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2012-03-21
|
Approximate rogue wave solutions of the forced and damped Nonlinear Schrödinger equation for water waves
|
We consider the effect of the wind and the dissipation on the nonlinear
stages of the modulational instability. By applying a suitable transformation,
we map the forced/damped Nonlinear Schr\"odinger (NLS) equation into the
standard NLS with constant coefficients. The transformation is valid as long as
|{\Gamma}t| \ll 1, with {\Gamma} the growth/damping rate of the waves due to
the wind/dissipation. Approximate rogue wave solutions of the equation are
presented and discussed. The results shed some lights on the effects of wind
and dissipation on the formation of rogue waves.
|
1203.4735v1
|
2012-04-02
|
Random Symmetry Breaking and Freezing in Chaotic Networks
|
Parameter space of a driven damped oscillator in a double well potential
presents either a chaotic trajectory with sign oscillating amplitude or a
non-chaotic trajectory with a fixed sign amplitude. A network of such delay
coupled damped oscillators is shown to present chaotic dynamics while the
amplitude sign of each damped oscillator is randomly frozen. This phenomenon of
random broken global symmetry of the network simultaneously with random
freezing of each degree of freedom is accompanied by the existence of
exponentially many randomly frozen chaotic attractors with the ize of the
network. Results are exemplified by a network of modified Duffing oscillators
with infinite ange pseudo-inverse delayed interactions.
|
1204.0528v1
|
2012-04-04
|
Nonlinear Damping in Graphene Resonators
|
Based on a continuum mechanical model for single-layer graphene we propose
and analyze a microscopic mechanism for dissipation in nanoelectromechanical
graphene resonators. We find that coupling between flexural modes and in-plane
phonons leads to linear and nonlinear damping of out-of-plane vibrations. By
tuning external parameters such as bias and ac voltages, one can cross over
from a linear to a nonlinear-damping dominated regime. We discuss the behavior
of the effective quality factor in this context.
|
1204.0911v2
|
2012-05-22
|
Heavy quark damping rate in hot viscous QCD plasma
|
We derive an expression for the heavy quark damping rate in hot quark gluon
plasma in presence of flow. Here all the bath particles here are out of
equilibrium due to the existence of non-zero velocity gradient. The magnetic
sector shows similar infrared divergences even after hard thermal loop
corrections as one encounters in case of non-viscous plasma. We estimate the
first order correction in ($\eta/s$) for heavy quark damping rate due to the
non-zero viscosity of the QCD plasma.
|
1205.4895v3
|
2012-07-24
|
Quantum capacity of an amplitude-damping channel with memory
|
We calculate the quantum capacity of an amplitude-damping channel with time
correlated Markov noise, for two channel uses. Our results show that memory of
the channel increases it's ability to transmit quantum information
significantly. We analyze and compare our findings with earlier numerical
results on amplitude-damping channel with memory. An upper bound on the amount
of quantum information transmitted over the channel in presence of memory, for
an arbitrary number of channel uses is also presented.
|
1207.5612v3
|
2012-08-21
|
Protecting quantum entanglement from amplitude damping
|
Quantum entanglement is a critical resource for quantum information and
quantum computation. However, entanglement of a quantum system is subjected to
change due to the interaction with the environment. One typical result of the
interaction is the amplitude damping that usually results in the reduction of
the entanglement. Here we propose a protocol to protect quantum entanglement
from the amplitude damping by applying Hadamard and CNOT gates. As opposed to
some recently studied methods, the scheme presented here does not require weak
measurement in the reversal process, leading to a faster recovery of
entanglement. We propose a possible experimental implementation based on linear
optical system.
|
1208.4187v2
|
2012-10-03
|
Exact solutions for discrete breathers in forced-damped chain
|
Exact solutions for symmetric discrete breathers (DBs) are obtained in
forced-damped linear chain with on-site vibro-impact constraints. The damping
is related to inelastic impacts; the forcing may be chosen from broad class of
periodic antisymmetric functions. Global conditions for existence and stability
of the DB are established. Some unusual phenomena, like non-monotonous
dependence of the stability boundary on the forcing amplitude, are revealed
analytically for the full system and illustrated numerically for small periodic
lattices.
|
1210.1085v1
|
2012-12-18
|
Using the mobile phone acceleration sensor in Physics experiments: free and damped harmonic oscillations
|
The mobile acceleration sensor has been used to in Physics experiments on
free and damped oscillations. Results for the period, frequency, spring
constant and damping constant match very well to measurements obtained by other
methods. The Accelerometer Monitor application for Android has been used to get
the outputs of the sensor. Perspectives for the Physics laboratory have also
been discussed.
|
1212.4403v1
|
2012-12-20
|
How long-range interactions tune the damping in compact stars
|
Long-range interactions lead to non-Fermi liquid effects in dense matter. We
show that, in contrast to other material properties, their effect on the bulk
viscosity of quark matter is significant since they shift its resonant maximum
and can thereby change the viscosity by many orders of magnitude. This is of
importance for the damping of oscillations of compact stars, like in particular
unstable r-modes, and the quest to detect signatures of deconfined matter in
astrophysical observations. We find that, in contrast to neutron stars with
standard damping mechanisms, compact stars that contain ungapped quark matter
are consistent with the observed data on low mass x-ray binaries.
|
1212.5242v1
|
2013-02-12
|
Impact of gluon damping on heavy-quark quenching
|
In this conference contribution, we discuss the influence of
gluon-bremsstrahlung damping in hot, absorptive QCD matter on the heavy-quark
radiation spectra. Within our Monte-Carlo implementation for the description of
the heavy-quark in-medium propagation we demonstrate that as a consequence of
gluon damping the quenching of heavy quarks becomes significantly affected at
higher transverse momenta.
|
1302.2934v1
|
2013-03-12
|
On nonlinear Schrodinger type equations with nonlinear damping
|
We consider equations of nonlinear Schrodinger type augmented by nonlinear
damping terms. We show that nonlinear damping prevents finite time blow-up in
several situations, which we describe. We also prove that the presence of a
quadratic confinement in all spatial directions drives the solution of our
model to zero for large time. In the case without external potential we prove
that the solution may not go to zero for large time due to (non-trivial)
scattering.
|
1303.3033v2
|
2013-06-15
|
A formula for damping interarea oscillations with generator redispatch
|
We derive a new formula for the sensitivity of electromechanical oscillation
damping with respect to generator redispatch. The formula could lead to some
combination of observations, computations and heuristics to more effectively
damp interarea oscillations.
|
1306.3590v2
|
2013-07-24
|
Eigenvalue asymptotics for the damped wave equation on metric graphs
|
We consider the linear damped wave equation on finite metric graphs and
analyse its spectral properties with an emphasis on the asymptotic behaviour of
eigenvalues. In the case of equilateral graphs and standard coupling conditions
we show that there is only a finite number of high-frequency abscissas, whose
location is solely determined by the averages of the damping terms on each
edge. We further describe some of the possible behaviour when the edge lengths
are no longer necessarily equal but remain commensurate.
|
1307.6377v3
|
2013-08-03
|
Hadamard well-posedness for a hyperbolic equation of viscoelasticity with supercritical sources and damping
|
Presented here is a study of a viscoelastic wave equation with supercritical
source and damping terms. We employ the theory of monotone operators and
nonlinear semigroups, combined with energy methods to establish the existence
of a unique local weak solution. In addition, it is shown that the solution
depends continuously on the initial data and is global provided the damping
dominates the source in an appropriate sense.
|
1308.0720v2
|
2013-10-14
|
Signatures of two-level defects in the temperature-dependent damping of nanomechanical silicon nitride resonators
|
The damping rates of high quality factor nanomechanical resonators are well
beyond intrinsic limits. Here, we explore the underlying microscopic loss
mechanisms by investigating the temperature-dependent damping of the
fundamental and third harmonic transverse flexural mode of a doubly clamped
silicon nitride string. It exhibits characteristic maxima reminiscent of
two-level defects typical for amorphous materials. Coupling to those defects
relaxes the momentum selection rules, allowing energy transfer from discrete
long wavelength resonator modes to the high frequency phonon environment.
|
1310.3671v1
|
2013-10-25
|
Quenched decoherence in qubit dynamics due to strong amplitude-damping noise
|
We study non-perturbatively the time evolution of a qubit subject to
amplitude-damping noise. We show that at strong coupling the qubit decoherence
can be quenched owing to large environment feedbacks, such that the qubit can
evolve coherently even in the long-time limit. As an application, we show that
for a quantum channel that consists of two independent qubits subject to
uncorrelated local amplitude-damping noises, it can maintain at strong coupling
finite entanglement and better than classical teleportation fidelity at long
times.
|
1310.6843v2
|
2013-11-16
|
Shear viscosity due to the Landau damping from quark-pion interaction
|
We have calculated the shear viscosity coefficient $\eta$ of the strongly
interacting matter in the relaxation time approximation, where a quasi particle
description of quarks with its dynamical mass is considered from NJL model. Due
to the thermodynamic scattering of quarks with pseudo scalar type condensate
(i.e. pion), a non zero Landau damping will be acquired by the propagating
quarks. This Landau damping may be obtained from the Landau cut contribution of
the in-medium self-energy of quark-pion loop, which is evaluated in the
framework of real-time thermal field theory.
|
1311.4070v1
|
2013-12-19
|
Cyclotron dynamics of interacting bosons in artificial magnetic fields
|
We study theoretically quantum dynamics of interacting bosons in artificial
magnetic fields as engineered in recent ultracold atomic experiments, where
quantum cyclotron orbital motion has been observed. With exact numerical
simulations and perturbative analyses, we find that interactions induce damping
in the cyclotron motion. The damping time is found to be dependent on
interaction and tunneling strengths monotonically, while its dependence on
magnetic flux is non-monotonic. Sufficiently strong interactions would render
bosons dynamically localized inhibiting the cyclotron motion. The damping
predicted by us can be construed as an interaction-induced quantum decoherence
of the cyclotron motion.
|
1312.5747v2
|
2014-01-11
|
Damping in two component Bose gas
|
We investigate the Landau and Baliaev damping of the collective modes in a
two-component Bose gas using the mean-field approximation. We show that due to
the two body atom-atom interaction, oscillations of each component is coupled
to the thermal excitations of the other component which gives rise to creation
or destruction of the elementary excitations that can take place in the two
separate components.In addition we find that the damping is also enhanced due
to inter-component coupling.
|
1401.2537v1
|
2014-03-24
|
Existence Results for Some Damped Second-Order Volterra Integro-Differential Equations
|
In this paper we make a subtle use of operator theory techniques and the
well-known Schauder fixed-point principle to establish the existence of
pseudo-almost automorphic solutions to some second-order damped
integro-differential equations with pseudo-almost automorphic coefficients. In
order to illustrate our main results, we will study the existence of
pseudo-almost automorphic solutions to a structurally damped plate-like
boundary value problem.
|
1403.5955v1
|
2014-04-25
|
The time singular limit for a fourth-order damped wave equation for MEMS
|
We consider a free boundary problem modeling electrostatic
microelectromechanical systems. The model consists of a fourth-order damped
wave equation for the elastic plate displacement which is coupled to an
elliptic equation for the electrostatic potential. We first review some recent
results on existence and non-existence of steady-states as well as on local and
global well-posedness of the dynamical problem, the main focus being on the
possible touchdown behavior of the elastic plate. We then investigate the
behavior of the solutions in the time singular limit when the ratio between
inertial and damping effects tends to zero.
|
1404.6342v1
|
2014-05-12
|
A note on a strongly damped wave equation with fast growing nonlinearities
|
A strongly damped wave equation including the displacement depending
nonlinear damping term and nonlinear interaction function is considered. The
main aim of the note is to show that under the standard dissipativity
restrictions on the nonlinearities involved the initial boundary value problem
for the considered equation is globally well-posed in the class of sufficiently
regular solutions and the semigroup generated by the problem possesses a global
attractor in the corresponding phase space. These results are obtained for the
nonlinearities of an arbitrary polynomial growth and without the assumption
that the considered problem has a global Lyapunov function.
|
1405.2707v1
|
2014-06-03
|
Optimal Estimation of a Classical Force with a Damped Oscillator in the non-Markovian Bath
|
We solve the optimal quantum limit of probing a classical force exactly by a
damped oscillator initially prepared in the factorized squeezed state. The
memory effects of the thermal bath on the oscillator evolution are
investigated. We show that the optimal force sensitivity obtained by the
quantum estimation theory approaches to zero for the non-Markovian bath,
whereas approaches to a finite non-zero value for the Markovian bath as the
energy of the damped oscillator goes to infinity.
|
1406.0658v1
|
2014-08-09
|
Local existence results for the Westervelt equation with nonlinear damping and Neumann as well as absorbing boundary conditions
|
We investigate the Westervelt equation with several versions of nonlinear
damping and lower order damping terms and Neumann as well as absorbing boundary
conditions. We prove local in time existence of weak solutions under the
assumption that the initial and boundary data are sufficiently small.
Additionally, we prove local well-posedness in the case of spatially varying
$L^{\infty}$ coefficients, a model relevant in high intensity focused
ultrasound (HIFU) applications.
|
1408.2160v1
|
2014-08-11
|
Characterization and suppression techniques for degree of radiation damping in inversion recovery measurements
|
Radiation damping (RD) has been shown to affect T1 measurement in inversion
recovery experiments. In this work, we demonstrate that the extent of RD
depends upon the T1 of the sample. RD difference spectroscopy (RADDSY) is used
to characterize the severity of RD, while gradient inversion recovery (GIR) is
used for RD suppression in T1 measurements. At 9.4 T, for the radiation damping
characteristic time (Trd) of 50 ms, these investigations show non-negligible RD
effects for T1 values greater than Trd, with severe distortions for T1 longer
than about 150 ms, showing reasonable agreement with the predicted Trd. We also
report a discrepancy between published expressions for the characteristic RD
time.
|
1408.2457v2
|
2014-09-28
|
Spin-electron acoustic waves: The Landau damping and ion contribution in the spectrum
|
Separated spin-up and spin-down quantum kinetics is derived for more detailed
research of the spin-electron acoustic waves. Kinetic theory allows to obtain
spectrum of the spin-electron acoustic waves including effects of occupation of
quantum states more accurately than quantum hydrodynamics. We apply quantum
kinetic to calculate the Landau damping of the spin-electron acoustic waves. We
have considered contribution of ions dynamics in the spin-electron acoustic
wave spectrum. We obtain contribution of ions in the Landau damping in
temperature regime of classic ions. Kinetic analysis for ion-acoustic, zero
sound, and Langmuir waves at separated spin-up and spin-down electron dynamics
is presented as well.
|
1409.7885v1
|
2014-10-05
|
Ultimate limit of field confinement by surface plasmon polaritons
|
We show that electric field confinement in surface plasmon polaritons
propagating at the metal/dielectric interfaces enhances the loss due to Landau
damping and which effectively limits the degree of confinement itself. We prove
that Landau damping and associated with it surface collision damping follow
directly from Lindhard formula for the dielectric constant of free electron gas
Furthermore, we demonstrate that even if all the conventional loss mechanisms,
caused by phonons, electron-electron, and interface roughness scattering, were
eliminated, the maximum attainable degree of confinement and the loss
accompanying it would not change significantly compared to the best existing
plasmonic materials, such as silver.
|
1410.1226v1
|
2014-10-15
|
Quasiparticle Damping of Surface Waves in Superfluid $^3$He and $^4$He
|
Oscillations on free surface of superfluids at the inviscid limit are damped
by quasiparticle scattering. We have studied this effect in both superfluids
$^3$He and $^4$He deep below the respective critical temperatures. Surface
oscillators offer several benefits over immersed mechanical oscillators
traditionally used for similar purposes. Damping is modeled as specular
scattering of ballistic quasiparticles from the moving free surface. The model
is in reasonable agreement with our measurements for superfluid $^4$He but
significant deviation is found for $^3$He.
|
1410.4071v1
|
2014-12-22
|
Long time behavior for a semilinear hyperbolic equation with asymtotically vanishing damping term and convex potential
|
We investigate the asymptotic behavior, as t goes to infinity, for a
semilinear hyperbolic equation with asymptotically smal dissipation and convex
potential. We prove that if the damping term behaves like K/t^\alpha for t
large enough, k>0 and 0</alpha<1 then every global solution converges weakly to
an equilibrium point. This result is a positive answer to a question left open
in the paper [A. Cabot and P. Frankel, Asymptotics for some semilinear
hyperbolic equation with non-autonomous damping. J. Differential Equations 252
(2012) 294-322.]
|
1412.7008v1
|
2015-03-03
|
Large Deviations for the Langevin equation with strong damping
|
We study large deviations in the Langevin dynamics, with damping of order
$\e^{-1}$ and noise of order $1$, as $\e\downarrow 0$. The damping coefficient
is assumed to be state dependent. We proceed first with a change of time and
then, we use a weak convergence approach to large deviations and their
equivalent formulation in terms of the Laplace principle, to determine the good
action functional.
Some applications of these results to the exit problem from a domain and to
the wave front propagation for a suitable class of reaction diffusion equations
are considered.
|
1503.01027v1
|
2015-03-14
|
Stabilization of the nonlinear damped wave equation via linear weak observability
|
We consider the problem of energy decay rates for nonlinearly damped abstract
infinite dimensional systems. We prove sharp, simple and quasi-optimal energy
decay rates through an indirect method, namely a weak observability estimate
for the corresponding undamped system. One of the main advantage of these
results is that they allow to combine the optimal-weight convexity method of
Alabau-Boussouira and a methodology of Ammari-Tucsnak for weak stabilization by
observability. Our results extend to nonlinearly damped systems, those of
Ammari and Tucsnak. At the end, we give an appendix on the weak stabilization
of linear evolution systems.
|
1503.04356v1
|
2015-06-02
|
On the the wave equation with hyperbolic dynamical boundary conditions, interior and boundary damping and source
|
The aim of the paper is to study local Hadamard well-posedness for wave
equation with an hyperbolic dynamical boundary condition, internal and/or
boundary damping and sources for initial data in the natural energy space.
Moreover the regularity of solutions is studied. Finally a dynamical system is
generated when sources are at most linear at infinity, or they are dominated by
the damping terms.
|
1506.00910v4
|
2015-06-15
|
Tautochrone in the damped cycloidal pendulum
|
The tautochrone on a cycloid curve is usually considered without drag force.
In this work, we investigate the motion of a damped cycloidal pendulum under
presence of a drag force. Using the Lagrange formulation, and considering
linear dependence with velocity for damping force, we found the dynamics of the
system to remain tautochrone. This dictates the possibility for studying the
tautochrone experimentally, e.g. the cycloidal pendulum in water or oil.
|
1506.04943v2
|
2015-07-04
|
Comments on turbulence theory by Qian and by Edwards and McComb
|
We reexamine Liouville equation based turbulence theories proposed by Qian
{[}Phys. Fluids \textbf{26}, 2098 (1983){]} and Edwards and McComb {[}J. Phys.
A: Math. Gen. \textbf{2}, 157 (1969){]}, which are compatible with Kolmogorov
spectrum. These theories obtained identical equation for spectral density
$q(k)$ and different results for damping coefficient. Qian proposed variational
approach and Edwards and McComb proposed maximal entropy principle to obtain
equation for the damping coefficient. We show that assumptions used in these
theories to obtain damping coefficient correspond to unphysical conditions.
|
1507.01124v1
|
2015-08-24
|
Scaling variables and asymptotic profiles for the semilinear damped wave equation with variable coefficients
|
We study the asymptotic behavior of solutions for the semilinear damped wave
equation with variable coefficients. We prove that if the damping is effective,
and the nonlinearity and other lower order terms can be regarded as
perturbations, then the solution is approximated by the scaled Gaussian of the
corresponding linear parabolic problem. The proof is based on the scaling
variables and energy estimates.
|
1508.05778v3
|
2015-10-01
|
Impact of surface collisions on enhancement and quenching of the luminescence near the metal nanoparticles
|
The fact that surface-induced damping rate of surface plasmon polaritons
(SPPs) in metal nanoparticles increases with the decrease of particle size is
well known. We show that this rate also increases with the degree of the mode
confinement, hence damping of the higher order nonradiative SPP modes in
spherical particles is greatly enhanced relative to damping of the fundamental
(dipole) SPP mode. Since higher order modes are the ones responsible for
quenching of luminescence in the vicinity of metal surfaces, the degree of
quenching increases resulting in a substantial decrease in the amount of
attainable enhancement of the luminescence
|
1510.00321v1
|
2015-10-22
|
On numerical Landau damping for splitting methods applied to the Vlasov-HMF model
|
We consider time discretizations of the Vlasov-HMF (Hamiltonian Mean-Field)
equation based on splitting methods between the linear and non-linear parts. We
consider solutions starting in a small Sobolev neighborhood of a spatially
homogeneous state satisfying a linearized stability criterion (Penrose
criterion). We prove that the numerical solutions exhibit a scattering behavior
to a modified state, which implies a nonlinear Landau damping effect with
polynomial rate of damping. Moreover, we prove that the modified state is close
to the continuous one and provide error estimates with respect to the time
stepsize.
|
1510.06555v1
|
2015-11-02
|
Asymptotic decomposition for nonlinear damped Klein-Gordon equations
|
In this paper, we proved that if the solution to damped focusing Klein-Gordon
equations is global forward in time, then it will decouple into a finite number
of equilibrium points with different shifts from the origin. The core
ingredient of our proof is the existence of the "concentration-compact
attractor" which yields a finite number of profiles. Using damping effect, we
can prove all the profiles are equilibrium points.
|
1511.00437v3
|
2015-11-11
|
Contact Stiffness and Damping of Liquid Films in Dynamic Atomic Force Microscopy
|
Small-amplitude dynamic atomic force microscopy (dynamic-AFM) in a simple
nonpolar liquid was studied through molecular dynamics simulations. We find
that within linear dynamics regime, the contact stiffness and damping of the
confined film exhibit the similar solvation force oscillations, and they are
generally out-of-phase. For the solidified film with integer monolayer
thickness, further compression of the film before layering transition leads to
higher stiffness and lower damping. We find that molecular diffusion in the
solidified film was nevertheless enhanced due to the mechanical excitation of
AFM tip.
|
1511.03580v1
|
2015-11-13
|
Nonlinear Radiation Damping of Nuclear Spin Waves and Magnetoelastic Waves in Antiferromagnets
|
Parallel pumping of nuclear spin waves in antiferromagnetic CsMnF3 at liquid
helium temperatures and magnetoelastic waves in antiferromagnetic FeBO3 at
liquid nitrogen temperature in a helical resonator was studied. It was found
that the absorbed microwave power is approximately equal to the irradiated
power from the sample and that the main restriction mechanism of absortption in
both cases is defined by the nonlinear radiation damping predicted about two
decades ago. We believe that the nonlinear radiation damping is a common
feature of parallel pumping technique of all normal magnetic excitations and it
can be detected by purposeful experiments.
|
1511.04396v1
|
2016-03-01
|
Damped vacuum states of light
|
We consider one-dimensional propagation of quantum light in the presence of a
block of material, with a full account of dispersion and absorption. The
electromagnetic zero-point energy for some frequencies is damped (suppressed)
by the block below the free-space value, while for other frequencies it is
increased. We also calculate the regularized (Casimir) zero-point energy at
each frequency and find that it too is damped below the free-space value (zero)
for some frequencies. The total Casimir energy is positive.
|
1603.00233v2
|
2016-04-18
|
Parameter Estimation of Gaussian-Damped Sinusoids from a Geometric Perspective
|
The five parameter gaussian damped sinusoid equation is a reasonable model
for betatron motion with chromatic decoherence of the proton bunch centroid
signal in the ring at the Spallation Neutron Source. A geometric method for
efficiently fitting this equation to the turn by turn signals to extract the
betatron tune and damping constant will be presented. This method separates the
parameters into global and local parameters and allows the use of vector
arithmetic to eliminate the local parameters from the parameter search space.
Furthermore, this method is easily generalized to reduce the parameter search
space for a larger class of problems.
|
1604.05167v1
|
2016-04-20
|
Landau damping in finite regularity for unconfined systems with screened interactions
|
We prove Landau damping for the collisionless Vlasov equation with a class of
$L^1$ interaction potentials (including the physical case of screened Coulomb
interactions) on $\mathbb R^3_x \times \mathbb R^3_v$ for localized
disturbances of an infinite, homogeneous background. Unlike the confined case
$\mathbb T^3_x \times \mathbb R_v^3$, results are obtained for initial data in
Sobolev spaces (as well as Gevrey and analytic classes). For spatial
frequencies bounded away from zero, the Landau damping of the density is
similar to the confined case. The finite regularity is possible due to an
additional dispersive mechanism available on $\mathbb R_x^3$ which reduces the
strength of the plasma echo resonance.
|
1604.05783v1
|
2016-04-26
|
Trigonometric Splines for Oscillator Simulation
|
We investigate the effects of numerical damping for oscillator simulation
with spline methods. Numerical damping results in an artificial loss of energy
and leads therefore to unreliable results in the simulation of autonomous
systems, as e.g.\ oscillators. We show that the negative effects of numerical
damping can be eliminated by the use of trigonometric splines. This will be in
particular important for spline based adaptive methods.
|
1604.07607v1
|
2016-07-13
|
Optimal decay rate for the wave equation on a square with constant damping on a strip
|
We consider the damped wave equation with Dirichlet boundary conditions on
the unit square. We assume the damping to be a characteristic function of a
strip. We prove the exact $t^{-4/3}$-decay rate for the energy of classical
solutions. This answers a question of Anantharaman and L\'eautaud (2014).
|
1607.03633v2
|
2016-08-29
|
Stochastic 3D Navier-Stokes equations with nonlinear damping: martingale solution, strong solution and small time large deviation principles
|
In this paper, by using classical Faedo-Galerkin approximation and
compactness method, the existence of martingale solutions for the stochastic 3D
Navier-Stokes equations with nonlinear damping is obtained. The existence and
uniqueness of strong solution are proved for $\beta > 3$ with any $\alpha>0$
and $\alpha \geq \frac12$ as $\beta = 3$. Meanwhile, a small time large
deviation principle for the stochastic 3D Navier-Stokes equation with damping
is proved for $\beta > 3$ with any $\alpha>0$ and $\alpha \geq \frac12$ as
$\beta = 3$.
|
1608.07996v1
|
2016-09-05
|
Estimates of lifespan and blow-up rates for the wave equation with a time-dependent damping and a power-type nonlinearity
|
We study blow-up behavior of solutions for the Cauchy problem of the
semilinear wave equation with time-dependent damping. When the damping is
effective, and the nonlinearity is subcritical, we show the blow-up rates and
the sharp lifespan estimates of solutions. Upper estimates are proved by an ODE
argument, and lower estimates are given by a method of scaling variables.
|
1609.01035v2
|
2016-09-06
|
Numerical Convergence Rate for a Diffusive Limit of Hyperbolic Systems: p-System with Damping
|
This paper deals with diffusive limit of the p-system with damping and its
approximation by an Asymptotic Preserving (AP) Finite Volume scheme. Provided
the system is endowed with an entropy-entropy flux pair, we give the
convergence rate of classical solutions of the p-system with damping towards
the smooth solutions of the porous media equation using a relative entropy
method. Adopting a semi-discrete scheme, we establish that the convergence rate
is preserved by the approximated solutions. Several numerical experiments
illustrate the relevance of this result.
|
1609.01436v1
|
2016-09-20
|
Global existence and asymptotic behavior of solutions to the Euler equations with time-dependent damping
|
We study the isentropic Euler equations with time-dependent damping, given by
$\frac{\mu}{(1+t)^\lambda}\rho u$. Here, $\lambda,\mu$ are two non-negative
constants to describe the decay rate of damping with respect to time. We will
investigate the global existence and asymptotic behavior of small data
solutions to the Euler equations when $0<\lambda<1,0<\mu$ in multi-dimensions
$n\geq 1$. The asymptotic behavior will coincide with the one that obtained by
many authors in the case $\lambda=0$. We will also show that the solution can
only decay polynomially in time while in the three dimensions, the vorticity
will decay exponentially fast.
|
1609.06286v1
|
2016-11-08
|
Emulated Inertia and Damping of Converter-Interfaced Power Source
|
Converter-interfaced power sources (CIPSs), like wind turbine and energy
storage, can be switched to the inertia emulation mode when the detected
frequency deviation exceeds a pre-designed threshold, i.e. dead band, to
support the frequency response of a power grid. This letter proposes an
approach to derive the emulated inertia and damping from a CIPS based on the
linearized model of the CIPS and the power grid, where the grid is represented
by an equivalent single machine. The emulated inertia and damping can be
explicitly expressed in time and turn out to be time-dependent.
|
1611.02698v1
|
2016-12-09
|
Ornstein-Uhlenbeck Process with Fluctuating Damping
|
This paper studies Langevin equation with random damping due to
multiplicative noise and its solution. Two types of multiplicative noise,
namely the dichotomous noise and fractional Gaussian noise are considered.
Their solutions are obtained explicitly, with the expressions of the mean and
covariance determined explicitly. Properties of the mean and covariance of the
Ornstein-Uhlenbeck process with random damping, in particular the asymptotic
behavior, are studied. The effect of the multiplicative noise on the stability
property of the resulting processes is investigated.
|
1612.03013v3
|
2016-12-20
|
Symmetry group classification and optimal reduction of a class of damped Timoshenko beam system with a nonlinear rotational moment
|
We consider a nonlinear Timoshenko system of partial differential equations
(PDEs) with a frictional damping term in rotation angle. The nonlinearity is
due to the arbitrary dependence on the rotation moment. A Lie symmetry group
classification of the arbitrary function of rotation moment is presented. An
optimal system of one-dimensional subalgebras of the nonlinear damped
Timoshenko system is derived for all the non-linear cases. All possible
invariant variables of the optimal systems for the three non-linear cases are
presented. The corresponding reduced systems of ordinary differential equations
(ODEs) are also provided.
|
1612.06775v1
|
2017-03-14
|
Landau damping in the multiscale Vlasov theory
|
Vlasov kinetic theory is extended by adopting an extra one particle
distribution function as an additional state variable characterizing the
micro-turbulence internal structure. The extended Vlasov equation keeps the
reversibility, the Hamiltonian structure, and the entropy conservation of the
original Vlasov equation. In the setting of the extended Vlasov theory we then
argue that the Fokker-Planck type damping in the velocity dependence of the
extra distribution function induces the Landau damping. The same type of
extension is made also in the setting of fluid mechanics.
|
1703.04577v2
|
2017-03-15
|
Energy decay and diffusion phenomenon for the asymptotically periodic damped wave equation
|
We prove local and global energy decay for the asymptotically periodic damped
wave equation on the Euclidean space. Since the behavior of high frequencies is
already mostly understood, this paper is mainly about the contribution of low
frequencies. We show in particular that the damped wave behaves like a solution
of a heat equation which depends on the H-limit of the metric and the mean
value of the absorption index.
|
1703.05112v1
|
2017-04-03
|
Linear inviscid damping and vorticity depletion for shear flows
|
In this paper, we prove the linear damping for the 2-D Euler equations around
a class of shear flows under the assumption that the linearized operator has no
embedding eigenvalues. For the symmetric flows, we obtain the explicit decay
estimates of the velocity, which is the same as one for monotone shear flows.
We confirm a new dynamical phenomena found by Bouchet and Morita: the depletion
of the vorticity at the stationary streamlines, which could be viewed as a new
mechanism leading to the damping for the base flows with stationary
streamlines.
|
1704.00428v1
|
2017-04-25
|
Diffusion phenomena for the wave equation with space-dependent damping term growing at infinity
|
In this paper, we study the asymptotic behavior of solutions to the wave
equation with damping depending on the space variable and growing at the
spatial infinity. We prove that the solution is approximated by that of the
corresponding heat equation as time tends to infinity. The proof is based on
semigroup estimates for the corresponding heat equation and weighted energy
estimates for the damped wave equation. To construct a suitable weight function
for the energy estimates, we study a certain elliptic problem.
|
1704.07650v1
|
2017-06-05
|
Mixed finite elements for global tide models with nonlinear damping
|
We study mixed finite element methods for the rotating shallow water
equations with linearized momentum terms but nonlinear drag. By means of an
equivalent second-order formulation, we prove long-time stability of the system
without energy accumulation. We also give rates of damping in unforced systems
and various continuous dependence results on initial conditions and forcing
terms. \emph{A priori} error estimates for the momentum and free surface
elevation are given in $L^2$ as well as for the time derivative and divergence
of the momentum. Numerical results confirm the theoretical results regarding
both energy damping and convergence rates.
|
1706.01352v1
|
2017-06-13
|
Uniform energy decay for wave equations with unbounded damping coefficients
|
We consider the Cauchy problem for wave equations with unbounded damping
coefficients in the whole space. For a general class of unbounded damping
coefficients, we derive uniform total energy decay estimates together with a
unique existence result of a weak solution. In this case we never impose strong
assumptions such as compactness of the support of the initial data. This means
that we never rely on the finite propagation speed property of the solution,
and we try to deal with an essential unbounded coefficient case.
|
1706.03942v1
|
2017-06-15
|
Fractional Driven Damped Oscillator
|
The resonances associated with a fractional damped oscillator which is driven
by an oscillatory external force are studied. It is shown that such resonances
can be manipulated by tuning up either the coefficient of the fractional
damping or the order of the corresponding fractional derivatives.
|
1706.08596v1
|
2017-07-11
|
Stability of partially locked states in the Kuramoto model through Landau damping with Sobolev regularity
|
The Kuramoto model is a mean-field model for the synchronisation behaviour of
oscillators, which exhibits Landau damping. In a recent work, the nonlinear
stability of a class of spatially inhomogeneous stationary states was shown
under the assumption of analytic regularity. This paper proves the nonlinear
Landau damping under the assumption of Sobolev regularity. The weaker
regularity required the construction of a different more robust bootstrap
argument, which focuses on the nonlinear Volterra equation of the order
parameter.
|
1707.03475v2
|
2017-08-27
|
Global well-posedness for the semilinear wave equation with time dependent damping in the overdamping case
|
We study global existence of solutions to the Cauchy problem for the wave
equation with time-dependent damping and a power nonlinearity in the
overdamping case. We prove the global well-posedness for small data in the
energy space for the whole energy-subcritical case. This result implies that
small data blow-up does not occur in the overdamping case, different from the
other cases, i.e. effective or non-effective damping.
|
1708.08044v2
|
2017-09-04
|
A note on the blowup of scale invariant damping wave equation with sub-Strauss exponent
|
We concern the blow up problem to the scale invariant damping wave equations
with sub-Strauss exponent. This problem has been studied by Lai, Takamura and
Wakasa (\cite{Lai17}) and Ikeda and Sobajima \cite{Ikedapre} recently. In
present paper, we extend the blowup exponent from $p_F(n)\leq p<p_S(n+2\mu)$ to
$1<p<p_S(n+\mu)$ without small restriction on $\mu$. Moreover, the upper bound
of lifespan is derived with uniform estimate $T(\varepsilon)\leq
C\varepsilon^{-2p(p-1)/\gamma(p,n+2\mu)}$. This result extends the blowup
result of semilinear wave equation and shows the wave-like behavior of scale
invariant damping wave equation's solution even with large $\mu>1$.
|
1709.00866v2
|
2017-09-13
|
Life-span of blowup solutions to semilinear wave equation with space-dependent critical damping
|
This paper is concerned with the blowup phenomena for initial value problem
of semilinear wave equation with critical space-dependent damping term
(DW:$V$). The main result of the present paper is to give a solution of the
problem and to provide a sharp estimate for lifespan for such a solution when
$\frac{N}{N-1}<p\leq p_S(N+V_0)$, where $p_S(N)$ is the Strauss exponent for
(DW:$0$). The main idea of the proof is due to the technique of test functions
for (DW:$0$) originated by Zhou--Han (2014, MR3169791). Moreover, we find a new
threshold value $V_0=\frac{(N-1)^2}{N+1}$ for the coefficient of critical and
singular damping $|x|^{-1}$.
|
1709.04401v1
|
2017-09-24
|
Suppression of Recurrence in the Hermite-Spectral Method for Transport Equations
|
We study the unphysical recurrence phenomenon arising in the numerical
simulation of the transport equations using Hermite-spectral method. From a
mathematical point of view, the suppression of this numerical artifact with
filters is theoretically analyzed for two types of transport equations. It is
rigorously proven that all the non-constant modes are damped exponentially by
the filters in both models, and formally shown that the filter does not affect
the damping rate of the electric energy in the linear Landau damping problem.
Numerical tests are performed to show the effect of the filters.
|
1709.08194v1
|
2017-11-01
|
Life-Span of Semilinear Wave Equations with Scale-invariant Damping: Critical Strauss Exponent Case
|
The blow up problem of the semilinear scale-invariant damping wave equation
with critical Strauss type exponent is investigated. The life span is shown to
be: $T(\varepsilon)\leq C\exp(\varepsilon^{-2p(p-1)})$ when $p=p_S(n+\mu)$ for
$0<\mu<\frac{n^2+n+2}{n+2}$. This result completes our previous study
\cite{Tu-Lin} on the sub-Strauss type exponent $p<p_S(n+\mu)$. Our novelty is
to construct the suitable test function from the modified Bessel function. This
approach might be also applied to the other type damping wave equations.
|
1711.00223v1
|
2017-11-14
|
Spin-Noise and Damping in Individual Metallic Ferromagnetic Nanoparticles
|
We introduce a highly sensitive and relatively simple technique to observe
magnetization motion in single Ni nanoparticles, based on charge sensing by
electron tunneling at millikelvin temperature. Sequential electron tunneling
via the nanoparticle drives nonequilibrium magnetization dynamics, which
induces an effective charge noise that we measure in real time. In the free
spin diffusion regime, where the electrons and magnetization are in detailed
balance, we observe that magnetic damping time exhibits a peak with the
magnetic field, with a record long damping time of $\simeq 10$~ms.
|
1711.05142v1
|
2017-12-04
|
Graviton-mediated dark matter model explanation the DAMPE electron excess and search at $e^+e^-$ colliders
|
The very recent result of the DAMPE cosmic ray spectrum of electrons shows a
narrow bump above the background at around 1.4 TeV. We attempt to explain the
DAMPE electron excess in a simplified Kaluza-Klein graviton-mediated dark
matter model, in which the graviton only interacts with leptons and dark
matter. The related phenomenological discussions are given and this simplified
graviton-mediated dark matter model has the potential to be cross-tested in
future lepton collider experiments.
|
1712.01143v1
|
2017-12-13
|
On nonlinear damped wave equations for positive operators. I. Discrete spectrum
|
In this paper we study a Cauchy problem for the nonlinear damped wave
equations for a general positive operator with discrete spectrum. We derive the
exponential in time decay of solutions to the linear problem with decay rate
depending on the interplay between the bottom of the operator's spectrum and
the mass term. Consequently, we prove global in time well-posedness results for
semilinear and for more general nonlinear equations with small data. Examples
are given for nonlinear damped wave equations for the harmonic oscillator, for
the twisted Laplacian (Landau Hamiltonian), and for the Laplacians on compact
manifolds.
|
1712.05009v1
|
2018-03-14
|
Damped Newton's Method on Riemannian Manifolds
|
A damped Newton's method to find a singularity of a vector field in
Riemannian setting is presented with global convergence study. It is ensured
that the sequence generated by the proposed method reduces to a sequence
generated by the Riemannian version of the classical Newton's method after a
finite number of iterations, consequently its convergence rate is
superlinear/quadratic. Moreover, numerical experiments illustrate that the
damped Newton's method has better performance than Newton's method in number of
iteration and computational time.
|
1803.05126v2
|
2018-05-29
|
Asymptotic profile of solutions for strongly damped Klein-Gordon equations
|
We consider the Cauchy problem in the whole space for strongly damped
Klein-Gordon equations. We derive asymptotic profles of solutions with weighted
initial data by a simple method introduced by R. Ikehata. The obtained results
show that the wave effect will be weak because of the mass term, especially in
the low dimensional case (n = 1,2) as compared with the strongly damped wave
equations without mass term (m = 0), so the most interesting topic in this
paper is the n = 1,2 cases.
|
1805.11975v1
|
2018-06-08
|
Brownian motion of magnetic domain walls and skyrmions, and their diffusion constants
|
Extended numerical simulations enable to ascertain the diffusive behavior at
finite temperatures of chiral walls and skyrmions in ultra-thin model Co layers
exhibiting symmetric - Heisenberg - as well as antisymmetric -
Dzyaloshinskii-Moriya - exchange interactions. The Brownian motion of walls and
skyrmions is shown to obey markedly different diffusion laws as a function of
the damping parameter. Topology related skyrmion diffusion suppression with
vanishing damping parameter, albeit already documented, is shown to be
restricted to ultra-small skyrmion sizes or, equivalently, to ultra-low damping
coefficients, possibly hampering observation.
|
1806.03172v1
|
2018-06-18
|
Damped second order flow applied to image denoising
|
In this paper, we introduce a new image denoising model: the damped flow
(DF), which is a second order nonlinear evolution equation associated with a
class of energy functionals of image. The existence, uniqueness and
regularization property of DF are proven. For the numerical implementation,
based on the St\"{o}rmer-Verlet method, a discrete damped flow, SV-DDF, is
developed. The convergence of SV-DDF is studied as well. Several numerical
experiments, as well as a comparison with other methods, are provided to
demonstrate the feasibility and effectiveness of the SV-DDF.
|
1806.06732v2
|
2018-07-10
|
Cyclotron Damping along an Uniform Magnetic Field
|
We prove cyclotron damping for the collisionless Vlasov-Maxwell equations on
$\mathbb{T}_{x}^{3}\times\mathbb{R}_{v}^{3}$ under the assumptions that the
electric induction is zero and $(\mathcal{\mathbf{PSC}})$ holds. It is a
crucial step to solve the stability problem of the Vlasov-Maxwell equations.
Our proof is based on a new dynamical system of the plasma particles,
originating from Faraday Law of Electromagnetic induction and Lenz's Law. On
the basis of it, we use the improved Newton iteration scheme to show the
damping mechanism.
|
1807.05254v3
|
2018-07-17
|
On the blow-up for critical semilinear wave equations with damping in the scattering case
|
We consider the Cauchy problem for semilinear wave equations with variable
coefficients and time-dependent scattering damping in $\mathbf{R}^n$, where
$n\geq 2$. It is expected that the critical exponent will be Strauss' number
$p_0(n)$, which is also the one for semilinear wave equations without damping
terms. Lai and Takamura (2018) have obtained the blow-up part, together with
the upper bound of lifespan, in the sub-critical case $p<p_0(n)$. In this
paper, we extend their results to the critical case $p=p_0(n)$. The proof is
based on Wakasa and Yordanov (2018), which concerns the blow-up and upper bound
of lifespan for critical semilinear wave equations with variable coefficients.
|
1807.06164v1
|
2018-08-22
|
Radiation Damping of a Yang-Mills Particle Revisited
|
The problem of a color-charged point particle interacting with a four
dimensional Yang-Mills gauge theory is revisited. The radiation damping is
obtained inspired in the Dirac's computation. The difficulties in the
non-abelian case were solved by using an ansatz for the Li\'enard-Wiechert
potentials, already used in the literature for finding solutions to the
Yang-Mills equations. Three non-trivial examples of radiation damping for the
non-abelian particle are discussed in detail.
|
1808.07533v2
|
2018-08-28
|
Enhancement of zonal flow damping due to resonant magnetic perturbations in the background of an equilibrium $E \times B$ sheared flow
|
Using a parametric interaction formalism, we show that the equilibrium
sheared rotation can enhance the zonal flow damping effect found in Ref. [M.
Leconte and P.H. Diamond, \emph{Phys. Plasmas} 19, 055903 (2012)]. This
additional damping contribution is proportional to $(L_s/L_V)^2 \times \delta
B_r^2 / B^2$, where $L_s/L_V$ is the ratio of magnetic shear length to the
scale-length of equilibrium $E \times B$ flow shear, and $\delta B_r / B$ is
the amplitude of the external magnetic perturbation normalized to the
background magnetic field.
|
1808.09110v1
|
2018-08-30
|
Optimal indirect stability of a weakly damped elastic abstract system of second order equations coupled by velocities
|
In this paper, by means of the Riesz basis approach, we study the stability
of a weakly damped system of two second order evolution equations coupled
through the velocities. If the fractional order damping becomes viscous and the
waves propagate with equal speeds, we prove exponential stability of the system
and, otherwise, we establish an optimal polynomial decay rate. Finally, we
provide some illustrative examples.
|
1808.10256v1
|
2018-09-10
|
Linear inviscid damping for the $β$-plane equation
|
In this paper, we study the linear inviscid damping for the linearized
$\beta$-plane equation around shear flows. We develop a new method to give the
explicit decay rate of the velocity for a class of monotone shear flows. This
method is based on the space-time estimate and the vector field method in sprit
of the wave equation. For general shear flows including the Sinus flow, we also
prove the linear damping by establishing the limiting absorption principle,
which is based on the compactness method introduced by Wei-Zhang-Zhao in
\cite{WZZ2}. The main difficulty is that the Rayleigh-Kuo equation has more
singular points due to the Coriolis effects so that the compactness argument
becomes more involved and delicate.
|
1809.03065v1
|
2018-10-14
|
Critical exponent for nonlinear damped wave equations with non-negative potential in 3D
|
We are studying possible interaction of damping coefficients in the
subprincipal part of the linear 3D wave equation and their impact on the
critical exponent of the corresponding nonlinear Cauchy problem with small
initial data. The main new phenomena is that certain relation between these
coefficients may cause very strong jump of the critical Strauss exponent in 3D
to the critical 5D Strauss exponent for the wave equation without damping
coefficients.
|
1810.05956v1
|
2018-10-23
|
Perfect absorption of water waves by linear or nonlinear critical coupling
|
We report on experiments of perfect absorption for surface gravity waves
impinging a wall structured by a subwavelength resonator. By tuning the
geometry of the resonator, a balance is achieved between the radiation damping
and the intrinsic viscous damping, resulting in perfect absorption by critical
coupling. Besides, it is shown that the resistance of the resonator, hence the
intrinsic damping, can be controlled by the wave amplitude, which provides a
way for perfect absorption tuned by nonlinear mechanisms. The perfect absorber
that we propose, without moving parts or added material, is simple, robust and
it presents a deeply subwavelength ratio wavelength/size $\simeq 18$.
|
1810.09884v1
|
2018-12-16
|
Damping of sound waves by bulk viscosity in reacting gases
|
The very long standing problem of sound waves propagation in fluids is
reexamined. In particular, from the analysis of the wave damping in reacting
gases following the work of Einsten \citep{Ein}, it is found that the damping
due to the chemical reactions occurs nonetheless the second (bulk) viscosity
introduced by Landau \& Lifshitz \citep{LL86} is zero. The simple but important
case of a recombining Hydrogen plasma is examined.
|
1812.06478v1
|
2019-02-27
|
Forward Discretely Self-Similar Solutions of the MHD Equations and the Viscoelastic Navier-Stokes Equations with Damping
|
In this paper, we prove the existence of forward discretely self-similar
solutions to the MHD equations and the viscoelastic Navier-Stokes equations
with damping with large weak $L^3$ initial data. The same proving techniques
are also applied to construct self-similar solutions to the MHD equations and
the viscoelastic Navier-Stokes equations with damping with large weak $L^3$
initial data. This approach is based on [Z. Bradshaw and T.-P. Tsai, Ann. Henri
Poincar'{e}, vol. 18, no. 3, 1095-1119, 2017].
|
1902.10771v3
|
2019-03-11
|
The effect of magnetic twist on resonant absorption of slow sausage waves in magnetic flux tubes
|
Observations show that twisted magnetic flux tubes are present throughout the
sun's atmosphere. The main aim of this work is to obtain the damping rate of
sausage modes in the presence of magnetic twist. Using the connection formulae
obtained by Sakurai et al. (1991), we investigate resonant absorption of the
sausage modes in the slow continuum under photosphere conditions. We derive the
dispersion relation and solve it numerically and consequently obtain the
frequencies and damping rates of the slow surface sausage modes. We conclude
that the magnetic twist can result in strong damping in comparison with the
untwisted case.
|
1903.04171v1
|
2019-03-14
|
Endpoint Strichartz estimate for the damped wave equation and its application
|
Recently, the Strichartz estimates for the damped wave equation was obtained
by the first author except for the wave endpoint case. In the present paper, we
give the Strichartz estimate in the wave endpoint case. We slightly modify the
argument of Keel--Tao. Moreover, we apply the endpoint Strichartz estimate to
the unconditional uniqueness for the energy critical nonlinear damped wave
equation. This problem seems not to be solvable as the perturbation of the wave
equation.
|
1903.05891v2
|
2019-04-02
|
Linear inviscid damping in Gevrey spaces
|
We prove linear inviscid damping near a general class of monotone shear flows
in a finite channel, in Gevrey spaces. It is an essential step towards proving
nonlinear inviscid damping for general shear flows that are not close to the
Couette flow, which is a major open problem in 2d Euler equations.
|
1904.01188v2
|
2019-04-16
|
Damping modes of harmonic oscillator in open quantum systems
|
Through a set of generators that preserves the hermiticity and trace of
density matrices, we analyze the damping of harmonic oscillator in open quantum
systems into four modes, distinguished by their specific effects on the
covariance matrix of position and momentum of the oscillator. The damping modes
could either cause exponential decay to the initial covariance matrix or shift
its components. They have to act together properly in actual dynamics to ensure
that the generalized uncertainty relation is satisfied. We use a few quantum
master equations to illustrate the results.
|
1904.07452v2
|
2019-05-20
|
Stabilization of two strongly coupled hyperbolic equations in exterior domains
|
In this paper we study the behavior of the total energy and the $L^2$-norm of
solutions of two coupled hyperbolic equations by velocities in exterior
domains. Only one of the two equations is directly damped by a localized
damping term. We show that, when the damping set contains the coupling one and
the coupling term is effective at infinity and on captive region, then the
total energy decays uniformly and the $L^2$-norm of smooth solutions is
bounded. In the case of two Klein-Gordon equations with equal speeds we deduce
an exponential decay of the energy.
|
1905.08370v1
|
2019-06-02
|
Mixed control of vibrational systems
|
We consider new performance measures for vibrational systems based on the
$H_2$ norm of linear time invariant systems. New measures will be used as an
optimization criterion for the optimal damping of vibrational systems. We
consider both theoretical and concrete cases in order to show how new measures
stack up against the standard measures. The quality and advantages of new
measures as well as the behaviour of optimal damping positions and
corresponding damping viscosities are illustrated in numerical experiments.
|
1906.00503v1
|
2019-06-27
|
Comments on the linear modified Poisson-Boltzmann equation in electrolyte solution theory
|
Three analytic results are proposed for a linear form of the modified
Poisson-Boltzmann equation in the theory of bulk electrolytes. Comparison is
also made with the mean spherical approximation results. The linear theories
predict a transition of the mean electrostatic potential from a
Debye-H\"{u}ckel type damped exponential to a damped oscillatory behaviour as
the electrolyte concentration increases beyond a critical value. The screening
length decreases with increasing concentration when the mean electrostatic
potential is damped oscillatory. A comparison is made with one set of recent
experimental screening results for aqueous NaCl electrolytes.
|
1906.11584v1
|
2019-09-19
|
Growth rate and gain of stimulated Brillouin scattering considering nonlinear Landau damping due to particle trapping
|
Growth rate and gain of SBS considering the reduced Landau damping due to
particle trapping has been proposed to predict the growth and average level of
SBS reflectivity. Due to particle trapping, the reduced Landau damping has been
taken used of to calculate the gain of SBS, which will make the simulation data
of SBS average reflectivity be consistent to the Tang model better. This work
will solve the pending questions in laser-plasma interaction and have wide
applications in parametric instabilities.
|
1909.11606v1
|
2019-11-26
|
Pullback Attractors for a Critical Degenerate Wave Equation with Time-dependent Damping
|
The aim of this paper is to analyze the long-time dynamical behavior of the
solution for a degenerate wave equation with time-dependent damping term
$\partial_{tt}u + \beta(t)\partial_tu = \mathcal{L}u(x,t) + f(u)$ on a bounded
domain $\Omega\subset\mathbb{R}^N$ with Dirichlet boundary conditions. Under
some restrictions on $\beta(t)$ and critical growth restrictions on the
nonlinear term $f$, we will prove the local and global well-posedness of the
solution and derive the existence of a pullback attractor for the process
associated with the degenerate damped hyperbolic problem.
|
1911.11432v1
|
2019-12-18
|
Blow-up criteria for linearly damped nonlinear Schrödinger equations
|
We consider the Cauchy problem for linearly damped nonlinear Schr\"odinger
equations
\[ i\partial_t u + \Delta u + i a u= \pm |u|^\alpha u, \quad (t,x) \in
[0,\infty) \times \mathbb{R}^N, \] where $a>0$ and $\alpha>0$. We prove the
global existence and scattering for a sufficiently large damping parameter in
the energy-critical case. We also prove the existence of finite time blow-up
$H^1$ solutions to the focusing problem in the mass-critical and
mass-supercritical cases.
|
1912.08752v2
|
2020-01-17
|
Bounding the Classical Capacity of Multilevel Damping Quantum Channels
|
A recent method to certify the classical capacity of quantum communication
channels is applied for general damping channels in finite dimension. The
method compares the mutual information obtained by coding on the computational
and a Fourier basis, which can be obtained by just two local measurement
settings and classical optimization. The results for large representative
classes of different damping structures are presented.
|
2001.06486v2
|
2020-01-27
|
Robustness of polynomial stability of damped wave equations
|
In this paper we present new results on the preservation of polynomial
stability of damped wave equations under addition of perturbing terms. We in
particular introduce sufficient conditions for the stability of perturbed
two-dimensional wave equations on rectangular domains, a one-dimensional weakly
damped Webster's equation, and a wave equation with an acoustic boundary
condition. In the case of Webster's equation, we use our results to compute
explicit numerical bounds that guarantee the polynomial stability of the
perturbed equation.
|
2001.10033v3
|
2020-02-09
|
Fujita modified exponent for scale invariant damped semilinear wave equations
|
The aim of this paper is to prove a blow up result of the solution for a
semilinear scale invariant damped wave equation under a suitable decay
condition on radial initial data. The admissible range for the power of the
nonlinear term depends both on the damping coefficient and on the pointwise
decay order of the initial data. In addition we give an upper bound estimate
for the lifespan of the solution, in terms of the power of the nonlinearity,
size and growth of initial data.
|
2002.03418v2
|
2020-02-16
|
Blow up results for semi-linear structural damped wave model with nonlinear memory
|
This article is to study the nonexistence of global solutions to semi-linear
structurally damped wave equation with nonlinear memory in $\R^n$ for any space
dimensions $n\ge 1$ and for the initial arbitrarily small data being subject to
the positivity assumption. We intend to apply the method of a modified test
function to establish blow-up results and to overcome some difficulties as well
caused by the well-known fractional Laplacian $(-\Delta)^{\sigma/2}$ in
structural damping terms.
|
2002.06582v1
|
2020-03-04
|
Existence and uniqueness of solutions to the damped Navier-Stokes equations with Navier boundary conditions for three dimensional incompressible fluid
|
In this article, we study the solutions of the damped Navier--Stokes equation
with Navier boundary condition in a bounded domain $\Omega$ in $\mathbb{R}^3$
with smooth boundary. The existence of the solutions is global with the damped
term $\vartheta |u|^{\beta-1}u, \vartheta >0.$ The regularity and uniqueness of
solutions with Navier boundary condition is also studied. This extends the
existing results in literature.
|
2003.01903v1
|
2020-04-22
|
Logarithmic stabilization of an acoustic system with a damping term of Brinkman type
|
We study the problem of stabilization for the acoustic system with a
spatially distributed damping. Without imposing any hypotheses on the
structural properties of the damping term, we identify logarithmic decay of
solutions with growing time. Logarithmic decay rate is shown by using a
frequency domain method and combines a contradiction argument with the
multiplier technique and a new Carleman estimate to carry out a special
analysis for the resolvent.
|
2004.10669v1
|
2020-05-24
|
A transmission problem for the Timoshenko system with one local Kelvin-Voigt damping and non-smooth coefficient at the interface
|
In this paper, we study the indirect stability of Timoshenko system with
local or global Kelvin-Voigt damping, under fully Dirichlet or mixed boundary
conditions. Unlike the results of H. L. Zhao, K. S. Liu, and C. G. Zhang and of
X. Tian and Q. Zhang, in this paper, we consider the Timoshenko system with
only one locally or globally distributed Kelvin-Voigt damping. Indeed, we prove
that the energy of the system decays polynomially and that the obtained decay
rate is in some sense optimal. The method is based on the frequency domain
approach combining with multiplier method.
|
2005.12756v1
|
2020-06-09
|
Lifespan of solutions to a damped fourth-order wave equation with logarithmic nonlinearity
|
This paper is devoted to the lifespan of solutions to a damped fourth-order
wave equation with logarithmic nonlinearity $$u_{tt}+\Delta^2u-\Delta
u-\omega\Delta u_t+\alpha(t)u_t=|u|^{p-2}u\ln|u|.$$ Finite time blow-up
criteria for solutions at both lower and high initial energy levels are
established, and an upper bound for the blow-up time is given for each case.
Moreover, by constructing a new auxiliary functional and making full use of the
strong damping term, a lower bound for the blow-up time is also derived.
|
2006.05006v1
|
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