,0)$. We formulate the exact decay behavior of the Green
matrices $G(t,s)$ with respect to $t$ and $s$ for both linear wave equations
and linear hyperbolic system, and finally derive the optimal decay rates for
the nonlinear Euler system.
|
2006.00401v1
|
2022-08-17
|
Anti-parity-time symmetry hidden in a damping linear resonator
|
Phase transition from the over-damping to under-damping states is a
ubiquitous phenomenon in physical systems. However, what kind of symmetry is
broken associated with this phase transition remains unclear. Here, we discover
that this phase transition is determined by an anti-parity-time
(anti-$\mathcal{PT}$) symmetry hidden in a single damping linear resonator,
which is significantly different from the conventional
anti-$\mathcal{PT}$-symmetric systems with two or more modes. We show that the
breaking of the anti-$\mathcal{PT}$ symmetry yields the phase transition from
the over-damping to under-damping states, with an exceptional point (EP)
corresponding to the critical-damping state. Moreover, we propose an
optomechanical scheme to show this anti-$\mathcal{PT}$ symmetry breaking by
using the optical spring effect in a quadratic optomechanical system. We also
suggest an optomechanical sensor with the sensitivity enhanced significantly
around the EPs for the anti-$\mathcal{PT}$ symmetry breaking. Our work unveils
the anti-$\mathcal{PT}$ symmetry hidden in damping oscillations and hence opens
up new possibilities for exploiting wide anti-$\mathcal{PT}$ symmetry
applications in single damping linear resonators.
|
2208.08187v2
|
1996-12-10
|
Collisional matter-phase damping in Bose-condensed gas
|
Collisional damping of the excitations in a Bose-condensed gas is
investigated over the wide range of energies and temperatures. Numerical
results for the damping rate are presented and a number of asymptotic and
interpolating expressions for it are derived.
|
9612086v1
|
2001-11-29
|
Tensor form of magnetization damping
|
A tensor form of phenomenological damping is derived for small magnetization
motions. This form reflects basic physical relaxation processes for a general
uniformly magnetized particle or film. Scalar Landau-Lifshitz damping is found
to occur only for two special cases of system symmetry.
|
0111566v1
|
1999-07-28
|
An effective relaxation-time approach to collisionless quark-gluon plasma
|
We present an effective relaxation-time theory to study the collisionless
quark-gluon plasma. Applying this method we calculate the damping rate to be of
order $g^2T$ and find plasmon scattering is the damping mechanism. The damping
for the transverse mode is stronger than the longitudinal one.
|
9907526v1
|
1999-11-16
|
Dynamical resummation and damping in the O(N) model
|
A general real-time formalism is developed to resum the self-energy operator
of broken symmetry scalar field theories in form of self-consistent gap
equations for the spectral function. The solution of the equations is
approximated with finite lifetime quasi-particles. In the Landau damping rates
viscosity terms, analogous to gauge theories, appear, what leads to a finite
damping rate for the long wavelength Goldstone modes.
|
9911374v1
|
1993-03-24
|
On the Quantizations of the Damped Systems
|
Based on a simple observation that a classical second order differential
equation may be decomposed into a set of two first order equations, we
introduce a Hamiltonian framework to quantize the damped systems. In
particular, we analyze the system of a linear damped harmonic oscillator and
demonstrate that the time evolution of the Schr\"odinger equation is
unambiguously determined.
|
9303137v1
|
2006-01-09
|
Energy decay for damped wave equations on partially rectangular domains
|
We consider the wave equation with a damping term on a partially rectangular
planar domain, assuming that the damping is concentrated close to the
non-rectangular part of the domain. Polynomial decay estimates for the energy
of the solution are established.
|
0601195v1
|
2002-06-07
|
Resonant states and classical damping
|
Using Koopman's approach to classical dynamical systems we show that the
classical damping may be interpreted as appearance of resonant states of the
corresponding Koopman's operator. It turns out that simple classical damped
systems give rise to discrete complex spectra. Therefore, the corresponding
generalized eigenvectors may be interpreted as classical resonant states.
|
0206009v1
|
2004-03-12
|
Factorization of damped wave equations with cubic nonlinearities
|
The recent factorization scheme that we introduced for nonlinear polynomial
ODEs in math-ph/0401040 is applied to the interesting case of damped wave
equations with cubic nonlinearities. Traveling kink solutions are possible in
the plane defined by the kink velocity versus the damping coefficient only
along hyperbolas that are plotted herein
|
0403022v1
|
2002-08-07
|
Toward a Universal Model of Damping--Modified Coulomb Friction
|
A modification of Coulomb's law of friction uses a variable coefficient of
friction that depends on a power law in the energy of mechanical oscillation.
Through the use of three different exponents: 0, 1/2 and 1; all commonly
encountered non-viscous forms of damping are accommodated. The nonlinear model
appears to yield good agreement with experiment in cases of surface, internal,
and amplitude dependent damping.
|
0208025v1
|
2002-12-19
|
Trapped particle bounds on stimulated scatter in the large k/kD regime
|
In the strongly damped regime, the convective gain rate for stimulated
scatter varies inversely with the plasma wave damping rate. Electron trapping
effects reduce the damping but also lead to loss of resonance for large enough
amplitude waves. This leads to a gain rate bound and corresponding optimum
scattered light frequency and plasma wave amplitude.
|
0212071v1
|
2003-02-03
|
Oscillator damping with more than one mechanism of internal friction dissipation
|
The author's modified Coulomb damping model has been generalized to
accommodate internal friction that derives from several dissipation mechanisms
acting simultaneously. Because of its fundamental nonlinear nature, internal
friction damping causes the quality factor Q of an oscillator in free-decay to
change in time. Examples are given which demonstrate reasonable agreement
between theory and experiment.
|
0302003v1
|
2003-02-15
|
Anisotropic Internal Friction Damping
|
The mechanical damping properties of sheet polaroid material have been
studied with a physical pendulum. The polaroid samples were placed under the
knife-edges of the pendulum, which was operated in free-decay at a period in
the vicinity of 10 s. With the edges oriented parallel to the direction of the
long molecular chains in the polaroid, it was found that the damping was more
than 10% smaller than when oriented perpendicular to the chains.
|
0302055v1
|
2006-08-07
|
Study of the Damped Pendulum
|
Experiments on the oscillatory motion of a suspended bar magnet throws light
on the damping effects acting on the pendulum. The viscous drag offered by air
was found the be the main contributor for slowing the pendulum down. The nature
and magnitude of the damping effects were shown to be strongly dependent on the
amplitude.
|
0608071v1
|
1995-02-27
|
Quantum Oscillator with Kronig-Penney Excitation in Different Regimes of Damping
|
There are discussed the exact solution of the time--dependent Schr\"{o}dinger
equation for a damped quantum oscillator subject to a periodical frequency
delta--kicks describing squeezed states which are expressed in terms of
Chebyshev polynomials. The cases of strong and weak damping are investigated in
the frame of Caldirola--Kanai model.
|
9502023v1
|
2007-03-12
|
Quantum estimation of a damping constant
|
We discuss an interferometric approach to the estimation of quantum
mechanical damping. We study specific classes of entangled and separable probe
states consisting of superpositions of coherent states. Based on the assumption
of limited quantum resources we show that entanglement improves the estimation
of an unknown damping constant.
|
0703091v2
|
2008-11-07
|
Asymptotic stability of the wave equation on compact surfaces and locally distributed damping - A sharp result
|
This paper is concerned with the study of the wave equation on compact
surfaces and locally distributed damping. We study the case where the damping
is effective in a well-chosen subset of arbitrarily small measure.
|
0811.1190v1
|
2008-11-07
|
Uniform Stabilization of the wave equation on compact surfaces and locally distributed damping
|
This paper is concerned with the study of the wave equation on compact
surfaces and locally distributed damping. We study the case where the damping
is effective on the complement of visible umbilical sets.
|
0811.1204v1
|
2010-11-20
|
Enhanced damping of ion acoustic waves in dense plasmas
|
A theory for the ion acoustic wave damping in dense plasmas and warm dense
matter, accounting for the Umklapp process, is presented. A higher decay rate
compared to the prediction from the Landau damping theory is predicted for
high-Z dense plasmas where the electron density ranges from $10^{21}$ to $
10^{24} \mathrm{cm^{-3}}$ and the electron temperature is moderately higher
than the Fermi energy.
|
1011.4607v1
|
2012-05-16
|
Enhanced coupling design of a detuned damped structure for clic
|
The key feature of the improved coupling design in the Damped Detuned
Structure (DDS) is focused on the four manifolds. Rectangular geometry slots
and rectangular manifolds are used. This results in a significantly stronger
coupling to the manifolds compared to the previous design. We describe the new
design together with its wakefield damping properties.
|
1205.3590v1
|
2012-06-26
|
On the $L^{2}$-critical nonlinear Schrödinger Equation with a nonlinear damping
|
We consider the Cauchy problem for the $L^{2}$-critical nonlinear
Schr\"{o}dinger equation with a nonlinear damping. According to the power of
the damping term, we prove the global existence or the existence of finite time
blowup dynamics with the log-log blow-up speed for $\|\nabla u(t)\|_{L^2}$.
|
1206.6082v4
|
2012-10-12
|
Semi-linear wave equations with effective damping
|
We study the Cauchy problem for the semi-linear damped wave equation in any
space dimension. We assume that the time-dependent damping term is effective.
We prove the global existence of small energy data solutions in the
supercritical case.
|
1210.3493v1
|
2012-12-08
|
A note on the lifespan of solutions to the semilinear damped wave equation
|
This paper concerns estimates of the lifespan of solutions to the semilinear
damped wave equation. We give upper estimates of the lifespan for the
semilinear damped wave equation with variable coefficients in all space
dimensions.
|
1212.1772v3
|
2012-12-10
|
Strongly damped wave equation with exponential nonlinearities
|
In this paper, we study the initial boundary value problem for the two
dimensional strong damped wave equation with exponentially growing source and
damping terms. We first show the well-posedness of this problem and then prove
the existence of the global attractor in $(H_{0}^{1}(\Omega)\cap
L^{\infty}(\Omega))\times L^{2}(\Omega)$.
|
1212.2180v2
|
2013-10-27
|
Exponential decay of solutions for the plate equation with localized damping
|
In this paper, we give positive answer to the open question raised in [E.
Zuazua, Exponential decay for the semilinear wave equation with localized
damping in unbounded domains. J. Math. Pures Appl., 70 (1991) 513--529] on the
exponential decay of solutions for the semilinear plate equation with localized
damping.
|
1310.7243v3
|
2014-03-07
|
Landau damping in Sobolev spaces for the Vlasov-HMF model
|
We consider the Vlasov-HMF (Hamiltonian Mean-Field) model. We consider
solutions starting in a small Sobolev neighborhood of a spatially homogeneous
state satisfying a linearized stability criterion (Penrose criterion). We prove
that these solutions exhibit a scattering behavior to a modified state, which
implies a nonlinear Landau damping effect with polynomial rate of damping.
|
1403.1668v2
|
2015-03-30
|
Damping to prevent the blow-up of the Korteweg-de Vries equation
|
We study the behavior of the solution of a generalized damped KdV equation
$u_t + u_x + u_{xxx} + u^p u_x + \mathscr{L}_{\gamma}(u)= 0$. We first state
results on the local well-posedness. Then when $p \geq 4$, conditions on
$\mathscr{L}_{\gamma}$ are given to prevent the blow-up of the solution.
Finally, we numerically build such sequences of damping.
|
1503.08559v1
|
2015-06-16
|
Fast energy decay for wave equations with variable damping coefficients in the 1-D half line
|
We derive fast decay estimates of the total energy for wave equations with
localized variable damping coefficients, which are dealt with in the one
dimensional half line $(0,\infty)$. The variable damping coefficient vanishes
near the boundary $x = 0$, and is effective critically near spatial infinity $x
= \infty$.
|
1506.04851v1
|
2015-11-25
|
A Proposal of a Damping Term for the Relativistic Euler Equations
|
We introduce a damping term for the special relativistic Euler equations in
$3$-D and show that the equations reduce to the non-relativistic damped Euler
equations in the Newtonian limit. We then write the equations as a symmetric
hyperbolic system for which local-in-time existence of smooth solutions can be
shown.
|
1511.08183v1
|
2016-01-27
|
Concatenated Codes for Amplitude Damping
|
We discuss a method to construct quantum codes correcting amplitude damping
errors via code concatenation. The inner codes are chosen as asymmetric
Calderbank-Shor-Steane (CSS) codes. By concatenating with outer codes
correcting symmetric errors, many new codes with good parameters are found,
which are better than the amplitude damping codes obtained by any previously
known construction.
|
1601.07423v1
|
2016-03-29
|
Generalized damped Milne-Pinney equation and Chiellini method
|
We adopt the Chiellini integrability method to find the solutions of various
generalizations of the damped Milne-Pinney equations. In particular, we find
the solution of the damped Ermakov-Painlev\'e II equation and generalized
dissipative Milne-Pinney equation.
|
1603.08747v2
|
2017-12-07
|
Damped wave equations on compact hyperbolic surfaces
|
We prove exponential decay of energy for solutions of the damped wave
equation on compact hyperbolic surfaces with regular initial data as long as
the damping is nontrivial. The proof is based on a similar strategy as in
Dyatlov-Jin and in particular, uses the fractal uncertainty principle proved in
Bourgain-Dyatlov.
|
1712.02692v1
|
2018-03-20
|
Stability of the wave equations on a tree with local Kelvin-Voigt damping
|
In this paper we study the stability problem of a tree of elastic strings
with local Kelvin-Voigt damping on some of the edges. Under the compatibility
condition of displacement and strain and continuity condition of damping
coefficients at the vertices of the tree, exponential/polynomial stability are
proved.
|
1803.07280v1
|
2018-09-10
|
Logarithmic Decay of a Wave Equation with Kelvin-Voigt Damping
|
In this paper we analyze the long time behavior of a wave equation with local
Kelvin-Voigt Damping. Through introducing proper class symbol and
pseudo-differential calculus, we obtain a Carleman estimate, and then establish
an estimate on the corresponding resolvent operator. As a result, we show the
logarithmic decay rate for energy of the system without any geometric
assumption on the subdomain on which the damping is effective.
|
1809.03196v1
|
2018-11-07
|
Slow-dissipation limit of the harmonic oscillator with general power-law damping
|
An approximate solution is presented for simple harmonic motion in the
presence of damping by a force which is a general power-law function of the
velocity. The approximation is shown to be quite robust, allowing for a simple
way to investigate amplitude decay in the presence of general types of weak,
nonlinear damping.
|
1811.02953v2
|
2019-09-25
|
Forced Coupled Duffing Oscillators with Nonlinear Damping: Resonance and Antiresonance
|
In this work, we investigate resonance and antiresonance behaviour in forced
coupled Duffing oscillators with nonlinear damping. Further, we will analyse
the parameter dependence of the frequency response and stability. In the course
of all the analysis, emphasis shall be on how different damping mechanisms
contrast against each other.
|
1909.11390v1
|
2020-04-21
|
Damping rate limitations for transverse dampers in large hadron colliders
|
The paper focuses on two issues important for design and operation of
bunch-by-bunch transverse damper in a very large hadron collider, where fast
damping is required to suppress beam instabilities and noise induced emittance
growth. The first issue is associated with kick variation along a bunch which
affects the damping of head-tail modes. The second issue is associated with
affect of damper noise on the instability threshold.
|
2004.10249v2
|
2021-02-01
|
Global existence for semilinear wave equations with scaling invariant damping in 3-D
|
Global existence for small data Cauchy problem of semilinear wave equations
with scaling invariant damping in 3-D is established in this work, assuming
that the data are radial and the constant in front of the damping belongs to
$[1.5, 2)$. The proof is based on a weighted $L^2-L^2$ estimate for
inhomogeneous wave equation, which is established by interpolating between
energy estimate and Morawetz type estimate.
|
2102.00909v1
|
2021-08-17
|
Spectral enclosures for the damped elastic wave equation
|
In this paper we investigate spectral properties of the damped elastic wave
equation. Deducing a correspondence between the eigenvalue problem of this
model and the one of Lam\'e operators with non self-adjoint perturbations, we
provide quantitative bounds on the location of the point spectrum in terms of
suitable norms of the damping coefficient.
|
2108.07676v1
|
2022-02-10
|
Stochastic optimal control for nonlinear damped network dynamics
|
We present a stochastic optimal control problem for a tree network. The
dynamics of the network are governed by transport equations with a special
emphasis on the non-linear damping function. Demand profiles at the network
sinks are modelled by a stochastic differential equations. An explicit optimal
inflow into the network is determined and numerical simulations are presented
to show the effects for different choices of the non-linear damping.
|
2202.05114v1
|
2022-03-03
|
Conformal symmetry in damped Pais-Uhlenbeck oscillator
|
Two Lagrangian formulations for describing of the damped harmonic oscillator
have been introduced by Bateman. For these models we construct higher
derivative generalization which enjoys the l-conformal Newton-Hooke symmetry.
The dynamics of generalized systems corresponds to the damped Pais-Uhlenbeck
oscillator for a particular choice of its frequencies.
|
2203.01651v1
|
2022-05-26
|
Ergodic results for the stochastic nonlinear Schrödinger equation with large damping
|
We study the nonlinear Schr\"odinger equation with linear damping, i.e. a
zero order dissipation, and additive noise. Working in $R^d$ with d = 2 or d =
3, we prove the uniqueness of the invariant measure when the damping
coefficient is sufficiently large.
|
2205.13364v1
|
2022-10-31
|
An adaptive damped Newton method for strongly monotone and Lipschitz continuous operator equations
|
We will consider the damped Newton method for strongly monotone and Lipschitz
continuous operator equations in a variational setting. We will provide a very
accessible justification why the undamped Newton method performs better than
its damped counterparts in a vicinity of a solution. Moreover, in the given
setting, an adaptive step-size strategy will be presented, which guarantees the
global convergence and favours an undamped update if admissible.
|
2210.17107v1
|
2022-11-19
|
Blow up and lifespan estimates for systems of semi-linear wave equations with damping and potential
|
In this paper, we consider the semi-linear wave systems with
power-nonlinearities and a large class of space-dependent damping and
potential. We obtain the same blow-up regions and the lifespan estimates for
three types wave systems, compared with the systems without damping and
potential.
|
2211.10639v1
|
2023-08-10
|
Pathwise uniqueness for stochastic heat and damped equations with Hölder continuous drift
|
In this paper, we prove pathwise uniqueness for stochastic differential
equations in infinite dimension. Under our assumptions, we are able to consider
the stochastic heat equation up to dimension $3$, the stochastic damped wave
equation in dimension $1$ and the stochastic Euler-Bernoulli damped beam
equation up to dimension $3$. We do not require that the so-called {\it
structure condition} holds true.
|
2308.05415v1
|
2023-10-30
|
Beliaev damping in Bose gas
|
According to the Bogoliubov theory the low energy behaviour of the Bose gas
at zero temperature can be described by non-interacting bosonic quasiparticles
called phonons. In this work the damping rate of phonons at low momenta, the
so-called Beliaev damping, is explained and computed with simple arguments
involving the Fermi Golden Rule and Bogoliubov's quasiparticles.
|
2310.20070v1
|
2023-11-25
|
Energy scattering for the unsteady damped nonlinear Schrodinger equation
|
We investigate the large time behavior of the solutions to the nonlinear
focusing Schr\"odinger equation with a time-dependent damping in the energy
sub-critical regime. Under non classical assumptions on the unsteady damping
term, we prove some scattering results in the energy space.
|
2311.14980v2
|
2017-10-18
|
Direct detection of metal-insulator phase transitions using the modified Backus-Gilbert method
|
The detection of the (semi)metal-insulator phase transition can be extremely
difficult if the local order parameter which characterizes the ordered phase is
unknown.In some cases, it is even impossible to define a local order parameter:
the most prominent example of such system is the spin liquid state. This state
was proposed to exist in theHubbard model on the hexagonal lattice in a region
between the semimetal phase and the antiferromagnetic insulator phase. The
existence of this phase has been the subject of a long debate. In order to
detect these exotic phases we must use alternative methods to those used for
more familiar examples of spontaneous symmetry breaking. We have modified the
Backus-Gilbert method of analytic continuation which was previously used in the
calculation of the pion quasiparticle mass in lattice QCD. The modification of
the method consists of the introduction of the Tikhonov regularization scheme
which was used to treat the ill-conditioned kernel. This modified
Backus-Gilbert method is applied to the Euclidean propagators in momentum space
calculated using the hybridMonte Carlo algorithm. In this way, it is possible
to reconstruct the full dispersion relation and to estimate the mass gap, which
is a direct signal of the transition to the insulating state. We demonstrate
the utility of this method in our calculations for the Hubbard model on the
hexagonal lattice. We also apply the method to the metal-insulator phase
transition in the Hubbard-Coulomb model on the square lattice.
|
1710.06675v1
|
2019-01-29
|
Bounding the spectral gap for an elliptic eigenvalue problem with uniformly bounded stochastic coefficients
|
A key quantity that occurs in the error analysis of several numerical methods
for eigenvalue problems is the distance between the eigenvalue of interest and
the next nearest eigenvalue. When we are interested in the smallest or
fundamental eigenvalue, we call this the spectral or fundamental gap. In a
recent manuscript [Gilbert et al., arXiv:1808.02639], the current authors,
together with Frances Kuo, studied an elliptic eigenvalue problem with
homogeneous Dirichlet boundary conditions, and with coefficients that depend on
an infinite number of uniformly distributed stochastic parameters. In this
setting, the eigenvalues, and in turn the eigenvalue gap, also depend on the
stochastic parameters. Hence, for a robust error analysis one needs to be able
to bound the gap over all possible realisations of the parameters, and because
the gap depends on infinitely-many random parameters, this is not trivial. This
short note presents, in a simplified setting, an important result that was
shown in the paper above. Namely, that, under certain decay assumptions on the
coefficient, the spectral gap of such a random elliptic eigenvalue problem can
be bounded away from 0, uniformly over the entire infinite-dimensional
parameter space.
|
1901.10470v1
|
2020-09-14
|
Bounds and Code Constructions for Partially Defect Memory Cells
|
This paper considers coding for so-called partially stuck memory cells. Such
memory cells can only store partial information as some of their levels cannot
be used due to, e.g., wear out. First, we present a new code construction for
masking such partially stuck cells while additionally correcting errors. This
construction (for cells with $q >2$ levels) is achieved by generalizing an
existing masking-only construction in [1] (based on binary codes) to correct
errors as well. Compared to previous constructions in [2], our new construction
achieves larger rates for many sets of parameters. Second, we derive a
sphere-packing (any number of $u$ partially stuck cells) and a
Gilbert-Varshamov bound ($u<q$ partially stuck cells) for codes that can mask a
certain number of partially stuck cells and correct errors additionally. A
numerical comparison between the new bounds and our previous construction of
PSMCs for the case $u<q$ in [2] shows that our construction lies above the
Gilbert-Varshamov-like bound for several code parameters.
|
2009.06512v3
|
2020-10-02
|
Multilevel quasi-Monte Carlo for random elliptic eigenvalue problems I: Regularity and error analysis
|
Stochastic PDE eigenvalue problems are useful models for quantifying the
uncertainty in several applications from the physical sciences and engineering,
e.g., structural vibration analysis, the criticality of a nuclear reactor or
photonic crystal structures. In this paper we present a multilevel quasi-Monte
Carlo (MLQMC) method for approximating the expectation of the minimal
eigenvalue of an elliptic eigenvalue problem with coefficients that are given
as a series expansion of countably-many stochastic parameters. The MLQMC
algorithm is based on a hierarchy of discretisations of the spatial domain and
truncations of the dimension of the stochastic parameter domain. To approximate
the expectations, randomly shifted lattice rules are employed. This paper is
primarily dedicated to giving a rigorous analysis of the error of this
algorithm. A key step in the error analysis requires bounds on the mixed
derivatives of the eigenfunction with respect to both the stochastic and
spatial variables simultaneously. Under stronger smoothness assumptions on the
parametric dependence, our analysis also extends to multilevel higher-order
quasi-Monte Carlo rules. An accompanying paper [Gilbert and Scheichl, 2022],
focusses on practical extensions of the MLQMC algorithm to improve efficiency,
and presents numerical results.
|
2010.01044v4
|
2021-03-05
|
Multilevel quasi-Monte Carlo for random elliptic eigenvalue problems II: Efficient algorithms and numerical results
|
Stochastic PDE eigenvalue problems often arise in the field of uncertainty
quantification, whereby one seeks to quantify the uncertainty in an eigenvalue,
or its eigenfunction. In this paper we present an efficient multilevel
quasi-Monte Carlo (MLQMC) algorithm for computing the expectation of the
smallest eigenvalue of an elliptic eigenvalue problem with stochastic
coefficients. Each sample evaluation requires the solution of a PDE eigenvalue
problem, and so tackling this problem in practice is notoriously
computationally difficult. We speed up the approximation of this expectation in
four ways: we use a multilevel variance reduction scheme to spread the work
over a hierarchy of FE meshes and truncation dimensions; we use QMC methods to
efficiently compute the expectations on each level; we exploit the smoothness
in parameter space and reuse the eigenvector from a nearby QMC point to reduce
the number of iterations of the eigensolver; and we utilise a two-grid
discretisation scheme to obtain the eigenvalue on the fine mesh with a single
linear solve. The full error analysis of a basic MLQMC algorithm is given in
the companion paper [Gilbert and Scheichl, 2022], and so in this paper we focus
on how to further improve the efficiency and provide theoretical justification
for using nearby QMC points and two-grid methods. Numerical results are
presented that show the efficiency of our algorithm, and also show that the
four strategies we employ are complementary.
|
2103.03407v3
|
2002-02-21
|
Mechanisms of spin-polarized current-driven magnetization switching
|
The mechanisms of the magnetization switching of magnetic multilayers driven
by a current are studied by including exchange interaction between local
moments and spin accumulation of conduction electrons. It is found that this
exchange interaction leads to two additional terms in the
Landau-Lifshitz-Gilbert equation: an effective field and a spin torque. Both
terms are proportional to the transverse spin accumulation and have comparable
magnitudes.
|
0202363v1
|
2005-10-30
|
Domain instability during precessional magnetization reversal
|
Spin wave equations in the non-equilibrium precessing state of a
ferromagnetic system are found. They show a spin-wave instability towards
growing domains of stable magnetization. Precession of the uniform
magnetization mode is described by the Landau Lifshitz equation with the
exponentially growing in time effective Gilbert dissipation constant that could
have both signs. On the developed stages of the domain instability a
non-stationary picture of domain chaos is observed.
|
0510817v1
|
1991-12-02
|
Perturbations of a Stringy Black Hole
|
We extend the three dimensional stringy black hole of Horne and Horowitz to
four dimensions. After a brief discussion of the global properties of the
metric, we discuss the stability of the background with respect to small
perturbations, following the methods of Gilbert and of Chandrasekhar. The
potential for axial perturbations is found to be positive definite.
|
9112001v2
|
1996-05-06
|
Finitely presented subgroups of automatic groups and their isoperimetric functions
|
We describe a general technique for embedding certain amalgamated products
into direct products. This technique provides us with a way of constructing a
host of finitely presented subgroups of automatic groups which are not even
asynchronously automatic. We can also arrange that such subgroups satisfy, at
best, an exponential isoperimetric inequality.
|
9605201v1
|
1999-07-22
|
Constructing Hyperbolic Manifolds
|
In this paper we show how to obtain representations of Coxeter groups acting
on H^n to certain classical groups. We determine when the kernel of such a
representation is torsion-free and thus the quotient a hyperbolic n-manifold.
|
9907139v1
|
2002-02-06
|
Quaternionic equation for electromagnetic fields in inhomogeneous media
|
We show that the Maxwell equations for arbitrary inhomogeneous media are
equivalent to a single quaternionic equation which can be considered as a
generalization of the Vekua equation for generalized analytic functions.
|
0202010v1
|
1996-02-29
|
Error Correction in Quantum Communication
|
We show how procedures which can correct phase and amplitude errors can be
directly applied to correct errors due to quantum entanglement. We specify
general criteria for quantum error correction, introduce quantum versions of
the Hamming and the Gilbert-Varshamov bounds and comment on the practical
implementation of quantum codes.
|
9602022v1
|
2007-05-19
|
Log-periodic drift oscillations in self-similar billiards
|
We study a particle moving at unit speed in a self-similar Lorentz billiard
channel; the latter consists of an infinite sequence of cells which are
identical in shape but growing exponentially in size, from left to right. We
present numerical computation of the drift term in this system and establish
the logarithmic periodicity of the corrections to the average drift.
|
0705.2790v1
|
2008-04-26
|
Asymptotic Bound on Binary Self-Orthogonal Codes
|
We present two constructions for binary self-orthogonal codes. It turns out
that our constructions yield a constructive bound on binary self-orthogonal
codes. In particular, when the information rate R=1/2, by our constructive
lower bound, the relative minimum distance \delta\approx 0.0595 (for GV bound,
\delta\approx 0.110). Moreover, we have proved that the binary self-orthogonal
codes asymptotically achieve the Gilbert-Varshamov bound.
|
0804.4194v1
|
2008-11-14
|
Scott and Swarup's regular neighbourhood as a tree of cylinders
|
Let G be a finitely presented group. Scott and Swarup have constructed a
canonical splitting of G which encloses all almost invariant sets over
virtually polycyclic subgroups of a given length. We give an alternative
construction of this regular neighbourhood, by showing that it is the tree of
cylinders of a JSJ splitting.
|
0811.2389v1
|
2009-05-04
|
Self-organized quantum transitions in a spin-electron coupled system
|
We investigate quantum dynamics of the excited electronic states in the
double-exchange model at half-filling by solving coupled equations for the
quantum evolution of electrons and Landau-Lifshits-Gilbert equation for
classical spins. The non-adiabatic quantum transitions driving the relaxation
are coordinated through the self-organized space-time structure of the
electron/spin dynamics leading to a resonant precession analogous to the ESR
process.
|
0905.0311v1
|
2009-05-04
|
Oscillating Ponomarenko dynamo in the highly conducting limit
|
This paper considers dynamo action in smooth helical flows in cylindrical
geometry, otherwise known as Ponomarenko dynamos, with periodic time
dependence. An asymptotic framework is developed that gives growth rates and
frequencies in the highly conducting limit of large magnetic Reynolds number,
when modes tend to be localized on resonant stream surfaces. This theory is
validated by means of numerical simulations.
|
0905.0415v1
|
2009-07-15
|
Barnett Effect in Thin Magnetic Films and Nanostructures
|
The Barnett effect refers to the magnetization induced by rotation of a
demagnetized ferromagnet. We describe the location and stability of stationary
states in rotating nanostructures using the Landau-Lifshitz-Gilbert equation.
The conditions for an experimental observation of the Barnett effect in
different materials and sample geometries are discussed.
|
0907.2648v1
|
2009-12-24
|
Scenarios of Gravitino Dark Matter and their Cosmological and Particle Physics Implications
|
I report on some scenarios where the gravitino is the dark matter and the
supersymmetry breaking mediated by a gauge sector.
|
0912.4885v1
|
2010-07-20
|
Factoring Permutation Matrices Into a Product of Tridiagonal Matrices
|
Gilbert Strang posited that a permutation matrix of bandwidth $w$ can be
written as a product of $N < 2w$ permutation matrices of bandwidth 1. A proof
employing a greedy ``parallel bubblesort'' algorithm on the rows of the
permutation matrix is detailed and further points of interest are elaborated.
|
1007.3467v1
|
2011-05-26
|
Qu'est-ce qu'une espèce de structures? Genèse et description
|
This is an overview (in french) of the Theory of Species for a general
audience. Basic notions are introduced in a non too technical manner, with an
explanation of why should one approach the notion of discrete structures in
this particular way.
|
1105.5406v1
|
2011-12-16
|
Reply to the comment of T.Gilbert and D.P.Sanders on "Capturing correlations in chaotic diffusion by approximation methods"
|
This is a reply to the comment by Gilbert and Sanders [arXiv:1111.6271
(2011)]. We point out that their comment is a follow-up of a previous
discussion which we briefly summarize before we refute their new criticism.
|
1112.3927v1
|
2012-03-24
|
A new look at finitely generated metabelian groups
|
A group is metabelian if its commutator subgroup is abelian. For finitely
generated metabelian groups, classical commutative algebra, algebraic geometry
and geometric group theory, especially the latter two subjects, can be brought
to bear on their study. The object of this paper is to describe some of the new
ideas and open problems that arise.
|
1203.5431v1
|
2012-06-05
|
A convergent and precise finite element scheme for Landau-Lifschitz-Gilbert equation
|
In this paper, we rigorously study an order 2 scheme that was previously
proposed by some of the authors. A slight modification is proposed that enables
us to prove the convergence of the scheme while simplifying in the same time
the inner iteration.
|
1206.0997v1
|
2013-01-20
|
Residual properties of groups defined by basic commutators
|
In this paper we study the residual nilpotence of groups defined by basic
commutators. We prove that the so-called Hydra groups as well as certain of
their generalizations and quotients are, in the main, residually torsion-free
nilpotent. By way of contrast we give an example of a group defined by two
basic commutators which is not residually torsion-free nilpotent.
|
1301.4629v2
|
2013-03-21
|
Anisimov's Theorem for inverse semigroups
|
The idempotent problem of a finitely generated inverse semigroup is the
formal language of all words over the generators representing idempotent
elements. This note proves that a finitely generated inverse semigroup with
regular idempotent problem is necessarily finite. This answers a question of
Gilbert and Noonan Heale, and establishes a generalisation to inverse
semigroups of Anisimov's Theorem for groups.
|
1303.5239v1
|
2013-10-13
|
Underwater Gas Expansion and Deflagration
|
The underwater combustion of a propane-air mixture in an acrylic cylinder is
captured on video from multiple angles. This experiment is designed to provide
visual data and pressure time-histories for future CFD validation studies.
|
1310.3523v1
|
2013-11-14
|
The dimension of the leafwise reduced cohomology
|
Geometric conditions are given so that the leafwise reduced cohomology is of
infinite dimension, specially for foliations with dense leaves on closed
manifolds. The main new definition involved is the intersection number of
subfoliations with "appropriate coefficients". The leafwise reduced cohomology
is also described for homogeneous foliations with dense leaves on closed
nilmanifolds.
|
1311.3518v1
|
2014-03-12
|
A semi-discrete scheme for the stochastic Landau-Lifshitz equation
|
We propose a new convergent time semi-discrete scheme for the stochastic
Landau-Lifshitz-Gilbert equation. The scheme is only linearly implicit and does
not require the resolution of a nonlinear problem at each time step. Using a
martingale approach, we prove the convergence in law of the scheme up to a
subsequence.
|
1403.3016v1
|
2014-03-17
|
Quantum codes from affine variety codes and their subfield-subcodes
|
We use affine variety codes and their subfield-subcodes for obtaining quantum
stabilizer codes via the CSS code construction. With this procedure, we get
codes with good parameters and a code whose parameters exceed the CSS quantum
Gilbert-Varshamov bound given by Feng and Ma.
|
1403.4060v2
|
2015-10-19
|
Decomposability of Finitely Generated Torsion-free Nilpotent Groups
|
We describe an algorithm for deciding whether or not a given finitely
generated torsion-free nilpotent group is decomposable as the direct product of
nontrivial subgroups.
|
1510.05632v2
|
2016-02-27
|
On automatic subsets of the Gaussian integers
|
Suppose that $a$ and $b$ are multiplicatively independent Gaussian integers,
that are both of modulus~$\geq \sqrt 5$. We prove that there exist a $X\subset
\mathbb Z[i]$ which is $a$-automatic but not $b$-automatic. This settles a
problem of Allouche, Cateland, Gilbert, Peitgen, Shallit, and Skordev.
|
1602.08579v3
|
2016-03-02
|
On self-dual double circulant codes
|
Self-dual double circulant codes of odd dimension are shown to be dihedral in
even characteristic and consta-dihedral in odd characteristic. Exact counting
formulae are derived for them and used to show they contain families of codes
with relative distance satisfying a modified Gilbert-Varshamov bound.
|
1603.00762v1
|
2016-09-22
|
Manipulation of magnetic Skyrmions with a Scanning Tunneling Microscope
|
The dynamics of a single magnetic Skyrmion in an atomic spin system under the
influence of Scanning Tunneling Microscope is investigated by computer
simulations solving the Landau-Lifshitz-Gilbert equation. Two possible
scenarios are described: manipulation with aid of a spin-polarized tunneling
current and by an electric field created by the scanning tunneling microscope.
The dynamics during the creation and annihilation process is studied and the
possibility to move single Skyrmions is showed.
|
1609.06797v1
|
2016-11-03
|
Quantile Reinforcement Learning
|
In reinforcement learning, the standard criterion to evaluate policies in a
state is the expectation of (discounted) sum of rewards. However, this
criterion may not always be suitable, we consider an alternative criterion
based on the notion of quantiles. In the case of episodic reinforcement
learning problems, we propose an algorithm based on stochastic approximation
with two timescales. We evaluate our proposition on a simple model of the TV
show, Who wants to be a millionaire.
|
1611.00862v1
|
2017-01-30
|
Elementary equivalence vs commensurability for hyperbolic groups
|
We study to what extent torsion-free (Gromov)-hyperbolic groups are
elementarily equivalent to their finite index subgroups. In particular, we
prove that a hyperbolic limit group either is a free product of cyclic groups
and surface groups, or admits infinitely many subgroups of finite index which
are pairwise non elementarily equivalent.
|
1701.08853v1
|
2017-08-01
|
Imaging from the Inside Out: Inverse Scattering with Photoactivated Internal Sources
|
We propose a method to reconstruct the optical properties of a scattering
medium with subwavelength resolution. The method is based on the solution to
the inverse scattering problem with photoactivated internal sources. Numerical
simulations of three-dimensional structures demonstrate that a resolution of
approximately $\lambda/25$ is achievable.
|
1708.00128v1
|
2017-09-22
|
On self-dual four circulant codes
|
Four circulant codes form a special class of $2$-generator, index $4$,
quasi-cyclic codes. Under some conditions on their generator matrices they can
be shown to be self-dual. Artin primitive root conjecture shows the existence
of an infinite subclass of these codes satisfying a modified Gilbert-Varshamov
bound.
|
1709.07548v1
|
2018-02-21
|
Enhanced global signal of neutral hydrogen due to excess radiation at cosmic dawn
|
We revisit the global 21cm signal calculation incorporating a possible radio
background at early times, and find that the global 21cm signal shows a much
stronger absorption feature, which could enhance detection prospects for future
21 cm experiments. In light of recent reports of a possible low-frequency
excess radio background, we propose that detailed 21 cm calculations should
include a possible early radio background.
|
1802.07432v1
|
2019-03-22
|
Nonlinear Iterative Hard Thresholding for Inverse Scattering
|
We consider the inverse scattering problem for sparse scatterers. An image
reconstruction algorithm is proposed that is based on a nonlinear
generalization of iterative hard thresholding. The convergence and error of the
method was analyzed by means of coherence estimates and compared to numerical
simulations.
|
1903.10875v1
|
2019-04-06
|
Phenomenological description of the dynamics of bipartite antiferromagnets in the limit of strong exchange
|
The equation of motion of the staggered order parameter is derived in a
step-by-step manner from the coupled Landau-Lifshitz-Gilbert dynamics of
bipartite spin moments in the limit of strong antiferromagnetic exchange
coupling.
|
1904.03529v4
|
2019-04-19
|
Variational approximation of functionals defined on $1$-dimensional connected sets in $\mathbb{R}^n$
|
In this paper we consider the Euclidean Steiner tree problem and, more
generally, (single sink) Gilbert--Steiner problems as prototypical examples of
variational problems involving 1-dimensional connected sets in $\mathbb{R}^n$.
Following the the analysis for the planar case presented in [4], we provide a
variational approximation through Ginzburg--Landau type energies proving a
$\Gamma$-convergence result for $n \geq 3$.
|
1904.09328v1
|
2020-03-02
|
Improved Gilbert-Varshamov Bound for Entanglement-Assisted Asymmetric Quantum Error Correction by Symplectic Orthogonality
|
We propose and prove an existential theorem for entanglement-assisted
asymmetric quantum error correction. Then we demonstrate its superiority over
the conventional one.
|
2003.00668v2
|
2020-07-14
|
Competitively Pricing Parking in a Tree
|
Motivated by demand-responsive parking pricing systems we consider
posted-price algorithms for the online metrical matching problem and the online
metrical searching problem in a tree metric. Our main result is a poly-log
competitive posted-price algorithm for online metrical searching.
|
2007.07294v2
|
2021-05-14
|
Very regular solution to Landau-Lifshitz system with spin-polarized transport
|
In this paper, we provide a precise description of the compatibility
conditions for the initial data so that one can show the existence and
uniqueness of regular short-time solution to the Neumann initial-boundary
problem of a class of Landau-Lifshitz-Gilbert system with spin-polarized
transport, which is a strong nonlinear coupled parabolic system with non-local
energy.
|
2105.06616v1
|
2022-09-23
|
Limiting Distributions of Sums with Random Spectral Weights
|
This paper studies the asymptotic properties of weighted sums of the form
$Z_n=\sum_{i=1}^n a_i X_i$, in which $X_1, X_2, \ldots, X_n$ are i.i.d.~random
variables and $a_1, a_2, \ldots, a_n$ correspond to either eigenvalues or
singular values in the classic Erd\H{o}s-R\'enyi-Gilbert model. In particular,
we prove central limit-type theorems for the sequences $n^{-1}Z_n$ with varying
conditions imposed on $X_1, X_2, \ldots, X_n$.
|
2209.11389v1
|
2023-09-16
|
Expansion of the Critical Intensity for the Random Connection Model
|
We derive an asymptotic expansion for the critical percolation density of the
random connection model as the dimension of the encapsulating space tends to
infinity. We calculate rigorously the first expansion terms for the Gilbert
disk model, the hyper-cubic model, the Gaussian connection kernel, and a
coordinate-wise Cauchy kernel.
|
2309.08830v1
|
2024-03-14
|
Remarks on the rate of linear vortex symmetrization
|
We reformulate results from the paper ``Linear vortex symmetrization: The
spectral density function" by Ionescu and the author in simplified forms and
derive rigorously the bounds given in Bassom and Gilbert (J. Fluid Mech.,
1998), which provided interesting insights on the vortex symmetrization
phenomenon.
|
2403.09397v1
|
2003-10-29
|
Comparing Chemical Abundances of the Damped Lya Systems and Metal-Poor Stars
|
I briefly draw comparisons between the fields of damped Lya and metal-poor
stellar abundances. In particular, I examine their complementary
age-metallicity relations and comparisons between the damped Lya and dwarf
galaxy abundance patterns. Regarding the latter, I describe a series of
problems concerning associating high z damped Lya systems with present-day
dwarfs.
|
0310850v1
|
2006-12-01
|
Stochastic excitation and damping of solar-type oscillations
|
A review on acoustic mode damping and excitation in solar-type stars is
presented. Current models for linear damping rates are discussed in the light
of recent low-degree solar linewidth measurements with emphasis on the
frequency-dependence of damping rates of low-order modes. Recent developments
in stochastic excitation models are reviewed and tested against the latest
high-quality data of solar-like oscillations, such as from alpha Cen A, and
against results obtained from hydrodynamical simulations.
|
0612024v1
|
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