publicationDate
stringlengths
1
2.79k
title
stringlengths
1
36.5k
abstract
stringlengths
1
37.3k
id
stringlengths
9
47
2019-06-12
A no-go result for the quantum damped harmonic oscillator
In this letter we show that it is not possible to set up a canonical quantization for the damped harmonic oscillator using the Bateman lagrangian. In particular, we prove that no square integrable vacuum exists for the {\em natural} ladder operators of the system, and that the only vacua can be found as distributions. ...
1906.05121v2
2019-06-26
Mismatched Estimation of Polynomially Damped Signals
In this work, we consider the problem of estimating the parameters of polynomially damped sinusoidal signals, commonly encountered in, for instance, spectroscopy. Generally, finding the parameter values of such signals constitutes a high-dimensional problem, often further complicated by not knowing the number of signal...
1906.11113v1
2019-06-27
Temperature-Dependent Lifetimes of Low-Frequency Adsorbate Modes from Non-Equilibrium Molecular Dynamics Simulations
We present calculations on the damping of a low-frequency adsorbate mode on a metal surface, namely the frustrated translation of Na on Cu(100). For the first time, vibrational lifetimes of excited adlayers are extracted from non-equilibrium molecular dynamics calculations accounting for both the phononic and the elect...
1906.11776v1
2019-07-10
Formal expansions in stochastic model for wave turbulence 1: kinetic limit
We consider the damped/driver (modified) cubic NLS equation on a large torus with a properly scaled forcing and dissipation, and decompose its solutions to formal series in the amplitude. We study the second order truncation of this series and prove that when the amplitude goes to zero and the torus' size goes to infin...
1907.04531v4
2019-07-22
Thresholds for low regularity solutions to wave equations with structural damping
We study the asymptotic behavior of solutions to wave equations with a structural damping term \[ u_{tt}-\Delta u+\Delta^2 u_t=0, \qquad u(0,x)=u_0(x), \,\,\, u_t(0,x)=u_1(x), \] in the whole space. New thresholds are reported in this paper that indicate which of the diffusion wave property and the non-diffusive struct...
1907.09299v1
2019-08-03
Lindblad dynamics of the damped and forced quantum harmonic oscillator
The quantum dynamics of a damped and forced harmonic oscillator is investigated in terms of a Lindblad master equation. Elementary algebraic techniques are employed allowing for example to analyze the long time behavior, i.e. the quantum limit cycle. The time evolution of various expectation values is obtained in close...
1908.01187v2
2019-08-07
Decay estimates for the linear damped wave equation on the Heisenberg group
This paper is devoted to the derivation of $L^2$ - $L^2$ decay estimates for the solution of the homogeneous linear damped wave equation on the Heisenberg group $\mathbf{H}_n$, for its time derivative and for its horizontal gradient. Moreover, we consider the improvement of these estimates when further $L^1(\mathbf{H}_...
1908.02657v1
2019-08-08
Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity
In this paper, we consider the Cauchy problem for the semilinear damped wave equation on the Heisenberg group with power nonlinearity. We prove that the critical exponent is the Fujita exponent $p_{\mathrm{Fuj}}(\mathscr{Q}) = 1+2 / \mathscr{Q}$, where $\mathscr{Q}$ is the homogeneous dimension of the Heisenberg group....
1908.02989v1
2019-09-01
Invariant measures for stochastic damped 2D Euler equations
We study the two-dimensional Euler equations, damped by a linear term and driven by an additive noise. The existence of weak solutions has already been studied; pathwise uniqueness is known for solutions that have vorticity in $L^\infty$. In this paper, we prove the Markov property and then the existence of an invarian...
1909.00424v2
2019-09-03
A blow-up result for semi-linear structurally damped $σ$-evolution equations
We would like to prove a blow-up result for semi-linear structurally damped $\sigma$-evolution equations, where $\sigma \ge 1$ and $\delta\in [0,\sigma)$ are assumed to be any fractional numbers. To deal with the fractional Laplacian operators $(-\Delta)^\sigma$ and $(-\Delta)^\delta$ as well-known non-local operators,...
1909.01181v1
2019-09-09
Action Functional for a Particle with Damping
In this brief report we discuss the action functional of a particle with damping, showing that it can be obtained from the dissipative equation of motion through a modification which makes the new dissipative equation invariant for time reversal symmetry. This action functional is exactly the effective action of Caldei...
1909.03694v2
2019-09-11
Equilibrium radiation in a plasma medium with spatial and frequency dispersion
Examination of equilibrium radiation in plasma media shows that the spectral energy distribution of such radiation is different from the Planck equilibrium radiation. Using the approach of quantum electrodynamics the general relation for the spectral energy density of equilibrium radiation in a system of charged partic...
1909.08056v1
2019-10-14
Blow-up of solutions to semilinear strongly damped wave equations with different nonlinear terms in an exterior domain
In this paper, we consider the initial boundary value problem in an exterior domain for semilinear strongly damped wave equations with power nonlinear term of the derivative-type $|u_t|^q$ or the mixed-type $|u|^p+|u_t|^q$, where $p,q>1$. On one hand, employing the Banach fixed-point theorem we prove local (in time) ex...
1910.05981v1
2019-11-03
Linear Inviscid Damping in Sobolev and Gevrey Spaces
In a recent article Jia established linear inviscid damping in Gevrey regularity for compactly supported Gevrey regular shear flows in a finite channel, which is of great interest in view of existing nonlinear results. In this article we provide an alternative very short proof of stability in Gevrey regularity as a con...
1911.00880v1
2019-11-03
A global existence result for two-dimensional semilinear strongly damped wave equation with mixed nonlinearity in an exterior domain
We study two-dimensional semilinear strongly damped wave equation with mixed nonlinearity $|u|^p+|u_t|^q$ in an exterior domain, where $p,q>1$. Assuming the smallness of initial data in exponentially weighted spaces and some conditions on powers of nonlinearity, we prove global (in time) existence of small data energy ...
1911.00899v1
2019-11-05
Critical exponent for a weakly coupled system of semi-linear $σ$-evolution equations with frictional damping
We are interested in studying the Cauchy problem for a weakly coupled system of semi-linear $\sigma$-evolution equations with frictional damping. The main purpose of this paper is two-fold. We would like to not only prove the global (in time) existence of small data energy solutions but also indicate the blow-up result...
1911.01946v1
2019-11-11
Existence and nonexistence of global solutions for a structurally damped wave system with power nonlinearities
Our interest itself of this paper is strongly inspired from an open problem in the paper [1] published by D'Abbicco. In this article, we would like to study the Cauchy problem for a weakly coupled system of semi-linear structurally damped wave equations. Main goal is to find the threshold, which classifies the global (...
1911.04412v1
2019-11-15
Some $L^1$-$L^1$ estimates for solutions to visco-elastic damped $σ$-evolution models
This note is to conclude $L^1-L^1$ estimates for solutions to the following Cauchy problem for visco-elastic damped $\sigma$-evolution models: \begin{equation} \begin{cases} u_{tt}+ (-\Delta)^\sigma u+ (-\Delta)^\sigma u_t = 0, &\quad x\in \mathbb{R}^n,\, t \ge 0, \\ u(0,x)= u_0(x),\quad u_t(0,x)=u_1(x), &\quad x\in \m...
1911.06563v1
2019-11-22
Long-time asymptotics for a coupled thermoelastic plate-membrane system
In this paper we consider a transmission problem for a system of a thermoelastic plate with (or without) rotational inertia term coupled with a membrane with different variants of damping for the plate and/or the membrane. We prove well-posedness of the problem and higher regularity of the solution and study the asympt...
1911.10161v1
2019-11-28
Tikhonov regularization of a second order dynamical system with Hessian driven damping
We investigate the asymptotic properties of the trajectories generated by a second-order dynamical system with Hessian driven damping and a Tikhonov regularization term in connection with the minimization of a smooth convex function in Hilbert spaces. We obtain fast convergence results for the function values along the...
1911.12845v2
2019-12-15
Negative mobility, sliding and delocalization for stochastic networks
We consider prototype configurations for quasi-one-dimensional stochastic networks that exhibit negative mobility, meaning that current decreases or even reversed as the bias is increased. We then explore the implications of disorder. In particular we ask whether lower and upper bias thresholds restrict the possibility...
1912.07059v2
2019-12-23
On a damped Szego equation (with an appendix in collaboration with Christian Klein)
We investigate how damping the lowest Fourier mode modifies the dynamics of the cubic Szeg{\"o} equation. We show that there is a nonempty open subset of initial data generating trajec-tories with high Sobolev norms tending to infinity. In addition, we give a complete picture of this phenomenon on a reduced phase space...
1912.10933v1
2020-01-29
The long time behavior and the rate of convergence of symplectic convex algorithms obtained via splitting discretizations of inertial damping systems
In this paper we propose new numerical algorithms in the setting of unconstrained optimization problems and we study the rate of convergence in the iterates of the objective function. Furthermore, our algorithms are based upon splitting and symplectic methods and they preserve the energy properties of the inherent cont...
2001.10831v2
2020-02-05
Long-time asymptotics of the one-dimensional damped nonlinear Klein-Gordon equation
For the one-dimensional nonlinear damped Klein-Gordon equation \[ \partial_{t}^{2}u+2\alpha\partial_{t}u-\partial_{x}^{2}u+u-|u|^{p-1}u=0 \quad \mbox{on $\mathbb{R}\times\mathbb{R}$,}\] with $\alpha>0$ and $p>2$, we prove that any global finite energy solution either converges to $0$ or behaves asymptotically as $t\to ...
2002.01826v1
2020-02-11
Distributional Solutions of the Damped Wave Equation
This work presents results on solutions of the one-dimensional damped wave equation, also called telegrapher's equation, when the initial conditions are general distributions, not only functions. We make a complete deduction of its fundamental solutions, both for positive and negative times. To obtain them we use only ...
2002.04249v2
2020-02-13
Description of the wavevector dispersion of surface plasmon-phonon-polaritons
We reported here the results of the calculations of wavevector dispersion of oscillations frequencies, $\omega'(k)$, and damping $\omega''(k)$ of the surface plasmon phonon polaritons (\mbox{SPPhP}) for the heavy-doped GaN sample. We showed that $\omega'(k)$- dependence consists of the three branches with the specific ...
2002.05473v1
2020-03-20
The Cauchy problem of the semilinear second order evolution equation with fractional Laplacian and damping
In the present paper, we prove time decay estimates of solutions in weighted Sobolev spaces to the second order evolution equation with fractional Laplacian and damping for data in Besov spaces. Our estimates generalize the estimates obtained in the previous studies. The second aim of this article is to apply these est...
2003.09239v1
2020-03-31
Time-Asymptotics of Physical Vacuum Free Boundaries for Compressible Inviscid Flows with Damping
In this paper, we prove the leading term of time-asymptotics of the moving vacuum boundary for compressible inviscid flows with damping to be that for Barenblatt self-similar solutions to the corresponding porous media equations obtained by simplifying momentum equations via Darcy's law plus the possible shift due to t...
2003.14072v2
2020-04-13
Landau damping for analytic and Gevrey data
In this paper, we give an elementary proof of the nonlinear Landau damping for the Vlasov-Poisson system near Penrose stable equilibria on the torus $\mathbb{T}^d \times \mathbb{R}^d$ that was first obtained by Mouhot and Villani in \cite{MV} for analytic data and subsequently extended by Bedrossian, Masmoudi, and Mouh...
2004.05979v3
2020-04-16
Strichartz estimates for mixed homogeneous surfaces in three dimensions
We obtain sharp mixed norm Strichartz estimates associated to mixed homogeneous surfaces in $\mathbb{R}^3$. Both cases with and without a damping factor are considered. In the case when a damping factor is considered our results yield a wide generalization of a result of Carbery, Kenig, and Ziesler [CKZ13]. The approac...
2004.07751v1
2020-04-17
Critical exponent for semi-linear structurally damped wave equation of derivative type
Main purpose of this paper is to study the following semi-linear structurally damped wave equation with nonlinearity of derivative type: $$u_{tt}- \Delta u+ \mu(-\Delta)^{\sigma/2} u_t= |u_t|^p,\quad u(0,x)= u_0(x),\quad u_t(0,x)=u_1(x),$$ with $\mu>0$, $n\geq1$, $\sigma \in (0,2]$ and $p>1$. In particular, we are goin...
2004.08486v2
2020-04-29
Exponential decay for damped Klein-Gordon equations on asymptotically cylindrical and conic manifolds
We study the decay of the global energy for the damped Klein-Gordon equation on non-compact manifolds with finitely many cylindrical and subconic ends up to bounded perturbation. We prove that under the Geometric Control Condition, the decay is exponential, and that under the weaker Network Control Condition, the decay...
2004.13894v2
2020-05-06
Zero-dimensional models for gravitational and scalar QED decoherence
We investigate the dynamics of two quantum mechanical oscillator system-bath toy models obtained by truncating to zero spatial dimensions linearized gravity coupled to a massive scalar field and scalar QED. The scalar-gravity toy model maps onto the phase damped oscillator, while the scalar QED toy model approximately ...
2005.02554v2
2020-05-16
On the asymptotic stability of wave equations coupled by velocities of anti-symmetric type
In this paper, we study the asymptotic stability of two wave equations coupled by velocities of anti-symmetric type via only one damping. We adopt the frequency domain method to prove that the system with smooth initial data is logarithmically stable, provided that the coupling domain and the damping domain intersect e...
2005.07977v2
2020-05-27
On the blow-up of solutions to semilinear damped wave equations with power nonlinearity in compact Lie groups
In this note, we prove a blow-up result for the semilinear damped wave equation in a compact Lie group with power nonlinearity $|u|^p$ for any $p>1$, under suitable integral sign assumptions for the initial data, by using an iteration argument. A byproduct of this method is the upper bound estimate for the lifespan of ...
2005.13479v2
2020-06-13
On the well-posedness of the damped time-harmonic Galbrun equation and the equations of stellar oscillations
We study the time-harmonic Galbrun equation describing the propagation of sound in the presence of a steady background flow. With additional rotational and gravitational terms these equations are also fundamental in helio- and asteroseismology as a model for stellar oscillations. For a simple damping model we prove wel...
2006.07658v1
2020-06-22
Prediction of short time qubit readout via measurement of the next quantum jump of a coupled damped driven harmonic oscillator
The dynamics of the next quantum jump for a qubit [two level system] coupled to a readout resonator [damped driven harmonic oscillator] is calculated. A quantum mechanical treatment of readout resonator reveals non exponential short time behavior which could facilitate detection of the state of the qubit faster than th...
2006.11950v1
2020-07-08
The interplay of critical regularity of nonlinearities in a weakly coupled system of semi-linear damped wave equations
We would like to study a weakly coupled system of semi-linear classical damped wave equations with moduli of continuity in nonlinearities whose powers belong to the critical curve in the $p-q$ plane. The main goal of this paper is to find out the sharp conditions of these moduli of continuity which classify between glo...
2007.04157v1
2020-07-09
Semi-uniform stability of operator semigroups and energy decay of damped waves
Only in the last fifteen years or so has the notion of semi-uniform stability, which lies between exponential stability and strong stability, become part of the asymptotic theory of $C_0$-semigroups. It now lies at the very heart of modern semigroup theory. After briefly reviewing the notions of exponential and strong ...
2007.04711v1
2020-07-10
Quasi-periodic travelling waves for a class of damped beams on rectangular tori
This article concerns a class of beam equations with damping on rectangular tori. When the generators satisfy certain relationship, by excluding some value of two model parameters, we prove that such models admit small amplitude quasi-periodic travelling wave solutions with two frequencies, which are continuations of t...
2007.05154v1
2020-07-24
A Framework to Control Inter-Area Oscillations with Local Measurement
Inter-area oscillations in power system limit of power transfer capability though tie-lines. For stable operation, wide-area power system stabilizers are deployed to provide sufficient damping. However, as the feedback is through a communication network, it brings challenges such as additional communication layer and c...
2007.12426v1
2020-08-17
Dynamics of spatially indistinguishable particles and entanglement protection
We provide a general framework which allows one to obtain the dynamics of $N$ noninteracting spatially indistinguishable particles locally coupled to separated environments. The approach is universal, being valid for both bosons and fermions and for any type of system-environment interaction. It is then applied to stud...
2008.07471v1
2020-09-02
Discriminating qubit amplitude damping channels
We address the issue of the discrimination between two-qubit amplitude damping channels by exploring several strategies. For the single-shot, we show that the excited state does not always give the optimal input, and that side entanglement assistance has limited benefit. On the contrary, feedback assistance from the en...
2009.01000v3
2020-09-03
Asymptotic behavior of 2D stably stratified fluids with a damping term in the velocity equation
This article is concerned with the asymptotic behavior of the two-dimensional inviscid Boussinesq equations with a damping term in the velocity equation. Precisely, we provide the time-decay rates of the smooth solutions to that system. The key ingredient is a careful analysis of the Green kernel of the linearized prob...
2009.01578v2
2020-08-05
The perturbational stability of the Schr$\ddot{o}$dinger equation
By using the Wigner transform, it is shown that the nonlinear Schr$\ddot{\textmd{o}}$dinger equation can be described, in phase space, by a kinetic theory similar to the Vlasov equation which is used for describing a classical collisionless plasma. In this paper we mainly show Landau damping in the quantum sense, namel...
2009.09855v1
2020-10-12
Long time behavior of solutions for a damped Benjamin-Ono equation
We consider the Benjamin-Ono equation on the torus with an additional damping term on the smallest Fourier modes (cos and sin). We first prove global well-posedness of this equation in $L^2_{r,0}(\mathbb{T})$. Then, we describe the weak limit points of the trajectories in $L^2_{r,0}(\mathbb{T})$ when time goes to infin...
2010.05520v1
2020-10-18
Classical limit of quantum mechanics for damped driven oscillatory systems: Quantum-classical correspondence
The investigation of quantum-classical correspondence may lead to gain a deeper understanding of the classical limit of quantum theory. We develop a quantum formalism on the basis of a linear-invariant theorem, which gives an exact quantum-classical correspondence for damped oscillatory systems that are perturbed by an...
2010.08971v1
2020-10-21
Initial boundary value problem for a strongly damped wave equation with a general nonlinearity
In this paper, a strongly damped semilinear wave equation with a general nonlinearity is considered. With the help of a newly constructed auxiliary functional and the concavity argument, a general finite time blow-up criterion is established for this problem. Furthermore, the lifespan of the weak solution is estimated ...
2010.10696v1
2020-10-21
MRI Image Recovery using Damped Denoising Vector AMP
Motivated by image recovery in magnetic resonance imaging (MRI), we propose a new approach to solving linear inverse problems based on iteratively calling a deep neural-network, sometimes referred to as plug-and-play recovery. Our approach is based on the vector approximate message passing (VAMP) algorithm, which is kn...
2010.11321v1
2020-11-05
Mathematical modelling of an unstable bent flow using the selective frequency damping method
The selective frequency damping method was applied to a bent flow. The method was used in an adaptive formulation. The most dangerous frequency was determined by solving an eigenvalue problem. It was found that one of the patterns, steady-state or pulsating, may exist at some relatively high Reynolds numbers. The perio...
2011.02646v1
2020-11-04
The "Dark disk" model in the light of DAMPE experiment
There are a lot of models considering the Dark Matter (DM) to be the origin of cosmic ray (CR) positron excess. However, they face an obstacle in the form of gamma-rays. Simple DM models tend to overproduce gamma-rays, leading to contradiction with isotropic gamma-ray background (IGRB). The <<dark disk>> model has been...
2011.04425v2
2020-12-15
On the stability of Bresse system with one discontinuous local internal Kelvin-Voigt damping on the axial force
In this paper, we investigate the stabilization of a linear Bresse system with one discontinuous local internal viscoelastic damping of Kelvin-Voigt type acting on the axial force, under fully Dirichlet boundary conditions. First, using a general criteria of Arendt-Batty, we prove the strong stability of our system. Fi...
2012.08219v1
2020-12-28
An efficient method for approximating resonance curves of weakly-damped nonlinear mechanical systems
A method is presented for tracing the locus of a specific peak in the frequency response under variation of a parameter. It is applicable to periodic, steady-state vibrations of harmonically forced nonlinear mechanical systems. It operates in the frequency domain and its central idea is to assume a constant phase lag b...
2012.14458v1
2021-01-16
Convergence of non-autonomous attractors for subquintic weakly damped wave equation
We study the non-autonomous weakly damped wave equation with subquintic growth condition on the nonlinearity. Our main focus is the class of Shatah--Struwe solutions, which satisfy the Strichartz estimates and are coincide with the class of solutions obtained by the Galerkin method. For this class we show the existence...
2101.06523v1
2021-01-20
A Damped Newton Algorithm for Generated Jacobian Equations
Generated Jacobian Equations have been introduced by Trudinger [Disc. cont. dyn. sys (2014), pp. 1663-1681] as a generalization of Monge-Amp{\`e}re equations arising in optimal transport. In this paper, we introduce and study a damped Newton algorithm for solving these equations in the semi-discrete setting, meaning th...
2101.08080v1
2021-02-04
Global existence results for semi-linear structurally damped wave equations with nonlinear convection
In this paper, we consider the Cauchy problem for semi-linear wave equations with structural damping term $\nu (-\Delta)^2 u_t$, where $\nu >0$ is a constant. As being mentioned in [8,10], the linear principal part brings both the diffusion phenomenon and the regularity loss of solutions. This implies that, for the non...
2102.02445v2
2021-02-15
Piezoelectric beam with magnetic effect, time-varying delay and time-varying weights
The main result of this work is to obtain the exponential decay of the solutions of a piezoelectric beam model with magnetic effect and delay term. The dampings are inserted into the equation of longitudinal displacement. The terms of damping, whose weight associated with them varies over time, are of the friction type...
2102.07538v1
2021-02-23
Effects of ground-state correlations on damping of giant dipole resonaces in $LS$ closed shell nuclei
The effects of ground-state correlations on the damping of isovector giant dipole resonances in $LS$ closed shell nuclei $^{16}$O and $^{40}$Ca are studied using extended random-phase-approximation (RPA) approaches derived from the time-dependent density-matrix theory. It is pointed out that unconventional two-body amp...
2102.11505v2
2021-03-01
On a damped nonlinear beam equation
In this note we analyze the large time behavior of solutions to an initial/boundary problem involving a damped nonlinear beam equation. We show that under physically realistic conditions on the nonlinear terms in the equation of motion the energy is a decreasing function of time and solutions converge to a stationary s...
2103.00969v3
2021-03-23
Fast convergence of dynamical ADMM via time scaling of damped inertial dynamics
In this paper, we propose in a Hilbertian setting a second-order time-continuous dynamic system with fast convergence guarantees to solve structured convex minimization problems with an affine constraint. The system is associated with the augmented Lagrangian formulation of the minimization problem. The corresponding d...
2103.12675v1
2021-03-29
Comparison between the Cauchy problem and the scattering problem for the Landau damping in the Vlasov-HMF equation
We analyze the analytic Landau damping problem for the Vlasov-HMF equation, by fixing the asymptotic behavior of the solution. We use a new method for this "scattering problem", closer to the one used for the Cauchy problem. In this way we are able to compare the two results, emphasizing the different influence of the ...
2103.15932v2
2021-04-06
Realising Einstein's mirror: Optomechanical damping with a thermal photon gas
In 1909 Einstein described the thermalization of a mirror within a blackbody cavity by collisions with thermal photons. While the time to thermalize the motion of even a microscale or nanoscale object is so long that it is not feasible, we show that it is using the high intensity light from an amplified thermal light s...
2104.02708v2
2021-04-12
The pressureless damped Euler-Riesz equations
In this paper, we analyze the pressureless damped Euler-Riesz equations posed in either $\mathbb{R}^d$ or $\mathbb{T}^d$. We construct the global-in-time existence and uniqueness of classical solutions for the system around a constant background state. We also establish large-time behaviors of classical solutions showi...
2104.05153v1
2021-04-12
Fractional time stepping and adjoint based gradient computation in an inverse problem for a fractionally damped wave equation
In this paper we consider the inverse problem of identifying the initial data in a fractionally damped wave equation from time trace measurements on a surface, as relevant in photoacoustic or thermoacoustic tomography. We derive and analyze a time stepping method for the numerical solution of the corresponding forward ...
2104.05577v1
2021-04-15
Explaining Neptune's Eccentricity
Early migration damped Neptune's eccentricity. Here, we assume that the damped value was much smaller than the value observed today, and show that the closest flyby of $\sim 0.1 \; \mathrm{M_{\odot}}$ star over $\sim 4.5 \mathrm{\; Gyr}$ in the field, at a distance of $\sim 10^3 \mathrm{\; AU}$ would explain the value ...
2104.07672v3
2021-04-17
Lifespan estimates for wave equations with damping and potential posed on asymptotically Euclidean manifolds
In this work, we investigate the problem of finite time blow up as well as the upper bound estimates of lifespan for solutions to small-amplitude semilinear wave equations with time dependent damping and potential, and mixed nonlinearities $c_1 |u_t|^p+c_2 |u|^q$, posed on asymptotically Euclidean manifolds, which is r...
2104.08497v2
2021-06-02
Convergent dynamics of optimal nonlinear damping control
Following Demidovich's concept and definition of convergent systems, we analyze the optimal nonlinear damping control, recently proposed [1] for the second-order systems. Targeting the problem of output regulation, correspondingly tracking of $\mathcal{C}^1$-trajectories, it is shown that all solutions of the control s...
2106.00962v1
2021-06-26
Role of Dissipation on the Stability of a Parametrically Driven Quantum Harmonic Oscillator
We study the dissipative dynamics of a single quantum harmonic oscillator subjected to a parametric driving with in an effective Hamiltonian approach. Using Liouville von Neumann approach, we show that the time evolution of a parametrically driven dissipative quantum oscillator has a strong connection with the classica...
2106.14018v1
2021-07-29
Global existence for damped $σ$-evolution equations with nonlocal nonlinearity
In this research, we would like to study the global (in time) existence of small data solutions to the following damped $\sigma$-evolution equations with nonlocal (in space) nonlinearity: \begin{equation*} \partial_{t}^{2}u+(-\Delta)^{\sigma}u+\partial_{t}u+(-\Delta)^{\sigma}\partial_{t}u=I_{\alpha}(|u|^{p}), \ \ t>0, ...
2107.13924v1
2021-08-17
Estimate of the attractive velocity of attractors for some dynamical systems
In this paper, we first prove an abstract theorem on the existence of polynomial attractors and the concrete estimate of their attractive velocity for infinite-dimensional dynamical systems, then apply this theorem to a class of wave equations with nonlocal weak damping and anti-damping in case that the nonlinear term~...
2108.07410v4
2021-08-27
Distributed Mirror Descent Algorithm with Bregman Damping for Nonsmooth Constrained Optimization
To solve distributed optimization efficiently with various constraints and nonsmooth functions, we propose a distributed mirror descent algorithm with embedded Bregman damping, as a generalization of conventional distributed projection-based algorithms. In fact, our continuous-time algorithm well inherits good capabili...
2108.12136v1
2021-08-27
Non relativistic and ultra relativistic limits in 2d stochastic nonlinear damped Klein-Gordon equation
We study the non relativistic and ultra relativistic limits in the two-dimensional nonlinear damped Klein-Gordon equation driven by a space-time white noise on the torus. In order to take the limits, it is crucial to clarify the parameter dependence in the estimates of solution. In this paper we present two methods to ...
2108.12183v4
2021-09-08
The isothermal limit for the compressible Euler equations with damping
We consider the isothermal Euler system with damping. We rigorously show the convergence of Barenblatt solutions towards a limit Gaussian profile in the isothermal limit $\gamma$ $\rightarrow$ 1, and we explicitly compute the propagation and the behavior of Gaussian initial data. We then show the weak L 1 convergence o...
2109.03590v1
2021-11-01
Strong solution of modified 3D-Navier-stockes equations
In this paper we study the incompressible Navier-Stokes equations with logarithme damping {\alpha} log(e + |u|2)|u|2u, where we used new methods, new tools and Fourier analysis
2111.00859v2
2021-11-02
Blow-up of solutions to semilinear wave equations with a time-dependent strong damping
The paper investigates a class of a semilinear wave equation with time-dependent damping term ($-\frac{1}{{(1+t)}^{\beta}}\Delta u_t$) and a nonlinearity $|u|^p$. We will show the influence of the the parameter $\beta$ in the blow-up results under some hypothesis on the initial data and the exponent $p$ by using the te...
2111.01433v1
2021-11-02
Around plane waves solutions of the Schr{ö}dinger-Langevin equation
We consider the logarithmic Schr{\"o}dinger equations with damping, also called Schr{\"o}dinger-Langevin equation. On a periodic domain, this equation possesses plane wave solutions that are explicit. We prove that these solutions are asymptotically stable in Sobolev regularity. In the case without damping, we prove th...
2111.01487v1
2021-11-12
GCGE: A Package for Solving Large Scale Eigenvalue Problems by Parallel Block Damping Inverse Power Method
We propose an eigensolver and the corresponding package, GCGE, for solving large scale eigenvalue problems. This method is the combination of damping idea, subspace projection method and inverse power method with dynamic shifts. To reduce the dimensions of projection subspaces, a moving mechanism is developed when the ...
2111.06552v1
2021-11-25
Continuity and topological structural stability for nonautonomous random attractors
In this work, we study continuity and topological structural stability of attractors for nonautonomous random differential equations obtained by small bounded random perturbations of autonomous semilinear problems. First, we study existence and permanence of unstable sets of hyperbolic solutions. Then, we use this to e...
2111.13006v1
2021-12-20
Dense Coding Capacity in Correlated Noisy Channels with Weak Measurement
Capacity of dense coding via correlated noisy channel is greater than that in uncorrelated noisy channel. It is shown that weak measurement and reversal measurement can make further effort to improve quantum dense coding capacity in correlated amplitude damping channel, but this effort is very small in correlated phase...
2112.10346v1
2021-12-22
Low-frequency squeezing spectrum of a laser drivenpolar quantum emitter
It was shown by a study of the incoherent part of the low-frequency resonance fluorescence spectrum of the polar quantum emitter driven by semiclassical external laser field and damped by non-squeezed vacuum reservoir that the emitted fluorescence field is squeezed to some degree nevertheless. As was also found, a high...
2112.11809v1
2022-01-13
Cavity optomechanics in a fiber cavity: the role of stimulated Brillouin scattering
We study the role of stimulated Brillouin scattering in a fiber cavity by numerical simulations and a simple theoretical model and find good agreement between experiment, simulation and theory. We also investigate an optomechanical system based on a fiber cavity in the presence on the nonlinear Brillouin scattering. Us...
2201.04987v1
2022-01-20
Vacuum and singularity formation for compressible Euler equations with time-dependent damping
In this paper, vacuum and singularity formation are considered for compressible Euler equations with time-dependent damping. For $1<\gamma\leq 3$, by constructing some new control functions ingeniously, we obtain the lower bounds estimates on density for arbitrary classical solutions. Basing on these lower estimates, w...
2201.07957v1
2022-03-19
The Equilibrium Temperature of Planets on Eccentric Orbits: Time Scales and Averages
From estimates of the near-surface heat capacity of planets it is shown that the thermal time scale is larger than the orbital period in the presence of a global ocean that is well-mixed to a depth of 100 m, or of an atmosphere with a pressure of several tens of bars. As a consequence, the temperature fluctuations of s...
2203.11723v1
2022-03-31
Long-time dynamical behavior for a piezoelectric system with magnetic effect and nonlinear dampings
This paper is concerned with the long-time dynamical behavior of a piezoelectric system with magnetic effect, which has nonlinear damping terms and external forces with a parameter. At first, we use the nonlinear semigroup theory to prove the well-posedness of solutions. Then, we investigate the properties of global at...
2203.16736v1
2022-04-04
Exponential ergodicity for damping Hamiltonian dynamics with state-dependent and non-local collisions
In this paper, we investigate the exponential ergodicity in a Wasserstein-type distance for a damping Hamiltonian dynamics with state-dependent and non-local collisions, which indeed is a special case of piecewise deterministic Markov processes while is very popular in numerous modelling situations including stochastic...
2204.01372v1
2022-04-08
Effect of Tamm surface states on hot electron generation and Landau damping in nanostructures metal-semiconductor
The hot electron generation in plasmonic nanoparticles is the key to efficient plasmonic photocatalysis. In the paper, we study theoretically for the first time the effect of Tamm states (TSs) at the interface metal-semiconductor on hot electron generation and Landau damping (LD) in metal nanoparticles. TSs can lead to...
2204.04021v1
2022-04-11
Certified Reduced Basis Method for the Damped Wave Equations on Networks
In this paper we present a reduced basis method which yields structure-preservation and a tight a posteriori error bound for the simulation of the damped wave equations on networks. The error bound is based on the exponential decay of the energy inside the system and therefore allows for sharp bounds without the need o...
2204.05010v1
2022-04-27
Spectrum of the wave equation with Dirac damping on a non-compact star graph
We consider the wave equation on non-compact star graphs, subject to a distributional damping defined through a Robin-type vertex condition with complex coupling. It is shown that the non-self-adjoint generator of the evolution problem admits an abrupt change in its spectral properties for a special coupling related to...
2204.12747v1
2022-04-27
Dependence on the thermodynamic state of self-diffusion of pseudo hard-spheres
Self-diffusion, $D$, in a system of particles that interact with a pseudo hard sphere potential is analyzed. Coupling with a solvent is represented by a Langevin thermostat, characterized by the damping time $t_d$. The hypotheses that $D=D_0 \varphi$ is proposed, where $D_0$ is the small concentration diffusivity and $...
2204.12969v1
2022-04-29
Plasmon damping rates in Coulomb-coupled two-dimensional layers in a heterostructure
The Coulomb excitations of charge density oscillation are calculated for a double-layer heterostructure. Specifically, we consider two-dimensional (2D) layers of silicene and graphene on a substrate. From the obtained surface response function, we calculated the plasmon dispersion relations which demonstrate the way in...
2205.00053v1
2022-05-08
A regularity criterion for a 3D tropical climate model with damping
In this paper we deal with the 3D tropical climate model with damping terms in the equation of the barotropic mode $u$ and in the equation of the first baroclinic mode $v$ of the velocity, and we establish a regularity criterion for this system thanks to which the local smooth solution $(u, v, \theta)$ can actually be ...
2205.03841v3
2022-06-04
Radiation backreaction in axion electrodynamics
Energy-momentum conservation of classical axion-electrodynamics is carefully analyzed in the Hamiltonian formulation of the theory. The term responsible for the energy transfer between the electromagnetic and the axion sectors is identified. As a special application the axion-to-light Primakoff-process in the backgroun...
2206.02052v1
2022-06-07
Strong attractors for weakly damped quintic wave equation in bounded domains
In this paper, we study the longtime dynamics for the weakly damped wave equation with quintic non-linearity in a bounded smooth domain of $\mathbb{R}^3.$ Based on the Strichartz estimates for the case of bounded domains, we establish the existence of a strong global attractor in the phase space $H^2(\Omega)\cap H^1_0(...
2206.03158v1
2022-06-07
Long-time dynamics of the wave equation with nonlocal weak damping and sup-cubic nonlinearity in 3-D domains
In this paper, we study the long-time dynamics for the wave equation with nonlocal weak damping and sup-cubic nonlinearity in a bounded smooth domain of $\mathbb{R}^3.$ Based on the Strichartz estimates for the case of bounded domains, we first prove the global well-posedness of the Shatah-Struwe solutions. Then we est...
2206.03163v1
2022-06-17
On energy-stable and high order finite element methods for the wave equation in heterogeneous media with perfectly matched layers
This paper presents a stable finite element approximation for the acoustic wave equation on second-order form, with perfectly matched layers (PML) at the boundaries. Energy estimates are derived for varying PML damping for both the discrete and the continuous case. Moreover, a priori error estimates are derived for con...
2206.08507v1
2022-06-20
Harmonic Oscillators of Mathematical Biology: Many Faces of a Predator-Prey Model
We show that a number of models in virus dynamics, epidemiology and plant biology can be presented as ``damped" versions of the Lotka-Volterra predator-prey model, by analogy to the damped harmonic oscillator. The analogy deepens with the use of Lyapunov functions, which allow us to characterize their dynamics and even...
2206.09561v1
2022-06-21
Phase-covariant mixtures of non-unital qubit maps
We analyze convex combinations of non-unital qubit maps that are phase-covariant. In particular, we consider the behavior of maps that combine amplitude damping, inverse amplitude damping, and pure dephasing. We show that mixing non-unital channels can result in restoring the unitality, whereas mixing commutative maps ...
2206.10742v1
2022-07-01
Stabilization results of a Lorenz piezoelectric beam with partial viscous dampings
In this paper, we investigate the stabilization of a one-dimensional Lorenz piezoelectric (Stretching system) with partial viscous dampings. First, by using Lorenz gauge conditions, we reformulate our system to achieve the existence and uniqueness of the solution. Next, by using General criteria of Arendt-Batty, we pro...
2207.00488v1
2022-07-06
Quantum Decomposition Algorithm For Master Equations of Stochastic Processes: The Damped Spin Case
We introduce a quantum decomposition algorithm (QDA) that decomposes the problem $\frac{\partial \rho}{\partial t}=\mathcal{L}\rho=\lambda \rho$ into a summation of eigenvalues times phase-space variables. One interesting feature of QDA stems from its ability to simulate damped spin systems by means of pure quantum har...
2207.02755v3
2022-07-25
Geometric modelling of polycrystalline materials: Laguerre tessellations and periodic semi-discrete optimal transport
In this paper we describe a fast algorithm for generating periodic RVEs of polycrystalline materials. In particular, we use the damped Newton method from semi-discrete optimal transport theory to generate 3D periodic Laguerre tessellations (or power diagrams) with cells of given volumes. Complex, polydisperse RVEs with...
2207.12036v1