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2020-05-13
|
Periodically Forced Nonlinear Oscillators With Hysteretic Damping
|
We perform a detailed study of the dynamics of a nonlinear, one-dimensional
oscillator driven by a periodic force under hysteretic damping, whose linear
version was originally proposed and analyzed by Bishop in [1]. We first add a
small quadratic stiffness term in the constitutive equation and construct the
periodic solution of the problem by a systematic perturbation method,
neglecting transient terms as $t\rightarrow \infty$. We then repeat the
analysis replacing the quadratic by a cubic term, which does not allow the
solutions to escape to infinity. In both cases, we examine the dependence of
the amplitude of the periodic solution on the different parameters of the model
and discuss the differences with the linear model. We point out certain
undesirable features of the solutions, which have also been alluded to in the
literature for the linear Bishop's model, but persist in the nonlinear case as
well. Finally, we discuss an alternative hysteretic damping oscillator model
first proposed by Reid [2], which appears to be free from these difficulties
and exhibits remarkably rich dynamical properties when extended in the
nonlinear regime.
|
2005.06187v1
|
2020-05-13
|
Magnetic circular dichroism spectra from resonant and damped coupled cluster response theory
|
A computational expression for the Faraday A term of magnetic circular
dichroism (MCD) is derived within coupled cluster response theory and
alternative computational expressions for the B term are discussed. Moreover,
an approach to compute the (temperature-independent) MCD ellipticity in the
context of coupled cluster damped response is presented, and its equivalence
with the stick-spectrum approach in the limit of infinite lifetimes is
demonstrated. The damped response approach has advantages for molecular systems
or spectral ranges with a high density of states. Illustrative results are
reported at the coupled cluster singles and doubles level and compared to
time-dependent density functional theory results.
|
2005.06190v1
|
2020-05-21
|
Convective Excitation and Damping of Solar-like Oscillations
|
The last decade has seen a rapid development in asteroseismology thanks to
the CoRoT and Kepler missions. With more detailed asteroseismic observations
available, it is becoming possible to infer exactly how oscillations are driven
and dissipated in solar-type stars. We have carried out three-dimensional (3D)
stellar atmosphere simulations together with one-dimensional (1D) stellar
structural models of key benchmark turn-off and subgiant stars to study this
problem from a theoretical perspective. Mode excitation and damping rates are
extracted from 3D and 1D stellar models based on analytical expressions. Mode
velocity amplitudes are determined by the balance between stochastic excitation
and linear damping, which then allows the estimation of the frequency of
maximum oscillation power, $\nu_{\max}$, for the first time based on ab initio
and parameter-free modelling. We have made detailed comparisons between our
numerical results and observational data and achieved very encouraging
agreement for all of our target stars. This opens the exciting prospect of
using such realistic 3D hydrodynamical stellar models to predict solar-like
oscillations across the HR-diagram, thereby enabling accurate estimates of
stellar properties such as mass, radius and age.
|
2005.10519v1
|
2020-05-21
|
Non-Markovian memory in a measurement-based quantum computer
|
We study the exact open system dynamics of single qubit gates during a
measurement-based quantum computation considering non-Markovian environments.
We obtain analytical solutions for the average gate fidelities and analyze it
for amplitude damping and dephasing channels. We show that the average fidelity
is identical for the X-gate and Z-gate and that neither fast application of the
projective measurements necessarily implies high gate fidelity, nor slow
application necessarily implies low gate fidelity. Indeed, for highly
non-Markovian environments, it is of utmost importance to know the best time to
perform the measurements, since a huge variation in the gate fidelity may occur
given this scenario. Furthermore, we show that while for the amplitude damping
the knowledge of the dissipative map is sufficient to determine the best
measurement times, i.e. the best times in which measures are taken, the same is
not necessarily true for the phase damping. To the later, the time of the set
of measures becomes crucial since a phase error in one qubit can fix the phase
error that takes place in another.
|
2005.10883v1
|
2020-05-22
|
Improving Dynamic Performance of Low-Inertia Systems through Eigensensitivity Optimization
|
An increasing penetration of renewable generation has led to reduced levels
of rotational inertia and damping in the system. The consequences are higher
vulnerability to disturbances and deterioration of the dynamic response of the
system. To overcome these challenges, novel converter control schemes that
provide virtual inertia and damping have been introduced, which raises the
question of optimal distribution of such devices throughout the network. This
paper presents a framework for performance-based allocation of virtual inertia
and damping to the converter-interfaced generators in a low-inertia system.
This is achieved through an iterative, eigensensitivity-based optimization
algorithm that determines the optimal controller gains. Two conceptually
different problem formulations are presented and validated on a 3-area, 12-bus
test system.
|
2005.11032v1
|
2020-05-24
|
Theory of Solutions for An Inextensible Cantilever
|
Recent equations of motion for the large deflections of a cantilevered
elastic beam are analyzed. In the traditional theory of beam (and plate) large
deflections, nonlinear restoring forces are due to the effect of stretching on
bending; for an inextensible cantilever, the enforcement of arc-length
preservation leads to quasilinear stiffness effects and inertial effects that
are both nonlinear and nonlocal. For this model, smooth solutions are
constructed via a spectral Galerkin approach. Additional compactness is needed
to pass to the limit, and this is obtained through a complex procession of
higher energy estimates. Uniqueness is obtained through a non-trivial
decomposition of the nonlinearity. The confounding effects of nonlinear inertia
are overcome via the addition of structural (Kelvin-Voigt) damping to the
equations of motion. Local well-posedness of smooth solutions is shown first in
the absence of nonlinear inertial effects, and then shown with these inertial
effects present, taking into account structural damping. With damping in force,
global-in-time, strong well-posedness result is obtained by achieving
exponential decay for small data.
|
2005.11836v2
|
2020-05-25
|
Nonlinear losses in magnon transport due to four-magnon scattering
|
We report on the impact of nonlinear four-magnon scattering on magnon
transport in microstructured Co25Fe75 waveguides with low magnetic damping. We
determine the magnon propagation length with microfocused Brillouin light
scattering over a broad range of excitation powers and detect a decrease of the
attenuation length at high powers. This is consistent with the onset of
nonlinear four-magnon scattering. Hence, it is critical to stay in the linear
regime, when deriving damping parameters from the magnon propagation length.
Otherwise, the intrinsic nonlinearity of magnetization dynamics may lead to a
misinterpretation of magnon propagation lengths and, thus, to incorrect values
of the magnetic damping of the system.
|
2005.12113v2
|
2020-06-02
|
Rigid body dynamics of diamagnetically levitating graphite resonators
|
Diamagnetic levitation is a promising technique for realizing resonant
sensors and energy harvesters, since it offers thermal and mechanical isolation
from the environment at zero power. To advance the application of
diamagnetically levitating resonators, it is important to characterize their
dynamics in the presence of both magnetic and gravitational fields. Here we
experimentally actuate and measure rigid body modes of a diamagnetically
levitating graphite plate. We numerically calculate the magnetic field and
determine the influence of magnetic force on the resonance frequencies of the
levitating plate. By analyzing damping mechanisms, we conclude that eddy
current damping dominates dissipation in mm-sized plates. We use finite element
simulations to model eddy current damping and find close agreement with
experimental results. We also study the size-dependent Q-factors (Qs) of
diamagnetically levitating plates and show that Qs above 100 million are
theoretically attainable by reducing the size of the diamagnetic resonator down
to microscale, making these systems of interest for next generation low-noise
resonant sensors and oscillators.
|
2006.01733v3
|
2020-06-11
|
Signatures of Spatial Curvature on Growth of Structures
|
We write down Boltzmann equation for massive particles in a spatially curved
FRW universe and solve the approximate line-of-sight solution for evolution of
matter density, including the effects of spatial curvature to the first order
of approximation. It is shown that memory of early time gravitational potential
is affected by presence of spatial curvature. Then we revisit Boltzmann
equation for photons in the general FRW background. Using it, we show that how
the frequency of oscillations and damping factor (known as Silk damping)
changed in presence of spatial curvature. At last, using this modified damping
factor in hydrodynamic regime of cosmological perturbations, we find our
analytic solution which shows the effects of spatial curvature on growing mode
of matter density.
|
2006.06347v2
|
2020-06-29
|
HFQPOs and discoseismic mode excitation in eccentric, relativistic discs. II. Magnetohydrodynamic simulations
|
Trapped inertial oscillations (r-modes) provide a promising explanation for
high-frequency quasi-periodic oscillations (HFQPOs) observed in the emission
from black hole X-ray binary systems. An eccentricity (or warp) can excite
r-modes to large amplitudes, but concurrently the oscillations are likely
damped by magnetohydrodynamic (MHD) turbulence driven by the magnetorotational
instability (MRI). We force eccentricity in global, unstratified, zero-net flux
MHD simulations of relativistic accretion discs, and find that a sufficiently
strong disc distortion generates trapped inertial waves despite this damping.
In our simulations, eccentricities above ~ 0.03 in the inner disc excite
trapped waves. In addition to the competition between r-mode damping and
driving, we observe that larger amplitude eccentric structures modify and in
some cases suppress MRI turbulence. Given the variety of distortions (warps as
well as eccentricities) capable of amplifying r-modes, the robustness of
trapped inertial wave excitation in the face of MRI turbulence in our
simulations provides support for a discoseismic explanation for HFQPOs.
|
2006.16266v2
|
2020-07-01
|
An integrable family of torqued, damped, rigid rotors
|
Expositions of the Euler equations for the rotation of a rigid body often
invoke the idea of a specially damped system whose energy dissipates while its
angular momentum magnitude is conserved in the body frame. An attempt to
explicitly construct such a damping function leads to a more general, but still
integrable, system of cubic equations whose trajectories are confined to nested
sets of quadric surfaces in angular momentum space. For some choices of
parameters, the lines of fixed points along both the largest and smallest
moment of inertia axes can be simultaneously attracting. Limiting cases are
those that conserve either the energy or the magnitude of the angular momentum.
Parallels with rod mechanics, micromagnetics, and particles with effective mass
are briefly discussed.
|
2007.00707v1
|
2020-07-10
|
Approximate Time-Optimal Trajectories for Damped Double Integrator in 2D Obstacle Environments under Bounded Inputs
|
This article provides extensions to existing path-velocity decomposition
based time optimal trajectory planning algorithm \cite{kant1986toward} to
scenarios in which agents move in 2D obstacle environment under double
integrator dynamics with drag term (damped double integrator). Particularly, we
extend the idea of a tangent graph \cite{liu1992path} to $\calC^1$-Tangent
graph to find continuously differentiable ($\calC^1$) shortest path between any
two points. $\calC^1$-Tangent graph has a continuously differentiable
($\calC^1$) path between any two nodes. We also provide analytical expressions
for a near time-optimal velocity profile for an agent moving on these shortest
paths under the damped double integrator with bounded acceleration.
|
2007.05155v2
|
2020-08-11
|
Ab initio results for the plasmon dispersion and damping of the warm dense electron gas
|
Warm dense matter (WDM) is an exotic state on the border between condensed
matter and dense plasmas. Important occurrences of WDM include dense
astrophysical objects, matter in the core of our Earth, as well as matter
produced in strong compression experiments. As of late, x-ray Thomson
scattering has become an advanced tool to diagnose WDM. The interpretation of
the data requires model input for the dynamic structure factor $S(q,\omega)$
and the plasmon dispersion $\omega(q)$. Recently the first \textit{ab initio}
results for $S(q,\omega)$ of the homogeneous warm dense electron gas were
obtained from path integral Monte Carlo simulations, [Dornheim \textit{et al.},
Phys. Rev. Lett. \textbf{121}, 255001 (2018)]. Here, we analyse the effects of
correlations and finite temperature on the dynamic dielectric function and the
plasmon dispersion. Our results for the plasmon dispersion and damping differ
significantly from the random phase approximation and from earlier models of
the correlated electron gas. Moreover, we show when commonly used weak damping
approximations break down and how the method of complex zeros of the dielectric
function can solve this problem for WDM conditions.
|
2008.04605v1
|
2020-08-18
|
Singularity formation for compressible Euler equations with time-dependent damping
|
In this paper, we consider the compressible Euler equations with
time-dependent damping \frac{\a}{(1+t)^\lambda}u in one space dimension. By
constructing 'decoupled' Riccati type equations for smooth solutions, we
provide some sufficient conditions under which the classical solutions must
break down in finite time. As a byproduct, we show that the derivatives blow
up, somewhat like the formation of shock wave, if the derivatives of initial
data are appropriately large at a point even when the damping coefficient goes
to infinity with a algebraic growth rate. We study the case \lambda\neq1 and
\lambda=1 respectively, moreover, our results have no restrictions on the size
of solutions and the positivity/monotonicity of the initial Riemann invariants.
In addition, for 1<\gamma<3 we provide time-dependent lower bounds on density
for arbitrary classical solutions, without any additional assumptions on the
initial data.
|
2008.07756v1
|
2020-08-18
|
Survey of 360$^{\circ}$ domain walls in magnetic heterostructures: topology, chirality and current-driven dynamics
|
Chirality and current-driven dynamics of topologically nontrivial
360$^{\circ}$ domain walls (360DWs) in magnetic heterostructures (MHs) are
systematically investigated. For MHs with normal substrates, the static 360DWs
are N\'{e}el-type with no chirality. While for those with heavy-metal
substrates, the interfacial Dzyaloshinskii-Moriya interaction (iDMI) therein
makes 360DWs prefer specific chirality. Under in-plane driving charge currents,
as the direct result of "full-circle" topology a certain 360DW does not undergo
the "Walker breakdown"-type process like a well-studied 180$^{\circ}$ domain
wall as the current density increases. Alternatively, it keeps a fixed
propagating mode (either steady-flow or precessional-flow, depending on the
effective damping constant of the MH) until it collapses or changes to other
types of solition when the current density becomes too high. Similarly, the
field-like spin-orbit torque (SOT) has no effects on the dynamics of 360DWs,
while the anti-damping SOT has. For both modes, modifications to the mobility
of 360DWs by iDMI and anti-damping SOT are provided.
|
2008.08196v1
|
2020-08-20
|
Combining $T_1$ and $T_2$ estimation with randomized benchmarking and bounding the diamond distance
|
The characterization of errors in a quantum system is a fundamental step for
two important goals. First, learning about specific sources of error is
essential for optimizing experimental design and error correction methods.
Second, verifying that the error is below some threshold value is required to
meet the criteria of threshold theorems. We consider the case where errors are
dominated by the generalized damping channel (encompassing the common intrinsic
processes of amplitude damping and dephasing) but may also contain additional
unknown error sources. We demonstrate the robustness of standard $T_1$ and
$T_2$ estimation methods and provide expressions for the expected error in
these estimates under the additional error sources. We then derive expressions
that allow a comparison of the actual and expected results of fine-grained
randomized benchmarking experiments based on the damping parameters. Given the
results of this comparison, we provide bounds that allow robust estimation of
the thresholds for fault-tolerance.
|
2008.09197v1
|
2020-08-25
|
The atomic damping basis and the collective decay of interacting two-level atoms
|
We find analytical solutions to the evolution of interacting two-level atoms
when the master equation is symmetric under the permutation of atomic labels.
The master equation includes atomic independent dissipation. The method to
obtain the solutions is: First, we use the system symmetries to describe the
evolution in an operator space whose dimension grows polynomially with the
number of atoms. Second, we expand the solutions in a basis composed of
eigenvectors of the dissipative part of the master equation that models the
independent dissipation of the atoms. This atomic damping basis is an atomic
analog to the damping basis used for bosonic fields. The solutions show that
the system decays as a sum of sub- and super-radiant exponential terms.
|
2008.11056v1
|
2020-09-11
|
Accuracy of relativistic Cowling approximation in protoneutron star asteroseismology
|
The relativistic Cowling approximation, where the metric perturbations are
neglected during the fluid oscillations, is often adopted for considering the
gravitational waves from the protoneutron stars (PNSs) provided via
core-collapse supernova explosions. In this study, we evaluate how the Cowling
approximation works well by comparing the frequencies with the Cowling
approximation to those without the approximation. Then, we find that the
behavior of the frequencies with the approximation is qualitatively the same
way as that without the approximation, where the frequencies with the
approximation can totally be determined within $\sim 20\%$ accuracy. In
particular, the fundamental mode with the Cowling approximation is
overestimated. In addition, we also discuss the damping time of various
eigenmodes in gravitational waves from the PNSs, where the damping time for the
PNSs before the avoided crossing between the $f$- and $g_1$-modes, is quite
different from that for cold neutron stars, but it is more or less similar to
that for cold neutron stars in the later phase. The damping time is long enough
compared to the typical time interval of short-Fourier transformation that
often used in the analysis, and that ideally guarantees the validity of the
transformation.
|
2009.05206v1
|
2020-09-17
|
Resonant absorption: transformation of compressive motions into vortical motions
|
This paper investigates the changes in spatial properties when
magnetohydrodynamic (MHD) waves undergo resonant damping in the Alfv\'en
continuum. The analysis is carried out for a 1D cylindrical pressure-less
plasma with a straight magnetic field. The effect of the damping on the spatial
wave variables is determined by using complex frequencies that arise as a
result of the resonant damping. Compression and vorticity are used to
characterise the spatial evolution of the MHD wave. The most striking result is
the huge spatial variation in the vorticity component parallel to the magnetic
field. Parallel vorticity vanishes in the uniform part of the equilibrium.
However, when the MHD wave moves into the non-uniform part, parallel vorticity
explodes to values that are orders of magnitude higher than those attained by
the transverse components in planes normal to the straight magnetic field. In
the non-uniform part of the equilibrium plasma, the MHD wave is controlled by
parallel vorticity and resembles an Alfv\'en wave, with the unfamiliar property
that it has pressure variations even in the linear regime.
|
2009.08152v1
|
2020-09-19
|
Random vibrations of stress-driven nonlocal beams with external damping
|
Stochastic flexural vibrations of small-scale Bernoulli-Euler beams with
external damping are investigated by stress-driven nonlocal mechanics. Damping
effects are simulated considering viscous interactions between beam and
surrounding environment. Loadings are modeled by accounting for their random
nature. Such a dynamic problem is characterized by a stochastic partial
differential equation in space and time governing time-evolution of the
relevant displacement field. Differential eigenanalyses are performed to
evaluate modal time coordinates and mode shapes, providing a complete
stochastic description of response solutions. Closed-form expressions of power
spectral density, correlation function, stationary and non-stationary variances
of displacement fields are analytically detected. Size-dependent dynamic
behaviour is assessed in terms of stiffness, variance and power spectral
density of displacements. The outcomes can be useful for design and
optimization of structural components of modern small-scale devices, such as
Micro- and Nano-Electro-Mechanical-Systems (MEMS and NEMS).
|
2009.09184v1
|
2020-09-20
|
Correction Method for the Readout Saturation of the DAMPE Calorimeter
|
The DArk Matter Particle Explorer (DAMPE) is a space-borne high energy
cosmic-ray and $\gamma$-ray detector which operates smoothly since the launch
on December 17, 2015. The bismuth germanium oxide (BGO) calorimeter is one of
the key sub-detectors of DAMPE used for energy measurement and electron proton
identification. For events with total energy deposit higher than decades of
TeV, the readouts of PMTs coupled on the BGO crystals would become saturated,
which results in an underestimation of the energy measurement. Based on
detailed simulations, we develop a correction method for the saturation effect
according to the shower development topologies and energies measured by
neighbouring BGO crystals. The verification with simulated and on-orbit events
shows that this method can well reconstruct the energy deposit in the saturated
BGO crystal.
|
2009.09438v1
|
2020-09-21
|
Complete complementarity relations in system-environment decoherent dynamics
|
We investigate the system-environment information flow from the point of view
ofcomplete complementarity relations. We consider some commonly used noisy
quantum channels:Amplitude damping, phase damping, bit flip, bit-phase flip,
phase flip, depolarizing, and correlatedamplitude damping. By starting with an
entangled bipartite pure quantum state, with the linearentropy being the
quantifier of entanglement, we study how entanglement is redistributed and
turnedinto general correlations between the degrees of freedom of the whole
system. For instance, it ispossible to express the entanglement entropy in
terms of the multipartite quantum coherence or interms of the correlated
quantum coherence of the different partitions of the system. In addition,we
notice that for the depolarizing and bit-phase flip channels the wave and
particle aspects candecrease or increase together. Besides, by considering the
environment as part of a pure quantumsystem, the linear entropy is shown to be
not just a measure of mixedness of a particular subsystem,but a correlation
measure of the subsystem with rest of the world.
|
2009.09769v3
|
2020-09-15
|
Delay-induced resonance suppresses damping-induced unpredictability
|
Combined effects of the damping and forcing in the underdamped time-delayed
Duffing oscillator are considered in this paper. We analyze the generation of a
certain damping-induced unpredictability, due to the gradual suppression of
interwell oscillations. We find the minimal amount of the forcing amplitude and
the right forcing frequency to revert the effect of the dissipation, so that
the interwell oscillations can be restored, for different time delay values.
This is achieved by using the delay-induced resonance, in which the time delay
replaces one of the two periodic forcings present in the vibrational resonance.
A discussion in terms of the time delay of the critical values of the forcing
for which the delay-induced resonance can tame the dissipation effect is
finally carried out.
|
2009.11760v1
|
2020-10-06
|
A dissiptive logarithmic type evolution equation: asymptotic profile and optimal estimates
|
We introduce a new model of the logarithmic type of wave-like equation with a
nonlocal logarithmic damping mechanism, which is rather weakly effective as
compared with frequently studied fractional damping cases. We consider the
Cauchy problem for this new model in the whole space, and study the asymptotic
profile and optimal decay and/or blowup rates of solutions as time goes to
infinity in L^{2}-sense. The operator L considered in this paper was used to
dissipate the solutions of the wave equation in the paper studied by
Charao-Ikehata in 2020, and in the low frequency parameters the principal part
of the equation and the damping term is rather weakly effective than those of
well-studied power type operators.
|
2010.02485v1
|
2020-10-12
|
Line-drag damping of Alfvén waves in radiatively driven winds of magnetic massive stars
|
Line-driven stellar winds from massive (OB) stars are subject to a strong
line-deshadowing instability. Recently, spectropolarimetric surveys have
collected ample evidence that a subset of Galactic massive stars hosts strong
surface magnetic fields. We investigate here the propagation and stability of
magneto-radiative waves in such a magnetised, line-driven wind. Our analytic,
linear stability analysis includes line-scattering from the stellar radiation,
and accounts for both radial and non-radial perturbations. We establish a
bridging law for arbitrary perturbation wavelength after which we analyse
separately the long- and short-wavelength limits. While long-wavelength
radiative and magnetic waves are found to be completely decoupled, a key result
is that short-wavelength, radially propagating Alfv\'en waves couple to the
scattered radiation field and are strongly damped due to the line-drag effect.
This damping of magnetic waves in a scattering-line-driven flow could have
important effects on regulating the non-linear wind dynamics, and so might also
have strong influence on observational diagnostics of the wind structure and
clumping of magnetic line-driven winds.
|
2010.05650v1
|
2020-10-20
|
Long Time Behavior of a Quasilinear Hyperbolic System Modelling Elastic Membranes
|
The paper studies the long time behavior of a system that describes the
motion of a piece of elastic membrane driven by surface tension and inner air
pressure. The system is a degenerate quasilinear hyperbolic one that involves
the mean curvature, and also includes a damping term that models the
dissipative nature of genuine physical systems. With the presence of damping, a
small perturbation of the sphere converges exponentially in time to the sphere,
and without the damping the evolution that is $\varepsilon$-close to the sphere
has life span longer than $\varepsilon^{-1/6}$. Both results are proved using a
new Nash-Moser-H\"{o}rmander type theorem proved by Baldi and Haus.
|
2010.10663v6
|
2020-10-09
|
Rapid parameter determination of discrete damped sinusoidal oscillations
|
We present different computational approaches for the rapid extraction of the
signal parameters of discretely sampled damped sinusoidal signals. We compare
time- and frequency-domain-based computational approaches in terms of their
accuracy and precision and computational time required in estimating the
frequencies of such signals, and observe a general trade-off between precision
and speed. Our motivation is precise and rapid analysis of damped sinusoidal
signals as these become relevant in view of the recent experimental
developments in cavity-enhanced polarimetry and ellipsometry, where the
relevant time scales and frequencies are typically within the $\sim1-10\,\mu$s
and $\sim1-100$MHz ranges, respectively. In such experimental efforts,
single-shot analysis with high accuracy and precision becomes important when
developing experiments that study dynamical effects and/or when developing
portable instrumentations. Our results suggest that online, running-fashion,
microsecond-resolved analysis of polarimetric/ellipsometric measurements with
fractional uncertainties at the $10^{-6}$ levels, is possible, and using a
proof-of-principle experimental demonstration we show that using a
frequency-based analysis approach we can monitor and analyze signals at kHz
rates and accurately detect signal changes at microsecond time-scales.
|
2010.11690v1
|
2020-10-22
|
Effective shear and bulk viscosities for anisotropic flow
|
We evaluate the viscous damping of anisotropic flow in heavy-ion collisions
for arbitrary temperature-dependent shear and bulk viscosities. We show that
the damping is solely determined by effective shear and bulk viscosities, which
are weighted averages over the temperature. We determine the relevant weights
for nucleus-nucleus collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV and 200 GeV,
corresponding to the maximum LHC and RHIC energies, by running ideal and
viscous hydrodynamic simulations. The effective shear viscosity is driven by
temperatures below $210$ MeV at RHIC, and below $280$ MeV at the LHC, with the
largest contributions coming from the lowest temperatures, just above
freeze-out. The effective bulk viscosity is driven by somewhat higher
temperatures, corresponding to earlier stages of the collision. We show that at
a fixed collision energy, the effective viscosity is independent of centrality
and system size, to the same extent as the mean transverse momentum of outgoing
hadrons. The variation of viscous damping is determined by Reynolds number
scaling.
|
2010.11919v2
|
2020-10-23
|
Is PSR J0855$-$4644 responsible for the 1.4 TeV electron spectral bump hinted by DAMPE?
|
DAMPE observation on the cosmic ray electron spectrum hints a narrow excess
at $\sim$ 1.4 TeV. Although the excess can be ascribed to dark matter
particles, pulsars and pulsar wind nebulae are believed to be a more natural
astrophysical origin: electrons injected from nearby pulsars at their early
ages can form a bump-like feature in the spectrum due to radiative energy
losses. In this paper, with a survey of nearby pulsars, we find 4 pulsars that
may have notable contributions to $\sim$ 1.4 TeV cosmic ray electrons. Among
them, PSR J0855$-$4644 has a spin down luminosity more than 50 times higher
than others and presumably dominates the electron fluxes from them. X-ray
observations on the inner compact part (which may represent a tunnel for the
transport of electrons from the pulsar) of PWN G267.0$-$01.0 are then used to
constrain the spectral index of high energy electrons injected by the pulsar.
We show that high-energy electrons released by PSR J0855$-$4644 could indeed
reproduce the 1.4 TeV spectral feature hinted by the DAMPE with reasonable
parameters.
|
2010.12170v1
|
2020-11-02
|
Effect of retardation on the frequency and linewidth of plasma resonances in a two-dimensional disk of electron gas
|
We theoretically analyze dominant plasma modes in a two-dimensional disk of
electron gas by calculating the absorption of an incident electromagnetic wave.
The problem is solved in a self-consistent approximation, taking into account
electromagnetic retardation effects. We use the Drude model to describe the
conductivity of the system. The absorption spectrum exhibits a series of peaks
corresponding to the excitation of plasma waves. The position and linewidth of
the peaks designating, respectively, the frequency and damping rate of the
plasma modes. We estimate the influence of retardation effects on the frequency
and linewidth of the fundamental (dipole) and axisymmetric (quadrupole) plasma
modes both numerically and analytically. We find the net damping rate of the
modes to be dependent on not only the sum of the radiative and collisional
decays but also their intermixture, even for small retardation. We show that
the net damping rate can be noticeably less than that determined by collisions
alone.
|
2011.00877v1
|
2020-11-05
|
Low-Complexity Models for Acoustic Scene Classification Based on Receptive Field Regularization and Frequency Damping
|
Deep Neural Networks are known to be very demanding in terms of computing and
memory requirements. Due to the ever increasing use of embedded systems and
mobile devices with a limited resource budget, designing low-complexity models
without sacrificing too much of their predictive performance gained great
importance. In this work, we investigate and compare several well-known methods
to reduce the number of parameters in neural networks. We further put these
into the context of a recent study on the effect of the Receptive Field (RF) on
a model's performance, and empirically show that we can achieve high-performing
low-complexity models by applying specific restrictions on the RFs, in
combination with parameter reduction methods. Additionally, we propose a
filter-damping technique for regularizing the RF of models, without altering
their architecture and changing their parameter counts. We will show that
incorporating this technique improves the performance in various low-complexity
settings such as pruning and decomposed convolution. Using our proposed filter
damping, we achieved the 1st rank at the DCASE-2020 Challenge in the task of
Low-Complexity Acoustic Scene Classification.
|
2011.02955v1
|
2020-11-14
|
Learning a Reduced Basis of Dynamical Systems using an Autoencoder
|
Machine learning models have emerged as powerful tools in physics and
engineering. Although flexible, a fundamental challenge remains on how to
connect new machine learning models with known physics. In this work, we
present an autoencoder with latent space penalization, which discovers finite
dimensional manifolds underlying the partial differential equations of physics.
We test this method on the Kuramoto-Sivashinsky (K-S), Korteweg-de Vries (KdV),
and damped KdV equations. We show that the resulting optimal latent space of
the K-S equation is consistent with the dimension of the inertial manifold. The
results for the KdV equation imply that there is no reduced latent space, which
is consistent with the truly infinite dimensional dynamics of the KdV equation.
In the case of the damped KdV equation, we find that the number of active
dimensions decreases with increasing damping coefficient. We then uncover a
nonlinear basis representing the manifold of the latent space for the K-S
equation.
|
2011.07346v1
|
2020-11-23
|
Sharp lifespan estimates for the weakly coupled system of semilinear damped wave equations in the critical case
|
The open question, which seems to be also the final part, in terms of
studying the Cauchy problem for the weakly coupled system of damped wave
equations or reaction-diffusion equations, is so far known as the sharp
lifespan estimates in the critical case. In this paper, we mainly investigate
lifespan estimates for solutions to the weakly coupled system of semilinear
damped wave equations in the critical case. By using a suitable test function
method associated with nonlinear differential inequalities, we catch upper
bound estimates for the lifespan. Moreover, we establish polynomial-logarithmic
type time-weighted Sobolev spaces to obtain lower bound estimates for the
lifespan in low spatial dimensions. Then, together with the derived lifespan
estimates, new and sharp results on estimates for the lifespan in the critical
case are claimed. Finally, we give an application of our results to the
semilinear reaction-diffusion system in the critical case.
|
2011.11366v2
|
2020-12-10
|
Stochastic Damped L-BFGS with Controlled Norm of the Hessian Approximation
|
We propose a new stochastic variance-reduced damped L-BFGS algorithm, where
we leverage estimates of bounds on the largest and smallest eigenvalues of the
Hessian approximation to balance its quality and conditioning. Our algorithm,
VARCHEN, draws from previous work that proposed a novel stochastic damped
L-BFGS algorithm called SdLBFGS. We establish almost sure convergence to a
stationary point and a complexity bound. We empirically demonstrate that
VARCHEN is more robust than SdLBFGS-VR and SVRG on a modified DavidNet problem
-- a highly nonconvex and ill-conditioned problem that arises in the context of
deep learning, and their performance is comparable on a logistic regression
problem and a nonconvex support-vector machine problem.
|
2012.05783v1
|
2020-12-29
|
Twist-induced Near-field Thermal Switch Using Nonreciprocal Surface Magnon-Polaritons
|
We explore that two ferromagnetic insulator slabs host a strong twist-induced
near-field radiative heat transfer in the presence of twisted magnetic fields.
Using the formalism of fluctuational electrodynamics, we find the existence of
large twist-induced thermal switch ratio in large damping condition and
nonmonotonic twist manipulation for heat transfer in small damping condition,
associated with the different twist-induced effects of nonreciprocal elliptic
surface magnon-polaritons, hyperbolic surface magnon-polaritons, and
twist-non-resonant surface magnon-polaritons. Moreover, the near-field
radiative heat transfer can be significantly enhanced by the twist-non-resonant
surface magnon-polaritons in the ultra-small damping condition. Such
twist-induced effect is applicable for other kinds of anisotropic slabs with
timereversal symmetry breaking. Our findings provide a way to twisted and
magnetic control in nanoscale thermal management and improve it with
twistronics concepts.
|
2012.14733v1
|
2021-01-04
|
The damped harmonic oscillator at the classical limit of the Snyder-de Sitter space
|
Valtancoli in his paper entitled [P. Valtancoli, Canonical transformations,
and minimal length J. Math. Phys. 56, 122107 (2015)] has shown how the
deformation of the canonical transformations can be made compatible with the
deformed Poisson brackets. Based on this work and through an appropriate
canonical transformation, we solve the problem of one dimensional (1D) damped
harmonic oscillator at the classical limit of the Snyder-de Sitter (SdS) space.
We show that the equations of the motion can be described by trigonometric
functions with frequency and period depending on the deformed and the damped
parameters. We eventually discuss the influences of these parameters on the
motion of the system.
|
2101.01223v2
|
2021-01-11
|
Damped (linear) response theory within the resolution-of-identity coupled cluster singles and approximate doubles (RI-CC2) method
|
An implementation of a complex solver for the solution of the response
equations required to compute the complex response functions of damped response
theory is presented for the resolution-of-identity (RI) coupled-cluster singles
and approximate doubles CC2 method. The implementation uses a partitioned
formulation that avoids the storage of double excitation amplitudes to make it
applicable to large molecules. The solver is the keystone element for the
development of the damped coupled-cluster response formalism for linear and
nonlinear effects in resonant frequency regions at the RI-CC2 level of theory.
Illustrative results are reported for the one-photon absorption cross section
of C60, the electronic circular dichroism of $n$-helicenes ($n$ = 5, 6, 7), and
the $C_6$ dispersion coefficients of a set of selected organic molecules and
fullerenes.
|
2101.03756v1
|
2021-01-26
|
Generalized Damped Newton Algorithms in Nonsmooth Optimization via Second-Order Subdifferentials
|
The paper proposes and develops new globally convergent algorithms of the
generalized damped Newton type for solving important classes of nonsmooth
optimization problems. These algorithms are based on the theory and
calculations of second-order subdifferentials of nonsmooth functions with
employing the machinery of second-order variational analysis and generalized
differentiation. First we develop a globally superlinearly convergent damped
Newton-type algorithm for the class of continuously differentiable functions
with Lipschitzian gradients, which are nonsmooth of second order. Then we
design such a globally convergent algorithm to solve a structured class of
nonsmooth quadratic composite problems with extended-real-valued cost
functions, which typically arise in machine learning and statistics. Finally,
we present the results of numerical experiments and compare the performance of
our main algorithm applied to an important class of Lasso problems with those
achieved by other first-order and second-order optimization algorithms.
|
2101.10555v3
|
2021-01-26
|
Damped and Driven Breathers and Metastability
|
In this article we prove the existence of a new family of periodic solutions
for discrete, nonlinear Schrodinger equations subject to spatially localized
driving and damping. They provide an alternate description of the metastable
behavior in such lattice systems which agrees with previous predictions for the
evolution of metastable states while providing more accurate approximations to
these states. We analyze the stability of these breathers, finding a very small
positive eigenvalue whose eigenvector lies almost tangent to the surface of the
cylinder formed by the family of breathers. This causes solutions to slide
along the cylinder without leaving its neighborhood for very long times.
|
2101.10999v2
|
2021-02-05
|
A simple artificial damping method for total Lagrangian smoothed particle hydrodynamics
|
In this paper, we present a simple artificial damping method to enhance the
robustness of total Lagrangian smoothed particle hydrodynamics (TL-SPH).
Specifically, an artificial damping stress based on the Kelvin-Voigt type
damper with a scaling factor imitating a von Neumann-Richtmyer type artificial
viscosity is introduced in the constitutive equation to alleviate the spurious
oscillation in the vicinity of the sharp spatial gradients. After validating
the robustness and accuracy of the present method with a set of benchmark tests
with very challenging cases, we demonstrate its potentials in the field of
bio-mechanics by simulating the deformation of complex stent structures.
|
2102.04898v1
|
2021-02-18
|
Probing black hole microstructure with the kinetic turnover of phase transition
|
By treating black hole as the macroscopic stable state on the free energy
landscape, we propose that the stochastic dynamics of the black hole phase
transition can be effectively described by the Langevin equation or
equivalently by the Fokker-Planck equation in phase space. We demonstrate the
turnover of the kinetics for the charged anti-de Sitter black hole phase
transition, which shows that the mean first passage time is linear with the
friction in the high damping regime and inversely proportional to the friction
in the low damping regime. The fluctuations in the kinetics are shown to be
large/small in the high/low damping regime and the switching behavior from the
small fluctuations to the large fluctuations takes place at the kinetic
turnover point. Because the friction is a reflection of the microscopic degrees
of freedom acting on the order parameter of the black hole, the turnover and
the corresponding fluctuations of the phase transition kinetics can be used to
probe the black hole microstructure.
|
2102.09439v1
|
2021-02-25
|
Energy Decay of some boundary coupled systems involving wave$\backslash$ Euler-Bernoulli beam with one locally singular fractional Kelvin-Voigt damping
|
In this paper, we investigate the energy decay of hyperbolic systems of
wave-wave, wave-Euler- Bernoulli beam and beam-beam types. The two equations
are coupled through boundary connection with only one localized non-smooth
fractional Kelvin-Voigt damping. First, we reformulate each system into an
augmented model and using a general criteria of Arendt-Batty, we prove that our
models are strongly stable. Next, by using frequency domain approach, combined
with multiplier technique and some interpolation inequalities, we establish
different types of polynomial energy decay rate which depends on the order of
the fractional derivative and the type of the damped equation in the system.
|
2102.12732v2
|
2021-03-01
|
Fluid-plate interaction under periodic forcing
|
The motion of a thin elastic plate interacting with a viscous fluid is
investigated. A periodic force acting on the plate is considered, which in a
setting without damping could lead to a resonant response. The interaction with
the viscous fluid provides a damping mechanism due to the energy dissipation in
the fluid. Moreover, an internal damping mechanism in the plate is introduced.
In this setting, we show that the periodic forcing leads to a time-periodic
(non-resonant) solution. We employ the Navier-Stokes and the Kirchhoff-Love
plate equation in a periodic cell structure to model the motion of the viscous
fluid and the elastic plate, respectively. Maximal Lp regularity for the
linearized system is established in a framework of time-periodic function
spaces. Existence of a solution to the fully nonlinear system is subsequently
shown with a fixed-point argument.
|
2103.00795v1
|
2021-03-25
|
Nonlinear inviscid damping and shear-buoyancy instability in the two-dimensional Boussinesq equations
|
We investigate the long-time properties of the two-dimensional inviscid
Boussinesq equations near a stably stratified Couette flow, for an initial
Gevrey perturbation of size $\varepsilon$. Under the classical Miles-Howard
stability condition on the Richardson number, we prove that the system
experiences a shear-buoyancy instability: the density variation and velocity
undergo an $O(t^{-1/2})$ inviscid damping while the vorticity and density
gradient grow as $O(t^{1/2})$. The result holds at least until the natural,
nonlinear timescale $t \approx \varepsilon^{-2}$. Notice that the density
behaves very differently from a passive scalar, as can be seen from the
inviscid damping and slower gradient growth. The proof relies on several
ingredients: (A) a suitable symmetrization that makes the linear terms amenable
to energy methods and takes into account the classical Miles-Howard spectral
stability condition; (B) a variation of the Fourier time-dependent energy
method introduced for the inviscid, homogeneous Couette flow problem developed
on a toy model adapted to the Boussinesq equations, i.e. tracking the potential
nonlinear echo chains in the symmetrized variables despite the vorticity
growth.
|
2103.13713v1
|
2021-03-31
|
Research of Damped Newton Stochastic Gradient Descent Method for Neural Network Training
|
First-order methods like stochastic gradient descent(SGD) are recently the
popular optimization method to train deep neural networks (DNNs), but
second-order methods are scarcely used because of the overpriced computing cost
in getting the high-order information. In this paper, we propose the Damped
Newton Stochastic Gradient Descent(DN-SGD) method and Stochastic Gradient
Descent Damped Newton(SGD-DN) method to train DNNs for regression problems with
Mean Square Error(MSE) and classification problems with Cross-Entropy
Loss(CEL), which is inspired by a proved fact that the hessian matrix of last
layer of DNNs is always semi-definite. Different from other second-order
methods to estimate the hessian matrix of all parameters, our methods just
accurately compute a small part of the parameters, which greatly reduces the
computational cost and makes convergence of the learning process much faster
and more accurate than SGD. Several numerical experiments on real datesets are
performed to verify the effectiveness of our methods for regression and
classification problems.
|
2103.16764v1
|
2021-04-08
|
Landau Damping in the Transverse Modulational Dynamics of Co-Propagating Light and Matter Beams
|
The optomechanical coupling and transverse stability of a co-propagating
monochromatic electromagnetic wave and mono-energetic beam of two-level atoms
is investigated in the collisionless regime. The coupled dynamics are studied
through a Landau stability analysis of the coupled gas- kinetic and paraxial
wave equations, including the effect of the electronic nonlinearity. The
resulting dispersion relation captures the interaction of kinetic and
saturation effects and shows that for blue detuning the combined nonlinear
interaction is unstable below a critical wavenumber which reduces to the result
of Bespalov and Talanov in the limit of a negligible kinetic nonlinearity. For
red detuning we find that under a saturation parameter threshold exists whereby
the system stabilizes unconditionally. With negligible saturation, an
optomechanical form of Landau damping stabilizes all wavenumbers above a
critical wavenumber determined by the combined strength of the kinetic and
refractive optomechanical feedback. The damping is mediated primarily by atoms
traveling along the primary diagonals of the Talbot carpet.
|
2104.04100v1
|
2021-04-15
|
Simulating cosmological supercooling with a cold atom system II
|
We perform an analysis of the supercooled state in an analogue of an early
universe phase transition based on a one dimensional, two-component Bose gas
with time-dependent interactions. We demonstrate that the system behaves in the
same way as a thermal, relativistic Bose gas undergoing a first order phase
transition. We propose a way to prepare the state of the system in the
metastable phase as an analogue to supercooling in the early universe. While we
show that parametric resonances in the system can be suppressed by thermal
damping, we find that the theoretically estimated thermal damping in our model
is too weak to suppress the resonances for realistic experimental parameters.
However, we propose that experiments to investigate the effective damping rate
in experiments would be worthwhile.
|
2104.07428v1
|
2021-04-29
|
Nano-patterning of surfaces by ion sputtering: Numerical study of the anisotropic damped Kuramoto-Sivashinsky equation
|
Nonlinear models for pattern evolution by ion beam sputtering on a material
surface present an ongoing opportunity for new numerical simulations. A
numerical analysis of the evolution of preexisting patterns is proposed to
investigate surface dynamics, based on a 2D anisotropic damped
Kuramoto-Sivashinsky equation, with periodic boundary conditions. A
finite-difference semi-implicit time splitting scheme is employed on the
discretization of the governing equation. Simulations were conducted with
realistic coefficients related to physical parameters (anisotropies, beam
orientation, diffusion). The stability of the numerical scheme is analyzed with
time step and grid spacing tests for the pattern evolution, and the Method of
Manufactured Solutions has been used to verify the proposed scheme. Ripples and
hexagonal patterns were obtained from a monomodal initial condition for certain
values of the damping coefficient, while spatiotemporal chaos appeared for
lower values. The anisotropy effects on pattern formation were studied, varying
the angle of incidence of the ion beam with respect to the irradiated surface.
Analytical discussions are based on linear and weakly nonlinear analysis.
|
2104.14104v1
|
2021-05-04
|
Linear response theory and damped modes of stellar clusters
|
Because all stars contribute to its gravitational potential, stellar clusters
amplify perturbations collectively. In the limit of small fluctuations, this is
described through linear response theory, via the so-called response matrix.
While the evaluation of this matrix is somewhat straightforward for unstable
modes (i.e. with a positive growth rate), it requires a careful analytic
continuation for damped modes (i.e. with a negative growth rate). We present a
generic method to perform such a calculation in spherically symmetric stellar
clusters. When applied to an isotropic isochrone cluster, we recover the
presence of a low-frequency weakly damped $\ell = 1$ mode. We finally use a set
of direct $N$-body simulations to test explicitly this prediction through the
statistics of the correlated random walk undergone by a cluster's density
centre.
|
2105.01371v1
|
2021-05-10
|
Passivity-based control of mechanical systems with linear damping identification
|
We propose a control approach for a class of nonlinear mechanical systems to
stabilize the system under study while ensuring that the oscillations of the
transient response are reduced. The approach is twofold: (i) we apply our
technique for linear viscous damping identification of the system to improve
the accuracy of the selected control technique, and (ii) we implement a
passivity-based controller to stabilize and reduce the oscillations by
selecting the control parameters properly in accordance with the identified
damping. Moreover, we provide an analysis for a particular passivity-based
control approach that has been shown successfully for reducing such
oscillations. Also, we validate the methodology by implementing it
experimentally in a planar manipulator.
|
2105.04324v4
|
2021-05-26
|
Decay dynamics of Localised Surface Plasmons: damping of coherences and populations of the oscillatory plasmon modes
|
Properties of plasmonic materials are associated with surface plasmons - the
electromagnetic excitations coupled to coherent electron charge density
oscillations on a metal/dielectric interface. Although decay of such
oscillations cannot be avoided, there are prospects for controlling plasmon
damping dynamics. In spherical metal nanoparticles (MNPs) the basic properties
of Localized Surface Plasmons (LSPs) can be controlled with their radius. The
present paper handles the link between the size-dependent description of LSP
properties derived from the dispersion relation based on Maxwell's equations
and the quantum picture in which MNPs are treated as "quasi-particles". Such
picture, based on the reduced density-matrix of quantum open systems ruled by
the master equation in the Lindblad form, enables to distinguish between
damping processes of populations and coherences of multipolar plasmon
oscillatory states and to establish the intrinsic relations between the rates
of these processes, independently of the size of MNP. The impact of the
radiative and the nonradiative energy dissipation channels is discussed.
|
2105.12463v1
|
2021-06-05
|
The electron acoustic waves in plasmas with two kappa-distributed electrons at the same temperatures and immobile ions
|
The linear electron acoustic waves propagating in plasmas with two
kappa-distributed electrons and stationary ions are investigated. The
temperatures of the two electrons are assumed to be the same, but the kappa
indices are not. It shows that if one kappa index is small enough and the other
one is large enough, a weak damping regime of the electron acoustic waves
exists. The dispersions and damping rates are numerically studied. The
parameter spaces for the weakly damped electron acoustic waves are analyzed.
Moreover, the electron acoustic waves in the present model are compared with
those in other models, especially the plasmas with two-temperature electrons.
At last, we perform Vlasov-Poisson simulations to verify the theory.
|
2106.02910v2
|
2021-06-18
|
Global existence and asymptotic behavior for semilinear damped wave equations on measure spaces
|
This paper is concerned with the semilinear damped wave equation on a measure
space with a self-adjoint operator, instead of the standard Laplace operator.
Under a certain decay estimate on the corresponding heat semigroup, we
establish the linear estimates which generalize the so-called Matsumura
estimates, and prove the small data global existence of solutions to the damped
wave equation based on the linear estimates. Our approach is based on a direct
spectral analysis analogous to the Fourier analysis. The self-adjoint operators
treated in this paper include some important examples such as the Laplace
operators on Euclidean spaces, the Dirichlet Laplacian on an arbitrary open
set, the Robin Laplacian on an exterior domain, the Schr\"odinger operator, the
elliptic operator, the Laplacian on Sierpinski gasket, and the fractional
Laplacian.
|
2106.10322v3
|
2021-06-21
|
On the small time asymptotics of stochastic Ladyzhenskaya-Smagorinsky equations with damping perturbed by multiplicative noise
|
The Ladyzhenskaya-Smagorinsky equations model turbulence phenomena, and are
given by $$\frac{\partial \boldsymbol{u}}{\partial t}-\mu
\mathrm{div}\left(\left(1+|\nabla\boldsymbol{u}|^2\right)^{\frac{p-2}{2}}\nabla\boldsymbol{u}\right)+(\boldsymbol{u}\cdot\nabla)\boldsymbol{u}+\nabla
p=\boldsymbol{f}, \ \nabla\cdot\boldsymbol{u}=0,$$ for $p\geq 2,$ in a bounded
domain $\mathcal{O}\subset\mathbb{R}^d$ ($2\leq d\leq 4$). In this work, we
consider the stochastic Ladyzhenskaya-Smagorinsky equations with the damping
$\alpha\boldsymbol{u}+\beta|\boldsymbol{u}|^{r-2}\boldsymbol{u},$ for $r\geq 2$
($\alpha,\beta\geq 0$), subjected to multiplicative Gaussian noise. We show the
local monotoincity ($p\geq \frac{d}{2}+1,\ r\geq 2$) as well as global
monotonicity ($p\geq 2,\ r\geq 4$) properties of the linear and nonlinear
operators, which along with an application of stochastic version of
Minty-Browder technique imply the existence of a unique pathwise strong
solution. Then, we discuss the small time asymptotics by studying the effect of
small, highly nonlinear, unbounded drifts (small time large deviation
principle) for the stochastic Ladyzhenskaya-Smagorinsky equations with damping.
|
2106.10861v1
|
2021-06-23
|
Improved convergence rates and trajectory convergence for primal-dual dynamical systems with vanishing damping
|
In this work, we approach the minimization of a continuously differentiable
convex function under linear equality constraints by a second-order dynamical
system with asymptotically vanishing damping term. The system is formulated in
terms of the augmented Lagrangian associated to the minimization problem. We
show fast convergence of the primal-dual gap, the feasibility measure, and the
objective function value along the generated trajectories. In case the
objective function has Lipschitz continuous gradient, we show that the
primal-dual trajectory asymptotically weakly converges to a primal-dual optimal
solution of the underlying minimization problem. To the best of our knowledge,
this is the first result which guarantees the convergence of the trajectory
generated by a primal-dual dynamical system with asymptotic vanishing damping.
Moreover, we will rediscover in case of the unconstrained minimization of a
convex differentiable function with Lipschitz continuous gradient all
convergence statements obtained in the literature for Nesterov's accelerated
gradient method.
|
2106.12294v1
|
2021-06-24
|
Landau damping of electron-acoustic waves due to multi-plasmon resonances
|
The linear and nonlinear theories of electron-acoustic waves (EAWs) are
studied in a partially degenerate quantum plasma with two-temperature electrons
and stationary ions. The initial equilibrium of electrons is assumed to be
given by the Fermi-Dirac distribution at finite temperature. By employing the
multi-scale asymptotic expansion technique to the one-dimensional Wigner-Moyal
and Poisson equations, it is shown that the effects of multi-plasmon resonances
lead to a modified complex Korteweg-de Vries (KdV) equation with a new nonlocal
nonlinearity. Besides giving rise to a nonlocal nonlinear term, the
wave-particle resonance also modifies the local nonlinear coupling coefficient
of the KdV equation. The latter is shown to conserve the number of particles,
however, the wave energy decays with time. A careful analysis shows that the
two-plasmon resonance is the dominant mechanism for nonlinear Landau damping of
EAWs. An approximate soliton solution of the KdV equation is also obtained, and
it is shown that the nonlinear Landau damping causes the wave amplitude to
decay slowly with time compared to the classical theory.
|
2106.12754v2
|
2021-07-01
|
On behavior of solutions to a Petrovsky equation with damping and variable-exponent source
|
This paper deals with the following Petrovsky equation with damping and
nonlinear source \[u_{tt}+\Delta^2 u-M(\|\nabla u\|_2^2)\Delta u-\Delta
u_t+|u_t|^{m(x)-2}u_t=|u|^{p(x)-2}u\] under initial-boundary value conditions,
where $M(s)=a+ bs^\gamma$ is a positive $C^1$ function with parameters
$a>0,~b>0,~\gamma\geq 1$, and $m(x),~p(x)$ are given measurable functions. The
upper bound of the blow-up time is derived for low initial energy using the
differential inequality technique. For $m(x)\equiv2$, in particular, the upper
bound of the blow-up time is obtained by the combination of Levine's concavity
method and some differential inequalities under high initial energy. In
addition, by making full use of the strong damping, the lower bound of the
blow-up time is discussed. Moreover, the global existence of solutions and an
energy decay estimate are presented by establishing some energy estimates and
by exploiting a key integral inequality.
|
2107.00273v2
|
2021-07-21
|
A combined volume penalization / selective frequency damping approach for immersed boundary methods applied to high-order schemes
|
There has been an increasing interest in developing efficient immersed
boundary method (IBM) based on Cartesian grids, recently in the context of
high-order methods. IBM based on volume penalization is a robust and easy to
implement method to avoid body-fitted meshes and has been recently adapted to
high order discretisations (Kou et al., 2021). This work proposes an
improvement over the classic penalty formulation for flux reconstruction high
order solvers. We include a selective frequency damping (SFD) approach
(Aakervik et al., 2006) acting only inside solid body defined through the
immersed boundary masking, to damp spurious oscillations. An encapsulated
formulation for the SFD method is implemented, which can be used as a wrapper
around an existing time-stepping code. The numerical properties have been
studied through eigensolution analysis based on the advection equation. These
studies not only show the advantages of using the SFD method as an alternative
of the traditional volume penalization, but also show the favorable properties
of combining both approaches. This new approach is then applied to the
Navier-Stokes equation to simulate steady flow past an airfoil and unsteady
flow past a circular cylinder. The advantages of the SFD method in providing
improved accuracy are reported.
|
2107.10177v1
|
2021-07-25
|
Dispatch of Virtual Inertia and Damping: Numerical Method with SDP and ADMM
|
Power grids are evolving toward 100% renewable energy interfaced by
inverters. Virtual inertia and damping provided by inverters are essential to
synchronism and frequency stability of future power grids. This paper
numerically addresses the problem of dispatch of virtual inertia and damping
(DID) among inverters in the transmission network. The DID problem is first
formulated as a nonlinear program (NLP) by the Radua collocation method which
is flexible to handle various types of disturbances and bounds constraints.
Since the NLP of DID is highly non-convex, semi-definite programming (SDP)
relaxation for the NLP is further derived to tackle the non-convexity, followed
by its sparsity being exploited hierarchically based on chordality of graphs to
seek enhancement of computational efficiency. Considering high dimension and
inexactness of the SDP relaxation, a feasibility-embedded distributed approach
is finally proposed under the framework of alternating direction method of
multipliers (ADMM), which achieves parallel computing and solution feasibility
regarding the original NLP. Numerical simulations carried out for five test
power systems demonstrate the proposed method and necessity of DID.
|
2107.11764v1
|
2021-07-29
|
Microscopic analysis of sound attenuation in low-temperature amorphous solids reveals quantitative importance of non-affine effects
|
Sound attenuation in low temperature amorphous solids originates from their
disordered structure. However, its detailed mechanism is still being debated.
Here we analyze sound attenuation starting directly from the microscopic
equations of motion. We derive an exact expression for the zero-temperature
sound damping coefficient. We verify that the sound damping coefficients
calculated from our expression agree very well with results from independent
simulations of sound attenuation. The small wavevector analysis of our
expression shows that sound attenuation is primarily determined by the
non-affine displacements' contribution to the sound wave propagation
coefficient coming from the frequency shell of the sound wave. Our expression
involves only quantities that pertain to solids' static configurations. It can
be used to evaluate the low temperature sound damping coefficients without
directly simulating sound attenuation.
|
2107.14254v2
|
2021-08-09
|
Damping perturbation based time integration asymptotic method for structural dynamics
|
The light damping hypothesis is usually assumed in structural dynamics since
dissipative forces are in general weak with respect to inertial and elastic
forces. In this paper a novel numerical method of time integration based on the
artificial perturbation of damping is proposed. The asymptotic expansion of the
transient response results in an infinite series which can be summed, leading
to a well-defined explicit iterative step-by-step scheme. Conditions for
convergence are rigorously analyzed, enabling the determination of the
methodology boundaries in form of maximum time step. The numerical properties
of the iterative scheme, i.e. stability, accuracy and computational effort are
also studied in detail. The approach is validated with two numerical examples,
showing a high accuracy and computational efficiency relative to other methods.
|
2108.03813v1
|
2021-08-12
|
The damping and diffusion of atoms moving in the background electromagnetic environment
|
The interaction between an atom and the quantized electromagnetic field
depends on the position of the atom. Then the atom experiences a force which is
the minus gradient of this interaction. Through the Heisenberg equations of
motion and the Born-Markov approximation, the mean and correlation of the force
are obtained, showing that the center-of-mass motion of the atom is damped and
diffused. This approach can be easily generalized to multi-level atoms, where
the damping force and diffusion coefficients are just the weighted average of
the contributions from all pairs of energy levels that have nonvanishing dipole
elements. It is shown that these results are invariant under Galilean
transformation, and in principle can be used to determine the velocity of the
lab relative to the background radiation.
|
2108.05590v3
|
2021-09-22
|
Antibunching via cooling by heating
|
We investigate statistics of the photon (phonon) field undergoing linear and
nonlinear damping processes. An effective two-photon (phonon) nonlinear
"cooling by heating" process is realized from linear damping by spectral
filtering of the heat baths present in the system. This cooling process driven
by incoherent quantum thermal noise can create quantum states of the photon
field. In fact, for high temperatures of the spectrally filtered heat baths,
sub-Poissonian statistics with strong antibunching in the photon (phonon) field
are reported. This notion of the emergence and control of quantumness by
incoherent thermal quantum noise is applied to a quantum system comprising of a
two-level system and a harmonic oscillator or analogous optomechanical setting.
Our analysis may provide a promising direction for the preparation and
protection of quantum features via nonlinear damping that can be controlled
with incoherent thermal quantum noise.
|
2109.10516v2
|
2021-10-13
|
Tutorial on stochastic systems
|
In this tutorial, three examples of stochastic systems are considered: A
strongly-damped oscillator, a weakly-damped oscillator and an undamped
oscillator (integrator) driven by noise. The evolution of these systems is
characterized by the temporal correlation functions and spectral densities of
their displacements, which are determined and discussed. Damped oscillators
reach steady stochastic states. Their correlations are decreasing functions of
the difference between the sample times and their spectra have peaks near their
resonance frequencies. An undamped oscillator never reaches a steady state. Its
energy increases with time and its spectrum is sharply peaked at low
frequencies. The required mathematical methods and physical concepts are
explained on a just-in-time basis, and some theoretical pitfalls are mentioned.
The insights one gains from studies of oscillators can be applied to a wide
variety of physical systems, such as atom and semiconductor lasers, which will
be discussed in a subsequent tutorial.
|
2110.06966v1
|
2021-10-18
|
Structured vector fitting framework for mechanical systems
|
In this paper, we develop a structure-preserving formulation of the
data-driven vector fitting algorithm for the case of modally damped mechanical
systems. Using the structured pole-residue form of the transfer function of
modally damped second-order systems, we propose two possible structured
extensions of the barycentric formula of system transfer functions. Integrating
these new forms within the classical vector fitting algorithm leads to the
formulation of two new algorithms that allow the computation of modally damped
mechanical systems from data in a least squares fashion. Thus, the learned
model is guaranteed to have the desired structure. We test the proposed
algorithms on two benchmark models.
|
2110.09220v1
|
2021-10-27
|
Integrability and solvability of polynomial Liénard differential systems
|
We provide the necessary and sufficient conditions of Liouvillian
integrability for Li\'{e}nard differential systems describing nonlinear
oscillators with a polynomial damping and a polynomial restoring force. We
prove that Li\'{e}nard differential systems are not Darboux integrable
excluding subfamilies with certain restrictions on the degrees of the
polynomials arising in the systems. We demonstrate that if the degree of a
polynomial responsible for the restoring force is greater than the degree of a
polynomial producing the damping, then a generic Li\'{e}nard differential
system is not Liouvillian integrable with the exception of linear Li\'{e}nard
systems. However, for any fixed degrees of the polynomials describing the
damping and the restoring force we present subfamilies possessing Liouvillian
first integrals. As a by-product of our results, we find a number of novel
Liouvillian integrable subfamilies. In addition, we study the existence of
non-autonomous Darboux first integrals and non-autonomous Jacobi last
multipliers with a time-dependent exponential factor.
|
2110.14306v2
|
2021-10-28
|
Global Solution to the Vacuum Free Boundary Problem with Physical Singularity of Compressible Euler Equations with Damping and Gravity
|
The global existence of smooth solutions to the vacuum free boundary problem
with physical singularity of compressible Euler equations with damping and
gravity is proved in space dimensions $n=1, 2, 3$, for the initial data being
small perturbations of the stationary solution. Moreover, the exponential decay
of the velocity is obtained for $n=1, 2, 3$. The exponentially fast convergence
of the density and vacuum boundary to those of the stationary solution is shown
for $n=1$, and it is proved for $n=2, 3$ that they stay close to those of the
stationary solution if they do so initially. The proof is based on the weighted
estimates of both hyperbolic and parabolic types with weights capturing the
singular behavior of higher-order normal derivatives near vacuum states,
exploring the balance between the physical singularity which pushes the vacuum
boundary outwards and the effect of gravity which pulls it inwards, and the
dissipation of the frictional damping. The results obtained in this paper are
the first ones on the global existence of solutions to the vacuum free boundary
problems of inviscid compressible fluids with the non-expanding background
solutions. Exponentially fast convergence when the vacuum state is involved
discovered in this paper is a new feature of the problem studied.
|
2110.14909v1
|
2021-10-29
|
Spinons and damped phonons in spin-1/2 quantum-liquid Ba$_{4}$Ir${}_3$O${}_{10}$ observed by Raman scattering
|
In spin-1/2 Mott insulators, non-magnetic quantum liquid phases are often
argued to arise when the system shows no magnetic ordering, but identifying
positive signatures of these phases or related spinon quasiparticles can be
elusive. Here we use Raman scattering to provide three signatures for spinons
in a possible spin-orbit quantum liquid material Ba${}_4$Ir${}_3$O${}_{10}$:
(1) A broad hump, which we show can arise from Luttinger Liquid spinons in
Raman with parallel photon polarizations normal to 1D chains; (2) Strong phonon
damping from phonon-spin coupling via the spin-orbit interaction; and (3) the
absence of (1) and (2) in the magnetically ordered phase that is produced when
2% of Ba is substituted by Sr
((Ba${}_{0.98}$Sr${}_{0.02}$)${}_4$Ir${}_3$O${}_{10}$). The phonon damping via
itinerant spinons seen in this quantum-liquid insulator suggests a new
mechanism for enhancing thermoelectricity in strongly correlated conductors,
through a neutral quantum liquid that need not affect electronic transport.
|
2110.15916v1
|
2021-11-03
|
Pointwise space-time estimates of two-phase fluid model in dimension three
|
In this paper, we investigate the pointwise space-time behavior of two-phase
fluid model derived by Choi \cite{Choi} [SIAM J. Math. Anal., 48(2016), pp.
3090-3122], which is the compressible damped Euler equations coupled with
compressible Naiver-Stokes equations. Based on Green's function method together
with frequency analysis and nonlinear coupling of different wave patterns, it
shows that both of two densities and momentums obey the generalized Huygens'
principle as the compressible Navier-Stokes equations \cite{LW}, however, it is
different from the compressible damped Euler equations \cite{Wang2}. The main
contributions include seeking suitable combinations to avoid the singularity
from the Hodge decomposition in the low frequency part of the Green's function,
overcoming the difficulty of the non-conservation arising from the damped
mechanism of the system, and developing the detailed description of the
singularities in the high frequency part of the Green's function. Finally, as a
byproduct, we extend $L^2$-estimate in \cite{Wugc} [SIAM J. Math. Anal.,
52(2020), pp. 5748-5774] to $L^p$-estimate with $p>1$.
|
2111.01987v1
|
2021-11-09
|
Turbulent cascades for a family of damped Szegö equations
|
In this paper, we study the transfer of energy from low to high frequencies
for a family of damped Szeg\"o equations. The cubic Szeg\"o equation has been
introduced as a toy model for a totally non-dispersive degenerate Hamiltonian
equation. It is a completely integrable system which develops growth of high
Sobolev norms, detecting transfer of energy and hence cascades phenomena.
Here, we consider a two-parameter family of variants of the cubic Szeg\"o
equation and prove that adding a damping term unexpectedly promotes the
existence of turbulent cascades. Furthermore, we give a panorama of the
dynamics for such equations on a six-dimensional submanifold.
|
2111.05247v1
|
2021-11-18
|
Sharp Stability of a String with Local Degenerate Kelvin-Voigt Damping
|
This paper is on the asymptotic behavior of the elastic string equation with
localized degenerate Kelvin--Voigt damping $$
u_{tt}(x,t)-[u_{x}(x,t)+b(x)u_{x,t}(x,t)]_{x}=0,\; x\in(-1,1),\; t>0,$$ where
$b(x)=0$ on $x\in (-1,0]$, and $b(x)=x^\alpha>0$ on $x\in (0,1)$ for
$\alpha\in(0,1)$. It is known that the optimal decay rate of solution is
$t^{-2}$ in the limit case $\alpha=0$, and exponential decay rate for
$\alpha\ge 1$. When $\alpha\in (0,1)$, the damping coefficient $b(x)$ is
continuous, but its derivative has a singularity at the interface $x=0$. In
this case, the best known decay rate is $t^{-\frac{3-\alpha}{2(1-\alpha)}}$.
Although this rate is consistent with the exponential one at $\alpha=1$, it
failed to match the optimal one at $\alpha=0$.
In this paper, we obtain a sharper polynomial decay rate
$t^{-\frac{2-\alpha}{1-\alpha}}$. More significantly, it is consistent with the
optimal polynomial decay rate at $\alpha=0$ and the exponential decay rate at
$\alpha = 1$.This is a big step toward the goal of obtaining eventually the
optimal decay rate.
|
2111.09500v1
|
2021-11-22
|
Global well-posedness for a generalized Keller-Segel system with degenerate dissipation and mixing
|
We study the mixing effect for a generalized Keller-Segel system with
degenerate dissipation and advection by a weakly mixing. Here the attractive
operator has weak singularity, namely, the negative derivative appears in the
nonlinear term by singular integral. Without advection, the solution of
equation blows up in finite time. We show that the global well-posedness of
solution with large advection. Since dissipation term degenerate into the
damping, the enhanced dissipation effect of mixing no longer occurs, we prove
that the mixing effect can weak the influence of nonlinear term. In this case,
the mixing effect is similar with inviscid damping of shear flow. Combining to
the mixing effect and damping effect of degenerate dissipation, the global
$L^\infty$ estimate of solution is established.
|
2111.11083v1
|
2021-11-26
|
Damping of Pseudo-Goldstone Fields
|
Approximate symmetries abound in Nature. If these symmetries are also
spontaneously broken, the would-be Goldstone modes acquire a small mass, or
inverse correlation length, and are referred to as pseudo-Goldstones. At
nonzero temperature, the effects of dissipation can be captured by
hydrodynamics at sufficiently long scales compared to the local equilibrium.
Here we show that in the limit of weak explicit breaking, locality of
hydrodynamics implies that the damping of pseudo-Goldstones is completely
determined by their mass and diffusive transport coefficients. We present many
applications: superfluids, QCD in the chiral limit, Wigner crystal and density
wave phases in the presence of an external magnetic field or not, nematic
phases and (anti-)ferromagnets. For electronic density wave phases,
pseudo-Goldstone damping generates a contribution to the resistivity
independent of the strength of disorder, which can have a linear temperature
dependence provided the associated diffusivity saturates a bound. This is
reminiscent of the phenomenology of strange metal high $T_c$ superconductors,
where charge density waves are observed across the phase diagram.
|
2111.13459v2
|
2021-11-26
|
Transition from order to chaos in reduced quantum dynamics
|
We study a damped kicked top dynamics of a large number of qubits ($N
\rightarrow \infty$) and focus on an evolution of a reduced single-qubit
subsystem. Each subsystem is subjected to the amplitude damping channel
controlled by the damping constant $r\in [0,1]$, which plays the role of the
single control parameter. In the parameter range for which the classical
dynamics is chaotic, while varying $r$ we find the universal period-doubling
behavior characteristic to one-dimensional maps: period-two dynamics starts at
$r_1 \approx 0.3181$, while the next bifurcation occurs at $ r_2 \approx
0.5387$. In parallel with period-four oscillations observed for $r \leq r_3
\approx 0.5672$, we identify a secondary bifurcation diagram around $r\approx
0.544$, responsible for a small-scale chaotic dynamics inside the attractor.
The doubling of the principal bifurcation tree continues until $r \leq
r_{\infty} \sim 0.578$, which marks the onset of the full scale chaos
interrupted by the windows of the oscillatory dynamics corresponding to the
Sharkovsky order.
|
2111.13477v1
|
2021-12-06
|
Damped physical oscillators, temperature and chemical clocks
|
The metaphor of a clock in physics describes near-equilibrium reversible
phenomena such as an oscillating spring. It is surprising that for chemical and
biological clocks the focus has been exclusively on the far-from-equilibrium
dissipative processes. We show here that one can represent chemical
oscillations (the Lotka-Volterra system and the Brusselator) by equations
analogous to Onsager's phenomenological equations when the condition of the
reciprocal relations, i.e. the symmetry in the coupling of thermodynamic forces
to fluxes is relaxed and antisymmetric contributions are permitted. We compare
these oscillations to damped oscillators in physics (e.g., springs, coupled
springs and electrical circuits) which are represented by similar equations.
Onsager's equations and harmonic Hamiltonian systems are shown to be limiting
cases of a more general formalism.
The central element of un-damped physical oscillations is the conservation of
entropy which unavoidably results in reversible temperature oscillations. Such
temperature oscillations exist in springs and electrical LC-circuits, but have
among others also been found in the oscillating Belousov-Zhabotinsky reaction,
in oscillations of yeast cells, and during the nervous impulse. This suggests
that such oscillations contain reversible entropy-conserving elements, and that
physical and chemical clocks may be more similar than expected.
|
2112.03083v1
|
2021-12-10
|
Existence of Zero-damped Quasinormal Frequencies for Nearly Extremal Black Holes
|
It has been observed that many spacetimes which feature a near-extremal
horizon exhibit the phenomenon of zero-damped modes. This is characterised by
the existence of a sequence of quasinormal frequencies which all converge to
some purely imaginary number $i\alpha$ in the extremal limit and cluster in a
neighbourhood of the line $\Im s=\alpha$. In this paper, we establish that this
property is present for the conformal Klein-Gordon equation on a
Reissner-Nordstr\"om-de Sitter background. This follows from a similar result
that we prove for a class of spherically symmetric black hole spacetimes with a
cosmological horizon. We also show that the phenomenon of zero-damped modes is
stable to perturbations that arise through adding a potential.
|
2112.05669v3
|
2021-12-22
|
Quantifying Spin-Orbit Torques in Antiferromagnet/Heavy Metal Heterostructures
|
The effect of spin currents on the magnetic order of insulating
antiferromagnets (AFMs) is of fundamental interest and can enable new
applications. Toward this goal, characterizing the spin-orbit torques (SOT)
associated with AFM/heavy metal (HM) interfaces is important. Here we report
the full angular dependence of the harmonic Hall voltages in a predominantly
easy-plane AFM, epitaxial c-axis oriented $\alpha$-Fe$_2$O$_3$ films, with an
interface to Pt. By modeling the harmonic Hall signals together with the
$\alpha$-Fe$_2$O$_3$ magnetic parameters, we determine the amplitudes of
field-like and damping-like SOT. Out-of-plane field scans are shown to be
essential to determining the damping-like component of the torques. In contrast
to ferromagnetic/heavy metal heterostructures, our results demonstrate that the
field-like torques are significantly larger than the damping-like torques,
which we correlate with the presence of a large imaginary component of the
interface spin-mixing conductance. Our work demonstrates a direct way of
characterizing SOT in AFM/HM heterostructures.
|
2112.12238v1
|
2022-01-04
|
Focusing of nonlinear eccentric waves in astrophysical discs. II. Excitation and damping of tightly-wound waves
|
In this paper I develop a nonlinear theory of tightly-wound (highly twisted)
eccentric waves in astrophysical discs, based on the averaged Lagrangian method
of Whitham. Viscous dissipation is included in the theory by use of a
pseudo-Lagrangian. This work is an extension of the theory developed by Lee \&
Goodman to 3D discs, with the addition of viscosity. I confirm that linear
tightly-wound eccentric waves are overstable and are excited by the presence of
a shear viscosity and show this persists for weakly nonlinear waves. I find the
waves are damped by shear viscosity when the wave become sufficiently
nonlinear, a result previously found in particulate discs. Additionally I
compare the results of this model to recent simulations of eccentric waves
propagating in the inner regions of black hole discs and show that an ingoing
eccentric wave can be strongly damped near the marginally stable orbit,
resulting in a nearly circular disc with a strong azimuthal variation in the
disc density.
|
2201.01156v1
|
2022-01-12
|
Local Well-Posedness of the Gravity-Capillary Water Waves System in the Presence of Geometry and Damping
|
We consider the gravity-capillary water waves problem in a domain $\Omega_t
\subset \mathbb{T} \times \mathbb{R}$ with substantial geometric features.
Namely, we consider a variable bottom, smooth obstacles in the flow and a
constant background current. We utilize a vortex sheet model introduced by
Ambrose, et. al. in arXiv:2108.01786. We show that the water waves problem is
locally-in-time well-posed in this geometric setting and study the lifespan of
solutions. We then add a damping term and derive evolution equations that
account for the damper. Ultimately, we show that the same well-posedness and
lifespan results apply to the damped system. We primarily utilize energy
methods.
|
2201.04713v2
|
2022-02-04
|
Finite-temperature plasmons, damping and collective behavior for $α-\mathcal{T}_3$ model
|
We have conducted a thorough theoretical and numerical investigation of the
electronic susceptibility, polarizability, plasmons, their damping rates, as
well as the static screening in pseudospin-1 Dirac cone materials with a flat
band, or for a general $\alpha - \mathcal{T}_3$ model, at finite temperatures.
This includes calculating the polarization function, plasmon dispersions and
their damping rates at arbitrary temperatures and obtaining analytical
approximations the long wavelength limit, low and high temperatures. We
demonstrate that the integral transformation of the polarization function
cannot be used directly for a dice lattice revealing some fundamental
properties and important applicability limits of the flat band dispersions
model. At $k_B T \ll E_F$, the largest temperature-induced change of the
polarization function and plasmons comes from the mismatch between the chemical
potential and the Fermi energy. We have also obtained a series of closed-form
semi-analytical expressions for the static limit of the polarization function
of an arbitrary $\alpha - \mathcal{T}_3$ material at any temperature with exact
analytical formulas for the high, low and zero temperature limits which is of
tremendous importance for all types of transport and screening calculations for
the flat band Dirac materials.
|
2202.01945v1
|
2022-02-04
|
Enhancing the Formation of Wigner Negativity in a Kerr Oscillator via Quadrature Squeezing
|
Motivated by quantum experiments with nanomechanical systems, the evolution
of a Kerr oscillator with focus on creation of states with a negative Wigner
function is investigated. Using the phase space formalism, results are
presented that demonstrate an asymptotic behavior in the large squeezing regime
for the negativity of a squeezed vacuum state under unitary evolution. The
analysis and model are extended to squeezed vacuum states of open systems,
adding the decoherence effects of damping and dephasing. To increase
experimental relevance, the regime of strong damping is considered. These
effects are investigated, yielding similar asymptotic results for the behavior
of these effects in the large squeezing regime. Combining these results, it is
shown that a weak nonlinearity as compared to damping may be improved by
increasing the squeezing of the initial state. It is also shown that this may
be done without exacerbating the effects of dephasing.
|
2202.02285v1
|
2022-02-11
|
Spin stiffness, spectral weight, and Landau damping of magnons in metallic spiral magnets
|
We analyze the properties of magnons in metallic electron systems with spiral
magnetic order. Our analysis is based on the random phase approximation for the
susceptibilities of tight binding electrons with a local Hubbard interaction in
two or three dimensions. We identify three magnon branches from poles in the
susceptibilities, one associated with in-plane, the other two associated with
out-of-plane fluctuations of the spiral order parameter. We derive general
expressions for the spin stiffnesses and the spectral weights of the magnon
modes, from which also the magnon velocities can be obtained. Moreover, we
determine the size of the decay rates of the magnons due to Landau damping.
While the decay rate of the in-plane mode is of the order of its excitation
energy, the decay rate of the out-of-plane mode is smaller so that these modes
are asymptotically stable excitations even in the presence of Landau damping.
|
2202.05660v1
|
2022-02-16
|
On the strong convergence of the trajectories of a Tikhonov regularized second order dynamical system with asymptotically vanishing damping
|
This paper deals with a second order dynamical system with vanishing damping
that contains a Tikhonov regularization term, in connection to the minimization
problem of a convex Fr\'echet differentiable function $g$.
We show that for appropriate Tikhonov regularization parameters the value of
the objective function in a generated trajectory converges fast to the global
minimum of the objective function and a trajectory generated by the dynamical
system converges weakly to a minimizer of the objective function. We also
obtain the fast convergence of the velocities towards zero and some integral
estimates. Nevertheless, our main goal is to extend and improve some recent
results obtained in \cite{ABCR} and \cite{AL-nemkoz} concerning the strong
convergence of the generated trajectories to an element of minimal norm from
the $\argmin$ set of the objective function $g$. Our analysis also reveals that
the damping coefficient and the Tikhonov regularization coefficient are
strongly correlated.
|
2202.08980v1
|
2022-04-01
|
Effect of interfacial spin mixing conductance on gyromagnetic ratio of Gd substituted Y$_{3}$Fe$_{5}$O$_{12}$
|
Due to its low intrinsic damping, Y$_3$Fe$_5$O$_{12}$ and its substituted
variations are often used for ferromagnetic layer at spin pumping experiment.
Spin pumping is an interfacial spin current generation in the interface of
ferromagnet and non-magnetic metal, governed by spin mixing conductance
parameter $G^{\uparrow\downarrow}$. $G^{\uparrow\downarrow}$ has been shown to
enhance the damping of the ferromagnetic layer. The theory suggested that the
effect of $G^{\uparrow\downarrow}$ on gyromagnetic ratio only come from its
negligible imaginary part. In this article, we show that the different damping
of ferrimagnetic lattices induced by $G^{\uparrow\downarrow}$ can affect the
gyromagnetic ratio of Gd-substituted Y$_3$Fe$_5$O$_{12}$.
|
2204.00310v1
|
2022-04-04
|
A Vanka-based parameter-robust multigrid relaxation for the Stokes-Darcy Brinkman problems
|
We propose a block-structured multigrid relaxation scheme for solving the
Stokes-Darcy Brinkman equations discretized by the marker and cell scheme. An
element-based additive Vanka smoother is used to solve the corresponding
shifted Laplacian operator. Using local Fourier analysis, we present the
stencil for the additive Vanka smoother and derive an optimal smoothing factor
for Vanka-based Braess-Sarazin relaxation for the Stokes-Darcy Brinkman
equations. Although the optimal damping parameter is dependent on meshsize and
physical parameter, it is very close to one. Numerical results of two-grid and
V(1,1)-cycle are presented, which show high efficiency of the proposed
relaxation scheme and its robustness to physical parameters and the meshsize.
Using a damping parameter equal to one gives almost the same results as these
for the optimal damping parameter at a lower computational overhead.
|
2204.01237v1
|
2022-04-19
|
Blow-up and lifespan estimate for wave equations with critical damping term of space-dependent type related to Glassey conjecture
|
The main purpose of the present paper is to study the blow-up problem of the
wave equation with space-dependent damping in the \textit{scale-invariant case}
and time derivative nonlinearity with small initial data. Under appropriate
initial data which are compactly supported, by using a test function method and
taking into account the effect of the damping term
($\frac{\mu}{\sqrt{1+|x|^2}}u_t$), we provide that in higher dimensions the
blow-up region is given by $p \in (1, p_G(N+\mu)]$ where $p_G(N)$ is the
Glassey exponent. Furthermore, we shall establish a blow-up region, independent
of $\mu$ given by $p\in (1, 1+\frac{2}{N}),$ for appropriate initial data in
the energy space with noncompact support.
|
2204.09156v1
|
2022-04-28
|
Strong coupling of quantum emitters and the exciton polariton in MoS$_2$ nanodisks
|
As a quasiparticle formed by light and excitons in semiconductors, the
exciton-polariton (EP) as a quantum bus is promising for the development of
quantum interconnect devices at room temperature. However, the significant
damping of EPs in the material generally causes a loss of quantum information.
We propose a mechanism to overcome the destructive effect of a damping EP on
its mediated correlation dynamics of quantum emitters (QEs). Via an
investigation of the near-field coupling between two QEs and the EP in a
monolayer MoS$_{2}$ nanodisk, we find that, with the complete dissipation of
the QEs efficiently avoided, a persistent quantum correlation between the QEs
can be generated and stabilized even to their steady state. This is due to the
fact that, with upon decreasing the QE-MoS$_2$ distance, the QEs become so
hybridized with the EP that one or two bound states are formed between them.
Our result supplies a useful way to avoid the destructive impact of EP damping,
and it refreshes our understanding of the light-matter interaction in absorbing
medium.
|
2204.13383v2
|
2022-05-09
|
Scalable all-optical cold damping of levitated nanoparticles
|
The field of levitodynamics has made significant progress towards controlling
and studying the motion of a levitated nanoparticle. Motional control relies on
either autonomous feedback via a cavity or measurement-based feedback via
external forces. Recent demonstrations of measurement-based ground-state
cooling of a single nanoparticle employ linear velocity feedback, also called
cold damping, and require the use of electrostatic forces on charged particles
via external electrodes. Here we introduce a novel all-optical cold damping
scheme based on spatial modulation of the trap position that is scalable to
multiple particles. The scheme relies on using programmable optical tweezers to
provide full independent control over trap frequency and position of each
tweezer. We show that the technique cools the center-of-mass motion of
particles down to $17\,$mK at a pressure of $2 \times 10^{-6}\,$mbar and
demonstrate its scalability by simultaneously cooling the motion of two
particles. Our work paves the way towards studying quantum interactions between
particles, achieving 3D quantum control of particle motion without cavity-based
cooling, electrodes or charged particles, and probing multipartite entanglement
in levitated optomechanical systems.
|
2205.04455v1
|
2022-06-08
|
Thermal ion kinetic effects and Landau damping in fishbone modes
|
The kinetic-MHD hybrid simulation approach for macroscopic instabilities in
plasmas can be extended to include the kinetic effects of both thermal ions and
energetic ions. The new coupling scheme includes synchronization of density and
parallel velocity between thermal ions and MHD, in addition to pressure
coupling, to ensure the quasineutrality condition and avoid numerical errors.
The new approach has been implemented in the kinetic-MHD code M3D-C1-K, and was
used to study the thermal ion kinetic effects and Landau damping in fishbone
modes in both DIII-D and NSTX. It is found that the thermal ion kinetic effects
can cause an increase of the frequencies of the non-resonant $n=1$ fishbone
modes driven by energetic particles for $q_\mathrm{min}>1$, and Landau damping
can provide additional stabilization effects. A nonlinear simulation for $n=1$
fishbone mode in NSTX is also performed, and the perturbation on magnetic flux
surfaces and the transport of energetic particles are calculated.
|
2206.03648v1
|
2022-07-12
|
Resonant Multilevel Amplitude Damping Channels
|
We introduce a new set of quantum channels: resonant multilevel amplitude
damping (ReMAD) channels. Among other instances, they can describe energy
dissipation effects in multilevel atomic systems induced by the interaction
with a zero-temperature bosonic environment. At variance with the already known
class of multilevel amplitude damping (MAD) channels, this new class of maps
allows the presence of an environment unable to discriminate transitions with
identical energy gaps. After characterizing the algebra of their composition
rules, by analyzing the qutrit case, we show that this new set of channels can
exhibit degradability and antidegradability in vast regions of the allowed
parameter space. There we compute their quantum capacity and private classical
capacity. We show that these capacities can be computed exactly also in regions
of the parameter space where the channels aren't degradable nor antidegradable.
|
2207.05646v2
|
2022-07-14
|
Estimates for the nonlinear viscoelastic damped wave equation on compact Lie groups
|
Let $G$ be a compact Lie group. In this article, we investigate the Cauchy
problem for a nonlinear wave equation with the viscoelastic damping on $G$.
More preciously, we investigate some $L^2$-estimates for the solution to the
homogeneous nonlinear viscoelastic damped wave equation on $G$ utilizing the
group Fourier transform on $G$. We also prove that there is no improvement of
any decay rate for the norm $\|u(t,\cdot)\|_{L^2(G)}$ by further assuming the
$L^1(G)$-regularity of initial data. Finally, using the noncommutative Fourier
analysis on compact Lie groups, we prove a local in time existence result in
the energy space $\mathcal{C}^1([0,T],H^1_{\mathcal L}(G)).$
|
2207.06645v3
|
2022-08-04
|
Normal and Quasinormal Modes of Holographic Multiquark Star
|
The quadrupole normal-mode oscillation frequency $f_{n}$ of multiquark star
are computed for $n=1-5$. At the transition from low to high density multiquark
in the core region, the first 2 modes jump to larger values, a distinctive
signature of the presence of the high-density core. When the star oscillation
couples with spacetime, gravitational waves~(GW) will be generated and the star
will undergo damped oscillation. The quasinormal modes~(QNMs) of the
oscillation are computed using two methods, direct scan and WKB, for QNMs with
small and large imaginary parts respectively. The small imaginary QNMs have
frequencies $1.5-2.6$ kHz and damping times $0.19-1.7$ secs for multiquark star
with mass $M=0.6-2.1 M_{\odot}$~(solar mass). The WKB QNMs with large imaginary
parts have frequencies $5.98-9.81$ kHz and damping times $0.13-0.46$ ms for
$M\simeq 0.3-2.1 M_{\odot}$. They are found to be the fluid $f-$modes and
spacetime curvature $w-$modes respectively.
|
2208.02761v2
|
2022-08-10
|
Erasure qubits: Overcoming the $T_1$ limit in superconducting circuits
|
The amplitude damping time, $T_1$, has long stood as the major factor
limiting quantum fidelity in superconducting circuits, prompting concerted
efforts in the material science and design of qubits aimed at increasing $T_1$.
In contrast, the dephasing time, $T_{\phi}$, can usually be extended above
$T_1$ (via, e.g., dynamical decoupling), to the point where it does not limit
fidelity. In this article we propose a scheme for overcoming the conventional
$T_1$ limit on fidelity by designing qubits in a way that amplitude damping
errors can be detected and converted into erasure errors. Compared to standard
qubit implementations our scheme improves the performance of fault-tolerant
protocols, as numerically demonstrated by the circuit-noise simulations of the
surface code. We describe two simple qubit implementations with superconducting
circuits and discuss procedures for detecting amplitude damping errors,
performing entangling gates, and extending $T_\phi$. Our results suggest that
engineering efforts should focus on improving $T_\phi$ and the quality of
quantum coherent control, as they effectively become the limiting factor on the
performance of fault-tolerant protocols.
|
2208.05461v1
|
2022-08-12
|
Critical exponent for nonlinear wave equations with damping and potential terms
|
The aim of this paper is to determine the critical exponent for the nonlinear
wave equations with damping and potential terms of the scale invariant order,
by assuming that these terms satisfy a special relation. We underline that our
critical exponent is different from the one for related equations such as the
nonlinear wave equation without lower order terms, only with a damping term,
and only with a potential term. Moreover, we study the effect of the decaying
order of initial data at spatial infinity. In fact, we prove that not only the
lower order terms but also the order of the initial data affects the critical
exponent, as well as the sharp upper and lower bounds of the maximal existence
time of the solution.
|
2208.06106v3
|
2022-08-17
|
Conservation laws and variational structure of damped nonlinear wave equations
|
All low-order conservation laws are found for a general class of nonlinear
wave equations in one dimension with linear damping which is allowed to be
time-dependent. Such equations arise in numerous physical applications and have
attracted much attention in analysis. The conservation laws describe
generalized momentum and boost momentum, conformal momentum, generalized
energy, dilational energy, and light-cone energies. Both the conformal momentum
and dilational energy have no counterparts for nonlinear undamped wave
equations in one dimension. All of the conservation laws are obtainable through
Noether's theorem, which is applicable because the damping term can be
transformed into a time-dependent self-interaction term by a change of
dependent variable. For several of the conservation laws, the corresponding
variational symmetries have a novel form which is different than any of the
well known variation symmetries admitted by nonlinear undamped wave equations
in one dimension.
|
2208.08026v2
|
2022-08-27
|
Impact of the free-streaming neutrinos to the second order induced gravitational waves
|
The damping effect of the free-streaming neutrinos on the second order
gravitational waves is investigated in detail. We solve the Boltzmann equation
and give the anisotropic stress induced by neutrinos to second order. The first
order tensor and its coupling with scalar perturbations induced gravitational
waves are considered. We give the analytic equations of the damping kernel
functions and finally obtain the energy density spectrum. The results show that
the free-streaming neutrinos suppress the density spectrum significantly for
low frequency gravitational waves and enlarge the logarithmic slope $n$ in the
infrared region ($k \ll k_*$) of the spectrum. For the spectrum of $k_*\sim
10^{-7}$Hz, the damping effect in the range of $k<k_*$ is significant. The
combined effect of the first and second order could reduce the amplitude by
$30\%$ and make $n$ jump from $1.54$ to $1.63$ at $k\sim 10^{-9}$Hz, which may
be probed by the pulsar timing arrays (PTA) in the future.
|
2208.12948v1
|
2022-08-28
|
The small mass limit for long time statistics of a stochastic nonlinear damped wave equation
|
We study the long time statistics of a class of semi--linear damped wave
equations with polynomial nonlinearities and perturbed by additive Gaussian
noise in dimensions 2 and 3. We find that if sufficiently many directions in
the phase space are stochastically forced, the system is exponentially
attractive toward its unique invariant measure with a convergent rate that is
uniform with respect to the mass. Then, in the small mass limit, we prove the
convergence of the first marginal of the invariant measures in a suitable
Wasserstein distance toward the unique invariant measure of a stochastic
reaction--diffusion equation. This together with uniform geometric ergodcity
implies the validity of the small mass limit for the solutions on the infinite
time horizon $[0,\infty)$, thereby extending previously known results
established for the damped wave equations under Lipschitz nonlinearities.
|
2208.13287v2
|
2022-08-30
|
Results on high energy galactic cosmic rays from the DAMPE space mission
|
DAMPE (Dark Matter Particle Explorer) is a satellite-born experiment launched
in 2015 in a sun-synchronous orbit at 500 km altitude, and it has been taking
data in stable conditions ever since. Its main goals include the spectral
measurements up to very high energies, cosmic electrons/positrons and gamma
rays up to tens of TeV, and protons and nuclei up to hundreds of TeV. The
detector's main features include the 32 radiation lengths deep calorimeter and
large geometric acceptance, making DAMPE one of the most powerful space
instruments in operation, covering with high statistics and small systematics
the high energy frontier up to several hundreds TeV. The results of spectral
measurements of different species are shown and discussed.
|
2208.14300v2
|
2022-09-05
|
Generation and routing of nanoscale droplet solitons without compensation of magnetic damping
|
Magnetic droplet soliton is a localized dynamic spin state which can serve as
a nanoscale information carrier and nonlinear oscillator. The present opinion
is that the formation of droplet solitons requires the compensation of magnetic
damping by a torque created by a spin-polarized electric current or pure spin
current. Here we demonstrate theoretically that nanoscale droplet solitons can
be generated and routed in ferromagnetic nanostructures with voltage-controlled
magnetic anisotropy in the presence of uncompensated magnetic damping.
Performing micromagnetic simulations for the MgO/Fe/MgO trilayer with almost
perpendicular-to-plane magnetization, we reveal the formation of the droplet
soliton under a nanoscale gate electrode subjected to a sub-nanosecond voltage
pulse. The soliton lives up to 50 ns at room temperature and can propagate over
micrometer distances in a ferromagnetic waveguide due to nonzero gradient of
the demagnetizing field. Furthermore, we show that an electrical routing of the
soliton to different outputs of a spintronic device can be realized with the
aid of an additional semiconducting nanostripe electrode creating controllable
gradient of the perpendicular magnetic anisotropy.
|
2209.01893v1
|
2022-09-06
|
Emergence of damped-localized excitations of the Mott state due to disorder
|
A key aspect of ultracold bosonic quantum gases in deep optical lattice
potential wells is the realization of the strongly interacting Mott insulating
phase. Many characteristics of this phase are well understood, however little
is known about the effects of a random external potential on its gapped
quasiparticle and quasihole low-energy excitations. In the present study we
investigate the effect of disorder upon the excitations of the Mott insulating
state at zero temperature described by the Bose-Hubbard model. Using a
field-theoretical approach we obtain a resummed expression for the disorder
ensemble average of the spectral function. Its analysis shows that disorder
leads to an increase of the effective mass of both quasiparticle and quasihole
excitations. Furthermore, it yields the emergence of damped states, which
exponentially decay during propagation in space and dominate the whole band
when disorder becomes comparable to interactions. We argue that such
damped-localized states correspond to single-particle excitations of the
Bose-glass phase.
|
2209.02435v2
|
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