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2018-04-15
Reevaluation of radiation reaction and consequences for light-matter interactions at the nanoscale
In the context of electromagnetism and nonlinear optical interactions damping is generally introduced as a phenomenological, viscous term that dissipates energy, proportional to the temporal derivative of the polarization. Here, we follow the radiation reaction method presented in [G. W. Ford and R. F. O'Connell, Phys. Lett. A, 157, 217 (1991)], which applies to non-relativistic electrons of finite size, to introduce an explicit reaction force in the Newtonian equation of motion, and derive a hydrodynamic equation that offers new insight on the influence of damping in generic plasmas, metal-based and/or dielectric structures. In these settings, we find new damping-dependent linear and nonlinear source terms that suggest the damping coefficient is proportional to the local charge density, and nonlocal contributions that stem from the spatial derivative of the magnetic field and discuss the conditions that could modify both linear and nonlinear electromagnetic responses.
1804.05369v1
2018-04-30
Wave-like blow-up for semilinear wave equations with scattering damping and negative mass term
In this paper we establish blow-up results and lifespan estimates for semilinear wave equations with scattering damping and negative mass term for subcritical power, which is the same as that of the corresponding problem without mass term, and also the same as that of the corresponding problem without both damping and mass term. For this purpose, we have to use the comparison argument twice, due to the damping and mass term, in additional to a key multiplier. Finally, we get the desired results by an iteration argument.
1804.11073v3
2018-05-22
Uniqueness of the Cauchy datum for the tempered-in-time response and conductivity operator of a plasma
We study the linear Vlasov equation with a given electric field $E \in \mathcal{S}$, where $\mathcal{S}$ is the space of Schwartz functions. The associated damped partial differential equation has a unique tempered solution, which fixes the needed Cauchy datum. This tempered solution then converges to the causal solution of the linear Vlasov equation when the damping parameter goes to zero. This result allows us to define the plasma conductivity operator $\sigma$, which gives the current density $j = \sigma (E)$ induced by the electric field $E$. We prove that $\sigma$ is continuous from $\mathcal{S}$ to its dual $\mathcal{S}^\prime$. We can treat rigorously the case of uniform non-magnetized non-relativistic plasma (linear Landau damping) and the case of uniform magnetized relativistic plasma (cyclotron damping). In both cases, we demonstrate that the main part of the conductivity operator is a pseudo-differential operator and we give its expression rigorously. This matches the formal results widely used in the theoretical physics community.
1805.08733v3
2018-05-26
Stabilization for the wave equation with singular Kelvin-Voigt damping
We consider the wave equation with Kelvin-Voigt damping in a bounded domain. The exponential stability result proposed by Liu and Rao or T\'ebou for that system assumes that the damping is localized in a neighborhood of the whole or a part of the boundary under some consideration. In this paper we propose to deal with this geometrical condition by considering a singular Kelvin-Voigt damping which is localized faraway from the boundary. In this particular case it was proved by Liu and Liu the lack of the uniform decay of the energy. However, we show that the energy of the wave equation decreases logarithmically to zero as time goes to infinity. Our method is based on the frequency domain method. The main feature of our contribution is to write the resolvent problem as a transmission system to which we apply a specific Carleman estimate.
1805.10430v1
2018-06-01
Fluctuation-damping of isolated, oscillating Bose-Einstein condensates
Experiments on the nonequilibrium dynamics of an isolated Bose-Einstein condensate (BEC) in a magnetic double-well trap exhibit a puzzling divergence: While some show dissipation-free Josephson oscillations, others find strong damping. Such damping in isolated BECs cannot be understood on the level of the coherent Gross-Pitaevskii dynamics. Using the Keldysh functional-integral formalism, we describe the time-dependent system dynamics by means of a multi-mode BEC coupled to fluctuations (single-particle excitations) beyond the Gross-Pitaevskii saddle point. We find that the Josephson oscillations excite an excess of fluctuations when the effective Josephson frequency, $\tilde{\omega}_J$, is in resonance with the effective fluctuation energy, $\tilde{\varepsilon}_m$, where both, $\tilde{\omega}_J$ and $\tilde{\varepsilon}_m$, are strongly renormalized with respect to their noninteracting values. Evaluating and using the model parameters for the respective experiments describes quantitatively the presence or absence of damping.
1806.00376v2
2018-06-05
Decoherence assisted spin squeezing generation in superposition of tripartite GHZ and W states
In the present paper, we study spin squeezing under decoherence in the superposition of tripartite maximally entangled GHZ and W states. Here we use amplitude damping, phase damping and depolarisation channel. We have investigated the dynamics of spin squeezing with the interplay of superposition and decoherence parameters with different directions of the mean spin vector. We have found the mixture of GHZ and W states is robust against spin squeezing generation for amplitude damping and phase damping channels for certain directions of the mean spin vector. However, the depolarisation channel performs well for spin squeezing generation and generates permanent spin squeezing in the superposition of GHZ and W states.
1806.01730v1
2018-07-31
Dark Matter Particle Explorer observations of high-energy cosmic ray electrons plus positrons and their physical implications
The DArk Matter Particle Explorer (DAMPE) is a satellite-borne, high-energy particle and $\gamma$-ray detector, which is dedicated to indirectly detecting particle dark matter and studying high-energy astrophysics. The first results about precise measurement of the cosmic ray electron plus positron spectrum between 25 GeV and 4.6 TeV were published recently. The DAMPE spectrum reveals an interesting spectral softening around $0.9$ TeV and a tentative peak around $1.4$ TeV. These results have inspired extensive discussion. The detector of DAMPE, the data analysis, and the first results are introduced. In particular, the physical interpretations of the DAMPE data are reviewed.
1807.11638v1
2018-08-08
A Hybrid Dynamic-regenerative Damping Scheme for Energy Regeneration in Variable Impedance Actuators
Increasing research efforts have been made to improve the energy efficiency of variable impedance actuators (VIAs) through reduction of energy consumption. However, the harvesting of dissipated energy in such systems remains underexplored. This study proposes a novel variable damping module design enabling energy regeneration in VIAs by exploiting the regenerative braking effect of DC motors. The proposed damping module uses four switches to combine regenerative and dynamic braking, in a hybrid approach that enables energy regeneration without reduction in the range of damping achievable. Numerical simulations and a physical experiment are presented in which the proposed module shows an optimal trade-off between task performance and energy efficiency.
1808.03143v1
2018-08-15
$L^1$ estimates for oscillating integrals and their applications to semi-linear models with $σ$-evolution like structural damping
The present paper is a continuation of our recent paper \cite{DaoReissig}. We will consider the following Cauchy problems for semi-linear structurally damped $\sigma$-evolution models: \begin{equation*} u_{tt}+ (-\Delta)^\sigma u+ \mu (-\Delta)^\delta u_t = f(u,u_t),\, u(0,x)= u_0(x),\, u_t(0,x)=u_1(x) \end{equation*} with $\sigma \ge 1$, $\mu>0$ and $\delta \in (\frac{\sigma}{2},\sigma]$. Our aim is to study two main models including $\sigma$-evolution models with structural damping $\delta \in (\frac{\sigma}{2},\sigma)$ and those with visco-elastic damping $\delta=\sigma$. Here the function $f(u,u_t)$ stands for power nonlinearities $|u|^{p}$ and $|u_t|^{p}$ with a given number $p>1$. We are interested in investigating the global (in time) existence of small data solutions to the above semi-linear models from suitable spaces basing on $L^q$ space by assuming additional $L^{m}$ regularity on the initial data, with $q\in (1,\infty)$ and $m\in [1,q)$.
1808.05484v2
2018-09-04
Separation of the two-magnon scattering contribution to damping for the determination of the spin mixing conductance
We present angle dependent measurements of the damping properties of epitaxial Fe layers with MgO, Al and Pt capping layers. Based on the preferential distribution of lattice defects following the crystal symmetry, we make use of a model of the defect density to separate the contribution of two-magnon scattering to the damping from the isotropic contribution originating in the spin pumping effect, the viscous Gilbert damping and the magnetic proximity effect. The separation of the two-magnon contribution, which depends strongly on the defect density, allows for the measurement of a value of the effective spin mixing conductance which is closer to the value exclusively due to spin pumping. The influence of the defect density for bilayers systems due to the different capping layers and to the unavoidable spread in defect density from sample to sample is thus removed. This shows the potential of studying spin pumping phenomena in fully ordered systems in which this separation is possible, contrary to polycrystalline or amorphous metallic thin films.
1809.01042v1
2018-09-30
Critical behavior of the damping rate of GHz acoustic phonons in SrTiO3 at the antiferrodistortive phase transition measured by time- and frequency-resolved Brillouin scattering
We determine the temperature dependent damping rate of longitudinal acoustic phonons in SrTiO3 using frequency domain Brillouin scattering and time domain Brillouin scattering. We investigate samples with (La,Sr)MnO3 and SrRuO3 capping layers, which result in compressive or tensile strain at the layer - substrate interface, respectively. The different strain states lead to dif- ferent domain structures in SrTiO3 that extend into the bulk of the SrTiO3 substrates and strongly affect the phonon propagation. Our experiments show that the damping rate of acoustic phonons in the interfacial STO layer depends strongly on the sample temperature and strain induced do- main structure. We also show that the damping rate as function of temperature exhibits a critical behavior close to the cubic-to-tetragonal phase transition of SrTiO3.
1810.00381v1
2018-12-04
Atmospheric oscillations provide simultaneous measurement of neutron star mass and radius
Neutron stars with near-Eddington observable luminosities were shown to harbor levitating atmospheres, suspended above their surface. We report a new method to simultaneously measure the mass and radius of a neutron star based on oscillations of such atmospheres. In this paper, we present an analytic derivation of a family of relativistic, oscillatory, spherically symmetric eigenmodes of the optically and geometrically thin levitating atmospheres, including the damping effects induced by the radiation drag. We discover characteristic maxima in the frequencies of the damped oscillations and show that using the frequency maxima, one can estimate mass and radius of the neutron star, given the observed frequency and the corresponding luminosity of the star during the X-ray burst. Thus, our model provides a new way to probe the stellar parameters. We also show that the ratio of any two undamped eigenfrequencies depends only on the adiabatic index of the atmosphere, while for the damped eigenfrequencies, this ratio varies with the luminosity. The damping coefficient is independent of the mode number of the oscillations. Signatures of these atmospheres' dynamics will be reflected in the source's X-ray light curves.
1812.01299v2
2018-12-04
Spin transport in a magnetic insulator with zero effective damping
Applications based on spin currents strongly profit from the control and reduction of their effective damping and their transport properties. We here experimentally observe magnon mediated transport of spin (angular) momentum through a 13.4 nm thin yttrium iron garnet film with full control of the magnetic damping via spin-orbit torque. Above a critical spin-orbit torque, the fully compensated damping manifests itself as an increase of magnon conductivity by almost two orders of magnitude. We compare our results to theoretical expectations based on recently predicted current induced magnon condensates and discuss other possible origins of the observed critical behaviour.
1812.01334v3
2019-01-10
Data-Driven Online Optimization for Enhancing Power System Oscillation Damping
This paper reports an initial work on power system oscillation damping improvement using a data-driven online optimization method. An online oscillation damping optimization mod-el is proposed and formulated in a form solvable by the data-driven method. Key issues in the online optimization procedures, including the damping sensitivity identification method, its compatibility with the dispatch plans, as well as other practical issues in real large-scale system are discussed. Simulation results based on the 2-area 4-machine system, and the NETS-NYPS 68-bus system verify the feasibility and efficiency of the proposed method. The results also show the capability of the proposed method to bridge the gap between online data analysis and complex optimization for power system dynamics.
1901.03167v2
2019-01-13
Nonexistence of global solutions for a weakly coupled system of semilinear damped wave equations in the scattering case with mixed nonlinear terms
In this paper we consider the blow-up of solutions to a weakly coupled system of semilinear damped wave equations in the scattering case with nonlinearities of mixed type, namely, in one equation a power nonlinearity and in the other a semilinear term of derivative type. The proof of the blow-up results is based on an iteration argument. As expected, due to the assumptions on the coefficients of the damping terms, we find as critical curve in the p-q plane for the pair of exponents (p,q) in the nonlinear terms the same one found by Hidano-Yokoyama and, recently, by Ikeda-Sobajima-Wakasa for the weakly coupled system of semilinear wave equations with the same kind of nonlinearities. In the critical and not-damped case we provide a different approach from the test function method applied by Ikeda-Sobajima-Wakasa to prove the blow-up of the solution on the critical curve, improving in some cases the upper bound estimate for the lifespan. More precisely, we combine an iteration argument with the so-called slicing method to show the blow-up dynamic of a weighted version of the functionals used in the subcritical case.
1901.04038v1
2019-01-15
Continuum damping effects in nuclear collisions associated with twisted boundary conditions
The time-dependent Skyrme Hartree-Fock calculations have been performed to study $^{24}$Mg +$^{24}$Mg collisions. The twisted boundary conditions, which can avoid finite box-size effects of the employed 3D coordinate space, have been implemented. The prolate deformed $^{24}$Mg has been set to different orientations to study vibrations and rotations of the compound nucleus $^{48}$Cr. Our time evolution results show continuum damping effects associated with the twist-averaged boundary condition play a persistent role after the fusion stage. In particular, a rotational damping in continuum is presented in calculations of both twist-averaged and absorbing boundary conditions, in which damping widths can be clearly extracted. It is unusual that the rotating compound nucleus in continuum evolves towards spherical but still has a considerable angular momentum.
1901.04736v2
2019-03-03
Spin wave damping in periodic and quasiperiodic magnonic structures
We investigated the lifetime of spin wave eigenmodes in periodic and quasiperiodic sequences of Py and Co wires. Those materials differ significantly in damping coefficients, therefore, the spatial distribution of the mode amplitude within the structure is important for the lifetime of collective spin wave excitations. Modes of the lower frequencies prefer to concentrate in Py wires, because of the lower FMR frequency for this material. This inhomogeneous distribution of amplitude of modes (with lower amplitude in material of higher damping and with higher amplitude in material of lower damping) is preferable for extending the lifetime of the collective excitations beyond the volume average of lifetimes for solid materials. We established the relation between the profile of the mode and its lifetime for periodic and quasiperiodic structures. We performed also the comparative studies in order to find the differences resulting from complexity of the structure and enhancement of localization in quasiperiodic system on the lifetime of spin waves.
1903.00856v1
2019-03-07
Investigating optically-excited THz standing spin waves using noncollinear magnetic bilayers
We investigate optically excited THz standing spin waves in noncollinear magnetic bilayers. Using femtosecond laser-pulse excitation, a spin current is generated in the first ferromagnetic (FM) layer, and flows through a conductive spacer layer to be injected into the second (transverse) FM layer, where it exerts a spin-transfer torque on the magnetization and excites higher-order standing spin waves. We show that the noncollinear magnetic bilayer is a convenient tool that allows easy excitation of THz spin waves, and can be used to investigate the dispersion and thereby the spin wave stiffness parameter in the thin-film regime. This is experimentally demonstrated using wedge-shaped Co and CoB (absorption) layers. Furthermore, the damping of these THz spin waves is investigated, showing a strong increase of the damping with decreasing absorption layer thickness, much stronger than expected from interface spin pumping effects. Additionally, a previously unseen sudden decrease in the damping for the thinnest films is observed. A model for the additional damping contribution incorporating both these observations is proposed.
1903.02802v1
2019-03-14
An analog simulation experiment to study free oscillations of a damped simple pendulum
The characteristics of drive-free oscillations of a damped simple pendulum under sinusoidal potential force field differ from those of the damped harmonic oscillations. The frequency of oscillation of a large amplitude simple pendulum decreases with increasing amplitude. Many prototype mechanical simple pendulum have been fabricated with precision and studied earlier in view of introducing them in undergraduate physics laboratories. However, fabrication and maintenance of such mechanical pendulum require special skill. In this work, we set up an analog electronic simulation experiment to serve the purpose of studying the force-free oscillations of a damped simple pendulum. We present the details of the setup and some typical results of our experiment. The experiment is simple enough to implement in undergraduate physics laboratories.
1903.06162v1
2019-03-15
Frictional Damping in Biomimetic Scale Beam Oscillations
Stiff scales adorn the exterior surfaces of fishes, snakes, and many reptiles. They provide protection from external piercing attacks and control over global deformation behavior to aid locomotion, slithering, and swimming across a wide range of environmental condition. In this letter, we investigate the dynamic behavior of biomimetic scale substrates for further understanding the origins of the nonlinearity that involve various aspect of scales interaction, sliding kinematics, interfacial friction, and their combination. Particularly, we study the vibrational characteristics through an analytical model and numerical investigations for the case of a simply supported scale covered beam. Our results reveal for the first time that biomimetic scale beams exhibit viscous damping behavior even when only Coulomb friction is postulated for free vibrations. We anticipate and quantify the anisotropy in the damping behavior with respect to curvature. We also find that unlike static pure bending where friction increases bending stiffness, a corresponding increase in natural frequency for the dynamic case does not arise for simply supported beam. Since both scale geometry, distribution and interfacial properties can be easily tailored, our study indicates a biomimetic strategy to design exceptional synthetic materials with tailorable damping behavior.
1903.06819v1
2019-04-08
Damping control in viscoelastic beam dynamics
Viscoelasticity plays a key role in many practical applications and in different reasearch fields, such as in seals, sliding-rolling contacts and crack propagation. In all these contexts, a proper knowledge of the viscoelastic modulus is very important. However, the experimental characterization of the frequency dependent modulus, carried out through different standard procedures, still presents some complexities, then possible alternative approaches are desirable. For example, the experimental investigation of viscoelastic beam dynamics would be challenging, especially for the intrinsic simplicity of this kind of test. This is why, a deep understanding of damping mechanisms in viscoelastic beams results to be a quite important task to better predict their dynamics. With the aim to enlighten damping properties in such structures, an analytical study of the transversal vibrations of a viscoelastic beam is presented in this paper. Some dimensionless parameters are defined, depending on the material properties and the beam geometry, which enable to shrewdly design the beam dynamics. In this way, by properly tuning such disclosed parameters, for example the dimensionless beam length or a chosen material, it is possible to enhance or suppress some resonant peaks, one at a time or more simultaneously. This is a remarkable possibility to efficiently control damping in these structures, and the results presented in this paper may help in elucidating experimental procedures for the characterization of viscoelastic materials.
1904.03875v1
2019-04-28
On the Kolmogorov dissipation law in a damped Navier-Stokes equation
We consider here the Navier-Stokes equations in $\mathbb{R}^{3}$ with a stationary, divergence-free external force and with an additional damping term that depends on two parameters. We first study the well-posedness of weak solutions for these equations and then, for a particular set of the damping parameters, we will obtain an upper and lower control for the energy dissipation rate $\varepsilon$ according to the Kolmogorov K41 theory. However, although the behavior of weak solutions corresponds to the K41 theory, we will show that in some specific cases the damping term introduced in the Navier-Stokes equations could annihilate the turbulence even though the Grashof number (which are equivalent to the Reynolds number) are large.
1904.12382v1
2019-04-23
Entanglement sudden death and birth effects in two qubits maximally entangled mixed states under quantum channels
In the present article, the robustness of entanglement in two qubits maximally entangled mixed states (MEME) have been studied under quantum decoherence channels. Here we consider bit flip, phase flip, bit-phase-flip, amplitude damping, phase damping and depolarization channels. To quantify the entanglement, the concurrence has been used as an entanglement measure. During this study interesting results have been found for sudden death and birth of entanglement under bit flip and bit-phase-flip channels. While amplitude damping channel produces entanglement sudden death and does not allow re-birth of entanglement. On the other hand, two qubits MEMS exhibit the robust character against the phase flip, phase damping and depolarization channels. The elegant behavior of all the quantum channels have been investigated with varying parameter of quantum state MEMS in different cases.
1904.12630v2
2019-05-23
Strauss exponent for semilinear wave equations with scattering space dependent damping
It is believed or conjectured that the semilinear wave equations with scattering space dependent damping admit the Strauss critical exponent, see Ikehata-Todorova-Yordanov \cite{ITY}(the bottom in page 2) and Nishihara-Sobajima-Wakasugi \cite{N2}(conjecture iii in page 4). In this work, we are devoted to showing the conjecture is true at least when the decay rate of the space dependent variable coefficients before the damping is larger than 2. Also, if the nonlinear term depends only on the derivative of the solution, we may prove the upper bound of the lifespan is the same as that of the solution of the corresponding problem without damping. This shows in another way the \lq\lq hyperbolicity" of the equation.
1905.09445v2
2019-05-24
Multicomponent Dark Matter in the Light of CALET and DAMPE
In the light of the latest measurements on the total $e^+ + e^-$ flux by CALET and DAMPE experiments, we revisit the multicomponent leptonically decaying dark matter (DM) explanations to the cosmic-ray electron/positron excesses observed previously. Especially, we use the single and double-component DM models to explore the compatibility of the AMS-02 positron fraction with the new CALET or DAMPE data. It turns out that neither single nor double-component DM models are able to fit the AMS-02 positron fraction and DAMPE total $e^+ + e^-$ flux data simultaneously. On the other hand, for the combined AMS-02 and CALET dataset, both the single and double-component DM models can provide reasonable fits. If we further take into the diffuse $\gamma$-ray constraints from Fermi-LAT, only the double-component DM models are allowed.
1905.10136v3
2019-05-30
Quantum dynamical speedup in correlated noisy channels
The maximal evolution speed of a quantum system can be represented by quantum speed limit time (QSLT).We investigate QSLT of a two-qubit system passing through a correlated channel (amplitude damping, phase damping, and depolarizing).By adjusting the correlation parameter of channel and the initial entanglement,a method to accelerate the evolution speed of the system for some specific channels is proposed.It is shown that, in amplitude damping channel and depolarizing channel,QSLT may be shortened in some cases by increasing correlation parameter of the channel and initial entanglement, which are in sharp contrast to phase damping channel.In particular, under depolarizing channels, the transition from no-speedup evolution to speedup evolution for the system can be realized by changing correlation strength of the channel.
1905.12911v3
2019-07-01
Probing superfluid $^4\mathrm{He}$ with high-frequency nanomechanical resonators down to $\mathrm{mK}$ temperatures
Superfluids, such as superfluid $^3\mathrm{He}$ and $^4\mathrm{He}$, exhibit a broad range of quantum phenomena and excitations which are unique to these systems. Nanoscale mechanical resonators are sensitive and versatile force detectors with the ability to operate over many orders of magnitude in damping. Using nanomechanical-doubly clamped beams of extremely high quality factors ($Q>10^6$), we probe superfluid $^4\mathrm{He}$ from the superfluid transition temperature down to $\mathrm{mK}$ temperatures at frequencies up to $11.6 \, \mathrm{MHz}$. Our studies show that nanobeam damping is dominated by hydrodynamic viscosity of the normal component of $^4\mathrm{He}$ above $1\,\mathrm{K}$. In the temperature range $0.3-0.8\,\mathrm{K}$, the ballistic quasiparticles (phonons and rotons) determine the beams' behavior. At lower temperatures, damping saturates and is determined either by magnetomotive losses or acoustic emission into helium. It is remarkable that all these distinct regimes can be extracted with just a single device, despite damping changing over six orders of magnitude.
1907.00970v1
2019-07-15
Asymptotic profiles of solutions for regularity-loss type generalized thermoelastic plate equations and their applications
In this paper, we consider generalized thermoelastic plate equations with Fourier's law of heat conduction. By introducing a threshold for decay properties of regularity-loss, we investigate decay estimates of solutions with/without regularity-loss in a framework of weighted $L^1$ spaces. Furthermore, asymptotic profiles of solutions are obtained by using representations of solutions in the Fourier space, which are derived by employing WKB analysis. Next, we study generalized thermoelastic plate equations with additional structural damping, and analysis the influence of structural damping on decay properties and asymptotic profiles of solutions. We find that the regularity-loss structure is destroyed by structural damping. Finally, we give some applications of our results on thermoelastic plate equations and damped Moore-Gibson-Thompson equation.
1907.06344v1
2019-07-23
Ignatyuk damping factor: A semiclassical formula
Data on nuclear level densities extracted from transmission data or gamma energy spectrum store the basic statistical information about nuclei at various temperatures. Generally this extracted data goes through model fitting using computer codes like CASCADE. However, recently established semiclassical methods involving no adjustable parameters to determine the level density parameter for magic and semi-magic nuclei give a good agreement with the experimental values. One of the popular ways to paramaterize the level density parameter which includes the shell effects and its damping was given by Ignatyuk. This damping factor is usually fitted from the experimental data on nuclear level density and it comes around 0.05 $MeV^{-1}$. In this work we calculate the Ignatyuk damping factor for various nuclei using semiclassical methods.
1907.09770v1
2019-08-13
Dynamics of Riemann waves with sharp measure-controlled damping
This paper is concerned with locally damped semilinear wave equations defined on compact Riemannian manifolds with boundary. We present a construction of measure-controlled damping regions which are sharp in the sense that their summed interior and boundary measures are arbitrarily small. The construction of this class of open sets is purely geometric and allows us to prove a new observability inequality in terms of potential energy rather than the usual one with kinetic energy. A unique continuation property is also proved. Then, in three-dimension spaces, we establish the existence of finite dimensional smooth global attractors for a class of wave equations with nonlinear damping and forces with critical Sobolev growth. In addition, by means of an obstacle control condition, we show that our class of measure-controlled regions satisfies the well-known geometric control condition (GCC). Therefore, many of known results for the stabilization of wave equations hold true in the present context.
1908.04814v1
2019-08-15
Sharp polynomial decay rates for the damped wave equation with Hölder-like damping
We study decay rates for the energy of solutions of the damped wave equation on the torus. We consider dampings invariant in one direction and bounded above and below by multiples of $x^{\beta}$ near the boundary of the support and show decay at rate $1/t^{\frac{\beta+2}{\beta+3}}$. In the case where $W$ vanishes exactly like $x^{\beta}$ this result is optimal by work of the second author. The proof uses a version of the Morawetz multiplier method.
1908.05631v3
2019-08-26
Revisiting the Coulomb-Damped Harmonic Oscillator
The force of dry friction is studied extensively in introductory physics but its effect on oscillations is hardly ever mentioned. Instead, to provide a mathematically tractable introduction to damping, virtually all authors adopt a viscous resistive force. While exposure to linear damping is of paramount importance to the student of physics, the omission of Coulomb damping might have a negative impact on the way the students conceive of the subject. In the paper, we propose to approximate the action of Coulomb friction on a harmonic oscillator by a sinusoidal resistive force whose amplitude is the model's only free parameter. We seek the value of this parameter that yields the best fit and obtain a closed-form analytic solution, which is shown to nicely fit the numerical one.
1908.10363v1
2019-09-21
Resonant absorption of kink oscillations in coronal flux tubes with continuous magnetic twist
There are observational evidences for the existence of twisted magnetic field in the solar corona. Here, we have investigated resonant damping of the magnetohydrodynamic (MHD) kink waves in magnetic flux tubes. A realistic model of the tube with continuous magnetic twist and radially inhomogeneous density profile has been considered. We have obtained the dispersion relation of the kink wave using the solution to the linear MHD equations outside the density inhomogeneity and the appropriate connection formula to the solutions across the thin transitional boundary layer. The dependence of the oscillation frequency and damping rate of the waves on the twist parameter and longitudinal wavenumber has been investigated. For the flux tube parameters considered in this paper, we obtain rapid damping of the kink waves comparable to the observations. In order to justify this rapid damping, depending on the sign of the azimuthal kink mode number, $m=+1$ or $m=-1$, the background magnetic field must have left handed or right handed twisted profile, respectively. For the model considered here, the resonant absorption occurs only when the twist parameter is in a range specified by the density contrast.
1909.09787v1
2019-10-22
Controlled nonlinear magnetic damping in spin-Hall nano-devices
Large-amplitude magnetization dynamics is substantially more complex compared to the low-amplitude linear regime, due to the inevitable emergence of nonlinearities. One of the fundamental nonlinear phenomena is the nonlinear damping enhancement, which imposes strict limitations on the operation and efficiency of magnetic nanodevices. In particular, nonlinear damping prevents excitation of coherent magnetization auto-oscillations driven by the injection of spin current into spatially extended magnetic regions. Here, we propose and experimentally demonstrate that nonlinear damping can be controlled by the ellipticity of magnetization precession. By balancing different contributions to anisotropy, we minimize the ellipticity and achieve coherent magnetization oscillations driven by spatially extended spin current injection into a microscopic magnetic disk. Our results provide a novel route for the implementation of efficient active spintronic and magnonic devices driven by spin current.
1910.09801v1
2019-11-05
Exceptional points in dissipatively coupled spin dynamics
We theoretically investigate dynamics of classical spins exchange-coupled through an isotropic medium. The coupling is treated at the adiabatic level of the medium's response, which mediates a first-order in frequency dissipative interaction along with an instantaneous Heisenberg exchange. The resultant damped spin precession yields exceptional points (EPs) in the coupled spin dynamics, which should be experimentally accessible with the existing magnetic heterostructures. In particular, we show that an EP is naturally approached in an antiferromagnetic dimer by controlling local damping, while the same is achieved by tuning the dissipative coupling between spins in the ferromagnetic case. Extending our treatment to one-dimensional spin chains, we show how EPs can emerge within the magnonic Brillouin zone by tuning the dissipative properties. The critical point, at which an EP pair emerges out of the Brillouin zone center, realizes a gapless Weyl point in the magnon spectrum. Tuning damping beyond this critical point produces synchronization (level attraction) of magnon modes over a finite range of momenta, both in ferro- and antiferromagnetic cases. We thus establish that damped magnons can generically yield singular points in their band structure, close to which their kinematic properties, such as group velocity, become extremely sensitive to the control parameters.
1911.01619v2
2019-11-08
Influence of Sensor Feedback Limitations on Power Oscillation Damping and Transient Stability
Fundamental sensor feedback limitations for improving rotor angle stability using local frequency or phase angle measurement are derived. Using a two-machine power system model, it is shown that improved damping of inter-area oscillations must come at the cost of reduced transient stability margins, regardless of the control design method. The control limitations stem from that the excitation of an inter-area mode by external disturbances cannot be estimated with certainty using local frequency information. The results are validated on a modified Kundur four-machine two-area test system where the active power is modulated on an embedded high-voltage dc link. Damping control using local phase angle measurements, unavoidably leads to an increased rotor angle deviation following certain load disturbances. For a highly stressed system, it is shown that this may lead to transient instability. The limitations derived in the paper may motivate the need for wide-area measurements in power oscillation damping control.
1911.03342v3
2019-11-12
Non-uniform Stability of Damped Contraction Semigroups
We investigate the stability properties of strongly continuous semigroups generated by operators of the form $A-BB^\ast$, where $A$ is a generator of a contraction semigroup and $B$ is a possibly unbounded operator. Such systems arise naturally in the study of hyperbolic partial differential equations with damping on the boundary or inside the spatial domain. As our main results we present general sufficient conditions for non-uniform stability of the semigroup generated by $A-BB^\ast$ in terms of selected observability-type conditions of the pair $(B^\ast,A)$. We apply the abstract results to obtain rates of energy decay in one-dimensional and two-dimensional wave equations, a damped fractional Klein--Gordon equation and a weakly damped beam equation.
1911.04804v3
2020-01-31
Dynamo in weakly collisional nonmagnetized plasmas impeded by Landau damping of magnetic fields
We perform fully kinetic simulations of flows known to produce dynamo in magnetohydrodynamics (MHD), considering scenarios with low Reynolds number and high magnetic Prandtl number, relevant for galaxy cluster scale fluctuation dynamos. We find that Landau damping on the electrons leads to a rapid decay of magnetic perturbations, impeding the dynamo. This collisionless damping process operates on spatial scales where electrons are nonmagnetized, reducing the range of scales where the magnetic field grows in high magnetic Prandtl number fluctuation dynamos. When electrons are not magnetized down to the resistive scale, the magnetic energy spectrum is expected to be limited by the scale corresponding to magnetic Landau damping or, if smaller, the electron gyroradius scale, instead of the resistive scale. In simulations we thus observe decaying magnetic fields where resistive MHD would predict a dynamo.
2001.11929v2
2020-03-05
Sound propagation and quantum limited damping in a two-dimensional Fermi gas
Strongly interacting two-dimensional Fermi systems are one of the great remaining challenges in many-body physics due to the interplay of strong local correlations and enhanced long-range fluctuations. Here, we probe the thermodynamic and transport properties of a 2D Fermi gas across the BEC-BCS crossover by studying the propagation and damping of sound modes. We excite particle currents by imprinting a phase step onto homogeneous Fermi gases trapped in a box potential and extract the speed of sound from the frequency of the resulting density oscillations. We measure the speed of sound across the BEC-BCS crossover and compare the resulting dynamic measurement of the equation of state both to a static measurement based on recording density profiles and to Quantum Monte Carlo calculations and find reasonable agreement between all three. We also measure the damping of the sound mode, which is determined by the shear and bulk viscosities as well as the thermal conductivity of the gas. We find that the damping is minimal in the strongly interacting regime and the diffusivity approaches the universal quantum bound $\hbar/m$ of a perfect fluid.
2003.02713v1
2020-03-09
Proof-of-principle direct measurement of Landau damping strength at the Large Hadron Collider with an anti-damper
Landau damping is an essential mechanism for ensuring collective beam stability in particle accelerators. Precise knowledge of how strong Landau damping is, is key to making accurate predictions on beam stability for state-of-the-art high energy colliders. In this paper we demonstrate an experimental procedure that would allow quantifying the strength of Landau damping and the limits of beam stability using an active transverse feedback as a controllable source of beam coupling impedance. In a proof-of-principle test performed at the Large Hadron Collider stability diagrams for a range of Landau Octupole strengths have been measured. In the future, the procedure could become an accurate way of measuring stability diagrams throughout the machine cycle.
2003.04383v1
2020-03-19
An inverse-system method for identification of damping rate functions in non-Markovian quantum systems
Identification of complicated quantum environments lies in the core of quantum engineering, which systematically constructs an environment model with the aim of accurate control of quantum systems. In this paper, we present an inverse-system method to identify damping rate functions which describe non-Markovian environments in time-convolution-less master equations. To access information on the environment, we couple a finite-level quantum system to the environment and measure time traces of local observables of the system. By using sufficient measurement results, an algorithm is designed, which can simultaneously estimate multiple damping rate functions for different dissipative channels. Further, we show that identifiability for the damping rate functions corresponds to the invertibility of the system and a necessary condition for identifiability is also given. The effectiveness of our method is shown in examples of an atom and three-spin-chain non-Markovian systems.
2003.08617v1
2020-04-23
Damping of gravitational waves in 2-2-holes
A 2-2-hole is an explicit realization of a horizonless object that can still very closely resemble a BH. An ordinary relativistic gas can serve as the matter source for the 2-2-hole solution of quadratic gravity, and this leads to a calculable area-law entropy. Here we show that it also leads to an estimate of the damping of a gravitational wave as it travels to the center of the 2-2-hole and back out again. We identify two frequency dependent effects that greatly diminish the damping. Spinning 2-2-hole solutions are not known, but we are still able to consider some spin dependent effects. The frequency and spin dependence of the damping helps to determine the possible echo resonance signal from the rotating remnants of merger events. It also controls the fate of the ergoregion instability.
2004.11285v3
2020-05-04
Plasmon damping in electronically open systems
Rapid progress in electrically-controlled plasmonics in solids poses a question about effects of electronic reservoirs on the properties of plasmons. We find that plasmons in electronically open systems [i.e. in (semi)conductors connected to leads] are prone to an additional damping due to charge carrier penetration into contacts and subsequent thermalization. We develop a theory of such lead-induced damping based on kinetic equation with self-consistent electric field, supplemented by microscopic carrier transport at the interfaces. The lifetime of plasmon in electronically open ballistic system appears to be finite, order of conductor length divided by carrier Fermi (thermal) velocity. The reflection loss of plasmon incident on the contact of semi-conductor and perfectly conducting metal also appears to be finite, order of Fermi velocity divided by wave phase velocity. Recent experiments on plasmon-assisted photodetection are discussed in light of the proposed lead-induced damping phenomenon.
2005.01680v1
2020-05-06
Helical damping and anomalous critical non-Hermitian skin effect
Non-Hermitian skin effect and critical skin effect are unique features of non-Hermitian systems. In this Letter, we study an open system with its dynamics of single-particle correlation function effectively dominated by a non-Hermitian damping matrix, which exhibits $\mathbb{Z}_2$ skin effect, and uncover the existence of a novel phenomenon of helical damping. When adding perturbations that break anomalous time reversal symmetry to the system, the critical skin effect occurs, which causes the disappearance of the helical damping in the thermodynamic limit although it can exist in small size systems. We also demonstrate the existence of anomalous critical skin effect when we couple two identical systems with $\mathbb{Z}_2$ skin effect. With the help of non-Bloch band theory, we unveil that the change of generalized Brillouin zone equation is the necessary condition of critical skin effect.
2005.02617v1
2020-05-16
Gravitational Landau Damping for massive scalar modes
We establish the possibility of Landau damping for gravitational scalar waves which propagate in a non-collisional gas of particles. In particular, under the hypothesis of homogeneity and isotropy, we describe the medium at the equilibrium with a J\"uttner-Maxwell distribution, and we analytically determine the damping rate from the Vlasov equation. We find that damping occurs only if the phase velocity of the wave is subluminal throughout the propagation within the medium. Finally, we investigate relativistic media in cosmological settings by adopting numerical techniques.
2005.08010v4
2020-05-21
On Strong Feller Property, Exponential Ergodicity and Large Deviations Principle for Stochastic Damping Hamiltonian Systems with State-Dependent Switching
This work focuses on a class of stochastic damping Hamiltonian systems with state-dependent switching, where the switching process has a countably infinite state space. After establishing the existence and uniqueness of a global weak solution via the martingale approach under very mild conditions, the paper next proves the strong Feller property for regime-switching stochastic damping Hamiltonian systems by the killing technique together with some resolvent and transition probability identities. The commonly used continuity assumption for the switching rates $q_{kl}(\cdot)$ in the literature is relaxed to measurability in this paper. Finally the paper provides sufficient conditions for exponential ergodicity and large deviations principle for regime-switching stochastic damping Hamiltonian systems. Several examples on regime-switching van der Pol and (overdamped) Langevin systems are studied in detail for illustration.
2005.10730v1
2020-06-09
Logarithmic decay for damped hypoelliptic wave and Schr{ö}dinger equations
We consider damped wave (resp. Schr{\"o}dinger and plate) equations driven by a hypoelliptic "sum of squares" operator L on a compact manifold and a damping function b(x). We assume the Chow-Rashevski-H{\"o}rmander condition at rank k (at most k Lie brackets needed to span the tangent space) together with analyticity of M and the coefficients of L. We prove decay of the energy at rate $log(t)^{-1/k}$ (resp. $log(t)^{-2/k}$ ) for data in the domain of the generator of the associated group. We show that this decay is optimal on a family of Grushin-type operators. This result follows from a perturbative argument (of independent interest) showing, in a general abstract setting, that quantitative approximate observability/controllability results for wave-type equations imply a priori decay rates for associated damped wave, Schr{\"o}dinger and plate equations. The adapted quantitative approximate observability/controllability theorem for hypoelliptic waves is obtained by the authors in [LL19, LL17].
2006.05122v1
2020-06-14
Bulk Viscous Damping of Density Oscillations in Neutron Star Mergers
In this paper, we discuss the damping of density oscillations in dense nuclear matter in the temperature range relevant to neutron star mergers. This damping is due to bulk viscosity arising from the weak interaction ``Urca'' processes of neutron decay and electron capture. The nuclear matter is modelled in the relativistic density functional approach. The bulk viscosity reaches a resonant maximum close to the neutrino trapping temperature, then drops rapidly as temperature rises into the range where neutrinos are trapped in neutron stars. We investigate the bulk viscous dissipation timescales in a post-merger object and identify regimes where these timescales are as short as the characteristic timescale $\sim$10 ms, and, therefore, might affect the evolution of the post-merger object. Our analysis indicates that bulk viscous damping would be important at not too high temperatures of the order of a few MeV and densities up to a few times saturation density.
2006.07975v2
2020-06-15
Exact solutions of a damped harmonic oscillator in a time dependent noncommutative space
In this paper we have obtained the exact eigenstates of a two dimensional damped harmonic oscillator in time dependent noncommutative space. It has been observed that for some specific choices of the damping factor and the time dependent frequency of the oscillator, there exists interesting solutions of the time dependent noncommutative parameters following from the solutions of the Ermakov-Pinney equation. Further, these solutions enable us to get exact analytic forms for the phase which relates the eigenstates of the Hamiltonian with the eigenstates of the Lewis invariant. We then obtain expressions for the matrix elements of the coordinate operators raised to a finite arbitrary power. From these general results we then compute the expectation value of the Hamiltonian. The expectation values of the energy are found to vary with time for different solutions of the Ermakov-Pinney equation corresponding to different choices of the damping factor and the time dependent frequency of the oscillator.
2006.08611v1
2020-06-16
Enhancing nonlinear damping by parametric-direct internal resonance
Mechanical sources of nonlinear damping play a central role in modern physics, from solid-state physics to thermodynamics. The microscopic theory of mechanical dissipation [M. I . Dykman, M. A. Krivoglaz, Physica Status Solidi (b) 68, 111 (1975)] suggests that nonlinear damping of a resonant mode can be strongly enhanced when it is coupled to a vibration mode that is close to twice its resonance frequency. To date, no experimental evidence of this enhancement has been realized. In this letter, we experimentally show that nanoresonators driven into parametric-direct internal resonance provide supporting evidence for the microscopic theory of nonlinear dissipation. By regulating the drive level, we tune the parametric resonance of a graphene nanodrum over a range of 40-70 MHz to reach successive two-to-one internal resonances, leading to a nearly two-fold increase of the nonlinear damping. Our study opens up an exciting route towards utilizing modal interactions and parametric resonance to realize resonators with engineered nonlinear dissipation over wide frequency range.
2006.09364v3
2020-06-22
Blow-up for wave equation with the scale-invariant damping and combined nonlinearities
In this article, we study the blow-up of the damped wave equation in the \textit{scale-invariant case} and in the presence of two nonlinearities. More precisely, we consider the following equation: $$u_{tt}-\Delta u+\frac{\mu}{1+t}u_t=|u_t|^p+|u|^q, \quad \mbox{in}\ \R^N\times[0,\infty), $$ with small initial data.\\ For $\mu < \frac{N(q-1)}{2}$ and $\mu \in (0, \mu_*)$, where $\mu_*>0$ is depending on the nonlinearties' powers and the space dimension ($\mu_*$ satisfies $(q-1)\left((N+2\mu_*-1)p-2\right) = 4$), we prove that the wave equation, in this case, behaves like the one without dissipation ($\mu =0$). Our result completes the previous studies in the case where the dissipation is given by $\frac{\mu}{(1+t)^\beta}u_t; \ \beta >1$ (\cite{LT3}), where, contrary to what we obtain in the present work, the effect of the damping is not significant in the dynamics. Interestingly, in our case, the influence of the damping term $\frac{\mu}{1+t}u_t$ is important.
2006.12600v1
2020-06-30
Negative Gilbert damping in cavity optomagnonics
Exceptional point (EP) associated with the parity-time (PT) symmetry breaking is receiving considerable recent attention by the broad physics community. By introducing balanced gain and loss, it has been realized in photonic, acoustic, and electronic structures. However, the observation of magnonic EP remains elusive. The major challenge is to experimentally generate the negative Gilbert damping, which was thought to be highly unlikely but is demanded by the PT symmetry. In this work, we study the magneto-optical interaction of circularly-polarized lasers with a submicron magnet placed in an optical cavity. We show that the off-resonant coupling between the driving laser and cavity photon in the far-blue detuning can induce the magnetic gain (or negative damping) exactly of the Gilbert type. A hyperbolic-tangent function ansatz is found to well describe the time-resolved spin switching as the intrinsic magnetization dissipation is overcome. When the optically pumped magnet interacts with a purely lossy one, we observe a phase transition from the imbalanced to passive PT symmetries by varying the detuning coeffcient. Our findings provide a feasible way to manipulate the sign of the magnetic damping parameter and to realize the EP in cavity optomagnonics.
2006.16510v1
2020-07-10
Decentralized Frequency Control using Packet-based Energy Coordination
This paper presents a novel frequency-responsive control scheme for demand-side resources, such as electric water heaters. A frequency-dependent control law is designed to provide damping from distributed energy resources (DERs) in a fully decentralized fashion. This local control policy represents a frequency-dependent threshold for each DER that ensures that the aggregate response provides damping during frequency deviations. The proposed decentralized policy is based on an adaptation of a packet-based DER coordination scheme where each device send requests for energy access (also called an "energy packet") to an aggregator. The number of previously accepted active packets can then be used a-priori to form an online estimate of the aggregate damping capability of the DER fleet in a dynamic power system. A simple two-area power system is used to illustrate and validate performance of the decentralized control policy and the accuracy of the online damping estimating for a fleet of 400,000 DERs.
2007.05624v1
2020-07-30
Origin of micron-scale propagation lengths of heat-carrying acoustic excitations in amorphous silicon
The heat-carrying acoustic excitations of amorphous silicon are of interest because their mean free paths may approach micron scales at room temperature. Despite extensive investigation, the origin of the weak acoustic damping in the heat-carrying frequencies remains a topic of debate. Here, we report measurements of the thermal conductivity mean free path accumulation function in amorphous silicon thin films from 60 - 315 K using transient grating spectroscopy. With additional picosecond acoustics measurements and considering the known frequency-dependencies of damping mechanisms in glasses, we reconstruct the mean free paths from $\sim 0.1-3$ THz. The mean free paths are independent of temperature and exhibit a Rayleigh scattering trend over most of this frequency range. The observed trend is inconsistent with the predictions of numerical studies based on normal mode analysis but agrees with diverse measurements on other glasses. The micron-scale MFPs in amorphous Si arise from the absence of anharmonic or two-level system damping in the sub-THz frequencies, leading to heat-carrying acoustic excitations with room-temperature damping comparable to that of other glasses at cryogenic temperatures.
2007.15777v2
2020-08-07
Quantifying the evidence for resonant damping of coronal waves with foot-point wave power asymmetry
We use Coronal Multi-channel Polarimeter (CoMP) observations of propagating waves in the solar corona and Bayesian analysis to assess the evidence of models with resonant damping and foot-point wave power asymmetries. Two nested models are considered. The reduced model considers resonant damping as the sole cause of the measured discrepancy between outward and inward wave power. The larger model contemplates an extra source of asymmetry with origin at the foot-points. We first compute probability distributions of parameters conditional on the models and the observed data. The obtained constraints are then used to calculate the evidence for each model in view of data. We find that we need to consider the larger model to explain CoMP data and to accurately infer the damping ratio, hence, to better assess the possible contribution of the waves to coronal heating.
2008.03004v1
2020-08-22
Sound damping in frictionless granular materials: The interplay between configurational disorder and inelasticity
We numerically investigate sound damping in a model of granular materials in two dimensions. We simulate evolution of standing waves in disordered frictionless disks and analyze their damped oscillations by velocity autocorrelation functions and power spectra. We control the strength of inelastic interactions between the disks in contact to examine the effect of energy dissipation on sound characteristics of disordered systems. Increasing the strength of inelastic interactions, we find that (i) sound softening vanishes and (ii) sound attenuation due to configurational disorder, i.e. the Rayleigh scattering at low frequencies and disorder-induced broadening at high frequencies, is completely dominated by the energy dissipation. Our findings suggest that sound damping in granular media is determined by the interplay between elastic heterogeneities and inelastic interactions.
2008.09760v1
2020-09-27
Squeezed comb states
Continuous-variable codes are an expedient solution for quantum information processing and quantum communication involving optical networks. Here we characterize the squeezed comb, a finite superposition of equidistant squeezed coherent states on a line, and its properties as a continuous-variable encoding choice for a logical qubit. The squeezed comb is a realistic approximation to the ideal code proposed by Gottesman, Kitaev, and Preskill [Phys. Rev. A 64, 012310 (2001)], which is fully protected against errors caused by the paradigmatic types of quantum noise in continuous-variable systems: damping and diffusion. This is no longer the case for the code space of finite squeezed combs, and noise robustness depends crucially on the encoding parameters. We analyze finite squeezed comb states in phase space, highlighting their complicated interference features and characterizing their dynamics when exposed to amplitude damping and Gaussian diffusion noise processes. We find that squeezed comb state are more suitable and less error-prone when exposed to damping, which speaks against standard error correction strategies that employ linear amplification to convert damping into easier-to-describe isotropic diffusion noise.
2009.12888v2
2020-11-16
Switchable Damping for a One-Particle Oscillator
The possibility to switch the damping rate for a one-electron oscillator is demonstrated, for an electron that oscillates along the magnetic field axis in a Penning trap. Strong axial damping can be switched on to allow this oscillation to be used for quantum nondemolition detection of the cyclotron and spin quantum state of the electron. Weak axial damping can be switched on to circumvent the backaction of the detection motion that has limited past measurements. The newly developed switch will reduce the linewidth of the cyclotron transition of one-electron by two orders of magnitude.
2011.08136v2
2020-11-17
Challenging an experimental nonlinear modal analysis method with a new strongly friction-damped structure
In this work, we show that a recently proposed method for experimental nonlinear modal analysis based on the extended periodic motion concept is well suited to extract modal properties for strongly nonlinear systems (i.e. in the presence of large frequency shifts, high and nonlinear damping, changes of the mode shape, and higher harmonics). To this end, we design a new test rig that exhibits a large extent of friction-induced damping (modal damping ratio up to 15 %) and frequency shift by 36 %. The specimen, called RubBeR, is a cantilevered beam under the influence of dry friction, ranging from full stick to mainly sliding. With the specimen's design, the measurements are well repeatable for a system subjected to dry frictional force. Then, we apply the method to the specimen and show that single-point excitation is sufficient to track the modal properties even though the deflection shape changes with amplitude. Computed frequency responses using a single nonlinear-modal oscillator with the identified modal properties agree well with measured reference curves of different excitation levels, indicating the modal properties' significance and accuracy.
2011.08527v1
2020-11-27
Thermal damping of Weak Magnetosonic Turbulence in the Interstellar Medium
We present a generic mechanism for the thermal damping of compressive waves in the interstellar medium (ISM), occurring due to radiative cooling. We solve for the dispersion relation of magnetosonic waves in a two-fluid (ion-neutral) system in which density- and temperature-dependent heating and cooling mechanisms are present. We use this dispersion relation, in addition to an analytic approximation for the nonlinear turbulent cascade, to model dissipation of weak magnetosonic turbulence. We show that in some ISM conditions, the cutoff wavelength for magnetosonic turbulence becomes tens to hundreds of times larger when the thermal damping is added to the regular ion-neutral damping. We also run numerical simulations which confirm that this effect has a dramatic impact on cascade of compressive wave modes.
2011.13879v3
2021-02-10
WAMS-Based Model-Free Wide-Area Damping Control by Voltage Source Converters
In this paper, a novel model-free wide-area damping control (WADC) method is proposed, which can achieve full decoupling of modes and damp multiple critical inter-area oscillations simultaneously using grid-connected voltage source converters (VSCs). The proposed method is purely measurement based and requires no knowledge of the network topology and the dynamic model parameters. Hence, the designed controller using VSCs can update the control signals online as the system operating condition varies. Numerical studies in the modified IEEE 68-bus system with grid-connected VSCs show that the proposed method can estimate the system dynamic model accurately and can damp inter-area oscillations effectively under different working conditions and network topologies.
2102.05494v1
2021-03-11
Magnetoelastic Gilbert damping in magnetostrictive Fe$_{0.7}$Ga$_{0.3}$ thin films
We report an enhanced magnetoelastic contribution to the Gilbert damping in highly magnetostrictive Fe$_{0.7}$Ga$_{0.3}$ thin films. This effect is mitigated for perpendicular-to-plane fields, leading to a large anisotropy of the Gilbert damping in all of the films (up to a factor of 10 at room temperature). These claims are supported by broadband measurements of the ferromagnetic resonance linewidths over a range of temperatures (5 to 400 K), which serve to elucidate the effect of both the magnetostriction and phonon relaxation on the magnetoelastic Gilbert damping.
2103.07008v1
2021-04-08
Fast optimization of viscosities for frequency-weighted damping of second-order systems
We consider frequency-weighted damping optimization for vibrating systems described by a second-order differential equation. The goal is to determine viscosity values such that eigenvalues are kept away from certain undesirable areas on the imaginary axis. To this end, we present two complementary techniques. First, we propose new frameworks using nonsmooth constrained optimization problems, whose solutions both damp undesirable frequency bands and maintain stability of the system. These frameworks also allow us to weight which frequency bands are the most important to damp. Second, we also propose a fast new eigensolver for the structured quadratic eigenvalue problems that appear in such vibrating systems. In order to be efficient, our new eigensolver exploits special properties of diagonal-plus-rank-one complex symmetric matrices, which we leverage by showing how each quadratic eigenvalue problem can be transformed into a short sequence of such linear eigenvalue problems. The result is an eigensolver that is substantially faster than standard techniques. By combining this new solver with our new optimization frameworks, we obtain our overall algorithm for fast computation of optimal viscosities. The efficiency and performance of our new methods are verified and illustrated on several numerical examples.
2104.04035v1
2021-04-09
Nonexistence result for the generalized Tricomi equation with the scale-invariant damping, mass term and time derivative nonlinearity
In this article, we consider the damped wave equation in the \textit{scale-invariant case} with time-dependent speed of propagation, mass term and time derivative nonlinearity. More precisely, we study the blow-up of the solutions to the following equation: $$ (E) \quad u_{tt}-t^{2m}\Delta u+\frac{\mu}{t}u_t+\frac{\nu^2}{t^2}u=|u_t|^p, \quad \mbox{in}\ \mathbb{R}^N\times[1,\infty), $$ that we associate with small initial data. Assuming some assumptions on the mass and damping coefficients, $\nu$ and $\mu>0$, respectively, that the blow-up region and the lifespan bound of the solution of $(E)$ remain the same as the ones obtained for the case without mass, {\it i.e.} $\nu=0$ in $(E)$. The latter case constitutes, in fact, a shift of the dimension $N$ by $\frac{\mu}{1+m}$ compared to the problem without damping and mass. Finally, we think that the new bound for $p$ is a serious candidate to the critical exponent which characterizes the threshold between the blow-up and the global existence regions.
2104.04393v2
2021-04-12
Slow periodic oscillation without radiation damping: New evolution laws for rate and state friction
The dynamics of sliding friction is mainly governed by the frictional force. Previous studies have shown that the laboratory-scale friction is well described by an empirical law stated in terms of the slip velocity and the state variable. The state variable represents the detailed physicochemical state of the sliding interface. Despite some theoretical attempts to derive this friction law, there has been no unique equation for time evolution of the state variable. Major equations known to date have their own merits and drawbacks. To shed light on this problem from a new aspect, here we investigate the feasibility of periodic motion without the help of radiation damping. Assuming a patch on which the slip velocity is perturbed from the rest of the sliding interface, we prove analytically that three major evolution laws fail to reproduce stable periodic motion without radiation damping. Furthermore, we propose two new evolution equations that can produce stable periodic motion without radiation damping. These two equations are scrutinized from the viewpoint of experimental validity and the relevance to slow earthquakes.
2104.05398v2
2021-04-27
Absence of a boson peak in anharmonic phonon models with Akhiezer-type damping
In a recent article M. Baggioli and A. Zaccone (Phys. Rev. Lett. {\bf 112}, 145501 (2019)) claimed that an anharmonic damping, leading to a sound attenuation proportional to $\omega^2$ (Akhiezer-type damping) would imply a boson peak, i.e.\ a maximum in the vibrational density of states, divided by the frequency squared (reduced density of states). This would apply both to glasses and crystals.Here we show that this is not the case. In a mathematically correct treatment of the model the reduced density of states monotonously decreases, i.e.\ there is no boson peak. We further show that the formula for the would-be boson peak, presented by the authors, corresponds to a very short one-dimensional damped oscillator system. The peaks they show correspond to resonances, which vanish in the thermodynamic limit.
2104.13076v1
2021-05-03
Damping and polarization rates in near equilibrium state
The collision terms in spin transport theory are analyzed in Kadanoff-Baym formalism for systems close to equilibrium. The non-equilibrium fluctuations in spin distribution include both damping and polarization, with the latter arising from the exchange between orbital and spin angular momenta. The damping and polarization rates or the relaxation times are expressed in terms of various Dirac components of the self-energy. Unlike the usually used Anderson-Witting relaxation time approximation assuming a single time scale for different degrees of freedom, the polarization effect is induced by the thermal vorticity and its time scale of thermalization is different from the damping. The numerical calculation in the Nambu--Jona-Lasinio model shows that, charge is thermalized earlier and spin is thermalized later.
2105.00915v1
2021-05-14
Exact solution of damped harmonic oscillator with a magnetic field in a time dependent noncommutative space
In this paper we have obtained the exact eigenstates of a two dimensional damped harmonic oscillator in the presence of an external magnetic field varying with respect to time in time dependent noncommutative space. It has been observed that for some specific choices of the damping factor, the time dependent frequency of the oscillator and the time dependent external magnetic field, there exists interesting solutions of the time dependent noncommutative parameters following from the solutions of the Ermakov-Pinney equation. Further, these solutions enable us to get exact analytic forms for the phase which relates the eigenstates of the Hamiltonian with the eigenstates of the Lewis invariant. Then we compute the expectation value of the Hamiltonian. The expectation values of the energy are found to vary with time for different solutions of the Ermakov-Pinney equation corresponding to different choices of the damping factor, the time dependent frequency of the oscillator and the time dependent applied magnetic field. We also compare our results with those in the absence of the magnetic field obtained earlier.
2106.05182v1
2021-06-21
Self-stabilization of light sails by damped internal degrees of freedom
We consider the motion of a light sail that is accelerated by a powerful laser beam. We derive the equations of motion for two proof-of-concept sail designs with damped internal degrees of freedom. Using linear stability analysis we show that perturbations of the sail movement in all lateral degrees of freedom can be damped passively. This analysis also shows complicated behaviour akin to that associated with exceptional points in PT-symmetric systems in optics and quantum mechanics. The excess heat that is produced by the damping mechanism is likely to be substantially smaller than the expected heating due to the partial absorption of the incident laser beam by the sail.
2106.10961v1
2021-07-14
Determining the source of phase noise: Response of a driven Duffing oscillator to low-frequency damping and resonance frequency fluctuations
We present an analytical calculation of the response of a driven Duffing oscillator to low-frequency fluctuations in the resonance frequency and damping. We find that fluctuations in these parameters manifest themselves distinctively, allowing them to be distinguished. In the strongly nonlinear regime, amplitude and phase noise due to resonance frequency fluctuations and amplitude noise due to damping fluctuations are strongly attenuated, while the transduction of damping fluctuations into phase noise remains of order $1$. We show that this can be seen by comparing the relative strengths of the amplitude fluctuations to the fluctuations in the quadrature components, and suggest that this provides a means to determine the source of low-frequency noise in a driven Duffing oscillator.
2107.06879v1
2021-07-27
Spin transport-induced damping of coherent THz spin dynamics in iron
We study the damping of perpendicular standing spin-waves (PSSWs) in ultrathin Fe films at frequencies up to 2.4 THz. The PSSWs are excited by optically generated ultrashort spin current pulses, and probed optically in the time domain. Analyzing the wavenumber and thickness dependence of the damping, we demonstrate that at sufficiently large wave vectors $k$ the damping is dominated by spin transport effects scaling with k^4 and limiting the frequency range of observable PSSWs. Although this contribution is known to originate in the spin diffusion, we argue that at moderate and large k a more general description is necessary and develop a model where the 'transverse spin mean free path' is the a key parameter, and estimate it to be ~0.5 nm.
2107.12812v2
2021-07-29
A N-dimensional elastic\viscoelastic transmission problem with Kelvin-Voigt damping and non smooth coefficient at the interface
We investigate the stabilization of a multidimensional system of coupled wave equations with only one Kelvin Voigt damping. Using a unique continuation result based on a Carleman estimate and a general criteria of Arendt Batty, we prove the strong stability of the system in the absence of the compactness of the resolvent without any geometric condition. Then, using a spectral analysis, we prove the non uniform stability of the system. Further, using frequency domain approach combined with a multiplier technique, we establish some polynomial stability results by considering different geometric conditions on the coupling and damping domains. In addition, we establish two polynomial energy decay rates of the system on a square domain where the damping and the coupling are localized in a vertical strip.
2107.13785v1
2021-09-03
Stabilization of the damped plate equation under general boundary conditions
We consider a damped plate equation on an open bounded subset of R^d, or a smooth manifold, with boundary, along with general boundary operators fulfilling the Lopatinskii-Sapiro condition. The damping term acts on a region without imposing a geometrical condition. We derive a resolvent estimate for the generator of the damped plate semigroup that yields a logarithmic decay of the energy of the solution to the plate equation. The resolvent estimate is a consequence of a Carleman inequality obtained for the bi-Laplace operator involving a spectral parameter under the considered boundary conditions. The derivation goes first though microlocal estimates, then local estimates, and finally a global estimate.
2109.01521v2
2021-09-07
Fluid energy cascade rate and kinetic damping: new insight from 3D Landau-fluid simulations
Using an exact law for incompressible Hall magnetohydrodynamics (HMHD) turbulence, the energy cascade rate is computed from three-dimensional HMHD-CGL (bi-adiabatic ions and isothermal electrons) and Landau fluid (LF) numerical simulations that feature different intensities of Landau damping over a broad range of wavenumbers, typically $0.05\lesssim k_\perp d_i \lesssim100$. Using three sets of cross-scale simulations where turbulence is initiated at large, medium and small scales, the ability of the fluid energy cascade to "sense" the kinetic Landau damping at different scales is tested. The cascade rate estimated from the exact law and the dissipation calculated directly from the simulation are shown to reflect the role of Landau damping in dissipating energy at all scales, with an emphasis on the kinetic ones. This result provides new prospects on using exact laws for simplified fluid models to analyze dissipation in kinetic simulations and spacecraft observations, and new insights into theoretical description of collisionless magnetized plasmas.
2109.03123v2
2021-09-24
Effect of nonlocal transformations on the linearizability and exact solvability of the nonlinear generalized modified Emden type equations
The nonlinear generalized modified Emden type equations (GMEE) are known to be linearizable into simple harmonic oscillator (HO) or damped harmonic oscillators (DHO) via some nonlocal transformations. Hereby, we show that the structure of the nonlocal transformation and the linearizability into HO or DHO determine the nature/structure of the dynamical forces involved (hence, determine the structure of the dynamical equation). Yet, a reverse engineering strategy is used so that the exact solutions of the emerging GMEE are nonlocally transformed to find the exact solutions of the HO and DHO dynamical equations. Consequently, whilst the exact solution for the HO remains a textbook one, the exact solution for the DHO (never reported elsewhere, to the best of our knowledge) turns out to be manifestly the most explicit and general solution that offers consistency and comprehensive coverage for the associated under-damping, critical-damping, and over-damping cases (i.e., no complex settings for the coordinates and/or the velocities are eminent/feasible). Moreover, for all emerging dynamical system, we report illustrative figures for each solution as well as the corresponding phase-space trajectories as they evolve in time.
2109.12059v1
2021-12-27
Trajectory attractors for 3D damped Euler equations and their approximation
We study the global attractors for the damped 3D Euler--Bardina equations with the regularization parameter $\alpha>0$ and Ekman damping coefficient $\gamma>0$ endowed with periodic boundary conditions as well as their damped Euler limit $\alpha\to0$. We prove that despite the possible non-uniqueness of solutions of the limit Euler system and even the non-existence of such solutions in the distributional sense, the limit dynamics of the corresponding dissipative solutions introduced by P.\,Lions can be described in terms of attractors of the properly constructed trajectory dynamical system. Moreover, the convergence of the attractors $\Cal A(\alpha)$ of the regularized system to the limit trajectory attractor $\Cal A(0)$ as $\alpha\to0$ is also established in terms of the upper semicontinuity in the properly defined functional space.
2112.13691v1
2022-01-12
Implicit Bias of MSE Gradient Optimization in Underparameterized Neural Networks
We study the dynamics of a neural network in function space when optimizing the mean squared error via gradient flow. We show that in the underparameterized regime the network learns eigenfunctions of an integral operator $T_{K^\infty}$ determined by the Neural Tangent Kernel (NTK) at rates corresponding to their eigenvalues. For example, for uniformly distributed data on the sphere $S^{d - 1}$ and rotation invariant weight distributions, the eigenfunctions of $T_{K^\infty}$ are the spherical harmonics. Our results can be understood as describing a spectral bias in the underparameterized regime. The proofs use the concept of "Damped Deviations", where deviations of the NTK matter less for eigendirections with large eigenvalues due to the occurence of a damping factor. Aside from the underparameterized regime, the damped deviations point-of-view can be used to track the dynamics of the empirical risk in the overparameterized setting, allowing us to extend certain results in the literature. We conclude that damped deviations offers a simple and unifying perspective of the dynamics when optimizing the squared error.
2201.04738v1
2022-01-19
Variance-Reduced Stochastic Quasi-Newton Methods for Decentralized Learning: Part II
In Part I of this work, we have proposed a general framework of decentralized stochastic quasi-Newton methods, which converge linearly to the optimal solution under the assumption that the local Hessian inverse approximations have bounded positive eigenvalues. In Part II, we specify two fully decentralized stochastic quasi-Newton methods, damped regularized limited-memory DFP (Davidon-Fletcher-Powell) and damped limited-memory BFGS (Broyden-Fletcher-Goldfarb-Shanno), to locally construct such Hessian inverse approximations without extra sampling or communication. Both of the methods use a fixed moving window of $M$ past local gradient approximations and local decision variables to adaptively construct positive definite Hessian inverse approximations with bounded eigenvalues, satisfying the assumption in Part I for the linear convergence. For the proposed damped regularized limited-memory DFP, a regularization term is added to improve the performance. For the proposed damped limited-memory BFGS, a two-loop recursion is applied, leading to low storage and computation complexity. Numerical experiments demonstrate that the proposed quasi-Newton methods are much faster than the existing decentralized stochastic first-order algorithms.
2201.07733v1
2022-01-19
Active tuning of plasmon damping via light induced magnetism
Circularly polarized optical excitation of plasmonic nanostructures causes coherent circulating motion of their electrons, which in turn, gives rise to strong optically induced magnetization - a phenomenon known as the inverse Faraday effect (IFE). In this study we report how the IFE also significantly decreases plasmon damping. By modulating the optical polarization state incident on achiral plasmonic nanostructures from linear to circular, we observe reversible increases of reflectance by 78% as well as simultaneous increases of optical field concentration by 35.7% under 10^9 W/m^2 continuous wave (CW) optical excitation. These signatures of decreased plasmon damping were also monitored in the presence of an externally applied magnetic field (0.2 T). The combined interactions allow an estimate of the light-induced magnetization, which corresponds to an effective magnetic field of ~1.3 T during circularly polarized CW excitation (10^9 W/m^2). We rationalize the observed decreases in plasmon damping in terms of the Lorentz forces acting on the circulating electron trajectories. Our results outline strategies for actively modulating intrinsic losses in the metal, and thereby, the optical mode quality and field concentration via opto-magnetic effects encoded in the polarization state of incident light.
2201.07842v1
2022-01-27
Effect of vertex corrections on the enhancement of Gilbert damping in spin pumping into a two-dimensional electron gas
We theoretically consider the effect of vertex correction on spin pumping from a ferromagnetic insulator (FI) into a two-dimensional electron gas (2DEG) in which the Rashba and Dresselhaus spin-orbit interactions coexist. The Gilbert damping in the FI is enhanced by elastic spin-flipping or magnon absorption. We show that the Gilbert damping due to elastic spin-flipping is strongly enhanced by the vertex correction when the ratio of the two spin-orbit interactions is near a special value at which the spin relaxation time diverges while that due to magnon absorption shows only small modification. We also show that the shift in the resonant frequency due to elastic spin-flipping is strongly enhanced in a similar way as the Gilbert damping.
2201.11498v3
2022-03-02
Simplified Stability Assessment of Power Systems with Variable-Delay Wide-Area Damping Control
Power electronic devices such as HVDC and FACTS can be used to improve the damping of poorly damped inter-area modes in large power systems. This involves the use of wide-area feedback signals, which are transmitted via communication networks. The performance of the closed-loop system is strongly influenced by the delay associated with wide-area signals. The random nature of this delay introduces a switched linear system model. The stability assessment of such a system requires linear matrix inequality based approaches. This makes the stability analysis more complicated as the system size increases. To address this challenge, this paper proposes a delay-processing strategy that simplifies the modelling and analysis in discrete-domain. In contrast to the existing stability assessment techniques, the proposed approach is advantageous because the stability, as well as damping performance, can be accurately predicted by a simplified analysis. The proposed methodology is verified with a case study on the 2-area 4-machine power system with a series compensated tie-line. The results are found to be in accordance with the predictions of the proposed simplified analysis.
2203.01362v1
2022-03-03
Forward-modulated damping estimates and nonlocalized stability of periodic Lugiato-Lefever wave
In an interesting recent analysis, Haragus-Johnson-Perkins-de Rijk have shown modulational stability under localized perturbations of steady periodic solutions of the Lugiato-Lefever equation (LLE), in the process pointing out a difficulty in obtaining standard "nonlinear damping estimates" on modulated perturbation variables to control regularity of solutions. Here, we point out that in place of standard "inverse-modulated" damping estimates, one can alternatively carry out a damping estimate on the "forward-modulated" perturbation, noting that norms of forward- and inverse-modulated variables are equivalent modulo absorbable errors, thus recovering the classical argument structure of Johnson-Noble-Rodrigues-Zumbrun for parabolic systems. This observation seems of general use in situations of delicate regularity. Applied in the context of (LLE) it gives the stronger result of stability and asymptotic behavior with respect to nonlocalized perturbations.
2203.01770v3
2022-03-31
Observing Particle Energization above the Nyquist Frequency: An Application of the Field-Particle Correlation Technique
The field-particle correlation technique utilizes single-point measurements to uncover signatures of various particle energization mechanisms in turbulent space plasmas. The signature of Landau damping by electrons has been found in both simulations and observations from Earth's magnetosheath using this technique, but instrumental limitations of spacecraft sampling rates present a challenge to discovering the full extent of the presence of Landau damping in the solar wind. Theory predicts that field-particle correlations can recover velocity-space energization signatures even from data that is undersampled with respect to the characteristic frequencies at which the wave damping occurs. To test this hypothesis, we perform a high-resoluation gyrokinetic simulation of space plasma turbulence, confirm that it contains signatures of electron Landau damping, and then systematically reduce the time resolution of the data to identify the point at which the signatures become impossible to recover. We find results in support of our theoretical prediction and look for a rule of thumb that can be compared with the measurement capabilities of spacecraft missions to inform the process of applying field-particle correlations to low time resolution data.
2204.00104v1
2022-04-06
A Potential Based Quantization Procedure of the Damped Oscillator
Nowadays, two of the most prospering fields of physics are quantum computing and spintronics. In both, the loss of information and dissipation plays a crucial role. In the present work we formulate the quantization of the dissipative oscillator, which aids understanding of the above mentioned, and creates a theoretical frame to overcome these issues in the future. Based on the Lagrangian framework of the damped spring system, the canonically conjugated pairs and the Hamiltonian of the system are obtained, by which the quantization procedure can be started and consistently applied. As a result, the damping quantum wave equation of the dissipative oscillator is deduced, by which an exact damping wave solution of this equation is obtained. Consequently, we arrive at such an irreversible quantum theory by which the quantum losses can be described.
2204.02893v2
2022-04-19
Role of shape anisotropy on thermal gradient-driven domain wall dynamics in magnetic nanowires
We investigate the magnetic domain wall (DW) dynamics in uniaxial/biaxial nanowires under a thermal gradient (TG). The findings reveal that the DW propagates toward the hotter region in both nanowires. The main physics of such observations is the magnonic angular momentum transfer to the DW. The hard (shape) anisotropy exists in biaxial nanowire, which contributes an additional torque, hence DW speed is larger than that in uniaxial nanowire. With lower damping, the DW velocity is smaller and DW velocity increases with damping which is opposite to usual expectation. To explain this, it is predicted that there is a probability to form the standing spin-waves (which do not carry net energy/momentum) together with travelling spin-waves if the propagation length of thermally-generated spin-waves is larger than the nanowire length. For larger-damping, DW decreases with damping since the magnon propagation length decreases. Therefore, the above findings might be useful in realizing the spintronic (racetrack memory) devices.
2204.09101v2
2022-04-25
Energy decay estimates for the wave equation with supercritical nonlinear damping
We consider a damped wave equation in a bounded domain. The damping is nonlinear and is homogeneous with degree p -- 1 with p > 2. First, we show that the energy of the strong solution in the supercritical case decays as a negative power of t; the rate of decay is the same as in the subcritical or critical cases, provided that the space dimension does not exceed ten. Next, relying on a new differential inequality, we show that if the initial displacement is further required to lie in L p , then the energy of the corresponding weak solution decays logarithmically in the supercritical case. Those new results complement those in the literature and open an important breach in the unknown land of super-critical damping mechanisms.
2204.11494v1
2022-05-07
Proposal for a Damping-Ring-Free Electron Injector for Future Linear Colliders
The current designs of future electron-positron linear colliders incorporate large and complex damping rings to produce asymmetric beams for beamstrahlung suppression. Here we present the design of an electron injector capable of delivering flat electron beams with phase-space partition comparable to the electron-beam parameters produced downstream of the damping ring in the proposed international linear collider (ILC) design. Our design does not employ a damping ring but is instead based on cross-plane phase-space-manipulation techniques. The performance of the proposed configuration, its sensitivity to jitter along with its impact on spin-polarization is investigated. The proposed paradigm could be adapted to other linear collider concepts under consideration and offers a path toward significant cost and complexity reduction.
2205.03736v1
2022-06-02
Optimal Control of the 3D Damped Navier-Stokes-Voigt Equations with Control Constraints
In this paper, we consider the 3D Navier-Stokes-Voigt (NSV) equations with nonlinear damping $|u|^{r-1}u, r\in[1,\infty)$ in bounded and space-periodic domains. We formulate an optimal control problem of minimizing the curl of the velocity field in the energy norm subject to the flow velocity satisfying the damped NSV equation with a distributed control force. The control also needs to obey box-type constraints. For any $r\geq 1,$ the existence and uniqueness of a weak solution is discussed when the domain $\Omega$ is periodic/bounded in $\mathbb R^3$ while a unique strong solution is obtained in the case of space-periodic boundary conditions. We prove the existence of an optimal pair for the control problem. Using the classical adjoint problem approach, we show that the optimal control satisfies a first-order necessary optimality condition given by a variational inequality. Since the optimal control problem is non-convex, we obtain a second-order sufficient optimality condition showing that an admissible control is locally optimal. Further, we derive optimality conditions in terms of adjoint state defined with respect to the growth of the damping term for a global optimal control.
2206.00988v2
2022-06-05
Stationary measures for stochastic differential equations with degenerate damping
A variety of physical phenomena involve the nonlinear transfer of energy from weakly damped modes subjected to external forcing to other modes which are more heavily damped. In this work we explore this in (finite-dimensional) stochastic differential equations in $\mathbb R^n$ with a quadratic, conservative nonlinearity $B(x,x)$ and a linear damping term $-Ax$ which is degenerate in the sense that $\mathrm{ker} A \neq \emptyset$. We investigate sufficient conditions to deduce the existence of a stationary measure for the associated Markov semigroups. Existence of such measures is straightforward if $A$ is full rank, but otherwise, energy could potentially accumulate in $\mathrm{ker} A$ and lead to almost-surely unbounded trajectories, making the existence of stationary measures impossible. We give a relatively simple and general sufficient condition based on time-averaged coercivity estimates along trajectories in neighborhoods of $\mathrm{ker} A$ and many examples where such estimates can be made.
2206.02240v1
2022-07-13
Energy decay for the time dependent damped wave equation
Energy decay is established for the damped wave equation on compact Riemannian manifolds where the damping coefficient is allowed to depend on time. Using a time dependent observability inequality, it is shown that the energy of solutions decays at an exponential rate if the damping coefficient satisfies a time dependent analogue of the classical geometric control condition. Existing time dependent observability inequalities are improved by removing technical assumptions on the permitted initial data.
2207.06260v4
2022-08-04
Lp-asymptotic stability of 1D damped wave equations with localized and nonlinear damping
In this paper, we study the $L^p$-asymptotic stability with $p\in (1,\infty)$ of the one-dimensional nonlinear damped wave equation with a localized damping and Dirichlet boundary conditions in a bounded domain $(0,1)$. We start by addressing the well-posedness problem. We prove the existence and the uniqueness of weak solutions for $p\in [2,\infty)$ and the existence and the uniqueness of strong solutions for all $p\in [1,\infty)$. The proofs rely on the well-posedness already proved in the $L^\infty$ framework by [4] combined with a density argument. Then we prove that the energy of strong solutions decays exponentially to zero. The proof relies on the multiplier method combined with the work that has been done in the linear case in [8].
2208.02779v1
2022-08-07
Damping of neutrino oscillations, decoherence and the lengths of neutrino wave packets
Spatial separation of the wave packets (WPs) of neutrino mass eigenstates leads to decoherence and damping of neutrino oscillations. Damping can also be caused by finite energy resolution of neutrino detectors or, in the case of experiments with radioactive neutrino sources, by finite width of the emitted neutrino line. We study in detail these two types of damping effects using reactor neutrino experiments and experiments with radioactive $^{51}$Cr source as examples. We demonstrate that the effects of decoherence by WP separation can always be incorporated into a modification of the energy resolution function of the detector and so are intimately entangled with it. We estimate for the first time the lengths $\sigma_x$ of WPs of reactor neutrinos and neutrinos from a radioactive $^{51}$Cr source. The obtained values, $\sigma_x = (2\times 10^{-5} - 1.4\times 10^{-4})$ cm, are at least six orders of magnitude larger than the currently available experimental lower bounds. We conclude that effects of decoherence by WP separation cannot be probed in reactor and radioactive source experiments.
2208.03736v2
2022-08-23
Fate of exceptional points in the presence of nonlinearities
The non-Hermitian dynamics of open systems deal with how intricate coherent effects of a closed system intertwine with the impact of coupling to an environment. The system-environment dynamics can then lead to so-called exceptional points, which are the open-system marker of phase transitions, i.e., the closing of spectral gaps in the complex spectrum. Even in the ubiquitous example of the damped harmonic oscillator, the dissipative environment can lead to an exceptional point, separating between under-damped and over-damped dynamics at a point of critical damping. Here, we examine the fate of this exceptional point in the presence of strong correlations, i.e., for a nonlinear oscillator. By employing a functional renormalization group approach, we identify non-perturbative regimes of this model where the nonlinearity makes the system more robust against the influence of dissipation and can remove the exceptional point altogether. The melting of the exceptional point occurs above a critical nonlinearity threshold. Interestingly, the exceptional point melts faster with increasing temperatures, showing a surprising flow to coherent dynamics when coupled to a warm environment.
2208.11205v2
2022-09-10
Data-driven, multi-moment fluid modeling of Landau damping
Deriving governing equations of complex physical systems based on first principles can be quite challenging when there are certain unknown terms and hidden physical mechanisms in the systems. In this work, we apply a deep learning architecture to learn fluid partial differential equations (PDEs) of a plasma system based on the data acquired from a fully kinetic model. The learned multi-moment fluid PDEs are demonstrated to incorporate kinetic effects such as Landau damping. Based on the learned fluid closure, the data-driven, multi-moment fluid modeling can well reproduce all the physical quantities derived from the fully kinetic model. The calculated damping rate of Landau damping is consistent with both the fully kinetic simulation and the linear theory. The data-driven fluid modeling of PDEs for complex physical systems may be applied to improve fluid closure and reduce the computational cost of multi-scale modeling of global systems.
2209.04726v1
2022-09-25
Formation of the cosmic-ray halo: The role of nonlinear Landau damping
We present a nonlinear model of self-consistent Galactic halo, where the processes of cosmic ray (CR) propagation and excitation/damping of MHD waves are included. The MHD-turbulence, which prevents CR escape from the Galaxy, is entirely generated by the resonant streaming instability. The key mechanism controlling the halo size is the nonlinear Landau (NL) damping, which suppresses the amplitude of MHD fluctuations and, thus, makes the halo larger. The equilibrium turbulence spectrum is determined by a balance of CR excitation and NL damping, which sets the regions of diffusive and advective propagation of CRs. The boundary $z_{cr}(E)$ between the two regions is the halo size, which slowly increases with the energy. For the vertical magnetic field of $\sim 1~\mu G$, we estimate $z_{cr} \sim 1$ kpc for GeV protons. The derived proton spectrum is in a good agreement with observational data.
2209.12302v1
2022-10-10
Finite time extinction for a critically damped Schr{ö}dinger equation with a sublinear nonlinearity
This paper completes some previous studies by several authors on the finite time extinction for nonlinear Schr{\"o}dinger equation when the nonlinear damping term corresponds to the limit cases of some ``saturating non-Kerr law'' $F(|u|^2)u=\frac{a}{\varepsilon+(|u|^2)^\alpha}u,$ with $a\in\mathbb{C},$ $\varepsilon\geqslant0,$ $2\alpha=(1-m)$ and $m\in[0,1).$ Here we consider the sublinear case $0<m<1$ with a critical damped coefficient: $a\in\mathbb{C}$ is assumed to be in the set $D(m)=\big\{z\in\mathbb{C}; \; \mathrm{Im}(z)>0 \text{ and } 2\sqrt{m}\mathrm{Im}(z)=(1-m)\mathrm{Re}(z)\big\}.$ Among other things, we know that this damping coefficient is critical, for instance, in order to obtain the monotonicity of the associated operator (see the paper by Liskevich and Perel'muter [16] and the more recent study by Cialdea and Maz'ya [14]). The finite time extinction of solutions is proved by a suitable energy method after obtaining appropiate a priori estimates. Most of the results apply to non-necessarily bounded spatial domains.
2210.04493v4
2022-10-14
Landau damping for gravitational waves in parity-violating theories
We discuss how tensor polarizations of gravitational waves can suffer Landau damping in the presence of velocity birefringence, when parity symmetry is explicitly broken. In particular, we analyze the role of the Nieh-Yan and Chern-Simons terms in modified theories of gravity, showing how the gravitational perturbation in collisionless media can be characterized by a subluminal phase velocity, circumventing the well-known results of General Relativity and allowing for the appearance of the kinematic damping. We investigate in detail the connection between the thermodynamic properties of the medium, such as temperature and mass of the particles interacting with the gravitational wave, and the parameters ruling the parity violating terms of the models. In this respect, we outline how the dispersion relations can give rise in each model to different regions of the wavenumber space, where the phase velocity is subluminal, superluminal or does not exist. Quantitative estimates on the considered models indicate that the phenomenon of Landau damping is not detectable given the sensitivity of present-day instruments.
2210.07673v2
2022-10-25
Formation of shifted shock for the 3D compressible Euler equations with damping
In this paper, we show the shock formation of the solutions to the 3-dimensional (3D) compressible isentropic and irrotational Euler equations with damping for the initial short pulse data which was first introduced by D.Christodoulou\cite{christodoulou2007}. Due to the damping effect, the largeness of the initial data is necessary for the shock formation and we will work on the class of large data (in energy sense). Similar to the undamped case, the formation of shock is characterized by the collapse of the characteristic hypersurfaces and the vanishing of the inverse foliation density function $\mu$, at which the first derivatives of the velocity and the density blow up. However, the damping effect changes the asymptotic behavior of the inverse foliation density function $\mu$ and then shifts the time of shock formation compared with the undamped case. The methods in the paper can also be extended to a class of $3D$ quasilinear wave equations for the short pulse initial data.
2210.13796v1
2022-10-30
Dynamics of a class of extensible beams with degenerate and non-degenerate nonlocal damping
This work is concerned with new results on long-time dynamics of a class of hyperbolic evolution equations related to extensible beams with three distinguished nonlocal nonlinear damping terms. In the first possibly degenerate case, the results feature the existence of a family of compact global attractors and a thickness estimate for their Kolmogorov's $\varepsilon$-entropy. Then, in the non-degenerate context, the structure of the helpful nonlocal damping leads to the existence of finite-dimensional compact global and exponential attractors. Lastly, in a degenerate and critical framework, it is proved the existence of a bounded closed global attractor but not compact. To the proofs, we provide several new technical results by means of refined estimates that open up perspectives for a new branch of nonlinearly damped problems.
2210.16851v1
2022-11-11
Nonlinear fractional damped wave equation on compact Lie groups
In this paper, we deal with the initial value fractional damped wave equation on $G$, a compact Lie group, with power-type nonlinearity. The aim of this manuscript is twofold. First, using the Fourier analysis on compact Lie groups, we prove a local in-time existence result in the energy space for the fractional damped wave equation on $G$. Moreover, a finite time blow-up result is established under certain conditions on the initial data. In the next part of the paper, we consider fractional wave equation with lower order terms, that is, damping and mass with the same power type nonlinearity on compact Lie groups, and prove the global in-time existence of small data solutions in the energy evolution space.
2211.06155v1