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2014-02-26
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Comparison of methods for numerical calculation of continuum damping
|
Continuum resonance damping is an important factor in determining the
stability of certain global modes in fusion plasmas. A number of analytic and
numerical approaches have been developed to compute this damping, particularly
in the case of the toroidicity-induced shear Alfv\'en eigenmode. This paper
compares results obtained using an analytical perturbative approach with those
found using resistive and complex contour numerical approaches. It is found
that the perturbative method does not provide accurate agreement with reliable
numerical methods for the range of parameters examined. This discrepancy exists
even in the limit where damping approaches zero. When the perturbative
technique is implemented using a standard finite element method, the damping
estimate fails to converge with radial grid resolution. The finite elements
used cannot accurately represent the eigenmode in the region of the continuum
resonance, regardless of the number of radial grid points used.
|
1402.6389v1
|
2014-05-16
|
Quantum corrections to nonlinear ion acoustic wave with Landau damping
|
Quantum corrections to nonlinear ion acoustic wave with Landau damping have
been computed using Wigner equation approach. The dynamical equation governing
the time development of nonlinear ion acoustic wave with semiclassical quantum
corrections is shown to have the form of higher KdV equation which has higher
order nonlinear terms coming from quantum corrections, with the usual classical
and quantum corrected Landau damping integral terms.
The conservation of total number of ions is shown from the evolution
equation. The decay rate of KdV solitary wave amplitude due to presence of
Landau damping terms has been calculated assuming the Landau damping parameter
$\alpha_1 = \sqrt{{m_e}/{m_i}}$ to be of the same order of the quantum
parameter $Q = {\hbar^2}/({24 m^2 c^2_{s} L^2})$. The amplitude is shown to
decay very slowly with time as determined by the quantum factor $ Q$.
|
1405.4107v1
|
2014-05-19
|
Mesh Size and Damped Edge Effects in Micromagnetic Spin Wave Simulation
|
We have studied the dependence of spin wave dispersion on the characteristics
of the mesh used in a finite element micromagnetic simulation. It is shown that
the dispersion curve has a cut off at a frequency which is analytically
predictable. The frequency depends on the average mesh length used for the
simulation. Based on this, a recipe to effectively obtain the dispersion
relation has been suggested. In a separate study, spin wave reflections are
absorbed by introducing highly damped edges in the device. However, an abrupt
change in the damping parameter causes reflections. We compare damping profiles
and identify an exponential damping profile as causing significantly less
reflections.
|
1405.4615v2
|
2014-07-08
|
Fourier-Hermite spectral representation for the Vlasov-Poisson system in the weakly collisional limit
|
We study Landau damping in the 1+1D Vlasov-Poisson system using a
Fourier-Hermite spectral representation. We describe the propagation of free
energy in phase space using forwards and backwards propagating Hermite modes
recently developed for gyrokinetics [Schekochihin et al. (2014)]. The change in
the electric field corresponds to the net Hermite flux via a free energy
evolution equation. In linear Landau damping, decay in the electric field
corresponds to forward propagating Hermite modes; in nonlinear damping, the
initial decay is followed by a growth phase characterised by the generation of
backwards propagating Hermite modes by the nonlinear term. The free energy
content of the backwards propagating modes increases exponentially until
balancing that of the forward propagating modes. Thereafter there is no
systematic net Hermite flux, so the electric field cannot decay and the
nonlinearity effectively suppresses Landau damping. These simulations are
performed using the fully-spectral 5D gyrokinetics code SpectroGK [Parker et
al. 2014], modified to solve the 1+1D Vlasov-Poisson system. This captures
Landau damping via an iterated L\'enard-Bernstein collision operator or via
Hou-Li filtering in velocity space. Therefore the code is applicable even in
regimes where phase-mixing and filamentation are dominant.
|
1407.1932v1
|
2014-08-15
|
Linear hyperbolic equations with time-dependent propagation speed and strong damping
|
We consider a second order linear equation with a time-dependent coefficient
c(t) in front of the "elastic" operator. For these equations it is well-known
that a higher space-regularity of initial data compensates a lower
time-regularity of c(t).
In this paper we investigate the influence of a strong dissipation, namely a
friction term which depends on a power of the elastic operator.
What we discover is a threshold effect. When the exponent of the elastic
operator in the friction term is greater than 1/2, the damping prevails and the
equation behaves as if the coefficient c(t) were constant. When the exponent is
less than 1/2, the time-regularity of c(t) comes into play. If c(t) is regular
enough, once again the damping prevails. On the contrary, when c(t) is not
regular enough the damping might be ineffective, and there are examples in
which the dissipative equation behaves as the non-dissipative one. As expected,
the stronger is the damping, the lower is the time-regularity threshold.
We also provide counterexamples showing the optimality of our results.
|
1408.3499v1
|
2014-08-14
|
Particle Dynamics in Damped Nonlinear Quadrupole Ion Traps
|
We examine the motions of particles in quadrupole ion traps as a function of
damping and trapping forces, including cases where nonlinear damping or
nonlinearities in the electric field geometry play significant roles. In the
absence of nonlinearities, particles are either damped to the trap center or
ejected, while their addition brings about a rich spectrum of stable closed
particle trajectories. In three-dimensional (3D) quadrupole traps, the extended
orbits are typically confined to the trap axis, and for this case we present a
1D analysis of the relevant equation of motion. We follow this with an analysis
of 2D quadrupole traps that frequently show diamond-shaped closed orbits. For
both the 1D and 2D cases we present experimental observations of the calculated
trajectories in microparticle ion traps. We also report the discovery of a new
collective behavior in damped 2D microparticle ion traps, where particles
spontaneously assemble into a remarkable knot of overlapping, corotating
diamond orbits, self-stabilized by air currents arising from the particle
motion.
|
1409.6262v1
|
2015-01-03
|
Finite-Parameters Feedback Control for Stabilizing Damped Nonlinear Wave Equations
|
In this paper we introduce a finite-parameters feedback control algorithm for
stabilizing solutions of various classes of damped nonlinear wave equations.
Specifically, stabilization the zero steady state solution of initial boundary
value problems for nonlinear weakly and strongly damped wave equations,
nonlinear wave equation with nonlinear damping term and some related nonlinear
wave equations, introducing a feedback control terms that employ parameters,
such as, finitely many Fourier modes, finitely many volume elements and
finitely many nodal observables and controllers. In addition, we also establish
the stabilization of the zero steady state solution to initial boundary value
problem for the damped nonlinear wave equation with a controller acting in a
proper subdomain. Notably, the feedback controllers proposed here can be
equally applied for stabilizing other solutions of the underlying equations.
|
1501.00556v1
|
2015-06-26
|
A Universal Damping Mechanism of Quantum Vibrations in Deep Sub-Barrier Fusion Reactions
|
We demonstrate the damping of quantum octupole vibrations near the touching
point when two colliding nuclei approach each other in the mass-asymmetric
$^{208}$Pb + $^{16}$O system, for which the strong fusion hindrance was clearly
observed. We, for the first time, apply the random-phase approximation method
to the heavy-mass asymmetric di-nuclear system to calculate the transition
strength $B$(E3) as a function of the center-of-mass distance. The obtained
$B$(E3) strengths are substantially damped near the touching point, because the
single-particle wave functions of the two nuclei strongly mix with each other
and a neck is formed. The energy-weighted sums of $B$(E3) are also strongly
correlated with the damping factor which is phenomenologically introduced in
the standard coupled-channel calculations to reproduce the fusion hindrance.
This strongly indicates that the damping of the quantum vibrations universally
occurs in the deep sub-barrier fusion reactions.
|
1506.07963v1
|
2015-07-28
|
Phenomenology of chiral damping in noncentrosymmetric magnets
|
A phenomenology of magnetic chiral damping is proposed in the context of
magnetic materials lacking inversion symmetry breaking. We show that the
magnetic damping tensor adopts a general form that accounts for a component
linear in magnetization gradient in the form of Lifshitz invariants. We propose
different microscopic mechanisms that can produce such a damping in
ferromagnetic metals, among which spin pumping in the presence of anomalous
Hall effect and an effective "$s$-$d$" Dzyaloshinskii-Moriya antisymmetric
exchange. The implication of this chiral damping in terms of domain wall motion
is investigated in the flow and creep regimes. These predictions have major
importance in the context of field- and current-driven texture motion in
noncentrosymmetric (ferro-, ferri-, antiferro-)magnets, not limited to metals.
|
1507.07762v1
|
2015-08-06
|
Phenomenological description of the nonlocal magnetization relaxation in magnonics, spintronics, and domain-wall dynamics
|
A phenomenological equation called Landau-Lifshitz-Baryakhtar (LLBar)
equation, which could be viewed as the combination of Landau-Lifshitz (LL)
equation and an extra "exchange damping" term, was derived by Baryakhtar using
Onsager's relations. We interpret the origin of this "exchange damping" as
nonlocal damping by linking it to the spin current pumping. The LLBar equation
is investigated numerically and analytically for the spin wave decay and domain
wall motion. Our results show that the lifetime and propagation length of
short-wavelength magnons in the presence of nonlocal damping could be much
smaller than those given by LL equation. Furthermore, we find that both the
domain wall mobility and the Walker breakdown field are strongly influenced by
the nonlocal damping.
|
1508.01478v1
|
2016-01-05
|
Vlasov Simulations of Electron-Ion Collision Effects on Damping of Electron Plasma Waves
|
Collisional effects can play an essential role in the dynamics of plasma
waves by setting a minimum damping rate and by interfering with wave-particle
resonances. Kinetic simulations of the effects of electron-ion pitch angle
scattering on Electron Plasma Waves (EPWs) are presented here. In particular,
the effects of such collisions on the frequency and damping of small-amplitude
EPWs for a range of collision rates and wave phase velocities are computed and
compared with theory. Both the Vlasov simulations and linear kinetic theory
find the direct contribution of electron-ion collisions to wave damping is
about a factor of two smaller than is obtained from linearized fluid theory. To
our knowledge, this simple result has not been published before.
Simulations have been carried out using a grid-based (Vlasov) approach, based
on a high-order conservative finite difference method for discretizing the
Fokker-Planck equation describing the evolution of the electron distribution
function. Details of the implementation of the collision operator within this
framework are presented. Such a grid-based approach, which is not subject to
numerical noise, is of particular interest for the accurate measurements of the
wave damping rates.
|
1601.01002v1
|
2016-02-13
|
The effect of orbital damping during planet migration on the Inclination and Eccentricity Distributions of Neptune Trojans
|
We explore planetary migration scenarios for formation of high inclination
Neptune Trojans (NTs) and how they are affected by the planetary migration of
Neptune and Uranus. If Neptune and Uranus's eccentricity and inclination were
damped during planetary migration, then their eccentricities and inclinations
were higher prior and during migration than their current values. Using test
particle integrations we study the stability of primordial NTs, objects that
were initially Trojans with Neptune prior to migration. We also study
Trans-Neptunian objects captured into resonance with Neptune and becoming NTs
during planet migration. We find that most primordial NTs were unstable and
lost if eccentricity and inclination damping took place during planetary
migration. With damping, secular resonances with Neptune can increase a low
eccentricity and inclination population of Trans-Neptunian objects increasing
the probability that they are captured into 1:1 resonance with Neptune,
becoming high inclination NTs. We suggest that the resonant trapping scenario
is a promising and more effective mechanism explaining the origin of NTs that
is particularly effective if Uranus and Neptune experienced eccentricity and
inclination damping during planetary migration.
|
1602.04303v1
|
2016-03-08
|
Damping of the Higgs and Nambu-Goldstone modes of superfluid Bose gases at finite temperatures
|
We study collective modes of superfluid Bose gases in optical lattices at
commensurate fillings. We focus on the vicinity of the quantum phase transition
to the Mott insulator, where there exists the Higgs amplitude mode in addition
to the Nambu-Goldstone phase mode associated with the spontaneous U(1) symmetry
breaking. We analyze finite-temperature effects on the damping of the
collective modes by using an effective spin-1 model and the field theoretical
methods based on the finite-temperature Green's function. We calculate the
damping rates up to 1-loop order and evaluate them analytically and
numerically. We show that the damping rate of the Higgs mode increases with
increasing the temperature but it remains underdamped up to a typical
temperature achieved in experiments. Moreover, we find that the Nambu-Goldstone
mode attenuates via a Landau damping process resulting from interactions with
the Higgs mode and it can be overdamped at the typical temperature in a certain
parameter region.
|
1603.02395v1
|
2016-04-12
|
Offline software for the DAMPE experiment
|
A software system has been developed for the DArk Matter Particle Explorer
(DAMPE) mission, a satellite-based experiment. The DAMPE software is mainly
written in C++ and steered using Python script. This article presents an
overview of the DAMPE offline software, including the major architecture design
and specific implementation for simulation, calibration and reconstruction. The
whole system has been successfully applied to DAMPE data analysis, based on
which some results from simulation and beam test experiments are obtained and
presented.
|
1604.03219v6
|
2016-04-18
|
Stabilization of Damped Waves on Spheres and Zoll Surfaces of Revolution
|
We study the strong stabilization of wave equations on some sphere-like
manifolds, with rough damping terms which do not satisfy the geometric control
condition posed by Rauch-Taylor and Bardos-Lebeau-Rauch. We begin with an
unpublished result of G. Lebeau, which states that on S^d , the indicator
function of the upper hemisphere strongly stabilizes the damped wave equation,
even though the equators, which are geodesics contained in the boundary of the
upper hemisphere, do not enter the damping region. Then we extend this result
on dimension 2, to Zoll surfaces of revolution, whose geometry is similar to
that of S^2 . In particular, geometric objects such as the equator, and the
hemi-surfaces are well defined. Our result states that the indicator function
of the upper hemi-surface strongly stabilizes the damped wave equation, even
though the equator, as a geodesic, does not enter the upper hemi-surface
either.
|
1604.05218v2
|
2016-07-25
|
Damping of parametrically excited magnons in the presence of the longitudinal spin Seebeck effect
|
The impact of the longitudinal spin Seebeck effect (LSSE) on the magnon
damping in magnetic-insulator/nonmagnetic-metal bilayers was recently discussed
in several reports. However, results of those experiments can be blurred by
multimode excitation within the measured linewidth. In order to avoid possible
intermodal interference, we investigated the damping of a single magnon group
in a platinum covered Yttrium Iron Garnet (YIG) film by measurement of the
threshold of its parametric excitation. Both dipolar and exchange spin-wave
branches were probed. It turned out that the LSSE-related modification of
spin-wave damping in a micrometer-thick YIG film is too weak to be observed in
the entire range of experimentally accessible wavevectors. At the same time,
the change in the mean temperature of the YIG layer, which can appear by
applying a temperature gradient, strongly modifies the damping value.
|
1607.07274v1
|
2016-07-27
|
Frequency dispersion of small-amplitude capillary waves in viscous fluids
|
This work presents a detailed study of the dispersion of capillary waves with
small amplitude in viscous fluids using an analytically derived solution to the
initial value problem of a small-amplitude capillary wave as well as direct
numerical simulation. A rational parametrization for the dispersion of
capillary waves in the underdamped regime is proposed, including predictions
for the wavenumber of critical damping based on a harmonic oscillator model.
The scaling resulting from this parametrization leads to a self-similar
solution of the frequency dispersion of capillary waves that covers the entire
underdamped regime, which allows an accurate evaluation of the frequency at a
given wavenumber, irrespective of the fluid properties. This similarity also
reveals characteristic features of capillary waves, for instance that critical
damping occurs when the characteristic timescales of dispersive and dissipative
mechanisms are balanced. In addition, the presented results suggest that the
widely adopted hydrodynamic theory for damped capillary waves does not
accurately predict the dispersion when viscous damping is significant and a new
definition of the damping rate, which provides consistent accuracy in the
underdamped regime, is presented.
|
1607.08266v1
|
2016-10-18
|
On the stability of the Bresse system with frictional damping
|
In this paper, we consider the Bresse system with frictional damping terms
and prove some optimal decay results for the $L^2$-norm of the solution and its
higher order derivatives. In fact, if we consider just one damping term acting
on the second equation of the solution, we show that the solution does not
decay at all. On the other hand, by considering one damping term alone acting
on the third equation, we show that this damping term is strong enough to
stabilize the whole system. In this case, we found a completely new stability
number that depends on the parameters in the system.
In addition, we prove the optimality of the results by using eigenvalues
expansions. Our obtained results have been proved under some assumptions on the
wave speeds of the three equations in the Bresse system.
|
1610.05500v2
|
2017-01-12
|
Blow-up for semilinear wave equations with the scale invariant damping and super-Fujita exponent
|
The blow-up for semilinear wave equations with the scale invariant damping
has been well-studied for sub-Fujita exponent. However, for super-Fujita
exponent, there is only one blow-up result which is obtained in 2014 by
Wakasugi in the case of non-effective damping. In this paper we extend his
result in two aspects by showing that: (I) the blow-up will happen for bigger
exponent, which is closely related to the Strauss exponent, the critical number
for non-damped semilinear wave equations; (II) such a blow-up result is
established for a wider range of the constant than the known non-effective one
in the damping term.
|
1701.03232v3
|
2017-02-17
|
Transition of multi-diffusive states in a biased periodic potential
|
We study a frequency-dependent damping model of hyper-diffusion within the
generalized Langevin equation. The model allows for the colored noise defined
by its spectral density, assumed to be proportional to $\omega^{\delta-1}$ at
low frequencies with $0<\delta<1$ (sub-Ohmic damping) or $1<\delta<2$
(super-Ohmic damping), where the frequency-dependent damping is deduced from
the noise by means of the fluctuation-dissipation theorem. It is shown that for
super-Ohmic damping and certain parameters, the diffusive process of the
particle in a titled periodic potential undergos sequentially four
time-regimes: thermalization, hyper-diffusion, collapse and asymptotical
restoration. For analysing transition phenomenon of multi-diffusive states, we
demonstrate that the first exist time of the particle escaping from the locked
state into the running state abides by an exponential distribution. The concept
of equivalent velocity trap is introduced in the present model, moreover,
reformation of ballistic diffusive system is also considered as a marginal
situation, however there does not exhibit the collapsed state of diffusion.
|
1702.05370v1
|
2017-09-27
|
Wave turbulence in vibrating plates : the effect of damping
|
The effect of damping in the wave turbulence regime for thin vibrating plates
is studied. An experimental method, allowing measurements of dissipation in the
system at all scales, is first introduced. Practical experimental devices for
increasing the dissipation are used. The main observable consequence of
increasing the damping is a significant modification in the slope of the power
spectral density, so that the observed power laws are not in a pure inertial
regime. However, the system still displays a turbulent behavior with a cut-off
frequency that is determined by the injected power which does not depend on
damping. By using the measured damping power-law in numerical simulations,
similar conclusions are drawn out.
|
1709.09438v1
|
2017-11-02
|
Vibration Damping of Carbon Nanotube Assembly Materials
|
Vibration reduction is of great importance in various engineering
applications, and a material that exhibits good vibration damping along with
high strength and modulus has become more and more vital. Owing to the superior
mechanical property of carbon nanotube (CNT), new types of vibration damping
material can be developed. This paper presents recent advancements, including
our progresses, in the development of high-damping macroscopic CNT assembly
materials, such as forests, gels, films, and fibers. In these assemblies,
structural deformation of CNTs, zipping and unzipping at CNT connection nodes,
strengthening and welding of the nodes, and sliding between CNTs or CNT bundles
are playing important roles in determining the viscoelasticity, and elasticity
as well. Towards the damping enhancement, strategies for micro-structure and
interface design are also discussed.
|
1711.00623v1
|
2017-12-05
|
Dark Matter Annihilation from Nearby Ultra-compact Micro Halos to Explain the Tentative Excess at ~1.4 TeV in DAMPE data
|
The tentative 1.4 TeV excess in the $e^+e^-$ spectrum measured by The DArk
Matter Particle Explorer (DAMPE) motivates the possible existence of one or
more local dark matter concentrated regions. In particular, Ultra-compact Micro
Halos (UCMHs) seeded by large density perturbations in the early universe,
allocated within ~0.3 kpc from the solar system, could provide the potential
source of electrons and positrons produced from dark matter annihilation,
enough to explain the DAMPE signal. Here we consider a UCMH with density
profile assuming radial in-fall and explore the preferred halo parameters to
explain the 1.4 TeV "DAMPE excess". We find that typical parameter space of
UCMHs can easily explain the "DAMPE excess" with usual thermal-averaged
annihilation cross section of WIMP. The fraction of dark matter stored in such
UCMHs in the Galactic-scale halo can be reduced to as small as $O(10^{-5})$,
well within the current cosmological and astrophysical constraints.
|
1712.01724v2
|
2017-12-21
|
A new charge reconstruction algorithm for the DAMPE silicon microstrip detector
|
The DArk Matter Particle Explorer (DAMPE) is one of the four satellites
within the Strategic Pioneer Research Program in Space Science of the Chinese
Academy of Science (CAS). The Silicon-Tungsten Tracker (STK), which is composed
of 768 singled-sided silicon microstrip detectors, is one of the four
subdetectors in DAMPE, providing track reconstruction and charge identification
for relativistic charged particles. The charge response of DAMPE silicon
microstrip detectors is complicated, depending on the incident angle and impact
position. A new charge reconstruction algorithm for the DAMPE silicon
microstrip detector is introduced in this paper. This algorithm can correct the
complicated charge response, and was proved applicable by the ion test beam.
|
1712.08011v1
|
2018-01-23
|
The dominancy of damping like torque for the current induced magnetization switching in Pt/Co/W multilayers
|
Two classes of spin-orbit coupling (SOC) mechanisms have been considered as
candidate sources for the spin orbit torque (SOT): the spin Hall Effect (SHE)
in heavy metals with strong SOC and the Rashba effect arising from broken
inversion symmetry at material surfaces and interfaces. In this work, we have
investigated the SOT in perpendicularly magnetized Pt/Co/W films, which is
compared with the results in Pt/Co/AlOx films. Theoretically, in the case of
the asymmetric structure of trilayers with opposite sign of spin Hall angle,
both damping like torque and field like torque due to the SHE and the Rashba
effect will be enhanced. Using the harmonic measurements, we have characterized
the effective fields corresponding to the damping like torque and the field
like torque, but we have found the dominancy of damping like torque in the
Pt/Co/W films. It is much different from the results in the Pt/Co/AlOx films,
in which both the damping like torque and the field like torque are strong.
|
1801.07408v1
|
2018-02-20
|
The damped wave equation with unbounded damping
|
We analyze new phenomena arising in linear damped wave equations on unbounded
domains when the damping is allowed to become unbounded at infinity. We prove
the generation of a contraction semigroup, study the relation between the
spectra of the semigroup generator and the associated quadratic operator
function, the convergence of non-real eigenvalues in the asymptotic regime of
diverging damping on a subdomain, and we investigate the appearance of
essential spectrum on the negative real axis. We further show that the presence
of the latter prevents exponential estimates for the semigroup and turns out to
be a robust effect that cannot be easily canceled by adding a positive
potential. These analytic results are illustrated by examples.
|
1802.07026v1
|
2018-04-06
|
Exponential Integrators Preserving Local Conservation Laws of PDEs with Time-Dependent Damping/Driving Forces
|
Structure-preserving algorithms for solving conservative PDEs with added
linear dissipation are generalized to systems with time-dependent
damping/driving terms. This study is motivated by several PDE models of
physical phenomena, such as Korteweg-de Vries, Klein-Gordon, Schr\"{o}dinger,
and Camassa-Holm equations, all with damping/driving terms and time-dependent
coefficients. Since key features of the PDEs under consideration are described
by local conservation laws, which are independent of the boundary conditions,
the proposed (second-order in time) discretizations are developed with the
intent of preserving those local conservation laws. The methods are
respectively applied to a damped-driven nonlinear Schr\"{o}dinger equation and
a damped Camassa-Holm equation. Numerical experiments illustrate the
structure-preserving properties of the methods, as well as favorable results
over other competitive schemes.
|
1804.02266v1
|
2018-05-29
|
Enhancing precision of damping rate by PT symmetric Hamiltonian
|
We utilize quantum Fisher information to investigate the damping parameter
precision of a dissipative qubit. PT symmetric non-Hermitian Hamiltonian is
used to enhance the parameter precision in two models: one is direct PT
symmetric quantum feedback; the other is that the damping rate is encoded into
a effective PT symmetric non-Hermitian Hamiltonian conditioned on the absence
of decay events. We find that compared with the case without feedback and with
Hermitian quantum feedback, direct PT symmetric non-Hermitan quantum feedback
can obtain better precision of damping rate. And in the second model the result
shows that the uncertainty of damping rate can be close to 0 at the exceptional
point. We also obtain that non-maximal multiparticle entanglement can improve
the precision to reach Heisenberg limit.
|
1805.11216v1
|
2018-05-31
|
Damping Effect on PageRank Distribution
|
This work extends the personalized PageRank model invented by Brin and Page
to a family of PageRank models with various damping schemes. The goal with
increased model variety is to capture or recognize a larger number of types of
network activities, phenomena and propagation patterns. The response in
PageRank distribution to variation in damping mechanism is then characterized
analytically, and further estimated quantitatively on 6 large real-world link
graphs. The study leads to new observation and empirical findings. It is found
that the difference in the pattern of PageRank vector responding to parameter
variation by each model among the 6 graphs is relatively smaller than the
difference among 3 particular models used in the study on each of the graphs.
This suggests the utility of model variety for differentiating network
activities and propagation patterns. The quantitative analysis of the damping
mechanisms over multiple damping models and parameters is facilitated by a
highly efficient algorithm, which calculates all PageRank vectors at once via a
commonly shared, spectrally invariant subspace. The spectral space is found to
be of low dimension for each of the real-world graphs.
|
1806.00127v1
|
2018-08-10
|
Relativistic charge solitons created due to nonlinear Landau damping: A candidate for explaining coherent radio emission in pulsars
|
A potential resolution for the generation of coherent radio emission in
pulsar plasma is the existence of relativistic charge solitons, which are
solutions of nonlinear Schr\"{o}dinger equation (NLSE). In an earlier study,
Melikidze et al. (2000) investigated the nature of these charge solitons;
however, their analysis ignored the effect of nonlinear Landau damping, which
is inherent in the derivation of the NLSE in the pulsar pair plasma. In this
paper we include the effect of nonlinear Landau damping and obtain solutions of
the NLSE by applying a suitable numerical scheme. We find that for reasonable
parameters of the cubic nonlinearity and nonlinear Landau damping, soliton-like
intense pulses emerge from an initial disordered state of Langmuir waves and
subsequently propagate stably over sufficiently long times, during which they
are capable of exciting the coherent curvature radiation in pulsars. We
emphasize that this emergence of {\em stable} intense solitons from a
disordered state does not occur in a purely cubic NLSE; thus, it is {\em
caused} by the nonlinear Landau damping.
|
1808.03657v1
|
2018-11-21
|
Super Damping of Mechanical Vibrations
|
We report the phenomenon of coherent super decay, where a linear sum of
several damped oscillators can collectively decay much faster than the
individual ones in the first stage, followed by stagnating ones after more than
90 percent of the energy has already been dissipated. The parameters of the
damped oscillators for CSD are determined by the process of response function
decomposition, which is to use several slow decay response functions to
approximate the response function of a fast decay reference resonator. Evidence
established in experiments and in finite element simulations not only strongly
supported the numerical investigations, but also uncovered an unexplored region
of the tuned mass damper parameter space where TMDs with total mass less than
0.2 percent of a primary free body can damp its first resonance up to a damping
ratio of 4.6 percent. Our findings also shed light onto the intriguing
underline connections between complex functions with different singular points.
|
1811.08621v2
|
2018-11-29
|
Flowing fibers as a proxy of turbulence statistics
|
The flapping states of a flexible fiber fully coupled to a three-dimensional
turbulent flow are investigated via state-of-the-art numerical methods. Two
distinct flapping regimes are predicted by the phenomenological theory recently
proposed by Rosti et al. [Phys. Rev. Lett. 121, 044501, 2018]: the under-damped
regime, where the elasticity strongly affects the fiber dynamics, and the
over-damped regime, where the elastic effects are strongly inhibited. In both
cases we can identify a critical value of the bending rigidity of the fiber by
a resonance condition, which further provides a distinction between different
flapping behaviors, especially in the under-damped case. We validate the theory
by means of direct numerical simulations and find that, both for the
over-damped regime and for the under-damped one, fibers are effectively slaved
to the turbulent fluctuations and can therefore be used as a proxy to measure
various two-point statistics of turbulence. Finally, we show that this holds
true also in the case of a passive fiber, without any feedback force on the
fluid.
|
1811.12023v2
|
2018-11-29
|
The Lugiato-Lefever equation with nonlinear damping caused by two photon absorption
|
In this paper we investigate the effect of nonlinear damping on the
Lugiato-Lefever equation $$ \i \partial_t a = -(\i-\zeta) a - da_{xx}
-(1+\i\kappa)|a|^2a +\i f $$ on the torus or the real line. For the case of the
torus it is shown that for small nonlinear damping $\kappa>0$ stationary
spatially periodic solutions exist on branches that bifurcate from constant
solutions whereas all nonconstant solutions disappear when the damping
parameter $\kappa$ exceeds a critical value. These results apply both for
normal ($d<0$) and anomalous ($d>0$) dispersion. For the case of the real line
we show by the Implicit Function Theorem that for small nonlinear damping
$\kappa>0$ and large detuning $\zeta\gg 1$ and large forcing $f\gg 1$ strongly
localized, bright solitary stationary solutions exists in the case of anomalous
dispersion $d>0$. These results are achieved by using techniques from
bifurcation and continuation theory and by proving a convergence result for
solutions of the time-dependent Lugiato-Lefever equation.
|
1811.12200v3
|
2018-11-26
|
Linear Theory of Electron-Plasma Waves at Arbitrary Collisionality
|
The dynamics of electron-plasma waves are described at arbitrary
collisionality by considering the full Coulomb collision operator. The
description is based on a Hermite-Laguerre decomposition of the velocity
dependence of the electron distribution function. The damping rate, frequency,
and eigenmode spectrum of electron-plasma waves are found as functions of the
collision frequency and wavelength. A comparison is made between the
collisionless Landau damping limit, the Lenard-Bernstein and Dougherty
collision operators, and the electron-ion collision operator, finding large
deviations in the damping rates and eigenmode spectra. A purely damped entropy
mode, characteristic of a plasma where pitch-angle scattering effects are
dominant with respect to collisionless effects, is shown to emerge numerically,
and its dispersion relation is analytically derived. It is shown that such a
mode is absent when simplified collision operators are used, and that
like-particle collisions strongly influence the damping rate of the entropy
mode.
|
1811.12855v2
|
2019-01-17
|
Influences of interfacial oxidization on surface magnetic energy, magnetic damping and spin-orbit-torques in Pt / ferromagnet / capping structures
|
We investigate the effect of capping layer (CAP) on the interfacial magnetic
anisotropy energy density (K_S), magnetic damping ({\alpha}), and spin-orbit
torques (SOTs) in heavy-metal (Pt) / ferromagnet (Co or Py) / CAP (MgO/Ta,
HfOx, or TaN). At room temperature (RT) the CAP materials influence the
effective magnitude of K_S, which is associated with a formation of interfacial
magnetic oxides. The dynamical dissipation parameters of Co are considerably
influenced by the CAP (especially MgO) while those of Py are not. This is
possibly due to an extra magnetic damping via spin-pumping process across the
Co/CoO interface and incoherent magnon generation (spin fluctuation) in the
interfacial CoO. It is also observed that both anti-damping and field-like SOT
efficiencies vary marginally with the CAP in the thickness ranges we examined.
Our results reveal the crucial role of interfacial oxides on the perpendicular
magnetic anisotropy, magnetic damping, and SOTs.
|
1901.05777v1
|
2019-05-31
|
The amplitude of solar p-mode oscillations from three-dimensional convection simulations
|
The amplitude of solar p-mode oscillations is governed by stochastic
excitation and mode damping, both of which take place in the surface convection
zone. However, the time-dependent, turbulent nature of convection makes it
difficult to self-consistently study excitation and damping processes through
the use of traditional one-dimensional hydrostatic models. To this end, we
carried out \textit{ab initio} three-dimensional, hydrodynamical numerical
simulations of the solar atmosphere to investigate how p-modes are driven and
dissipated in the Sun. The description of surface convection in the simulations
is free from the tuneable parameters typically adopted in traditional
one-dimensional models. Mode excitation and damping rates are computed based on
analytical expressions whose ingredients are evaluated directly from the
three-dimensional model. With excitation and damping rates both available, we
estimate the theoretical oscillation amplitude and frequency of maximum power,
$\nu_{\max}$, for the Sun. We compare our numerical results with helioseismic
observations, finding encouraging agreement between the two. The numerical
method presented here provides a novel way to investigate the physical
processes responsible for mode driving and damping, and should be valid for all
solar-type oscillating stars.
|
1905.13397v2
|
2019-10-03
|
Many-body collision contributions to electron momentum damping rates in a plasma influenced by electron strong coupling
|
Experimental studies of electron-ion collision rates in an ultracold neutral
plasma (UNP) can be conducted through measuring the rate of electron plasma
oscillation damping. For sufficiently cold and dense conditions where strong
coupling influences are important, the measured damping rate was faster by 37\%
than theoretical expectations [W. Chen, C. Witte, and J. Roberts, Phys. Rev. E
\textbf{96}, 013203 (2017)]. We have conducted a series of numerical
simulations to isolate the primary source of this difference. By analyzing the
distribution of electron velocity changes due to collisions in a molecular
dynamics simulation, examining the trajectory of electrons with high deflection
angle in such simulations, and examining the oscillation damping rate while
varying the ratio of two-body to three-body electron-ion collision rates, we
have found that the difference is consistent with the effect due to many-body
collisions leading to bound electrons. This has implications for other
electron-ion collision related transport properties in addition to electron
oscillation damping.
|
1910.01707v1
|
2019-10-18
|
Escape of a forced-damped particle from weakly nonlinear truncated potential well
|
Escape from a potential well is an extreme example of transient behavior. We
consider the escape of the harmonically forced particle under viscous damping
from the benchmark truncated weakly nonlinear potential well. Main attention is
paid to most interesting case of primary 1:1 resonance. The treatment is based
on multiple-scales analysis and exploration of the slow-flow dynamics. Contrary
to Hamiltonian case described in earlier works, in the case with damping the
slow-flow equations are not integrable. However, if the damping is small
enough, it is possible to analyze the perturbed slow-flow equations. The effect
of the damping on the escape threshold is evaluated in the explicit analytic
form. Somewhat unexpectedly, the escape mechanisms in terms of the slow flow
are substantially different for the linear and weakly nonlinear cases.
|
1910.08545v1
|
2019-10-24
|
Topological damping Rashba spin orbit torque in ballistic magnetic domain walls
|
Rashba spin orbit torque derived from the broken inversion symmetry at
ferromagnet/heavy metal interfaces has potential application in spintronic
devices. In conventional description of the precessional and damping components
of the Rashba spin orbit torque in magnetization textures, the decomposition
coefficients are assumed to be independent of the topology of the underlying
structure. Contrary to this common wisdom, for Schr\"{o}dinger electrons
trespassing ballistically across a magnetic domain wall, we found that the
decomposition coefficient of the damping component is determined by the
topology of the domain wall. The resultant damping Rashba spin orbit torque is
protected by the topology of the underlying magnetic domain wall and robust
against small deviations from the ideal domain wall profile. Our identification
of a topological damping Rashba spin orbit torque component in magnetic domain
walls will help to understand experiments on current driven domain wall motion
in ferromagnet/heavy metal systems with broken inversion symmetry and to
facilitate its utilization in innovative device designs.
|
1910.10977v2
|
2019-11-13
|
Dipole oscillations of fermionic superfluids along the BEC-BCS crossover in disordered potentials
|
We investigate dipole oscillations of ultracold Fermi gases along the BEC-BCS
crossover through disordered potentials. We observe a disorder-induced damping
of oscillations as well as a change of the fundamental Kohn-mode frequency. The
measurement results are compared to numerical density matrix renormalization
group calculations as well as to a three-dimensional simulation of
non-interacting fermions. Experimentally, we find a disorder-dependent damping,
which grows approximately with the second power of the disorder strength.
Moreover, we observe experimentally a change of oscillation frequency which
deviates from the expected behavior of a damped harmonic oscillator on a
percent level. While this behavior is qualitatively expected from the
theoretical models used, quantitatively the experimental observations show a
significantly stronger effect than predicted by theory. Furthermore, while the
frequency shift seems to scale differently with interaction strength in the BEC
versus BCS regime, the damping coefficient apparently decreases with the
strength of interaction, but not with the sign, which changes for BEC and BCS
type Fermi gases. This is surprising, as the dominant damping mechanisms are
expected to be different in the two regimes.
|
1911.05638v1
|
2020-02-07
|
Model of damping and anisotropy at elevated temperatures: application to granular FePt films
|
Understanding the damping mechanism in finite size systems and its dependence
on temperature is a critical step in the development of magnetic
nanotechnologies. In this work, nano-sized materials are modeled via atomistic
spin dynamics, the damping parameter being extracted from Ferromagnetic
Resonance (FMR) simulations applied for FePt systems, generally used for
heat-assisted magnetic recording media (HAMR). We find that the damping
increases rapidly close to Tc and the effect is enhanced with decreasing system
size, which is ascribed to scattering at the grain boundaries. Additionally,
FMR methods provide the temperature dependence of both damping and the
anisotropy, important for the development of HAMR. Semi-analytical calculations
show that, in the presence of a grain size distribution, the FMR linewidth can
decrease close to the Curie temperature due to a loss of inhomogeneous line
broadening. Although FePt has been used in this study, the results presented in
the current work are general and valid for any ferromagnetic material.
|
2002.02865v1
|
2020-04-06
|
Damping-like Torque in Monolayer 1T-TaS$_2$
|
A damping-like spin orbit torque (SOT) is a prerequisite for ultralow power
spin logic devices. Here, we report on the damping-like SOT in just one
monolayer of the conducting transition metal dichalcogenide (TMD) TaS$_2$
interfaced with a NiFe (Py) ferromagnetic layer. The charge-spin conversion
efficiency is found to be 0.25$\pm$0.03 and the spin Hall conductivity (2.63
$\times$ 10$^5$ $\frac{\hbar}{2e}$ $\Omega^{-1}$ m$^{-1}$) is found to be
superior to values reported for other TMDs. The origin of this large
damping-like SOT can be found in the interfacial properties of the TaS$_2$/Py
heterostructure, and the experimental findings are complemented by the results
from density functional theory calculations. The dominance of damping-like
torque demonstrated in our study provides a promising path for designing next
generation conducting TMD based low-powered quantum memory devices.
|
2004.02649v1
|
2020-05-15
|
Calibration and performance of the neutron detector onboard of the DAMPE mission
|
The DArk Matter Particle Explorer (DAMPE), one of the four space-based
scientific missions within the framework of the Strategic Pioneer Program on
Space Science of the Chinese Academy of Sciences, has been successfully
launched on Dec. 17th 2015 from Jiuquan launch center. One of the most
important scientific goals of DAMPE is to search for the evidence of dark
matter indirectly by measuring the spectrum of high energy cosmic-ray
electrons. The neutron detector, one of the four sub-payloads of DAMPE, is
designed to distinguish high energy electrons from hadron background by
measuring the secondary neutrons produced in the shower. In this paper, a
comprehensive introduction of the neutron detector is presented, including the
design, the calibration and the performance. The analysis with simulated data
and flight data indicates a powerful proton rejection capability of the neutron
detector, which plays an essential role for TeV electron identification of
DAMPE.
|
2005.07828v1
|
2020-05-16
|
Simultaneous observation of anti-damping and inverse spin Hall effect in La$_{0.67}$Sr$_{0.33}$MnO$_{3}$/Pt bilayer system
|
Manganites have shown potential in spintronics because they exhibit high spin
polarization. Here, by ferromagnetic resonance we have studied the damping
properties of La$_{0.67}$Sr$_{0.33}$MnO$_{3}$/Pt bilayers which are prepared by
oxide molecular beam epitaxy. The damping coefficient ($\alpha$) of
La$_{0.67}$Sr$_{0.33}$MnO$_{3}$ (LSMO) single layer is found to be 0.0104.
However the LSMO/Pt bilayers exhibit decrease in $\alpha$ with increase in Pt
thickness. This decrease in the value of $\alpha$ is probably due to high
anti-damping like torque. Further, we have investigated the angle dependent
inverse spin Hall effect (ISHE) to quantify the spin pumping voltage from other
spin rectification effects such as anomalous Hall effect and anisotropic
magnetoresistance. We have observed high spin pumping voltage ($\sim$~20 $ \mu
V$). The results indicate that both anti-damping and spin pumping phenomena are
occuring simultaneously.
|
2005.07848v3
|
2020-07-16
|
Linearized wave-damping structure of Vlasov-Poisson in $\mathbb R^3$
|
In this paper we study the linearized Vlasov-Poisson equation for localized
disturbances of an infinite, homogeneous Maxwellian background distribution in
$\mathbb R^3_x \times \mathbb R^3_v$. In contrast with the confined case
$\mathbb T^d _x \times \mathbb R_v ^d$, or the unconfined case $\mathbb R^d_x
\times \mathbb R^d_v$ with screening, the dynamics of the disturbance are not
scattering towards free transport as $t \to \pm \infty$: we show that the
electric field decomposes into a very weakly-damped Klein-Gordon-type evolution
for long waves and a Landau-damped evolution. The Klein-Gordon-type waves
solve, to leading order, the compressible Euler-Poisson equations linearized
about a constant density state, despite the fact that our model is
collisionless, i.e. there is no trend to local or global thermalization of the
distribution function in strong topologies. We prove dispersive estimates on
the Klein-Gordon part of the dynamics. The Landau damping part of the electric
field decays faster than free transport at low frequencies and damps as in the
confined case at high frequencies; in fact, it decays at the same rate as in
the screened case. As such, neither contribution to the electric field behaves
as in the vacuum case.
|
2007.08580v1
|
2020-07-25
|
Using a Lindbladian approach to model decoherence in two coupled nuclear spins via correlated phase-damping and amplitude damping noise channels
|
In this work, we studied the relaxation dynamics of coherences of different
order present in a system of two coupled nuclear spins. We used a previously
designed model for intrinsic noise present in such systems which considers the
Lindblad master equation for Markovian relaxation. We experimentally created
zero-, single- and double- quantum coherences in several two-spin systems and
performed a complete state tomography and computed state fidelity. We
experimentally measured the decay of zero- and double- quantum coherences in
these systems. The experimental data fitted well to a model that considers the
main noise channels to be a correlated phase damping channel acting
simultaneously on both spins in conjunction with a generalized amplitude
damping channel acting independently on both spins. The differential relaxation
of multiple-quantum coherences can be ascribed to the action of a correlated
phase damping channel acting simultaneously on both the spins.
|
2007.12972v1
|
2020-09-29
|
The effects of nonlinear damping on degenerate parametric amplification
|
This paper considers the dynamic response of a single degree of freedom
system with nonlinear stiffness and nonlinear damping that is subjected to both
resonant direct excitation and resonant parametric excitation, with a general
phase between the two. This generalizes and expands on previous studies of
nonlinear effects on parametric amplification, notably by including the effects
of nonlinear damping, which is commonly observed in a large variety of systems,
including micro- and nano-scale resonators. Using the method of averaging, a
thorough parameter study is carried out that describes the effects of the
amplitudes and relative phase of the two forms of excitation. The effects of
nonlinear damping on the parametric gain are first derived. The transitions
among various topological forms of the frequency response curves, which can
include isolae, dual peaks, and loops, are determined, and bifurcation analyses
in parameter spaces of interest are carried out. In general, these results
provide a complete picture of the system response and allow one to select drive
conditions of interest that avoid bistability while providing maximum amplitude
gain, maximum phase sensitivity, or a flat resonant peak, in systems with
nonlinear damping.
|
2009.14284v2
|
2020-11-10
|
Damped oscillators within the general theory of Casimir and van der Waals forces
|
It is demonstrated that the general theory of Casimir and van der Waals
forces describes the interaction-induced equilibrium thermodynamic potentials
of the damped harmonic oscillator bilinearly coupled to the environment. An
extended model for a damped oscillator is suggested along the lines of the
general theory of Casimir and van der Waals forces, and the corresponding
thermodynamic quantities obtained. While the original model involves a heat
bath consisting of a large number of free oscillators having infinitesimal
damping functions, the extended model allows any generally admissible frequency
and temperature dependent dissipative susceptibilities of the heat bath
constituents, influenced by the additional dissipative environmental channels
that are not directly linked to the system oscillator. Consequently, the
results obtained are applicable to the frequency and temperature dependent
damping function of the system oscillator.
|
2011.04960v2
|
2020-11-16
|
Technology to Counter Online Flaming Based on the Frequency-Dependent Damping Coefficient in the Oscillation Model
|
Online social networks, which are remarkably active, often experience
explosive user dynamics such as online flaming, which can significantly impact
the real world. However, countermeasures based on social analyses of the
individuals causing flaming are too slow to be effective because of the
rapidity with which the influence of online user dynamics propagates. A
countermeasure technology for the flaming phenomena based on the oscillation
model, which describes online user dynamics, has been proposed; it is an
immediate solution as it does not depend on social analyses of individuals.
Conventional countermeasures based on the oscillation model assume that the
damping coefficient is a constant regardless of the eigenfrequency. This
assumption is, however, problematic as the damping coefficients are, in
general, inherently frequency-dependent; the theory underlying the dependence
is being elucidated. This paper discusses a design method that uses the damping
coefficient to prevent flaming under general conditions considering the
frequency-dependence of the damping coefficient and proposes a countermeasure
technology for the flaming phenomena.
|
2011.08117v1
|
2021-01-03
|
The effect of flow on resonant absorption of slow MHD waves in magnetic flux tubes
|
In this paper, we study kink and sausage oscillations in the presence of
longitudinal background flow. We study resonant absorption of the kink and
sausage modes in the slow continuum under magnetic pore conditions in the
presence of flow. we determine the dispersion relation then solve it
numerically, and find the frequencies and damping rates of the slow kink and
sausage surface modes. We also, obtain analytical solution for the damping rate
of the slow surface mode in the long wavelength limit. We show that in the
presence of plasma flow, resonance absorption can result in strong damping for
forward waves and can be considered as an efficient mechanism to justify the
extremely rapid damping of slow surface sausage waves observed in magnetic
pores. Also, the plasma flow reduces the efficiency of resonance absorption to
damp backward waves. Furthermore, for the pore conditions, the resonance
instability is avoided in our model.
|
2101.02064v1
|
2021-02-01
|
Blow-up and lifespan estimates for a damped wave equation in the Einstein-de Sitter spacetime with nonlinearity of derivative type
|
In this article, we investigate the blow-up for local solutions to a
semilinear wave equation in the generalized Einstein - de Sitter spacetime with
nonlinearity of derivative type. More precisely, we consider a semilinear
damped wave equation with a time-dependent and not summable speed of
propagation and with a time-dependent coefficient for the linear damping term
with critical decay rate. We prove in this work that the results obtained in a
previous work, where the damping coefficient takes two particular values $0$ or
$2$, can be extended for any positive damping coefficient. In the blow-up case,
the upper bound of the exponent of the nonlinear term is given, and the
lifespan estimate of the global existence time is derived as well.
|
2102.01137v2
|
2021-02-02
|
Analysis of Lower Hybrid Drift Waves in Kappa Distributions over Solar Atmosphere
|
Kappa distributions and with loss cone features have been frequently observed
with flares emissions with the signatures of Lower hybrid waves. We have
analysed the plasma with Kappa distributions and with loss cone features for
the drift wave instabilities in perpendicular propagation for Large flare and
Normal flare and Coronal condition . While analysing the growth/damping rate,
we understand that the growth of propagation of EM waves increases with kappa
distribution index for all the three cases. In comparing the propagation large
flare shows lesser growth in compared with the normal and the coronal plasmas.
When added the loss cone features to Kappa distributions, we find that the
damping of EM wave propagation takes place. The damping rate EM waves is
increases with perpendicular temperature and loss cone index l, in all the
three cases but damping is very high for large flare and then normal in
comparision with coronal condition. This shows that the lower hybrid damping
may be the source of coronal heating.
|
2102.01323v1
|
2021-02-25
|
Regularity and stability of the semigroup associated with some interacting elastic systems I: A degenerate damping case
|
In this paper, we examine regularity and stability issues for two damped
abstract elastic systems. The damping involves the average velocity and a
fractional power $\theta$, with $\theta$ in $[-1,1]$, of the principal
operator. The matrix operator defining the damping mechanism for the coupled
system is degenerate. First, we prove that for $\theta$ in $(1/2,1]$, the
underlying semigroup is not analytic, but is differentiable for $\theta$ in
$(0,1)$; this is in sharp contrast with known results for a single similarly
damped elastic system, where the semigroup is analytic for $\theta$ in
$[1/2,1]$; this shows that the degeneracy dominates the dynamics of the
interacting systems, preventing analyticity in that range. Next, we show that
for $\theta$ in $(0,1/2]$, the semigroup is of certain Gevrey classes. Finally,
we show that the semigroup decays exponentially for $\theta$ in $[0,1]$, and
polynomially for $\theta$ in $[-1,0)$. To prove our results, we use the
frequency domain method, which relies on resolvent estimates. Optimality of our
resolvent estimates is also established. Several examples of application are
provided.
|
2102.13217v4
|
2021-03-05
|
Existence and congruence of global attractors for damped and forced integrable and nonintegrable discrete nonlinear Schrödinger equations
|
We study two damped and forced discrete nonlinear Schr\"odinger equations on
the one-dimensional infinite lattice. Without damping and forcing they are
represented by the integrable Ablowitz-Ladik equation (AL) featuring non-local
cubic nonlinear terms, and its standard (nonintegrable) counterpart with local
cubic nonlinear terms (DNLS). The global existence of a unique solution to the
initial value problem for both, the damped and forced AL and DNLS, is proven.
It is further shown that for sufficiently close initial data, their
corresponding solutions stay close for all times. Concerning the asymptotic
behaviour of the solutions to the damped and forced AL and DNLS, for the former
a sufficient condition for the existence of a restricted global attractor is
established while it is shown that the latter possesses a global attractor.
Finally, we prove the congruence of the restricted global AL attractor and the
DNLS attractor for dynamics ensuing from initial data contained in an
appropriate bounded subset in a Banach space.
|
2103.03533v1
|
2021-05-17
|
Dissipation of Oscillation Energy and Distribution of Damping Power in a Multimachine Power System: A Small-signal Analysis
|
This paper revisits the concept of damping torque in a multimachine power
system and its relation to the dissipation of oscillation energy in synchronous
machine windings. As a multimachine extension of an existing result on a
single-machine-infinite-bus (SMIB) system, we show that the total damping power
for a mode stemming from the interaction of electromagnetic torques and rotor
speeds is equal to the sum of average power dissipations in the generator
windings corresponding to the modal oscillation. Further, counter-intuitive to
the SMIB result, we demonstrate that, although the equality holds on an
aggregate, such is not the case for individual machines in an interconnected
system. To that end, distribution factors are derived for expressing the
average damping power of each generator as a linear combination of average
powers of modal energy dissipation in the windings of all machines in the
system. These factors represent the distribution of damping power in a
multimachine system. The results are validated on IEEE 4-machine and 16-machine
test systems.
|
2105.07618v2
|
2021-06-04
|
Imaging spin-wave damping underneath metals using electron spins in diamond
|
Spin waves in magnetic insulators are low-damping signal carriers that could
enable a new generation of spintronic devices. The excitation, control, and
detection of spin waves by metal electrodes is crucial for interfacing these
devices to electrical circuits. It is therefore important to understand
metal-induced damping of spin-wave transport, but characterizing this process
requires access to the underlying magnetic films. Here we show that spins in
diamond enable imaging of spin waves that propagate underneath metals in
magnetic insulators, and then use this capability to reveal a 100-fold increase
in spin-wave damping. By analyzing spin-wave-induced currents in the metal, we
derive an effective damping parameter that matches these observations well. We
furthermore detect buried scattering centers, highlighting the technique's
power for assessing spintronic device quality. Our results open new avenues for
studying metal - spin-wave interaction and provide access to interfacial
processes such as spin-wave injection via the spin-Hall effect.
|
2106.02508v2
|
2021-06-04
|
Inherent Non-Linear Damping in Resonators with Inertia Amplification
|
Inertia amplification is a mechanism coupling degrees of freedom within a
vibrating structure. Its goal is to achieve an apparent high dynamic mass and,
accordingly, a low resonance frequency. Such structures have been described for
use in locally resonant metamaterials and phononic crystals to lower the
starting frequency of a band gap without adding mass to the system. This study
shows that any non-linear kinematic coupling between translational or
rotational vibrations leads to the appearance of amplitude-dependent damping.
The analytical derivation of the equation of motion of a resonator with inertia
amplification creates insight in the damping process, and shows that the
vibration damping increases with its amplitude. The theoretical study is
validated by experimental evidence from two types of inertia-amplification
resonators. Finally, the importance of amplitude-dependent damping is
illustrated when the structure is used as a tuned mass damper for a cantilever
beam.
|
2106.02576v2
|
2021-06-30
|
On the effect of perturbations in first-order optimization methods with inertia and Hessian driven damping
|
Second-order continuous-time dissipative dynamical systems with viscous and
Hessian driven damping have inspired effective first-order algorithms for
solving convex optimization problems. While preserving the fast convergence
properties of the Nesterov-type acceleration, the Hessian driven damping makes
it possible to significantly attenuate the oscillations. To study the stability
of these algorithms with respect to perturbations, we analyze the behaviour of
the corresponding continuous systems when the gradient computation is subject
to exogenous additive errors. We provide a quantitative analysis of the
asymptotic behaviour of two types of systems, those with implicit and explicit
Hessian driven damping. We consider convex, strongly convex, and non-smooth
objective functions defined on a real Hilbert space and show that, depending on
the formulation, different integrability conditions on the perturbations are
sufficient to maintain the convergence rates of the systems. We highlight the
differences between the implicit and explicit Hessian damping, and in
particular point out that the assumptions on the objective and perturbations
needed in the implicit case are more stringent than in the explicit case.
|
2106.16159v2
|
2021-07-13
|
A new approach to the quantization of the damped harmonic oscillator
|
In this paper, a new approach for constructing Lagrangians for driven and
undriven linearly damped systems is proposed, by introducing a redefined time
coordinate and an associated coordinate transformation to ensure that the
resulting Lagrangian satisfies the Helmholtz conditions. The approach is
applied to canonically quantize the damped harmonic oscillator and although it
predicts an energy spectrum that decays at the same rate to previous models,
unlike those approaches it recovers the classical critical damping condition,
which determines transitions between energy eigenstates, and is therefore
consistent with the correspondence principle. It is also demonstrated how to
apply the procedure to a driven damped harmonic oscillator.
|
2107.05827v3
|
2021-10-26
|
Theory of sound attenuation in amorphous solids from nonaffine motions
|
We present a theoretical derivation of acoustic phonon damping in amorphous
solids based on the nonaffine response formalism for the viscoelasticity of
amorphous solids. The analytical theory takes into account the nonaffine
displacements in transverse waves and is able to predict both the ubiquitous
low-energy diffusive damping $\sim k^{2}$, as well as a novel contribution to
the Rayleigh damping $\sim k^{4}$ at higher wavevectors and the crossover
between the two regimes observed experimentally. The coefficient of the
diffusive term is proportional to the microscopic viscous (Langevin-type)
damping in particle motion (which arises from anharmonicity), and to the
nonaffine correction to the static shear modulus, whereas the Rayleigh damping
emerges in the limit of low anharmonicity, consistent with previous
observations and macroscopic models. Importantly, the $k^4$ Rayleigh
contribution derived here does not arise from harmonic disorder or elastic
heterogeneity effects and it is the dominant mechanism for sound attenuation in
amorphous solids as recently suggested by molecular simulations.
|
2110.13446v2
|
2021-11-21
|
Energy Transport in 1-Dimensional Oscillator Arrays With Hysteretic Damping
|
Energy transport in 1-dimensional oscillator arrays has been extensively
studied to date in the conservative case, as well as under weak viscous
damping. When driven at one end by a sinusoidal force, such arrays are known to
exhibit the phenomenon of supratransmission, i.e. a sudden energy surge above a
critical driving amplitude. In this paper, we study 1-dimensional oscillator
chains in the presence of hysteretic damping, and include nonlinear stiffness
forces that are important for many materials at high energies. We first employ
Reid's model of local hysteretic damping, and then study a new model of nearest
neighbor dependent hysteretic damping to compare their supratransmission and
wave packet spreading properties in a deterministic as well as stochastic
setting. The results have important quantitative differences, which should be
helpful when comparing the merits of the two models in specific engineering
applications.
|
2111.10816v3
|
2021-12-15
|
An Innovative Transverse Emittance Cooling Technique using a Laser-Plasma Wiggler
|
We propose an innovative beam cooling scheme based on laser driven plasma
wakefields to address the challenge of high luminosity generation for a future
linear collider. For linear colliders, beam cooling is realised by means of
damping rings equipped with wiggler magnets and accelerating cavities. This
scheme ensures systematic reduction of phase space volume through synchrotron
radiation emission whilst compensating for longitudinal momentum loss via an
accelerating cavity. In this paper, the concept of a plasma wiggler and its
effective model analogous to a magnetic wiggler are introduced; relation of
plasma wiggler characteristics with damping properties are demonstrated;
underpinning particle-in-cell simulations for laser propagation optimisation
are presented. The oscillation of transverse wakefields and resulting
sinusoidal probe beam trajectory are numerically demonstrated. The formation of
an order of magnitude larger effective wiggler field compared to conventional
wigglers is successfully illustrated. Potential damping ring designs on the
basis of this novel plasma-based technology are presented and performance in
terms of damping times and footprint was compared to an existing conventional
damping ring design.
|
2112.08163v1
|
2021-12-21
|
ISS-Based Robustness to Various Neglected Damping Mechanisms for the 1-D Wave PDE
|
This paper is devoted to the study of the robustness properties of the 1-D
wave equation for an elastic vibrating string under four different damping
mechanisms that are usually neglected in the study of the wave equation: (i)
friction with the surrounding medium of the string (or viscous damping), (ii)
thermoelastic phenomena (or thermal damping), (iii) internal friction of the
string (or Kelvin-Voigt damping), and (iv) friction at the free end of the
string (the so-called passive damper). The passive damper is also the simplest
boundary feedback law that guarantees exponential stability for the string. We
study robustness with respect to distributed inputs and boundary disturbances
in the context of Input-to-State Stability (ISS). By constructing appropriate
ISS Lyapunov functionals, we prove the ISS property expressed in various
spatial norms.
|
2112.11287v1
|
2022-01-20
|
Derivation of the linear Boltzmann equation from the damped quantum Lorentz gas with a general scatterer configuration
|
It is a fundamental problem in mathematical physics to derive macroscopic
transport equations from microscopic models. In this paper we derive the linear
Boltzmann equation in the low-density limit of a damped quantum Lorentz gas for
a large class of deterministic and random scatterer configurations. Previously
this result was known only for the single-scatterer problem on the flat torus,
and for uniformly random scatterer configurations where no damping is required.
The damping is critical in establishing convergence -- in the absence of
damping the limiting behaviour depends on the exact configuration under
consideration, and indeed, the linear Boltzmann equation is not expected to
appear for periodic and other highly ordered configurations.
|
2201.08229v2
|
2022-01-22
|
Effect of MagneticField on the Damping Behavior of a Ferrofluid based Damper
|
This paper is an extension of our earlier work where we had reported a proof
of concept for a ferrofluid based damper. The damper used ferrofluid as damping
medium and it was seen that damping efficiency of the damper changes on
application of magnetic field. The present paper deals with a systematic study
of the effect of magnetic field on the damping efficiency of the damper.
Results of these studies are reported. It is seen that damping ratio varies
linearly with magnetic field ({\zeta} / H = 0.028 per kG) for magnetic field in
range of 0.0 to 4.5 kG. It may be mentioned that ferrofluid is different from
magnetorheological fluid even though both of them are magnetic field-responsive
fluids. The ferrofluid-dampers are better suited than MR Fluid-dampers for
their use in automobiles.
|
2201.09027v1
|
2022-01-28
|
Machine learning-based method of calorimeter saturation correction for helium flux analysis with DAMPE experiment
|
DAMPE is a space-borne experiment for the measurement of the cosmic-ray
fluxes at energies up to around 100 TeV per nucleon. At energies above several
tens of TeV, the electronics of DAMPE calorimeter would saturate, leaving
certain bars with no energy recorded. In the present work we discuss the
application of machine learning techniques for the treatment of DAMPE data, to
compensate the calorimeter energy lost by saturation.
|
2201.12185v3
|
2022-03-10
|
Accelerated gradient methods combining Tikhonov regularization with geometric damping driven by the Hessian
|
In a Hilbert setting, for convex differentiable optimization, we consider
accelerated gradient dynamics combining Tikhonov regularization with
Hessian-driven damping. The Tikhonov regularization parameter is assumed to
tend to zero as time tends to infinity, which preserves equilibria. The
presence of the Tikhonov regularization term induces a strong convexity
property which vanishes asymptotically. To take advantage of the exponential
convergence rates attached to the heavy ball method in the strongly convex
case, we consider the inertial dynamic where the viscous damping coefficient is
taken proportional to the square root of the Tikhonov regularization parameter,
and therefore also converges towards zero. Moreover, the dynamic involves a
geometric damping which is driven by the Hessian of the function to be
minimized, which induces a significant attenuation of the oscillations. Under
an appropriate tuning of the parameters, based on Lyapunov's analysis, we show
that the trajectories have at the same time several remarkable properties: they
provide fast convergence of values, fast convergence of gradients towards zero,
and strong convergence to the minimum norm minimizer. This study extends a
previous paper by the authors where similar issues were examined but without
the presence of Hessian driven damping.
|
2203.05457v2
|
2022-04-01
|
On the Importance of High-Frequency Damping in High-Order Conservative Finite-Difference Schemes for Viscous Fluxes
|
This paper discusses the importance of high-frequency damping in high-order
conservative finite-difference schemes for viscous terms in the Navier-Stokes
equations. Investigating nonlinear instability encountered in a high-resolution
viscous shock-tube simulation, we have discovered that a modification to the
viscous scheme rather than the inviscid scheme resolves a problem with spurious
oscillations around shocks. The modification introduces a term responsible for
high-frequency damping that is missing in a conservative high-order viscous
scheme. The importance of damping has been known for schemes designed for
unstructured grids. However, it has not been recognized well in very high-order
difference schemes, especially in conservative difference schemes. Here, we
discuss how it is easily missed in a conservative scheme and how to improve
such schemes by a suitably designed damping term.
|
2204.00393v1
|
2022-06-20
|
Stability and Damping in the Disks of Massive Galaxies
|
After their initial formation, disk galaxies are observed to be rotationally
stable over periods of >6 Gyr, implying that any large velocity disturbances of
stars and gas clouds are damped rapidly on the timescale of their rotation.
However, it is also known that despite this damping, there must be a degree of
random local motion to stabilize the orbits against degenerate collapse. A
mechanism for such damping is proposed by a combination of inter-stellar
gravitational interactions, and interactions with the Oort clouds and exo-Oort
objects associated with each star. Analysis of the gravitational interactions
between two stars is a three-body problem, because the stars are also in orbit
round the large virtual mass of the galaxy. These mechanisms may produce rapid
damping of large perturbations within a time period that is short on the scale
of observational look-back time, but long on the scale of the disk rotational
period for stars with small perturbations. This mechanism may also account for
the locally observed mean perturbations in the Milky Way of 8-15~km/s for
younger stars and 20-30~km/s for older stars.
|
2206.09671v2
|
2022-08-25
|
The Effect of Frequency Droop Damping on System Parameters and Battery Sizing During Load Change Condition
|
Inverter-based resources (IBR) have been widely studied for their advantages
on the current power systems. This increase in the penetration of renewable
energy has raised some concerns about the stability of the existing grid.
Historically, power systems are dominated by synchronous generators that can
easily react to system instability due to high inertia and damping
characteristics. However, with IBR, the control of the inverter plays a crucial
role in contributing to the system stability and enhancing the functionality of
the inverters. One of these novel control methods is droop control. Droop
characteristics are used to control voltage, frequency, and active and reactive
power. This paper presents the impact of frequency droop damping on system
frequency, real power, and the rate of change of frequency with distributed
energy resources. Also, battery sizing is suggested based on the results. The
results also show the need for optimal selection for the frequency droop
damping to fulfill the appropriate battery size in terms of cost and
performance. The simulations are carried out in an electromagnetic transient
program (EMTP)
|
2208.12291v1
|
2022-09-15
|
Superfluid $^4$He as a rigorous test bench for different damping models in nanoelectromechanical resonators
|
We have used nanoelectromechanical resonators to probe superfluid $^4$He at
different temperature regimes, spanning over four orders of magnitude in
damping. These regimes are characterized by the mechanisms which provide the
dominant contributions to damping and the shift of the resonance frequency:
tunneling two level systems at the lowest temperatures, ballistic phonons and
rotons at few hundred mK, and laminar drag in the two-fluid regime below the
superfluid transition temperature as well as in the normal fluid. Immersing the
nanoelectromechanical resonators in fluid increases their effective mass
substantially, decreasing their resonance frequency. Dissipationless superflow
gives rise to a unique possibility to dramatically change the mechanical
resonance frequency in situ, allowing rigorous tests on different damping
models in mechanical resonators. We apply this method to characterize tunneling
two-level system losses and magnetomotive damping in the devices.
|
2209.07229v2
|
2022-11-08
|
On the injection scale of the turbulence in the partially ionized very local interstellar medium
|
The cascade of magnetohydrodynamic (MHD) turbulence is subject to ion-neutral
collisional damping and neutral viscous damping in the partially ionized
interstellar medium. By examining the damping effects in the warm and partially
ionized local interstellar medium, we find that the interstellar turbulence is
damped by neutral viscosity at $\sim 261$ au and cannot account for the
turbulent magnetic fluctuations detected by Voyager 1 and 2. The MHD turbulence
measured by Voyager in the very local interstellar medium (VLISM) should be
locally injected in the regime where ions are decoupled from neutrals for its
cascade to survive the damping effects. With the imposed ion-neutral decoupling
condition, and the strong turbulence condition for the observed Kolmogorov
magnetic energy spectrum, we find that the turbulence in the VLISM is
sub-Alfv\'{e}nic, and its largest possible injection scale is $\sim 194$ au.
|
2211.04496v1
|
2022-12-11
|
The overtone level spacing of a black hole quasinormal frequencies: a fingerprint of a local $SL(2,\mathbb{R})$ symmetry
|
The imaginary part of the quasinormal frequencies spectrum for a static and
spherically symmetric black hole is analytically known to be equally spaced,
both for the highly damped and the weakly damped families of quasinormal modes.
Some interesting attempts have been made in the last twenty years to understand
in simple ways this level spacing for the only case of highly damped
quasinormal frequencies. Here, we show that the overtone level spacing, for
both the highly damped and weakly damped families of quasinormal modes, can
simply be understood as a fingerprint of a hidden local $SL(2,\mathbb{R})$
symmetry, near different regions of the black hole spacetime, i.e. the
near-horizon and the near-photon sphere regions.
|
2212.05538v1
|
2022-12-15
|
Formation of shifted shock for the 3D compressible Euler equations with time-dependent damping
|
In this paper, we show the shock formation to the compressible Euler
equations with time-dependent damping $\frac{a\p u}{(1+t)^{\lam}}$ in three
spatial dimensions without any symmetry conditions. It's well-known that for
$\lam>1$, the damping is too weak to prevent the shock formation for suitably
large data. However, the classical results only showed the finite existence of
the solution. Follow the work by D.Christodoulou in\cite{christodoulou2007},
starting from the initial isentropic and irrotational short pulse data, we show
the formation of shock is characterized by the collapse of the characteristic
hypersurfaces and the vanishing of the inverse foliation density function
$\mu$, at which the first derivatives of the velocity and the density blow up,
and the lifespan $T_{\ast}(a,\lam)$ is exponentially large. Moreover, the
damping effect will shift the time of shock formation $T_{\ast}$. The methods
in the paper can also be extended to the Euler equations with general
time-decay damping.
|
2212.07828v1
|
2023-01-15
|
Damped-driven system of bouncing droplets leading to deterministic diffusive behavior
|
Damped-driven systems are ubiquitous in science, however the damping and
driving mechanisms are often quite convoluted. This manuscript presents an
experimental and theoretical investigation of a fluidic droplet on a vertically
vibrating fluid bath as a damped-driven system. We study a fluidic droplet in
an annular cavity with the fluid bath forced above the Faraday wave threshold.
We model the droplet as a kinematic point particle in air and as inelastic
collisions during impact with the bath. In both experiments and the model the
droplet is observed to chaotically change velocity with a Gaussian
distribution. Finally, the statistical distributions from experiments and
theory are analyzed. Incredibly, this simple deterministic interaction of
damping and driving of the droplet leads to more complex Brownian-like and
Levy-like behavior.
|
2301.06041v2
|
2023-03-01
|
Generation of intraparticle quantum correlations in amplitude damping channel and its robustness
|
Quantum correlations between two or more different degrees of freedom of the
same particle is sometimes referred to as intraparticle entanglement. In this
work, we study these intra-particle correlations between two different degrees
of freedom under various decoherence channels viz. amplitude damping,
depolarising and phase damping channels. We observe a unique feature of the
amplitude damping channel, wherein entanglement is shown to arise starting from
separable states. In case of non maximally entangled input states, in addition
to entanglement sudden death, the creation of entanglement is also observed,
having an asymptotic decay over a long time. These counter-intuitive behaviours
arise due to the subtle interplay of channel and input state parameters, and
are not seen for interparticle entanglement without consideration of
non-Markovian noise. It is also not observed for maximally entangled input
states. Furthermore, investigation of entanglement evolution in phase damping
and depolarizing channels shows its robustness against decoherence as compared
to interparticle entanglement.
|
2303.01238v1
|
2023-03-16
|
Quantum Brownian Motion in the Caldeira-Leggett Model with a Damped Environment
|
We model a quantum system coupled to an environment of damped harmonic
oscillators by following the approach of Caldeira-Leggett and adopting the
Caldirola-Kanai Lagrangian for the bath oscillators. In deriving the master
equation of the quantum system of interest (a particle in a general potential),
we show that the potential is modified non-trivially by a new inverted harmonic
oscillator term, induced by the damping of the bath oscillators. We analyze
numerically the case of a particle in a double-well potential, and find that
this modification changes both the rate of decoherence at short times and the
well-transfer probability at longer times. We also identify a simple rescaling
condition that keeps the potential fixed despite changes in the environmental
damping. Here, the increase of environmental damping leads to a slowing of
decoherence.
|
2303.09516v1
|
2023-03-22
|
A Numerical Study of Landau Damping with PETSc-PIC
|
We present a study of the standard plasma physics test, Landau damping, using
the Particle-In-Cell (PIC) algorithm. The Landau damping phenomenon consists of
the damping of small oscillations in plasmas without collisions. In the PIC
method, a hybrid discretization is constructed with a grid of finitely
supported basis functions to represent the electric, magnetic and/or
gravitational fields, and a distribution of delta functions to represent the
particle field. Approximations to the dispersion relation are found to be
inadequate in accurately calculating values for the electric field frequency
and damping rate when parameters of the physical system, such as the plasma
frequency or thermal velocity, are varied. We present a full derivation and
numerical solution for the dispersion relation, and verify the PETSC-PIC
numerical solutions to the Vlasov-Poisson for a large range of wave numbers and
charge densities.
|
2303.12620v1
|
2023-04-07
|
Shifted shock formation for the 3D compressible Euler equations with damping and variation of the vorticity
|
In this paper, we consider the shock formation problem for the
3-dimensional(3D) compressible Euler equations with damping inspired by the
work \cite{BSV3Dfulleuler}. It will be shown that for a class of large data,
the damping can not prevent the formation of point shock, and the damping
effect shifts the shock time and the wave amplitude while the shock location
and the blow up direction remain the same with the information of this point
shock being computed explicitly. Moreover, the vorticity is concentrated in the
non-blow-up direction, which varies exponentially due to the damping effect.
Our proof is based on the estimates for the modulated self-similar variables
and lower bounds for the Lagrangian trajectories.
|
2304.03506v2
|
2023-07-05
|
Bayesian evidence for two slow-wave damping models in hot coronal loops
|
We compute the evidence in favour of two models, one based on field-aligned
thermal conduction alone and another that includes thermal misbalance as well,
in explaining the damping of slow magneto-acoustic waves in hot coronal loops.
Our analysis is based on the computation of the marginal likelihood and the
Bayes factor for the two damping models. We quantify their merit in explaining
the apparent relationship between slow mode periods and damping times, measured
with SOHO/SUMER in a set of hot coronal loops. The results indicate evidence in
favour of the model with thermal misbalance in the majority of the sample, with
a small population of loops for which thermal conduction alone is more
plausible. The apparent possibility of two different regimes of slow-wave
damping, if due to differences between the loops of host active regions and/or
the photospheric dynamics, may help with revealing the coronal heating
mechanism.
|
2307.02439v1
|
2023-07-24
|
From characteristic functions to multivariate distribution functions and European option prices by the damped COS method
|
We provide a unified framework for the computation of the distribution
function and the computation of prices of financial options from the
characteristic function of some density by the COS method. The classical COS
method is numerically very efficient in one-dimension but cannot deal very well
with certain financial options in general dimensions. Therefore, we introduce
the damped COS method which can handle a large class of integrands very
efficiently. We prove the convergence of the (damped) COS method and study its
order of convergence. The (damped) COS method converges exponentially if the
characteristic function decays exponentially. To apply the (damped) COS method,
one has to specify two parameters: a truncation range for the multivariate
density and the number of terms to approximate the truncated density by a
cosine series. We provide an explicit formula for the truncation range and an
implicit formula for the number of terms. Numerical experiments up to five
dimensions confirm the theoretical results.
|
2307.12843v6
|
2023-07-26
|
A Nonlinear Damped Metamaterial: Wideband Attenuation with Nonlinear Bandgap and Modal Dissipation
|
In this paper, we incorporate the effect of nonlinear damping with the
concept of locally resonant metamaterials to enable vibration attenuation
beyond the conventional bandgap range. The proposed design combines a linear
host cantilever beam and periodically distributed inertia amplifiers as
nonlinear local resonators. The geometric nonlinearity induced by the inertia
amplifiers causes an amplitude-dependent nonlinear damping effect. Through the
implementation of both modal superposition and numerical harmonic methods the
finite nonlinear metamaterial is accurately modelled. The resulting nonlinear
frequency response reveals the bandgap is both amplitude-dependent and
broadened. Furthermore, the modal frequencies are also attenuated due to the
nonlinear damping effect. The theoretical results are validated experimentally.
By embedding the nonlinear damping effect into locally resonant metamaterials,
wideband attenuation of the proposed metamaterial is achieved, which opens new
possibilities for versatile metamaterials beyond the limit of their linear
counterparts.
|
2307.14165v2
|
2023-07-28
|
Premature jump-down mimicks nonlinear damping in nanoresonators
|
Recent experiments on nano-resonators in a bistable regime use the
`jump-down' point between states to infer mechanical properties of the membrane
or a load, but often suggest the presence of some nonlinear damping. Motivated
by such experiments, we develop a mechanical model of a membrane subject to a
uniform, oscillatory load and linear damping. We solve this model numerically
and compare its jump-down behaviour with standard asymptotic predictions for a
one-dimensional Duffing oscillator with strain stiffening. We show that the
axisymmetric, but spatially-varying, problem can be mapped to the Duffing
problem with coefficients determined rationally from the model's Partial
Differential Equations. However, we also show that jump-down happens earlier
than expected (i.e.~at lower frequency, and with a smaller oscillation
amplitude). Although this premature jump-down is often interpreted as the
signature of a nonlinear damping in experiments, its appearance in numerical
simulations with only linear damping suggests instead that indicate that the
limitations of asymptotic results may, at least sometimes, be the cause. We
therefore suggest that care should be exercised in interpreting the results of
nano-resonator experiments.
|
2307.15656v1
|
2023-09-22
|
Long time energy averages and a lower resolvent estimate for damped waves
|
We consider the damped wave equation on a compact manifold. We propose
different ways of measuring decay of the energy (time averages of lower energy
levels, decay for frequency localized data...) and exhibit links with resolvent
estimates on the imaginary axis. As an application we prove a universal
logarithmic lower resolvent bound on the imaginary axis for the damped wave
operator when the Geometric Control Condition (GCC) is not satisfied. This is
to be compared to the uniform boundedness of the resolvent on that set when GCC
holds. The proofs rely on (i) various (re-)formulations of the damped wave
equation as a conservative hyperbolic part perturbed by a lower order damping
term;(ii) a "Plancherel-in-time" argument as in classical proofs of the
Gearhart-Huang-Pr{\"u}ss theorem; and (iii) an idea of Bony-Burq-Ramond of
propagating a coherent state along an undamped trajectory up to Ehrenfest time.
|
2309.12709v1
|
2023-10-11
|
Damping Density of an Absorptive Shoebox Room Derived from the Image-Source Method
|
The image-source method is widely applied to compute room impulse responses
(RIRs) of shoebox rooms with arbitrary absorption. However, with increasing RIR
lengths, the number of image sources grows rapidly, leading to slow
computation. In this paper, we derive a closed-form expression for the damping
density, which characterizes the overall multi-slope energy decay. The
omnidirectional energy decay over time is directly derived from the damping
density. The resulting energy decay model accurately matches the late
reverberation simulated via the image-source method. The proposed model allows
the fast stochastic synthesis of late reverberation by shaping noise with the
energy envelope. Simulations of various wall damping coefficients demonstrate
the model's accuracy. The proposed model consistently outperforms the energy
decay prediction accuracy compared to a state-of-the-art approximation method.
The paper elaborates on the proposed damping density's applicability to
modeling multi-sloped sound energy decay, predicting reverberation time in
non-diffuse sound fields, and fast frequency-dependent RIR synthesis.
|
2310.07363v1
|
2023-10-14
|
Exploring Damping Effect of Inner Control Loops for Grid-Forming VSCs
|
This paper presents an analytical approach to explore the damping effect of
inner loops on grid-forming converters. First, an impedance model is proposed
to characterize the behaviors of inner loops, thereby illustrating their
influence on output impedance shaping. Then, based on the impedance
representation, the complex torque coefficient method is employed to assess the
contribution of inner loops to system damping. The interactions among inner
loops, outer loops, and the ac grid are analyzed. It reveals that inner loops
shape the electrical damping torque coefficient and consequently influence both
synchronous and sub-synchronous oscillation modes. The virtual admittance and
current control-based inner-loop scheme is employed to illustrate the proposed
analytical approach. The case study comprises the analysis of impedance
profiles, the analysis of damping torque contributed by inner loops under
various grid strengths, and the comparison between dq-frame and
{\alpha}\b{eta}-frame realizations of inner loops. Finally, simulation and
experimental tests collaborate with theoretical approaches and findings.
|
2310.09660v1
|
2023-10-24
|
Frictional weakening of a granular sheared layer due to viscous rolling revealed by Discrete Element Modeling
|
Considering a 3D sheared granular layer modeled with discrete elements, it is
well known the rolling resistance significantly influences the mechanical
behavior. Even if the rolling resistance role has been deeply investigated as
it is commonly used to represent the the roughness of the grains and the
interparticle locking, the role of rolling viscous damping coefficient has been
largely overlooked so far. This parameter is rarely used or only to dissipate
the energy and to converge numerically. This paper revisits the physical role
of those coefficients with a parametric study of the rolling friction and the
rolling damping for a sheared layer at different shear speeds and different
confinement pressures. It has been observed that the damping coefficient
induces a frictional weakening. Hence, competition between the rolling
resistance and the rolling damping occurs. Angular resistance aims to avoid
grains rolling, decreasing the difference between the angular velocities of
grains. Whereas, angular damping acts in the opposite, avoiding a change in the
difference between the angular velocities of grains. In consequence, grains
keep rolling and the sample strength decreases. This effect must be considered
to not overestimate the frictional response of a granular layer.
|
2310.15945v1
|
2023-12-12
|
Coordination of Damping Controllers: A Data-Informed Approach for Adaptability
|
This work proposes a data-informed approach for an adaptable coordination of
damping controllers. The novel concept of coordination is based on minimizing
the Total Action, a single metric that measures the system's dynamic response
post-disturbance. This is a performance measure based on the physics of the
power system, which encapsulates the oscillation energy related to synchronous
generators. Deep learning theory is used to propose a Total Action function
approximator, which captures the relationship between the system wide-area
measurements, the status of damping controllers, and the conditions of the
disturbance. By commissioning the switching status (on/off) of damping
controllers in real-time, the oscillation energy is reduced, enhancing the
power system stability. The concept is tested in the Western North America
Power System (wNAPS) and compared with a model-based approach for the
coordination of damping controllers. The data-informed coordination outperforms
the model-based approach, demonstrating exceptional adaptability and
performance to handle multi-modal events. The proposed scheme shows outstanding
reductions in low-frequency oscillations even under various operating
conditions, fault locations, and time delay considerations.
|
2312.07739v1
|
2024-01-26
|
Efficient Control of Magnetization Dynamics Via W/CuO$_\text{x}$ Interface
|
Magnetization dynamics, which determine the speed of magnetization switching
and spin information propagation, play a central role in modern spintronics.
Gaining its control will satisfy the different needs of various spintronic
devices. In this work, we demonstrate that the surface oxidized Cu
(CuO$_\text{x}$) can be employed for the tunability of magnetization dynamics
of ferromagnet (FM)/heavy metal (HM) bilayer system. The capping CuO$_\text{x}$
layer in CoFeB/W/CuO$_\text{x}$ trilayer reduces the magnetic damping value in
comparison with the CoFeB/W bilayer. The magnetic damping even becomes lower
than that of the CoFeB/CuO$_\text{x}$ by ~ 16% inferring the stabilization of
anti-damping phenomena. Further, the reduction in damping is accompanied by a
very small reduction in the spin pumping-induced output DC voltage in the
CoFeB/W/CuO$_\text{x}$ trilayer. The simultaneous observation of anti-damping
and spin-to-charge conversion can be attributed to the orbital Rashba effect
observed at the HM/CuO$_\text{x}$ interface. Our experimental findings
illustrate that the cost-effective CuO$_\text{x}$ can be employed as an
integral part of modern spintronics devices owing to its rich underneath
spin-orbital physics.
|
2401.14708v1
|
2024-02-08
|
The stability analysis based on viscous theory of Faraday waves in Hele-Shaw cells
|
The linear instability of Faraday waves in Hele-Shaw cells is investigated
with consideration of the viscosity of fluids after gap-averaging the governing
equations due to the damping from two lateral walls and the dynamic behavior of
contact angle. A new hydrodynamic model is thus derived and solved
semi-analytically. The contribution of viscosity to critical acceleration
amplitude is slight compared to other factors associated with dissipation, and
the potential flow theory is sufficient to describe onset based on the present
study, but the rotational component of velocity can change the timing of onset
largely, which paradoxically comes from the viscosity. The model degenerates
into a novel damped Mathieu equation if the viscosity is dropped with two
damping terms referring to the gap-averaged damping and dissipation from
dynamic contact angle, respectively. The former increases when the gap size
decreases, and the latter grows as frequency rises. When it comes to the
dispersion relation of Faraday waves, an unusual detuning emerges due to the
imaginary part of the gap-averaged damping.
|
2402.05505v2
|
2024-02-09
|
Damping of density oscillations from bulk viscosity in quark matter
|
We study the damping of density oscillations in the quark matter phase that
might occur in compact stars. To this end we compute the bulk viscosity and the
associated damping time in three-flavor quark matter, considering both
nonleptonic and semileptonic electroweak processes. We use two different
equations of state of quark matter, more precisely, the MIT bag model and
perturbative QCD, including the leading order corrections in the strong
coupling constant. We analyze the dependence of our results on the density,
temperature and value of strange quark mass in each case. We then find that the
maximum of the bulk viscosity is in the range of temperature from 0.01 to 0.1
MeV for frequencies around 1 kHz, while the associated minimal damping times of
the density oscillations at those temperatures might be in the range of few to
hundreds milliseconds. Our results suggest that bulk viscous damping might be
relevant in the post-merger phase after the collision of two neutron stars if
deconfined matter is achieved in the process.
|
2402.06595v1
|
2003-08-05
|
Reliability of Calderbank-Shor-Steane Codes and Security of Quantum Key Distribution
|
After Mayers (1996, 2001) gave a proof of the security of the
Bennett-Brassard 1984 (BB84) quantum key distribution protocol, Shor and
Preskill (2000) made a remarkable observation that a Calderbank-Shor-Steane
(CSS) code had been implicitly used in the BB84 protocol, and suggested its
security could be proven by bounding the fidelity, say F(n), of the
incorporated CSS code of length n in the form 1-F(n) <= exp[-n E+o(n)] for some
positive number E. This work presents such a number E=E(R) as a function of the
rate of a code R, and a threshold R' such that E(R)>0 whenever R < R', which is
larger than the achievable rate based on the Gilbert-Varshamov bound that is
essentially due to Shor and Preskill (2000). The codes in the present work are
robust against fluctuations of channel parameters, which fact is needed to
establish the security rigorously and was not proved for rates above the
Gilbert-Varshamov rate before in the literature. As a byproduct, the security
of a modified BB84 protocol against any joint (coherent) attacks is proved
quantitatively.
|
0308029v6
|
2011-07-13
|
(In-)Stability of Singular Equivariant Solutions to the Landau-Lifshitz-Gilbert Equation
|
In this paper we use formal asymptotic arguments to understand the stability
proper- ties of equivariant solutions to the Landau-Lifshitz-Gilbert model for
ferromagnets. We also analyze both the harmonic map heatflow and Schrodinger
map flow limit cases. All asymptotic results are verified by detailed numerical
experiments, as well as a robust topological argument. The key result of this
paper is that blowup solutions to these problems are co-dimension one and hence
both unstable and non-generic. Solutions permitted to deviate from radial
symmetry remain global for all time but may, for suitable initial data,
approach arbitrarily close to blowup. A careful asymptotic analysis of
solutions near blowup shows that finite-time blowup corresponds to a saddle
fixed point in a low dimensional dynamical system. Radial symmetry precludes
motion anywhere but on the stable manifold towards blowup. A similar scenario
emerges in the equivariant setting: blowup is unstable. To be more precise,
blowup is co-dimension one both within the equivariant symmetry class and in
the unrestricted class of initial data. The value of the parameter in the
Landau-Lifshitz-Gilbert equation plays a very subdued role in the analysis of
equivariant blowup, leading to identical blowup rates and spatial scales for
all parameter values. One notable exception is the angle between solution in
inner scale (which bubbles off) and outer scale (which remains), which does
depend on parameter values. Analyzing near-blowup solutions, we find that in
the inner scale these solution quickly rotate over an angle {\pi}. As a
consequence, for the blowup solution it is natural to consider a continuation
scenario after blowup where one immediately re-attaches a sphere (thus
restoring the energy lost in blowup), yet rotated over an angle {\pi}. This
continuation is natural since it leads to continuous dependence on initial
data.
|
1107.2620v1
|
1996-09-10
|
The Damping Tail of CMB Anisotropies
|
By decomposing the damping tail of CMB anisotropies into a series of transfer
functions representing individual physical effects, we provide ingredients that
will aid in the reconstruction of the cosmological model from small-scale CMB
anisotropy data. We accurately calibrate the model-independent effects of
diffusion and reionization damping which provide potentially the most robust
information on the background cosmology. Removing these effects, we uncover
model-dependent processes such as the acoustic peak modulation and
gravitational enhancement that can help distinguish between alternate models of
structure formation and provide windows into the evolution of fluctuations at
various stages in their growth.
|
9609079v1
|
1997-09-16
|
Lyman-alpha emission as a tool to study high redshift damped systems
|
We report a quantitative study of the escape of Lyman-alpha photons from an
inhomogeneous optically thick medium that mimics the structure of damped
Lyman-alpha absorbers. Modeling the optically thick disk with 3 components
(massive stars and HII regions, dust, and neutral hydrogen), we study the
resulting emission line profile that may arise near the extended damped
absorption profile.
|
9709150v1
|
1997-10-17
|
The chemical evolution of galaxies causing damped Ly$α$ absorption
|
We have compiled all available data on chemical abundances in damped Lyman
alpha absorption systems for comparison with results from our combined chemical
and spectrophotometric galaxy evolution models. Preliminary results from
chemically consistent calculations are in agreement with observations of damped
Ly$\alpha$ systems.
|
9710193v1
|
1998-01-26
|
Are Damped Lyman alpha Systems Rotating Disks ?
|
We report on high spectral resolution observations of five damped Lyman alpha
systems whose line velocity profiles and abundances are analyzed. By combining
these data with information from the literature, we study the kinematics of the
low and high ionization phases of damped systems and discuss the possibility
that part of the motions is due to rotation.
|
9801243v1
|
2001-10-29
|
Damping of inhomogeneities in neutralino dark matter
|
The lightest supersymmetric particle, most likely the neutralino, might
account for a large fraction of dark matter in the Universe. We show that the
primordial spectrum of density fluctuations in neutralino cold dark matter
(CDM) has a sharp cut-off due to two damping mechanisms: collisional damping
during the kinetic decoupling of the neutralinos at O(10 MeV) and free
streaming after last scattering of neutralinos. The cut-off in the primordial
spectrum defines a minimal mass for CDM objects in hierarchical structure
formation. For typical neutralino and sfermion masses the first gravitationally
bound neutralino clouds have masses above 10^(-6) M_\odot.
|
0110601v1
|
2002-08-03
|
Adiabatic Index of Dense Matter and Damping of Neutron Star Pulsations
|
The adiabatic index Gamma_1 for perturbations of dense matter is studied
under various physical conditions which can prevail in neutron star cores. The
dependence of Gamma_1 on the composition of matter (in particular, on the
presence of hyperons), on the stellar pulsation amplitude, and on the baryon
superfluidity is analyzed. Timescales of damping of stellar pulsations are
estimated at different compositions, temperatures, and pulsation amplitudes.
Damping of pulsations by bulk viscosity in the neutron-star cores can prevent
the stars to pulsate with relative amplitudes > (1-15)% (depending on the
composition of matter).
|
0208078v1
|
2003-01-07
|
Damping of Neutron Star Shear Modes by Superfluid Friction
|
The forced motion of superfluid vortices in shear oscillations of rotating
solid neutron star matter produces damping of the mode. A simple model of the
unpinning and repinning processes is described, with numerical calculations of
the consequent energy decay times. These are of the order of 1 s or more for
typical anomalous X-ray pulsars but become very short for the general
population of radio pulsars. The superfluid friction processes considered here
may also be significant for the damping of r-modes in rapidly rotating neutron
stars.
|
0301112v1
|
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