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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