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2009-05-24
|
Computer assisted proof of the existence of homoclinic tangency for the Henon map and for the forced-damped pendulum
|
We present a topological method for the efficient computer assisted
verification of the existence of the homoclinic tangency which unfolds
generically in a one-parameter family of planar maps. The method has been
applied to the Henon map and the forced damped pendulum ODE.
|
0905.3924v1
|
2009-08-15
|
Antigravitation, Dark Energy, Dark Matter - Alternative Solution
|
Collisional damping of gravitational waves in the Newtonian matter is
investigated. The generalized theory of Landau damping is applied to the
gravitational physical systems in the context of the plasma gravitational
analogy.
|
0908.2180v3
|
2009-08-31
|
A comment about the existence of a weak solution for a non linear wave equation damped propagation
|
We give a proof for the existence of a weak solution on the initial-value
problem of a non-linear damped propagation
|
0909.0052v2
|
2009-09-15
|
Quantum Parrondo's games under decoherence
|
We study the effect of quantum noise on history dependent quantum Parrondo's
games by taking into account different noise channels. Our calculations show
that entanglement can play a crucial role in quantum Parrondo's games. It is
seen that for the maximally entangled initial state in the presence of
decoherence, the quantum phases strongly influence the payoffs for various
sequences of the game. The effect of amplitude damping channel leads to winning
payoffs. Whereas the depolarizing and phase damping channels lead to the losing
payoffs. In case of amplitude damping channel, the payoffs are enhanced in the
presence of decoherence for the sequence AAB. This is because the quantum
phases interfere constructively which leads to the quantum enhancement of the
payoffs in comparison to the undecohered case. It is also seen that the quantum
phase angles damp the payoffs significantly in the presence of decoherence.
Furthermore, it is seen that for multiple games of sequence AAB, under the
influence of amplitude damping channel, the game still remains a winning game.
However, the quantum enhancement reduces in comparison to the single game of
sequence AAB because of the destructive interference of phase dependent terms.
In case of depolarizing channel, the game becomes a loosing game. It is seen
that for the game sequence B the game is loosing one and the behavior of
sequences B and BB is similar for amplitude damping and depolarizing channels.
In addition, the repeated games of A are only influenced by the amplitude
damping channel and the game remains a losing game. Furthermore, it is also
seen that for any sequence when played in series, the phase damping channel
does not influence the game.
|
0909.2897v2
|
2009-10-01
|
Global attractor for weakly damped Nonlinear Schrödinger equations in $L^2(\R)$
|
We prove that the weakly damped nonlinear Schr\"odinger flow in
$L^2(\mathbb{R})$ provides a dynamical system which possesses a global
attractor. The proof relies on the continuity of the Schr\"odinger flow for the
weak topology in $L^2(\R)$.
|
0910.0172v1
|
2009-12-11
|
Waves, damped wave and observation
|
We consider the wave equation in a bounded domain (eventually convex). Two
kinds of inequality are described when occurs trapped ray. Applications to
control theory are given. First, we link such kind of estimate with the damped
wave equation and its decay rate. Next, we describe the design of an
approximate control function by an iterative time reversal method.
|
0912.2202v1
|
2010-01-01
|
Exponential Energy Decay for Damped Klein-Gordon Equation with Nonlinearities of Arbitrary Growth
|
We derive a uniform exponential decay of the total energy for the nonlinear
Klein-Gordon equation with a damping around spatial infinity in the whole space
or in the exterior of a star shaped obstacle.
|
1001.0209v1
|
2010-03-10
|
Covariant Constitutive Relations, Landau Damping and Non-stationary Inhomogeneous Plasmas
|
Models of covariant linear electromagnetic constitutive relations are
formulated that have wide applicability to the computation of susceptibility
tensors for dispersive and inhomogeneous media. A perturbative framework is
used to derive a linear constitutive relation for a globally neutral plasma
enabling one to describe in this context a generalized Landau damping mechanism
for non-stationary inhomogeneous plasma states.
|
1003.2062v1
|
2010-06-16
|
Hysteresis effects in Bose-Einstein condensates
|
Here, we consider damped two-components Bose-Einstein condensates with
many-body interactions. We show that, when the external trapping potential has
a double-well shape and when the nonlinear coupling factors are modulated in
time, hysteresis effects may appear under some circumstances. Such hysteresis
phenomena are a result of the joint contribution between the appearance of
saddle node bifurcations and damping effect.
|
1006.3240v1
|
2010-09-25
|
Different Network Topologies for Distributed Electric Damping of Beam Vibrations
|
In this work passive electric damping of structural vibrations by distributed
piezoelectric transducers and electric networks is analyzed. Different
distributed electric controllers are examined as finite degrees of freedom
systems and their performances are compared. Modal reduction is used to
optimize the electric parameters
|
1009.5001v1
|
2010-12-27
|
The Relativistic kinetics of gravitational waves collisional damping in hot Universe
|
The article is a translation of authors paper printed earlier in the
inaccessible edition and summarizing the results of research of gravitational
waves damping problem in the cosmologic plasma due to the different
interactions of elementary particles.
|
1012.5582v1
|
2011-01-14
|
Blowup for the Damped $L^{2}$-Critical Nonlinear Schrödinger Equation
|
We consider the Cauchy problem for the $L^{2}$-critical damped nonlinear
Schr\"odinger equation. We prove existence and stability of finite time blowup
dynamics with the log-log blow-up speed for $\|\nabla u(t)\|_{L^2}$.
|
1101.2763v3
|
2011-02-05
|
Partial regularity of weak solutions of the viscoelastic Navier-Stokes equations with damping
|
We prove an analog of the Caffarelli-Kohn-Nirenberg theorem for weak
solutions of a system of PDE that model a viscoelastic fluid in the presence of
an energy damping mechanism. The system was recently introduced as a possible
method of establishing the global in time existence of weak solutions of the
well known Oldroyd system.
|
1102.1112v1
|
2011-02-21
|
The One Dimensional Damped Forced Harmonic Oscillator Revisited
|
In this paper we give a general solution to the problem of the damped
harmonic oscillator under the influence of an arbitrary time-dependent external
force. We employ simple methods accessible for beginners and useful for
undergraduate students and professors in an introductory course of mechanics.
|
1102.4112v1
|
2011-03-18
|
Soliton complexity in the damped-driven nonlinear Schrödinger equation: stationary, periodic, quasiperiodic complexes
|
Stationary and oscillatory bound states, or complexes, of the damped-driven
solitons are numerically path-followed in the parameter space. We compile a
chart of the two-soliton attractors, complementing the one-soliton attractor
chart.
|
1103.3607v1
|
2011-09-27
|
Exponential energy decay of solutions for a system of viscoelastic wave equations of Kirchhoff type with strong damping
|
The initial boundary value problem for a system of viscoelastic wave
equations of Kirchhoff type with strong damping is considered. We prove that,
under suitable assumptions on relaxation functions and certain initial data,
the decay rate of the solutions energy is exponential.
|
1109.5921v1
|
2011-12-04
|
On the Apparent Superluminal Motion of a Damped Gaussian Pulse
|
Alicki has demonstrated that a travelling Gaussian pulse subject to damping
is indistinguishable from an undamped pulse moving with greater speed; such an
effect could create the illusion of a pulse moving faster than light. In this
note, an alternative derivation of the same result is presented. However, it is
unlikely that this particular illusion could explain the superluminal
neutrino-velocities reported by OPERA.
|
1112.1324v1
|
2011-12-28
|
Photon Damping in One-Loop HTL Perturbation Theory
|
We determine the damping rates of slow-moving photons in next-to-leading
order hard-thermal-loop perturbation of massless QED. We find both longitudinal
and transverse rates finite, positive, and equal at zero momentum. Various
divergences, light-cone and at specific momenta, but not infrared, appear and
cancel systematically.
|
1112.6065v2
|
2012-04-06
|
Late time evolution of the gravitational wave damping in the early Universe
|
An analytical solution for time evolution of the gravitational wave damping
in the early Universe due to freely streaming neutrinos is found in the late
time regime. The solution is represented by a convergent series of spherical
Bessel functions of even order and was possible with the help of a new compact
formula for the convolution of spherical Bessel functions of integer order.
|
1204.1384v2
|
2012-05-30
|
Beam Dynamics Studies for the CLIC Main Linac
|
The implications of long-range wakefields on the beam quality are
investigated through a detailed beam dynamics study. Injection offsets are
considered and the resulting emittance dilution recorded, including systematic
sources of error. These simulations have been conducted for damped and detuned
structures (DDS) and for waveguide damped structures-both for the CLIC
collider.
|
1205.6623v2
|
2012-07-31
|
Energy decay rates for solutions of the wave equations with nonlinear damping in exterior domain
|
In this paper we study the behaviors of the energy of solutions of the wave
equations with localized nonlinear damping in exterior domains.
|
1207.7336v3
|
2012-11-02
|
A modified test function method for damped waves
|
In this paper we use a modified test function method to derive nonexistence
results for the semilinear wave equation with time-dependent speed and damping.
The obtained critical exponent is the same exponent of some recent results on
global existence of small data solution.
|
1211.0453v1
|
2012-12-15
|
Damping and Pseudo-fermions
|
After a short abstract introduction on the time evolution driven by non
self-adjoint hamiltonians, we show how the recently introduced concept of {\em
pseudo-fermion} can be used in the description of damping in finite dimensional
quantum systems, and we compare the results deduced adopting the Schr\"odinger
and the Heisenberg representations.
|
1212.3663v1
|
2013-01-14
|
On estimating the output entropy of a tensor product of the quantum phase-damping channel with an arbitrary channel
|
We obtained the estimation from below for the output entropy of a tensor
product of the quantum phase-damping channel with an arbitrary channel. It is
shown that from this estimation immediately follows that the strong
superadditivity of the output entropy holds for this channel as well as for the
quantum depolarizing channel.
|
1301.2886v1
|
2013-06-10
|
Smooth attractors for the quintic wave equations with fractional damping
|
Dissipative wave equations with critical quintic nonlinearity and damping
term involving the fractional Laplacian are considered. The additional
regularity of energy solutions is established by constructing the new
Lyapunov-type functional and based on this, the global well-posedness and
dissipativity of the energy solutions as well as the existence of a smooth
global and exponential attractors of finite Hausdorff and fractal dimension is
verified.
|
1306.2294v1
|
2013-07-20
|
Entanglement-assisted capacities of time-correlated amplitude-damping channel
|
We calculate the information capacities of a time-correlated
amplitude-damping channel, provided the sender and receiver share prior
entanglement. Our analytical results show that the noisy channel with zero
capacity can transmit information if it has finite memory. The capacities
increase as the memory increases attaining maximum value for perfect memory
channel.
|
1307.5403v1
|
2013-07-23
|
Comment on Damping Force in the Transit-time Method of Optical Stochastic Cooling
|
In this brief report we pointed at mistake in paper A. Zholents, Damping
Force in the Transit-Time Method of Optical Stochastic Cooling, PRLST. Mar 1,
2012. 2 pp. Published in Phys.Rev.ST Accel. Beams 15 (2012) 032801.
|
1307.6185v1
|
2013-08-23
|
Stability results for second-order evolution equations with switching time-delay
|
We consider second-order evolution equations in an abstract setting with
intermittently delayed/ not-delayed damping. We give sufficient conditions for
asymptotic and exponential stability, improving and generalising our previous
results from [19]. In particular, under suitable conditions, we can consider
unbounded damping operators. Some concrete examples are finally presented.
|
1308.5100v1
|
2013-09-10
|
Convergence of global solutions for some classes of nonlinear damped wave equations
|
We consider the asymptotic behavior of the soltion to the wave equation with
time-dependent damping and analytic nonlinearity. Our main goal is to prove the
convergence of a global solution to an equilibrium as time goes to infinity by
means of a suitable Lojasiewicz-Simon type inequality.
|
1309.2364v1
|
2013-09-13
|
On diffusion phenomena for the linear wave equation with space-dependent damping
|
In this paper, we prove the diffusion phenomenon for the linear wave equation
with space-dependent damping. We prove that the asymptotic profile of the
solution is given by a solution of the corresponding heat equation in the
$L^2$-sense.
|
1309.3377v1
|
2013-10-28
|
Large deviations for a damped telegraph process
|
In this paper we consider a slight generalization of the damped telegraph
process in Di Crescenzo and Martinucci (2010). We prove a large deviation
principle for this process and an asymptotic result for its level crossing
probabilities (as the level goes to infinity). Finally we compare our results
with the analogous well-known results for the standard telegraph process.
|
1310.7332v1
|
2013-10-29
|
Blow-up for the wave equation with nonlinear source and boundary damping terms
|
The paper deals with blow--up for the solutions of wave equation with
nonlinear source and nonlinear boudary damping terms, posed in a bounded and
regular domain. The initial data are posed in the energy space. The aim of the
paper is to improve previous blow-up results concerning the problem.
|
1310.7734v1
|
2013-11-24
|
Global small solution to the 2D MHD system with a velocity damping term
|
This paper studies the global well-posedness of the incompressible
magnetohydrodynamic (MHD) system with a velocity damping term. We establish the
global existence and uniqueness of smooth solutions when the initial data is
close to an equilibrium state. In addition, explicit large-time decay rates for
various Sobolev norms of the solutions are also given.
|
1311.6185v1
|
2014-08-25
|
Asymptotic behavior of global entropy solutions for nonstrictly hyperbolic systems with linear damping
|
In this paper we investigate the large time behavior of the global weak
entropy solutions to the symmetric Keyftiz-Kranzer system with linear damping.
It is proved that as t tends to infinite the entropy solutions tend to zero in
the L p norm
|
1408.5856v1
|
2014-08-26
|
Stability of an abstract-wave equation with delay and a Kelvin-Voigt damping
|
In this paper we consider a stabilization problem for the abstract-wave
equation with delay. We prove an exponential stability result for appropriate
damping coefficient. The proof of the main result is based on a
frequency-domain approach.
|
1408.6261v2
|
2015-02-02
|
Spontaneous toroidal rotation, anomalous radial particle flux, and the electron-ion asymmetric anomalous viscous damping
|
AA spontaneous toroidal rotation due to the electron-ion asymmetric anomalous
viscous damping and the turbulent radial particle flux has been found, which
explains the experimental observation of the anomalous toroidal momentum source
in the edge of a tokamak plasma.
|
1502.00499v3
|
2015-03-06
|
Concentration Of Laplace Eigenfunctions And Stabilization Of Weakly Damped Wave Equation
|
- In this article, we prove some universal bounds on the speed of
concentration on small (frequency-dependent) neighborhoods of submanifolds of L
2-norms of quasi modes for Laplace operators on compact manifolds. We deduce
new results on the rate of decay of weakly damped wave equations.
R{\'e}sum{\'e}.
|
1503.02058v1
|
2015-03-11
|
Upper bounds for the attractor dimension of damped Navier-Stokes equations in $\mathbb R^2$
|
We consider finite energy solutions for the damped and driven two-dimensional
Navier--Stokes equations in the plane and show that the corresponding dynamical
system possesses a global attractor. We obtain upper bounds for its fractal
dimension when the forcing term belongs to the whole scale of homogeneous
Sobolev spaces from -1 to 1
|
1503.03415v1
|
2015-03-18
|
Laplace Eigenfunctions And Damped Wave Equation Ii: Product Manifolds
|
- The purpose of this article is to study possible concentrations of
eigenfunc-tions of Laplace operators (or more generally quasi-modes) on product
manifolds. We show that the approach of the first author and Zworski [10, 11]
applies (modulo rescalling) and deduce new stabilization results for weakly
damped wave equations which extend to product manifolds previous results by
Leautaud-Lerner [12] obtained for products of tori.
|
1503.05513v1
|
2015-10-14
|
The General Solution to Vlasov Equation and Linear Landau Damping
|
A general solution to linearized Vlasov equation for an electron
electrostatic wave in a homogeneous unmagnetized plasma is derived. The
quasi-linear diffusion coefficient resulting from this solution is a continuous
function of omega in contrast to that derived from the traditional Vlasov
treatment. The general solution is also equivalent to the Landau treatment of
the plasma normal oscillations, and hence leads to the well-known Landau
damping.
|
1510.03949v1
|
2016-01-13
|
Non uniform decay of the energy of some dissipative evolution systems
|
In this paper we consider second order evolution equations with bounded
damping. We give a characterization of a non uniform decay for the damped
problem using a kind of observability estimate for the associated undamped
problem.
|
1601.03373v1
|
2016-01-27
|
Forward self-similar solutions to the viscoelastic Navier-Stokes equation with damping
|
Motivated by \cite{JS}, we prove that there exists a global, forward
self-similar solution to the viscoelastic Navier-Stokes equation with damping,
that is smooth for $t>0$, for any initial data that is homogeneous of degree
$-1$.
|
1601.07478v1
|
2016-03-14
|
Phase speed and frequency-dependent damping of longitudinal intensity oscillations in coronal loop structures observed with AIA/SDO
|
Longitudinal intensity oscillations along coronal loops that are interpreted
as signatures of magneto-acoustic waves are observed frequently in different
coronal structures. The aim of this paper is to estimate the physical
parameters of the slow waves and the quantitative dependence of these
parameters on their frequencies in the solar corona loops that are situated
above active regions with the Atmospheric Imaging Assembly (AIA) onboard Solar
Dynamic Observatory (SDO). The observed data on 2012-Feb-12, consisting of 300
images with an interval of 24 seconds in the 171 $\rm{\AA}$ and 193 $\rm{\AA}$
passbands is analyzed for evidence of propagating features as slow waves along
the loop structures. Signatures of longitudinal intensity oscillations that are
damped rapidly as they travel along the loop structures were found, with
periods in the range of a few minutes to few tens of minutes. Also, the
projected (apparent) phase speeds, projected damping lengths, damping times and
damping qualities of filtered intensities centred on the dominant frequencies
are measured in the range of $\rm{C_s}\simeq 38-79~ \rm {km~s^{-1}}$,
$\rm{L_d}\simeq 23-68 ~\rm{Mm }$, $\rm{\tau_d}\simeq 7- 21 ~\rm {min}$ and
$\rm{\tau_d/P}\simeq 0.34- 0.77$, respectively. The theoretical and
observational results of this study indicate that the damping times and damping
lengths increase with increasing the oscillation periods, and are highly
sensitive function of oscillation period, but the projected speeds and the
damping qualities are not very sensitive to the oscillation periods.
Furthermore, the magnitude values of physical parameters are in good agreement
with the prediction of the theoretical dispersion relations of high-frequency
MHD waves ($>1.1~ \rm{mHz}$) in a coronal plasma with electron number density
in the range of $\rm{n_e}\simeq 10^{7} - 10^{12} ~\rm{cm^{-3}}$.
|
1603.04207v1
|
2016-04-27
|
Critical exponent for nonlinear wave equations with frictional and viscoelastic damping terms
|
In this paper, we study the Cauchy problem for a nonlinear wave equation with
frictional and viscoelastic damping terms. Our aim is to obtain the threshold,
to classify the global existence of solution for small data or the finite time
blow-up pf the solution, with respect to the growth order of the nonlinearity.
|
1604.08265v1
|
2016-05-19
|
On circular flows: linear stability and damping
|
In this article we establish linear inviscid damping with optimal decay rates
around 2D Taylor-Couette flow and similar monotone flows in an annular domain
$B_{r_{2}}(0) \setminus B_{r_{1}}(0) \subset \mathbb{R}^{2}$. Following recent
results by Wei, Zhang and Zhao, we establish stability in weighted norms, which
allow for a singularity formation at the boundary, and additional provide a
description of the blow-up behavior.
|
1605.05959v1
|
2016-08-04
|
Resonance Damping of the THz-frequency Transverse Acoustic Phonon in the Relaxor Ferroelectric KTa1-xNbxO3
|
The damping ($\Gamma_a$) of the transverse acoustic (TA) phonon in single
crystals of the relaxor $KTa_{1-x}Nb_xO_3$ with x=0.15-0.17 was studied by
means of high resolution inelastic cold neutron scattering near the (200) B.Z.
point where diffuse scattering is absent, although it is present near (110). In
a wide range of temperatures centered on the phase transition, T=195K-108K, the
TA phonon width (damping) exhibits a step increase around momentum q=0.07, goes
through a shallow maximum at q=0.09-0.12 and remains high up to the highest
momentum studied of q=0.16. These experimental results are explained in terms
of a resonant interaction between the TA phonon and the collective or
correlated reorientation through tunneling of the off-center Nb+5 ions. The
observed TA damping is successfully reproduced in a simple model that includes
an interaction between the TA phonon and a dispersionless localized mode (LM)
with frequency $\omega_L$ and damping $\Gamma_L$ ($\Gamma_L < \omega_L$),
itself coupled to the transverse optic (TO) mode. Maximum damping of the TA
phonon occurs when its frequency $\omega_a \approx{\omega_L}$. $\omega_L$ and
$\Gamma_L$ are moderately dependent on temperature but the oscillator strength,
$M_2$, of the resonant damping exhibits a strong maximum in the range
$T\sim{150 K-120 K}$ in which neutron diffuse scattering near the (110) B.Z.
point is also maximum and the dielectric susceptibility exhibits the relaxor
behavior. The maximum value of M appears to be due to the increasing number of
polar nanodomains. In support of the proposed model, the observed value of
$\omega_L$ is found to be similar to the estimate previously obtained by
Girshberg and Yacoby. Alternatively, the TA phonon damping can be successfully
fitted in the framework of an empirical Havriliak - Negami (HN) relaxation
model that includes a strong resonance-like transient contribution.
|
1608.01591v1
|
2016-08-26
|
Cheillini integrability and quadratically damped oscillators
|
In this paper a new approach to study an equation of the Lienard type with a
strong quadratic damping is proposed based on Jacobi's last multiplier and
Cheillini's integrability condition. We obtain a closed form solution of the
transcendental characteristic equation of the Lienard type equation using the
Lambert W-function.
|
1608.07377v1
|
2016-11-27
|
Nonlinear Wave Equation with Damping: Periodic Forcing and Non-Resonant Solutions to the Kuznetsov Equation
|
Existence of non-resonant solutions of time-periodic type are established for
the Kuznetsov equation with a periodic forcing term. The equation is considered
in a three-dimensional whole-space, half-space and bounded domain, and with
both non-homogeneous Dirichlet and Neumann boundary values. A method based on
Lp estimates of the corresponding linearization, namely the wave equation with
Kelvin-Voigt damping, is employed.
|
1611.08883v1
|
2017-02-02
|
Stationary solutions for stochastic damped Navier-Stokes equations in $\mathbb R^d$
|
We consider the stochastic damped Navier-Stokes equations in $\mathbb R^d$
($d=2,3$), assuming as in our previous work [4] that the covariance of the
noise is not too regular, so It\^o calculus cannot be applied in the space of
finite energy vector fields. We prove the existence of an invariant measure
when $d=2$ and of a stationary solution when $d=3$.
|
1702.00697v1
|
2017-03-08
|
Moderate deviations for the Langevin equation with strong damping
|
In this paper, we establish a moderate deviations principle for the Langevin
dynamics with strong damping. The weak convergence approach plays an important
role in the proof.
|
1703.03033v3
|
2017-03-17
|
Damping in a Superconducting Mechanical Resonator
|
We study a mechanical resonator made of aluminum near the normal to super
conductivity phase transition. A sharp drop in the rate of mechanical damping
is observed below the critical temperature. The experimental results are
compared with predictions based on the Bardeen Cooper Schrieffer theory of
superconductivity and a fair agreement is obtained.
|
1703.05912v1
|
2017-03-27
|
On the $L^{2}$-critical nonlinear Schrodinger equation with an inhomogeneous damping term
|
We consider the $L^2$-critical nonlinear Schrodinger equation with an
inhomogeneous damping term. We prove that there exists an initial data such
that the corresponding solution is global in $H^1(R^d)$ and we give the minimal
time of the blow up for some initial data.
|
1703.09101v1
|
2017-06-22
|
Asymptotic profile of solutions for some wave equations with very strong structural damping
|
We consider the Cauchy problem in R^n for some types of damped wave
equations. We derive asymptotic profiles of solutions with weighted
L^{1,1}(R^n) initial data by employing a simple method introduced by the first
author. The obtained results will include regularity loss type estimates, which
are essentially new in this kind of equations.
|
1706.07174v1
|
2017-08-11
|
Global existence of a diffusion limit with damping for the compressible radiative Euler system coupled to an electromagnetic field
|
We study the Cauchy problem for a system of equations corresponding to a
singular limit of radiative hydrodynamics, namely the 3D radiative compressible
Euler system coupled to an electromagnetic field through the MHD approximation.
Assuming the presence of damping together with suitable smallness hypotheses
for the data, we prove that this problem admits a unique global smooth
solution.
|
1708.03681v1
|
2017-08-21
|
A remark on the critical exponent for the semilinear damped wave equation on the half-space
|
In this short notice, we prove the non-existence of global solutions to the
semilinear damped wave equation on the half-space, and we determine the
critical exponent for any space dimension.
|
1708.06429v1
|
2017-08-24
|
Nonlinear network dynamics for interconnected micro-grids
|
This paper deals with transient stability in interconnected micro-grids. The
main contribution involves i) robust classification of transient dynamics for
different intervals of the micro-grid parameters (synchronization, inertia, and
damping); ii) exploration of the analogies with consensus dynamics and bounds
on the damping coefficient separating underdamped and overdamped dynamics iii)
the extension to the case of disturbed measurements due to hackering or
parameter uncertainties.
|
1708.07296v1
|
2017-12-04
|
Radiative seesaw models linking to dark matter candidates inspired by the DAMPE excess
|
We propose two possibilities to explain an excess of electron/positron flux
around 1.4 TeV recently reported by Dark Matter Explore (DAMPE) in the
framework of radiative seesaw models where one of them provides a fermionic
dark matter candidate, and the other one provides a bosonic dark matter
candidate. We also show unique features of both models regarding neutrino mass
structure.
|
1712.00941v1
|
2018-01-06
|
Multiscale analysis of semilinear damped stochastic wave equations
|
In this paper we proceed with the multiscale analysis of semilinear damped
stochastic wave motions. The analysis is made by combining the well-known sigma
convergence method with its stochastic counterpart, associated to some
compactness results such as the Prokhorov and Skorokhod theorems. We derive the
equivalent model, which is of the same type as the micro-model.
|
1801.02036v1
|
2018-07-06
|
Global existence for the 3-D semilinear damped wave equations in the scattering case
|
We study the global existence of solutions to semilinear damped wave
equations in the scattering case with derivative power-type nonlinearity on
(1+3) dimensional nontrapping asymptotically Euclidean manifolds. The main idea
is to exploit local energy estimate, together with local existence to convert
the parameter $\mu$ to small one.
|
1807.02403v1
|
2018-09-22
|
Asymptotic behavior of solutions to 3D incompressible Navier-Stokes equations with damping
|
In this paper, we study the upper bound of the time decay rate of solutions
to the Navier-Stokes equations and generalized Navier-Stokes equations with
damping term $|u|^{\beta-1}u$ ($\beta>1$) in $\mathbb{R}^3$.
|
1809.08394v2
|
2018-10-22
|
Optimal leading term of solutions to wave equations with strong damping terms
|
We analyze the asymptotic behavior of solutions to wave equations with strong
damping terms. If the initial data belong to suitable weighted $L^1$ spaces,
lower bounds for the difference between the solutions and the leading terms in
the Fourier space are obtained, which implies the optimality of expanding
methods and some estimates proposed in this paper.
|
1810.09114v1
|
2018-10-29
|
Apples with Apples comparison of 3+1 conformal numerical relativity schemes
|
This paper contains a comprehensive comparison catalog of `Apples with
Apples' tests for the BSSNOK, CCZ4 and Z4c numerical relativity schemes, with
and without constraint damping terms for the latter two. We use basic numerical
methods and reach the same level of accuracy as existing results in the
literature. We find that the best behaving scheme is generically CCZ4 with
constraint damping terms.
|
1810.12346v1
|
2018-11-07
|
Statistical complexity of the quasiperiodical damped systems
|
We consider the concept of statistical complexity to write the
quasiperiodical damped systems applying the snapshot attractors. This allows us
to understand the behaviour of these dynamical systems by the probability
distribution of the time series making a difference between the regular, random
and structural complexity on finite measurements. We interpreted the
statistical complexity on snapshot attractor and determined it on the
quasiperiodical forced pendulum.
|
1811.02958v1
|
2018-12-13
|
Rapid exponential stabilization of a 1-D transmission wave equation with in-domain anti-damping
|
We consider the problem of pointwise stabilization of a one-dimensional wave
equation with an internal spatially varying anti-damping term. We design a
feedback law based on the backstepping method and prove exponential stability
of the closed-loop system with a desired decay rate.
|
1812.11035v1
|
2019-01-20
|
Stationary Solutions of Damped Stochastic 2-dimensional Euler's Equation
|
Existence of stationary point vortices solution to the damped and
stochastically driven Euler's equation on the two dimensional torus is proved,
by taking limits of solutions with finitely many vortices. A central limit
scaling is used to show in a similar manner the existence of stationary
solutions with white noise marginals.
|
1901.06744v1
|
2019-03-13
|
Solar $p$-mode damping rates: insight from a 3D hydrodynamical simulation
|
Space-borne missions CoRoT and Kepler have provided a rich harvest of
high-quality photometric data for solar-like pulsators. It is now possible to
measure damping rates for hundreds of main-sequence and thousands of red-giant.
However, among the seismic parameters, mode damping rates remain poorly
understood and thus barely used for inferring the physical properties of stars.
Previous approaches to model mode damping rates were based on mixing-length
theory or a Reynolds-stress approach to model turbulent convection. While able
to grasp the main physics of the problem, those approaches are of little help
to provide quantitative estimates as well as a definitive answer on the
relative contribution of each physical mechanism. Our aim is thus to assess the
ability of 3D hydrodynamical simulations to infer the physical mechanisms
responsible for damping of solar-like oscillations. To this end, a solar
high-spatial resolution and long-duration hydrodynamical 3D simulation computed
with the ANTARES code allows probing the coupling between turbulent convection
and the normal modes of the simulated box. Indeed, normal modes of the
simulation experience realistic driving and damping in the super-adiabatic
layers of the simulation. Therefore, investigating the properties of the normal
modes in the simulation provides a unique insight into the mode physics. We
demonstrate that such an approach provides constraints on the solar damping
rates and is able to disentangle the relative contribution related to the
perturbation of the turbulent pressure, the gas pressure, the radiative flux,
and the convective flux contributions. Finally, we conclude that using the
normal modes of a 3D numerical simulation is possible and is potentially able
to unveil the respective role of the different physical mechanisms responsible
for mode damping provided the time-duration of the simulation is long enough.
|
1903.05479v1
|
2019-04-15
|
Carleman estimate for an adjoint of a damped beam equation and an application to null controllability
|
In this article we consider a control problem of a linear Euler-Bernoulli
damped beam equation with potential in dimension one with periodic boundary
conditions. We derive a new Carleman estimate for an adjoint of the equation
under consideration. Then using a well known duality argument we obtain
explicitly the control function which can be used to drive the solution
trajectory of the control problem to zero state.
|
1904.07038v1
|
2019-05-01
|
Dissipative structure and diffusion phenomena for doubly dissipative elastic waves in two space dimensions
|
In this paper we study the Cauchy problem for doubly dissipative elastic
waves in two space dimensions, where the damping terms consist of two different
friction or structural damping. We derive energy estimates and diffusion
phenomena with different assumptions on initial data. Particularly, we find the
dominant influence on diffusion phenomena by introducing a new threshold of
diffusion structure.
|
1905.00257v1
|
2019-06-21
|
Unique determination of the damping coefficient in the wave equation using point source and receiver data
|
In this article, we consider the inverse problems of determining the damping
coefficient appearing in the wave equation. We prove the unique determination
of the coefficient from the data coming from a single coincident
source-receiver pair. Since our problem is under-determined, so some extra
assumption on the coefficient is required to prove the uniqueness.
|
1906.08987v1
|
2019-07-12
|
Non-Existence of Periodic Orbits for Forced-Damped Potential Systems in Bounded Domains
|
We prove Lr-estimates on periodic solutions of periodically-forced,
linearly-damped mechanical systems with polynomially-bounded potentials. The
estimates are applied to obtain a non-existence result of periodic solutions in
bounded domains, depending on an upper bound on the gradient of the potential.
The results are illustrated on examples.
|
1907.05778v1
|
2019-09-02
|
On the inclusion of damping terms in the hyperbolic MBO algorithm
|
The hyperbolic MBO is a threshold dynamic algorithm which approximates
interfacial motion by hyperbolic mean curvature flow. We introduce a
generalization of this algorithm for imparting damping terms onto the equation
of motion. We also construct corresponding numerical methods, and perform
numerical tests. We also use our results to show that the generalized
hyperbolic MBO is able to approximate motion by the standard mean curvature
flow.
|
1909.00552v1
|
2019-09-07
|
Lindblad dynamics of the damped and forced quantum harmonic oscillator: General solution
|
The quantum dynamics of a damped and forced harmonic oscillator described by
a Lindblad master equation is analyzed. The master equation is converted into a
matrix-vector representation and the resulting non-Hermitian Schr\"odinger
equation is solved by Lie-algebraic techniques allowing the construction of the
general solution for the density operator.
|
1909.03206v1
|
2019-10-17
|
Modified different nonlinearities for weakly coupled systems of semilinear effectively damped waves with different time-dependent coefficients in the dissipation terms
|
We prove the global existence of small data solution in all space dimension
for weakly coupled systems of semi-linear effectively damped wave, with
different time-dependent coefficients in the dissipation terms. Moreover,
nonlinearity terms $ f(t,u) $ and $ g(t,v) $ satisfying some properties of the
parabolic equation. We study the problem in several classes of regularity.
|
1910.07731v1
|
2019-11-01
|
Convergence of a damped Newton's method for discrete Monge-Ampere functions with a prescribed asymptotic cone
|
We prove the convergence of a damped Newton's method for the nonlinear system
resulting from a discretization of the second boundary value problem for the
Monge-Ampere equation. The boundary condition is enforced through the use of
the notion of asymptotic cone. The differential operator is discretized based
on a partial discrete analogue of the subdifferential.
|
1911.00260v2
|
2019-12-17
|
Comment on "On the Origin of Frictional Energy Dissipation"
|
In their interesting study (Ref. [1]) Hu et al have shown that for a simple
"harmonium" solid model the slip-induced motion of surface atoms is close to
critically damped. This result is in fact well known from studies of
vibrational damping of atoms and molecules at surfaces. However, for real
practical cases the situation may be much more complex and the conclusions of
Hu et al invalid.
|
1912.07799v1
|
2020-01-23
|
Nonlinear inviscid damping for a class of monotone shear flows in finite channel
|
We prove the nonlinear inviscid damping for a class of monotone shear flows
in $T\times [0,1]$ for initial perturbation in Gevrey-$1/s$($s>2$) class with
compact support. The main idea of the proof is to use the wave operator of a
slightly modified Rayleigh operator in a well chosen coordinate system.
|
2001.08564v1
|
2020-02-26
|
Bistability in the dissipative quantum systems I: Damped and driven nonlinear oscillator
|
We revisit quantum dynamics of the damped and driven nonlinear oscillator. In
the classical case this system has two stationary solutions (the limit cycles)
in the certain parameter region, which is the origin of the celebrated
bistability phenomenon. The quantum-classical correspondence for the oscillator
dynamics is discussed in details.
|
2002.11373v1
|
2020-04-08
|
Scattering and asymptotic order for the wave equations with the scale-invariant damping and mass
|
We consider the linear wave equation with the time-dependent scale-invariant
damping and mass. We also treat the corresponding equation with the energy
critical nonlinearity. Our aim is to show that the solution scatters to a
modified linear wave solution and to obtain its asymptotic order.
|
2004.03832v2
|
2020-04-24
|
Infinite energy solutions for weakly damped quintic wave equations in $\mathbb{R}^3$
|
The paper gives a comprehensive study of infinite-energy solutions and their
long-time behavior for semi-linear weakly damped wave equations in
$\mathbb{R}^3$ with quintic nonlinearities. This study includes global
well-posedness of the so-called Shatah-Struwe solutions, their dissipativity,
the existence of a locally compact global attractors (in the uniformly local
phase spaces) and their extra regularity.
|
2004.11864v1
|
2020-07-30
|
Delta shock solution to the generalized one-dimensional zero-pressure gas dynamics system with linear damping
|
In this paper, we propose a time-dependent viscous system and by using the
vanishing viscosity method we show the existence of delta shock solution for a
particular $2 \times 2$ system of conservation laws with linear damping.
|
2007.15184v2
|
2020-08-06
|
On global attractors for 2D damped driven nonlinear Schrödinger equations
|
Well-posedness and global attractor are established for 2D damped driven
nonlinear Schr\"odinger equation with almost periodic pumping in a bounded
region. The key role is played by a novel application of the energy equation.
|
2008.02741v1
|
2020-08-30
|
Influence of dissipation on extreme oscillations of a forced anharmonic oscillator
|
Dynamics of a periodically forced anharmonic oscillator (AO) with cubic
nonlinearity, linear damping, and nonlinear damping, is studied. To begin with,
the authors examine the dynamics of an AO. Due to this symmetric nature, the
system has two neutrally stable elliptic equilibrium points in positive and
negative potential-wells. Hence, the unforced system can exhibit both
single-well and double-well periodic oscillations depending on the initial
conditions. Next, the authors include nonlinear damping into the system. Then,
the symmetry of the system is broken instantly and the stability of the two
elliptic points is altered to result in stable focus and unstable focus in the
positive and negative potential-wells, respectively. Consequently, the system
is dual-natured and is either non-dissipative or dissipative, depending on
location in the phase space. Furthermore, when one includes a periodic external
forcing with suitable parameter values into the nonlinearly damped AO system
and starts to increase the damping strength, the symmetry of the system is not
broken right away, but it occurs after the damping reaches a threshold value.
As a result, the system undergoes a transition from double-well chaotic
oscillations to single-well chaos mediated through extreme events (EEs).
Furthermore, it is found that the large-amplitude oscillations developed in the
system are completely eliminated if one incorporates linear damping into the
system. The numerically calculated results are in good agreement with the
theoretically obtained results on the basis of Melnikov's function. Further, it
is demonstrated that when one includes linear damping into the system, this
system has a dissipative nature throughout the entire phase space of the
system. This is believed to be the key to the elimination of EEs.
|
2008.13172v1
|
2020-09-16
|
Exponential decay for semilinear wave equations with viscoelastic damping and delay feedback
|
In this paper we study a class of semilinear wave type equations with
viscoelastic damping and delay feedback with time variable coefficient. By
combining semigroup arguments, careful energy estimates and an iterative
approach we are able to prove, under suitable assumptions, a well-posedness
result and an exponential decay estimate for solutions corresponding to small
initial data. This extends and concludes the analysis initiated in [16] and
then developed in [13, 17].
|
2009.07777v1
|
2020-09-18
|
Vanishing viscosity limit for Riemann solutions to a $2 \times 2$ hyperbolic system with linear damping
|
In this paper, we propose a time-dependent viscous system and by using the
vanishing viscosity method we show the existence of %delta shock solution
solutions for the Riemann problem to a particular $2 \times 2$ system of
conservation laws with linear damping.
|
2009.09041v1
|
2020-11-28
|
A Smoluchowski-Kramers approximation for an infinite dimensional system with state-dependent damping
|
We study the validity of a Smoluchowski-Kramers approximation for a class of
wave equations in a bounded domain of $\mathbb{R}^n$ subject to a
state-dependent damping and perturbed by a multiplicative noise. We prove that
in the small mass limit the solution converges to the solution of a stochastic
quasilinear parabolic equation where a noise-induced extra drift is created.
|
2011.14236v2
|
2020-12-13
|
Uniform Stabilization of the Petrovsky-Wave Nonlinear coupled system with strong damping
|
This paper concerns the well-posedness and uniform stabilization of the
Petrovsky-Wave Nonlinear coupled system with strong damping. Existence of
global weak solutions for this problem is established by using the Galerkin
method. Meanwhile, under a clever use of the multiplier method, we estimate the
total energy decay rate.
|
2012.07109v3
|
2021-03-24
|
On the long-time statistical behavior of smooth solutions of the weakly damped, stochastically-driven KdV equation
|
This paper considers the damped periodic Korteweg-de Vries (KdV) equation in
the presence of a white-in-time and spatially smooth stochastic source term and
studies the long-time behavior of solutions. We show that the integrals of
motion for KdV can be exploited to prove regularity and ergodic properties of
invariant measures for damped stochastic KdV. First, by considering non-trivial
modifications of the integrals of motion, we establish Lyapunov structure by
proving that moments of Sobolev norms of solutions at all orders of regularity
are bounded globally-in-time; existence of invariant measures follows as an
immediate consequence. Next, we prove a weak Foias-Prodi type estimate for
damped stochastic KdV, for which the synchronization occurs in expected value.
This estimate plays a crucial role throughout our subsequent analysis. As a
first novel application, we combine the Foias-Prodi estimate with the Lyapunov
structure to establish that invariant measures are supported on $C^\infty$
functions provided that the external driving forces belong to $C^\infty$. We
then establish ergodic properties of invariant measures, treating the regimes
of arbitrary damping and large damping separately. For arbitrary damping, we
demonstrate that the framework of `asymptotic coupling' can be implemented for
a compact proof of uniqueness of the invariant measure provided that
sufficiently many directions in phase space are stochastically forced. Our
proof is paradigmatic for SPDEs for which a weak Foias-Prodi type property
holds. Lastly, for large damping, we establish the existence of a spectral gap
with respect to a Wasserstein-like distance, and exponential mixing and
uniqueness of the invariant measure follows.
|
2103.12942v2
|
2021-04-21
|
On absorbing set for 3D Maxwell--Schrödinger damped driven equations in bounded region
|
We consider the 3D damped driven Maxwell--Schr\"odinger equations in a
bounded region under suitable boundary conditions. We establish new a priori
estimates, which provide the existence of global finite energy weak solutions
and bounded absorbing set. The proofs rely on the Sobolev type estimates for
magnetic Schr\"odinger operator.
|
2104.10723v1
|
2021-06-23
|
Pitt inequality for the linear structurally damped $σ$-evolution equations
|
This work is devoted to improve the time decay estimates for the solution and
some of its derivatives of the linear structurally damped $\sigma$-evolution
equations. The Pitt inequality is the main tool provided that the initial data
lies in some weighted spaces.
|
2106.12342v1
|
2021-07-22
|
Dimension estimates for the attractor of the regularized damped Euler equations on the sphere
|
We prove existence of the global attractor of the damped and driven
Euler--Bardina equations on the 2D sphere and on arbitrary domains on the
sphere
and give explicit estimates of its fractal dimension in terms of the physical
parameters.
|
2107.10779v1
|
2021-09-22
|
State-space representation of Matérn and Damped Simple Harmonic Oscillator Gaussian processes
|
Gaussian processes (GPs) are used widely in the analysis of astronomical time
series. GPs with rational spectral densities have state-space representations
which allow O(n) evaluation of the likelihood. We calculate analytic state
space representations for the damped simple harmonic oscillator and the
Mat\'ern 1/2, 3/2 and 5/2 processes.
|
2109.10685v1
|
2021-10-10
|
Global existence of solutions for semilinear damped wave equations with variable coefficients
|
We consider the Cauchy problem for the damped wave equations with variable
coefficients a(x) having power type nonlinearity |u|^p. We discuss the global
existence of solutions for small initial data and investigate the relation
between the range of a(x) and the order p.
|
2110.04718v2
|
2021-10-21
|
Stability properties of dissipative evolution equations with nonautonomous and nonlinear damping
|
In this paper, we obtain some stability results of (abstract) dissipative
evolution equations with a nonautonomous and nonlinear damping using the
exponential stability of the retrograde problem with a linear and autonomous
feedback and a comparison principle. We then illustrate our abstract statements
for different concrete examples, where new results are achieved. In a
preliminary step, we prove some well-posedness results for some nonlinear and
nonautonomous evolution equations.
|
2110.11122v1
|
2021-11-23
|
Logistic damping effect in chemotaxis models with density-suppressed motility
|
This paper is concerned with a parabolic-elliptic chemotaxis model with
density-suppressed motility and general logistic source in an $n$-dimensional
smooth bounded domain with Neumann boundary conditions. Under the minimal
conditions for the density-suppressed motility function, we explore how strong
the logistic damping can warrant the global boundedness of solutions, and
further establish the asymptotic behavior of solutions on top of the
conditions.
|
2111.11669v1
|
2022-01-04
|
Global existence and decay estimates for a viscoelastic plate equation with nonlinear damping and logarithmic nonlinearity
|
In this article, we consider a viscoelastic plate equation with a logarithmic
nonlinearity in the presence of nonlinear frictional damping term. Using the
the Faedo-Galerkin method we establish the global existence of the solution of
the problem and we also prove few general decay rate results.
|
2201.00983v1
|
2022-01-20
|
Long Time Decay of Leray Solution of 3D-NSE With Damping
|
In \cite{CJ}, the authors show that the Cauchy problem of the Navier-Stokes
equations with damping $\alpha|u|^{\beta-1}u(\alpha>0,\;\beta\geq1)$ has global
weak solutions in $L^2(\R^3)$. In this paper, we prove the uniqueness, the
continuity in $L^2$ for $\beta>3$, also the large time decay is proved for
$\beta\geq\frac{10}3$. Fourier analysis and standard techniques are used.
|
2201.08427v1
|
2022-02-20
|
On a non local non-homogeneous fractional Timoshenko system with frictional and viscoelastic damping terms
|
We are devoted to the study of a nonhomogeneous time-fractional Timoshenko
system with frictional and viscoelastic damping terms. We are concerned with
the well-posedness of the given problem. The approach relies on some
functional-analysis tools, operator theory, a prori estimates, and density
arguments.
|
2202.09879v1
|
2022-04-05
|
Large time behavior of solutions to nonlinear beam equations
|
In this note we analyze the large time behavior of solutions to a class of
initial/boundary problems involving a damped nonlinear beam equation. We show
that under mild conditions on the damping term of the equation of motions the
solutions of the dynamical problem converge to the solution of the stationary
problem. We also show that this convergence is exponential.
|
2204.02151v1
|
2022-05-09
|
Energy asymptotics for the strongly damped Klein-Gordon equation
|
We consider the strongly damped Klein Gordon equation for defocusing
nonlinearity and we study the asymptotic behaviour of the energy for periodic
solutions. We prove first the exponential decay to zero for zero mean
solutions. Then, we characterize the limit of the energy, when the time tends
to infinity, for solutions with small enough initial data and we finally prove
that such limit is not necessary zero.
|
2205.04205v1
|
2022-06-07
|
Asymptotic study of Leray Solution of 3D-NSE With Exponential Damping
|
We study the uniqueness, the continuity in $L^2$ and the large time decay for
the Leray solutions of the $3D$ incompressible Navier-Stokes equations with the
nonlinear exponential damping term $a (e^{b |u|^{\bf 2}}-1)u$, ($a,b>0$)
studied by the second author in \cite{J1}.
|
2206.03138v1
|
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