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