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2024-03-07
The stochastic Ravine accelerated gradient method with general extrapolation coefficients
In a real Hilbert space domain setting, we study the convergence properties of the stochastic Ravine accelerated gradient method for convex differentiable optimization. We consider the general form of this algorithm where the extrapolation coefficients can vary with each iteration, and where the evaluation of the gradient is subject to random errors. This general treatment models a breadth of practical algorithms and numerical implementations. We show that, under a proper tuning of the extrapolation parameters, and when the error variance associated with the gradient evaluations or the step-size sequences vanish sufficiently fast, the Ravine method provides fast convergence of the values both in expectation and almost surely. We also improve the convergence rates from O(.) to o(.). Moreover, we show almost sure summability property of the gradients, which implies the fast convergence of the gradients towards zero. This property reflects the fact that the high-resolution ODE of the Ravine method includes a Hessian-driven damping term. When the space is also separable, our analysis allows also to establish almost sure weak convergence of the sequence of iterates provided by the algorithm. We finally specialize the analysis to consider different parameter choices, including vanishing and constant (heavy ball method with friction) damping parameter, and present a comprehensive landscape of the tradeoffs in speed and accuracy associated with these parameter choices and statistical properties on the sequence of errors in the gradient computations. We provide a thorough discussion of the similarities and differences with the Nesterov accelerated gradient which satisfies similar asymptotic convergence rates.
2403.04860v2
1998-02-18
Damping rates of hot Giant Dipole Resonances
The damping rate of hot giant dipole resonances (GDR) is investigated. Besides Landau damping we consider collisions and density fluctuations as contributions to the damping of GDR. Within the nonequilibrium Green's function method we derive a non-Markovian kinetic equation. The linearization of the latter one leads to complex dispersion relations. The complex solution provides the centroid energy and the damping width of giant resonances. The experimental damping widths are the full width half maximum (FWHM) and can be reproduced by the full width of the structure function. Within simple finite size scaling we give a relation between the minimal interaction strength which is required for a collective oscillation and the clustersize. We investigate the damping of giant dipole resonances within a Skyrme type of interaction. Different collision integrals are compared with each other in order to incorporate correlations. The inclusion of a conserving relaxation time approximation allows to find the $T^2$-dependence of the damping rate with a temperature known from the Fermi-liquid theory. However, memory effects turn out to be essential for a proper treatment of the damping of collective modes. We derive a Landau like formula for the one--particle relaxation time similar to the damping of zero sound.
9802052v2
2015-12-11
Ultra-low magnetic damping of a metallic ferromagnet
The phenomenology of magnetic damping is of critical importance for devices that seek to exploit the electronic spin degree of freedom since damping strongly affects the energy required and speed at which a device can operate. However, theory has struggled to quantitatively predict the damping, even in common ferromagnetic materials. This presents a challenge for a broad range of applications in spintronics and spin-orbitronics that depend on materials and structures with ultra-low damping. Such systems enable many experimental investigations that further our theoretical understanding of numerous magnetic phenomena such as damping and spin-transport mediated by chirality and the Rashba effect. Despite this requirement, it is believed that achieving ultra-low damping in metallic ferromagnets is limited due to the scattering of magnons by the conduction electrons. However, we report on a binary alloy of Co and Fe that overcomes this obstacle and exhibits a damping parameter approaching 0.0001, which is comparable to values reported only for ferrimagnetic insulators. We explain this phenomenon by a unique feature of the bandstructure in this system: The density of states exhibits a sharp minimum at the Fermi level at the same alloy concentration at which the minimum in the magnetic damping is found. This discovery provides both a significant fundamental understanding of damping mechanisms as well as a test of theoretical predictions.
1512.03610v1
2020-05-12
Effective Viscous Damping Enables Morphological Computation in Legged Locomotion
Muscle models and animal observations suggest that physical damping is beneficial for stabilization. Still, only a few implementations of mechanical damping exist in compliant robotic legged locomotion. It remains unclear how physical damping can be exploited for locomotion tasks, while its advantages as sensor-free, adaptive force- and negative work-producing actuators are promising. In a simplified numerical leg model, we studied the energy dissipation from viscous and Coulomb damping during vertical drops with ground-level perturbations. A parallel spring-damper is engaged between touch-down and mid-stance, and its damper auto-disengages during mid-stance and takeoff. Our simulations indicate that an adjustable and viscous damper is desired. In hardware we explored effective viscous damping and adjustability and quantified the dissipated energy. We tested two mechanical, leg-mounted damping mechanisms; a commercial hydraulic damper, and a custom-made pneumatic damper. The pneumatic damper exploits a rolling diaphragm with an adjustable orifice, minimizing Coulomb damping effects while permitting adjustable resistance. Experimental results show that the leg-mounted, hydraulic damper exhibits the most effective viscous damping. Adjusting the orifice setting did not result in substantial changes of dissipated energy per drop, unlike adjusting damping parameters in the numerical model. Consequently, we also emphasize the importance of characterizing physical dampers during real legged impacts to evaluate their effectiveness for compliant legged locomotion.
2005.05725v2
2023-06-30
A finite element method to compute the damping rate of oscillating fluids inside microfluidic nozzles
We introduce a finite element method for computing the damping rate of fluid oscillations in nozzles of drop-on-demand (DoD) microfluidic devices. Accurate knowledge of the damping rates for the least-damped oscillation modes following droplet ejection is paramount for assessing jetting stability at higher jetting frequencies, as ejection from a non-quiescent meniscus can result in deviations from nominal droplet properties. Computational fluid dynamics (CFD) simulations often struggle to accurately predict meniscus damping in the limit of low viscosity and high surface tension. Moreover, their use in design loops aimed at optimizing the nozzle geometry for stable jetting is slow and computationally expensive. The faster alternative we adopt here is to compute the damping rate directly from the eigenvalues of the linearized problem. Starting from a variational formulation of the linearized governing equations, we obtain a generalized eigenvalue problem for the oscillation modes, and approximate its solutions with a finite element method that uses Taylor-Hood elements. We solve the matrix eigenvalue problem with a sparse, parallelized implementation of the Krylov-Schur algorithm. The spatial shape and temporal evolution (angular frequency and damping rate) of the set of least-damped oscillation modes are obtained in a matter of minutes, compared to days for a CFD simulation. We verify that the method can reproduce an analytical benchmark problem, and then determine numerical convergence rates on two examples with axisymmetric geometry. We also prove that the method is free of spurious modes with zero or positive damping rates. The method's ability to quickly generate accurate estimates of fluid oscillation damping rates makes it suitable for integration into design loops for prototyping microfluidic nozzles.
2307.00094v1
2023-07-05
Optimal damping of vibrating systems: dependence on initial conditions
Common criteria used for measuring performance of vibrating systems have one thing in common: they do not depend on initial conditions of the system. In some cases it is assumed that the system has zero initial conditions, or some kind of averaging is used to get rid of initial conditions. The aim of this paper is to initiate rigorous study of the dependence of vibrating systems on initial conditions in the setting of optimal damping problems. We show that, based on the type of initial conditions, especially on the ratio of potential and kinetic energy of the initial conditions, the vibrating system will have quite different behavior and correspondingly the optimal damping coefficients will be quite different. More precisely, for single degree of freedom systems and the initial conditions with mostly potential energy, the optimal damping coefficient will be in the under-damped regime, while in the case of the predominant kinetic energy the optimal damping coefficient will be in the over-damped regime. In fact, in the case of pure kinetic initial energy, the optimal damping coefficient is $+\infty$! Qualitatively, we found the same behavior in multi degree of freedom systems with mass proportional damping. We also introduce a new method for determining the optimal damping of vibrating systems, which takes into account the peculiarities of initial conditions and the fact that, although in theory these systems asymptotically approach equilibrium and never reach it exactly, in nature and in experiments they effectively reach equilibrium in some finite time.
2307.02352v2
2024-01-18
Multithermal apparent damping of slow waves due to strands with a Gaussian temperature distribution
Context. Slow waves in solar coronal loops are strongly damped. The current theory of damping by thermal conduction cannot explain some observational features.\n Aims. We investigate the propagation of slow waves in a coronal loop built up from strands of different temperatures. \n Methods. We consider the loop to have a multithermal, Gaussian temperature distribution. The different propagation speeds in different strands lead to an multithermal apparent damping of the wave, similar to observational phase mixing. We use an analytical model to predict the damping length and propagation speed for the slow waves, including in imaging with filter telescopes. \n Results. We compare the damping length due to this multithermal apparent damping with damping due to thermal conduction and find that the multithermal apparent damping is more important for shorter period slow waves. We have found the influence of instrument filters on the wave's propagation speed and damping. This allows us to compare our analytical theory to forward models of numerical simulations. \n Conclusions. We find that our analytical model matches the numerical simulations very well. Moreover, we offer an outlook for using the slow wave properties to infer the loop's thermal properties.
2401.09803v1
2000-12-20
Possible evidence for a variable fine structure constant from QSO absorption lines: motivations, analysis and results
An experimental search for variation in the fundamental coupling constants is strongly motivated by modern high-energy physics theories. Comparison of quasar absorption line spectra with laboratory spectra provides a sensitive probe for variability of the fine structure constant, alpha, over cosmological time-scales. We have previously developed and applied a new method providing an order of magnitude gain in precision over previous optical astrophysical constraints. Here we extend that work by including new quasar spectra of damped Lyman-alpha absorption systems. We also re-analyse our previous lower redshift data and confirm our initial results. The constraints on alpha come from simultaneous fitting of absorption lines of subsets of the following species: Mg I, Mg II, Al II, Al III, Si II, Cr II, Fe II, Ni II and Zn II. We present a detailed description of our methods and results based on an analysis of 49 quasar absorption systems (towards 28 QSOs) covering the redshift range 0.5 < z < 3.5. There is statistical evidence for a smaller alpha at earlier epochs: da/a = (-0.72 +/- 0.18) * 10^{-5}. The new and original samples are independent but separately yield consistent and significant non-zero values of da/a. We summarise the results of a thorough investigation of systematic effects published in a companion paper. The value we quote above is the raw value, not corrected for any of these systematic effects. The only significant systematic effects so far identified, if removed from our data, would lead to a more significant deviation of da/a from zero.
0012419v5
2006-06-04
k-Essence, Avoidance of the Weinberg's Cosmological Constant No-Go Theorem and Other Dark Energy Effects of Two Measures Field Theory
The dilaton-gravity sector of the Two Measures Field Theory (TMT) is explored in detail in the context of cosmology. The dilaton \phi dependence of the effective Lagrangian appears only as a result of the spontaneous breakdown of the scale invariance. If no fine tuning is made, the effective \phi-Lagrangian p(\phi,X) depends quadratically upon the kinetic energy X. Hence TMT may represent an explicit example of the effective k-essence resulting from first principles without any exotic term in the fundamental action intended for obtaining this result. Depending of the choice of regions in the parameter space, TMT exhibits different possible outputs for cosmological dynamics: a) Possibility of resolution of the old cosmological constant (CC) problem. From the point of view of TMT, it becomes clear why the old CC problem cannot be solved (without fine tuning) in the conventional field theories (i.e theories with only the measure of integration \sqrt{-g} in the action). b) The power law inflation without any fine tuning can end with damped oscillations of \phi around the state with zero CC. d) There is a broad range of the parameters such that: in the late time universe w=p/\rho <-1 and asymptotically (as t\to\infty) approaches -1 from below; \rho approaches a cosmological constant. The smallness of the CC may be achieved without fine tuning of dimensionfull parameters: either by a seesaw type mechanism or due to a correspondence principle between TMT and conventional field theories.
0606017v2
2006-03-20
Higgs-Inflaton Symbiosis, Cosmological Constant Problem and Superacceleration Phase of the Universe in Two Measures Field Theory with Spontaneously Broken Scale Invariance
We study the scalar sector of the Two Measures Field Theory (TMT) model in the context of cosmological dynamics. The scalar sector includes the inflaton \phi and the Higgs \upsilon fields. The model possesses gauge and scale invariance. The latter is spontaneously broken due to intrinsic features of the TMT dynamics. In the model with the inflaton \phi alone, in different regions of the parameter space the following different effects can take place without fine tuning of the parameters and initial conditions: a) Possibility of resolution of the old cosmological constant problem: this is done in a consistent way hinted by S. Weinberg in his comment concerning the question of how one can avoid his no-go theorem. b) The power law inflation without any fine tuning may end with damped oscillations of $\phi$ around the state with zero cosmological constant. c) There are regions of the parameters where the equation-of-state w=p/\rho in the late time universe is w<-1 and w asymptotically (as t\to\infty) approaches -1 from below. This effect is achieved without any exotic term in the action. In a model with both \phi and \upsilon fields, a scenario which resembles the hybrid inflation is realized but there are essential differences, for example: the Higgs field undergos transition to a gauge symmetry broken phase <\upsilon>\neq 0 soon after the end of a power law inflation; there are two oscillatory regimes of \upsilon, one around \upsilon =0 at 50 e-folding before the end of inflation, another - during transition to a gauge symmetry broken phase where the scalar dark energy density approaches zero without fine tuning; the gauge symmetry breakdown is achieved without tachyonic mass term in the action.
0603150v1
2020-10-28
Testing Gravity on Cosmic Scales: A Case Study of Jordan-Brans-Dicke Theory
We provide an end-to-end exploration of a distinct modified gravitational theory in Jordan-Brans-Dicke (JBD) gravity, from an analytical and numerical description of the background expansion and linear perturbations, to the nonlinear regime captured with a hybrid suite of $N$-body simulations, to the parameter constraints from existing cosmological probes. The nonlinear corrections to the matter power spectrum due to baryons, massive neutrinos, and modified gravity are simultaneously modeled and propagated in the cosmological analysis for the first time. In the combined analysis of the Planck CMB temperature, polarization, and lensing reconstruction, Pantheon supernova distances, BOSS measurements of BAO distances, the Alcock-Paczynski effect, and the growth rate, along with the joint ($3\times2$pt) dataset of cosmic shear, galaxy-galaxy lensing, and overlapping redshift-space galaxy clustering from KiDS and 2dFLenS, we constrain the JBD coupling constant, $\omega_{\rm BD}>1540$ (95% CL), the effective gravitational constant, $G_{\rm matter}/G=0.997\pm0.029$, the sum of neutrino masses, $\sum m_{\nu}<0.12$ eV (95% CL), and the baryonic feedback amplitude, $B<2.8$ (95% CL), all in agreement with the standard model expectation. We show that the uncertainty in the gravitational theory alleviates the tension between KiDS$\times$2dFLenS and Planck to below $1\sigma$ and the tension in the Hubble constant between Planck and the direct measurement of Riess et al. (2019) down to ~$3\sigma$; however, we find no substantial model selection preference for JBD gravity relative to $\Lambda$CDM. We further show that the neutrino mass bound degrades by up to a factor of three as the $\omega_{\rm BD}$ parameterization becomes more restrictive and that a positive shift in $G_{\rm matter}/G$ suppresses the CMB damping tail in a way that might complicate future inferences of small-scale physics. (Abridged)
2010.15278v2
2022-01-31
A lower bound on the space overhead of fault-tolerant quantum computation
The threshold theorem is a fundamental result in the theory of fault-tolerant quantum computation stating that arbitrarily long quantum computations can be performed with a polylogarithmic overhead provided the noise level is below a constant level. A recent work by Fawzi, Grospellier and Leverrier (FOCS 2018) building on a result by Gottesman (QIC 2013) has shown that the space overhead can be asymptotically reduced to a constant independent of the circuit provided we only consider circuits with a length bounded by a polynomial in the width. In this work, using a minimal model for quantum fault tolerance, we establish a general lower bound on the space overhead required to achieve fault tolerance. For any non-unitary qubit channel $\mathcal{N}$ and any quantum fault tolerance schemes against $\mathrm{i.i.d.}$ noise modeled by $\mathcal{N}$, we prove a lower bound of $\max\left\{\mathrm{Q}(\mathcal{N})^{-1}n,\alpha_\mathcal{N} \log T\right\}$ on the number of physical qubits, for circuits of length $T$ and width $n$. Here, $\mathrm{Q}(\mathcal{N})$ denotes the quantum capacity of $\mathcal{N}$ and $\alpha_\mathcal{N}>0$ is a constant only depending on the channel $\mathcal{N}$. In our model, we allow for qubits to be replaced by fresh ones during the execution of the circuit and we allow classical computation to be free and perfect. This improves upon results that assumed classical computations to be also affected by noise, and that sometimes did not allow for fresh qubits to be added. Along the way, we prove an exponential upper bound on the maximal length of fault-tolerant quantum computation with amplitude damping noise resolving a conjecture by Ben-Or, Gottesman, and Hassidim (2013).
2202.00119v2
1996-06-07
Abundances at High Redshifts: the Chemical Enrichment History of Damped Lyman-alpha Galaxies
Damped Lyman-alpha absorption systems found in the spectra of high redshift quasars are believed to trace the interstellar gas in high redshift galaxies. In this paper, we study the elemental abundances of C, N, O, Al, Si, S, Cr, Mn, Fe, Ni, and Zn in a sample of 14 damped Lyman-alpha systems using high quality echelle spectra of quasars obtained with the 10m Keck telescope. These abundances are combined with similar measurements in the literature in order to investigate the chemical evolution of damped Lyman-alpha galaxies in the redshift range 0.7<z<4.4. Among the things investigated are: the metallicity distribution of damped Lyman-alpha galaxy, its evolution with redshift (ie, age-metallicity relation), the relative abundance patterns of the heavy metals and implications for their nucleosynthetic origin, the effects of dust, the nature of the star formation process in damped Lyman-alpha galaxies, and the nature of damped Lyman-alpha galaxies themselves.
9606044v1
1998-07-17
Chaotic scattering on surfaces and collisional damping of collective modes
The damping of hot giant dipole resonances is investigated. The contribution of surface scattering is compared with the contribution from interparticle collisions. A unified response function is presented which includes surface damping as well as collisional damping. The surface damping enters the response via the Lyapunov exponent and the collisional damping via the relaxation time. The former is calculated for different shape deformations of quadrupole and octupole type. The surface as well as the collisional contribution each reproduce almost the experimental value, therefore we propose a proper weighting between both contributions related to their relative occurrence due to collision frequencies between particles and of particles with the surface. We find that for low and high temperatures the collisional contribution dominates whereas the surface damping is dominant around the temperatures $\sqrt{3}/2\pi$ of the centroid energy.
9807185v4
2000-09-08
Probing High-Redshift Disks with Damped Lyman Alpha Systems
Evidence is presented that the damped Lyman alpha absorption systems are the high-redshift (z > 3) progenitors of galaxy disks. I discuss kinematic evidence that the damped Lyman Alpha systems are rotating disks. I also discuss implications of the lack of metal-poor damped Lyman alpha systems with line width Delta v > 100 {\kms}. I then present new evidence stemming from correlations between element-abundance ratios and [Fe/H], which connects damped systems to the thick stellar disk of the Galaxy. I discuss the connections between damped Lyman alpha systems and Lyman break galaxies, and how [CII] 158 micron emission from damped Lyman alpha systems discriminates among competing theories of galaxy formation. ~
0009126v1
2006-09-10
Damping of Compressional MHD Waves In Quiescent Prominences and Prominence-Corona Transition Region (PCTR)
The effects of radiative losses due to Newtonian cooling and MHD turbulence have been considered to examine the spatial damping of linear compressional waves in quiescent prominences and prominence-corona transition region (PCTR). The radiative losses give acceptable damping lengths for the slow mode wave for the radiative relaxation time in the range (10-1000s). From prominence seismology, the values of opacity and turbulent kinematic viscosity have been inferred. It has been found that for a given value of radiative relaxation time, the high frequency slow mode waves are highly damped. We have also investigated the possible role of MHD turbulence in damping of MHD waves and found a turbulent viscosity can re-produce the observed damping time and damping length in prominences, especially in PCTR.
0609266v1
1997-10-14
Damping of low-energy excitations of a trapped Bose condensate at finite temperatures
We present the theory of damping of low-energy excitations of a trapped Bose condensate at finite temperatures, where the damping is provided by the interaction of these excitations with the thermal excitations. We emphasize the key role of stochastization in the behavior of the thermal excitations for damping in non-spherical traps. The damping rates of the lowest excitations, following from our theory, are in fair agreement with the data of recent JILA and MIT experiments. The damping of quasiclassical excitations is determined by the condensate boundary region, and the result for the damping rate is drastically different from that in a spatially homogeneous gas.
9710128v3
2001-12-09
Soliton dynamics in damped and forced Boussinesq equations
We investigate the dynamics of a lattice soliton on a monatomic chain in the presence of damping and external forces. We consider Stokes and hydrodynamical damping. In the quasi-continuum limit the discrete system leads to a damped and forced Boussinesq equation. By using a multiple-scale perturbation expansion up to second order in the framework of the quasi-continuum approach we derive a general expression for the first-order velocity correction which improves previous results. We compare the soliton position and shape predicted by the theory with simulations carried out on the level of the monatomic chain system as well as on the level of the quasi-continuum limit system. For this purpose we restrict ourselves to specific examples, namely potentials with cubic and quartic anharmonicities as well as the truncated Morse potential, without taking into account external forces. For both types of damping we find a good agreement with the numerical simulations both for the soliton position and for the tail which appears at the rear of the soliton. Moreover we clarify why the quasi-continuum approximation is better in the hydrodynamical damping case than in the Stokes damping case.
0112148v1
2006-04-17
The Highly Damped Quasinormal Modes of $d$-dimensional Reissner-Nordstrom Black Holes in the Small Charge Limit
We analyze in detail the highly damped quasinormal modes of $d$-dimensional Reissner-Nordstr$\ddot{\rm{o}}$m black holes with small charge, paying particular attention to the large but finite damping limit in which the Schwarzschild results should be valid. In the infinite damping limit, we confirm using different methods the results obtained previously in the literature for higher dimensional Reissner-Nordstr$\ddot{\rm{o}}$m black holes. Using a combination of analytic and numerical techniques we also calculate the transition of the real part of the quasinormal mode frequency from the Reissner-Nordstr$\ddot{\rm{o}}$m value for very large damping to the Schwarzschild value of $\ln(3) T_{bh}$ for intermediate damping. The real frequency does not interpolate smoothly between the two values. Instead there is a critical value of the damping at which the topology of the Stokes/anti-Stokes lines change, and the real part of the quasinormal mode frequency dips to zero.
0604073v2
2005-02-16
Damping signatures in future neutrino oscillation experiments
We discuss the phenomenology of damping signatures in the neutrino oscillation probabilities, where either the oscillating terms or the probabilities can be damped. This approach is a possibility for tests of non-oscillation effects in future neutrino oscillation experiments, where we mainly focus on reactor and long-baseline experiments. We extensively motivate different damping signatures due to small corrections by neutrino decoherence, neutrino decay, oscillations into sterile neutrinos, or other mechanisms, and classify these signatures according to their energy (spectral) dependencies. We demonstrate, at the example of short baseline reactor experiments, that damping can severely alter the interpretation of results, e.g., it could fake a value of $\sin(2\theta_{13})$ smaller than the one provided by Nature. In addition, we demonstrate how a neutrino factory could constrain different damping models with emphasis on how these different models could be distinguished, i.e., how easily the actual non-oscillation effects could be identified. We find that the damping models cluster in different categories, which can be much better distinguished from each other than models within the same cluster.
0502147v2
2000-08-22
Local and Fundamental Mode Coupler Damping of the Transverse Wakefield in RDDS1 Linacs
In damping the wakefield generated by an electron beam traversing several thousand X-band linacs in the NLC we utilise a Gaussian frequency distribution of dipole modes to force the modes to deconstructively interfere, supplemented with moderate damping achieved by coupling these modes to four attached manifolds. Most of these modes are adequately damped by the manifolds. However, the modes towards the high frequency end of the lower dipole band are not adequately damped because the last few cells are, due to mechanical fabrication requirements, not coupled to the manifolds. To mitigate this problem in the present RDDS1 design, the output coupler for the accelerating mode has been designed so as to also couple out those dipole modes which reach the output coupler cell. In order to couple out both dipole mode polarizations, the output coupler has four ports. We also report on the results of a study of the benefits which can be achieved by supplementing manifold damping with local damping for a limited number of cells at the downstream end of the structure.
0008211v1
2007-10-25
Damping of Condensate Oscillation of a Trapped Bose Gas in a One-Dimensional Optical Lattice at Finite Temperatures
We study damping of a dipole oscillation in a Bose-Condensed gas in a combined cigar-shaped harmonic trap and one-dimensional (1D) optical lattice potential at finite temperatures. In order to include the effect of thermal excitations in the radial direction, we derive a quasi-1D model of the Gross-Pitaeavskii equation and the Bogoliubov equations. We use the Popov approximation to calculate the temperature dependence of the condensate fraction with varying lattice depth. We then calculate the Landau damping rate of a dipole oscillation as a function of the lattice depth and temperature. The damping rate increases with increasing lattice depth, which is consistent with experimental observations. The magnitude of the damping rate is in reasonable agreement with experimental data. We also find that the damping rate has a strong temperature dependence, showing a sharp increase with increasing temperature. Finally, we emphasize the importance of the radial thermal excitations in both equilibrium properties and the Landau damping.
0710.4610v1
2008-01-03
Spin orbit precession damping in transition metal ferromagnets
We provide a simple explanation, based on an effective field, for the precession damping rate due to the spin-orbit interaction. Previous effective field treatments of spin-orbit damping include only variations of the state energies with respect to the magnetization direction, an effect referred to as the breathing Fermi surface. Treating the interaction of the rotating spins with the orbits as a perturbation, we include also changes in the state populations in the effective field. In order to investigate the quantitative differences between the damping rates of iron, cobalt, and nickel, we compute the dependence of the damping rate on the density of states and the spin-orbit parameter. There is a strong correlation between the density of states and the damping rate. The intraband terms of the damping rate depend on the spin-orbit parameter cubed while the interband terms are proportional to the spin-orbit parameter squared. However, the spectrum of band gaps is also an important quantity and does not appear to depend in a simple way on material parameters.
0801.0549v1
2009-02-03
Damping of filament thread oscillations: effect of the slow continuum
Transverse oscillations of small amplitude are commonly seen in high-resolution observations of filament threads, i.e. the fine-structures of solar filaments/prominences, and are typically damped in a few periods. Kink wave modes supported by the thread body offer a consistent explanation of these observed oscillations. Among the proposed mechanisms to explain the kink mode damping, resonant absorption in the Alfven continuum seems to be the most efficient as it produces damping times of about 3 periods. However, for a nonzero-beta plasma and typical prominence conditions, the kink mode is also resonantly coupled to slow (or cusp) continuum modes, which could further reduce the damping time. In this Letter, we explore for the first time both analytically and numerically the effect of the slow continuum on the damping of transverse thread oscillations. The thread model is composed of a homogeneous and straight cylindrical plasma, an inhomogeneous transitional layer, and the homogeneous coronal plasma. We find that the damping of the kink mode due to the slow resonance is much less efficient than that due to the Alfven resonance.
0902.0572v2
2010-11-23
Magnetohydrodynamic kink waves in two-dimensional non-uniform prominence threads
We analyse the oscillatory properties of resonantly damped transverse kink oscillations in two-dimensional prominence threads. The fine structures are modelled as cylindrically symmetric magnetic flux tubes with a dense central part with prominence plasma properties and an evacuated part, both surrounded by coronal plasma. The equilibrium density is allowed to vary non-uniformly in both the transverse and the longitudinal directions.We examine the influence of longitudinal density structuring on periods, damping times, and damping rates for transverse kink modes computed by numerically solving the linear resistive magnetohydrodynamic (MHD) equations. The relevant parameters are the length of the thread and the density in the evacuated part of the tube, two quantities that are difficult to directly estimate from observations. We find that both of them strongly influence the oscillatory periods and damping times, and to a lesser extent the damping ratios. The analysis of the spatial distribution of perturbations and of the energy flux into the resonances allows us to explain the obtained damping times. Implications for prominence seismology, the physics of resonantly damped kink modes in two-dimensional magnetic flux tubes, and the heating of prominence plasmas are discussed.
1011.5175v2
2011-04-04
Plasmonic abilities of gold and silver spherical nanoantennas in terms of size dependent multipolar resonance frequencies and plasmon damping rates
Absorbing and emitting optical properties of a spherical plasmonic nanoantenna are described in terms of the size dependent resonance frequencies and damping rates of the multipolar surface plasmons (SP). We provide the plasmon size characteristics for gold and silver spherical particles up to the large size retardation regime where the plasmon radiative damping is significant. We underline the role of the radiation damping in comparison with the energy dissipation damping in formation of receiving and transmitting properties of a plasmonic particle. The size dependence of both: the multipolar SP resonance frequencies and corresponding damping rates can be a convenient tool in tailoring the characteristics of plasmonic nanoantennas for given application. Such characteristics enable to control an operation frequency of a plasmonic nanoantenna and to change the operation range from the spectrally broad to spectrally narrow and vice versa. It is also possible to switch between particle receiving (enhanced absorption) and emitting (enhanced scattering) abilities. Changing the polarization geometry of observation it is possible to effectively separate the dipole and the quadrupole plasmon radiation from all the non-plasmonic contributions to the scattered light. Keywords: surface plasmon (SP) resonance, plasmon damping rates, multipolar plasmon
1104.0565v1
2011-11-16
Three-player quantum Kolkata restaurant problem under decoherence
Effect of quantum decoherence in a three-player quantum Kolkata restaurant problem is investigated using tripartite entangled qutrit states. Amplitude damping, depolarizing, phase damping, trit-phase flip and phase flip channels are considered to analyze the behaviour of players payoffs. It is seen that Alice's payoff is heavily influenced by the amplitude damping channel as compared to the depolarizing and flipping channels. However, for higher level of decoherence, Alice's payoff is strongly affected by depolarizing noise. Whereas the behaviour of phase damping channel is symmetrical around 50 % decoherence. It is also seen that for maximum decoherence (p=1), the influence of amplitude damping channel dominates over depolarizing and flipping channels. Whereas, phase damping channel has no effect on the Alice's payoff. Therefore, the problem becomes noiseless one at maximum decoherence in case of phase damping channel. Furthermore, the Nash equilibrium of the problem does not change under decoherence.
1111.3913v2
2012-07-27
The effect of non-uniform damping on flutter in axial flow and energy harvesting strategies
The problem of energy harvesting from flutter instabilities in flexible slender structures in axial flows is considered. In a recent study, we used a reduced order theoretical model of such a system to demonstrate the feasibility for harvesting energy from these structures. Following this preliminary study, we now consider a continuous fluid-structure system. Energy harvesting is modelled as strain-based damping and the slender structure under investigation lies in a moderate fluid loading range, for which {the flexible structure} may be destabilised by damping. The key goal of this work is to {analyse the effect of damping distribution and intensity on the amount of energy harvested by the system}. The numerical results {indeed} suggest that non-uniform damping distributions may significantly improve the power harvesting capacity of the system. For low damping levels, clustered dampers at the position of peak curvature are shown to be optimal. Conversely for higher damping, harvesters distributed over the whole structure are more effective.
1207.6484v1
2012-11-20
Damping rates of surface plasmons for particles of size from nano- to micrometers; reduction of the nonradiative decay
Damping rates of multipolar, localized surface plasmons (SP) of gold and silver nanospheres of radii up to $1000nm$ were found with the tools of classical electrodynamics. The significant increase in damping rates followed by noteworthy decrease for larger particles takes place along with substantial red-shift of plasmon resonance frequencies as a function of particle size. We also introduced interface damping into our modeling, which substantially modifies the plasmon damping rates of smaller particles. We demonstrate unexpected reduction of the multipolar SP damping rates in certain size ranges. This effect can be explained by the suppression of the nonradiative decay channel as a result of the lost competition with the radiative channel. We show that experimental dipole damping rates [H. Baida, et al., Nano Lett. 9(10) (2009) 3463, and C. S\"onnichsen, et al., Phys. Rev. Lett. 88 (2002) 077402], and the resulting resonance quality factors can be described in a consistent and straightforward way within our modeling extended to particle sizes still unavailable experimentally.
1211.4781v1
2013-10-23
Landau damping in a collisionless dipolar Bose gas
We present a theory for the Landau damping of low energy quasi-particles in a collisionless, quasi-2D dipolar Bose gas and produce expressions for the damping rate in uniform and non-uniform systems. Using simple energy-momentum conservation arguments, we show that in the homogeneous system, the nature of the low energy dispersion in a dipolar Bose gas severely inhibits Landau damping of long wave-length excitations. For a gas with contact and dipolar interactions, the damping rate for phonons tends to decrease with increasing dipolar interactions; for strong dipole-dipole interactions, phonons are virtually undamped over a broad range of temperature. The damping rate for maxon-roton excitations is found to be significantly larger than the damping rate for phonons.
1310.6386v1
2014-11-28
Non-equilibrium thermodynamics of damped Timoshenko and damped Bresse systems
In this paper, we cast damped Timoshenko and damped Bresse systems into a general framework for non-equilibrium thermodynamics, namely the GENERIC (General Equation for Non-Equilibrium Reversible-Irreversible Coupling) framework. The main ingredients of GENERIC consist of five building blocks: a state space, a Poisson operator, a dissipative operator, an energy functional, and an entropy functional. The GENERIC formulation of damped Timoshenko and damped Bresse systems brings several benefits. First, it provides alternative ways to derive thermodynamically consistent models of these systems by construct- ing building blocks instead of invoking conservation laws and constitutive relations. Second, it reveals clear physical and geometrical structures of these systems, e.g., the role of the energy and the entropy as the driving forces for the reversible and irreversible dynamics respectively. Third, it allows us to introduce a new GENERIC model for damped Timoshenko systems that is not existing in the literature.
1412.0038v2
2014-12-08
Bi-$\cal{PT}$ symmetry in nonlinearly damped dynamical systems and tailoring $\cal{PT}$ regions with position dependent loss-gain profiles
We investigate the remarkable role of position dependent damping in determining the parametric regions of symmetry breaking in nonlinear $\cal{PT}$-symmetric systems. We illustrate the nature of $\cal{PT}$-symmetry preservation and breaking with reference to a remarkable integrable scalar nonlinear system. In the two dimensional cases of such position dependent damped systems, we unveil the existence of a class of novel bi-$\cal{PT}$-symmetric systems which have two fold $\cal{PT}$ symmetries. We analyze the dynamics of these systems and show how symmetry breaking occurs, that is whether the symmetry breaking of the two $\cal{PT}$ symmetries occurs in pair or occurs one by one. The addition of linear damping in these nonlinearly damped systems induces competition between the two types of damping. This competition results in a $\cal{PT}$ phase transition in which the $\cal{PT}$ symmetry is broken for lower loss/gain strength and is restored by increasing the loss/gain strength. We also show that by properly designing the form of the position dependent damping, we can tailor the $\cal{PT}$-symmetric regions of the system.
1412.2574v3
2015-09-04
Damped transverse oscillations of interacting coronal loops
Damped transverse oscillations of magnetic loops are routinely observed in the solar corona. This phenomenon is interpreted as standing kink magnetohydrodynamic waves, which are damped by resonant absorption owing to plasma inhomogeneity across the magnetic field. The periods and damping times of these oscillations can be used to probe the physical conditions of the coronal medium. Some observations suggest that interaction between neighboring oscillating loops in an active region may be important and can modify the properties of the oscillations compared to those of an isolated loop. Here we theoretically investigate resonantly damped transverse oscillations of interacting non-uniform coronal loops. We provide a semi-analytic method, based on the T-matrix theory of scattering, to compute the frequencies and damping rates of collective oscillations of an arbitrary configuration of parallel cylindrical loops. The effect of resonant damping is included in the T-matrix scheme in the thin boundary approximation. Analytic and numerical results in the specific case of two interacting loops are given as an application.
1509.01487v1
2015-09-14
Beliaev damping in quasi-2D dipolar condensates
We study the effects of quasiparticle interactions in a quasi-two dimensional (quasi-2D), zero-temperature Bose-Einstein condensate of dipolar atoms, which can exhibit a roton-maxon feature in its quasiparticle spectrum. Our focus is the Beliaev damping process, in which a quasiparticle collides with the condensate and resonantly decays into a pair of quasiparticles. Remarkably, the rate for this process exhibits a highly non-trivial dependence on the quasiparticle momentum and the dipolar interaction strength. For weak interactions, the low energy phonons experience no damping, and the higher energy quasiparticles undergo anomalously weak damping. In contrast, the Beliaev damping rates become anomalously large for stronger dipolar interactions, as rotons become energetically accessible as final states. Further, we find a qualitative anisotropy in the damping rates when the dipoles are tilted off the axis of symmetry. Our study reveals the unconventional nature of Beliaev damping in dipolar condensates, and has important implications for ongoing studies of equilibrium and non-equilibrium dynamics in these systems.
1509.04217v1
2015-12-08
Thermal energies of classical and quantum damped oscillators coupled to reservoirs
We consider the global thermal state of classical and quantum harmonic oscillators that interact with a reservoir. Ohmic damping of the oscillator can be exactly treated with a 1D scalar field reservoir, whereas general non-Ohmic damping is conveniently treated with a continuum reservoir of harmonic oscillators. Using the diagonalized Hamiltonian of the total system, we calculate a number of thermodynamic quantities for the damped oscillator: the mean force internal energy, mean force free energy, and another internal energy based on the free-oscillator Hamiltonian. The classical mean force energy is equal to that of a free oscillator, for both Ohmic and non-Ohmic damping and no matter how strong the coupling to the reservoir. In contrast, the quantum mean force energy depends on the details of the damping and diverges for strictly Ohmic damping. These results give additional insight into the steady-state thermodynamics of open systems with arbitrarily strong coupling to a reservoir, complementing results for energies derived within dynamical approaches (e.g. master equations) in the weak-coupling regime.
1512.02551v2
2016-05-17
Simultaneous Identification of Damping Coefficient and Initial Value in PDEs from boundary measurement
In this paper, the simultaneous identification of damping or anti-damping coefficient and initial value for some PDEs is considered. An identification algorithm is proposed based on the fact that the output of system happens to be decomposed into a product of an exponential function and a periodic function. The former contains information of the damping coefficient, while the latter does not. The convergence and error analysis are also developed. Three examples, namely an anti-stable wave equation with boundary anti-damping, the Schr\"odinger equation with internal anti-damping, and two connected strings with middle joint anti-damping, are investigated and demonstrated by numerical simulations to show the effectiveness of the proposed algorithm.
1605.05063v1
2016-08-30
Optimal damping ratios of multi-axial perfectly matched layers for elastic-wave modeling in general anisotropic media
The conventional Perfectly Matched Layer (PML) is unstable for certain kinds of anisotropic media. This instability is intrinsic and independent of PML formulation or implementation. The Multi-axial PML (MPML) removes such instability using a nonzero damping coefficient in the direction parallel with the interface between a PML and the investigated domain. The damping ratio of MPML is the ratio between the damping coefficients along the directions parallel with and perpendicular to the interface between a PML and the investigated domain. No quantitative approach is available for obtaining these damping ratios for general anisotropic media. We develop a quantitative approach to determining optimal damping ratios to not only stabilize PMLs, but also minimize the artificial reflections from MPMLs. Numerical tests based on finite-difference method show that our new method can effectively provide a set of optimal MPML damping ratios for elastic-wave propagation in 2D and 3D general anisotropic media.
1608.08326v3
2016-10-10
A Five-Freedom Active Damping and Alignment Device Used in the Joule Balance
Damping devices are necessary for suppressing the undesired coil motions in the watt/joule balance. In this paper, an active electromagnetic damping device, located outside the main magnet, is introduced in the joule balance project. The presented damping device can be used in both dynamic and static measurement modes. With the feedback from a detection system, five degrees of freedom of the coil, i.e. the horizontal displacement $x$, $y$ and the rotation angles $\theta_x$, $\theta_y$, $\theta_z$, can be controlled by the active damping device. Hence, two functions, i.e. suppressing the undesired coil motions and reducing the misalignment error, can be realized with this active damping device. The principle, construction and performance of the proposed active damping device are presented.
1610.02799v1
2016-10-01
The destabilizing effect of external damping: Singular flutter boundary for the Pfluger column with vanishing external dissipation
Elastic structures loaded by nonconservative positional forces are prone to instabilities induced by dissipation: it is well-known in fact that internal viscous damping destabilizes the marginally stable Ziegler's pendulum and Pfluger column (of which the Beck's column is a special case), two structures loaded by a tangential follower force. The result is the so-called 'destabilization paradox', where the critical force for flutter instability decreases by an order of magnitude when the coefficient of internal damping becomes infinitesimally small. Until now external damping, such as that related to air drag, is believed to provide only a stabilizing effect, as one would intuitively expect. Contrary to this belief, it will be shown that the effect of external damping is qualitatively the same as the effect of internal damping, yielding a pronounced destabilization paradox. Previous results relative to destabilization by external damping of the Ziegler's and Pfluger's elastic structures are corrected in a definitive way leading to a new understanding of the destabilizating role played by viscous terms.
1611.03886v1
2017-10-10
A four-field gyrofluid model with neoclassical effects for the study of the rotation velocity of magnetic islands in tokamaks
A four-field system of equations which includes the neoclassical flow damping effects and the lowest-order finite-Larmor-radius (FLR) corrections is deduced from a system of gyrofluid equations. The FLR corrections to the poloidal flow damping are calculated by solving a simplified version of the gyrokinetic equation. This system of equations is applied to the study of a chain of freely rotating magnetic islands in a tokamak, resulting from the nonlinear evolution of a resistive tearing mode, to determine the islands rotation velocity consistently with the fields radial profiles close to the resonant surface. The island rotation velocity is determined by imposing the torque-balance condition. The equations thus deduced are applied to the study of two different collisional regimes, namely the weak-damping regime and the intermediate damping regime. The equations reduce, in the weak damping regime, to a form already obtained in previous works, while an additional term, containing the lowest order FLR corrections to the poloidal flow damping, appears in the intermediate damping regime. The numerical integration of the final system of equations permits to determine the dependence of the island rotation velocity on the plasma collisionality and the islands width compared to the ion Larmor radius.
1710.03585v1
2017-10-13
Mode-Dependent Damping in Metallic Antiferromagnets Due to Inter-Sublattice Spin Pumping
Damping in magnetization dynamics characterizes the dissipation of magnetic energy and is essential for improving the performance of spintronics-based devices. While the damping of ferromagnets has been well studied and can be artificially controlled in practice, the damping parameters of antiferromagnetic materials are nevertheless little known for their physical mechanisms or numerical values. Here we calculate the damping parameters in antiferromagnetic dynamics using the generalized scattering theory of magnetization dissipation combined with the first-principles transport computation. For the PtMn, IrMn, PdMn and FeMn metallic antiferromagnets, the damping coefficient associated with the motion of magnetization ($\alpha_m$) is one to three orders of magnitude larger than the other damping coefficient associated with the variation of the N\'eel order ($\alpha_n$), in sharp contrast to the assumptions made in the literature.
1710.04766v1
2017-12-04
Resonance oscillation of a damped driven simple pendulum
The resonance characteristics of a driven damped harmonic oscillator are well known. Unlike harmonic oscillators which are guided by parabolic potentials, a simple pendulum oscillates under sinusoidal potentials. The problem of an undamped pendulum has been investigated to a great extent. However, the resonance characteristics of a driven damped pendulum have not been re- ported so far due to the difficulty in solving the problem analytically. In the present work we report the resonance characteristics of a driven damped pendulum calculated numerically. The results are compared with the resonance characteristics of a damped driven harmonic oscillator. The work can be of pedagogic interest too as it reveals the richness of driven damped motion of a simple pendulum in comparison to and how strikingly it differs from the motion of a driven damped harmonic oscillator. We confine our work only to the nonchaotic regime of pendulum motion.
1712.01032v1
2018-01-17
On Global Existence and Blow-up for Damped Stochastic Nonlinear Schrödinger Equation
In this paper, we consider the well-posedness of the weakly damped stochastic nonlinear Schr\"odinger(NLS) equation driven by multiplicative noise. First, we show the global existence of the unique solution for the damped stochastic NLS equation in critical case. Meanwhile, the exponential integrability of the solution is proved, which implies the continuous dependence on the initial data. Then, we analyze the effect of the damped term and noise on the blow-up phenomenon. By modifying the associated energy, momentum and variance identity, we deduce a sharp blow-up condition for damped stochastic NLS equation in supercritical case. Moreover, we show that when the damped effect is large enough, the damped effect can prevent the blow-up of the solution with high probability.
1801.05630v1
2018-05-04
Effective damping enhancement in noncollinear spin structures
Damping mechanisms in magnetic systems determine the lifetime, diffusion and transport properties of magnons, domain walls, magnetic vortices, and skyrmions. Based on the phenomenological Landau-Lifshitz-Gilbert equation, here the effective damping parameter in noncollinear magnetic systems is determined describing the linewidth in resonance experiments or the decay parameter in time-resolved measurements. It is shown how the effective damping can be calculated from the elliptic polarization of magnons, arising due to the noncollinear spin arrangement. It is concluded that the effective damping is larger than the Gilbert damping, and it may significantly differ between excitation modes. Numerical results for the effective damping are presented for the localized magnons in isolated skyrmions, with parameters based on the Pd/Fe/Ir(111) model-type system.
1805.01815v2
2018-05-16
Stabilization rates for the damped wave equation with Hölder-regular damping
We study the decay rate of the energy of solutions to the damped wave equation in a setup where the geometric control condition is violated. We consider damping coefficients which are $0$ on a strip and vanish like polynomials, $x^{\beta}$. We prove that the semigroup cannot be stable at rate faster than $1/t^{(\beta+2)/(\beta+3)}$ by producing quasimodes of the associated stationary damped wave equation. We also prove that the semigroup is stable at rate at least as fast as $1/t^{(\beta+2)/(\beta+4)}$. These two results establish an explicit relation between the rate of vanishing of the damping and rate of decay of solutions. Our result partially generalizes a decay result of Nonnemacher in which the damping is an indicator function on a strip.
1805.06535v3
2018-08-20
Gilbert damping of [Co/Pd]n/Py multilayer thin films
Understanding the Gilbert damping in exchange-coupled multilayer materials is particularly important to develop future fast switching spintronics devices. Here, we report an experimental investigation of temperature-dependent Gilbert damping in [Co/Pd]n/Py multilayer films of varying the number of Co/Pd repetitions by ferromagnetic resonance. The results demonstrate that three independent contributions to the Gilbert damping are identified, namely the intrinsic Gilbert damping, the inhomogeneous linewidth broadening and the two-magnon scattering contribution. Of particular interest, the two-magnon scattering intensity increases as the enlargement of number repetitions of Co/Pd due to the larger pinning effect at the interface between Py and the Co/Pd layers. The Gilbert damping increases monotonically as the temperature decreases from 300K to 50K. Our findings open the door to comprehend the physical origin of the Gilbert damping in ultrathin exchange-coupled multilayer films.
1808.06515v2
2019-03-01
Comprehensive Study of Neutrino-Dark Matter Mixed Damping
Mixed damping is a physical effect that occurs when a heavy species is coupled to a relativistic fluid which is itself free streaming. As a cross-case between collisional damping and free-streaming, it is crucial in the context of neutrino-dark matter interactions. In this work, we establish the parameter space relevant for mixed damping, and we derive an analytical approximation for the evolution of dark matter perturbations in the mixed damping regime to illustrate the physical processes responsible for the suppression of cosmological perturbations. Although extended Boltzmann codes implementing neutrino-dark matter scattering terms automatically include mixed damping, this effect has not been systematically studied. In order to obtain reliable numerical results, it is mandatory to reconsider several aspects of neutrino-dark matter interactions, such as the initial conditions, the ultra-relativistic fluid approximation and high order multiple moments in the neutrino distribution. Such a precise treatment ensures the correct assessment of the relevance of mixed damping in neutrino-dark matter interactions.
1903.00540v2
2019-08-04
Efficient spin excitation via ultrafast damping-like torques in antiferromagnets
Damping effects form the core of many emerging concepts for high-speed spintronic applications. Important characteristics such as device switching times and magnetic domain-wall velocities depend critically on the damping rate. While the implications of spin damping for relaxation processes are intensively studied, damping effects during impulsive spin excitations are assumed to be negligible because of the shortness of the excitation process. Herein, we show that, unlike in ferromagnets, ultrafast damping plays a crucial role in antiferromagnets because of their strongly elliptical spin precession. In time-resolved measurements, we find that ultrafast damping results in an immediate spin canting along the short precession axis. The interplay between antiferromagnetic exchange and magnetic anisotropy amplifies this canting by several orders of magnitude towards large-amplitude modulations of the antiferromagnetic order parameter. This leverage effect discloses a highly efficient route towards the ultrafast manipulation of magnetism in antiferromagnetic spintronics.
1908.01359v3
2019-10-31
Gyrokinetic investigation of the damping channels of Alfvén modes in ASDEX Upgrade
The linear destabilization and nonlinear saturation of energetic-particle driven Alfv\'enic instabilities in tokamaks strongly depend on the damping channels. In this work, the collisionless damping mechanisms of Alfv\'enic modes are investigated within a gyrokinetic framework, by means of global simulations with the particle-in-cell code ORB5, and compared with the eigenvalue code LIGKA and reduced models. In particular, the continuum damping and the Landau damping (of ions and electrons) are considered. The electron Landau damping is found to be dominant on the ion Landau damping for experimentally relevant cases. As an application, the linear and nonlinear dynamics of toroidicity induced Alfv\'en eigenmodes and energetic-particle driven modes in ASDEX Upgrade is investigated theoretically and compared with experimental measurements.
1910.14489v1
2020-03-13
Anharmonic phonon damping enhances the $T_c$ of BCS-type superconductors
A theory of superconductivity is presented where the effect of anharmonicity, as entailed in the acoustic, or optical, phonon damping, is explicitly considered in the pairing mechanism. The gap equation is solved including diffusive Akhiezer damping for longitudinal acoustic phonons or Klemens damping for optical phonons, with a damping coefficient which, in either case, can be directly related to the Gruneisen parameter and hence to the anharmonic coefficients in the interatomic potential. The results show that the increase of anharmonicity has a strikingly non-monotonic effect on the critical temperature $T_{c}$. The optimal damping coefficient yielding maximum $T_c$ is set by the velocity of the bosonic mediator. This theory may open up unprecedented opportunities for material design where $T_{c}$ may be tuned via the anharmonicity of the interatomic potential, and presents implications for the superconductivity in the recently discovered hydrides, where anharmonicity is very strong and for which the anharmonic damping is especially relevant.
2003.06220v2
2020-03-29
Stability results for an elastic-viscoelastic waves interaction systems with localized Kelvin-Voigt damping and with an internal or boundary time delay
We investigate the stability of a one-dimensional wave equation with non smooth localized internal viscoelastic damping of Kelvin-Voigt type and with boundary or localized internal delay feedback. The main novelty in this paper is that the Kelvin-Voigt and the delay damping are both localized via non smooth coefficients. In the case that the Kelvin-Voigt damping is localized faraway from the tip and the wave is subjected to a locally distributed internal or boundary delay feedback, we prove that the energy of the system decays polynomially of type t^{-4}. However, an exponential decay of the energy of the system is established provided that the Kelvin-Voigt damping is localized near a part of the boundary and a time delay damping acts on the second boundary. While, when the Kelvin-Voigt and the internal delay damping are both localized via non smooth coefficients near the tip, the energy of the system decays polynomially of type t^{-4}. Frequency domain arguments combined with piecewise multiplier techniques are employed.
2003.12967v1
2020-09-16
Fast convex optimization via inertial dynamics combining viscous and Hessian-driven damping with time rescaling
In a Hilbert setting, we develop fast methods for convex unconstrained optimization. We rely on the asymptotic behavior of an inertial system combining geometric damping with temporal scaling. The convex function to minimize enters the dynamic via its gradient. The dynamic includes three coefficients varying with time, one is a viscous damping coefficient, the second is attached to the Hessian-driven damping, the third is a time scaling coefficient. We study the convergence rate of the values under general conditions involving the damping and the time scale coefficients. The obtained results are based on a new Lyapunov analysis and they encompass known results on the subject. We pay particular attention to the case of an asymptotically vanishing viscous damping, which is directly related to the accelerated gradient method of Nesterov. The Hessian-driven damping significantly reduces the oscillatory aspects. As a main result, we obtain an exponential rate of convergence of values without assuming the strong convexity of the objective function. The temporal discretization of these dynamics opens the gate to a large class of inertial optimization algorithms.
2009.07620v1
2020-12-27
Quantum speed limit time in relativistic frame
We investigate the roles of the relativistic effect on the speed of evolution of a quantum system coupled with amplitude damping channels. We find that the relativistic effect speed-up the quantum evolution to a uniform evolution speed of open quantum systems for the damping parameter $p_{\tau}\lesssim p_{\tau_{c0}}.$ Moreover, we point out a non-monotonic behavior of the quantum speed limit time (QSLT) with acceleration in the damping limit $p_{\tau_{c0}}\lesssim p_{\tau}\lesssim p_{\tau_{c1}},$ where the relativistic effect first speed-up and then slow down the quantum evolution process of the damped system. For the damping strength $p_{\tau_{c1}}\lesssim p_{\tau}$, we observe a monotonic increasing behavior of QSLT, leads to slow down the quantum evolution of the damped system. In addition, we examine the roles of the relativistic effect on the speed limit time for a system coupled with the phase damping channels.
2012.13859v2
2021-01-07
Mechanisms behind large Gilbert damping anisotropies
A method with which to calculate the Gilbert damping parameter from a real-space electronic structure method is reported here. The anisotropy of the Gilbert damping with respect to the magnetic moment direction and local chemical environment is calculated for bulk and surfaces of Fe$_{50}$Co$_{50}$ alloys from first principles electronic structure in a real space formulation. The size of the damping anisotropy for Fe$_{50}$Co$_{50}$ alloys is demonstrated to be significant. Depending on details of the simulations, it reaches a maximum-minimum damping ratio as high as 200%. Several microscopic origins of the strongly enhanced Gilbert damping anisotropy have been examined, where in particular interface/surface effects stand out, as do local distortions of the crystal structure. Although theory does not reproduce the experimentally reported high ratio of 400% [Phys. Rev. Lett. 122, 117203 (2019)], it nevertheless identifies microscopic mechanisms that can lead to huge damping anisotropies.
2101.02794v2
2021-06-23
Regularization of central forces with damping in two and three-dimensions
Regularization of damped motion under central forces in two and three-dimensions are investigated and equivalent, undamped systems are obtained. The dynamics of a particle moving in $\frac{1}{r}$ potential and subjected to a damping force is shown to be regularized a la Levi-Civita. We then generalize this regularization mapping to the case of damped motion in the potential $r^{-\frac{2N}{N+1}}$. Further equation of motion of a damped Kepler motion in 3-dimensions is mapped to an oscillator with inverted sextic potential and couplings, in 4-dimensions using Kustaanheimo-Stiefel regularization method. It is shown that the strength of the sextic potential is given by the damping co-efficient of the Kepler motion. Using homogeneous Hamiltonian formalism, we establish the mapping between the Hamiltonian of these two models. Both in 2 and 3-dimensions, we show that the regularized equation is non-linear, in contrast to undamped cases. Mapping of a particle moving in a harmonic potential subjected to damping to an undamped system with shifted frequency is then derived using Bohlin-Sudman transformation.
2106.12134v1
2021-07-06
Theory of vibrators with variable-order fractional forces
In this paper, we present a theory of six classes of vibrators with variable-order fractional forces of inertia, damping, and restoration. The novelty and contributions of the present theory are reflected in six aspects. 1) Equivalent motion equations of those variable-order fractional vibrators are proposed. 2) The analytical expressions of the effective mass, damping, and stiffness of those variable-order fractional vibrators are presented. 3) The asymptotic properties of the effective mass, damping, and stiffness of a class of variable-order fractional vibrators are given. 4) The restricted effective parameters (damping ratio, damping free natural frequency, damped natural frequency, frequency ratio) of the variable-order fractional vibrators are put forward. 5) We bring forward the analytical representations of the free responses, the impulse responses, and the frequency transfer functions of those variable-order fractional vibrators. 6) We propose a solution to an open problem of how to mathematically explain the Rayleigh damping assumption based on the present theory of variable-order fractional vibrations.
2107.02340v2
2021-08-15
Exponential stability of a damped beam-string-beam transmission problem
We consider a beam-string-beam transmission problem, where two structurally damped or undamped beams are coupled with a frictionally damped string by transmission conditions. We show that for this type of structure, the dissipation produced by the frictional part is strong enough to produce exponential decay of the solution no matter how small is its size: for the exponential stability in the damped-damped-damped situation we use energy method and in the undamped-damped-undamped situation we use a frequency domain method from the semigroups theory, which combines a contradiction argument with the multiplier technique to carry out a special analysis for the resolvent. Additionally, we show that the solution first defined by the weak formulation, in fact, has higher Sobolev space regularity.
2108.06749v1
2021-09-10
Fourth-order dynamics of the damped harmonic oscillator
It is shown that the classical damped harmonic oscillator belongs to the family of fourth-order Pais-Uhlenbeck oscillators. It follows that the solutions to the damped harmonic oscillator equation make the Pais-Uhlenbeck action stationary. Two systematic approaches are given for deriving the Pais-Uhlenbeck action from the damped harmonic oscillator equation, and it may be possible to use these methods to identify stationary action principles for other dissipative systems which do not conform to Hamilton's principle. It is also shown that for every damped harmonic oscillator $x$, there exists a two-parameter family of dual oscillators $y$ satisfying the Pais-Uhlenbeck equation. The damped harmonic oscillator and any of its duals can be interpreted as a system of two coupled oscillators with atypical spring stiffnesses (not necessarily positive and real-valued). For overdamped systems, the resulting coupled oscillators should be physically achievable and may have engineering applications. Finally, a new physical interpretation is given for the optimal damping ratio $\zeta=1/\sqrt{2}$ in control theory.
2109.06034v1
2022-01-13
Damping of Alfvén waves in MHD turbulence and implications for cosmic ray streaming instability and galactic winds
Alfv\'{e}nic component of MHD turbulence damps Alfv\'{e}nic waves. The consequences of this effect are important for many processes, from cosmic ray (CR) propagation to launching outflows and winds in galaxies and other magnetized systems. We discuss the differences in the damping of the streaming instability by turbulence and the damping of a plane parallel wave. The former takes place in the system of reference aligned with the local direction of magnetic field along which CRs stream. The latter is in the reference frame of the mean magnetic field and traditionally considered in plasma studies. We also compare the turbulent damping of streaming instability with ion-neutral collisional damping, which becomes the dominant damping effect at a sufficiently low ionization fraction. Numerical testing and astrophysical implications are also discussed.
2201.05168v1
2022-03-14
Investigation of nonlinear squeeze-film damping involving rarefied gas effect in micro-electro-mechanical-systems
In this paper, the nonlinear squeeze-film damping (SFD) involving rarefied gas effect in the micro-electro-mechanical-systems (MEMS) is investigated. Considering the motion of structures (beam, cantilever, and membrane) in MEMS, the dynamic response of structure will be influenced largely by the squeeze-film damping. In the traditional model, a viscous damping assumption that damping force is linear with moving velocity is used. As the nonlinear damping phenomenon is observed for a micro-structure oscillating with a high-velocity, this assumption is invalid and will generates error result for predicting the response of micro-structure. In addition, due to the small size of device and the low pressure of encapsulation, the gas in MEMS usually is rarefied gas. Therefore, to correctly predict the damping force, the rarefied gas effect must be considered. To study the nonlinear SFD phenomenon involving the rarefied gas effect, a kinetic method, namely discrete unified gas kinetic scheme (DUGKS), is introduced. And based on DUGKS, two solving methods, a traditional decoupled method (Eulerian scheme) and a coupled framework (arbitrary Lagrangian-Eulerian scheme), are adopted. With these two methods, two basic motion forms, linear (perpendicular) and tilting motions of a rigid micro-beam, are studied with forced and free oscillations.
2203.06902v1
2022-05-21
Noether symmetries and first integrals of damped harmonic oscillator
Noether theorem establishes an interesting connection between symmetries of the action integral and conservation laws of a dynamical system. The aim of the present work is to classify the damped harmonic oscillator problem with respect to Noether symmetries and to construct corresponding conservation laws for all over-damped, under damped and critical damped cases. For each case we obtain maximum five linearly independent group generators which provide related five conserved quantities. Remarkably, after obtaining complete set of invariant quantities we obtain analytical solutions for each case. In the current work, we also introduce a new Lagrangian for the damped harmonic oscillator. Though the form of this new Lagrangian and presented by Bateman are completely different, yet it generates same set of Noether symmetries and conserved quantities. So, this new form of Lagrangian we are presenting here may be seriously interesting for the physicists. Moreover, we also find the Lie algebras of Noether symmetries and point out some interesting aspects of results related to Noether symmetries and first integrals of damped harmonic oscillator which perhaps not reported in the earlier studies.
2205.10525v1
2023-01-31
The emergence of soft-glassy mechanics in simulated foams
Several seemingly different soft materials, including foams, cells, and many complex fluids, exhibit remarkably similar rheological properties and microscopic dynamics, termed soft glassy mechanics. Here, we show that such behavior emerges from a simple model of a damped ripening foam, for sufficiently weak damping. In particular, we observe intermittent avalanchey dynamics, bubble super-diffusion, and power-law rheology that vary as the damping factor is changed. In the limit of weak damping, the dynamics are determined by the tortuous low-lying portions of the energy landscape, as described in a recent study. For strong damping the viscous stresses cause the system configuration to evolve along higher energy paths, washing out small-scale tortuosity and producing motion with an increasingly ballistic character. Using a microrheological approach, the linear viscoelastic response of the model can be efficiently calculated. This resembles the power-law rheology expected for soft glassy mechanics, but unexpectedly, is only weakly sensitive to the damping parameter. Lastly, we study the reported memory effect in foams after large perturbations and find that the timescale of the memory goes to zero as the damping parameter vanishes, suggesting that the effect is due to viscous stress relaxation rather than slow structural changes stabilized by the energy landscape.
2301.13400v1
2023-02-13
Thickness and temperature dependent damping in La$_{0.67}$Sr$_{0.33}$MnO$_{3}$ epitaxial films
The damping of La0.67Sr0.33MnO3 (LSMO) epitaxial films as a function of thickness at different temperatures was studied. The competition between two scattering types (\r{ho}-like and {\sigma}-like) with entirely distinct thickness and temperature dependencies resulted in complicated damping behavior. The behavior of {\sigma}-like damping in LSMO films is consistent with the behavior in magnetic metal films. However, because \r{ho}-like damping is sensitive to the fine electron structure near the Fermi surface, the distortion of the oxygen octahedra controlled by the film thickness is an important factor in controlling the damping. Our study demonstrates that the complexity of damping in LSMO epitaxial films is a consequence of strong-correlation effects, which are characteristic of complex transition-metal oxides.
2302.06099v3
2023-09-15
On the formation of singularities for the slightly supercritical NLS equation with nonlinear damping
We consider the focusing, mass-supercritical NLS equation augmented with a nonlinear damping term. We provide sufficient conditions on the nonlinearity exponents and damping coefficients for finite-time blow-up. In particular, singularities are formed for focusing and dissipative nonlinearities of the same power, provided that the damping coefficient is sufficiently small. Our result thus rigorously proves the non-regularizing effect of nonlinear damping in the mass-supercritical case, which was suggested by previous numerical and formal results. We show that, under our assumption, the damping term may be controlled in such a way that the self-similar blow-up structure for the focusing NLS is approximately retained even within the dissipative evolution. The nonlinear damping contributes as a forcing term in the equation for the perturbation around the self-similar profile, that may produce a growth over finite time intervals. We estimate the error terms through a modulation analysis and a careful control of the time evolution of total momentum and energy functionals.
2309.08281v1
1998-05-07
Discovery of z=0.0912 and z=0.2212 Damped Lyman-alpha Absorption Line Systems Toward the Quasar OI 363: Limits on the Nature of Damped Lyman-alpha Galaxies
The discovery of a z_abs = 0.0912 damped Lyman-alpha absorption-line system in the HST-FOS ultraviolet spectrum of the quasar OI 363 (0738+313) is reported. This is the lowest redshift quasar damped Lyman-alpha system known. Its neutral hydrogen column density is N(HI) = 1.5(+/- 0.2) E21 atoms/cm^2, which easily exceeds the classical criterion for damped Lyman-alpha of N(HI) greater than or equal to 2E20 atoms/cm^2. Remarkably, a z_abs = 0.2212 damped system with N(HI) = 7.9(+/- 1.4) E20 atoms/cm^2 has also been discovered in the same spectrum. In the past, the standard paradigm for damped Lyman-alpha systems has been that they arise in galactic or protogalactic HI disks with low impact parameters in luminous galaxies. However, WIYN imaging of the OI 363 field shows that none of the galaxies visible in the vicinity of the quasar is a luminous gas-rich spiral with low impact parameter, either at z = 0.0912 or z = 0.2212. Thus, these damped systems are among the clearest examples yet of cases that are inconsistent with the standard damped Lyman-alpha - HI-disk paradigm.
9805093v1
2008-01-24
Attenuation of small-amplitude oscillations in a prominence-corona model with a transverse magnetic field
Small-amplitude prominence oscillations are usually damped after a few periods. We study the attenuation of non-adiabatic magnetoacoustic waves in a slab prominence embedded in the coronal medium. We assume an equilibrium configuration with a transverse magnetic field to the slab axis and investigate wave damping by thermal conduction and radiative losses. The differential MHD equations that govern linear slow and fast modes are numerically solved to obtain the complex oscillatory frequency and the corresponding eigenfunctions. We find that coronal thermal conduction and radiative losses from the prominence plasma reveal as the most relevant damping mechanisms. Both mechanisms govern together the attenuation of hybrid modes, whereas prominence radiation is responsible for the damping of internal modes and coronal conduction essentially dominates the attenuation of external modes. In addition, the energy transfer between the prominence and the corona caused by thermal conduction has a noticeable effect on the wave stability, radiative losses from the prominence plasma being of paramount importance for the thermal stability of fast modes. We conclude that slow modes are efficiently damped, with damping times compatible with observations. On the contrary, fast modes are less attenuated by non-adiabatic effects and their damping times are several orders of magnitude larger than those observed. The presence of the corona causes a decrease of the damping times with respect to those of an isolated prominence slab, but its effect is still insufficient to obtain damping times of the order of the period in the case of fast modes.
0801.3744v2
2010-04-26
Selective spatial damping of propagating kink waves due to resonant absorption
There is observational evidence of propagating kink waves driven by photospheric motions. These disturbances, interpreted as kink magnetohydrodynamic (MHD) waves are attenuated as they propagate upwards in the solar corona. In this paper we show that resonant absorption provides a simple explanation to the spatial damping of these waves. Kink MHD waves are studied using a cylindrical model of solar magnetic flux tubes which includes a non-uniform layer at the tube boundary. Assuming that the frequency is real and the longitudinal wavenumber complex, the damping length and damping per wavelength produced by resonant absorption are analytically calculated. The damping length of propagating kink waves due resonant absorption is a monotonically decreasing function of frequency. For kink waves with low frequencies the damping length is exactly inversely proportional to frequency and we denote this as the TGV relation. When moving to high frequencies the TGV relation continues to be an exceptionally good approximation of the actual dependency of the damping length on frequency. This dependency means that resonant absorption is selective as it favours low frequency waves and can efficiently remove high frequency waves from a broad band spectrum of kink waves. It is selective as the damping length is inversely proportional to frequency so that the damping becomes more severe with increasing frequency. This means that radial inhomogeneity can cause solar waveguides to be a natural low-pass filter for broadband disturbances. Hence kink wave trains travelling along, e.g., coronal loops, will have a greater proportion of the high frequency components dissipated lower down in the atmosphere. This could have important consequences with respect to the spatial distribution of wave heating in the solar atmosphere.
1004.4468v1
2011-04-10
Spatial Damping of Propagating Kink Waves Due to Resonant Absorption: Effect of Background Flow
Observations show the ubiquitous presence of propagating magnetohydrodynamic (MHD) kink waves in the solar atmosphere. Waves and flows are often observed simultaneously. Due to plasma inhomogeneity in the perpendicular direction to the magnetic field, kink waves are spatially damped by resonant absorption. The presence of flow may affect the wave spatial damping. Here, we investigate the effect of longitudinal background flow on the propagation and spatial damping of resonant kink waves in transversely nonuniform magnetic flux tubes. We combine approximate analytical theory with numerical investigation. The analytical theory uses the thin tube (TT) and thin boundary (TB) approximations to obtain expressions for the wavelength and the damping length. Numerically, we verify the previously obtained analytical expressions by means of the full solution of the resistive MHD eigenvalue problem beyond the TT and TB approximations. We find that the backward and forward propagating waves have different wavelengths and are damped on length scales that are inversely proportional to the frequency as in the static case. However, the factor of proportionality depends on the characteristics of the flow, so that the damping length differs from its static analogue. For slow, sub-Alfvenic flows the backward propagating wave gets damped on a shorter length scale than in the absence of flow, while for the forward propagating wave the damping length is longer. The different properties of the waves depending on their direction of propagation with respect to the background flow may be detected by the observations and may be relevant for seismological applications.
1104.1791v1
2013-02-08
On the Damping-Induced Self-Recovery Phenomenon in Mechanical Systems with Several Unactuated Cyclic Variables
The damping-induced self-recovery phenomenon refers to the fundamental property of underactuated mechanical systems: if an unactuated cyclic variable is under a viscous damping-like force and the system starts from rest, then the cyclic variable will always move back to its initial condition as the actuated variables come to stop. The regular momentum conservation phenomenon can be viewed as the limit of the damping-induced self-recovery phenomenon in the sense that the self-recovery phenomenon disappears as the damping goes to zero. This paper generalizes the past result on damping-induced self-recovery for the case of a single unactuated cyclic variable to the case of multiple unactuated cyclic variables. We characterize a class of external forces that induce new conserved quantities, which we call the damping-induced momenta. The damping-induced momenta yield first-order asymptotically stable dynamics for the unactuated cyclic variables under some conditions, thereby inducing the self-recovery phenomenon. It is also shown that the viscous damping-like forces impose bounds on the range of trajectories of the unactuated cyclic variables. Two examples are presented to demonstrate the analytical discoveries: the planar pendulum with gimbal actuators and the three-link planar manipulator on a horizontal plane.
1302.2109v1
2016-07-06
Damping of Alfven waves by Turbulence and its Consequences: from Cosmic-Rays Streaming to Launching Winds
This paper considers turbulent damping of Alfven waves in magnetized plasmas. We identify two cases of damping, one related to damping of cosmic rays streaming instability, the other related to damping of Alfven waves emitted by a macroscopic wave source, e.g. stellar atmosphere. The physical difference between the two cases is that in the former case the generated waves are emitted in respect to the local direction of magnetic field, in the latter in respect to the mean field. The scaling of damping is different in the two cases. We the regimes of turbulence ranging from subAlfvenic to superAlfvenic we obtain analytical expressions for the damping rates and define the ranges of applicability of these expressions. Describing the damping of the streaming instability, we find that for subAlfvenic turbulence the range of cosmic ray energies influenced by weak turbulence is unproportionally large compared to the range of scales that the weak turbulence is present. On the contrary, the range of cosmic ray energies affected by strong Alfvenic turbulence is rather limited. A number of astrophysical applications of the process ranging from launching of stellar and galactic winds to propagation of cosmic rays in galaxies and clusters of galaxies is considered. In particular, we discuss how to reconcile the process of turbulent damping with the observed isotropy of the Milky Way cosmic rays.
1607.02042v1
2018-01-18
Quantum Landau damping in dipolar Bose-Einstein condensates
We consider Landau damping of elementary excitations in Bose-Einstein condensates (BECs) with dipolar interactions. We discuss quantum and quasi-classical regimes of Landau damping. We use a generalized wave-kinetic description of BECs which, apart from the long range dipolar interactions, also takes into account the quantum fluctuations and the finite energy corrections to short-range interactions. Such a description is therefore more general than the usual mean field approximation. The present wave-kinetic approach is well suited for the study of kinetic effects in BECs, such as those associated with Landau damping, atom trapping and turbulent diffusion. The inclusion of quantum fluctuations and energy corrections change the dispersion relation and the damping rates, leading to possible experimental signatures of these effects. Quantum Landau damping is described with generality, and particular examples of dipole condensates in two and three dimensions are studied. The occurrence of roton-maxon configurations, and their relevance to Landau damping is also considered in detail, as well as the changes introduced by the three different processes, associated with dipolar interactions, quantum fluctuations and finite energy range collisions. The present approach is mainly based on a linear perturbative procedure, but the nonlinear regime of Landau damping, which includes atom trapping and atom diffusion, is also briefly discussed.
1801.06256v1
2019-02-26
Enhanced Gilbert Damping in Re doped FeCo Films: A Combined Experimental and Theoretical Study
The effects of rhenium doping in the range 0 to 10 atomic percent on the static and dynamic magnetic properties of Fe65Co35 thin films have been studied experimentally as well as with first principles electronic structure calculations focusing on the change of the saturation magnetization and the Gilbert damping parameter. Both experimental and theoretical results show that the saturation magnetization decreases with increasing Re doping level, while at the same time Gilbert damping parameter increases. The experimental low temperature saturation magnetic induction exhibits a 29 percent decrease, from 2.31 T to 1.64 T, in the investigated doping concentration range, which is more than predicted by the theoretical calculations. The room temperature value of the damping parameter obtained from ferromagnetic resonance measurements, correcting for extrinsic contributions to the damping, is for the undoped sample 0.0027, which is close to the theoretically calculated Gilbert damping parameter. With 10 atomic percent Re doping, the damping parameter increases to 0.0090, which is in good agreement with the theoretical value of 0.0073. The increase in damping parameter with Re doping is explained by the increase in density of states at Fermi level, mostly contributed by the spin-up channel of Re. Moreover, both experimental and theoretical values for the damping parameter are observed to be weakly decreasing with decreasing temperature.
1902.09896v1
2020-05-31
Optimal decay rates of the compressible Euler equations with time-dependent damping in $\mathbb R^n$: (I) under-damping case
This paper is concerned with the multi-dimensional compressible Euler equations with time-dependent damping of the form $-\frac{\mu}{(1+t)^\lambda}\rho\boldsymbol u$ in $\mathbb R^n$, where $n\ge2$, $\mu>0$, and $\lambda\in[0,1)$. When $\lambda>0$ is bigger, the damping effect time-asymptotically gets weaker, which is called under-damping. We show the optimal decay estimates of the solutions such that $\|\partial_x^\alpha (\rho-1)\|_{L^2(\mathbb R^n)}\approx (1+t)^{-\frac{1+\lambda}{2}(\frac{n}{2}+|\alpha|)}$, and $\|\partial_x^\alpha \boldsymbol u\|_{L^2(\mathbb R^n)}\approx (1+t)^{-\frac{1+\lambda}{2}(\frac{n}{2}+|\alpha|)-\frac{1-\lambda}{2}}$, and see how the under-damping effect influences the structure of the Euler system. Different from the traditional view that the stronger damping usually makes the solutions decaying faster, here surprisingly we recognize that the weaker damping with $0\le\lambda<1$ enhances the faster decay for the solutions. The adopted approach is the technical Fourier analysis and the Green function method. The main difficulties caused by the time-dependent damping lie in twofold: non-commutativity of the Fourier transform of the linearized operator precludes explicit expression of the fundamental solution; time-dependent evolution implies that the Green matrix $G(t,s)$ is not translation invariant, i.e., $G(t,s)\ne G(t-s,0)$. We formulate the exact decay behavior of the Green matrices $G(t,s)$ with respect to $t$ and $s$ for both linear wave equations and linear hyperbolic system, and finally derive the optimal decay rates for the nonlinear Euler system.
2006.00401v1
2022-08-17
Anti-parity-time symmetry hidden in a damping linear resonator
Phase transition from the over-damping to under-damping states is a ubiquitous phenomenon in physical systems. However, what kind of symmetry is broken associated with this phase transition remains unclear. Here, we discover that this phase transition is determined by an anti-parity-time (anti-$\mathcal{PT}$) symmetry hidden in a single damping linear resonator, which is significantly different from the conventional anti-$\mathcal{PT}$-symmetric systems with two or more modes. We show that the breaking of the anti-$\mathcal{PT}$ symmetry yields the phase transition from the over-damping to under-damping states, with an exceptional point (EP) corresponding to the critical-damping state. Moreover, we propose an optomechanical scheme to show this anti-$\mathcal{PT}$ symmetry breaking by using the optical spring effect in a quadratic optomechanical system. We also suggest an optomechanical sensor with the sensitivity enhanced significantly around the EPs for the anti-$\mathcal{PT}$ symmetry breaking. Our work unveils the anti-$\mathcal{PT}$ symmetry hidden in damping oscillations and hence opens up new possibilities for exploiting wide anti-$\mathcal{PT}$ symmetry applications in single damping linear resonators.
2208.08187v2
1996-12-10
Collisional matter-phase damping in Bose-condensed gas
Collisional damping of the excitations in a Bose-condensed gas is investigated over the wide range of energies and temperatures. Numerical results for the damping rate are presented and a number of asymptotic and interpolating expressions for it are derived.
9612086v1
2001-11-29
Tensor form of magnetization damping
A tensor form of phenomenological damping is derived for small magnetization motions. This form reflects basic physical relaxation processes for a general uniformly magnetized particle or film. Scalar Landau-Lifshitz damping is found to occur only for two special cases of system symmetry.
0111566v1
1999-07-28
An effective relaxation-time approach to collisionless quark-gluon plasma
We present an effective relaxation-time theory to study the collisionless quark-gluon plasma. Applying this method we calculate the damping rate to be of order $g^2T$ and find plasmon scattering is the damping mechanism. The damping for the transverse mode is stronger than the longitudinal one.
9907526v1
1999-11-16
Dynamical resummation and damping in the O(N) model
A general real-time formalism is developed to resum the self-energy operator of broken symmetry scalar field theories in form of self-consistent gap equations for the spectral function. The solution of the equations is approximated with finite lifetime quasi-particles. In the Landau damping rates viscosity terms, analogous to gauge theories, appear, what leads to a finite damping rate for the long wavelength Goldstone modes.
9911374v1
1993-03-24
On the Quantizations of the Damped Systems
Based on a simple observation that a classical second order differential equation may be decomposed into a set of two first order equations, we introduce a Hamiltonian framework to quantize the damped systems. In particular, we analyze the system of a linear damped harmonic oscillator and demonstrate that the time evolution of the Schr\"odinger equation is unambiguously determined.
9303137v1
2006-01-09
Energy decay for damped wave equations on partially rectangular domains
We consider the wave equation with a damping term on a partially rectangular planar domain, assuming that the damping is concentrated close to the non-rectangular part of the domain. Polynomial decay estimates for the energy of the solution are established.
0601195v1
2002-06-07
Resonant states and classical damping
Using Koopman's approach to classical dynamical systems we show that the classical damping may be interpreted as appearance of resonant states of the corresponding Koopman's operator. It turns out that simple classical damped systems give rise to discrete complex spectra. Therefore, the corresponding generalized eigenvectors may be interpreted as classical resonant states.
0206009v1
2004-03-12
Factorization of damped wave equations with cubic nonlinearities
The recent factorization scheme that we introduced for nonlinear polynomial ODEs in math-ph/0401040 is applied to the interesting case of damped wave equations with cubic nonlinearities. Traveling kink solutions are possible in the plane defined by the kink velocity versus the damping coefficient only along hyperbolas that are plotted herein
0403022v1
2002-08-07
Toward a Universal Model of Damping--Modified Coulomb Friction
A modification of Coulomb's law of friction uses a variable coefficient of friction that depends on a power law in the energy of mechanical oscillation. Through the use of three different exponents: 0, 1/2 and 1; all commonly encountered non-viscous forms of damping are accommodated. The nonlinear model appears to yield good agreement with experiment in cases of surface, internal, and amplitude dependent damping.
0208025v1
2002-12-19
Trapped particle bounds on stimulated scatter in the large k/kD regime
In the strongly damped regime, the convective gain rate for stimulated scatter varies inversely with the plasma wave damping rate. Electron trapping effects reduce the damping but also lead to loss of resonance for large enough amplitude waves. This leads to a gain rate bound and corresponding optimum scattered light frequency and plasma wave amplitude.
0212071v1
2003-02-03
Oscillator damping with more than one mechanism of internal friction dissipation
The author's modified Coulomb damping model has been generalized to accommodate internal friction that derives from several dissipation mechanisms acting simultaneously. Because of its fundamental nonlinear nature, internal friction damping causes the quality factor Q of an oscillator in free-decay to change in time. Examples are given which demonstrate reasonable agreement between theory and experiment.
0302003v1
2003-02-15
Anisotropic Internal Friction Damping
The mechanical damping properties of sheet polaroid material have been studied with a physical pendulum. The polaroid samples were placed under the knife-edges of the pendulum, which was operated in free-decay at a period in the vicinity of 10 s. With the edges oriented parallel to the direction of the long molecular chains in the polaroid, it was found that the damping was more than 10% smaller than when oriented perpendicular to the chains.
0302055v1
2006-08-07
Study of the Damped Pendulum
Experiments on the oscillatory motion of a suspended bar magnet throws light on the damping effects acting on the pendulum. The viscous drag offered by air was found the be the main contributor for slowing the pendulum down. The nature and magnitude of the damping effects were shown to be strongly dependent on the amplitude.
0608071v1
1995-02-27
Quantum Oscillator with Kronig-Penney Excitation in Different Regimes of Damping
There are discussed the exact solution of the time--dependent Schr\"{o}dinger equation for a damped quantum oscillator subject to a periodical frequency delta--kicks describing squeezed states which are expressed in terms of Chebyshev polynomials. The cases of strong and weak damping are investigated in the frame of Caldirola--Kanai model.
9502023v1
2008-11-07
Asymptotic stability of the wave equation on compact surfaces and locally distributed damping - A sharp result
This paper is concerned with the study of the wave equation on compact surfaces and locally distributed damping. We study the case where the damping is effective in a well-chosen subset of arbitrarily small measure.
0811.1190v1
2008-11-07
Uniform Stabilization of the wave equation on compact surfaces and locally distributed damping
This paper is concerned with the study of the wave equation on compact surfaces and locally distributed damping. We study the case where the damping is effective on the complement of visible umbilical sets.
0811.1204v1
2010-11-20
Enhanced damping of ion acoustic waves in dense plasmas
A theory for the ion acoustic wave damping in dense plasmas and warm dense matter, accounting for the Umklapp process, is presented. A higher decay rate compared to the prediction from the Landau damping theory is predicted for high-Z dense plasmas where the electron density ranges from $10^{21}$ to $ 10^{24} \mathrm{cm^{-3}}$ and the electron temperature is moderately higher than the Fermi energy.
1011.4607v1
2012-05-16
Enhanced coupling design of a detuned damped structure for clic
The key feature of the improved coupling design in the Damped Detuned Structure (DDS) is focused on the four manifolds. Rectangular geometry slots and rectangular manifolds are used. This results in a significantly stronger coupling to the manifolds compared to the previous design. We describe the new design together with its wakefield damping properties.
1205.3590v1
2012-06-26
On the $L^{2}$-critical nonlinear Schrödinger Equation with a nonlinear damping
We consider the Cauchy problem for the $L^{2}$-critical nonlinear Schr\"{o}dinger equation with a nonlinear damping. According to the power of the damping term, we prove the global existence or the existence of finite time blowup dynamics with the log-log blow-up speed for $\|\nabla u(t)\|_{L^2}$.
1206.6082v4
2012-10-12
Semi-linear wave equations with effective damping
We study the Cauchy problem for the semi-linear damped wave equation in any space dimension. We assume that the time-dependent damping term is effective. We prove the global existence of small energy data solutions in the supercritical case.
1210.3493v1
2012-12-08
A note on the lifespan of solutions to the semilinear damped wave equation
This paper concerns estimates of the lifespan of solutions to the semilinear damped wave equation. We give upper estimates of the lifespan for the semilinear damped wave equation with variable coefficients in all space dimensions.
1212.1772v3
2012-12-10
Strongly damped wave equation with exponential nonlinearities
In this paper, we study the initial boundary value problem for the two dimensional strong damped wave equation with exponentially growing source and damping terms. We first show the well-posedness of this problem and then prove the existence of the global attractor in $(H_{0}^{1}(\Omega)\cap L^{\infty}(\Omega))\times L^{2}(\Omega)$.
1212.2180v2
2013-10-27
Exponential decay of solutions for the plate equation with localized damping
In this paper, we give positive answer to the open question raised in [E. Zuazua, Exponential decay for the semilinear wave equation with localized damping in unbounded domains. J. Math. Pures Appl., 70 (1991) 513--529] on the exponential decay of solutions for the semilinear plate equation with localized damping.
1310.7243v3
2014-03-07
Landau damping in Sobolev spaces for the Vlasov-HMF model
We consider the Vlasov-HMF (Hamiltonian Mean-Field) model. We consider solutions starting in a small Sobolev neighborhood of a spatially homogeneous state satisfying a linearized stability criterion (Penrose criterion). We prove that these solutions exhibit a scattering behavior to a modified state, which implies a nonlinear Landau damping effect with polynomial rate of damping.
1403.1668v2
2015-03-30
Damping to prevent the blow-up of the Korteweg-de Vries equation
We study the behavior of the solution of a generalized damped KdV equation $u_t + u_x + u_{xxx} + u^p u_x + \mathscr{L}_{\gamma}(u)= 0$. We first state results on the local well-posedness. Then when $p \geq 4$, conditions on $\mathscr{L}_{\gamma}$ are given to prevent the blow-up of the solution. Finally, we numerically build such sequences of damping.
1503.08559v1
2015-06-16
Fast energy decay for wave equations with variable damping coefficients in the 1-D half line
We derive fast decay estimates of the total energy for wave equations with localized variable damping coefficients, which are dealt with in the one dimensional half line $(0,\infty)$. The variable damping coefficient vanishes near the boundary $x = 0$, and is effective critically near spatial infinity $x = \infty$.
1506.04851v1