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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
|
2015-04-23
|
Magnetization damping in noncollinear spin valves with antiferromagnetic interlayer couplings
|
We study the magnetic damping in the simplest of synthetic antiferromagnets,
i.e. antiferromagnetically exchange-coupled spin valves in which applied
magnetic fields tune the magnetic configuration to become noncollinear. We
formulate the dynamic exchange of spin currents in a noncollinear texture based
on the spindiffusion theory with quantum mechanical boundary conditions at the
ferrromagnet|normal-metal interfaces and derive the Landau-Lifshitz-Gilbert
equations coupled by the static interlayer non-local and the dynamic exchange
interactions. We predict non-collinearity-induced additional damping that can
be sensitively modulated by an applied magnetic field. The theoretical results
compare favorably with published experiments.
|
1504.06042v1
|
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
|
2016-04-20
|
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
|
2016-05-05
|
Theory of magnon motive force in chiral ferromagnets
|
We predict that magnon motive force can lead to temperature dependent,
nonlinear chiral damping in both conducting and insulating ferromagnets. We
estimate that this damping can significantly influence the motion of skyrmions
and domain walls at finite temperatures. We also find that in systems with low
Gilbert damping moving chiral magnetic textures and resulting magnon motive
forces can induce large spin and energy currents in the transverse direction.
|
1605.01694v2
|
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
|
2016-11-08
|
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
|
2017-11-01
|
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
|
2018-04-19
|
Damping of magnetization dynamics by phonon pumping
|
We theoretically investigate pumping of phonons by the dynamics of a magnetic
film into a non-magnetic contact. The enhanced damping due to the loss of
energy and angular momentum shows interference patterns as a function of
resonance frequency and magnetic film thickness that cannot be described by
viscous ("Gilbert") damping. The phonon pumping depends on magnetization
direction as well as geometrical and material parameters and is observable,
e.g., in thin films of yttrium iron garnet on a thick dielectric substrate.
|
1804.07080v2
|
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
|
2018-06-18
|
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
|
2020-07-05
|
Oscillation of damped second order quasilinear wave equations with mixed arguments
|
Following the previous work [1], we investigate the impact of damping on the
oscillation of smooth solutions to some kind of quasilinear wave equations with
Robin and Dirichlet boundary condition. By using generalized Riccati
transformation and technical inequality method, we give some sufficient
conditions to guarantee the oscillation of all smooth solutions. From the
results, we conclude that positive damping can ``hold back" oscillation. At
last, some examples are presented to confirm our main results.
|
2007.02284v1
|
2020-07-08
|
A competition on blow-up for semilinear wave equations with scale-invariant damping and nonlinear memory term
|
In this paper, we investigate blow-up of solutions to semilinear wave
equations with scale-invariant damping and nonlinear memory term in
$\mathbb{R}^n$, which can be represented by the Riemann-Liouville fractional
integral of order $1-\gamma$ with $\gamma\in(0,1)$. Our main interest is to
study mixed influence from damping term and the memory kernel on blow-up
conditions for the power of nonlinearity, by using test function method or
generalized Kato's type lemma. We find a new competition, particularly for the
small value of $\gamma$, on the blow-up range between the effective case and
the non-effective case.
|
2007.03954v2
|
2020-08-02
|
Quantum capacity analysis of multi-level amplitude damping channels
|
The set of Multi-level Amplitude Damping (MAD) quantum channels is introduced
as a generalization of the standard qubit Amplitude Damping Channel to quantum
systems of finite dimension $d$. In the special case of $d=3$, by exploiting
degradability, data-processing inequalities, and channel isomorphism, we
compute the associated quantum and private classical capacities for a rather
wide class of maps, extending the set of solvable models known so far. We
proceed then to the evaluation of the entanglement assisted, quantum and
classical, capacities.
|
2008.00477v3
|
2020-08-11
|
An inverse spectral problem for a damped wave operator
|
This paper proposes a new and efficient numerical algorithm for recovering
the damping coefficient from the spectrum of a damped wave operator, which is a
classical Borg-Levinson inverse spectral problem. The algorithm is based on
inverting a sequence of trace formulas, which are deduced by a recursive
formula, bridging geometrical and spectrum information explicitly in terms of
Fredholm integral equations. Numerical examples are presented to illustrate the
efficiency of the proposed algorithm.
|
2008.04523v1
|
2020-08-17
|
Asymptotic profiles and singular limits for the viscoelastic damped wave equation with memory of type I
|
In this paper, we are interested in the Cauchy problem for the viscoelastic
damped wave equation with memory of type I. By applying WKB analysis and
Fourier analysis, we explain the memory's influence on dissipative structures
and asymptotic profiles of solutions to the model with weighted $L^1$ initial
data. Furthermore, concerning standard energy and the solution itself, we
establish singular limit relations between the Moore-Gibson-Thompson equation
with memory and the viscoelastic damped wave equation with memory.
|
2008.07151v1
|
2020-08-18
|
A class of Finite difference Methods for solving inhomogeneous damped wave equations
|
In this paper, a class of finite difference numerical techniques is presented
to solve the second-order linear inhomogeneous damped wave equation. The
consistency, stability, and convergences of these numerical schemes are
discussed. The results obtained are compared to the exact solution, ordinary
explicit, implicit finite difference methods, and the fourth-order compact
method (FOCM). The general idea of these methods is developed by using the
C0-semigroups operator theory. We also showed that the stability region for the
explicit finite difference scheme depends on the damping coefficient.
|
2008.08043v2
|
2020-09-10
|
Blow-up results for semilinear damped wave equations in Einstein-de Sitter spacetime
|
We prove by using an iteration argument some blow-up results for a semilinear
damped wave equation in generalized Einstein-de Sitter spacetime with a
time-dependent coefficient for the damping term and power nonlinearity. Then,
we conjecture an expression for the critical exponent due to the main blow-up
results, which is consistent with many special cases of the considered model
and provides a natural generalization of Strauss exponent. In the critical
case, we consider a non-autonomous and parameter-dependent Cauchy problem for a
linear ODE of second-order, whose explicit solutions are determined by means of
special functions' theory.
|
2009.05372v1
|
2020-09-11
|
Asymptotic profiles for a wave equation with parameter dependent logarithmic damping
|
We study a nonlocal wave equation with logarithmic damping which is rather
weak in the low frequency zone as compared with frequently studied strong
damping case. We consider the Cauchy problem for this model in the whole space
and we study the asymptotic profile and optimal estimates of the solutions and
the total energy as time goes to infinity in L^{2}-sense. In that case some
results on hypergeometric functions are useful.
|
2009.06395v1
|
2020-09-17
|
Sensitivity of steady states in a degenerately-damped stochastic Lorenz system
|
We study stability of solutions for a randomly driven and degenerately damped
version of the Lorenz '63 model. Specifically, we prove that when damping is
absent in one of the temperature components, the system possesses a unique
invariant probability measure if and only if noise acts on the convection
variable. On the other hand, if there is a positive growth term on the vertical
temperature profile, we prove that there is no normalizable invariant state.
Our approach relies on the derivation and analysis of non-trivial Lyapunov
functions which ensure positive recurrence or null-recurrence/transience of the
dynamics.
|
2009.08429v1
|
2021-01-23
|
Oscillation time and damping coefficients in a nonlinear pendulum
|
We establish a relationship between the normalized damping coefficients and
the time that takes a nonlinear pendulum to complete one oscillation starting
from an initial position with vanishing velocity. We establish some conditions
on the nonlinear restitution force so that this oscillation time does not
depend monotonically on the viscosity damping coefficient.
|
2101.09400v2
|
2021-02-20
|
Lifespan estimates for semilinear wave equations with space dependent damping and potential
|
In this work, we investigate the influence of general damping and potential
terms on the blow-up and lifespan estimates for energy solutions to power-type
semilinear wave equations. The space-dependent damping and potential functions
are assumed to be critical or short range, spherically symmetric perturbation.
The blow up results and the upper bound of lifespan estimates are obtained by
the so-called test function method. The key ingredient is to construct special
positive solutions to the linear dual problem with the desired asymptotic
behavior, which is reduced, in turn, to constructing solutions to certain
elliptic "eigenvalue" problems.
|
2102.10257v1
|
2021-02-24
|
Attractors for locally damped Bresse systems and a unique continuation property
|
This paper is devoted to Bresse systems, a robust model for circular beams,
given by a set of three coupled wave equations. The main objective is to
establish the existence of global attractors for dynamics of semilinear
problems with localized damping. In order to deal with localized damping a
unique continuation property (UCP) is needed. Therefore we also provide a
suitable UCP for Bresse systems. Our strategy is to set the problem in a
Riemannian geometry framework and see the system as a single equation with
different Riemann metrics. Then we perform Carleman-type estimates to get our
result.
|
2102.12025v1
|
2021-03-09
|
Global weak solution of 3D-NSE with exponential damping
|
In this paper we prove the global existence of incompressible Navier-Stokes
equations with damping $\alpha (e^{\beta |u|^2}-1)u$, where we use Friedrich
method and some new tools. The delicate problem in the construction of a global
solution, is the passage to the limit in exponential nonlinear term. To solve
this problem, we use a polynomial approximation of the damping part and a new
type of interpolation between $L^\infty(\mathbb{R}^+,L^2(\mathbb{R}^3))$ and
the space of functions $f$ such that $(e^{\beta|f|^2}-1)|f|^2\in
L^1(\mathbb{R}^3)$. Fourier analysis and standard techniques are used.
|
2103.05388v1
|
2021-05-03
|
Enhanced and unenhanced dampings of the Kolmogorov flow
|
In the present study, Kolmogorov flow represents the stationary sinusoidal
solution $(\sin y,0)$ to a two-dimensional spatially periodic Navier-Stokes
system, driven by an external force. This system admits the additional
non-stationary solution $(\sin y,0)+e^{-\nu t} (\sin y,0)$, which tends
exponentially to the Kolmogorov flow at the minimum decay rate determined by
the viscosity $\nu$. Enhanced damping or enhanced dissipation of the problem is
obtained by presenting higher decay rate for the difference between a solution
and the non-stationary basic solution. Moreover, for the understanding of the
metastability problem in an explicit manner, a variety of exact solutions are
presented to show enhanced and unenhanced dampings.
|
2105.00730v3
|
2021-05-06
|
On Linear Damping Around Inhomogeneous Stationary States of the Vlasov-HMF Model
|
We study the dynamics of perturbations around an inhomogeneous stationary
state of the Vlasov-HMF (Hamiltonian Mean-Field) model, satisfying a linearized
stability criterion (Penrose criterion). We consider solutions of the
linearized equation around the steady state, and prove the algebraic decay in
time of the Fourier modes of their density. We prove moreover that these
solutions exhibit a scattering behavior to a modified state, implying a linear
Landau damping effect with an algebraic rate of damping.
|
2105.02484v1
|
2021-05-31
|
Blowup of Solutions to a Damped Euler Equation with Homogeneous Three-Point Boundary Condition
|
It has been established that solutions to the inviscid Proudman-Johnson
equation subject to a homogeneous three-point boundary condition can develop
singularities in finite time. In this paper, we consider the possibility of
singularity formation in solutions of the generalized, inviscid
Proudman-Johnson equation with damping subject to the same homogeneous
three-point boundary condition. In particular, we derive conditions the initial
data must satisfy in order for solutions to blowup in finite time with either
bounded or unbounded smooth damping term.
|
2106.00068v1
|
2021-06-16
|
Sharp upper and lower bounds of the attractor dimension for 3D damped Euler-Bardina equations
|
The dependence of the fractal dimension of global attractors for the damped
3D Euler--Bardina equations on the regularization parameter $\alpha>0$ and
Ekman damping coefficient $\gamma>0$ is studied. We present explicit upper
bounds for this dimension for the case of the whole space, periodic boundary
conditions, and the case of bounded domain with Dirichlet boundary conditions.
The sharpness of these estimates when $\alpha\to0$ and $\gamma\to0$ (which
corresponds in the limit to the classical Euler equations) is demonstrated on
the 3D Kolmogorov flows on a torus.
|
2106.09077v1
|
2021-06-23
|
Damping of the Franz-Keldysh oscillations in the presence of disorder
|
Franz-Keldysh oscillations of the optical absorption in the presence of
short-range disorder are studied theoretically. The magnitude of the effect
depends on the relation between the mean-free path in a zero field and the
distance between the turning points in electric field. Damping of the
Franz-Keldysh oscillations by the disorder develops at high absorption
frequency. Effect of damping is amplified by the fact that, that electron and
hole are most sensitive to the disorder near the turning points. This is
because, near the turning points, velocities of electron and hole turn to zero.
|
2106.12691v1
|
2021-06-25
|
Perturbed primal-dual dynamics with damping and time scaling coefficients for affine constrained convex optimization problems
|
In Hilbert space, we propose a family of primal-dual dynamical system for
affine constrained convex optimization problem. Several damping coefficients,
time scaling coefficients, and perturbation terms are thus considered. By
constructing the energy functions, we investigate the convergence rates with
different choices of the damping coefficients and time scaling coefficients.
Our results extend the inertial dynamical approaches for unconstrained convex
optimization problems to affine constrained convex optimization problems.
|
2106.13702v1
|
2021-07-01
|
Event-triggering mechanism to damp the linear wave equation
|
This paper aims at proposing a sufficient matrix inequality condition to
carry out the global exponential stability of the wave equation under an
event-triggering mechanism that updates a damping source term. The damping is
distributed in the whole space but sampled in time. The wellposedness of the
closed-loop event-triggered control system is shown. Furthermore, the avoidance
of Zeno behavior is ensured provided that the initial data are more regular.
The interest of the results is drawn through some numerical simulations.
|
2107.00292v1
|
2022-01-28
|
Quantum metrology with a non-linear kicked Mach-Zehnder interferometer
|
We study the sensitivity of a Mach-Zehnder interferometer that contains in
addition to the phase shifter a non-linear element. By including both elements
in a cavity or a loop that the light transverses many times, a non-linear
kicked version of the interferometer arises. We study its sensitivity as
function of the phase shift, the kicking strength, the maximally reached
average number of photons, and damping due to photon loss for an initial
coherent state. We find that for vanishing damping Heisenberg-limited scaling
of the sensitivity arises if squeezing dominates the total photon number. For
small to moderate damping rates the non-linear kicks can considerably increase
the sensitivity as measured by the quantum Fisher information per unit time.
|
2201.12255v1
|
2022-02-27
|
The time asymptotic expansion for the compressible Euler equations with time-dependent damping
|
In this paper, we study the compressible Euler equations with time-dependent
damping $-\frac{1}{(1+t)^{\lambda}}\rho u$. We propose a time asymptotic
expansion around the self-similar solution of the generalized porous media
equation (GPME) and rigorously justify this expansion as $\lambda \in
(\frac17,1)$. In other word, instead of the self-similar solution of GPME, the
expansion is the best asymptotic profile of the solution to the compressible
Euler equations with time-dependent damping.
|
2202.13385v1
|
2022-03-12
|
Stability for nonlinear wave motions damped by time-dependent frictions
|
We are concerned with the dynamical behavior of solutions to semilinear wave
systems with time-varying damping and nonconvex force potential. Our result
shows that the dynamical behavior of solution is asymptotically stable without
any bifurcation and chaos. And it is a sharp condition on the damping
coefficient for the solution to converge to some equilibrium. To illustrate our
theoretical results, we provide some numerical simulations for dissipative
sine-Gordon equation and dissipative Klein-Gordon equation.
|
2203.06312v1
|
2022-03-30
|
A Toy Model for Damped Water Waves
|
We consider a toy model for a damped water waves system in a domain $\Omega_t
\subset \mathbb{T} \times \mathbb{R}$. The toy model is based on the
paradifferential water waves equation derived in the work of
Alazard-Burq-Zuily. The form of damping we utilize we utilize is a modified
sponge layer proposed for the three-dimensional water waves system by Clamond,
et. al. We show that, in the case of small Cauchy data, solutions to the toy
model exhibit a quadratic lifespan. This is done via proving energy estimates
with the energy being constructed from appropriately chosen vector fields.
|
2203.16645v1
|
2022-05-10
|
Global attractor for the weakly damped forced Kawahara equation on the torus
|
We study the long time behaviour of solutions for the weakly damped forced
Kawahara equation on the torus. More precisely, we prove the existence of a
global attractor in $L^2$, to which as time passes all solutions draw closer.
In fact, we show that the global attractor turns out to lie in a smoother space
$H^2$ and be bounded therein. Further, we give an upper bound of the size of
the attractor in $H^2$ that depends only on the damping parameter and the norm
of the forcing term.
|
2205.04642v1
|
2022-06-07
|
Decay property of solutions to the wave equation with space-dependent damping, absorbing nonlinearity, and polynomially decaying data
|
We study the large time behavior of solutions to the semilinear wave equation
with space-dependent damping and absorbing nonlinearity in the whole space or
exterior domains. Our result shows how the amplitude of the damping
coefficient, the power of the nonlinearity, and the decay rate of the initial
data at the spatial infinity determine the decay rates of the energy and the
$L^2$-norm of the solution. In Appendix, we also give a survey of basic results
on the local and global existence of solutions and the properties of weight
functions used in the energy method.
|
2206.03218v2
|
2022-10-24
|
The time asymptotic expansion for the compressible Euler equations with damping
|
In 1992, Hsiao and Liu \cite{Hsiao-Liu-1} firstly showed that the solution to
the compressible Euler equations with damping time-asymptotically converges to
the diffusion wave $(\bar v, \bar u)$ of the porous media equation. In
\cite{Geng-Huang-Jin-Wu}, we proposed a time-asymptotic expansion around the
diffusion wave $(\bar v, \bar u)$, which is a better asymptotic profile than
$(\bar v, \bar u)$. In this paper, we rigorously justify the time-asymptotic
expansion by the approximate Green function method and the energy estimates.
Moreover, the large time behavior of the solution to compressible Euler
equations with damping is accurately characterized by the time asymptotic
expansion.
|
2210.13157v1
|
2022-12-18
|
Exponential decay of solutions of damped wave equations in one dimensional space in the $L^p$ framework for various boundary conditions
|
We establish the decay of the solutions of the damped wave equations in one
dimensional space for the Dirichlet, Neumann, and dynamic boundary conditions
where the damping coefficient is a function of space and time. The analysis is
based on the study of the corresponding hyperbolic systems associated with the
Riemann invariants. The key ingredient in the study of these systems is the use
of the internal dissipation energy to estimate the difference of solutions with
their mean values in an average sense.
|
2212.09164v1
|
2023-02-09
|
A remark on the logarithmic decay of the damped wave and Schrödinger equations on a compact Riemannian manifold
|
In this paper we consider a compact Riemannian manifold (M, g) of class C 1
$\cap$ W 2,$\infty$ and the damped wave or Schr\"odinger equations on M , under
the action of a damping function a = a(x). We establish the following fact: if
the measure of the set {x $\in$ M ; a(x) = 0} is strictly positive, then the
decay in time of the associated energy is at least logarithmic.
|
2302.04498v1
|
2023-03-02
|
Using vibrating wire in non-linear regime as a thermometer in superfluid $^3$He-B
|
Vibrating wires are common temperature probes in $^3$He experiments. By
measuring mechanical resonance of a wire driven by AC current in magnetic field
one can directly obtain temperature-dependent viscous damping. This is easy to
do in a linear regime where wire velocity is small enough and damping force is
proportional to velocity. At lowest temperatures in superfluid $^3$He-B a
strong non-linear damping appears and linear regime shrinks to a very small
velocity range. Expanding measurements to the non-linear area can significantly
improve sensitivity. In this note I describe some technical details useful for
analyzing such temperature measurements.
|
2303.01189v1
|
2023-04-06
|
A turbulent study for a damped Navier-Stokes equation: turbulence and problems
|
In this article we consider a damped version of the incompressible
Navier-Stokes equations in the whole three-dimensional space with a
divergence-free and time-independent external force. Within the framework of a
well-prepared force and with a particular choice of the damping parameter, when
the Grashof numbers are large enough, we are able to prove some estimates from
below and from above between the fluid characteristic velocity and the energy
dissipation rate according to the Kolmogorov dissipation law. Precisely, our
main contribution concerns the estimate from below which is not often studied
in the existing literature. Moreover, we address some remarks which open the
door to a deep discussion on the validity of this theory of turbulence.
|
2304.03134v1
|
2023-05-03
|
Lyapunov functions for linear damped wave equations in one-dimensional space with dynamic boundary conditions
|
We establish the exponential decay of the solutions of the damped wave
equations in one-dimensional space where the damping coefficient is a
nowhere-vanishing function of space. The considered PDE is associated with
several dynamic boundary conditions, also referred to as Wentzell/Ventzel
boundary conditions in the literature. The analysis is based on the
determination of appropriate Lyapunov functions and some further analysis. This
result is associated with a regulation problem inspired by a real experiment
with a proportional-integral control. Some numerical simulations and additional
results on closed wave equations are also provided.
|
2305.01969v2
|
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