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2018-01-23
The effect of liquid on the vibrational intensity of a wineglass at steady state resonance
As a liquid is inserted into a wineglass, the natural frequency of the wineglass decreases. This phenomenon, known as pitch lowering, is well explained in past papers. However, previous literature have not yet mentioned that pitch lowering also reduces the resonance intensity of a wineglass. Thus, this present paper aims to extend the body of research on this topic by describing the relationship between pitch lowering and its effect on resonation intensity. To do so, we identify the vibrating wineglass wall as a damped harmonic oscillator, derive a theoretical model, and find that the resonance intensity of the wineglass is proportional to the square of its natural frequency, under the assumption that damping stays constant. However, our experiments showed the coefficient of damping to increase with respect to the amount of liquid, which caused the data to deviate from its theoretical predictions. We conclude by discussing the accuracy and limitation of our proposed model.
1801.07514v5
2018-02-12
Chance-constrained optimal location of damping control actuators under wind power variability
This paper proposes a new probabilistic energy-based method to determine the optimal installation location of electronically-interfaced resources (EIRs) considering dynamic reinforcement under wind variability in systems with high penetration of wind power. The oscillation energy and total action are used to compare the dynamic performance for different EIR locations. A linear approximation of the total action critically reduces the computational time from hours to minutes. Simulating an IEEE-39 bus system with 30% of power generation sourced from wind, a chance-constrained optimization is carried out to decide the location of an energy storage system (ESS) adding damping to the system oscillations. The results show that the proposed method, selecting the bus location that guarantees the best dynamic performance with highest probability, is superior to both traditional dominant mode analysis and arbitrary benchmarks for damping ratios.
1802.04354v1
2018-02-21
On the vibron-polaron damping in quasi 1D macromolecular chains
The properties of the intramolecular vibrational excitation (vibron) in a quasi 1D macromolecular structure are studied. It is supposed that due to the vibron interaction with optical phonon modes, a vibron might form partially dressed small polaron states. The properties of these states are investigated in dependence on the basic system parameters and temperature of a thermal bath. We also investigate the process of damping of the polaron amplitude as a function of temperature and vibron-phonon coupling strength. Two different regimes of the polaron damping are found and discussed.
1802.07424v1
2018-02-27
Impact of damping on superconducting gap oscillations induced by intense Terahertz pulses
We investigate the interplay between gap oscillations and damping in the dynamics of superconductors taken out of equilibrium by strong optical pulses with sub-gap Terahertz frequencies. A semi-phenomenological formalism is developed to include the damping within the electronic subsystem that arises from effects beyond BCS, such as interactions between Bogoliubov quasiparticles and decay of the Higgs mode. Such processes are conveniently expressed as $T_{1}$ and $T_{2}$ times in the standard pseudospin language for superconductors. Comparing with data on NbN that we report here, we argue that the superconducting dynamics in the picosecond time scale, after the pump is turned off, is governed by the $T_{2}$ process.
1802.09711v2
2018-02-28
Analysis of imperfections in the coherent optical excitation of single atoms to Rydberg states
We study experimentally various physical limitations and technical imperfections that lead to damping and finite contrast of optically-driven Rabi oscillations between ground and Rydberg states of a single atom. Finite contrast is due to preparation and detection errors and we show how to model and measure them accurately. Part of these errors originates from the finite lifetime of Rydberg states and we observe its $n^3$-scaling with the principal quantum number $n$. To explain the damping of Rabi oscillations, we use simple numerical models, taking into account independently measured experimental imperfections, and show that the observed damping actually results from the accumulation of several small effects, each at the level of a few percents. We discuss prospects for improving the coherence of ground-Rydberg Rabi oscillations in view of applications in quantum simulation and quantum information processing with arrays of single Rydberg atoms.
1802.10424v1
2018-03-07
Connecting dissipation and noncommutativity: A Bateman system case study
Quantum effects on a pair of Bateman oscillators embedded in an ambient noncommutative space (Moyal plane) is analyzed using both path integral and canonical quantization schemes within the framework of Hilbert-Schmidt operator formulation. We adopt a method which is distinct from the one which employs 't Hooft's scheme of quantization, carried out earlier in the literature where the ambient space was taken to be commutative. Our quantization shows that we end up finally again with a Bateman system except that the damping factor undergoes renormalization. The corresponding expression shows that the renormalized damping factor can be non-zero even if "bare" one is zero to begin with. Conversely, the noncommuatative parameter $\theta$, taken to be a free one now, can be fine-tuned to get a vanishing renormalized damping factor. This indicates a duality between dissipative commutative theory and non-dissipative noncommutative theory.
1803.03334v1
2018-03-18
A machine learning method to separate cosmic ray electrons from protons from 10 to 100 GeV using DAMPE data
DArk Matter Particle Explorer (DAMPE) is a general purpose high energy cosmic ray and gamma ray observatory, aiming to detect high energy electrons and gammas in the energy range 5 GeV to 10 TeV and hundreds of TeV for nuclei. This paper provides a method using machine learning to identify electrons and separate them from gammas,protons,helium and heavy nuclei with the DAMPE data from 2016 January 1 to 2017 June 30, in energy range from 10 to 100 GeV.
1803.06628v2
2018-03-20
Estimating Participation Factors and Mode Shapes for Electromechanical Oscillations in Ambient Conditions
In this paper, a new technique is applied to conduct mode identification using ambient measurement data. The proposed hybrid measurement- and model-based method can accurately estimate the system state matrix in ambient conditions, the eigenvalues and eigenvectors of which readily provide all the modal knowledge including frequencies, damping ratios, mode shapes, and more importantly, participation factors. Numerical simulations show that the proposed technique is able to provide accurate estimation of modal knowledge for all modes. In addition, the discrepancy between the participation factor and the mode shape is shown through a numerical example, demonstrating that using the mode shape may not effectively pinpoint the best location for damping control. Therefore, the proposed technique capable of estimating participation factors may greatly facilitate designing damping controls.
1803.07264v1
2018-03-21
Globally Stable Output Feedback Synchronization of Teleoperation with Time-Varying Delays
This paper presents a globally stable teleoperation control strategy for systems with time-varying delays that eliminates the need for velocity measurements through novel augmented Immersion and Invariance velocity observers. The new observers simplify a recent constructive Immersion and Invariance velocity observer to achieve globally convergent velocity estimation with only $n+2$ states, where $n$ is the number of degrees of freedom of the master and slave robots. They introduce dynamic scaling factors to accelerate the speed of convergence of the velocity estimates and, thus, to limit the energy generated by the velocity estimation errors and to guarantee sufficient estimate-based damping injection to dissipate the energy generated by the time-varying delays. The paper shows that Proportional plus damping control with the simplified and augmented Immersion and Invariance-based velocity observers can synchronize the free master and slave motions in the presence of time-varying delays without using velocity measurements. Numerical results illustrate the estimation performance of the new observers and the stability of a simulated two degrees-of-freedom nonlinear teleoperation system with time-varying delays under the proposed output feedback Proportional plus damping control.
1803.08159v1
2018-03-29
Stochastic conformal multi-symplectic method for damped stochastic nonlinear Schrodinger equation
In this paper, we propose a stochastic conformal multi-symplectic method for a class of damped stochastic Hamiltonian partial differential equations in order to inherit the intrinsic properties, and apply the numerical method to solve a kind of damped stochastic nonlinear Schrodinger equation with multiplicative noise. It is shown that the stochastic conformal multi-symplectic method preserves the discrete stochastic conformal multi-symplectic conservation law, the discrete charge exponential dissipation law almost surely, and we also deduce the recurrence relation of the discrete global energy. Numerical experiments are preformed to verify the good performance of the proposed stochastic conformal multi-symplectic method, compared with a Crank-Nicolson type method. Finally, we present the mean square convergence result of the proposed numerical method in temporal direction numerically.
1803.10885v1
2018-04-01
Bounded Connectivity-Preserving Coordination of Networked Euler-Lagrange Systems
This paper derives sufficient conditions for bounded distributed connectivity-preserving coordination of Euler-Lagrange systems with only position measurements and with system uncertainties, respectively. The paper proposes two strategies that suitably scale conventional gradient-based controls to account for the actuation bounds and to reserve sufficient actuation for damping injection. For output feedback control of networked systems with only position measurements, the paper incorporates a first-order filter to estimate velocities and to inject damping for stability. For networks of uncertain systems, the paper augments conventional linear filter-based adaptive compensation with damping injection to maintain the local connectivity of the network. Analyses based on monotonically decreasing Lyapunov-like functions and Barbalat's lemma lead to sufficient conditions for bounded local connectivity-preserving coordination of Euler-Lagrange networks under the two strategies. The sufficient conditions clarify the interrelationships among the bounded actuations, initial system velocities and initial inter-system distances. Simulation results validate these conditions.
1804.00333v1
2018-04-09
Damping and clustering into crowded environment of catalytic chemical oscillators
A system formed by a crowded environment of catalytic obstacles and complex oscillatory chemical reactions is inquired. The obstacles are static spheres of equal radius, which are placed in a random way. The chemical reactions are carried out in a fluid following a multiparticle collision scheme where the mass, energy and local momentum are conserved. Firstly, it is explored how the presence of catalytic obstacles changes the oscillatory dynamics from a limit cycle to a fix point reached after a damping. The damping is characterized by the decay constant, which grows linearly with volume fraction for low values of the mesoscale collision time and the catalytic reaction constant. Additionally, it is shown that, although the distribution of obstacles is random, there are regions in the system where the catalytic chemical reactions are favored. This entails that in average the radius of gyrations of catalytic chemical reaction does not match with the radius of gyration of obstacles, that is, clusters of reactions emerge on the catalytic obstacles, even when the diffusion is significant.
1804.03174v1
2018-04-11
A global existence result for a semilinear wave equation with scale-invariant damping and mass in even space dimension
In the present article a semilinear wave equation with scale-invariant damping and mass is considered. The global (in time) existence of radial symmetric solutions in even spatial dimension $n$ is proved using weighted $L^\infty-L^\infty$ estimates, under the assumption that the multiplicative constants, which appear in the coefficients of damping and of mass terms, fulfill an interplay condition which yields somehow a "wave-like" model. In particular, combining this existence result with a recently proved blow-up result, a suitable shift of Strauss exponent is proved to be the critical exponent for the considered model. Moreover, the still open part of a conjecture done by D'Abbicco - Lucente - Reissig is proved to be true in the massless case.
1804.03978v1
2018-04-17
Modelling linewidths of Kepler red giants in NGC 6819
We present a comparison between theoretical, frequency-dependent, damping rates and linewidths of radial-mode oscillations in red-giant stars located in the open cluster NGC 6819. The calculations adopt a time-dependent non-local convection model, with the turbulent pressure profile being calibrated to results of 3D hydrodynamical simulations of stellar atmospheres. The linewidths are obtained from extensive peakbagging of Kepler lightcurves. These observational results are of unprecedented quality owing to the long continuous observations by Kepler. The uniqueness of the Kepler mission also means that, for asteroseismic properties, this is the best data that will be available for a long time to come. We therefore take great care in modelling nine RGB stars in NGC 6819 using information from 3D simulations to obtain realistic temperature stratifications and calibrated turbulent pressure profiles. Our modelled damping rates reproduce well the Kepler observations, including the characteristic depression in the linewidths around the frequency of maximum oscillation power. Furthermore, we thoroughly test the sensitivity of the calculated damping rates to changes in the parameters of the nonlocal convection model.
1804.06255v1
2018-04-24
$\text{Co}_{25}\text{Fe}_{75}$ Thin Films with Ultralow Total Damping
We measure the dynamic properties of $\text{Co}_{25}\text{Fe}_{75}$ thin films grown by dc magnetron sputtering. Using ferromagnetic resonance spectroscopy, we demonstrate an ultralow total damping parameter in the out-of-plane configuration of < 0.0013, whereas for the in-plane configuration we find a minimum total damping of < 0.0020. In both cases, we observe low inhomogeneous linewidth broadening in macroscopic films. We observe a minimum full-width half-maximum linewidth of 1 mT at 10 GHz resonance frequency for a 12 nm thick film. We characterize the morphology and structure of these films as a function of seed layer combinations and find large variation of the qualitative behavior of the in-plane linewidth vs. resonance frequency. Finally, we use wavevector-dependent Brillouin light scattering spectroscopy to characterize the spin-wave dispersion at wave vectors up to 23 $\mu \text{m}^{-1}$.
1804.08786v1
2018-05-15
Simple Nonlinear Models with Rigorous Extreme Events and Heavy Tails
Extreme events and the heavy tail distributions driven by them are ubiquitous in various scientific, engineering and financial research. They are typically associated with stochastic instability caused by hidden unresolved processes. Previous studies have shown that such instability can be modeled by a stochastic damping in conditional Gaussian models. However, these results are mostly obtained through numerical experiments, while a rigorous understanding of the underlying mechanism is sorely lacking. This paper contributes to this issue by establishing a theoretical framework, in which the tail density of conditional Gaussian models can be rigorously determined. In rough words, we show that if the stochastic damping takes negative values, the tail is polynomial; if the stochastic damping is nonnegative but takes value zero, the tail is between exponential and Gaussian. The proof is established by constructing a novel, product-type Lyapunov function, where a Feynman-Kac formula is applied. The same framework also leads to a non-asymptotic large deviation bound for long-time averaging processes.
1805.05615v3
2018-06-18
Theoretical interpretations of DAMPE first results: a critical review
The DAMPE experiment recently published its first results on the lepton ($e^+ + e^-$) cosmic-ray (CRs) flux. These results are of importance since they account for the first direct detection of the lepton break around the energy of 1 TeV and confirm the discoveries of ground-based Cherenkov detectors. Meanwhile they reveal a new high-energy feature in the spectrum which triggered a lot of excitement on the theory side, when interpreted as the typical signature of leptophilic dark-matter annihilation. In this proceeding I mainly focus on the theoretical understanding of the lepton break. Then I quickly review the status of the more speculative line-like DAMPE excess, whose astrophysical (pulsar) or exotic (dark matter) explanation is strongly constrained by multi-messenger astronomy.
1806.06534v1
2018-06-22
Optimal Design of Virtual Inertia and Damping Coefficients for Virtual Synchronous Machines
Increased penetration of inverter-connected renewable energy sources (RES) in the power system has resulted in a decrease in available rotational inertia which serves as an immediate response to frequency deviation due to disturbances. The concept of virtual inertia has been proposed to combat this decrease by enabling the inverters to produce active power in response to a frequency deviation like a synchronous generator. In this paper, we present an algorithm to optimally design the inertia and damping coefficient required for an inverter-based virtual synchronous machine (VSM) to participate efficiently in the inertia response portion of primary frequency control. We design the objective function to explicitly trade-off between competing objectives such as the damping rate the the frequency nadir. Specifically, we formulate the design problem as a constrained and regularized H2 norm minimization problem, and develop an efficient gradient algorithm for this non-convex problem. This proposed algorithm is applied to a test case to demonstrate its performance against existing methods.
1806.08488v1
2018-07-17
Bipartite and Tripartite Entanglement for Three Damped Driven Qubits
We investigate bipartite and tripartite entanglement in an open quantum system, specifically three qubits, all of which are damped, and one of which is driven. We adapt a systematic approach in calculating the entanglement of various bipartite splits usinga generalized concurrence as an indicator of entanglement. Our calculations are based on a direct detection scheme that is a particular unravelling of the density matrix. This system has a collective dipole-dipole energy shift that couples the atoms and the dissipation is via partially collective spontaneous emission described by the Lehmberg-Agarwal master equation.Our results are unravelling dependent, but apply to applications of entanglement based on direct detection. We also calculate the three-way tangle or residual entanglement for this system. We present calculations for a variety of driving and damping rates, and examine what decay rate is adequate for the system to be reduced to two qubits with a readout port. We also consider a specific model of three atoms located at particular positions in free space.
1807.06178v1
2018-07-17
Boundary-to-Displacement Asymptotic Gains for Wave Systems With Kelvin-Voigt Damping
We provide estimates for the asymptotic gains of the displacement of a vibrating string with endpoint forcing, modeled by the wave equation with Kelvin-Voigt and viscous damping and a boundary disturbance. Two asymptotic gains are studied: the gain in the L2 spatial norm and the gain in the spatial sup norm. It is shown that the asymptotic gain property holds in the L2 norm of the displacement without any assumption for the damping coefficients. The derivation of the upper bounds for the asymptotic gains is performed by either employing an eigenfunction expansion methodology or by means of a small-gain argument, whereas a novel frequency analysis methodology is employed for the derivation of the lower bounds for the asymptotic gains. The graphical illustration of the upper and lower bounds for the gains shows that that the asymptotic gain in the L2 norm is estimated much more accurately than the asymptotic gain in the sup norm.
1807.06549v1
2018-07-24
Stabilization of an unstable wave equation using an infinite dimensional dynamic controller
This paper deals with the stabilization of an anti-stable string equation with Dirichlet actuation where the instability appears because of the uncontrolled boundary condition. Then, infinitely many unstable poles are generated and an infinite dimensional control law is therefore proposed to exponentially stabilize the system. The idea behind the choice of the controller is to extend the domain of the PDE so that the anti-damping term is compensated by a damping at the other boundary condition. Additionally, notice that the system can then be exponentially stabilized with a chosen decay-rate and is robust to uncertainties on the wave speed and the anti-damped coefficient of the wave equation, with the only use of a point-wise boundary measurement. The efficiency of this new control strategy is then compared to the backstepping approach.
1807.08999v2
2018-07-24
Interplay between intermittency and dissipation in collisionless plasma turbulence
We study the damping of collisionless Alfv\'enic turbulence by two mechanisms: stochastic heating (whose efficiency depends on the local turbulence amplitude $\delta z_\lambda$) and linear Landau damping (whose efficiency is independent of $\delta z_\lambda$), describing in detail how they affect and are affected by intermittency. The overall efficiency of linear Landau damping is not affected by intermittency in critically balanced turbulence, while stochastic heating is much more efficient in the presence of intermittent turbulence. Moreover, stochastic heating leads to a drop in the scale-dependent kurtosis over a narrow range of scales around the ion gyroscale.
1807.09301v2
2018-07-31
Input-to-State Stability of a Clamped-Free Damped String in the Presence of Distributed and Boundary Disturbances
This note establishes the Exponential Input-to-State Stability (EISS) property for a clamped-free damped string with respect to distributed and boundary disturbances. While efficient methods for establishing ISS properties for distributed parameter systems with respect to distributed disturbances have been developed during the last decades, establishing ISS properties with respect to boundary disturbances remains challenging. One of the well-known methods for well-posedness analysis of systems with boundary inputs is the use of a lifting operator for transferring the boundary disturbance to a distributed one. However, the resulting distributed disturbance involves time derivatives of the boundary perturbation. Thus, the subsequent ISS estimate depends on its amplitude, and may not be expressed in the strict form of ISS properties. To solve this problem, we show for a clamped-free damped string equation that the projection of the original system trajectories in an adequate Riesz basis can be used to establish the desired EISS property.
1807.11696v2
2018-07-31
Spin absorption at ferromagnetic-metal/platinum-oxide interface
We investigate the absorption of a spin current at a ferromagnetic-metal/Pt-oxide interface by measuring current-induced ferromagnetic resonance. The spin absorption was characterized by the magnetic damping of the heterostructure. We show that the magnetic damping of a Ni$_{81}$Fe$_{19}$ film is clearly enhanced by attaching Pt-oxide on the Ni$_{81}$Fe$_{19}$ film. The damping enhancement is disappeared by inserting an ultrathin Cu layer between the Ni$_{81}$Fe$_{19}$ and Pt-oxide layers. These results demonstrate an essential role of the direct contact between the Ni$_{81}$Fe$_{19}$ and Pt-oxide to induce sizable interface spin-orbit coupling. Furthermore, the spin-absorption parameter of the Ni$_{81}$Fe$_{19}$/Pt-oxide interface is comparable to that of intensively studied heterostructures with strong spin-orbit coupling, such as an oxide interface, topological insulators, metallic junctions with Rashba spin-orbit coupling. This result illustrates strong spin-orbit coupling at the ferromagnetic-metal/Pt-oxide interface, providing an important piece of information for quantitative understanding the spin absorption and spin-charge conversion at the ferromagnetic-metal/metallic-oxide interface.
1807.11806v1
2018-08-16
Stability analysis of dissipative systems subject to nonlinear damping via Lyapunov techniques
In this article, we provide a general strategy based on Lyapunov functionals to analyse global asymptotic stability of linear infinite-dimensional systems subject to nonlinear dampings under the assumption that the origin of the system is globally asymp-totically stable with a linear damping. To do so, we first characterize, in terms of Lyapunov functionals, several types of asymptotic stability for linear infinite-dimensional systems, namely the exponential and the polynomial stability. Then, we derive a Lyapunov functional for the nonlinear system, which is the sum of a Lyapunov functional coming from the linear system and another term with compensates the nonlinearity. Our results are then applied to the linearized Korteweg-de Vries equation and some wave equations.
1808.05370v1
2018-08-30
The influence of the coefficients of a system of coupled wave equations with fractional damping on its stabilization
In this work, we consider a system of two wave equations coupled by velocities in one-dimensional space, with one boundary fractional damping. First, we show that the system is strongly asymptotically stable if and only if the coupling parameter b of the two equations is outside a discrete set of exceptional real values. Next, we show that our system is not uniformly stable. Hence, we look for a polynomial decay rate for smooth initial data. Using frequency domain approach combining with multiplier method, we prove that the energy decay rate is greatly influenced by the nature of the coupling parameter b, the arithmetic property of the ratio of the wave propagation speeds a, the order of the fractional damping. Indeed, under the equal speed propagation condition, we establish an optimal polynomial energy decay rate. Furthermore, when the wave propagate with different speeds, under some arithmetic conditions on the ratio of the wave propagation speeds, we prove that the energy of our system decays polynomially to zero.
1808.10285v4
2018-09-05
On the forced Euler and Navier-Stokes equations: Linear damping and modified scattering
We study the asymptotic behavior of the forced linear Euler and nonlinear Navier-Stokes equations close to Couette flow in a periodic channel. As our main result we show that for smooth time-periodic forcing linear inviscid damping persists, i.e. the velocity field (weakly) asymptotically converges. However, stability and scattering to the transport problem fail in $H^{s}, s>-1$. We further show that this behavior is consistent with the nonlinear Euler equations and that a similar result also holds for the nonlinear Navier-Stokes equations. Hence, these results provide an indication that nonlinear inviscid damping may still hold in Sobolev regularity in the above sense despite the Gevrey regularity instability results of [Deng-Masmoudi 2018].
1809.01729v1
2018-09-12
Theory of bifurcation amplifiers utilizing the nonlinear dynamical response of an optically damped mechanical oscillator
We consider a standard optomechanical system where a mechanical oscillator is coupled to a cavity mode through the radiation pressure interaction. The oscillator is coherently driven at its resonance frequency, whereas the cavity mode is driven below its resonance, providing optical damping of the mechanical oscillations. We study the nonlinear coherent response of the mechanical oscillator in this setup. For large mechanical amplitudes, we find that the system can display dynamical multistability if the optomechanical cooperativity exceeds a critical value. This analysis relates standard optomechanical damping to the dynamical attractors known from the theory of optomechanical self-sustained oscillations. We also investigate the effect of thermal and quantum noise and estimate the noise-induced switching rate between the stable states of the system. We then consider applications of this system and primarily focus on how it can be used as bifurcation amplifiers for the detection of small mechanical or optical signals. Finally, we show that in a related but more complicated setup featuring resonant optomechanical interactions, the same effects can be realized with a relaxed requirement on the size of the mechanical oscillations.
1809.04592v2
2018-09-13
Second order asymptotical regularization methods for inverse problems in partial differential equations
We develop Second Order Asymptotical Regularization (SOAR) methods for solving inverse source problems in elliptic partial differential equations with both Dirichlet and Neumann boundary data. We show the convergence results of SOAR with the fixed damping parameter, as well as with a dynamic damping parameter, which is a continuous analog of Nesterov's acceleration method. Moreover, by using Morozov's discrepancy principle together with a newly developed total energy discrepancy principle, we prove that the approximate solution of SOAR weakly converges to an exact source function as the measurement noise goes to zero. A damped symplectic scheme, combined with the finite element method, is developed for the numerical implementation of SOAR, which yields a novel iterative regularization scheme for solving inverse source problems. Several numerical examples are given to show the accuracy and the acceleration effect of SOAR. A comparison with the state-of-the-art methods is also provided.
1809.04971v2
2018-09-24
Oscillation Damping Control of Pendulum-like Manipulation Platform using Moving Masses
This paper presents an approach to damp out the oscillatory motion of the pendulum-like hanging platform on which a robotic manipulator is mounted. To this end, moving masses were installed on top of the platform. In this paper, asymptotic stability of the platform (which implies oscillation damping) is achieved by designing reference acceleration of the moving masses properly. A main feature of this work is that we can achieve asymptotic stability of not only the platform, but also the moving masses, which may be challenging due to the under-actuation nature. The proposed scheme is validated by the simulation studies.
1809.08819v1
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
2019-06-10
Global existence of weak solutions to the compressible quantum Navier-Stokes equations with degenerate viscosity
We study the compressible quantum Navier-Stokes (QNS) equations with degenerate viscosity in the three dimensional periodic domains. On the one hand, we consider QNS with additional damping terms. Motivated by the recent works [Li-Xin, arXiv:1504.06826] and [Antonelli-Spirito, Arch. Ration. Mech. Anal., 203(2012), 499--527], we construct a suitable approximate system which has smooth solutions satisfying the energy inequality and the BD entropy estimate. Using this system, we obtain the global existence of weak solutions to the compressible QNS equations with damping terms for large initial data. Moreover, we obtain some new a priori estimates, which can avoid using the assumption that the gradient of the velocity is a well-defined function, which is indeed used directly in [Vasseur-Yu, SIAM J. Math. Anal., 48 (2016), 1489--1511; Invent. Math., 206 (2016), 935--974]. On the other hand, in the absence of damping terms, we also prove the global existence of weak solutions to the compressible QNS equations without the lower bound assumption on the dispersive coefficient, which improves the previous result due to [Antonelli-Spirito, Arch. Ration. Mech. Anal., 203(2012), 499--527].
1906.03971v1
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
2019-08-19
Time Delay in the Swing Equation: A Variety of Bifurcations
The present paper addresses the swing equation with additional delayed damping as an example for pendulum-like systems. In this context, it is proved that recurring sub- and supercritical Hopf bifurcations occur if time delay is increased. To this end, a general formula for the first Lyapunov coefficient in second order systems with additional delayed damping and delay-free nonlinearity is given. In so far the paper extends results about stability switching of equilibria in linear time delay systems from Cooke and Grossman. In addition to the analytical results, periodic solutions are numerically dealt with. The numerical results demonstrate how a variety of qualitative behaviors is generated in the simple swing equation by only introducing time delay in a damping term.
1908.07996v3
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
2019-12-30
A Link Between Relativistic Rest Energy and Fractionary Momentum Operators of Order 1/2
The solution of a causal fractionary wave equation in an infinite potential well was obtained. First, the so-called "free particle" case was solved, giving as normalizable solutions a superposition of damped oscillations similar to a wave packet. From this results, the infinite potential well case was then solved. The damping coefficient of the equation obtained was matched with the exponent appearing in the Yucawa potential or "screened" Coulomb potential. When this matching was forced, the particle aquires an offset energy of E = mc^2/2 which then can be increased by each energy level. The expontential damping of the wave solutions in the box was found to be closely related with the radius of the proton when the particle has a mass equal to the mass of the proton. Lastly the fractionary wave equation was expressed in spherical coordinates and remains to be solved through analytical or numerical methods.
1912.12770v4
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
2020-05-04
Remarks on asymptotic order for the linear wave equation with the scale-invariant damping and mass with $L^r$-data
In the present paper, we consider the linear wave equation with the scale-invariant damping and mass. It is known that the global behavior of the solution depends on the size of the coefficients in front of the damping and mass at initial time $t=0$. Indeed, the solution satisfies the similar decay estimate to that of the corresponding heat equation if it is large and to that of the modified wave equation if it is small. In our previous paper, we obtain the scattering result and its asymptotic order for the data in the energy space $H^1\times L^2$ when the coefficients are in the wave regime. In fact, the threshold of the coefficients relies on the spatial decay of the initial data. Namely, it varies depending on $r$ when the initial data is in $L^r$ ($1\leq r < 2$). In the present paper, we will show the scattering result and the asymptotic order in the wave regime for $L^r$-data, which is wider than the wave regime for the data in the energy space. Moreover, we give an improvement of the asymptotic order obtained in our previous paper for the data in the energy space.
2005.01335v2