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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
2022-06-25
Decay estimate in a viscoelastic plate equation with past history, nonlinear damping, and logarithmic nonlinearity
In this article, we consider a viscoelastic plate equation with past history, nonlinear damping, and logarithmic nonlinearity. We prove explicit and general decay rate results of the solution to the viscoelastic plate equation with past history. Convex properties, logarithmic inequalities, and generalised Young's inequality are mainly used to prove the decay estimate.
2206.12561v1
2022-06-30
Effect of a viscous fluid shell on the propagation of gravitational waves
In this paper we show that there are circumstances in which the damping of gravitational waves (GWs) propagating through a viscous fluid can be highly significant; in particular, this applies to Core Collapse Supernovae (CCSNe). In previous work, we used linearized perturbations on a fixed background within the Bondi-Sachs formalism, to determine the effect of a dust shell on GW propagation. Here, we start with the (previously found) velocity field of the matter, and use it to determine the shear tensor of the fluid flow. Then, for a viscous fluid, the energy dissipated is calculated, leading to an equation for GW damping. It is found that the damping effect agrees with previous results when the wavelength $\lambda$ is much smaller than the radius $r_i$ of the matter shell; but if $\lambda\gg r_i$, then the damping effect is greatly increased. Next, the paper discusses an astrophysical application, CCSNe. There are several different physical processes that generate GWs, and many models have been presented in the literature. The damping effect thus needs to be evaluated with each of the parameters $\lambda,r_i$ and the coefficient of shear viscosity $\eta$, having a range of values. It is found that in most cases there will be significant damping, and in some cases that it is almost complete. We also consider the effect of viscous damping on primordial gravitational waves (pGWs) generated during inflation in the early Universe. Two cases are investigated where the wavelength is either much shorter than the shell radii or much longer; we find that there are conditions that will produce significant damping, to the extent that the waves would not be detectable.
2206.15103v2
2022-09-07
Blow up and lifespan estimates for systems of semi-linear wave equations with dampings and potentials
In this paper, we consider the semi-linear wave systems with power-nonlinearities and space-dependent dampings and potentials. We obtain the blow-up regions for three types wave systems as well as the lifespan estimates.
2209.02920v1
2022-12-04
Inverse problem of recovering the time-dependent damping and nonlinear terms for wave equations
In this paper, we consider the inverse boundary problems of recovering the time-dependent nonlinearity and damping term for a semilinear wave equation on a Riemannian manifold. The Carleman estimate and the construction of Gaussian beams together with the higher order linearization are respectively used to derive the uniqueness results of recovering the coefficients.
2212.01815v2
2022-12-14
Gevrey regularity for the Euler-Bernoulli beam equation with localized structural damping
We study a Euler-Bernoulli beam equation with localized discontinuous structural damping. As our main result, we prove that the associated $C_0$-semigroup $(S(t))_{t\geq0}$ is of Gevrey class $\delta>24$ for $t>0$, hence immediately differentiable. Moreover, we show that $(S(t))_{t\geq0}$ is exponentially stable.
2212.07110v1
2022-12-28
On extended lifespan for 1d damped wave equation
In this manuscript, a sharp lifespan estimate of solutions to semilinear classical damped wave equation is investigated in one dimensional case, when the sum of initial position and speed is $0$ pointwisely. Especially, an extension of lifespan is shown in this case. Moreover, existence of some global solutions are obtained by a direct computation.
2212.13845v1
2023-02-06
Uniform stabilization of an acoustic system
We study the problem of stabilization for the acoustic system with a spatially distributed damping. With imposing hypothesis on the structural properties of the damping term, we identify exponential decay of solutions with growing time.
2302.02726v1
2023-04-23
Decay rates for a variable-coefficient wave equation with nonlinear time-dependent damping
In this paper, a class of variable-coefficient wave equations equipped with time-dependent damping and the nonlinear source is considered. We show that the total energy of the system decays to zero with an explicit and precise decay rate estimate under different assumptions on the feedback with the help of the method of weighted energy integral.
2304.11522v1
2023-05-22
Fast energy decay for wave equation with a monotone potential and an effective damping
We consider the total energy decay of the Cauchy problem for wave equations with a potential and an effective damping. We treat it in the whole one-dimensional Euclidean space. Fast energy decay is established with the help of potential. The proofs of main results rely on a multiplier method and modified techniques adopted in [8].
2305.12666v1
2023-08-03
Blow-up for semilinear wave equations with damping and potential in high dimensional Schwarzschild spacetime
In this work, we study the blow up results to power-type semilinear wave equation in the high dimensional Schwarzschild spacetime, with damping and potential terms. We can obtain the upper bound estimates of lifespan without the assumption that the support of the initial date should be far away from the black hole.
2308.01691v1
2023-08-22
Lifespan estimates for 1d damped wave equation with zero moment initial data
In this manuscript, a sharp lifespan estimate of solutions to semilinear classical damped wave equation is investigated in one dimensional case when the Fourier 0th moment of sum of initial position and speed is $0$. Especially, it is shown that the behavior of lifespan changes with $p=3/2$ with respect to the size of the initial data.
2308.11113v1
2023-09-01
Damped Euler system with attractive Riesz interaction forces
We consider the barotropic Euler equations with pairwise attractive Riesz interactions and linear velocity damping in the periodic domain. We establish the global-in-time well-posedness theory for the system near an equilibrium state. We also analyze the large-time behavior of solutions showing the exponential rate of convergence toward the equilibrium state as time goes to infinity.
2309.00210v1
2023-10-02
The damped wave equation and associated polymer
Considering the damped wave equation with a Gaussian noise $F$ where $F$ is white in time and has a covariance function depending on spatial variables, we will see that this equation has a mild solution which is stationary in time $t$. We define a weakly self-avoiding polymer with intrinsic length $J$ associated to this SPDE. Our main result is that the polymer has an effective radius of approximately $J^{5/3}$.
2310.01631v1
2023-10-17
Indirect boundary stabilization for weakly coupled degenerate wave equations under fractional damping
In this paper, we consider the well-posedness and stability of a one-dimensional system of degenerate wave equations coupled via zero order terms with one boundary fractional damping acting on one end only. We prove optimal polynomial energy decay rate of order $1/t^{(3-\tau)}$. The method is based on the frequency domain approach combined with multiplier technique.
2310.11174v1
2024-03-11
Uniform estimates for solutions of nonlinear focusing damped wave equations
For a damped wave (or Klein-Gordon) equation on a bounded domain, with a focusing power-like nonlinearity satisfying some growth conditions, we prove that a global solution is bounded in the energy space, uniformly in time. Our result applies in particular to the case of a cubic equation on a bounded domain of dimension 3.
2403.06541v1
1995-10-27
A modified R1 X R1 method for helioseismic rotation inversions
We present an efficient method for two dimensional inversions for the solar rotation rate using the Subtractive Optimally Localized Averages (SOLA) method and a modification of the R1 X R1 technique proposed by Sekii (1993). The SOLA method is based on explicit construction of averaging kernels similar to the Backus-Gilbert method. The versatility and reliability of the SOLA method in reproducing a target form for the averaging kernel, in combination with the idea of the R1 X R1 decomposition, results in a computationally very efficient inversion algorithm. This is particularly important for full 2-D inversions of helioseismic data in which the number of modes runs into at least tens of thousands.
9510143v1
1997-10-22
Globular Cluster Microlensing: Globular Clusters as Microlensing Targets
We investigate the possibility of using globular clusters as targets for microlensing searches. Such searches will be challenging and require more powerful telescopes than now employed, but are feasible in the 0 future. Although expected event rates are low, we show that the wide variety of lines of sight to globular clusters greatly enhances the ability to distinguish between halo models using microlensing observations as compared to LMC/SMC observations alone.
9710251v1
2002-12-17
An Intrinsic Baldwin Effect in the H-beta Broad Emission Line in the Spectrum of NGC 5548
We investigate the possibility of an intrinsic Baldwin Effect (i.e.,nonlinear emission-line response to continuum variations) in the broad H-beta emission line of the active galaxy NGC 5548 using cross-correlation techniques to remove light travel-time effects from the data. We find a nonlinear relationship between the H-beta emission line and continuum fluxes that is in good agreement with theoretical predictions. We suggest that similar analysis of multiple lines might provide a useful diagnostic of physical conditions in the broad-line region.
0212379v1
2002-12-28
Detecting supersymmetric dark matter in M31 with CELESTE ?
It is widely believed that dark matter exists within galaxies and clusters of galaxies. Under the assumption that this dark matter is composed of the lightest, stable supersymmetric particle, assumed to be the neutralino, the feasibility of its indirect detection via observations of a diffuse gamma-ray signal due to neutralino annihilation within M31 is examined.
0212560v1
2003-03-18
Model-Independent Reionization Observables in the CMB
We represent the reionization history of the universe as a free function in redshift and study the potential for its extraction from CMB polarization spectra. From a principal component analysis, we show that the ionization history information is contained in 5 modes, resembling low-order Fourier modes in redshift space. The amplitude of these modes represent a compact description of the observable properties of reionization in the CMB, easily predicted given a model for the ionization fraction. Measurement of these modes can ultimately constrain the total optical depth, or equivalently the initial amplitude of fluctuations to the 1% level regardless of the true model for reionization.
0303400v1
2006-05-08
Discovery of an Extended Halo of Metal-poor Stars in the Andromeda Spiral Galaxy
This paper has been withdrawn. Please see astro-ph/0502366.
0605172v3
1995-01-02
Dynamics of homogeneous magnetizations in strong transverse driving fields
Spatially homogeneous solutions of the Landau--Lifshitz--Gilbert equation are analysed. The conservative as well as the dissipative case is considered explicitly. For the linearly polarized driven Hamiltonian system we apply canonical perturbation theory to uncover the main resonances as well as the global phase space structure. In the case of circularly polarized driven dissipative motion we present the complete bifurcation diagram including bifurcations up to codimension three.
9501002v1
2000-09-18
Electronic properties of the degenerate Hubbard Model : A dynamical mean field approach
We have investigated electronic properties of the degenerate multi-orbital Hubbard model, in the limit of large spatial dimension. A new local model, including a doubly degenerate strongly correlated site has been introduced and solved in the framework of the non-crossing approximation (NCA). Mott-Hubbard transitions have been examined in details, including the calculation of Coulomb repulsion critical values and electronic densities of states for any regime of parameters.
0009253v1
2001-01-11
Theoretical and Experimental Approach to Spin Dynamics in Thin Magnetic Films
The Landau-Lifshitz (L-L) equation describing the time dependence of the magnetisation vector is numerically integrated fully without any simplifying assumptions in the time domain and the magnetisation time series obtained is Fourier transformed (FFT) to yield the permeability spectrum up to 10 GHz. The non linear results are compared to the experimental results obtained on magnetic amorphous thin films of Co-Zr, Co-Zr-Re. We analyse our results with the frequency response obtained directly from the Landau-Lifshitz equation as well as with the second order Gilbert frequency response.
0101154v1
2004-08-13
Finite lattice size effect in the ground state phase diagram of quasi-two-dimensional magnetic dipolar dots array with perpendicular anisotropy
A prototype Hamiltonian for the generic patterned magnetic structures, of dipolar interaction with perpendicular anisotropy, is investigated within the finite-size framework by Landau-Lifshift-Gilbert classical spin dynamics. Modifications on the ground state phase diagram are discussed with an emphasis on the disappearance of continuous degeneracy in the ground state of in-plane phase due to the finite lattice size effect. The symmetry-governed ground state evolution upon the lattice size increase provides a critical insight into the systematic transition to the infinite extreme.
0408324v1
2004-10-01
Current-spin coupling for ferromagnetic domain walls in fine wires
The coupling between a current and a domain wall is examined. In the presence of a finite current and the absence of a potential which breaks the translational symmetry, there is a perfect transfer of angular momentum from the conduction electrons to the wall. As a result, the ground state is in uniform motion. This remains the case when relaxation is accounted for. This is described by, appropriately modified, Landau-Lifshitz-Gilbert equations.
0410035v1
2004-12-17
Hysteresis loops of magnetic thin films with perpendicular anisotropy
We model the magnetization of quasi two-dimensional systems with easy perpendicular (z-)axis anisotropy upon change of external magnetic field along z. The model is derived from the Landau-Lifshitz-Gilbert equation for magnetization evolution, written in closed form in terms of the z component of the magnetization only. The model includes--in addition to the external field--magnetic exchange, dipolar interactions and structural disorder. The phase diagram in the disorder/interaction strength plane is presented, and the different qualitative regimes are analyzed. The results compare very well with observed experimental hysteresis loops and spatial magnetization patterns, as for instance for the case of Co-Pt multilayers.
0412461v1
2006-01-11
Relaxing-Precessional Magnetization Switching
A new way of magnetization switching employing both the spin-transfer torque and the torque by a magnetic field is proposed. The solution of the Landau-Lifshitz-Gilbert equation shows that the dynamics of the magnetization in the initial stage of the switching is similar to that in the precessional switching, while that in the final stage is rather similar to the relaxing switching. We call the present method the relaxing-precessional switching. It offers a faster and lower-power-consuming way of switching than the relaxing switching and a more controllable way than the precessional switching.
0601227v1
2006-04-01
Magnetization reversal through synchronization with a microwave
Based on the Landau-Lifshitz-Gilbert equation, it can be shown that a circularly-polarized microwave can reverse the magnetization of a Stoner particle through synchronization. In comparison with magnetization reversal induced by a static magnetic field, it can be shown that when a proper microwave frequency is used the minimal switching field is much smaller than that of precessional magnetization reversal. A microwave needs only to overcome the energy dissipation of a Stoner particle in order to reverse magnetization unlike the conventional method with a static magnetic field where the switching field must be of the order of magnetic anisotropy.
0604013v1
2006-05-25
Time Quantified Monte Carlo Algorithm for Interacting Spin Array Micromagnetic Dynamics
In this paper, we reexamine the validity of using time quantified Monte Carlo (TQMC) method [Phys. Rev. Lett. 84, 163 (2000); Phys. Rev. Lett. 96, 067208 (2006)] in simulating the stochastic dynamics of interacting magnetic nanoparticles. The Fokker-Planck coefficients corresponding to both TQMC and Langevin dynamical equation (Landau-Lifshitz-Gilbert, LLG) are derived and compared in the presence of interparticle interactions. The time quantification factor is obtained and justified. Numerical verification is shown by using TQMC and Langevin methods in analyzing spin-wave dispersion in a linear array of magnetic nanoparticles.
0605621v1
2006-06-26
Self Consistent NEGF-LLG Model for Spin-Torque Based Devices
We present here a self consistent solution of quantum transport, using the Non Equilibrium Green's Function (NEGF) method, and magnetization dynamics, using the Landau-Lifshitz-Gilbert (LLG) formulation. We have applied this model to study current induced magnetic switching due to `spin torque' in a device where the electronic transport is ballistic and the free magnetic layer is sandwiched between two anti-parallel ferromagnetic contacts. The device shows clear hysteretic current-voltage characteristics, at room temperature, with a sharp transition between the bistable states and hence can be used as a non-volatile memory. We show that the proposed design may allow reducing the switching current by an order of magnitude.
0606648v2
2006-07-25
Thermally-Assisted Current-Driven Domain Wall Motion
Starting from the stochastic Landau-Lifschitz-Gilbert equation, we derive Langevin equations that describe the nonzero-temperature dynamics of a rigid domain wall. We derive an expression for the average drift velocity of the domain wall as a function of the applied current, and find qualitative agreement with recent magnetic semiconductor experiments. Our model implies that at any nonzero temperature the average domain-wall velocity initially varies linearly with current, even in the absence of non-adiabatic spin torques.
0607663v1
2006-09-08
Large cone angle magnetization precession of an individual nanomagnet with dc electrical detection
We demonstrate on-chip resonant driving of large cone-angle magnetization precession of an individual nanoscale permalloy element. Strong driving is realized by locating the element in close proximity to the shorted end of a coplanar strip waveguide, which generates a microwave magnetic field. We used a microwave frequency modulation method to accurately measure resonant changes of the dc anisotropic magnetoresistance. Precession cone angles up to $9^{0}$ are determined with better than one degree of resolution. The resonance peak shape is well-described by the Landau-Lifshitz-Gilbert equation.
0609190v1
2006-12-30
Low relaxation rate in a low-Z alloy of iron
The longest relaxation time and sharpest frequency content in ferromagnetic precession is determined by the intrinsic (Gilbert) relaxation rate \emph{$G$}. For many years, pure iron (Fe) has had the lowest known value of $G=\textrm{57 Mhz}$ for all pure ferromagnetic metals or binary alloys. We show that an epitaxial iron alloy with vanadium (V) possesses values of $G$ which are significantly reduced, to 35$\pm$5 Mhz at 27% V. The result can be understood as the role of spin-orbit coupling in generating relaxation, reduced through the atomic number $Z$.
0701004v1
2004-09-07
Distance properties of expander codes
We study the minimum distance of codes defined on bipartite graphs. Weight spectrum and the minimum distance of a random ensemble of such codes are computed. It is shown that if the vertex codes have minimum distance $\ge 3$, the overall code is asymptotically good, and sometimes meets the Gilbert-Varshamov bound. Constructive families of expander codes are presented whose minimum distance asymptotically exceeds the product bound for all code rates between 0 and 1.
0409010v1
1996-06-11
Radiative corrections to $e^+e^-\to H^+ H^-$
We study the 1-loop corrections to the charged Higgs production both in the Minimal Supersymmetric Standard Model (MSSM) and in a more general type II two-Higgs-doublet model (THDM-II). We consider the full set of corrections (including soft photon contributions as well as box diagrams), and define a parametrization that allows a comparison between the two models. Besides the soft photon radiation there can be prominent model-dependent effects.
9606300v1
1997-05-15
Analytic constraints from electroweak symmetry breaking in the MSSM
We report on how a straightforward (albeit technically involved) analytic study of the 1-loop effective potential in the Minimal Supersymmetric Standard Model, modifies the usual electroweak symmetry breaking conditions involving $\tan \beta$ and the other free parameters of the model. The study implies new constraints which (in contrast with the existing ones like $1 \leq \tan \beta \leq m_t/m_b$) are fully model-independent and exclude more restrictively a region around $\tan \beta \sim 1$. Further results of this study will be only touched upon here.
9705330v1
1998-10-01
Extracting chargino/neutralino mass parameters from physical observables
I report on two papers, hep-ph/9806279 and hep-ph/9807336, where complementary strategies are proposed for the determination of the chargino/neutralino sector parameters, $M_1, M_2, \mu $ and $\tan \beta$, from the knowledge of some physical observables. This determination and the occurrence of possible ambiguities are studied as far as possible analytically within the context of the unconstrained MSSM, assuming however no CP-violation.
9810214v1
1999-12-28
Associated H$^{-}$ W$^{+}$ Production in High Energy $e^+e^-$ Collisions
We study the associated production of charged Higgs bosons with $W$ gauge bosons in high energy $e^+ e^-$ collisions at the one loop level. We present the analytical results and give a detailed discussion for the total cross section predicted in the context of a general Two Higgs Doublet Model (THDM).
9912527v2
2001-03-25
Comment on ``Infrared Fixed Point Structure in Minimal Supersymmetric Standard Model with Baryon and Lepton Number Violation"
We reconsider the Infrared Quasi Fixed Points which were studied recently in the literature in the context of the Baryon and Lepton number violating Minimal Supersymmetric Standard Model (hep-ph/0011274). The complete analysis requires further care and reveals more structure than what was previously shown. The formalism we develop here is quite general, and can be readily applied to a large class of models.
0103270v1
1991-11-21
"the Instability of String-Theoretic Black Holes"
It is demonstrated that static, charged, spherically--symmetric black holes in string theory are classically and catastrophically unstable to linearized perturbations in four dimensions, and moreover that unstable modes appear for arbitrarily small positive values of the charge. This catastrophic classical instability dominates and is distinct from much smaller and less significant effects such as possible quantum mechanical evaporation. The classical instability of the string--theoretic black hole contrasts sharply with the situation which obtains for the Reissner--Nordstr\"om black hole of general relativity, which has been shown by Chandrasekhar to be perfectly stable to linearized perturbations at the event horizon.
9111042v1
1997-12-09
The combinatorics of biased riffle shuffles
This paper studies biased riffle shuffles, first defined by Diaconis, Fill, and Pitman. These shuffles generalize the well-studied Gilbert-Shannon-Reeds shuffle and convolve nicely. An upper bound is given for the time for these shuffles to converge to the uniform distribution; this matches lower bounds of Lalley. A careful version of a bijection of Gessel leads to a generating function for cycle structure after one of these shuffles and gives new results about descents in random permutations. Results are also obtained about the inversion and descent structure of a permutation after one of these shuffles.
9712240v1
2000-08-16
Homotopies and automorphisms of crossed modules of groupoids
We give a detailed description of the structure of the actor 2-crossed module related to the automorphisms of a crossed module of groupoids. This generalises work of Brown and Gilbert for the case of crossed modules of groups, and part of this is needed for work on 2-dimensional holonomy to be developed elsewhere (see math.DG/0009082).
0008117v2
2005-06-14
Transitive and Self-dual Codes Attaining the Tsfasman-Vladut-Zink Bound
We introduce - as a generalization of cyclic codes - the notion of transitive codes, and we show that the class of transitive codes is asymptotically good. Even more, transitive codes attain the Tsfasman-Vladut-Zink bound over F_q, for all aquares q=l^2. We also show that self-orthogonal and self-dual codes attain the Tsfasman-Vladut-Zink bound, thus improving previous results about self-dual codes attaining the Gilbert-Varshamov bound. The main tool is a new asymptotically optimal tower (E_n) of function fields over F_q where all extensions E_n/E_0 are Galois.
0506264v1
2005-09-01
Counting unlabelled toroidal graphs with no K33-subdivisions
We provide a description of unlabelled enumeration techniques, with complete proofs, for graphs that can be canonically obtained by substituting 2-pole networks for the edges of core graphs. Using structure theorems for toroidal and projective-planar graphs containing no K33-subdivisions, we apply these techniques to obtain their unlabelled enumeration.
0509004v2
2006-05-19
Deformation spaces of trees
Let G be a finitely generated group. Two simplicial G-trees are said to be in the same deformation space if they have the same elliptic subgroups (if H fixes a point in one tree, it also does in the other). Examples include Culler-Vogtmann's outer space, and spaces of JSJ decompositions. We discuss what features are common to trees in a given deformation space, how to pass from one tree to all other trees in its deformation space, and the topology of deformation spaces. In particular, we prove that all deformation spaces are contractible complexes.
0605545v2
1999-10-12
Uniform spectral properties of one-dimensional quasicrystals, III. $α$-continuity
We study the spectral properties of discrete one-dimensional Schr\"odinger operators with Sturmian potentials. It is shown that the point spectrum is always empty. Moreover, for rotation numbers with bounded density, we establish purely $\alpha$-continuous spectrum, uniformly for all phases. The proofs rely on the unique decomposition property of Sturmian potentials, a mass-reproduction technique based upon a Gordon-type argument, and on the Jitomirskaya-Last extension of the Gilbert-Pearson theory of subordinacy.
9910017v1
2003-08-18
Vector Coherent States on Clifford algebras
The well-known canonical coherent states are expressed as an infinite series in powers of a complex number $z$ together with a positive sequence of real numbers $\rho(m)=m$. In this article, in analogy with the canonical coherent states, we present a class of vector coherent states by replacing the complex variable $z$ by a real Clifford matrix. We also present another class of vector coherent states by simultaneously replacing $z$ by a real Clifford matrix and $\rho(m)$ by a real matrix. As examples, we present vector coherent states on quaternions and octonions with their real matrix representations.
0308020v2
2000-07-10
Fractal Dimensions of the Hydrodynamic Modes of Diffusion
We consider the time-dependent statistical distributions of diffusive processes in relaxation to a stationary state for simple, two dimensional chaotic models based upon random walks on a line. We show that the cumulative functions of the hydrodynamic modes of diffusion form fractal curves in the complex plane, with a Hausdorff dimension larger than one. In the limit of vanishing wavenumber, we derive a simple expression of the diffusion coefficient in terms of this Hausdorff dimension and the positive Lyapunov exponent of the chaotic model.
0007008v1
2000-10-06
The Fractality of the Hydrodynamic Modes of Diffusion
Transport by normal diffusion can be decomposed into the so-called hydrodynamic modes which relax exponentially toward the equilibrium state. In chaotic systems with two degrees of freedom, the fine scale structure of these hydrodynamic modes is singular and fractal. We characterize them by their Hausdorff dimension which is given in terms of Ruelle's topological pressure. For long-wavelength modes, we derive a striking relation between the Hausdorff dimension, the diffusion coefficient, and the positive Lyapunov exponent of the system. This relation is tested numerically on two chaotic systems exhibiting diffusion, both periodic Lorentz gases, one with hard repulsive forces, the other with attractive, Yukawa forces. The agreement of the data with the theory is excellent.
0010017v1
2007-01-12
Non-equilibrium Lorentz gas on a curved space
The periodic Lorentz gas with external field and iso-kinetic thermostat is equivalent, by conformal transformation, to a billiard with expanding phase-space and slightly distorted scatterers, for which the trajectories are straight lines. A further time rescaling allows to keep the speed constant in that new geometry. In the hyperbolic regime, the stationary state of this billiard is characterized by a phase-space contraction rate, equal to that of the iso-kinetic Lorentz gas. In contrast to the iso-kinetic Lorentz gas where phase-space contraction occurs in the bulk, the phase-space contraction rate here takes place at the periodic boundaries.
0701024v1
1998-05-29
Atom cooling and trapping by disorder
We demonstrate the possibility of three-dimensional cooling of neutral atoms by illuminating them with two counterpropagating laser beams of mutually orthogonal linear polarization, where one of the lasers is a speckle field, i.e. a highly disordered but stationary coherent light field. This configuration gives rise to atom cooling in the transverse plane via a Sisyphus cooling mechanism similar to the one known in standard two-dimensional optical lattices formed by several plane laser waves. However, striking differences occur in the spatial diffusion coefficients as well as in local properties of the trapped atoms.
9805037v1
2006-02-23
Equivalence of two mathematical forms for the bound angular momentum of the electromagnetic field
It is shown that the mathematical form, obtained in a recent paper, for the angular momentum of the electromagnetic field in the vicinity of electric charge is equivalent to another form obtained previously by Cohen-Tannoudji, Dupont-Roc and Gilbert. In this version of the paper an improved derivation is given.
0602157v3
2006-10-13
Senescence Can Explain Microbial Persistence
It has been known for many years that small fractions of persister cells resist killing in many bacterial colony-antimicrobial confrontations. These persisters are not believed to be mutants. Rather it has been hypothesized that they are phenotypic variants. Current models allow cells to switch in and out of the persister phenotype. Here we suggest a different explanation, namely senescence, for persister formation. Using a mathematical model including age structure, we show that senescence provides a natural explanation for persister-related phenomena including the observations that persister fraction depends on growth phase in batch culture and dilution rate in continuous culture.
0610026v1