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2018-07-16
A unified N-SECE strategy for highly coupled piezoelectric energy scavengers
This paper proposes a novel vibration energy harvesting strategy based on an extension of the Synchronous Electric Charge Extraction (SECE) approach, enabling both the maximization of the harvested power and a consequent bandwidth enlargement in the case of highly coupled/lightly damped piezoelectric energy harvesters. The proposed strategy relies on the tuning of the frequency of the energy extraction events, which is either N times greater than the vibration frequency (Multiple SECE case, N > 1) or 1/N times smaller (Regenerative SECE, N < 1). We first prove analytically than increasing or decreasing N both lead to a damping reduction. While N has no impact on the system's resonance frequency in the Regenerative case (N < 1), we show that this resonant frequency becomes a function of N in the Multiple SECE case (N > 1). Experimental results on a highly coupled/lowly damped piezoelectric harvester (k^2= 0.44, Q_m = 20) demonstrates the potential of this strategy, leading to 257% harvested power improvement compared to SECE (N = 1). and the possibility to tune the resonant frequency on a range as large as 35% of the short-circuit resonant frequency of the harvester.
1809.09685v1
2018-10-09
The lifespan of solutions of semilinear wave equations with the scale-invariant damping in one space dimension
The critical constant of time-decaying damping in the scale-invariant case is recently conjectured. It also has been expected that the lifespan estimate is the same as for the associated semilinear heat equations if the constant is in the \heat-like" domain. In this paper, we point out that this is not true if the total integral of the sum of initial position and speed vanishes. In such a case, we have a new type of the lifespan estimates which is closely related to the non-damped case in shifted space dimensions.
1810.03780v2
2018-10-24
Justification of the Lugiato-Lefever model from a damped driven $φ^4$ equation
The Lugiato-Lefever equation is a damped and driven version of the well-known nonlinear Schr\"odinger equation. It is a mathematical model describing complex phenomena in dissipative and nonlinear optical cavities. Within the last two decades, the equation has gained a wide attention as it becomes the basic model describing optical frequency combs. Recent works derive the Lugiato-Lefever equation from a class of damped driven $\phi^4$ equations closed to resonance. In this paper, we provide a justification of the envelope approximation. From the analysis point of view, the result is novel and non-trivial as the drive yields a perturbation term that is not square integrable. The main approach proposed in this work is to decompose the solutions into a combination of the background and the integrable component. This paper is the first part of a two-manuscript series.
1810.10630v1
2018-11-06
Decay properties and asymptotic profiles for elastic waves with Kelvin-Voigt damping in 2D
In this paper we consider elastic waves with Kelvin-Voigt damping in 2D. For the linear problem, applying pointwise estimates of the partial Fourier transform of solutions in the Fourier space and asymptotic expansions of eigenvalues and their eigenprojections, we obtain sharp energy decay estimates with additional $L^m$ regularity and $L^p-L^q$ estimates on the conjugate line. Furthermore, we derive asymptotic profiles of solutions under different assumptions of initial data. For the semilinear problem, we use the derived $L^2-L^2$ estimates with additional $L^m$ regularity to prove global (in time) existence of small data solutions to the weakly coupled system. Finally, to deal with elastic waves with Kelvin-Voigt damping in 3D, we apply the Helmholtz decomposition.
1811.02223v3
2018-12-06
Damping and Anti-Damping Phenomena in Metallic Antiferromagnets: An ab-initio Study
We report on a first principles study of anti-ferromagnetic resonance (AFMR) phenomena in metallic systems [MnX (X=Ir,Pt,Pd,Rh) and FeRh] under an external electric field. We demonstrate that the AFMR linewidth can be separated into a relativistic component originating from the angular momentum transfer between the collinear AFM subsystem and the crystal through the spin orbit coupling (SOC), and an exchange component that originates from the spin exchange between the two sublattices. The calculations reveal that the latter component becomes significant in the low temperature regime. Furthermore, we present results for the current-induced intersublattice torque which can be separated into the Field-Like (FL) and Damping-Like (DL) components, affecting the intersublattice exchange coupling and AFMR linewidth, respectively.
1812.02844v2
2018-12-12
Extreme wave events for a nonlinear Schrödinger equation with linear damping and Gaussian driving
We perform a numerical study of the initial-boundary value problem, with vanishing boundary conditions, of a driven nonlinear Schr\"odinger equation (NLS) with linear damping and a Gaussian driver. We identify Peregrine-like rogue waveforms, excited by two different types of vanishing initial data decaying at an algebraic or exponential rate. The observed extreme events emerge on top of a decaying support. Depending on the spatial/temporal scales of the driver, the transient dynamics -- prior to the eventual decay of the solutions -- may resemble the one in the semiclassical limit of the integrable NLS, or may, e.g., lead to large-amplitude breather-like patterns. The effects of the damping strength and driving amplitude, in suppressing or enhancing respectively the relevant features, as well as of the phase of the driver in the construction of a diverse array of spatiotemporal patterns, are numerically analyzed.
1812.05439v3
2018-12-13
Stability of elastic transmission systems with a local Kelvin-Voigt damping
In this paper, we consider the longitudinal and transversal vibrations of the transmission Euler-Bernoulli beam with Kelvin-Voigt damping distributed locally on any subinterval of the region occupied by the beam and only in one side of the transmission point. We prove that the semigroup associated with the equation for the transversal motion of the beam is exponentially stable, although the semigroup associated with the equation for the longitudinal motion of the beam is polynomially stable. Due to the locally distributed and unbounded nature of the damping, we use a frequency domain method and combine a contradiction argument with the multiplier technique to carry out a special analysis for the resolvent.
1812.05923v1
2018-12-13
Energy decay estimates of elastic transmission wave/beam systems with a local Kelvin-Voigt damping
We consider a beam and a wave equations coupled on an elastic beam through transmission conditions. The damping which is locally distributed acts through one of the two equations only; its effect is transmitted to the other equation through the coupling. First we consider the case where the dissipation acts through the beam equation. Using a recent result of Borichev and Tomilov on polynomial decay characterization of bounded semigroups we provide a precise decay estimates showing that the energy of this coupled system decays polynomially as the time variable goes to infinity. Second, we discuss the case where the damping acts through the wave equation. Proceeding as in the first case, we prove that this system is also polynomially stable and we provide precise polynomial decay estimates for its energy. Finally, we show the lack of uniform exponential decay of solutions for both models.
1812.05924v1
2018-12-20
Sound attenuation in stable glasses
Understanding the difference between universal low-temperature properties of amorphous and crystalline solids requires an explanation of the stronger damping of long-wavelength phonons in amorphous solids. A longstanding sound attenuation scenario, resulting from a combination of experiments, theories, and simulations, leads to a quartic scaling of sound attenuation with the wavevector, which is commonly attributed to Rayleigh scattering of the sound. Modern computer simulations offer conflicting conclusions regarding the validity of this picture. We simulate glasses with an unprecedentedly broad range of stabilities to perform the first microscopic analysis of sound damping in model glass formers across a range of experimentally relevant preparation protocols. We present a convincing evidence that quartic scaling is recovered for small wavevectors irrespective of the glass's stability. With increasing stability, the wavevector where the quartic scaling begins increases by approximately a factor of three and the sound attenuation decreases by over an order of magnitude. Our results uncover an intimate connection between glass stability and sound damping.
1812.08736v2
2018-12-21
Reply to the Comment on "Negative Landau damping in bilayer graphene"
Here we address the concerns of Svintsov and Ryzhii [arXiv:1812.03764] on our article on negative Landau damping in graphene [Phys. Rev. Lett. 119, 133901 (2017)]. We prove that due to the differences between the kinetic and canonical momenta, the conductivity of drift-current biased graphene is ruled by a Galilean transformation when the electron-electron interactions predominate and force the electron gas to move with constant velocity, similar to a moving medium. Furthermore, it is shown that the nonlocal effects in graphene neither preclude a negative Landau damping nor the emergence of instabilities in graphene platforms.
1812.09103v3
2018-12-27
Nonexistence of global solutions for a weakly coupled system of semilinear damped wave equations of derivative type in the scattering case
In this paper we consider the blow-up for solutions to a weakly coupled system of semilinear damped wave equations of derivative type in the scattering case. After introducing suitable functionals proposed by Lai-Takamura for the corresponding single semilinear equation, we employ Kato's lemma to derive the blow-up result in the subcritical case. On the other hand, in the critical case an iteration procedure based on the slicing method is employed. Let us point out that we find as critical curve in the p-q plane for the pair of exponents (p, q) in the nonlinear terms the same one as for the weakly coupled system of semilinear not-damped wave equations with the same kind of nonlinearities.
1812.10653v1
2018-12-30
Smooth, Time-invariant Regulation of Nonholonomic Systems via Energy Pumping-and-Damping
In this paper we propose an energy pumping-and-damping technique to regulate nonholonomic systems described by kinematic models. The controller design follows the widely popular interconnection and damping assignment passivity-based methodology, with the free matrices partially structured. Two asymptotic regulation objectives are considered: drive to zero the state or drive the systems total energy to a desired constant value. In both cases, the control laws are smooth, time-invariant, state-feedbacks. For the nonholonomic integrator we give an almost global solution for both problems, with the objectives ensured for all system initial conditions starting outside a set that has zero Lebesgue measure and is nowhere dense. For the general case of higher-order nonholonomic systems in chained form, a local stability result is given. Simulation results comparing the performance of the proposed controller with other existing designs are also provided.
1812.11538v2
2019-01-05
Simulations of wobble damping in viscoelastic rotators
Using a damped mass-spring model, we simulate wobble of spinning homogeneous viscoelastic ellipsoids undergoing non-principal axis rotation. Energy damping rates are measured for oblate and prolate bodies with different spin rates, spin states, viscoelastic relaxation timescales, axis ratios, and strengths. Analytical models using a quality factor by Breiter et al. (2012) and for the Maxwell rheology by Frouard & Efroimsky (2018) match our numerical measurements of the energy dissipation rate after we modify their predictions for the numerically simulated Kelvin-Voigt rheology. Simulations of nearly spherical but wobbling bodies with hard and soft cores show that the energy dissipation rate is more sensitive to the material properties in the core than near the surface. The sensitivity to viscoelastic model implies that inferred statistics of tumbling lifetimes in asteroids might be interpreted in terms of differences in their material properties.
1901.01439v3
2019-01-16
Laboratory investigations of the bending rheology of floating saline ice, and physical mechanisms of wave damping, in the HSVA ice tank
An experiment on the propagation of flexural-gravity waves was performed in the HSVA ice tank. Physical characteristics of the water-ice system were measured in different locations in the tank during the tests, with a number of sensors deployed in the water, on the ice and in the air. Water velocity was measured with an acoustic doppler velocimeter (ADV) and an acoustic doppler current profiler (ADCP); wave amplitudes were measured with ultrasonic sensors and the optical system Qualisys; in-plane deformations of the ice and the temperature of the ice and water were measured by fiber optic sensors, and acoustic emissions were recorded with compressional crystal sensors. All together 61 tests were performed, with ice thicknesses of 3 cm and 5 cm. The experimental setup and selected results of the tests are discussed in this paper. We show that cyclic motion of the ice along the tank, imitating ice drift, causes an increase in wave damping. We also show that the formation of non-through cracks in the ice, caused by the action of waves, increases wave damping.
1901.05333v1
2019-01-24
Generalized framework for testing gravity with gravitational-wave propagation. III. Future prospect
The properties of gravitational-wave (GW) propagation are modified in alternative theories of gravity and are crucial observables to test gravity at cosmological distance. The propagation speed has already been measured from GW170817 so precisely and pinned down to the speed of light, while other properties of GW propagation have not constrained tightly yet. In this paper, we investigate the measurement precisions of the amplitude damping rate (equivalently, the time variation of the gravitational coupling for GWs) and graviton mass in the generalized framework of GW propagation with the future detectors such as Voyager, Cosmic Explorer, and Einstein Telescope. As a result, we show that the future GW observation can reach 1% error for the amplitude damping. We also study the time variation of the gravitational couplings in Horndeski theory by performing Monte Carlo-based numerical simulations. From the simulation results, we find that the current accelerating Universe prefers the models with less damping of GWs and that the equivalence principle can be tested at the level of 1% by the future GW observation.
1901.08249v2
2019-01-31
Perturbed Markov Chains and Information Networks
The paper is devoted to studies of perturbed Markov chains commonly used for description of information networks. In such models, the matrix of transition probabilities for the corresponding Markov chain is usually regularised by adding a special damping matrix multiplied by a small damping (perturbation) parameter $\varepsilon$. We give effective upper bounds for the rate of approximation for stationary distributions of unperturbed Markov chains by stationary distributions of perturbed Markov chains with regularised matrices of transition probabilities, asymptotic expansions for approximating stationary distributions with respect to damping parameter, as well as explicit upper bounds for the rate of convergence in ergodic theorems for $n$-step transition probabilities in triangular array mode, where perturbation parameter $\varepsilon \to 0$ and $n \to \infty$, simultaneously. The results of numerical experiments are also presented
1901.11483v3
2019-02-14
Dynamic Interconnection and Damping Injection for Input-to-State Stable Bilateral Teleoperation
In bilateral teleoperation, the human who operates the master and the environment which interacts with the slave are part of the force feedback loop. Yet, both have time-varying and unpredictable dynamics and are challenging to model. A conventional strategy for sidestepping the demand for their models in the stability analysis is to assume passive user and environment, and to control the master-communications-slave system to be passive as well. This paper circumvents the need to model the user and environment in a novel way: it regards their forces as external excitations for a semi-autonomous force feedback loop, which it outfits with a dynamic interconnection and damping injection controller that renders bilateral teleoperation with time-varying delays exponentially input-to-state stable. The controller uses the position and velocity measurements of the local robot and the delayed position transmitted from the other robot to robustly synchronize the master and slave under the user and environment perturbations. Lyapunov-Krasovskii stability analysis shows that the proposed strategy (i) can confine the position error between the master and slave to an invariant set, and (ii) can drive it exponentially to a globally attractive set. Thus, the dynamic interconnection and damping injection approach has practical relevance for telemanipulation tasks with given precision requirements.
1902.05500v1
2019-02-15
Evidence for Electron Landau Damping in Space Plasma Turbulence
How turbulent energy is dissipated in weakly collisional space and astrophysical plasmas is a major open question. Here, we present the application of a field-particle correlation technique to directly measure the transfer of energy between the turbulent electromagnetic field and electrons in the Earth's magnetosheath, the region of solar wind downstream of the Earth's bow shock. The measurement of the secular energy transfer from the parallel electric field as a function of electron velocity shows a signature consistent with Landau damping. This signature is coherent over time, close to the predicted resonant velocity, similar to that seen in kinetic Alfv\'en turbulence simulations, and disappears under phase randomisation. This suggests that electron Landau damping could play a significant role in turbulent plasma heating, and that the technique is a valuable tool for determining the particle energisation processes operating in space and astrophysical plasmas.
1902.05785v1
2019-02-22
Thermal induced monochromatic microwave generation in magnon-polariton
We propose thermal induced generation of monochromatic microwave radiation in magnon-polariton. Mechanism of thermal to microwave energy transformation is based on intrinsic energy loss compensation of coupled magnon and microwave cavity oscillators by thermal induced "negative damping". A singularity at an exceptional point is achieved when at the critical value of "negative damping" the damping of the system is fully compensated. At the exceptional point, the input energy is equally distributed between the magnon and photon subsystems of the magnon-polariton. The efficiency of transformation of thermal energy into useful microwave radiation is estimated to be as large as 17 percent due to magnon-photon coupling mediated direct conversation of spin current into microwave photons.
1902.08383v1
2019-03-04
Nonlinear inviscid damping for zero mean perturbation of the 2D Euler Couette flow
In this note we revisit the proof of Bedrossian and Masmoudi [arXiv:1306.5028] about the inviscid damping of planar shear flows in the 2D Euler equations under the assumption of zero mean perturbation. We prove that a small perturbation to the 2D Euler Couette flow in $\mathbb{T}\times \mathbb{R}$ strongly converge to zero, under the additional assumption that the average in $x$ is always zero. In general the mean is not a conserved quantity for the nonlinear dynamics, for this reason this is a particular case. Nevertheless our assumption allow the presence of echoes in the problem, which we control by an approximation of the weight built in [arXiv:1306.5028]. The aim of this note is to present the mathematical techniques used in [arXiv:1306.5028] and can be useful as a first approach to the nonlinear inviscid damping.
1903.01543v1
2019-03-10
Orbital stabilization of nonlinear systems via Mexican sombrero energy shaping and pumping-and-damping injection
In this paper we show that a slight modification to the widely popular interconnection and damping assignment passivity-based control method---originally proposed for stabilization of equilibria of nonlinear systems---allows us to provide a solution to the more challenging orbital stabilization problem. Two different, though related, ways how this procedure can be applied are proposed. First, the assignment of an energy function that has a minimum in a closed curve, i.e., with the shape of a Mexican sombrero. Second, the use of a damping matrix that changes "sign" according to the position of the state trajectory relative to the desired orbit, that is, pumping or dissipating energy. The proposed methodologies are illustrated with the example of the induction motor and prove that it yields the industry standard field oriented control.
1903.04070v3
2019-03-11
Impact of thermal effects on the evolution of eccentricity and inclination of low-mass planets
Using linear perturbation theory, we evaluate the time-dependent force exerted on an eccentric and inclined low-mass planet embedded in a gaseous protoplanetary disc with finite thermal diffusivity $\chi$. We assume the eccentricity and inclination to be small compared to the size of the thermal lobes $\lambda\sim(\chi/\Omega)^{1/2}$, itself generally much smaller than the scalelength of pressure $H$. When the planet is non-luminous, we find that its eccentricity and inclination are vigorously damped by the disc, over a timescale shorter by a factor $H/\lambda$ than the damping timescale in adiabatic discs. On the contrary, when the luminosity-to-mass ratio of the planet exceeds a threshold that depends on the disc's properties, its eccentricity and inclination undergo an exponential growth. In the limit of a large luminosity, the growth rate of the eccentricity is 2.5~times larger than that of the inclination, in agreement with previous numerical work. Depending on their luminosity, planetary embryos therefore exhibit much more diverse behaviours than the mild damping of eccentricity and inclination considered hitherto.
1903.04470v2
2019-03-14
The Strichartz estimates for the damped wave equation and the behavior of solutions for the energy critical nonlinear equation
For the linear damped wave equation (DW), the $L^p$-$L^q$ type estimates have been well studied. Recently, Watanabe showed the Strichartz estimates for DW when $d=2,3$. In the present paper, we give Strichartz estimates for DW in higher dimensions. Moreover, by applying the estimates, we give the local well-posedness of the energy critical nonlinear damped wave equation (NLDW) $\partial_t^2 u - \Delta u +\partial_t u = |u|^{\frac{4}{d-2}}u$, $(t,x) \in [0,T) \times \mathbb{R}^d$, where $3 \leq d \leq 5$. Especially, we show the small data global existence for NLDW. In addition, we investigate the behavior of the solutions to NLDW. Namely, we give a decay result for solutions with finite Strichartz norm and a blow-up result for solutions with negative Nehari functional.
1903.05887v1
2019-04-17
Decays for Kelvin-Voigt damped wave equations I : the black box perturbative method
We show in this article how perturbative approaches~from our work with Hitrik (see also the work by Anantharaman-Macia) and the {\em black box} strategy from~ our work with Zworski allow to obtain decay rates for Kelvin-Voigt damped wave equations from quite standard resolvent estimates : Carleman estimates or geometric control estimates for Helmoltz equationCarleman or other resolvent estimates for the Helmoltz equation. Though in this context of Kelvin Voigt damping, such approach is unlikely to allow for the optimal results when additional geometric assumptions are considered (see \cite{BuCh, Bu19}), it turns out that using this method, we can obtain the usual logarithmic decay which is optimal in general cases. We also present some applications of this approach giving decay rates in some particular geometries (tori).
1904.08318v2
2019-04-17
Non-Hermitian skin effect and chiral damping in open quantum systems
One of the unique features of non-Hermitian Hamiltonians is the non-Hermitian skin effect, namely that the eigenstates are exponentially localized at the boundary of the system. For open quantum systems, a short-time evolution can often be well described by the effective non-Hermitian Hamiltonians, while long-time dynamics calls for the Lindblad master equations, in which the Liouvillian superoperators generate time evolution. In this Letter, we find that Liouvillian superoperators can exhibit the non-Hermitian skin effect, and uncover its unexpected physical consequences. It is shown that the non-Hermitian skin effect dramatically shapes the long-time dynamics, such that the damping in a class of open quantum systems is algebraic under periodic boundary condition but exponential under open boundary condition. Moreover, the non-Hermitian skin effect and non-Bloch bands cause a chiral damping with a sharp wavefront. These phenomena are beyond the effective non-Hermitian Hamiltonians; instead, they belong to the non-Hermitian physics of full-fledged open quantum dynamics.
1904.08432v2
2019-04-19
Plasmon-Emitter Interactions at the Nanoscale
Plasmon-emitter interactions are of paramount importance in modern nanoplasmonics and are generally maximal at short emitter-surface separations. However, when the separation falls below 10-20 nm, the classical theory progressively deteriorates due to its neglect of quantum mechanical effects such as nonlocality, electronic spill-out, and Landau damping. Here, we show how this neglect can be remedied by presenting a unified theoretical treatment of mesoscopic electrodynamics grounded on the framework of Feibelman $d$-parameters. Crucially, our technique naturally incorporates nonclassical resonance shifts and surface-enabled Landau damping - a nonlocal damping effect - which have a dramatic impact on the amplitude and spectral distribution of plasmon-emitter interactions. We consider a broad array of plasmon-emitter interactions ranging from dipolar and multipolar spontaneous emission enhancement, to plasmon-assisted energy transfer and enhancement of two-photon transitions. The formalism presented here gives a complete account of both plasmons and plasmon-emitter interactions at the nanoscale, constituting a simple yet rigorous and general platform to incorporate nonclassical effects in plasmon-empowered nanophotonic phenomena.
1904.09279v1
2019-04-23
Ultrafast depinning of domain wall in notched antiferromagnetic nanostructures
The pinning and depinning of antiferromagnetic (AFM) domain wall is certainly the core issue of AFM spintronics. In this work, we study theoretically the N\'eel-type domain wall pinning and depinning at a notch in an antiferromagnetic (AFM) nano-ribbon. The depinning field depending on the notch dimension and intrinsic physical parameters are deduced and also numerically calculated. Contrary to conventional conception, it is revealed that the depinning field is remarkably dependent of the damping constant and the time-dependent oscillation of the domain wall position in the weakly damping regime benefits to the wall depinning, resulting in a gradual increase of the depinning field up to a saturation value with increasing damping constant. A one-dimensional model accounting of the internal dynamics of domain wall is used to explain perfectly the simulated results. It is demonstrated that the depinning mechanism of an AFM domain wall differs from ferromagnetic domain wall by exhibiting a depinning speed typically three orders of magnitude faster than the latter, suggesting the ultrafast dynamics of an AFM system.
1904.10197v2
2019-05-08
Discrete Energy behavior of a damped Timoshenko system
In this article, we consider a one-dimensional Timoshenko system subject to different types of dissipation (linear and nonlinear dampings). Based on a combination between the finite element and the finite difference methods, we design a discretization scheme for the different Timoshenko systems under consideration. We first come up with a numerical scheme to the free-undamped Timoshenko system. Then, we adapt this numerical scheme to the corresponding linear and nonlinear damped systems. Interestingly, this scheme reaches to reproduce the most important properties of the discrete energy. Namely, we show for the discrete energy the positivity, the energy conservation property and the different decay rate profiles. We numerically reproduce the known analytical results established on the decay rate of the energy associated with each type of dissipation.
1905.03050v1
2019-05-08
Attractors for semilinear wave equations with localized damping and external forces
This paper is concerned with long-time dynamics of semilinear wave equations defined on bounded domains of $\mathbb{R}^3$ with cubic nonlinear terms and locally distributed damping. The existence of regular finite-dimensional global attractors established by Chueshov, Lasiecka and Toundykov (2008) reflects a good deal of the current state of the art on this matter. Our contribution is threefold. First, we prove uniform boundedness of attractors with respect to a forcing parameter. Then, we study the continuity of attractors with respect to the parameter in a residual dense set. Finally, we show the existence of generalized exponential attractors. These aspects were not previously considered for wave equations with localized damping.
1905.03285v1
2019-05-16
Global attractors and their upper semicontinuity for a structural damped wave equation with supercritical nonlinearity on $\mathbb{R}^{N}$
The paper investigates the existence of global attractors and their upper semicontinuity for a structural damped wave equation on $\mathbb{R}^{N}: u_{tt}-\Delta u+(-\Delta)^\alpha u_{t}+u_{t}+u+g(u)=f(x)$, where $\alpha\in (1/2, 1)$ is called a dissipative index. We propose a new method based on the harmonic analysis technique and the commutator estimate to exploit the dissipative effect of the structural damping $(-\Delta)^\alpha u_{t}$ and to overcome the essential difficulty: "both the unbounded domain $\mathbb{R}^N$ and the supercritical nonlinearity cause that the Sobolev embedding loses its compactness"; Meanwhile we show that there exists a supercritical index $p_\alpha\equiv\frac{N+4\alpha}{N-4\alpha}$ depending on $\alpha$ such that when the growth exponent $p$ of the nonlinearity $g(u)$ is up to the supercritical range: $1\leqslant p<p_\alpha$: (i) the IVP of the equation is well-posed and its solution is of additionally global smoothness when $t>0$; (ii) the related solution semigroup possesses a global attractor $\mathcal{A}_\alpha$ in natural energy space for each $\alpha\in (1/2, 1)$; (iii) the family of global attractors $\{\mathcal{A}_\alpha\}_{\alpha\in (1/2, 1) }$ is upper semicontinuous at each point $\alpha_0\in (1/2, 1)$.
1905.06778v1
2019-05-20
Quantum parameter-estimation of frequency and damping of a harmonic-oscillator
We determine the quantum Cram\'er-Rao bound for the precision with which the oscillator frequency and damping constant of a damped quantum harmonic oscillator in an arbitrary Gaussian state can be estimated. This goes beyond standard quantum parameter estimation of a single mode Gaussian state for which typically a mode of fixed frequency is assumed. We present a scheme through which the frequency estimation can nevertheless be based on the known results for single-mode quantum parameter estimation with Gaussian states. Based on these results, we investigate the optimal measurement time. For measuring the oscillator frequency, our results unify previously known partial results and constitute an explicit solution for a general single-mode Gaussian state. Furthermore, we show that with existing carbon nanotube resonators (see J. Chaste et al.~Nature Nanotechnology 7, 301 (2012)) it should be possible to achieve a mass sensitivity of the order of an electron mass $\text{Hz}^{-1/2}$.
1905.08288v1
2019-05-24
Damped oscillations of the probability of random events followed by absolute refractory period: exact analytical results
There are numerous examples of natural and artificial processes that represent stochastic sequences of events followed by an absolute refractory period during which the occurrence of a subsequent event is impossible. In the simplest case of a generalized Bernoulli scheme for uniform random events followed by the absolute refractory period, the event probability as a function of time can exhibit damped transient oscillations. Using stochastically-spiking point neuron as a model example, we present an exact and compact analytical description for the oscillations without invoking the standard renewal theory. The resulting formulas stand out for their relative simplicity, allowing one to analytically obtain the amplitude damping of the 2nd and 3rd peaks of the event probability.
1905.10172v3
2019-06-11
Study of semi-linear $σ$-evolution equations with frictional and visco-elastic damping
In this article, we study semi-linear $\sigma$-evolution equations with double damping including frictional and visco-elastic damping for any $\sigma\ge 1$. We are interested in investigating not only higher order asymptotic expansions of solutions but also diffusion phenomenon in the $L^p-L^q$ framework, with $1\le p\le q\le \infty$, to the corresponding linear equations. By assuming additional $L^{m}$ regularity on the initial data, with $m\in [1,2)$, we prove the global (in time) existence of small data energy solutions and indicate the large time behavior of the global obtained solutions as well to semi-linear equations. Moreover, we also determine the so-called critical exponent when $\sigma$ is integers.
1906.04471v1
2019-07-08
Damping of density oscillations in neutrino-transparent nuclear matter
We calculate the bulk-viscous dissipation time for adiabatic density oscillations in nuclear matter at densities of 1-7 times nuclear saturation density and at temperatures ranging from 1 MeV, where corrections to previous low-temperature calculations become important, up to 10 MeV, where the assumption of neutrino transparency is no longer valid. Under these conditions, which are expected to occur in neutron star mergers, damping of density oscillations arises from beta equilibration via weak interactions. We find that for 1 kHz oscillations the shortest dissipation times are in the 5 to 20 ms range, depending on the equation of state, which means that bulk viscous damping could affect the dynamics of a neutron star merger. For higher frequencies the dissipation time can be even shorter.
1907.03795v2
2019-07-12
Decoherence of collective motion in warm nuclei
Collective states in cold nuclei are represented by a wave function that assigns coherent phases to the participating nucleons. The degree of coherence decreases with excitation energy above the yrast line because of coupling to the increasingly dense background of quasiparticle excitations. The consequences of decoherence are discussed, starting with the well studied case of rotational damping. In addition to superdeformed bands, a highly excited oblate band is presented as a new example of screening from rotational damping. Suppression of pair correlation leads to incoherent thermal M1 radiation, which appears as an exponential spike (LEMAR) at zero energy in the $\gamma$ strength function of spherical nuclei. In deformed nuclei a Scissors Resonance appears and LEMAR changes to damped magnetic rotation, which is interpreted as partial restoration of coherence.
1907.05569v1
2019-07-24
First-order optimization algorithms via inertial systems with Hessian driven damping
In a Hilbert space setting, for convex optimization, we analyze the convergence rate of a class of first-order algorithms involving inertial features. They can be interpreted as discrete time versions of inertial dynamics involving both viscous and Hessian-driven dampings. The geometrical damping driven by the Hessian intervenes in the dynamics in the form $\nabla^2 f (x(t)) \dot{x} (t)$. By treating this term as the time derivative of $ \nabla f (x (t)) $, this gives, in discretized form, first-order algorithms in time and space. In addition to the convergence properties attached to Nesterov-type accelerated gradient methods, the algorithms thus obtained are new and show a rapid convergence towards zero of the gradients. On the basis of a regularization technique using the Moreau envelope, we extend these methods to non-smooth convex functions with extended real values. The introduction of time scale factors makes it possible to further accelerate these algorithms. We also report numerical results on structured problems to support our theoretical findings.
1907.10536v2
2019-07-26
L^p-asymptotic stability analysis of a 1D wave equation with a nonlinear damping
This paper is concerned with the asymptotic stability analysis of a one dimensional wave equation with Dirichlet boundary conditions subject to a nonlinear distributed damping with an L p functional framework, p $\in$ [2, $\infty$]. Some well-posedness results are provided together with exponential decay to zero of trajectories, with an estimation of the decay rate. The well-posedness results are proved by considering an appropriate functional of the energy in the desired functional spaces introduced by Haraux in [11]. Asymptotic behavior analysis is based on an attractivity result on a trajectory of an infinite-dimensional linear time-varying system with a special structure, which relies on the introduction of a suitable Lyapunov functional. Note that some of the results of this paper apply for a large class of nonmonotone dampings.
1907.11712v1
2019-08-13
A Gevrey class semigroup, exponential decay and Lack of analyticity for a system formed by a Kirchhoff-Love plate equation and the equation of a membrane-like electric network with indirect fractional damping
The emphasis in this paper is on the Coupled System of a Kirchhoff-Love Plate Equation with the Equation of a Membrane-like Electrical Network, where the coupling is of higher order given by the Laplacian of the displacement velocity $\gamma\Delta u_t$ and the Laplacian of the electric potential field $\gamma\Delta v_t $, here only one of the equations is conservative and the other has dissipative properties. The dissipative mechanism is given by an intermediate damping $(-\Delta)^\theta v_t$ between the electrical damping potential for $\theta=0$ and the Laplacian of the electric potential for $\theta=1$. We show that $S(t)=e^{\mathbb{B}t}$ is not analytic for $\theta\in[0, 1)$ and analytic for $\theta=1$, however $S(t)=e^{\mathbb{B}t}$ decays exponentially for $0\leq \theta\leq 1$ and $S(t)$ is of Gevrey class $s> \frac{2+\theta}{\theta}$ when the parameter $\theta$ lies in the interval $(0,1)$.
1908.04826v3
2019-08-20
Partial Optomechanical Refrigeration via Multimode Cold-Damping Feedback
We provide a fully analytical treatment for the partial refrigeration of the thermal motion of a quantum mechanical resonator under the action of feedback. As opposed to standard cavity optomechanics where the aim is to isolate and cool a single mechanical mode, the aim here is to extract the thermal energy from many vibrational modes within a large frequency bandwidth. We consider a standard cold-damping technique where homodyne read-out of the cavity output field is fed into a feedback loop that provides a cooling action directly applied on the mechanical resonator. Analytical and numerical results predict that low final occupancies are achievable independently of the number of modes addressed by the feedback as long as the cooling rate is smaller than the intermode frequency separation. For resonators exhibiting a few nearly degenerate pairs of modes cooling is less efficient and a weak dependence on the number of modes is obtained. These scalings hint towards the design of frequency resolved mechanical resonators where efficient refrigeration is possible via simultaneous cold-damping feedback.
1908.07348v2
2019-08-26
Description and classification of 2-solitary waves for nonlinear damped Klein-Gordon equations
We describe completely 2-solitary waves related to the ground state of the nonlinear damped Klein-Gordon equation \begin{equation*} \partial_{tt}u+2\alpha\partial_{t}u-\Delta u+u-|u|^{p-1}u=0 \end{equation*} on $\bf R^N$, for $1\leq N\leq 5$ and energy subcritical exponents $p>2$. The description is twofold. First, we prove that 2-solitary waves with same sign do not exist. Second, we construct and classify the full family of 2-solitary waves in the case of opposite signs. Close to the sum of two remote solitary waves, it turns out that only the components of the initial data in the unstable direction of each ground state are relevant in the large time asymptotic behavior of the solution. In particular, we show that $2$-solitary waves have a universal behavior: the distance between the solitary waves is asymptotic to $\log t$ as $t\to \infty$. This behavior is due to damping of the initial data combined with strong interactions between the solitary waves.
1908.09527v1
2019-08-30
Magnetization reversal, damping properties and magnetic anisotropy of L10-ordered FeNi thin films
L10 ordered magnetic alloys such as FePt, FePd, CoPt and FeNi are well known for their large magnetocrystalline anisotropy. Among these, L10-FeNi alloy is economically viable material for magnetic recording media because it does not contain rare earth and noble elements. In this work, L10-FeNi films with three different strengths of anisotropy were fabricated by varying the deposition process in molecular beam epitaxy system. We have investigated the magnetization reversal along with domain imaging via magneto optic Kerr effect based microscope. It is found that in all three samples, the magnetization reversal is happening via domain wall motion. Further ferromagnetic resonance (FMR) spectroscopy was performed to evaluate the damping constant and magnetic anisotropy. It was observed that the FeNi sample with moderate strength of anisotropy exhibits low value of damping constant ~ 4.9X10^-3. In addition to this, it was found that the films possess a mixture of cubic and uniaxial anisotropies.
1908.11761v1
2019-09-24
DAMPE Excess from Leptophilic Vector Dark Matter: Model Independent Approach
We study all extensions of the Standard Model (SM) with a vector dark matter (VDM) candidate which can explain the peak structure observed by recent DAMPE experiment in electron-positron cosmic ray spectrum. In this regard, we consider all leptophilic renormalizable VDM-SM interactions through scalar, spinor, and vector mediators. We show that only two out of six possible models could produce DAMPE signal by annihilation of VDM with the mass about 1.5 TeV in a nearby subhalo whilst simultaneously satisfying constraints from DM relic density, direct/indirect detection, and the collider bounds. These two models are the ones with scalar/pseudoscalar mediator $ \phi $ with $ M_{\phi} \in [1500,3000] $ GeV.
1909.10729v2
2019-09-24
Evaluating the Impacts of Transmission Expansion on Sub-Synchronous Resonance Risk
While transmission expansions are planned to have positive impact on reliability of power grids, they could increase the risk and severity of some of the detrimental incidents in power grid mainly by virtue of changing system configuration, consequently electrical distance. This paper aims to evaluate and quantify the impact of transmission expansion projects on Sub-Synchronous Resonance (SSR) risk through a two-step approach utilizing outage count index and Sub-synchronous damping index. A graph-theory based SSR screening tool is introduced to quantify the outage count associated with all grid contingencies which results in radial connection between renewable generation resources and nearby series compensated lines. Moreover, a frequency-scan based damping analysis is performed to assess the impact of transmission expansion on the system damping in sub-synchronous frequency range. The proposed approach has been utilized to evaluate the impact of recently-built transmission expansion project on SSR risk in a portion of Electric Reliability Council of Texas (ERCOT) grid.
1909.11024v1
2019-10-02
Data-Driven Identification of Rayleigh-Damped Second-Order Systems
In this paper, we present a data-driven approach to identify second-order systems, having internal Rayleigh damping. This means that the damping matrix is given as a linear combination of the mass and stiffness matrices. These systems typically appear when performing various engineering studies, e.g., vibrational and structural analysis. In an experimental setup, the frequency response of a system can be measured via various approaches, for instance, by measuring the vibrations using an accelerometer. As a consequence, given frequency samples, the identification of the underlying system relies on rational approximation. To that aim, we propose an identification of the corresponding second-order system, extending the Loewner framework for this class of systems. The efficiency of the proposed method is demonstrated by means of various numerical benchmarks.
1910.00838v1
2019-10-06
Deterministic and random attractors for a wave equation with sign changing damping
The paper gives a detailed study of long-time dynamics generated by weakly damped wave equations in bounded 3D domains where the damping exponent depends explicitly on time and may change sign. It is shown that in the case when the non-linearity is superlinear, the considered equation remains dissipative if the weighted mean value of the dissipation rate remains positive and that the conditions of this type are not sufficient in the linear case. Two principally different cases are considered. In the case when this mean is uniform (which corresponds to deterministic dissipation rates), it is shown that the considered system possesses smooth uniform attractors as well as non-autonomous exponential attractors. In the case where the mean is not uniform (which corresponds to the random dissipation rate, for instance, when this dissipation rate is generated by the Bernoulli process), the tempered random attractor is constructed. In contrast to the usual situation, this random attractor is expected to have infinite Hausdorff and fractal dimension. The simplified model example which demonstrates infinite-dimensionality of the random attractor is also presented.
1910.02430v1
2019-10-23
On the exponential stability of a stratified flow to the 2D IDEAL MHD equations with damping
We study the stability of a type of stratified flows of the two dimensional inviscid incompressible MHD equations with velocity damping. The exponential stability for the perturbation near certain stratified flow is investigated in a strip-type area R*[0,1]. Although the magnetic filed potential is governed by a transport equation, by using the algebraic structure of the incompressible condition, it turns out that the linearized MHD equations around the given stratified flow retain a non-local damping mechanism. After carefully analyzing the non-linear structure and introducing some suitable weighted energy norms, we get the exponential stability by combining the exponential decay in time in the lower order energy with that in the high order energy.
1910.10598v1
2019-10-24
Wigner instability analysis of the damped Hirota equation
We address the modulation instability of the Hirota equation in the presence of stochastic spatial incoherence and linear time-dependent amplification/attenuation processes via the Wigner function approach. We show that the modulation instability remains baseband type, though the damping mechanisms substantially reduce the unstable spectrum independent of the higher-order contributions (e.g. the higher-order nonlinear interaction and the third-order dispersion). Additionally, we find out that the unstable structure due to the Kerr interaction exhibits a significant resilience to the third-order-dispersion stabilizing effects in comparison with the higher-order nonlinearity, as well as a moderate Lorentzian spectrum damping may assist the rising of instability. Finally, we also discuss the relevance of our results in the context of current experiments exploring extreme wave events driven by the modulation instability (e.g. the generation of the so-called rogue waves).
1910.11045v2
2019-11-01
The spherical multipole resonance probe: kinetic damping in its spectrum
The multipole resonance probe is one of the recently developed measurement devices to measure plasma parameter like electron density and temperature based on the concept of active plasma resonance spectroscopy. The dynamical interaction between the probe and the plasma in electrostatic, kinetic description can be modeled in an abstract notation based on functional analytic methods. These methods provide the opportunity to derive a general solution, which is given as the response function of the probe-plasma system. It is defined by the matrix elements of the resolvent of an appropriate dynamical operator. Based on the general solution a residual damping for vanishing pressure can be predicted and can only be explained by kinetic effects. Within this manuscript an explicit response function of the multipole resonance probe is derived. Therefore, the resolvent is determined by its algebraic representation based on an expansion in orthogonal basis functions. This allows to compute an approximated response function and its corresponding spectra, which show additional damping due to kinetic effects.
1911.00514v1
2019-11-04
Current-driven skyrmion motion in granular films
Current-driven skyrmion motion in random granular films is investigated with interesting findings. For a given current, there exists a critical disorder strength below which its transverse motion could either be boosted below a critical damping or be hindered above the critical damping, resulting in current and disorder dependences of skyrmion Hall angle. The boosting comes mainly from the random force that is opposite to the driving force (current). The critical damping depends on the current density and disorder strength. However, the longitudinal motion of a skyrmion is always hindered by the disorder. Above the critical disorder strength, skyrmions are pinned. The disorder-induced random force on a skyrmion can be classified as static and kinetic ones, similar to the friction force in the Newtonian mechanics. In the pinning phase, the static (pinning) random force is transverse to the current density. The kinetic random force is opposite to the skyrmion velocity when skyrmions are in motion. Furthermore, we provide strong evidences that the Thiele equation can perfectly describe skyrmion dynamics in granular films. These findings provide insight to skyrmion motion and should be important for skyrmiontronics.
1911.01245v1
2019-11-05
Reduction of damped, driven Klein-Gordon equations into a discrete nonlinear Schrödinger equation: justification and numerical comparisons
We consider a discrete nonlinear Klein-Gordon equations with damping and external drive. Using a small amplitude ansatz, one usually approximates the equation using a damped, driven discrete nonlinear Schr\"odinger equation. Here, we show for the first time the justification of this approximation by finding the error bound using energy estimate. Additionally, we prove the local and global existence of the Schr\"odinger equation. Numerical simulations are performed that describe the analytical results. Comparisons between discrete breathers of the Klein-Gordon equation and discrete solitons of the discrete nonlinear Schr\"odinger equation are presented.
1911.01631v1
2019-11-14
Stability of coupled solitary wave in biomembranes and nerves
In this work, we consider the electromechanical density pulse as a coupled solitary waves represented by a longitudinal compression wave and an out-of-plane transversal wave (i.e., perpendicular to the membrane surface). We analyzed using, the variational approach, the characteristics of the coupled solitary waves in the presence of damping within the framework of coupled nonlinear Burger-Korteweg-de Vries-Benjamin-Bona-Mahony (BKdV-BBM) equation. It is shown that, the inertia parameter increases the stability of coupled solitary waves while the damping parameter decreases it. Moreover, the presence of damping term induces a discontinuity of stable regions in the inertia-speed parameter space, appearing in he form of an island of points. Bell shape and solitary-shock like wave profiles were obtained by varying the propagation speed and their linear stability spectrum computed. It is shown that bell shape solitary wave exhibit bound state eigenvalue spectrum, therefore stable. On the other hand, the solitary-shock like wave profiles exhibit unbound state eigenvalue spectrum and are therefore generally unstable.
1911.05993v1
2019-11-19
On the theory of the nonlinear Landau damping
An exact solution of the collisionless time-dependent Vlasov equation is found for the first time. By means of this solution the behavior of the Langmuir waves in the nonlinear stage is considered. The analysis is restricted by the consideration of the first nonlinear approximation keeping the second power of the electric strength. It is shown that in general the waves with finite amplitudes are not subject to damping. Only in the linear approximation, when the wave amplitude is very small, are the waves experiencing damping. It is shown that with the definite resonance conditions imposed, the waves become unstable.
1911.08294v2
2019-11-16
Justification of the discrete nonlinear Schrödinger equation from a parametrically driven damped nonlinear Klein-Gordon equation and numerical comparisons
We consider a damped, parametrically driven discrete nonlinear Klein-Gordon equation, that models coupled pendula and micromechanical arrays, among others. To study the equation, one usually uses a small-amplitude wave ansatz, that reduces the equation into a discrete nonlinear Schr\"odinger equation with damping and parametric drive. Here, we justify the approximation by looking for the error bound with the method of energy estimates. Furthermore, we prove the local and global existence of {solutions to the discrete nonlinear} Schr\"odinger equation. To illustrate the main results, we consider numerical simulations showing the dynamics of errors made by the discrete nonlinear equation. We consider two types of initial conditions, with one of them being a discrete soliton of the nonlinear Schr\"odinger equation, that is expectedly approximate discrete breathers of the nonlinear Klein-Gordon equation.
1911.08514v1
2019-11-26
On the Complexity of Minimum-Cost Networked Estimation of Self-Damped Dynamical Systems
In this paper, we consider the optimal design of networked estimators to minimize the communication/measurement cost under the networked observability constraint. This problem is known as the minimum-cost networked estimation problem, which is generally claimed to be NP-hard. The main contribution of this work is to provide a polynomial-order solution for this problem under the constraint that the underlying dynamical system is self-damped. Using structural analysis, we subdivide the main problem into two NP-hard subproblems known as (i) optimal sensor selection, and (ii) minimum-cost communication network. For self-damped dynamical systems, we provide a polynomial-order solution for subproblem (i). Further, we show that the subproblem (ii) is of polynomial-order complexity if the links in the communication network are bidirectional. We provide an illustrative example to explain the methodologies.
1911.11381v1
2020-01-06
A continuous contact force model for impact analysis in multibody dynamics
A new continuous contact force model for contacting problems with regular or irregular contacting surfaces and energy dissipations in multibody systems is presented and discussed in this work. The model is developed according to Hertz law and a hysteresis damping force is introduced for modeling the energy dissipation during the contact process. As it is almost impossible to obtain an analytical solution based on the system dynamic equation, an approximate dynamic equation for the collision system is proposed, achieving a good approximation of the system dynamic equation. An approximate function between deformation velocity and deformation is founded on the approximate dynamic equation, then it is utilized to calculate the energy loss due to the damping force. The model is established through modifying the original formula of the hysteresis damping parameter derived by combining the energy balance and the law of conservation of linear momentum. Numerical results of five different continuous contact models reveal the capability of our new model as well as the effect of the geometry of the contacting surfaces on the dynamic system response.
2001.01344v1
2020-01-06
Boresight Alignment of DArk Matter Particle Explorer
The DArk Matter Particle Explorer (DAMPE) can measure $\gamma$-rays in the energy range from a few GeV to about 10 TeV. The direction of each $\gamma$-ray is reconstructed with respect to the reference system of the DAMPE payload. In this paper, we adopt a maximum likelihood method and use the $\gamma$-ray data centered around several bright point-like sources to measure and correct the angular deviation from the real celestial coordinate system, the so called ``boresight alignment'' of the DAMPE payload. As a check, we also estimate the boresight alignment for some sets of simulation data with artificial orientation and obtain consistent results. The time-dependent boresight alignment analysis does not show evidence for significant variation of the parameters.
2001.01804v1
2020-01-09
Nonlinear inviscid damping near monotonic shear flows
We prove nonlinear asymptotic stability of a large class of monotonic shear flows among solutions of the 2D Euler equations in the channel $\mathbb{T}\times[0,1]$. More precisely, we consider shear flows $(b(y),0)$ given by a function $b$ which is Gevrey smooth, strictly increasing, and linear outside a compact subset of the interval $(0,1)$ (to avoid boundary contributions which are incompatible with inviscid damping). We also assume that the associated linearized operator satisfies a suitable spectral condition, which is needed to prove linear inviscid damping. Under these assumptions, we show that if $u$ is a solution which is a small and Gevrey smooth perturbation of such a shear flow $(b(y),0)$ at time $t=0$, then the velocity field $u$ converges strongly to a nearby shear flow as the time goes to infinity. This is the first nonlinear asymptotic stability result for Euler equations around general steady solutions for which the linearized flow cannot be explicitly solved.
2001.03087v1
2020-02-03
Semi-active $\mathcal{H}_{\infty}$ damping optimization by adaptive interpolation
In this work we consider the problem of semi-active damping optimization of mechanical systems with fixed damper positions. Our goal is to compute a damping that is locally optimal with respect to the $\mathcal{H}_\infty$-norm of the transfer function from the exogenous inputs to the performance outputs. We make use of a new greedy method for computing the $\mathcal{H}_\infty$-norm of a transfer function based on rational interpolation. In this paper, this approach is adapted to parameter-dependent transfer functions. The interpolation leads to parametric reduced-order models that can be optimized more efficiently. At the optimizers we then take new interpolation points to refine the reduced-order model and to obtain updated optimizers. In our numerical examples we show that this approach normally converges fast and thus can highly accelerate the optimization procedure. Another contribution of this work are heuristics for choosing initial interpolation points.
2002.00617v1
2020-03-25
A Novel Wide-Area Control Strategy for Damping of Critical Frequency Oscillations via Modulation of Active Power Injections
This paper proposes a novel wide-area control strategy for modulating the active power injections to damp the critical frequency oscillations in power systems, this includes the inter-area oscillations and the transient frequency swing. The proposed method pursues an efficient utilization of the limited power reserve of existing distributed energy resources (DERs) to mitigate these oscillations. This is accomplished by decoupling the damping control actions at different sites using the oscillation signals of the concerned mode as the power commands. A theoretical basis for this decoupled modulating control is provided. Technically, the desired sole modal oscillation signals are filtered out by linearly combining the system-wide frequencies, which is determined by the linear quadratic regulator based sparsity-promoting (LQRSP) technique. With the proposed strategy, the modulation of each active power injection can be effectively engineered considering the response limit and steady-state output capability of the supporting device. The method is validated based on a two-area test system and is further demonstrated based on the New England 39-bus test system.
2003.11397v1
2020-03-25
Sharp ultimate velocity bounds for the general solution of some linear second order evolution equation with damping and bounded forcing
We consider a class of linear second order differential equations with damping and external force. We investigate the link between a uniform bound on the forcing term and the corresponding ultimate bound on the velocity of solutions, and we study the dependence of that bound on the damping and on the "elastic force". We prove three results. First of all, in a rather general setting we show that different notions of bound are actually equivalent. Then we compute the optimal constants in the scalar case. Finally, we extend the results of the scalar case to abstract dissipative wave-type equations in Hilbert spaces. In that setting we obtain rather sharp estimates that are quite different from the scalar case, in both finite and infinite dimensional frameworks. The abstract theory applies, in particular, to dissipative wave, plate and beam equations.
2003.11579v1
2020-03-28
Energy correction based on fluorescence attenuation of DAMPE
The major scientific goals of DArk Matter Particle Explorer (DAMPE) are to study cosmic-ray electrons (including positrons) and gamma rays from 5 GeV to 10 TeV and nuclei from Z = 1 to 26 up to 100 TeV. The deposited energy measured by the Bismuth Germanate Oxide (BGO) calorimeter of DAMPE is affected by fluorescence attenuation in BGO crystals that are 600 mm long. In this work, an in-orbit attenuation calibration method is reported, and energy correction of the sensitive detector unit of the BGO calorimeter is also presented.
2003.12717v1
2020-04-02
A finite element model for seismic response analysis of free-standing rocking columns with vertical dampers
This paper investigates finite-element modeling of a vertically damped free-standing rocking column. The paper first derives the nonlinear equation of motion for the coupled system and then compares the analytical solution with finite-element model. Finite-element model is being produced using open source framework named OpenSees. The rocking surface is modeled using zero-length fiber cross-section element and the dampers are modeled with two node link elements. In order to simulate energy dissipation during the rocking motion Hilber-Hughes-Taylor numerical dissipative time step integration is being adopted. The paper also compares two types of hysteretic and viscous damping devices and it shows that the viscous damping behavior is favorable when it is used along with a rocking block. The results of analytical model of a rigid block with viscous dampers in MATLAB is then compared with OpenSees model and the paper concludes that the finite-element model compares satisfactory with the analytical model.
2004.01060v1
2020-04-02
Simulating the effect of weak measurements by a phase damping channel and determining different measures of bipartite correlations in nuclear magnetic resonance
Quantum discord is a measure based on local projective measurements which captures quantum correlations that may not be fully captured by entanglement. A change in the measurement process, achieved by replacing rank-one projectors with a weak positive operator-valued measure (POVM), allows one to define weak variants of quantum discord. In this work, we experimentally simulate the effect of a weak POVM on a nuclear magnetic resonance quantum information processor. The two-qubit system under investigation is part of a three-qubit system, where one of the qubits is used as an ancillary to implement the phase damping channel. The strength of the weak POVM is controlled by varying the strength of the phase damping channel. We experimentally observed two weak variants of quantum discord namely, super quantum discord and weak quantum discord, in two-qubit Werner and Bell-diagonal states. The resultant dynamics of the states is investigated as a function of the measurement strength.
2004.01237v2
2020-04-24
A rigorous derivation and energetics of a wave equation with fractional damping
We consider a linear system that consists of a linear wave equation on a horizontal hypersurface and a parabolic equation in the half space below. The model describes longitudinal elastic waves in organic monolayers at the water-air interface, which is an experimental setup that is relevant for understanding wave propagation in biological membranes. We study the scaling regime where the relevant horizontal length scale is much larger than the vertical length scale and provide a rigorous limit leading to a fractionally-damped wave equation for the membrane. We provide the associated existence results via linear semigroup theory and show convergence of the solutions in the scaling limit. Moreover, based on the energy-dissipation structure for the full model, we derive a natural energy and a natural dissipation function for the fractionally-damped wave equation with a time derivative of order 3/2
2004.11830v1
2020-04-25
Pulse-assisted magnetization switching in magnetic nanowires at picosecond and nanosecond timescales with low energy
Detailed understanding of spin dynamics in magnetic nanomaterials is necessary for developing ultrafast, low-energy and high-density spintronic logic and memory. Here, we develop micromagnetic models and analytical solutions to elucidate the effect of increasing damping and uniaxial anisotropy on magnetic field pulse-assisted switching time, energy and field requirements of nanowires with perpendicular magnetic anisotropy and yttrium iron garnet-like spin transport properties. A nanowire is initially magnetized using an external magnetic field pulse (write) and self-relaxation. Next, magnetic moments exhibit deterministic switching upon receiving 2.5 ns-long external magnetic pulses in both vertical polarities. Favorable damping ({\alpha}~0.1-0.5) and anisotropy energies (10^4-10^5 J m^-3) allow for as low as picosecond magnetization switching times. Magnetization reversal with fields below coercivity was observed using spin precession instabilities. A competition or a nanomagnetic trilemma arises among the switching rate, energy cost and external field required. Developing magnetic nanowires with optimized damping and effective anisotropy could reduce the switching energy barrier down to 3163kBT at room temperature. Thus, pulse-assisted picosecond and low energy switching in nanomagnets could enable ultrafast nanomagnetic logic and cellular automata.
2004.12243v1
2020-05-01
Stability of Forced-Damped Response in Mechanical Systems from a Melnikov Analysis
Frequency responses of multi-degree-of-freedom mechanical systems with weak forcing and damping can be studied as perturbations from their conservative limit. Specifically, recent results show how bifurcations near resonances can be predicted analytically from conservative families of periodic orbits (nonlinear normal modes). However, the stability of forced-damped motions is generally determined a posteriori via numerical simulations. In this paper, we present analytic results on the stability of periodic orbits that perturb from conservative nonlinear normal modes. In contrast with prior approaches to the same problem, our method can tackle strongly nonlinear oscillations, high-order resonances and arbitrary types of non-conservative forces affecting the system, as we show with specific examples.
2005.00444v2
2020-05-13
Periodically Forced Nonlinear Oscillators With Hysteretic Damping
We perform a detailed study of the dynamics of a nonlinear, one-dimensional oscillator driven by a periodic force under hysteretic damping, whose linear version was originally proposed and analyzed by Bishop in [1]. We first add a small quadratic stiffness term in the constitutive equation and construct the periodic solution of the problem by a systematic perturbation method, neglecting transient terms as $t\rightarrow \infty$. We then repeat the analysis replacing the quadratic by a cubic term, which does not allow the solutions to escape to infinity. In both cases, we examine the dependence of the amplitude of the periodic solution on the different parameters of the model and discuss the differences with the linear model. We point out certain undesirable features of the solutions, which have also been alluded to in the literature for the linear Bishop's model, but persist in the nonlinear case as well. Finally, we discuss an alternative hysteretic damping oscillator model first proposed by Reid [2], which appears to be free from these difficulties and exhibits remarkably rich dynamical properties when extended in the nonlinear regime.
2005.06187v1
2020-05-13
Magnetic circular dichroism spectra from resonant and damped coupled cluster response theory
A computational expression for the Faraday A term of magnetic circular dichroism (MCD) is derived within coupled cluster response theory and alternative computational expressions for the B term are discussed. Moreover, an approach to compute the (temperature-independent) MCD ellipticity in the context of coupled cluster damped response is presented, and its equivalence with the stick-spectrum approach in the limit of infinite lifetimes is demonstrated. The damped response approach has advantages for molecular systems or spectral ranges with a high density of states. Illustrative results are reported at the coupled cluster singles and doubles level and compared to time-dependent density functional theory results.
2005.06190v1
2020-05-21
Convective Excitation and Damping of Solar-like Oscillations
The last decade has seen a rapid development in asteroseismology thanks to the CoRoT and Kepler missions. With more detailed asteroseismic observations available, it is becoming possible to infer exactly how oscillations are driven and dissipated in solar-type stars. We have carried out three-dimensional (3D) stellar atmosphere simulations together with one-dimensional (1D) stellar structural models of key benchmark turn-off and subgiant stars to study this problem from a theoretical perspective. Mode excitation and damping rates are extracted from 3D and 1D stellar models based on analytical expressions. Mode velocity amplitudes are determined by the balance between stochastic excitation and linear damping, which then allows the estimation of the frequency of maximum oscillation power, $\nu_{\max}$, for the first time based on ab initio and parameter-free modelling. We have made detailed comparisons between our numerical results and observational data and achieved very encouraging agreement for all of our target stars. This opens the exciting prospect of using such realistic 3D hydrodynamical stellar models to predict solar-like oscillations across the HR-diagram, thereby enabling accurate estimates of stellar properties such as mass, radius and age.
2005.10519v1
2020-05-21
Non-Markovian memory in a measurement-based quantum computer
We study the exact open system dynamics of single qubit gates during a measurement-based quantum computation considering non-Markovian environments. We obtain analytical solutions for the average gate fidelities and analyze it for amplitude damping and dephasing channels. We show that the average fidelity is identical for the X-gate and Z-gate and that neither fast application of the projective measurements necessarily implies high gate fidelity, nor slow application necessarily implies low gate fidelity. Indeed, for highly non-Markovian environments, it is of utmost importance to know the best time to perform the measurements, since a huge variation in the gate fidelity may occur given this scenario. Furthermore, we show that while for the amplitude damping the knowledge of the dissipative map is sufficient to determine the best measurement times, i.e. the best times in which measures are taken, the same is not necessarily true for the phase damping. To the later, the time of the set of measures becomes crucial since a phase error in one qubit can fix the phase error that takes place in another.
2005.10883v1
2020-05-22
Improving Dynamic Performance of Low-Inertia Systems through Eigensensitivity Optimization
An increasing penetration of renewable generation has led to reduced levels of rotational inertia and damping in the system. The consequences are higher vulnerability to disturbances and deterioration of the dynamic response of the system. To overcome these challenges, novel converter control schemes that provide virtual inertia and damping have been introduced, which raises the question of optimal distribution of such devices throughout the network. This paper presents a framework for performance-based allocation of virtual inertia and damping to the converter-interfaced generators in a low-inertia system. This is achieved through an iterative, eigensensitivity-based optimization algorithm that determines the optimal controller gains. Two conceptually different problem formulations are presented and validated on a 3-area, 12-bus test system.
2005.11032v1
2020-05-24
Theory of Solutions for An Inextensible Cantilever
Recent equations of motion for the large deflections of a cantilevered elastic beam are analyzed. In the traditional theory of beam (and plate) large deflections, nonlinear restoring forces are due to the effect of stretching on bending; for an inextensible cantilever, the enforcement of arc-length preservation leads to quasilinear stiffness effects and inertial effects that are both nonlinear and nonlocal. For this model, smooth solutions are constructed via a spectral Galerkin approach. Additional compactness is needed to pass to the limit, and this is obtained through a complex procession of higher energy estimates. Uniqueness is obtained through a non-trivial decomposition of the nonlinearity. The confounding effects of nonlinear inertia are overcome via the addition of structural (Kelvin-Voigt) damping to the equations of motion. Local well-posedness of smooth solutions is shown first in the absence of nonlinear inertial effects, and then shown with these inertial effects present, taking into account structural damping. With damping in force, global-in-time, strong well-posedness result is obtained by achieving exponential decay for small data.
2005.11836v2
2020-05-25
Nonlinear losses in magnon transport due to four-magnon scattering
We report on the impact of nonlinear four-magnon scattering on magnon transport in microstructured Co25Fe75 waveguides with low magnetic damping. We determine the magnon propagation length with microfocused Brillouin light scattering over a broad range of excitation powers and detect a decrease of the attenuation length at high powers. This is consistent with the onset of nonlinear four-magnon scattering. Hence, it is critical to stay in the linear regime, when deriving damping parameters from the magnon propagation length. Otherwise, the intrinsic nonlinearity of magnetization dynamics may lead to a misinterpretation of magnon propagation lengths and, thus, to incorrect values of the magnetic damping of the system.
2005.12113v2
2020-06-02
Rigid body dynamics of diamagnetically levitating graphite resonators
Diamagnetic levitation is a promising technique for realizing resonant sensors and energy harvesters, since it offers thermal and mechanical isolation from the environment at zero power. To advance the application of diamagnetically levitating resonators, it is important to characterize their dynamics in the presence of both magnetic and gravitational fields. Here we experimentally actuate and measure rigid body modes of a diamagnetically levitating graphite plate. We numerically calculate the magnetic field and determine the influence of magnetic force on the resonance frequencies of the levitating plate. By analyzing damping mechanisms, we conclude that eddy current damping dominates dissipation in mm-sized plates. We use finite element simulations to model eddy current damping and find close agreement with experimental results. We also study the size-dependent Q-factors (Qs) of diamagnetically levitating plates and show that Qs above 100 million are theoretically attainable by reducing the size of the diamagnetic resonator down to microscale, making these systems of interest for next generation low-noise resonant sensors and oscillators.
2006.01733v3
2020-06-11
Signatures of Spatial Curvature on Growth of Structures
We write down Boltzmann equation for massive particles in a spatially curved FRW universe and solve the approximate line-of-sight solution for evolution of matter density, including the effects of spatial curvature to the first order of approximation. It is shown that memory of early time gravitational potential is affected by presence of spatial curvature. Then we revisit Boltzmann equation for photons in the general FRW background. Using it, we show that how the frequency of oscillations and damping factor (known as Silk damping) changed in presence of spatial curvature. At last, using this modified damping factor in hydrodynamic regime of cosmological perturbations, we find our analytic solution which shows the effects of spatial curvature on growing mode of matter density.
2006.06347v2
2020-06-29
HFQPOs and discoseismic mode excitation in eccentric, relativistic discs. II. Magnetohydrodynamic simulations
Trapped inertial oscillations (r-modes) provide a promising explanation for high-frequency quasi-periodic oscillations (HFQPOs) observed in the emission from black hole X-ray binary systems. An eccentricity (or warp) can excite r-modes to large amplitudes, but concurrently the oscillations are likely damped by magnetohydrodynamic (MHD) turbulence driven by the magnetorotational instability (MRI). We force eccentricity in global, unstratified, zero-net flux MHD simulations of relativistic accretion discs, and find that a sufficiently strong disc distortion generates trapped inertial waves despite this damping. In our simulations, eccentricities above ~ 0.03 in the inner disc excite trapped waves. In addition to the competition between r-mode damping and driving, we observe that larger amplitude eccentric structures modify and in some cases suppress MRI turbulence. Given the variety of distortions (warps as well as eccentricities) capable of amplifying r-modes, the robustness of trapped inertial wave excitation in the face of MRI turbulence in our simulations provides support for a discoseismic explanation for HFQPOs.
2006.16266v2
2020-07-01
An integrable family of torqued, damped, rigid rotors
Expositions of the Euler equations for the rotation of a rigid body often invoke the idea of a specially damped system whose energy dissipates while its angular momentum magnitude is conserved in the body frame. An attempt to explicitly construct such a damping function leads to a more general, but still integrable, system of cubic equations whose trajectories are confined to nested sets of quadric surfaces in angular momentum space. For some choices of parameters, the lines of fixed points along both the largest and smallest moment of inertia axes can be simultaneously attracting. Limiting cases are those that conserve either the energy or the magnitude of the angular momentum. Parallels with rod mechanics, micromagnetics, and particles with effective mass are briefly discussed.
2007.00707v1
2020-07-10
Approximate Time-Optimal Trajectories for Damped Double Integrator in 2D Obstacle Environments under Bounded Inputs
This article provides extensions to existing path-velocity decomposition based time optimal trajectory planning algorithm \cite{kant1986toward} to scenarios in which agents move in 2D obstacle environment under double integrator dynamics with drag term (damped double integrator). Particularly, we extend the idea of a tangent graph \cite{liu1992path} to $\calC^1$-Tangent graph to find continuously differentiable ($\calC^1$) shortest path between any two points. $\calC^1$-Tangent graph has a continuously differentiable ($\calC^1$) path between any two nodes. We also provide analytical expressions for a near time-optimal velocity profile for an agent moving on these shortest paths under the damped double integrator with bounded acceleration.
2007.05155v2
2020-08-11
Ab initio results for the plasmon dispersion and damping of the warm dense electron gas
Warm dense matter (WDM) is an exotic state on the border between condensed matter and dense plasmas. Important occurrences of WDM include dense astrophysical objects, matter in the core of our Earth, as well as matter produced in strong compression experiments. As of late, x-ray Thomson scattering has become an advanced tool to diagnose WDM. The interpretation of the data requires model input for the dynamic structure factor $S(q,\omega)$ and the plasmon dispersion $\omega(q)$. Recently the first \textit{ab initio} results for $S(q,\omega)$ of the homogeneous warm dense electron gas were obtained from path integral Monte Carlo simulations, [Dornheim \textit{et al.}, Phys. Rev. Lett. \textbf{121}, 255001 (2018)]. Here, we analyse the effects of correlations and finite temperature on the dynamic dielectric function and the plasmon dispersion. Our results for the plasmon dispersion and damping differ significantly from the random phase approximation and from earlier models of the correlated electron gas. Moreover, we show when commonly used weak damping approximations break down and how the method of complex zeros of the dielectric function can solve this problem for WDM conditions.
2008.04605v1
2020-08-18
Survey of 360$^{\circ}$ domain walls in magnetic heterostructures: topology, chirality and current-driven dynamics
Chirality and current-driven dynamics of topologically nontrivial 360$^{\circ}$ domain walls (360DWs) in magnetic heterostructures (MHs) are systematically investigated. For MHs with normal substrates, the static 360DWs are N\'{e}el-type with no chirality. While for those with heavy-metal substrates, the interfacial Dzyaloshinskii-Moriya interaction (iDMI) therein makes 360DWs prefer specific chirality. Under in-plane driving charge currents, as the direct result of "full-circle" topology a certain 360DW does not undergo the "Walker breakdown"-type process like a well-studied 180$^{\circ}$ domain wall as the current density increases. Alternatively, it keeps a fixed propagating mode (either steady-flow or precessional-flow, depending on the effective damping constant of the MH) until it collapses or changes to other types of solition when the current density becomes too high. Similarly, the field-like spin-orbit torque (SOT) has no effects on the dynamics of 360DWs, while the anti-damping SOT has. For both modes, modifications to the mobility of 360DWs by iDMI and anti-damping SOT are provided.
2008.08196v1
2020-08-20
Combining $T_1$ and $T_2$ estimation with randomized benchmarking and bounding the diamond distance
The characterization of errors in a quantum system is a fundamental step for two important goals. First, learning about specific sources of error is essential for optimizing experimental design and error correction methods. Second, verifying that the error is below some threshold value is required to meet the criteria of threshold theorems. We consider the case where errors are dominated by the generalized damping channel (encompassing the common intrinsic processes of amplitude damping and dephasing) but may also contain additional unknown error sources. We demonstrate the robustness of standard $T_1$ and $T_2$ estimation methods and provide expressions for the expected error in these estimates under the additional error sources. We then derive expressions that allow a comparison of the actual and expected results of fine-grained randomized benchmarking experiments based on the damping parameters. Given the results of this comparison, we provide bounds that allow robust estimation of the thresholds for fault-tolerance.
2008.09197v1
2020-08-25
The atomic damping basis and the collective decay of interacting two-level atoms
We find analytical solutions to the evolution of interacting two-level atoms when the master equation is symmetric under the permutation of atomic labels. The master equation includes atomic independent dissipation. The method to obtain the solutions is: First, we use the system symmetries to describe the evolution in an operator space whose dimension grows polynomially with the number of atoms. Second, we expand the solutions in a basis composed of eigenvectors of the dissipative part of the master equation that models the independent dissipation of the atoms. This atomic damping basis is an atomic analog to the damping basis used for bosonic fields. The solutions show that the system decays as a sum of sub- and super-radiant exponential terms.
2008.11056v1
2020-09-11
Accuracy of relativistic Cowling approximation in protoneutron star asteroseismology
The relativistic Cowling approximation, where the metric perturbations are neglected during the fluid oscillations, is often adopted for considering the gravitational waves from the protoneutron stars (PNSs) provided via core-collapse supernova explosions. In this study, we evaluate how the Cowling approximation works well by comparing the frequencies with the Cowling approximation to those without the approximation. Then, we find that the behavior of the frequencies with the approximation is qualitatively the same way as that without the approximation, where the frequencies with the approximation can totally be determined within $\sim 20\%$ accuracy. In particular, the fundamental mode with the Cowling approximation is overestimated. In addition, we also discuss the damping time of various eigenmodes in gravitational waves from the PNSs, where the damping time for the PNSs before the avoided crossing between the $f$- and $g_1$-modes, is quite different from that for cold neutron stars, but it is more or less similar to that for cold neutron stars in the later phase. The damping time is long enough compared to the typical time interval of short-Fourier transformation that often used in the analysis, and that ideally guarantees the validity of the transformation.
2009.05206v1
2020-09-17
Resonant absorption: transformation of compressive motions into vortical motions
This paper investigates the changes in spatial properties when magnetohydrodynamic (MHD) waves undergo resonant damping in the Alfv\'en continuum. The analysis is carried out for a 1D cylindrical pressure-less plasma with a straight magnetic field. The effect of the damping on the spatial wave variables is determined by using complex frequencies that arise as a result of the resonant damping. Compression and vorticity are used to characterise the spatial evolution of the MHD wave. The most striking result is the huge spatial variation in the vorticity component parallel to the magnetic field. Parallel vorticity vanishes in the uniform part of the equilibrium. However, when the MHD wave moves into the non-uniform part, parallel vorticity explodes to values that are orders of magnitude higher than those attained by the transverse components in planes normal to the straight magnetic field. In the non-uniform part of the equilibrium plasma, the MHD wave is controlled by parallel vorticity and resembles an Alfv\'en wave, with the unfamiliar property that it has pressure variations even in the linear regime.
2009.08152v1
2020-09-19
Random vibrations of stress-driven nonlocal beams with external damping
Stochastic flexural vibrations of small-scale Bernoulli-Euler beams with external damping are investigated by stress-driven nonlocal mechanics. Damping effects are simulated considering viscous interactions between beam and surrounding environment. Loadings are modeled by accounting for their random nature. Such a dynamic problem is characterized by a stochastic partial differential equation in space and time governing time-evolution of the relevant displacement field. Differential eigenanalyses are performed to evaluate modal time coordinates and mode shapes, providing a complete stochastic description of response solutions. Closed-form expressions of power spectral density, correlation function, stationary and non-stationary variances of displacement fields are analytically detected. Size-dependent dynamic behaviour is assessed in terms of stiffness, variance and power spectral density of displacements. The outcomes can be useful for design and optimization of structural components of modern small-scale devices, such as Micro- and Nano-Electro-Mechanical-Systems (MEMS and NEMS).
2009.09184v1
2020-09-20
Correction Method for the Readout Saturation of the DAMPE Calorimeter
The DArk Matter Particle Explorer (DAMPE) is a space-borne high energy cosmic-ray and $\gamma$-ray detector which operates smoothly since the launch on December 17, 2015. The bismuth germanium oxide (BGO) calorimeter is one of the key sub-detectors of DAMPE used for energy measurement and electron proton identification. For events with total energy deposit higher than decades of TeV, the readouts of PMTs coupled on the BGO crystals would become saturated, which results in an underestimation of the energy measurement. Based on detailed simulations, we develop a correction method for the saturation effect according to the shower development topologies and energies measured by neighbouring BGO crystals. The verification with simulated and on-orbit events shows that this method can well reconstruct the energy deposit in the saturated BGO crystal.
2009.09438v1
2020-09-21
Complete complementarity relations in system-environment decoherent dynamics
We investigate the system-environment information flow from the point of view ofcomplete complementarity relations. We consider some commonly used noisy quantum channels:Amplitude damping, phase damping, bit flip, bit-phase flip, phase flip, depolarizing, and correlatedamplitude damping. By starting with an entangled bipartite pure quantum state, with the linearentropy being the quantifier of entanglement, we study how entanglement is redistributed and turnedinto general correlations between the degrees of freedom of the whole system. For instance, it ispossible to express the entanglement entropy in terms of the multipartite quantum coherence or interms of the correlated quantum coherence of the different partitions of the system. In addition,we notice that for the depolarizing and bit-phase flip channels the wave and particle aspects candecrease or increase together. Besides, by considering the environment as part of a pure quantumsystem, the linear entropy is shown to be not just a measure of mixedness of a particular subsystem,but a correlation measure of the subsystem with rest of the world.
2009.09769v3
2020-09-15
Delay-induced resonance suppresses damping-induced unpredictability
Combined effects of the damping and forcing in the underdamped time-delayed Duffing oscillator are considered in this paper. We analyze the generation of a certain damping-induced unpredictability, due to the gradual suppression of interwell oscillations. We find the minimal amount of the forcing amplitude and the right forcing frequency to revert the effect of the dissipation, so that the interwell oscillations can be restored, for different time delay values. This is achieved by using the delay-induced resonance, in which the time delay replaces one of the two periodic forcings present in the vibrational resonance. A discussion in terms of the time delay of the critical values of the forcing for which the delay-induced resonance can tame the dissipation effect is finally carried out.
2009.11760v1
2020-10-06
A dissiptive logarithmic type evolution equation: asymptotic profile and optimal estimates
We introduce a new model of the logarithmic type of wave-like equation with a nonlocal logarithmic damping mechanism, which is rather weakly effective as compared with frequently studied fractional damping cases. We consider the Cauchy problem for this new model in the whole space, and study the asymptotic profile and optimal decay and/or blowup rates of solutions as time goes to infinity in L^{2}-sense. The operator L considered in this paper was used to dissipate the solutions of the wave equation in the paper studied by Charao-Ikehata in 2020, and in the low frequency parameters the principal part of the equation and the damping term is rather weakly effective than those of well-studied power type operators.
2010.02485v1
2020-10-12
Line-drag damping of Alfvén waves in radiatively driven winds of magnetic massive stars
Line-driven stellar winds from massive (OB) stars are subject to a strong line-deshadowing instability. Recently, spectropolarimetric surveys have collected ample evidence that a subset of Galactic massive stars hosts strong surface magnetic fields. We investigate here the propagation and stability of magneto-radiative waves in such a magnetised, line-driven wind. Our analytic, linear stability analysis includes line-scattering from the stellar radiation, and accounts for both radial and non-radial perturbations. We establish a bridging law for arbitrary perturbation wavelength after which we analyse separately the long- and short-wavelength limits. While long-wavelength radiative and magnetic waves are found to be completely decoupled, a key result is that short-wavelength, radially propagating Alfv\'en waves couple to the scattered radiation field and are strongly damped due to the line-drag effect. This damping of magnetic waves in a scattering-line-driven flow could have important effects on regulating the non-linear wind dynamics, and so might also have strong influence on observational diagnostics of the wind structure and clumping of magnetic line-driven winds.
2010.05650v1
2020-10-20
Long Time Behavior of a Quasilinear Hyperbolic System Modelling Elastic Membranes
The paper studies the long time behavior of a system that describes the motion of a piece of elastic membrane driven by surface tension and inner air pressure. The system is a degenerate quasilinear hyperbolic one that involves the mean curvature, and also includes a damping term that models the dissipative nature of genuine physical systems. With the presence of damping, a small perturbation of the sphere converges exponentially in time to the sphere, and without the damping the evolution that is $\varepsilon$-close to the sphere has life span longer than $\varepsilon^{-1/6}$. Both results are proved using a new Nash-Moser-H\"{o}rmander type theorem proved by Baldi and Haus.
2010.10663v6
2020-10-09
Rapid parameter determination of discrete damped sinusoidal oscillations
We present different computational approaches for the rapid extraction of the signal parameters of discretely sampled damped sinusoidal signals. We compare time- and frequency-domain-based computational approaches in terms of their accuracy and precision and computational time required in estimating the frequencies of such signals, and observe a general trade-off between precision and speed. Our motivation is precise and rapid analysis of damped sinusoidal signals as these become relevant in view of the recent experimental developments in cavity-enhanced polarimetry and ellipsometry, where the relevant time scales and frequencies are typically within the $\sim1-10\,\mu$s and $\sim1-100$MHz ranges, respectively. In such experimental efforts, single-shot analysis with high accuracy and precision becomes important when developing experiments that study dynamical effects and/or when developing portable instrumentations. Our results suggest that online, running-fashion, microsecond-resolved analysis of polarimetric/ellipsometric measurements with fractional uncertainties at the $10^{-6}$ levels, is possible, and using a proof-of-principle experimental demonstration we show that using a frequency-based analysis approach we can monitor and analyze signals at kHz rates and accurately detect signal changes at microsecond time-scales.
2010.11690v1
2020-10-22
Effective shear and bulk viscosities for anisotropic flow
We evaluate the viscous damping of anisotropic flow in heavy-ion collisions for arbitrary temperature-dependent shear and bulk viscosities. We show that the damping is solely determined by effective shear and bulk viscosities, which are weighted averages over the temperature. We determine the relevant weights for nucleus-nucleus collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV and 200 GeV, corresponding to the maximum LHC and RHIC energies, by running ideal and viscous hydrodynamic simulations. The effective shear viscosity is driven by temperatures below $210$ MeV at RHIC, and below $280$ MeV at the LHC, with the largest contributions coming from the lowest temperatures, just above freeze-out. The effective bulk viscosity is driven by somewhat higher temperatures, corresponding to earlier stages of the collision. We show that at a fixed collision energy, the effective viscosity is independent of centrality and system size, to the same extent as the mean transverse momentum of outgoing hadrons. The variation of viscous damping is determined by Reynolds number scaling.
2010.11919v2
2020-10-23
Is PSR J0855$-$4644 responsible for the 1.4 TeV electron spectral bump hinted by DAMPE?
DAMPE observation on the cosmic ray electron spectrum hints a narrow excess at $\sim$ 1.4 TeV. Although the excess can be ascribed to dark matter particles, pulsars and pulsar wind nebulae are believed to be a more natural astrophysical origin: electrons injected from nearby pulsars at their early ages can form a bump-like feature in the spectrum due to radiative energy losses. In this paper, with a survey of nearby pulsars, we find 4 pulsars that may have notable contributions to $\sim$ 1.4 TeV cosmic ray electrons. Among them, PSR J0855$-$4644 has a spin down luminosity more than 50 times higher than others and presumably dominates the electron fluxes from them. X-ray observations on the inner compact part (which may represent a tunnel for the transport of electrons from the pulsar) of PWN G267.0$-$01.0 are then used to constrain the spectral index of high energy electrons injected by the pulsar. We show that high-energy electrons released by PSR J0855$-$4644 could indeed reproduce the 1.4 TeV spectral feature hinted by the DAMPE with reasonable parameters.
2010.12170v1
2020-11-02
Effect of retardation on the frequency and linewidth of plasma resonances in a two-dimensional disk of electron gas
We theoretically analyze dominant plasma modes in a two-dimensional disk of electron gas by calculating the absorption of an incident electromagnetic wave. The problem is solved in a self-consistent approximation, taking into account electromagnetic retardation effects. We use the Drude model to describe the conductivity of the system. The absorption spectrum exhibits a series of peaks corresponding to the excitation of plasma waves. The position and linewidth of the peaks designating, respectively, the frequency and damping rate of the plasma modes. We estimate the influence of retardation effects on the frequency and linewidth of the fundamental (dipole) and axisymmetric (quadrupole) plasma modes both numerically and analytically. We find the net damping rate of the modes to be dependent on not only the sum of the radiative and collisional decays but also their intermixture, even for small retardation. We show that the net damping rate can be noticeably less than that determined by collisions alone.
2011.00877v1
2020-11-05
Low-Complexity Models for Acoustic Scene Classification Based on Receptive Field Regularization and Frequency Damping
Deep Neural Networks are known to be very demanding in terms of computing and memory requirements. Due to the ever increasing use of embedded systems and mobile devices with a limited resource budget, designing low-complexity models without sacrificing too much of their predictive performance gained great importance. In this work, we investigate and compare several well-known methods to reduce the number of parameters in neural networks. We further put these into the context of a recent study on the effect of the Receptive Field (RF) on a model's performance, and empirically show that we can achieve high-performing low-complexity models by applying specific restrictions on the RFs, in combination with parameter reduction methods. Additionally, we propose a filter-damping technique for regularizing the RF of models, without altering their architecture and changing their parameter counts. We will show that incorporating this technique improves the performance in various low-complexity settings such as pruning and decomposed convolution. Using our proposed filter damping, we achieved the 1st rank at the DCASE-2020 Challenge in the task of Low-Complexity Acoustic Scene Classification.
2011.02955v1
2020-11-23
Sharp lifespan estimates for the weakly coupled system of semilinear damped wave equations in the critical case
The open question, which seems to be also the final part, in terms of studying the Cauchy problem for the weakly coupled system of damped wave equations or reaction-diffusion equations, is so far known as the sharp lifespan estimates in the critical case. In this paper, we mainly investigate lifespan estimates for solutions to the weakly coupled system of semilinear damped wave equations in the critical case. By using a suitable test function method associated with nonlinear differential inequalities, we catch upper bound estimates for the lifespan. Moreover, we establish polynomial-logarithmic type time-weighted Sobolev spaces to obtain lower bound estimates for the lifespan in low spatial dimensions. Then, together with the derived lifespan estimates, new and sharp results on estimates for the lifespan in the critical case are claimed. Finally, we give an application of our results to the semilinear reaction-diffusion system in the critical case.
2011.11366v2
2020-12-10
Stochastic Damped L-BFGS with Controlled Norm of the Hessian Approximation
We propose a new stochastic variance-reduced damped L-BFGS algorithm, where we leverage estimates of bounds on the largest and smallest eigenvalues of the Hessian approximation to balance its quality and conditioning. Our algorithm, VARCHEN, draws from previous work that proposed a novel stochastic damped L-BFGS algorithm called SdLBFGS. We establish almost sure convergence to a stationary point and a complexity bound. We empirically demonstrate that VARCHEN is more robust than SdLBFGS-VR and SVRG on a modified DavidNet problem -- a highly nonconvex and ill-conditioned problem that arises in the context of deep learning, and their performance is comparable on a logistic regression problem and a nonconvex support-vector machine problem.
2012.05783v1
2020-12-29
Twist-induced Near-field Thermal Switch Using Nonreciprocal Surface Magnon-Polaritons
We explore that two ferromagnetic insulator slabs host a strong twist-induced near-field radiative heat transfer in the presence of twisted magnetic fields. Using the formalism of fluctuational electrodynamics, we find the existence of large twist-induced thermal switch ratio in large damping condition and nonmonotonic twist manipulation for heat transfer in small damping condition, associated with the different twist-induced effects of nonreciprocal elliptic surface magnon-polaritons, hyperbolic surface magnon-polaritons, and twist-non-resonant surface magnon-polaritons. Moreover, the near-field radiative heat transfer can be significantly enhanced by the twist-non-resonant surface magnon-polaritons in the ultra-small damping condition. Such twist-induced effect is applicable for other kinds of anisotropic slabs with timereversal symmetry breaking. Our findings provide a way to twisted and magnetic control in nanoscale thermal management and improve it with twistronics concepts.
2012.14733v1
2021-01-04
The damped harmonic oscillator at the classical limit of the Snyder-de Sitter space
Valtancoli in his paper entitled [P. Valtancoli, Canonical transformations, and minimal length J. Math. Phys. 56, 122107 (2015)] has shown how the deformation of the canonical transformations can be made compatible with the deformed Poisson brackets. Based on this work and through an appropriate canonical transformation, we solve the problem of one dimensional (1D) damped harmonic oscillator at the classical limit of the Snyder-de Sitter (SdS) space. We show that the equations of the motion can be described by trigonometric functions with frequency and period depending on the deformed and the damped parameters. We eventually discuss the influences of these parameters on the motion of the system.
2101.01223v2