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2017-03-10
|
Negative Landau damping in bilayer graphene
|
We theoretically demonstrate that a system formed by two coupled graphene
sheets enables a negative damping regime wherein graphene plasmons are pumped
by a DC current. This effect is triggered by electrons drifting through one of
the graphene sheets and leads to the spontaneous light emission (spasing) and
wave instabilities in the mid-infrared range. It is shown that there is a deep
link between the drift-induced instabilities and wave instabilities in moving
media, as both result from the hybridization of oscillators with oppositely
signed frequencies. With a thickness of few nanometers and wide spectral
tunability, the proposed structure may find interesting applications in
nanophotonic circuitry as an on-chip light source.
|
1703.03623v1
|
2017-03-10
|
Effects on the CMB from magnetic field dissipation before recombination
|
Magnetic fields present before decoupling are damped due to radiative
viscosity. This energy injection affects the thermal and ionization history of
the cosmic plasma. The implications for the CMB anisotropies and polarization
are investigated for different parameter choices of a non helical stochastic
magnetic field. Assuming a Gaussian smoothing scale determined by the magnetic
damping wave number at recombination it is found that magnetic fields with
present day strength less than 0.1 nG and negative magnetic spectral indices
have a sizeable effect on the CMB temperature anisotropies and polarization.
|
1703.03650v1
|
2017-03-28
|
(1+1) Newton-Hooke Group for the Simple and Damped Harmonic Oscillator
|
It is demonstrated that, in the framework of the orbit method, a simple and
damped harmonic oscillators are indistinguishable at the level of an abstract
Lie algebra. This opens a possibility for treating the dissipative systems
within the orbit method. In depth analysis of the coadjoint orbits of the
$(1+1)$ dimensional Newton-Hooke group are presented. Further, it is argued
that the physical interpretation is carried by a specific realisation of the
Lie algebra of smooth functions on a phase space rather than by an abstract Lie
algebra.
|
1703.09583v2
|
2017-04-09
|
Controllability of the Strongly Damped Impulsive Semilinear Wave Equation with Memory and Delay
|
This article is devoted to study the interior approximated controllability of
the strongly damped semilinear wave equation with memory, impulses and delay
terms. The problem is challenging since the state equation contains memory and
impulsive terms yielding to potential unbounded control sequences steering the
system to a neighborhood of the final state, thus fixed point theorems cannot
be used directly. As alternative, the A.E Bashirov and et al. techniques are
applied and together with the delay allow the control solution to be directed
to fixed curve in a short time interval and achieve our result.
|
1704.02561v1
|
2017-04-12
|
Damping parametric instabilities in future gravitational wave detectors by means of electrostatic actuators
|
It has been suggested that the next generation of interferometric
gravitational wave detectors may observe spontaneously excited parametric
oscillatory instabilities. We present a method of actively suppressing any such
instability through application of electrostatic forces to the interferometers'
test masses. Using numerical methods we quantify the actuation force required
to damp candidate instabilities and find that such forces are readily
achievable. Our predictions are subsequently verified experimentally using
prototype Advanced LIGO hardware, conclusively demonstrating the effectiveness
of our approach.
|
1704.03587v1
|
2017-04-28
|
Cross-damping effects in 1S-3S spectroscopy of hydrogen and deuterium
|
We calculate the cross-damping frequency shift of a laser-induced two-photon
transition monitored through decay fluorescence, by adapting the analogy with
Raman scattering developed by Amaro et al. [P. Amaro et al., PRA 92, 022514
(2015)]. We apply this method to estimate the frequency shift of the 1S-3S
transition in hydrogen and deuterium. Taking into account our experimental
conditions, we find a frequency shift of less than 1 kHz, that is smaller than
our current statistical uncertainty.
|
1704.09003v1
|
2017-05-15
|
Damping self-forces and Asymptotic Symmetries
|
Energy conservation in radiating processes requires, at the classical level,
to take into account damping forces on the sources. These forces can be
represented in terms of asymptotic data and lead to charges defined as
integrals over the asymptotic boundary. For scattering processes these charges,
in case of zero radiated energy, are conserved and encode the information about
the sub-leading soft theorems and matching conditions. The QED version of the
self forces is associated with the dependence of the differential cross section
on the infrared resolution scale.
|
1705.05297v2
|
2017-05-17
|
Exact Model Reduction for Damped-Forced Nonlinear Beams: An Infinite-Dimensional Analysis
|
We use invariant manifold results on Banach spaces to conclude the existence
of spectral submanifolds (SSMs) in a class of nonlinear, externally forced beam
oscillations. SSMs are the smoothest nonlinear extensions of spectral subspaces
of the linearized beam equation. Reduction of the governing PDE to SSMs
provides an explicit low-dimensional model which captures the correct
asymptotics of the full, infinite-dimensional dynamics. Our approach is general
enough to admit extensions to other types of continuum vibrations. The
model-reduction procedure we employ also gives guidelines for a mathematically
self-consistent modeling of damping in PDEs describing structural vibrations.
|
1705.06133v1
|
2017-06-26
|
Weighted energy estimates for wave equation with space-dependent damping term for slowly decaying initial data
|
This paper is concerned with weighted energy estimates for solutions to wave
equation $\partial_t^2u-\Delta u + a(x)\partial_tu=0$ with space-dependent
damping term $a(x)=|x|^{-\alpha}$ $(\alpha\in [0,1))$ in an exterior domain
$\Omega$ having a smooth boundary. The main result asserts that the weighted
energy estimates with weight function like polymonials are given and these
decay rate are almost sharp, even when the initial data do not have compact
support in $\Omega$. The crucial idea is to use special solution of $\partial_t
u=|x|^{\alpha}\Delta u$ including Kummer's confluent hypergeometric functions.
|
1706.08311v1
|
2017-08-09
|
Global well-posedness for the 2D Boussinesq equations with a velocity damping term
|
In this paper, we prove global well-posedness of smooth solutions to the
two-dimensional incompressible Boussinesq equations with only a velocity
damping term when the initial data is close to an nontrivial equilibrium state
$(0,x_2)$. As a by-product, under this equilibrium state, our result gives a
positive answer to the question proposed by [ACWX] (see P.3597).
|
1708.02695v4
|
2017-08-18
|
Second sound in systems of one-dimensional fermions
|
We study sound in Galilean invariant systems of one-dimensional fermions. At
low temperatures, we find a broad range of frequencies in which in addition to
the waves of density there is a second sound corresponding to ballistic
propagation of heat in the system. The damping of the second sound mode is
weak, provided the frequency is large compared to a relaxation rate that is
exponentially small at low temperatures. At lower frequencies the second sound
mode is damped, and the propagation of heat is diffusive.
|
1708.05733v2
|
2017-08-21
|
Equilibrium of a Brownian particle with coordinate dependent diffusivity and damping: Generalized Boltzmann distribution
|
Fick's law for coordinate dependent diffusivity is derived. Corresponding
diffusion current in the presence of coordinate dependent diffusivity is
consistent with the form as given by Kramers-Moyal expansion. We have obtained
the equilibrium solution of the corresponding Smoluchowski equation. The
equilibrium distribution is a generalization of the Boltzmann distribution.
This generalized Boltzmann distribution involves an effective potential which
is a function of coordinate dependent diffusivity. We discuss various
implications of the existence of this generalized Boltzmann distribution for
equilibrium of systems with coordinate dependent diffusivity and damping.
|
1708.06132v5
|
2017-08-21
|
Global small solutions of 3D incompressible Oldroyd-B model without damping mechanism
|
In this paper, we prove the global existence of small smooth solutions to the
three-dimensional incompressible Oldroyd-B model without damping on the stress
tensor. The main difficulty is the lack of full dissipation in stress tensor.
To overcome it, we construct some time-weighted energies based on the special
coupled structure of system. Such type energies show the partial dissipation of
stress tensor and the strongly full dissipation of velocity. In the view of
treating "nonlinear term" as a "linear term", we also apply this result to 3D
incompressible viscoelastic system with Hookean elasticity and then prove the
global existence of small solutions without the physical assumption (div-curl
structure) as previous works.
|
1708.06172v2
|
2017-10-13
|
$L^2$ asymptotic profiles of solutions to linear damped wave equations
|
In this paper we obtain higher order asymptotic profilles of solutions to the
Cauchy problem of the linear damped wave equation in $\textbf{R}^n$
\begin{equation*} u_{tt}-\Delta u+u_t=0, \qquad u(0,x)=u_0(x), \quad
u_t(0,x)=u_1(x), \end{equation*} where $n\in\textbf{N}$ and $u_0$, $u_1\in
L^2(\textbf{R}^n)$. Established hyperbolic part of asymptotic expansion seems
to be new in the sense that the order of the expansion of the hyperbolic part
depends on the spatial dimension.
|
1710.04870v1
|
2017-11-06
|
Linear inviscid damping and enhanced dissipation for the Kolmogorov flow
|
In this paper, we prove the linear inviscid damping and voticity depletion
phenomena for the linearized Euler equations around the Kolmogorov flow. These
results confirm Bouchet and Morita's predictions based on numerical analysis.
By using the wave operator method introduced by Li, Wei and Zhang, we solve
Beck and Wayne's conjecture on the optimal enhanced dissipation rate for the
2-D linearized Navier-Stokes equations around the bar state called Kolmogorov
flow. The same dissipation rate is proved for the Navier-Stokes equations if
the initial velocity is included in a basin of attraction of the Kolmogorov
flow with the size of $\nu^{\frac 23+}$, here $\nu$ is the viscosity
coefficient.
|
1711.01822v1
|
2017-11-27
|
Statistical mechanics of Landau damping
|
Landau damping is the tendency of solutions to the Vlasov equation towards
spatially homogeneous distribution functions. The distribution functions
however approach the spatially homogeneous manifold only weakly, and Boltzmann
entropy is not changed by Vlasov equation. On the other hand, density and
kinetic energy density, which are integrals of the distribution function,
approach spatially homogeneous states strongly, which is accompanied by growth
of the hydrodynamic entropy. Such a behavior can be seen when Vlasov equation
is reduced to the evolution equations for density and kinetic energy density by
means of the Ehrenfest reduction.
|
1711.10022v1
|
2017-11-29
|
Lepton-portal Dark Matter in Hidden Valley model and the DAMPE recent results
|
We study the recent $e^\pm$ cosmic ray excess reported by DAMPE in a Hidden
Valley Model with lepton-portal dark matter. We find the electron-portal can
account for the excess well and satisfy the DM relic density and direct
detection bounds, while electron+muon/electron+muon+tau-portal suffers from
strong constraints from lepton flavor violating observables, such as $\mu \to 3
e$. We also discuss possible collider signatures of our model, both at the LHC
and a future 100 TeV hadron collider.
|
1711.11058v3
|
2017-11-30
|
Radiative Dirac neutrino mass, DAMPE dark matter and leptogenesis
|
We explain the electron-positron excess reported by the DAMPE collaboration
recently in a radiative Dirac seesaw model where a dark $U(1)_X$ gauge symmetry
can (i) forbid the tree-level Yukawa couplings of three right-handed neutrinos
to the standard model lepton and Higgs doublets, (ii) predict the existence of
three dark fermions for the gauge anomaly cancellation, (iii) mediate a
testable scattering of the lightest dark fermion off the nucleons. Our model
can also accommodate a successful leptogenesis to generate the cosmic baryon
asymmetry.
|
1711.11333v2
|
2017-12-13
|
Sub-logistic source can prevent blow-up in the 2D minimal Keller-Segel chemotaxis system
|
It is well-known that the Neumann initial-boundary value problem for the
minimal-chemotaxis-logistic system in a 2D bounded smooth domain has no blow-up
for any choice of parameters. Here, for a large class of kinetic terms
including sub-logistic sources, we show that the corresponding 2D Neumann
initial-boundary value problems do not possess any blow-up. This illustrates a
new phenomenon that even a class of sub-logistic sources can prevent blow-up
for the 2D problem, indicating that logistic damping is not the weakest damping
to guarantee uniform-in-time boundedness for the 2D minimal Keller-Segel
chemotaxis model.
|
1712.04739v1
|
2017-12-16
|
Convergence to Equilibrium in Wasserstein distance for damped Euler equations with interaction forces
|
We develop tools to construct Lyapunov functionals on the space of
probability measures in order to investigate the convergence to global
equilibrium of a damped Euler system under the influence of external and
interaction potential forces with respect to the 2-Wasserstein distance. We
also discuss the overdamped limit to a nonlocal equation used in the modelling
of granular media with respect to the 2-Wasserstein distance, and provide
rigorous proofs for particular examples in one spatial dimension.
|
1712.05923v2
|
2017-12-27
|
Normal-mode-based analysis of electron plasma waves with second-order Hermitian formalism
|
The classic problem of the dynamic evolution of Langmuir electron waves in a
collisionless plasma and their Landau damping is cast as a second-order,
self-adjoint problem with a continuum spectrum of real and positive squared
frequencies. The corresponding complete basis of singular normal modes is
obtained, along with their orthogonality relation. This yields easily the
general expression of the time-reversal-invariant solution for any
initial-value problem. An example is given for a specific initial condition
that illustrates the Landau damping of the macroscopic moments of the
perturbation.
|
1712.09682v1
|
2018-01-19
|
Discontinuous energy shaping control of the Chaplygin sleigh
|
In this paper we present an energy shaping control law for set-point
regulation of the Chaplygin sleigh. It is well known that nonholonomic
mechanical systems cannot be asymptotically stabilised using smooth control
laws as they do no satisfy Brockett's necessary condition for smooth
stabilisation. Here, we propose a discontinuous control law that can be seen as
a potential energy shaping and damping injection controller. The proposed
controller is shown to be robust against the parameters of both the inertia
matrix and the damping structure of the open-loop system.
|
1801.06278v1
|
2018-01-19
|
Robust integral action of port-Hamiltonian systems
|
Interconnection and damping assignment, passivity-based control (IDA-PBC) has
proven to be a successful control technique for the stabilisation of many
nonlinear systems. In this paper, we propose a method to robustify a system
which has been stabilised using IDA-PBC with respect to constant, matched
disturbances via the addition of integral action. The proposed controller
extends previous work on the topic by being robust against the damping of the
system, a quantity which may not be known in many applications.
|
1801.06279v1
|
2018-01-19
|
A study of Landau damping with random initial inputs
|
For the Vlasov-Poisson equation with random uncertain initial data, we prove
that the Landau damping solution given by the deterministic counterpart
(Caglioti and Maffei, {\it J. Stat. Phys.}, 92:301-323, 1998) depends smoothly
on the random variable if the time asymptotic profile does, under the
smoothness and smallness assumptions similar to the deterministic case. The
main idea is to generalize the deterministic contraction argument to more
complicated function spaces to estimate derivatives in space, velocity and
random variables. This result suggests that the random space regularity can
persist in long-time even in time-reversible nonlinear kinetic equations.
|
1801.06304v1
|
2018-01-31
|
Smoluchowski-Kramers approximation for the damped stochastic wave equation with multiplicative noise in any spatial dimension
|
We show that the solutions to the damped stochastic wave equation converge
pathwise to the solution of a stochastic heat equation. This is called the
Smoluchowski-Kramers approximation. Cerrai and Freidlin have previously
demonstrated that this result holds in the cases where the system is exposed to
additive noise in any spatial dimension or when the system is exposed to
multiplicative noise and the spatial dimension is one. The current paper proves
that the Smoluchowski-Kramers approximation is valid in any spatial dimension
when the system is exposed to multiplicative noise.
|
1801.10538v1
|
2018-02-26
|
Controllability and observability for non-autonomous evolution equations: the averaged Hautus test
|
We consider the observability problem for non-autonomous evolution systems
(i.e., the operators governing the system depend on time). We introduce an
averaged Hautus condition and prove that for skew-adjoint operators it
characterizes exact observability. Next, we extend this to more general class
of operators under a growth condition on the associated evolution family. We
give an application to the Schr\"odinger equation with time dependent potential
and the damped wave equation with a time dependent damping coefficient.
|
1802.09224v1
|
2018-02-28
|
Global-in-time Stability of 2D MHD boundary Layer in the Prandtl-Hartmann Regime
|
In this paper, we prove global existence of solutions with analytic
regularity to the 2D MHD boundary layer equations in the mixed Prandtl and
Hartmann regime derived by formal multi-scale expansion in \cite{GP}. The
analysis shows that the combined effect of the magnetic diffusivity and
transveral magnetic field on the boundary leads to a linear damping on the
tangential velocity field near the boundary. And this damping effect yields the
global in time analytic norm estimate in the tangential space variable on the
perturbation of the classical steady Hartmann profile.
|
1802.10494v3
|
2018-02-28
|
Modal approach to the controllability problem of distributed parameter systems with damping
|
This paper is devoted to the controllability analysis of a class of linear
control systems in a Hilbert space. It is proposed to use the minimum energy
controls of a reduced lumped parameter system for solving the infinite
dimensional steering problem approximately. Sufficient conditions of the
approximate controllability are formulated for a modal representation of a
flexible structure with small damping.
|
1803.00129v1
|
2018-03-14
|
Study of Quantum Walk over a Square Lattice
|
Quantum random walk finds application in efficient quantum algorithms as well
as in quantum network theory. Here we study the mixing time of a discrete
quantum walk over a square lattice in presence percolation and decoherence. We
consider bit-flip and phase damping noise, and evaluate the instantaneous
mixing time for both the cases. Using numerical analysis we show that in case
of phase damping noise probability distribution of walker's position is
sufficiently close to the uniform distribution after infinite time. However,
during the action of bit-flip noise, even after infinite time the total
variation distance between the two probability distributions is large enough.
|
1803.05152v1
|
2018-03-15
|
Improving the capacity of quantum dense coding by weak measurement and reversal measurement
|
A protocol of quantum dense coding protection of two qubits is proposed in
amplitude damping (AD) channel using weak measurement and reversal measurement.
It is found that the capacity of quantum dense coding under the weak
measurement and reversal measurement is always greater than that without weak
measurement and reversal measurement. When the protocol is applied, for the AD
channels with different damping coefficient, the result reflects that quantum
entanglement can be protected and quantum dense coding becomes successful.
|
1803.05678v1
|
2018-04-10
|
Motion of a superconducting loop in an inhomogeneous magnetic field: a didactic experiment
|
We present an experiment conductive to an understanding of both Faraday's law
and the properties of the superconducting state. It consists in the analysis of
the motion of a superconducting loop moving under the influence of gravity in
an inhomogeneous horizontal magnetic field. Gravity, conservation of magnetic
flux, and friction combine to give damped harmonic oscillations. The measured
frequency of oscillation and the damping constant as a function of the magnetic
field strength (the only free parameter) are in good agreement with the
theoretical model.
|
1804.03553v1
|
2018-05-08
|
Optomechanical damping as the origin of sideband asymmetry
|
Sideband asymmetry in cavity optomechanics has been explained by particle
creation and annihilation processes, which bestow an amplitude proportional to
'n+1' and 'n' excitations to each of the respective sidebands. We discuss the
issues with this as well as other interpretations, such as quantum backaction
and noise interference, and show that the asymmetry is due to the
optomechanical damping caused by the probe and the cooling lasers instead.
|
1805.02952v4
|
2018-05-11
|
On the asymptotic stability of stratified solutions for the 2D Boussinesq equations with a velocity damping term
|
We consider the 2D Boussinesq equations with a velocity damping term in a
strip $\mathbb{T}\times[-1,1]$, with impermeable walls. In this physical
scenario, where the \textit{Boussinesq approximation} is accurate when
density/temperature variations are small, our main result is the asymptotic
stability for a specific type of perturbations of a stratified solution. To
prove this result, we use a suitably weighted energy space combined with linear
decay, Duhamel's formula and "bootstrap" arguments.
|
1805.05179v2
|
2018-06-30
|
A linearized and conservative Fourier pseudo-spectral method for the damped nonlinear Schrödinger equation in three dimensions
|
In this paper, we propose a linearized Fourier pseudo-spectral method, which
preserves the total mass and energy conservation laws, for the damped nonlinear
Schr\"{o}dinger equation in three dimensions. With the aid of the semi-norm
equivalence between the Fourier pseudo-spectral method and the finite
difference method, an optimal $L^2$-error estimate for the proposed method
without any restriction on the grid ratio is established by analyzing the real
and imaginary parts of the error function. Numerical results are addressed to
confirm our theoretical analysis.
|
1807.00091v3
|
2018-07-11
|
Global existence and blow-up for semilinear damped wave equations in three space dimensions
|
We consider initial value problem for semilinear damped wave equations in
three space dimensions. We show the small data global existence for the problem
without the spherically symmetric assumption and obtain the sharp lifespan of
the solutions. This paper is devoted to a proof of the Takamura's conjecture on
the lifespan of solutions.
|
1807.04327v3
|
2018-07-18
|
B-field induced mixing between Langmuir waves and axions
|
We present an analytic study of the dispersion relation for an isotropic
magnetized plasma interacting with axions. We provide a quantitative picture of
the electromagnetic plasma oscillations in both the ultrarelativistic and
nonrelativistic regimes and considering both non-degenerate and degenerate
media, accounting for the dispersion curves as a function of the plasma
temperature and the ratio of the plasma phase velocity to the characteristic
velocity of particles. We include the modifications on the Landau damping of
plasma waves induced by the presence of the axion field, and we comment on the
effects of damping on subluminal plasma oscillations.
|
1807.06828v2
|
2018-07-26
|
Moment conditions and lower bounds in expanding solutions of wave equations with double damping terms
|
In this report we obtain higher order asymptotic expansions of solutions to
wave equations with frictional and viscoelastic damping terms. Although the
diffusion phenomena are dominant, differences between the solutions we deal
with and those of heat equations can be seen by comparing the second order
expansions of them. In order to analyze such effects we consider the weighted
L1 initial data. We also give some lower bounds which show the optimality of
obtained expansions.
|
1807.10020v1
|
2018-08-16
|
Continuity of the set equilibria of non-autonomous damped wave equations with terms concentrating on the boundary
|
In this paper we are interested in the behavior of the solutions of
non-autonomous damped wave equations when some reaction terms are concentrated
in a neighborhood of the boundary and this neighborhood shrinks to boundary as
a parameter \varepsilon goes to zero. We prove the conti- nuity of the set
equilibria of these equations. Moreover, if an equilibrium solution of the
limit problem is hyperbolic, then we show that the per- turbed equation has one
and only one equilibrium solution nearby.
|
1808.05667v1
|
2018-08-30
|
Protecting temporal correlations of two-qubit states using quantum channels with memory
|
Quantum temporal correlations exhibited by violations of Leggett-Garg
Inequality (LGI) and Temporal Steering Inequality (TSI) are in general found to
be non-increasing under decoherence channels when probed on two-qubit pure
entangled states. We study the action of decoherence channels, such as
amplitude damping, phase-damping and depolarising channels when partial memory
is introduced in a way such that two consecutive uses of the channels are
time-correlated. We show that temporal correlations demonstrated by violations
of the above temporal inequalities can be protected against decoherence using
the effect of memory.
|
1808.10345v1
|
2018-09-17
|
Global existence for weakly coupled systems of semi-linear structurally damped $σ$-evolution models with different power nonlinearities
|
In this paper, we study the Cauchy problems for weakly coupled systems of
semi-linear structurally damped $\sigma$-evolution models with different power
nonlinearities. By assuming additional $L^m$ regularity on the initial data,
with $m \in [1,2)$, we use $(L^m \cap L^2)- L^2$ and $L^2- L^2$ estimates for
solutions to the corresponding linear Cauchy problems to prove the global (in
time) existence of small data Sobolev solutions to the weakly coupled systems
of semi-linear models from suitable function spaces.
|
1809.06744v2
|
2018-09-25
|
On the energy decay rates for the 1D damped fractional Klein-Gordon equation
|
We consider the fractional Klein-Gordon equation in one spatial dimension,
subjected to a damping coefficient, which is non-trivial and periodic, or more
generally strictly positive on a periodic set. We show that the energy of the
solution decays at the polynomial rate $O(t^{-\frac{s}{4-2s}})$ for $0< s<2 $
and at some exponential rate when $s\geq 2$. Our approach is based on the
asymptotic theory of $C_0$ semigroups in which one can relate the decay rate of
the energy in terms of the resolvent growth of the semigroup generator. The
main technical result is a new observability estimate for the fractional
Laplacian, which may be of independent interest.
|
1809.09531v1
|
2018-10-15
|
Global well-posedness in the critical Besov spaces for the incompressible Oldroyd-B model without damping mechanism
|
We prove the global well-posedness in the critical Besov spaces for the
incompressible Oldroyd-B model without damping mechanism on the stress tensor
in $\mathbb{R}^d$ for the small initial data. Our proof is based on the
observation that the behaviors of Green's matrix to the system of
$\big(u,(-\Delta)^{-\frac12}\mathbb{P}\nabla\cdot\tau\big)$ as well as the
effects of $\tau$ change from the low frequencies to the high frequencies and
the construction of the appropriate energies in different frequencies.
|
1810.06171v1
|
2018-10-18
|
Global solutions to the $n$-dimensional incompressible Oldroyd-B model without damping mechanism
|
The present work is dedicated to the global solutions to the incompressible
Oldroyd-B model without damping on the stress tensor in $\mathbb{R}^n(n=2,3)$.
This result allows to construct global solutions for a class of highly
oscillating initial velocity. The proof uses the special structure of the
system. Moreover, our theorem extends the previous result by Zhu [19] and
covers the recent result by Chen and Hao [4].
|
1810.08048v3
|
2018-10-30
|
Global well-posedness for nonlinear wave equations with supercritical source and damping terms
|
We prove the global well-posedness of weak solutions for nonlinear wave
equations with supercritical source and damping terms on a three-dimensional
torus $\mathbb T^3$ of the prototype \begin{align*} &u_{tt}-\Delta
u+|u_t|^{m-1}u_t=|u|^{p-1}u, \;\; (x,t) \in \mathbb T^3 \times \mathbb R^+ ;
\notag\\ &u(0)=u_0 \in H^1(\mathbb T^3)\cap L^{m+1}(\mathbb T^3), \;\;
u_t(0)=u_1\in L^2(\mathbb T^3), \end{align*} where $1\leq p\leq \min\{
\frac{2}{3} m + \frac{5}{3} , m \}$. Notably, $p$ is allowed to be larger than
$6$.
|
1810.12476v1
|
2018-11-02
|
Nonlinear Damped Timoshenko Systems with Second Sound - Global Existence and Exponential Stability
|
In this paper, we consider nonlinear thermoelastic systems of Timoshenko type
in a one-dimensional bounded domain. The system has two dissipative mechanisms
being present in the equation for transverse displacement and rotation angle -
a frictional damping and a dissipation through hyperbolic heat conduction
modelled by Cattaneo's law, respectively. The global existence of small, smooth
solutions and the exponential stability in linear and nonlinear cases are
established.
|
1811.01128v1
|
2018-11-14
|
Quantum witness of a damped qubit with generalized measurements
|
We evaluate the quantum witness based on the no-signaling-in-time condition
of a damped two-level system for nonselective generalized measurements of
varying strength. We explicitly compute its dependence on the measurement
strength for a generic example. We find a vanishing derivative for weak
measurements and an infinite derivative in the limit of projective
measurements. The quantum witness is hence mostly insensitive to the strength
of the measurement in the weak measurement regime and displays a singular,
extremely sensitive dependence for strong measurements. We finally relate this
behavior to that of the measurement disturbance defined in terms of the
fidelity between pre-measurement and post-measurement states.
|
1811.06013v1
|
2018-12-11
|
Blow up of solutions to semilinear non-autonomous wave equations under Robin boundary conditions
|
The problem of blow up of solutions to the initial boundary value problem for
non-autonomous semilinear wave equation with damping and accelerating terms
under the Robin boundary condition is studied. Sufficient conditions of blow up
in a finite time of solutions to semilinear damped wave equations with
arbitrary large initial energy are obtained. A result on blow up of solutions
with negative initial energy of semilinear second order wave equation with
accelerating term is also obtained.
|
1812.04595v1
|
2018-12-23
|
Global existence of weak solutions for strongly damped wave equations with nonlinear boundary conditions and balanced potentials
|
We demonstrate the global existence of weak solutions to a class of
semilinear strongly damped wave equations possessing nonlinear hyperbolic
dynamic boundary conditions. Our work assumes $(-\Delta_W)^\theta \partial_tu$
with $\theta\in[\frac{1}{2},1)$ and where $\Delta_W$ is the Wentzell-Laplacian.
Hence, the associated linear operator admits a compact resolvent. A balance
condition is assumed to hold between the nonlinearity defined on the interior
of the domain and the nonlinearity on the boundary. This allows for arbitrary
(supercritical) polynomial growth on each potential, as well as mixed
dissipative/anti-dissipative behavior. Moreover, the nonlinear function defined
on the interior of the domain is assumed to be only $C^0$.
|
1812.09781v1
|
2018-12-24
|
Cold Damping of an Optically Levitated Nanoparticle to micro-Kelvin Temperatures
|
We implement a cold damping scheme to cool one mode of the center-of-mass
motion of an optically levitated nanoparticle in ultrahigh vacuum from room
temperature to a record-low temperature of 100 micro-Kelvin. The measured
temperature dependence on feedback gain and thermal decoherence rate is in
excellent agreement with a parameter-free model. We determine the
imprecision-backaction product for our system and provide a roadmap towards
ground-state cooling of optically levitated nanoparticles.
|
1812.09875v1
|
2019-01-18
|
Decay of semilinear damped wave equations:cases without geometric control condition
|
We consider the semilinear damped wave equation $\partial_{tt}^2
u(x,t)+\gamma(x)\partial_t u(x,t)=\Delta u(x,t)-\alpha u(x,t)-f(x,u(x,t))$. In
this article, we obtain the first results concerning the stabilization of this
semilinear equation in cases where $\gamma$ does not satisfy the geometric
control condition. When some of the geodesic rays are trapped, the
stabilization of the linear semigroup is semi-uniform in the sense that
$\|e^{At}A^{-1}\|\leq h(t)$ for some function $h$ with $h(t)\rightarrow 0$ when
$t\rightarrow +\infty$. We provide general tools to deal with the semilinear
stabilization problem in the case where $h(t)$ has a sufficiently fast decay.
|
1901.06169v1
|
2019-02-04
|
Non-Markovian Effects on Overdamped Systems
|
We study the consequences of adopting the memory dependent, non-Markovian,
physics with the memory-less over-damped approximation usually employed to
investigate Brownian particles. Due to the finite correlation time scale
associated with the noise, the stationary behavior of the system is not
described by the Boltzmann-Gibbs statistics. However, the presence of a very
weak external white noise can be used to regularize the equilibrium properties.
Surprisingly, the coupling to another bath effectively restores the dynamical
aspects missed by the over-damped treatment.
|
1902.01356v1
|
2019-02-06
|
Stability analysis of a 1D wave equation with a nonmonotone distributed damping
|
This paper is concerned with the asymptotic stability analysis of a one
dimensional wave equation subject to a nonmonotone distributed damping. A
well-posedness result is provided together with a precise characterization of
the asymptotic behavior of the trajectories of the system under consideration.
The well-posedness is proved in the nonstandard L p functional spaces, with p
$\in$ [2, $\infty$], and relies mostly on some results collected in Haraux
(2009). The asymptotic behavior analysis is based on an attractivity result on
a specific infinite-dimensional linear time-variant system.
|
1902.02050v1
|
2019-02-13
|
Comment on "Quantization of the damped harmonic oscillator" [Serhan et al, J. Math. Phys. 59, 082105 (2018)]
|
A recent paper [J. Math. Phys. {\bf 59}, 082105 (2018)] constructs a
Hamiltonian for the (dissipative) damped harmonic oscillator. We point out that
non-Hermiticity of this Hamiltonian has been ignored to find real discrete
eigenvalues which are actually non-real. We emphasize that non-Hermiticity in
Hamiltonian is crucial and it is a quantal signature of dissipation.
|
1902.04895v1
|
2019-02-15
|
Memory effects teleportation of quantum Fisher information under decoherence
|
We have investigated how memory effects on the teleportation of quantum
Fisher information(QFI) for a single qubit system using a class of X-states as
resources influenced by decoherence channels with memory, including amplitude
damping, phase-damping and depolarizing channels. Resort to the definition of
QFI, we first derive the explicit analytical results of teleportation of QFI
with respect to weight parameter $\theta$ and phase parameter $\phi$ under the
decoherence channels. Component percentages, the teleportation of QFI for a
two-qubit entanglement system has also been addressed. The remarkable
similarities and differences among these two situations are also analyzed in
detail and some significant results are presented.
|
1902.05668v1
|
2019-02-23
|
Uniform decay rates for a suspension bridge with locally distributed nonlinear damping
|
We study a nonlocal evolution equation modeling the deformation of a bridge,
either a footbridge or a suspension bridge. Contrarily to the previous
literature we prove the asymptotic stability of the considered model with a
minimum amount of damping which represents less cost of material. The result is
also numerically proved.
|
1902.09963v1
|
2019-03-01
|
Spectra of the Dissipative Spin Chain
|
This paper generalizes the (0+1)-dimensional spin-boson problem to the
corresponding (1+1)-dimensional version. Monte Carlo simulation is used to find
the phase diagram and imaginary time correlation function. The real frequency
spectrum is recovered by the newly developed P\'ade regression analytic
continuation method. We find that, as dissipation strength $\alpha$ is
increased, the sharp quasi-particle spectrum is broadened and the peak
frequency is lower. According to the behavior of the low frequency spectrum, we
classify the dynamical phase into three different regions: weakly damped,
linear $k$-edge, and strongly damped.
|
1903.00567v1
|
2019-03-17
|
Sensing Kondo correlations in a suspended carbon nanotube mechanical resonator with spin-orbit coupling
|
We study electron mechanical coupling in a suspended carbon nanotube (CNT)
quantum dot device. Electron spin couples to the flexural vibration mode due to
spin-orbit coupling in the electron tunneling processes. In the weak coupling
limit, i.e. electron-vibration coupling is much smaller than the electron
energy scale, the damping and resonant frequency shift of the CNT resonator can
be obtained by calculating the dynamical spin susceptibility. We find that
strong spin-flip scattering processes in Kondo regime significantly affect the
mechanical motion of the carbon nanotube: Kondo effect induces strong damping
and frequency shift of the CNT resonator.
|
1903.07049v1
|
2019-03-27
|
Lifespan of semilinear generalized Tricomi equation with Strauss type exponent
|
In this paper, we consider the blow-up problem of semilinear generalized
Tricomi equation. Two blow-up results with lifespan upper bound are obtained
under subcritical and critical Strauss type exponent. In the subcritical case,
the proof is based on the test function method and the iteration argument. In
the critical case, an iteration procedure with the slicing method is employed.
This approach has been successfully applied to the critical case of semilinear
wave equation with perturbed Laplacian or the damped wave equation of
scattering damping case. The present work gives its application to the
generalized Tricomi equation.
|
1903.11351v2
|
2019-04-01
|
A remark on semi-linear damped $σ$-evolution equations with a modulus of continuity term in nonlinearity
|
In this article, we indicate that under suitable assumptions of a modulus of
continuity we obtain either the global (in time) existence of small data
Sobolev solutions or the blow-up result of local (in time) Sobolev solutions to
semi-linear damped $\sigma$-evolution equations with a modulus of continuity
term in nonlinearity.
|
1904.00698v3
|
2019-04-05
|
Critical regularity of nonlinearities in semilinear classical damped wave equations
|
In this paper we consider the Cauchy problem for the semilinear damped wave
equation
$u_{tt}-\Delta u + u_t = h(u);\qquad u(0;x) = f(x); \quad u_t(0;x) = g(x);$
where $h(s) = |s|^{1+2/n}\mu(|s|)$. Here n is the space dimension and $\mu$
is a modulus of continuity. Our goal is to obtain sharp conditions on $\mu$ to
obtain a threshold between global (in time) existence of small data solutions
(stability of the zerosolution) and blow-up behavior even of small data
solutions.
|
1904.02939v1
|
2019-04-29
|
Origin of the DAMPE 1.4 TeV peak
|
Recent accurate measurements of cosmic ray electron flux by the Dark Matter
Particle Explorer (DAMPE) reveal a sharp peak structure near 1.4 TeV, which is
difficult to explain by standard astrophysical processes. In this letter, we
propose a simple model that the enhanced dark matter annihilation via the
$e^+e^-$ channel and with the thermal relic annihilation cross section around
the current nearest black hole (A0620-00) can satisfactorily account for the
sharp peak structure. The predicted dark matter mass is $\sim 1.5-3$ TeV.
|
1904.12418v1
|
2019-05-07
|
Decay estimate for the solution of the evolutionary damped $p$-Laplace equation
|
In this note, we study the asymptotic behavior, as $t$ tends to infinity, of
the solution $u$ to the evolutionary damped $p$-Laplace equation
\begin{equation*}
u_{tt}+a\, u_t =\Delta_p u \end{equation*}
with Dirichlet boundary values. Let $u^*$ denote the stationary solution with
same boundary values, then the $W^{1,p}$-norm of $u(t) - u^{*}$ decays for
large $t$ like $t^{-\frac{1}{(p-1)p}}$, in the degenerate case $ p > 2$.
|
1905.03597v2
|
2019-05-10
|
Asymptotic profiles for damped plate equations with rotational inertia terms
|
We consider the Cauchy problem for plate equations with rotational inertia
and frictional damping terms. We will derive asymptotic profiles of the
solution in L^2-sense as time goes to infinity in the case when the initial
data have high and low regularity, respectively. Especially, in the low
regularity case of the initial data one encounters the regularity-loss
structure of the solutions, and the analysis is more delicate. We employ the
so-called Fourier splitting method combined with the explicit expression of the
solutions (high frequency estimates) and the method due to Ikehata (low
frequency estimates).
|
1905.04012v1
|
2019-05-20
|
Small perturbations for a Duffing-like evolution equation involving non-commuting operators
|
We consider an abstract evolution equation with linear damping, a nonlinear
term of Duffing type, and a small forcing term. The abstract problem is
inspired by some models for damped oscillations of a beam subject to external
loads or magnetic fields, and shaken by a transversal force.
The main feature is that very natural choices of the boundary conditions lead
to equations whose linear part involves two operators that do not commute.
We extend to this setting the results that are known in the commutative case,
namely that for asymptotically small forcing terms all solutions are eventually
close to the three equilibrium points of the unforced equation, two stable and
one unstable.
|
1905.07942v1
|
2019-05-30
|
A study of coherence based measure of quantumness in (non) Markovian channels
|
We make a detailed analysis of quantumness for various quantum noise
channels, both Markovian and non-Markovian. The noise channels considered
include dephasing channels like random telegraph noise, non-Markovian dephasing
and phase damping, as well as the non-dephasing channels such as generalized
amplitude damping and Unruh channels. We make use of a recently introduced
witness for quantumness based on the square $l_1$ norm of coherence. It is
found that the increase in the degree of non-Markovianity increases the
quantumness of the channel.
|
1905.12872v1
|
2019-05-30
|
Stabilization for vibrating plate with singular structural damping
|
We consider the dynamic elasticity equation, modeled by the Euler-Bernoulli
plate equation, with a locally distributed singular structural (or viscoelastic
) damping in a boundary domain. Using a frequency domain method combined, based
on the Burq's result, combined with an estimate of Carleman type we provide
precise decay estimate showing that the energy of the system decays
logarithmically as the type goes to the infinity.
|
1905.13089v1
|
2019-06-12
|
A no-go result for the quantum damped harmonic oscillator
|
In this letter we show that it is not possible to set up a canonical
quantization for the damped harmonic oscillator using the Bateman lagrangian.
In particular, we prove that no square integrable vacuum exists for the {\em
natural} ladder operators of the system, and that the only vacua can be found
as distributions. This implies that the procedure proposed by some authors is
only formally correct, and requires a much deeper analysis to be made rigorous.
|
1906.05121v2
|
2019-06-26
|
Mismatched Estimation of Polynomially Damped Signals
|
In this work, we consider the problem of estimating the parameters of
polynomially damped sinusoidal signals, commonly encountered in, for instance,
spectroscopy. Generally, finding the parameter values of such signals
constitutes a high-dimensional problem, often further complicated by not
knowing the number of signal components or their specific signal structures. In
order to alleviate the computational burden, we herein propose a mismatched
estimation procedure using simplified, approximate signal models. Despite the
approximation, we show that such a procedure is expected to yield predictable
results, allowing for statistically and computationally efficient estimates of
the signal parameters.
|
1906.11113v1
|
2019-06-27
|
Temperature-Dependent Lifetimes of Low-Frequency Adsorbate Modes from Non-Equilibrium Molecular Dynamics Simulations
|
We present calculations on the damping of a low-frequency adsorbate mode on a
metal surface, namely the frustrated translation of Na on Cu(100). For the
first time, vibrational lifetimes of excited adlayers are extracted from
non-equilibrium molecular dynamics calculations accounting for both the
phononic and the electronic dissipation channels. The relative contributions of
the two damping mechanisms, which we show to be additive, are found to disagree
with textbook predictions. A simple model based on separable harmonic and
anharmonic contributions is able to semi-quantitatively reproduce the
temperature dependence of the computed lifetimes.
|
1906.11776v1
|
2019-07-10
|
Formal expansions in stochastic model for wave turbulence 1: kinetic limit
|
We consider the damped/driver (modified) cubic NLS equation on a large torus
with a properly scaled forcing and dissipation, and decompose its solutions to
formal series in the amplitude. We study the second order truncation of this
series and prove that when the amplitude goes to zero and the torus' size goes
to infinity the energy spectrum of the truncated solutions becomes close to a
solution of the damped/driven wave kinetic equation. Next we discuss higher
order truncations of the series.
|
1907.04531v4
|
2019-07-22
|
Thresholds for low regularity solutions to wave equations with structural damping
|
We study the asymptotic behavior of solutions to wave equations with a
structural damping term \[ u_{tt}-\Delta u+\Delta^2 u_t=0, \qquad
u(0,x)=u_0(x), \,\,\, u_t(0,x)=u_1(x), \] in the whole space. New thresholds
are reported in this paper that indicate which of the diffusion wave property
and the non-diffusive structure dominates in low regularity cases. We develop
to that end the previous author's research in 2019 where they have proposed a
threshold that expresses whether the parabolic-like property or the wave-like
property strongly appears in the solution to some regularity-loss type
dissipative wave equation.
|
1907.09299v1
|
2019-08-03
|
Lindblad dynamics of the damped and forced quantum harmonic oscillator
|
The quantum dynamics of a damped and forced harmonic oscillator is
investigated in terms of a Lindblad master equation. Elementary algebraic
techniques are employed allowing for example to analyze the long time behavior,
i.e. the quantum limit cycle. The time evolution of various expectation values
is obtained in closed form as well as the entropy and the Husimi phase space
distribution. We also discuss the related description in terms of a
non-Hermitian Hamiltonian.
|
1908.01187v2
|
2019-08-07
|
Decay estimates for the linear damped wave equation on the Heisenberg group
|
This paper is devoted to the derivation of $L^2$ - $L^2$ decay estimates for
the solution of the homogeneous linear damped wave equation on the Heisenberg
group $\mathbf{H}_n$, for its time derivative and for its horizontal gradient.
Moreover, we consider the improvement of these estimates when further
$L^1(\mathbf{H}_n)$ regularity is required for the Cauchy data. Our approach
will rely strongly on the group Fourier transform of $\mathbf{H}_n$ and on the
properties of the Hermite functions that form a maximal orthonormal system for
$L^2(\mathbb{R}^n)$ of eigenfunctions of the harmonic oscillator.
|
1908.02657v1
|
2019-08-08
|
Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity
|
In this paper, we consider the Cauchy problem for the semilinear damped wave
equation on the Heisenberg group with power nonlinearity. We prove that the
critical exponent is the Fujita exponent $p_{\mathrm{Fuj}}(\mathscr{Q}) = 1+2 /
\mathscr{Q}$, where $\mathscr{Q}$ is the homogeneous dimension of the
Heisenberg group. On the one hand, we will prove the global existence of small
data solutions for $p >p_{\mathrm{Fuj}}(\mathscr{Q})$ in an exponential
weighted energy space. On the other hand, a blow-up result for $1 < p \leq
p_{\mathrm{Fuj}}(\mathscr{Q})$ under certain integral sign assumptions for the
Cauchy data by using the test function method.
|
1908.02989v1
|
2019-09-01
|
Invariant measures for stochastic damped 2D Euler equations
|
We study the two-dimensional Euler equations, damped by a linear term and
driven by an additive noise. The existence of weak solutions has already been
studied; pathwise uniqueness is known for solutions that have vorticity in
$L^\infty$. In this paper, we prove the Markov property and then the existence
of an invariant measure in the space $L^\infty$ by means of a
Krylov-Bogoliubov's type method, working with the weak$\star$ and the bounded
weak$\star$ topologies in $L^\infty$.
|
1909.00424v2
|
2019-09-03
|
A blow-up result for semi-linear structurally damped $σ$-evolution equations
|
We would like to prove a blow-up result for semi-linear structurally damped
$\sigma$-evolution equations, where $\sigma \ge 1$ and $\delta\in [0,\sigma)$
are assumed to be any fractional numbers. To deal with the fractional Laplacian
operators $(-\Delta)^\sigma$ and $(-\Delta)^\delta$ as well-known non-local
operators, in general, it seems difficult to apply the standard test function
method directly. For this reason, in this paper we shall construct new test
functions to overcome this difficulty.
|
1909.01181v1
|
2019-09-09
|
Action Functional for a Particle with Damping
|
In this brief report we discuss the action functional of a particle with
damping, showing that it can be obtained from the dissipative equation of
motion through a modification which makes the new dissipative equation
invariant for time reversal symmetry. This action functional is exactly the
effective action of Caldeira-Leggett model but, in our approach, it is derived
without the assumption that the particle is weakly coupled to a bath of
infinite harmonic oscillators.
|
1909.03694v2
|
2019-09-11
|
Remark on global existence of solutions to the 1D compressible Euler equation with time-dependent damping
|
In this paper, we consider the 1D compressible Euler equation with the
damping coefficient $\lambda/(1+t)^{\mu}$. Under the assumption that $0\leq \mu
<1$ and $\lambda >0$ or $\mu=1$ and $\lambda > 2$, we prove that solutions
exist globally in time, if initial data are small $C^1$ perturbation near
constant states. In particular, we remove the conditions on the limit
$\lim_{|x| \rightarrow \infty} (u (0,x), v (0,x))$, assumed in previous
results.
|
1909.05683v1
|
2019-09-11
|
Equilibrium radiation in a plasma medium with spatial and frequency dispersion
|
Examination of equilibrium radiation in plasma media shows that the spectral
energy distribution of such radiation is different from the Planck equilibrium
radiation. Using the approach of quantum electrodynamics the general relation
for the spectral energy density of equilibrium radiation in a system of charged
particles is found. The obtained result takes into account the influence of
plasma on equilibrium radiation through the explicit transverse dielectric
permittivity which takes into account spatial and frequency dispersion, as well
as the finite collisional damping. For the limiting case of an infinitesimal
damping the result coincides with the known expression.
|
1909.08056v1
|
2019-10-14
|
Blow-up of solutions to semilinear strongly damped wave equations with different nonlinear terms in an exterior domain
|
In this paper, we consider the initial boundary value problem in an exterior
domain for semilinear strongly damped wave equations with power nonlinear term
of the derivative-type $|u_t|^q$ or the mixed-type $|u|^p+|u_t|^q$, where
$p,q>1$. On one hand, employing the Banach fixed-point theorem we prove local
(in time) existence of mild solutions. On the other hand, under some conditions
for initial data and the exponents of power nonlinear terms, the blow-up
results are derived by applying the test function method.
|
1910.05981v1
|
2019-11-03
|
Linear Inviscid Damping in Sobolev and Gevrey Spaces
|
In a recent article Jia established linear inviscid damping in Gevrey
regularity for compactly supported Gevrey regular shear flows in a finite
channel, which is of great interest in view of existing nonlinear results. In
this article we provide an alternative very short proof of stability in Gevrey
regularity as a consequence of stability in high Sobolev regularity. Here, we
consider both the setting of a finite channel with compactly supported
perturbations and of an infinite channel without this restriction. Furthermore,
we consider the setting where perturbations vanish only of finite order.
|
1911.00880v1
|
2019-11-03
|
A global existence result for two-dimensional semilinear strongly damped wave equation with mixed nonlinearity in an exterior domain
|
We study two-dimensional semilinear strongly damped wave equation with mixed
nonlinearity $|u|^p+|u_t|^q$ in an exterior domain, where $p,q>1$. Assuming the
smallness of initial data in exponentially weighted spaces and some conditions
on powers of nonlinearity, we prove global (in time) existence of small data
energy solution with suitable higher regularity by using a weighted energy
method.
|
1911.00899v1
|
2019-11-05
|
Critical exponent for a weakly coupled system of semi-linear $σ$-evolution equations with frictional damping
|
We are interested in studying the Cauchy problem for a weakly coupled system
of semi-linear $\sigma$-evolution equations with frictional damping. The main
purpose of this paper is two-fold. We would like to not only prove the global
(in time) existence of small data energy solutions but also indicate the
blow-up result for Sobolev solutions when $\sigma$ is assumed to be any
fractional number.
|
1911.01946v1
|
2019-11-11
|
Existence and nonexistence of global solutions for a structurally damped wave system with power nonlinearities
|
Our interest itself of this paper is strongly inspired from an open problem
in the paper [1] published by D'Abbicco. In this article, we would like to
study the Cauchy problem for a weakly coupled system of semi-linear
structurally damped wave equations. Main goal is to find the threshold, which
classifies the global (in time) existence of small data solutions or the
nonexistence of global solutions under the growth condition of the
nonlinearities.
|
1911.04412v1
|
2019-11-15
|
Some $L^1$-$L^1$ estimates for solutions to visco-elastic damped $σ$-evolution models
|
This note is to conclude $L^1-L^1$ estimates for solutions to the following
Cauchy problem for visco-elastic damped $\sigma$-evolution models:
\begin{equation} \begin{cases} u_{tt}+ (-\Delta)^\sigma u+ (-\Delta)^\sigma u_t
= 0, &\quad x\in \mathbb{R}^n,\, t \ge 0, \\ u(0,x)= u_0(x),\quad
u_t(0,x)=u_1(x), &\quad x\in \mathbb{R}^n, \label{pt1.1} \end{cases}
\end{equation} where $\sigma> 1$, in all space dimensions $n\ge 1$.
|
1911.06563v1
|
2019-11-22
|
Long-time asymptotics for a coupled thermoelastic plate-membrane system
|
In this paper we consider a transmission problem for a system of a
thermoelastic plate with (or without) rotational inertia term coupled with a
membrane with different variants of damping for the plate and/or the membrane.
We prove well-posedness of the problem and higher regularity of the solution
and study the asymptotic behaviour of the solution, depending on the damping
and on the presence of the rotational term.
|
1911.10161v1
|
2019-11-28
|
Tikhonov regularization of a second order dynamical system with Hessian driven damping
|
We investigate the asymptotic properties of the trajectories generated by a
second-order dynamical system with Hessian driven damping and a Tikhonov
regularization term in connection with the minimization of a smooth convex
function in Hilbert spaces. We obtain fast convergence results for the function
values along the trajectories. The Tikhonov regularization term enables the
derivation of strong convergence results of the trajectory to the minimizer of
the objective function of minimum norm.
|
1911.12845v2
|
2019-12-15
|
Negative mobility, sliding and delocalization for stochastic networks
|
We consider prototype configurations for quasi-one-dimensional stochastic
networks that exhibit negative mobility, meaning that current decreases or even
reversed as the bias is increased. We then explore the implications of
disorder. In particular we ask whether lower and upper bias thresholds restrict
the possibility to witness non-zero current (sliding and anti-sliding
transitions respectively), and whether a delocalization effect manifest itself
(crossover from over-damped to under-damped relaxation). In the latter context
detailed analysis of the relaxation spectrum as a function of the bias is
provided for both on-chain and off-chain disorder.
|
1912.07059v2
|
2019-12-23
|
On a damped Szego equation (with an appendix in collaboration with Christian Klein)
|
We investigate how damping the lowest Fourier mode modifies the dynamics of
the cubic Szeg{\"o} equation. We show that there is a nonempty open subset of
initial data generating trajec-tories with high Sobolev norms tending to
infinity. In addition, we give a complete picture of this phenomenon on a
reduced phase space of dimension 6. An appendix is devoted to numerical
simulations supporting the generalisation of this picture to more general
initial data.
|
1912.10933v1
|
2020-01-29
|
The long time behavior and the rate of convergence of symplectic convex algorithms obtained via splitting discretizations of inertial damping systems
|
In this paper we propose new numerical algorithms in the setting of
unconstrained optimization problems and we study the rate of convergence in the
iterates of the objective function. Furthermore, our algorithms are based upon
splitting and symplectic methods and they preserve the energy properties of the
inherent continuous dynamical system that contains a Hessian perturbation. At
the same time, we show that Nesterov gradient method is equivalent to a
Lie-Trotter splitting applied to a Hessian driven damping system. Finally, some
numerical experiments are presented in order to validate the theoretical
results.
|
2001.10831v2
|
2020-02-05
|
Long-time asymptotics of the one-dimensional damped nonlinear Klein-Gordon equation
|
For the one-dimensional nonlinear damped Klein-Gordon equation \[
\partial_{t}^{2}u+2\alpha\partial_{t}u-\partial_{x}^{2}u+u-|u|^{p-1}u=0 \quad
\mbox{on $\mathbb{R}\times\mathbb{R}$,}\] with $\alpha>0$ and $p>2$, we prove
that any global finite energy solution either converges to $0$ or behaves
asymptotically as $t\to \infty$ as the sum of $K\geq 1$ decoupled solitary
waves. In the multi-soliton case $K\geq 2$, the solitary waves have alternate
signs and their distances are of order $\log t$.
|
2002.01826v1
|
2020-02-11
|
Distributional Solutions of the Damped Wave Equation
|
This work presents results on solutions of the one-dimensional damped wave
equation, also called telegrapher's equation, when the initial conditions are
general distributions, not only functions. We make a complete deduction of its
fundamental solutions, both for positive and negative times. To obtain them we
use only self-similarity arguments and distributional calculus, making no use
of Fourier or Laplace transforms. We next use these fundamental solutions to
prove both the existence and the uniqueness of solutions to the distributional
initial value problem. As applications we recover the semigroup property for
initial data in classical function spaces and also the probability distribution
function for a certain financial model of evolution of prices.
|
2002.04249v2
|
2020-02-13
|
Description of the wavevector dispersion of surface plasmon-phonon-polaritons
|
We reported here the results of the calculations of wavevector dispersion of
oscillations frequencies, $\omega'(k)$, and damping $\omega''(k)$ of the
surface plasmon phonon polaritons (\mbox{SPPhP}) for the heavy-doped GaN
sample. We showed that $\omega'(k)$- dependence consists of the three branches
with the specific anticrossing behavior due to the interaction of surface
plasmon polariton (SPP) with surface phonon polariton(SPhP). The strong
renormalization of the damping $\omega''(k)$ in the vicinity of the
anticrossing region was found. The obtained dispersions of the $\omega'(k)$ and
$\omega''(k)$ were applied for the analytical analysis of exact electrodynamic
simulation of the resonant behavior of the reflectivity spectrum of the n-GaN
grating.
|
2002.05473v1
|
2020-03-20
|
The Cauchy problem of the semilinear second order evolution equation with fractional Laplacian and damping
|
In the present paper, we prove time decay estimates of solutions in weighted
Sobolev spaces to the second order evolution equation with fractional Laplacian
and damping for data in Besov spaces. Our estimates generalize the estimates
obtained in the previous studies. The second aim of this article is to apply
these estimates to prove small data global well-posedness for the Cauchy
problem of the equation with power nonlinearities. Especially, the estimates
obtained in this paper enable us to treat more general conditions on the
nonlinearities and the spatial dimension than the results in the previous
studies.
|
2003.09239v1
|
2020-03-31
|
Time-Asymptotics of Physical Vacuum Free Boundaries for Compressible Inviscid Flows with Damping
|
In this paper, we prove the leading term of time-asymptotics of the moving
vacuum boundary for compressible inviscid flows with damping to be that for
Barenblatt self-similar solutions to the corresponding porous media equations
obtained by simplifying momentum equations via Darcy's law plus the possible
shift due to the movement of the center of mass, in the one-dimensional and
three-dimensional spherically symmetric motions, respectively. This gives a
complete description of the large time asymptotic behavior of solutions to the
corresponding vacuum free boundary problems. The results obtained in this paper
are the first ones concerning the large time asymptotics of physical vacuum
boundaries for compressible inviscid fluids, to the best of our knowledge.
|
2003.14072v2
|
2020-04-13
|
Landau damping for analytic and Gevrey data
|
In this paper, we give an elementary proof of the nonlinear Landau damping
for the Vlasov-Poisson system near Penrose stable equilibria on the torus
$\mathbb{T}^d \times \mathbb{R}^d$ that was first obtained by Mouhot and
Villani in \cite{MV} for analytic data and subsequently extended by Bedrossian,
Masmoudi, and Mouhot \cite{BMM} for Gevrey-$\gamma$ data,
$\gamma\in(\frac13,1]$. Our proof relies on simple pointwise resolvent
estimates and a standard nonlinear bootstrap analysis, using an ad-hoc family
of analytic and Gevrey-$\gamma$ norms.
|
2004.05979v3
|
2020-04-16
|
Strichartz estimates for mixed homogeneous surfaces in three dimensions
|
We obtain sharp mixed norm Strichartz estimates associated to mixed
homogeneous surfaces in $\mathbb{R}^3$. Both cases with and without a damping
factor are considered. In the case when a damping factor is considered our
results yield a wide generalization of a result of Carbery, Kenig, and Ziesler
[CKZ13]. The approach we use is to first classify all possible singularities
locally, after which one can tackle the problem by appropriately modifying the
methods from the paper of Ginibre and Velo [GV92], and by using the recently
developed methods by Ikromov and M\"uller [IM16].
|
2004.07751v1
|
2020-04-17
|
Critical exponent for semi-linear structurally damped wave equation of derivative type
|
Main purpose of this paper is to study the following semi-linear structurally
damped wave equation with nonlinearity of derivative type: $$u_{tt}- \Delta u+
\mu(-\Delta)^{\sigma/2} u_t= |u_t|^p,\quad u(0,x)= u_0(x),\quad
u_t(0,x)=u_1(x),$$ with $\mu>0$, $n\geq1$, $\sigma \in (0,2]$ and $p>1$. In
particular, we are going to prove the non-existence of global weak solutions by
using a new test function and suitable sign assumptions on the initial data in
both the subcritical case and the critical case.
|
2004.08486v2
|
2020-04-29
|
Exponential decay for damped Klein-Gordon equations on asymptotically cylindrical and conic manifolds
|
We study the decay of the global energy for the damped Klein-Gordon equation
on non-compact manifolds with finitely many cylindrical and subconic ends up to
bounded perturbation. We prove that under the Geometric Control Condition, the
decay is exponential, and that under the weaker Network Control Condition, the
decay is logarithmic, by developing the global Carleman estimate with multiple
weights.
|
2004.13894v2
|
2020-05-06
|
Zero-dimensional models for gravitational and scalar QED decoherence
|
We investigate the dynamics of two quantum mechanical oscillator system-bath
toy models obtained by truncating to zero spatial dimensions linearized gravity
coupled to a massive scalar field and scalar QED. The scalar-gravity toy model
maps onto the phase damped oscillator, while the scalar QED toy model
approximately maps onto an oscillator system subject to two-photon damping. The
toy models provide potentially useful insights into solving for open system
quantum dynamics relevant to the full scalar QED and weak gravitational field
systems, in particular operational probes of the decoherence for initial scalar
field system superposition states.
|
2005.02554v2
|
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