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2018-04-15
|
Reevaluation of radiation reaction and consequences for light-matter interactions at the nanoscale
|
In the context of electromagnetism and nonlinear optical interactions damping
is generally introduced as a phenomenological, viscous term that dissipates
energy, proportional to the temporal derivative of the polarization. Here, we
follow the radiation reaction method presented in [G. W. Ford and R. F.
O'Connell, Phys. Lett. A, 157, 217 (1991)], which applies to non-relativistic
electrons of finite size, to introduce an explicit reaction force in the
Newtonian equation of motion, and derive a hydrodynamic equation that offers
new insight on the influence of damping in generic plasmas, metal-based and/or
dielectric structures. In these settings, we find new damping-dependent linear
and nonlinear source terms that suggest the damping coefficient is proportional
to the local charge density, and nonlocal contributions that stem from the
spatial derivative of the magnetic field and discuss the conditions that could
modify both linear and nonlinear electromagnetic responses.
|
1804.05369v1
|
2018-04-30
|
Wave-like blow-up for semilinear wave equations with scattering damping and negative mass term
|
In this paper we establish blow-up results and lifespan estimates for
semilinear wave equations with scattering damping and negative mass term for
subcritical power, which is the same as that of the corresponding problem
without mass term, and also the same as that of the corresponding problem
without both damping and mass term. For this purpose, we have to use the
comparison argument twice, due to the damping and mass term, in additional to a
key multiplier. Finally, we get the desired results by an iteration argument.
|
1804.11073v3
|
2018-05-22
|
Uniqueness of the Cauchy datum for the tempered-in-time response and conductivity operator of a plasma
|
We study the linear Vlasov equation with a given electric field $E \in
\mathcal{S}$, where $\mathcal{S}$ is the space of Schwartz functions. The
associated damped partial differential equation has a unique tempered solution,
which fixes the needed Cauchy datum. This tempered solution then converges to
the causal solution of the linear Vlasov equation when the damping parameter
goes to zero. This result allows us to define the plasma conductivity operator
$\sigma$, which gives the current density $j = \sigma (E)$ induced by the
electric field $E$. We prove that $\sigma$ is continuous from $\mathcal{S}$ to
its dual $\mathcal{S}^\prime$. We can treat rigorously the case of uniform
non-magnetized non-relativistic plasma (linear Landau damping) and the case of
uniform magnetized relativistic plasma (cyclotron damping). In both cases, we
demonstrate that the main part of the conductivity operator is a
pseudo-differential operator and we give its expression rigorously. This
matches the formal results widely used in the theoretical physics community.
|
1805.08733v3
|
2018-05-26
|
Stabilization for the wave equation with singular Kelvin-Voigt damping
|
We consider the wave equation with Kelvin-Voigt damping in a bounded domain.
The exponential stability result proposed by Liu and Rao or T\'ebou for that
system assumes that the damping is localized in a neighborhood of the whole or
a part of the boundary under some consideration. In this paper we propose to
deal with this geometrical condition by considering a singular Kelvin-Voigt
damping which is localized faraway from the boundary. In this particular case
it was proved by Liu and Liu the lack of the uniform decay of the energy.
However, we show that the energy of the wave equation decreases logarithmically
to zero as time goes to infinity. Our method is based on the frequency domain
method. The main feature of our contribution is to write the resolvent problem
as a transmission system to which we apply a specific Carleman estimate.
|
1805.10430v1
|
2018-06-01
|
Fluctuation-damping of isolated, oscillating Bose-Einstein condensates
|
Experiments on the nonequilibrium dynamics of an isolated Bose-Einstein
condensate (BEC) in a magnetic double-well trap exhibit a puzzling divergence:
While some show dissipation-free Josephson oscillations, others find strong
damping. Such damping in isolated BECs cannot be understood on the level of the
coherent Gross-Pitaevskii dynamics. Using the Keldysh functional-integral
formalism, we describe the time-dependent system dynamics by means of a
multi-mode BEC coupled to fluctuations (single-particle excitations) beyond the
Gross-Pitaevskii saddle point. We find that the Josephson oscillations excite
an excess of fluctuations when the effective Josephson frequency,
$\tilde{\omega}_J$, is in resonance with the effective fluctuation energy,
$\tilde{\varepsilon}_m$, where both, $\tilde{\omega}_J$ and
$\tilde{\varepsilon}_m$, are strongly renormalized with respect to their
noninteracting values. Evaluating and using the model parameters for the
respective experiments describes quantitatively the presence or absence of
damping.
|
1806.00376v2
|
2018-06-05
|
Decoherence assisted spin squeezing generation in superposition of tripartite GHZ and W states
|
In the present paper, we study spin squeezing under decoherence in the
superposition of tripartite maximally entangled GHZ and W states. Here we use
amplitude damping, phase damping and depolarisation channel. We have
investigated the dynamics of spin squeezing with the interplay of superposition
and decoherence parameters with different directions of the mean spin vector.
We have found the mixture of GHZ and W states is robust against spin squeezing
generation for amplitude damping and phase damping channels for certain
directions of the mean spin vector. However, the depolarisation channel
performs well for spin squeezing generation and generates permanent spin
squeezing in the superposition of GHZ and W states.
|
1806.01730v1
|
2018-07-31
|
Dark Matter Particle Explorer observations of high-energy cosmic ray electrons plus positrons and their physical implications
|
The DArk Matter Particle Explorer (DAMPE) is a satellite-borne, high-energy
particle and $\gamma$-ray detector, which is dedicated to indirectly detecting
particle dark matter and studying high-energy astrophysics. The first results
about precise measurement of the cosmic ray electron plus positron spectrum
between 25 GeV and 4.6 TeV were published recently. The DAMPE spectrum reveals
an interesting spectral softening around $0.9$ TeV and a tentative peak around
$1.4$ TeV. These results have inspired extensive discussion. The detector of
DAMPE, the data analysis, and the first results are introduced. In particular,
the physical interpretations of the DAMPE data are reviewed.
|
1807.11638v1
|
2018-08-08
|
A Hybrid Dynamic-regenerative Damping Scheme for Energy Regeneration in Variable Impedance Actuators
|
Increasing research efforts have been made to improve the energy efficiency
of variable impedance actuators (VIAs) through reduction of energy consumption.
However, the harvesting of dissipated energy in such systems remains
underexplored. This study proposes a novel variable damping module design
enabling energy regeneration in VIAs by exploiting the regenerative braking
effect of DC motors. The proposed damping module uses four switches to combine
regenerative and dynamic braking, in a hybrid approach that enables energy
regeneration without reduction in the range of damping achievable. Numerical
simulations and a physical experiment are presented in which the proposed
module shows an optimal trade-off between task performance and energy
efficiency.
|
1808.03143v1
|
2018-08-15
|
$L^1$ estimates for oscillating integrals and their applications to semi-linear models with $σ$-evolution like structural damping
|
The present paper is a continuation of our recent paper \cite{DaoReissig}. We
will consider the following Cauchy problems for semi-linear structurally damped
$\sigma$-evolution models: \begin{equation*} u_{tt}+ (-\Delta)^\sigma u+ \mu
(-\Delta)^\delta u_t = f(u,u_t),\, u(0,x)= u_0(x),\, u_t(0,x)=u_1(x)
\end{equation*} with $\sigma \ge 1$, $\mu>0$ and $\delta \in
(\frac{\sigma}{2},\sigma]$. Our aim is to study two main models including
$\sigma$-evolution models with structural damping $\delta \in
(\frac{\sigma}{2},\sigma)$ and those with visco-elastic damping
$\delta=\sigma$. Here the function $f(u,u_t)$ stands for power nonlinearities
$|u|^{p}$ and $|u_t|^{p}$ with a given number $p>1$. We are interested in
investigating the global (in time) existence of small data solutions to the
above semi-linear models from suitable spaces basing on $L^q$ space by assuming
additional $L^{m}$ regularity on the initial data, with $q\in (1,\infty)$ and
$m\in [1,q)$.
|
1808.05484v2
|
2018-09-04
|
Separation of the two-magnon scattering contribution to damping for the determination of the spin mixing conductance
|
We present angle dependent measurements of the damping properties of
epitaxial Fe layers with MgO, Al and Pt capping layers. Based on the
preferential distribution of lattice defects following the crystal symmetry, we
make use of a model of the defect density to separate the contribution of
two-magnon scattering to the damping from the isotropic contribution
originating in the spin pumping effect, the viscous Gilbert damping and the
magnetic proximity effect. The separation of the two-magnon contribution, which
depends strongly on the defect density, allows for the measurement of a value
of the effective spin mixing conductance which is closer to the value
exclusively due to spin pumping. The influence of the defect density for
bilayers systems due to the different capping layers and to the unavoidable
spread in defect density from sample to sample is thus removed. This shows the
potential of studying spin pumping phenomena in fully ordered systems in which
this separation is possible, contrary to polycrystalline or amorphous metallic
thin films.
|
1809.01042v1
|
2018-09-30
|
Critical behavior of the damping rate of GHz acoustic phonons in SrTiO3 at the antiferrodistortive phase transition measured by time- and frequency-resolved Brillouin scattering
|
We determine the temperature dependent damping rate of longitudinal acoustic
phonons in SrTiO3 using frequency domain Brillouin scattering and time domain
Brillouin scattering. We investigate samples with (La,Sr)MnO3 and SrRuO3
capping layers, which result in compressive or tensile strain at the layer -
substrate interface, respectively. The different strain states lead to dif-
ferent domain structures in SrTiO3 that extend into the bulk of the SrTiO3
substrates and strongly affect the phonon propagation. Our experiments show
that the damping rate of acoustic phonons in the interfacial STO layer depends
strongly on the sample temperature and strain induced do- main structure. We
also show that the damping rate as function of temperature exhibits a critical
behavior close to the cubic-to-tetragonal phase transition of SrTiO3.
|
1810.00381v1
|
2018-12-04
|
Atmospheric oscillations provide simultaneous measurement of neutron star mass and radius
|
Neutron stars with near-Eddington observable luminosities were shown to
harbor levitating atmospheres, suspended above their surface. We report a new
method to simultaneously measure the mass and radius of a neutron star based on
oscillations of such atmospheres. In this paper, we present an analytic
derivation of a family of relativistic, oscillatory, spherically symmetric
eigenmodes of the optically and geometrically thin levitating atmospheres,
including the damping effects induced by the radiation drag. We discover
characteristic maxima in the frequencies of the damped oscillations and show
that using the frequency maxima, one can estimate mass and radius of the
neutron star, given the observed frequency and the corresponding luminosity of
the star during the X-ray burst. Thus, our model provides a new way to probe
the stellar parameters. We also show that the ratio of any two undamped
eigenfrequencies depends only on the adiabatic index of the atmosphere, while
for the damped eigenfrequencies, this ratio varies with the luminosity. The
damping coefficient is independent of the mode number of the oscillations.
Signatures of these atmospheres' dynamics will be reflected in the source's
X-ray light curves.
|
1812.01299v2
|
2018-12-04
|
Spin transport in a magnetic insulator with zero effective damping
|
Applications based on spin currents strongly profit from the control and
reduction of their effective damping and their transport properties. We here
experimentally observe magnon mediated transport of spin (angular) momentum
through a 13.4 nm thin yttrium iron garnet film with full control of the
magnetic damping via spin-orbit torque. Above a critical spin-orbit torque, the
fully compensated damping manifests itself as an increase of magnon
conductivity by almost two orders of magnitude. We compare our results to
theoretical expectations based on recently predicted current induced magnon
condensates and discuss other possible origins of the observed critical
behaviour.
|
1812.01334v3
|
2019-01-10
|
Data-Driven Online Optimization for Enhancing Power System Oscillation Damping
|
This paper reports an initial work on power system oscillation damping
improvement using a data-driven online optimization method. An online
oscillation damping optimization mod-el is proposed and formulated in a form
solvable by the data-driven method. Key issues in the online optimization
procedures, including the damping sensitivity identification method, its
compatibility with the dispatch plans, as well as other practical issues in
real large-scale system are discussed. Simulation results based on the 2-area
4-machine system, and the NETS-NYPS 68-bus system verify the feasibility and
efficiency of the proposed method. The results also show the capability of the
proposed method to bridge the gap between online data analysis and complex
optimization for power system dynamics.
|
1901.03167v2
|
2019-01-13
|
Nonexistence of global solutions for a weakly coupled system of semilinear damped wave equations in the scattering case with mixed nonlinear terms
|
In this paper we consider the blow-up of solutions to a weakly coupled system
of semilinear damped wave equations in the scattering case with nonlinearities
of mixed type, namely, in one equation a power nonlinearity and in the other a
semilinear term of derivative type. The proof of the blow-up results is based
on an iteration argument. As expected, due to the assumptions on the
coefficients of the damping terms, we find as critical curve in the p-q plane
for the pair of exponents (p,q) in the nonlinear terms the same one found by
Hidano-Yokoyama and, recently, by Ikeda-Sobajima-Wakasa for the weakly coupled
system of semilinear wave equations with the same kind of nonlinearities. In
the critical and not-damped case we provide a different approach from the test
function method applied by Ikeda-Sobajima-Wakasa to prove the blow-up of the
solution on the critical curve, improving in some cases the upper bound
estimate for the lifespan. More precisely, we combine an iteration argument
with the so-called slicing method to show the blow-up dynamic of a weighted
version of the functionals used in the subcritical case.
|
1901.04038v1
|
2019-01-15
|
Continuum damping effects in nuclear collisions associated with twisted boundary conditions
|
The time-dependent Skyrme Hartree-Fock calculations have been performed to
study $^{24}$Mg +$^{24}$Mg collisions. The twisted boundary conditions, which
can avoid finite box-size effects of the employed 3D coordinate space, have
been implemented. The prolate deformed $^{24}$Mg has been set to different
orientations to study vibrations and rotations of the compound nucleus
$^{48}$Cr. Our time evolution results show continuum damping effects associated
with the twist-averaged boundary condition play a persistent role after the
fusion stage. In particular, a rotational damping in continuum is presented in
calculations of both twist-averaged and absorbing boundary conditions, in which
damping widths can be clearly extracted. It is unusual that the rotating
compound nucleus in continuum evolves towards spherical but still has a
considerable angular momentum.
|
1901.04736v2
|
2019-03-03
|
Spin wave damping in periodic and quasiperiodic magnonic structures
|
We investigated the lifetime of spin wave eigenmodes in periodic and
quasiperiodic sequences of Py and Co wires. Those materials differ
significantly in damping coefficients, therefore, the spatial distribution of
the mode amplitude within the structure is important for the lifetime of
collective spin wave excitations. Modes of the lower frequencies prefer to
concentrate in Py wires, because of the lower FMR frequency for this material.
This inhomogeneous distribution of amplitude of modes (with lower amplitude in
material of higher damping and with higher amplitude in material of lower
damping) is preferable for extending the lifetime of the collective excitations
beyond the volume average of lifetimes for solid materials. We established the
relation between the profile of the mode and its lifetime for periodic and
quasiperiodic structures. We performed also the comparative studies in order to
find the differences resulting from complexity of the structure and enhancement
of localization in quasiperiodic system on the lifetime of spin waves.
|
1903.00856v1
|
2019-03-07
|
Investigating optically-excited THz standing spin waves using noncollinear magnetic bilayers
|
We investigate optically excited THz standing spin waves in noncollinear
magnetic bilayers. Using femtosecond laser-pulse excitation, a spin current is
generated in the first ferromagnetic (FM) layer, and flows through a conductive
spacer layer to be injected into the second (transverse) FM layer, where it
exerts a spin-transfer torque on the magnetization and excites higher-order
standing spin waves. We show that the noncollinear magnetic bilayer is a
convenient tool that allows easy excitation of THz spin waves, and can be used
to investigate the dispersion and thereby the spin wave stiffness parameter in
the thin-film regime. This is experimentally demonstrated using wedge-shaped Co
and CoB (absorption) layers. Furthermore, the damping of these THz spin waves
is investigated, showing a strong increase of the damping with decreasing
absorption layer thickness, much stronger than expected from interface spin
pumping effects. Additionally, a previously unseen sudden decrease in the
damping for the thinnest films is observed. A model for the additional damping
contribution incorporating both these observations is proposed.
|
1903.02802v1
|
2019-03-14
|
An analog simulation experiment to study free oscillations of a damped simple pendulum
|
The characteristics of drive-free oscillations of a damped simple pendulum
under sinusoidal potential force field differ from those of the damped harmonic
oscillations. The frequency of oscillation of a large amplitude simple pendulum
decreases with increasing amplitude. Many prototype mechanical simple pendulum
have been fabricated with precision and studied earlier in view of introducing
them in undergraduate physics laboratories. However, fabrication and
maintenance of such mechanical pendulum require special skill. In this work, we
set up an analog electronic simulation experiment to serve the purpose of
studying the force-free oscillations of a damped simple pendulum. We present
the details of the setup and some typical results of our experiment. The
experiment is simple enough to implement in undergraduate physics laboratories.
|
1903.06162v1
|
2019-03-15
|
Frictional Damping in Biomimetic Scale Beam Oscillations
|
Stiff scales adorn the exterior surfaces of fishes, snakes, and many
reptiles. They provide protection from external piercing attacks and control
over global deformation behavior to aid locomotion, slithering, and swimming
across a wide range of environmental condition. In this letter, we investigate
the dynamic behavior of biomimetic scale substrates for further understanding
the origins of the nonlinearity that involve various aspect of scales
interaction, sliding kinematics, interfacial friction, and their combination.
Particularly, we study the vibrational characteristics through an analytical
model and numerical investigations for the case of a simply supported scale
covered beam. Our results reveal for the first time that biomimetic scale beams
exhibit viscous damping behavior even when only Coulomb friction is postulated
for free vibrations. We anticipate and quantify the anisotropy in the damping
behavior with respect to curvature. We also find that unlike static pure
bending where friction increases bending stiffness, a corresponding increase in
natural frequency for the dynamic case does not arise for simply supported
beam. Since both scale geometry, distribution and interfacial properties can be
easily tailored, our study indicates a biomimetic strategy to design
exceptional synthetic materials with tailorable damping behavior.
|
1903.06819v1
|
2019-04-08
|
Damping control in viscoelastic beam dynamics
|
Viscoelasticity plays a key role in many practical applications and in
different reasearch fields, such as in seals, sliding-rolling contacts and
crack propagation. In all these contexts, a proper knowledge of the
viscoelastic modulus is very important. However, the experimental
characterization of the frequency dependent modulus, carried out through
different standard procedures, still presents some complexities, then possible
alternative approaches are desirable. For example, the experimental
investigation of viscoelastic beam dynamics would be challenging, especially
for the intrinsic simplicity of this kind of test. This is why, a deep
understanding of damping mechanisms in viscoelastic beams results to be a quite
important task to better predict their dynamics. With the aim to enlighten
damping properties in such structures, an analytical study of the transversal
vibrations of a viscoelastic beam is presented in this paper. Some
dimensionless parameters are defined, depending on the material properties and
the beam geometry, which enable to shrewdly design the beam dynamics. In this
way, by properly tuning such disclosed parameters, for example the
dimensionless beam length or a chosen material, it is possible to enhance or
suppress some resonant peaks, one at a time or more simultaneously. This is a
remarkable possibility to efficiently control damping in these structures, and
the results presented in this paper may help in elucidating experimental
procedures for the characterization of viscoelastic materials.
|
1904.03875v1
|
2019-04-28
|
On the Kolmogorov dissipation law in a damped Navier-Stokes equation
|
We consider here the Navier-Stokes equations in $\mathbb{R}^{3}$ with a
stationary, divergence-free external force and with an additional damping term
that depends on two parameters. We first study the well-posedness of weak
solutions for these equations and then, for a particular set of the damping
parameters, we will obtain an upper and lower control for the energy
dissipation rate $\varepsilon$ according to the Kolmogorov K41 theory. However,
although the behavior of weak solutions corresponds to the K41 theory, we will
show that in some specific cases the damping term introduced in the
Navier-Stokes equations could annihilate the turbulence even though the Grashof
number (which are equivalent to the Reynolds number) are large.
|
1904.12382v1
|
2019-04-23
|
Entanglement sudden death and birth effects in two qubits maximally entangled mixed states under quantum channels
|
In the present article, the robustness of entanglement in two qubits
maximally entangled mixed states (MEME) have been studied under quantum
decoherence channels. Here we consider bit flip, phase flip, bit-phase-flip,
amplitude damping, phase damping and depolarization channels. To quantify the
entanglement, the concurrence has been used as an entanglement measure. During
this study interesting results have been found for sudden death and birth of
entanglement under bit flip and bit-phase-flip channels. While amplitude
damping channel produces entanglement sudden death and does not allow re-birth
of entanglement. On the other hand, two qubits MEMS exhibit the robust
character against the phase flip, phase damping and depolarization channels.
The elegant behavior of all the quantum channels have been investigated with
varying parameter of quantum state MEMS in different cases.
|
1904.12630v2
|
2019-05-23
|
Strauss exponent for semilinear wave equations with scattering space dependent damping
|
It is believed or conjectured that the semilinear wave equations with
scattering space dependent damping admit the Strauss critical exponent, see
Ikehata-Todorova-Yordanov \cite{ITY}(the bottom in page 2) and
Nishihara-Sobajima-Wakasugi \cite{N2}(conjecture iii in page 4). In this work,
we are devoted to showing the conjecture is true at least when the decay rate
of the space dependent variable coefficients before the damping is larger than
2. Also, if the nonlinear term depends only on the derivative of the solution,
we may prove the upper bound of the lifespan is the same as that of the
solution of the corresponding problem without damping. This shows in another
way the \lq\lq hyperbolicity" of the equation.
|
1905.09445v2
|
2019-05-24
|
Multicomponent Dark Matter in the Light of CALET and DAMPE
|
In the light of the latest measurements on the total $e^+ + e^-$ flux by
CALET and DAMPE experiments, we revisit the multicomponent leptonically
decaying dark matter (DM) explanations to the cosmic-ray electron/positron
excesses observed previously. Especially, we use the single and
double-component DM models to explore the compatibility of the AMS-02 positron
fraction with the new CALET or DAMPE data. It turns out that neither single nor
double-component DM models are able to fit the AMS-02 positron fraction and
DAMPE total $e^+ + e^-$ flux data simultaneously. On the other hand, for the
combined AMS-02 and CALET dataset, both the single and double-component DM
models can provide reasonable fits. If we further take into the diffuse
$\gamma$-ray constraints from Fermi-LAT, only the double-component DM models
are allowed.
|
1905.10136v3
|
2019-05-30
|
Quantum dynamical speedup in correlated noisy channels
|
The maximal evolution speed of a quantum system can be represented by quantum
speed limit time (QSLT).We investigate QSLT of a two-qubit system passing
through a correlated channel (amplitude damping, phase damping, and
depolarizing).By adjusting the correlation parameter of channel and the initial
entanglement,a method to accelerate the evolution speed of the system for some
specific channels is proposed.It is shown that, in amplitude damping channel
and depolarizing channel,QSLT may be shortened in some cases by increasing
correlation parameter of the channel and initial entanglement, which are in
sharp contrast to phase damping channel.In particular, under depolarizing
channels, the transition from no-speedup evolution to speedup evolution for the
system can be realized by changing correlation strength of the channel.
|
1905.12911v3
|
2019-07-01
|
Probing superfluid $^4\mathrm{He}$ with high-frequency nanomechanical resonators down to $\mathrm{mK}$ temperatures
|
Superfluids, such as superfluid $^3\mathrm{He}$ and $^4\mathrm{He}$, exhibit
a broad range of quantum phenomena and excitations which are unique to these
systems. Nanoscale mechanical resonators are sensitive and versatile force
detectors with the ability to operate over many orders of magnitude in damping.
Using nanomechanical-doubly clamped beams of extremely high quality factors
($Q>10^6$), we probe superfluid $^4\mathrm{He}$ from the superfluid transition
temperature down to $\mathrm{mK}$ temperatures at frequencies up to $11.6 \,
\mathrm{MHz}$. Our studies show that nanobeam damping is dominated by
hydrodynamic viscosity of the normal component of $^4\mathrm{He}$ above
$1\,\mathrm{K}$. In the temperature range $0.3-0.8\,\mathrm{K}$, the ballistic
quasiparticles (phonons and rotons) determine the beams' behavior. At lower
temperatures, damping saturates and is determined either by magnetomotive
losses or acoustic emission into helium. It is remarkable that all these
distinct regimes can be extracted with just a single device, despite damping
changing over six orders of magnitude.
|
1907.00970v1
|
2019-07-15
|
Asymptotic profiles of solutions for regularity-loss type generalized thermoelastic plate equations and their applications
|
In this paper, we consider generalized thermoelastic plate equations with
Fourier's law of heat conduction. By introducing a threshold for decay
properties of regularity-loss, we investigate decay estimates of solutions
with/without regularity-loss in a framework of weighted $L^1$ spaces.
Furthermore, asymptotic profiles of solutions are obtained by using
representations of solutions in the Fourier space, which are derived by
employing WKB analysis. Next, we study generalized thermoelastic plate
equations with additional structural damping, and analysis the influence of
structural damping on decay properties and asymptotic profiles of solutions. We
find that the regularity-loss structure is destroyed by structural damping.
Finally, we give some applications of our results on thermoelastic plate
equations and damped Moore-Gibson-Thompson equation.
|
1907.06344v1
|
2019-07-23
|
Ignatyuk damping factor: A semiclassical formula
|
Data on nuclear level densities extracted from transmission data or gamma
energy spectrum store the basic statistical information about nuclei at various
temperatures. Generally this extracted data goes through model fitting using
computer codes like CASCADE. However, recently established semiclassical
methods involving no adjustable parameters to determine the level density
parameter for magic and semi-magic nuclei give a good agreement with the
experimental values. One of the popular ways to paramaterize the level density
parameter which includes the shell effects and its damping was given by
Ignatyuk. This damping factor is usually fitted from the experimental data on
nuclear level density and it comes around 0.05 $MeV^{-1}$. In this work we
calculate the Ignatyuk damping factor for various nuclei using semiclassical
methods.
|
1907.09770v1
|
2019-08-13
|
Dynamics of Riemann waves with sharp measure-controlled damping
|
This paper is concerned with locally damped semilinear wave equations defined
on compact Riemannian manifolds with boundary. We present a construction of
measure-controlled damping regions which are sharp in the sense that their
summed interior and boundary measures are arbitrarily small. The construction
of this class of open sets is purely geometric and allows us to prove a new
observability inequality in terms of potential energy rather than the usual one
with kinetic energy. A unique continuation property is also proved. Then, in
three-dimension spaces, we establish the existence of finite dimensional smooth
global attractors for a class of wave equations with nonlinear damping and
forces with critical Sobolev growth. In addition, by means of an obstacle
control condition, we show that our class of measure-controlled regions
satisfies the well-known geometric control condition (GCC). Therefore, many of
known results for the stabilization of wave equations hold true in the present
context.
|
1908.04814v1
|
2019-08-15
|
Sharp polynomial decay rates for the damped wave equation with Hölder-like damping
|
We study decay rates for the energy of solutions of the damped wave equation
on the torus. We consider dampings invariant in one direction and bounded above
and below by multiples of $x^{\beta}$ near the boundary of the support and show
decay at rate $1/t^{\frac{\beta+2}{\beta+3}}$. In the case where $W$ vanishes
exactly like $x^{\beta}$ this result is optimal by work of the second author.
The proof uses a version of the Morawetz multiplier method.
|
1908.05631v3
|
2019-08-26
|
Revisiting the Coulomb-Damped Harmonic Oscillator
|
The force of dry friction is studied extensively in introductory physics but
its effect on oscillations is hardly ever mentioned. Instead, to provide a
mathematically tractable introduction to damping, virtually all authors adopt a
viscous resistive force. While exposure to linear damping is of paramount
importance to the student of physics, the omission of Coulomb damping might
have a negative impact on the way the students conceive of the subject. In the
paper, we propose to approximate the action of Coulomb friction on a harmonic
oscillator by a sinusoidal resistive force whose amplitude is the model's only
free parameter. We seek the value of this parameter that yields the best fit
and obtain a closed-form analytic solution, which is shown to nicely fit the
numerical one.
|
1908.10363v1
|
2019-09-21
|
Resonant absorption of kink oscillations in coronal flux tubes with continuous magnetic twist
|
There are observational evidences for the existence of twisted magnetic field
in the solar corona. Here, we have investigated resonant damping of the
magnetohydrodynamic (MHD) kink waves in magnetic flux tubes. A realistic model
of the tube with continuous magnetic twist and radially inhomogeneous density
profile has been considered. We have obtained the dispersion relation of the
kink wave using the solution to the linear MHD equations outside the density
inhomogeneity and the appropriate connection formula to the solutions across
the thin transitional boundary layer. The dependence of the oscillation
frequency and damping rate of the waves on the twist parameter and longitudinal
wavenumber has been investigated. For the flux tube parameters considered in
this paper, we obtain rapid damping of the kink waves comparable to the
observations. In order to justify this rapid damping, depending on the sign of
the azimuthal kink mode number, $m=+1$ or $m=-1$, the background magnetic field
must have left handed or right handed twisted profile, respectively. For the
model considered here, the resonant absorption occurs only when the twist
parameter is in a range specified by the density contrast.
|
1909.09787v1
|
2019-10-22
|
Controlled nonlinear magnetic damping in spin-Hall nano-devices
|
Large-amplitude magnetization dynamics is substantially more complex compared
to the low-amplitude linear regime, due to the inevitable emergence of
nonlinearities. One of the fundamental nonlinear phenomena is the nonlinear
damping enhancement, which imposes strict limitations on the operation and
efficiency of magnetic nanodevices. In particular, nonlinear damping prevents
excitation of coherent magnetization auto-oscillations driven by the injection
of spin current into spatially extended magnetic regions. Here, we propose and
experimentally demonstrate that nonlinear damping can be controlled by the
ellipticity of magnetization precession. By balancing different contributions
to anisotropy, we minimize the ellipticity and achieve coherent magnetization
oscillations driven by spatially extended spin current injection into a
microscopic magnetic disk. Our results provide a novel route for the
implementation of efficient active spintronic and magnonic devices driven by
spin current.
|
1910.09801v1
|
2019-11-05
|
Exceptional points in dissipatively coupled spin dynamics
|
We theoretically investigate dynamics of classical spins exchange-coupled
through an isotropic medium. The coupling is treated at the adiabatic level of
the medium's response, which mediates a first-order in frequency dissipative
interaction along with an instantaneous Heisenberg exchange. The resultant
damped spin precession yields exceptional points (EPs) in the coupled spin
dynamics, which should be experimentally accessible with the existing magnetic
heterostructures. In particular, we show that an EP is naturally approached in
an antiferromagnetic dimer by controlling local damping, while the same is
achieved by tuning the dissipative coupling between spins in the ferromagnetic
case. Extending our treatment to one-dimensional spin chains, we show how EPs
can emerge within the magnonic Brillouin zone by tuning the dissipative
properties. The critical point, at which an EP pair emerges out of the
Brillouin zone center, realizes a gapless Weyl point in the magnon spectrum.
Tuning damping beyond this critical point produces synchronization (level
attraction) of magnon modes over a finite range of momenta, both in ferro- and
antiferromagnetic cases. We thus establish that damped magnons can generically
yield singular points in their band structure, close to which their kinematic
properties, such as group velocity, become extremely sensitive to the control
parameters.
|
1911.01619v2
|
2019-11-08
|
Influence of Sensor Feedback Limitations on Power Oscillation Damping and Transient Stability
|
Fundamental sensor feedback limitations for improving rotor angle stability
using local frequency or phase angle measurement are derived. Using a
two-machine power system model, it is shown that improved damping of inter-area
oscillations must come at the cost of reduced transient stability margins,
regardless of the control design method. The control limitations stem from that
the excitation of an inter-area mode by external disturbances cannot be
estimated with certainty using local frequency information. The results are
validated on a modified Kundur four-machine two-area test system where the
active power is modulated on an embedded high-voltage dc link. Damping control
using local phase angle measurements, unavoidably leads to an increased rotor
angle deviation following certain load disturbances. For a highly stressed
system, it is shown that this may lead to transient instability. The
limitations derived in the paper may motivate the need for wide-area
measurements in power oscillation damping control.
|
1911.03342v3
|
2019-11-12
|
Non-uniform Stability of Damped Contraction Semigroups
|
We investigate the stability properties of strongly continuous semigroups
generated by operators of the form $A-BB^\ast$, where $A$ is a generator of a
contraction semigroup and $B$ is a possibly unbounded operator. Such systems
arise naturally in the study of hyperbolic partial differential equations with
damping on the boundary or inside the spatial domain. As our main results we
present general sufficient conditions for non-uniform stability of the
semigroup generated by $A-BB^\ast$ in terms of selected observability-type
conditions of the pair $(B^\ast,A)$. We apply the abstract results to obtain
rates of energy decay in one-dimensional and two-dimensional wave equations, a
damped fractional Klein--Gordon equation and a weakly damped beam equation.
|
1911.04804v3
|
2020-01-31
|
Dynamo in weakly collisional nonmagnetized plasmas impeded by Landau damping of magnetic fields
|
We perform fully kinetic simulations of flows known to produce dynamo in
magnetohydrodynamics (MHD), considering scenarios with low Reynolds number and
high magnetic Prandtl number, relevant for galaxy cluster scale fluctuation
dynamos. We find that Landau damping on the electrons leads to a rapid decay of
magnetic perturbations, impeding the dynamo. This collisionless damping process
operates on spatial scales where electrons are nonmagnetized, reducing the
range of scales where the magnetic field grows in high magnetic Prandtl number
fluctuation dynamos. When electrons are not magnetized down to the resistive
scale, the magnetic energy spectrum is expected to be limited by the scale
corresponding to magnetic Landau damping or, if smaller, the electron
gyroradius scale, instead of the resistive scale. In simulations we thus
observe decaying magnetic fields where resistive MHD would predict a dynamo.
|
2001.11929v2
|
2020-03-05
|
Sound propagation and quantum limited damping in a two-dimensional Fermi gas
|
Strongly interacting two-dimensional Fermi systems are one of the great
remaining challenges in many-body physics due to the interplay of strong local
correlations and enhanced long-range fluctuations. Here, we probe the
thermodynamic and transport properties of a 2D Fermi gas across the BEC-BCS
crossover by studying the propagation and damping of sound modes. We excite
particle currents by imprinting a phase step onto homogeneous Fermi gases
trapped in a box potential and extract the speed of sound from the frequency of
the resulting density oscillations. We measure the speed of sound across the
BEC-BCS crossover and compare the resulting dynamic measurement of the equation
of state both to a static measurement based on recording density profiles and
to Quantum Monte Carlo calculations and find reasonable agreement between all
three. We also measure the damping of the sound mode, which is determined by
the shear and bulk viscosities as well as the thermal conductivity of the gas.
We find that the damping is minimal in the strongly interacting regime and the
diffusivity approaches the universal quantum bound $\hbar/m$ of a perfect
fluid.
|
2003.02713v1
|
2020-03-09
|
Proof-of-principle direct measurement of Landau damping strength at the Large Hadron Collider with an anti-damper
|
Landau damping is an essential mechanism for ensuring collective beam
stability in particle accelerators. Precise knowledge of how strong Landau
damping is, is key to making accurate predictions on beam stability for
state-of-the-art high energy colliders. In this paper we demonstrate an
experimental procedure that would allow quantifying the strength of Landau
damping and the limits of beam stability using an active transverse feedback as
a controllable source of beam coupling impedance. In a proof-of-principle test
performed at the Large Hadron Collider stability diagrams for a range of Landau
Octupole strengths have been measured. In the future, the procedure could
become an accurate way of measuring stability diagrams throughout the machine
cycle.
|
2003.04383v1
|
2020-03-19
|
An inverse-system method for identification of damping rate functions in non-Markovian quantum systems
|
Identification of complicated quantum environments lies in the core of
quantum engineering, which systematically constructs an environment model with
the aim of accurate control of quantum systems. In this paper, we present an
inverse-system method to identify damping rate functions which describe
non-Markovian environments in time-convolution-less master equations. To access
information on the environment, we couple a finite-level quantum system to the
environment and measure time traces of local observables of the system. By
using sufficient measurement results, an algorithm is designed, which can
simultaneously estimate multiple damping rate functions for different
dissipative channels. Further, we show that identifiability for the damping
rate functions corresponds to the invertibility of the system and a necessary
condition for identifiability is also given. The effectiveness of our method is
shown in examples of an atom and three-spin-chain non-Markovian systems.
|
2003.08617v1
|
2020-04-23
|
Damping of gravitational waves in 2-2-holes
|
A 2-2-hole is an explicit realization of a horizonless object that can still
very closely resemble a BH. An ordinary relativistic gas can serve as the
matter source for the 2-2-hole solution of quadratic gravity, and this leads to
a calculable area-law entropy. Here we show that it also leads to an estimate
of the damping of a gravitational wave as it travels to the center of the
2-2-hole and back out again. We identify two frequency dependent effects that
greatly diminish the damping. Spinning 2-2-hole solutions are not known, but we
are still able to consider some spin dependent effects. The frequency and spin
dependence of the damping helps to determine the possible echo resonance signal
from the rotating remnants of merger events. It also controls the fate of the
ergoregion instability.
|
2004.11285v3
|
2020-05-04
|
Plasmon damping in electronically open systems
|
Rapid progress in electrically-controlled plasmonics in solids poses a
question about effects of electronic reservoirs on the properties of plasmons.
We find that plasmons in electronically open systems [i.e. in (semi)conductors
connected to leads] are prone to an additional damping due to charge carrier
penetration into contacts and subsequent thermalization. We develop a theory of
such lead-induced damping based on kinetic equation with self-consistent
electric field, supplemented by microscopic carrier transport at the
interfaces. The lifetime of plasmon in electronically open ballistic system
appears to be finite, order of conductor length divided by carrier Fermi
(thermal) velocity. The reflection loss of plasmon incident on the contact of
semi-conductor and perfectly conducting metal also appears to be finite, order
of Fermi velocity divided by wave phase velocity. Recent experiments on
plasmon-assisted photodetection are discussed in light of the proposed
lead-induced damping phenomenon.
|
2005.01680v1
|
2020-05-06
|
Helical damping and anomalous critical non-Hermitian skin effect
|
Non-Hermitian skin effect and critical skin effect are unique features of
non-Hermitian systems. In this Letter, we study an open system with its
dynamics of single-particle correlation function effectively dominated by a
non-Hermitian damping matrix, which exhibits $\mathbb{Z}_2$ skin effect, and
uncover the existence of a novel phenomenon of helical damping. When adding
perturbations that break anomalous time reversal symmetry to the system, the
critical skin effect occurs, which causes the disappearance of the helical
damping in the thermodynamic limit although it can exist in small size systems.
We also demonstrate the existence of anomalous critical skin effect when we
couple two identical systems with $\mathbb{Z}_2$ skin effect. With the help of
non-Bloch band theory, we unveil that the change of generalized Brillouin zone
equation is the necessary condition of critical skin effect.
|
2005.02617v1
|
2020-05-16
|
Gravitational Landau Damping for massive scalar modes
|
We establish the possibility of Landau damping for gravitational scalar waves
which propagate in a non-collisional gas of particles. In particular, under the
hypothesis of homogeneity and isotropy, we describe the medium at the
equilibrium with a J\"uttner-Maxwell distribution, and we analytically
determine the damping rate from the Vlasov equation. We find that damping
occurs only if the phase velocity of the wave is subluminal throughout the
propagation within the medium. Finally, we investigate relativistic media in
cosmological settings by adopting numerical techniques.
|
2005.08010v4
|
2020-05-21
|
On Strong Feller Property, Exponential Ergodicity and Large Deviations Principle for Stochastic Damping Hamiltonian Systems with State-Dependent Switching
|
This work focuses on a class of stochastic damping Hamiltonian systems with
state-dependent switching, where the switching process has a countably infinite
state space. After establishing the existence and uniqueness of a global weak
solution via the martingale approach under very mild conditions, the paper next
proves the strong Feller property for regime-switching stochastic damping
Hamiltonian systems by the killing technique together with some resolvent and
transition probability identities. The commonly used continuity assumption for
the switching rates $q_{kl}(\cdot)$ in the literature is relaxed to
measurability in this paper. Finally the paper provides sufficient conditions
for exponential ergodicity and large deviations principle for regime-switching
stochastic damping Hamiltonian systems. Several examples on regime-switching
van der Pol and (overdamped) Langevin systems are studied in detail for
illustration.
|
2005.10730v1
|
2020-06-09
|
Logarithmic decay for damped hypoelliptic wave and Schr{ö}dinger equations
|
We consider damped wave (resp. Schr{\"o}dinger and plate) equations driven by
a hypoelliptic "sum of squares" operator L on a compact manifold and a damping
function b(x). We assume the Chow-Rashevski-H{\"o}rmander condition at rank k
(at most k Lie brackets needed to span the tangent space) together with
analyticity of M and the coefficients of L. We prove decay of the energy at
rate $log(t)^{-1/k}$ (resp. $log(t)^{-2/k}$ ) for data in the domain of the
generator of the associated group. We show that this decay is optimal on a
family of Grushin-type operators. This result follows from a perturbative
argument (of independent interest) showing, in a general abstract setting, that
quantitative approximate observability/controllability results for wave-type
equations imply a priori decay rates for associated damped wave,
Schr{\"o}dinger and plate equations. The adapted quantitative approximate
observability/controllability theorem for hypoelliptic waves is obtained by the
authors in [LL19, LL17].
|
2006.05122v1
|
2020-06-14
|
Bulk Viscous Damping of Density Oscillations in Neutron Star Mergers
|
In this paper, we discuss the damping of density oscillations in dense
nuclear matter in the temperature range relevant to neutron star mergers. This
damping is due to bulk viscosity arising from the weak interaction ``Urca''
processes of neutron decay and electron capture. The nuclear matter is modelled
in the relativistic density functional approach. The bulk viscosity reaches a
resonant maximum close to the neutrino trapping temperature, then drops rapidly
as temperature rises into the range where neutrinos are trapped in neutron
stars. We investigate the bulk viscous dissipation timescales in a post-merger
object and identify regimes where these timescales are as short as the
characteristic timescale $\sim$10 ms, and, therefore, might affect the
evolution of the post-merger object. Our analysis indicates that bulk viscous
damping would be important at not too high temperatures of the order of a few
MeV and densities up to a few times saturation density.
|
2006.07975v2
|
2020-06-15
|
Exact solutions of a damped harmonic oscillator in a time dependent noncommutative space
|
In this paper we have obtained the exact eigenstates of a two dimensional
damped harmonic oscillator in time dependent noncommutative space. It has been
observed that for some specific choices of the damping factor and the time
dependent frequency of the oscillator, there exists interesting solutions of
the time dependent noncommutative parameters following from the solutions of
the Ermakov-Pinney equation. Further, these solutions enable us to get exact
analytic forms for the phase which relates the eigenstates of the Hamiltonian
with the eigenstates of the Lewis invariant. We then obtain expressions for the
matrix elements of the coordinate operators raised to a finite arbitrary power.
From these general results we then compute the expectation value of the
Hamiltonian. The expectation values of the energy are found to vary with time
for different solutions of the Ermakov-Pinney equation corresponding to
different choices of the damping factor and the time dependent frequency of the
oscillator.
|
2006.08611v1
|
2020-06-16
|
Enhancing nonlinear damping by parametric-direct internal resonance
|
Mechanical sources of nonlinear damping play a central role in modern
physics, from solid-state physics to thermodynamics. The microscopic theory of
mechanical dissipation [M. I . Dykman, M. A. Krivoglaz, Physica Status Solidi
(b) 68, 111 (1975)] suggests that nonlinear damping of a resonant mode can be
strongly enhanced when it is coupled to a vibration mode that is close to twice
its resonance frequency. To date, no experimental evidence of this enhancement
has been realized. In this letter, we experimentally show that nanoresonators
driven into parametric-direct internal resonance provide supporting evidence
for the microscopic theory of nonlinear dissipation. By regulating the drive
level, we tune the parametric resonance of a graphene nanodrum over a range of
40-70 MHz to reach successive two-to-one internal resonances, leading to a
nearly two-fold increase of the nonlinear damping. Our study opens up an
exciting route towards utilizing modal interactions and parametric resonance to
realize resonators with engineered nonlinear dissipation over wide frequency
range.
|
2006.09364v3
|
2020-06-22
|
Blow-up for wave equation with the scale-invariant damping and combined nonlinearities
|
In this article, we study the blow-up of the damped wave equation in the
\textit{scale-invariant case} and in the presence of two nonlinearities. More
precisely, we consider the following equation: $$u_{tt}-\Delta
u+\frac{\mu}{1+t}u_t=|u_t|^p+|u|^q, \quad \mbox{in}\ \R^N\times[0,\infty), $$
with small initial data.\\ For $\mu < \frac{N(q-1)}{2}$ and $\mu \in (0,
\mu_*)$, where $\mu_*>0$ is depending on the nonlinearties' powers and the
space dimension ($\mu_*$ satisfies $(q-1)\left((N+2\mu_*-1)p-2\right) = 4$), we
prove that the wave equation, in this case, behaves like the one without
dissipation ($\mu =0$). Our result completes the previous studies in the case
where the dissipation is given by $\frac{\mu}{(1+t)^\beta}u_t; \ \beta >1$
(\cite{LT3}), where, contrary to what we obtain in the present work, the effect
of the damping is not significant in the dynamics. Interestingly, in our case,
the influence of the damping term $\frac{\mu}{1+t}u_t$ is important.
|
2006.12600v1
|
2020-06-30
|
Negative Gilbert damping in cavity optomagnonics
|
Exceptional point (EP) associated with the parity-time (PT) symmetry breaking
is receiving considerable recent attention by the broad physics community. By
introducing balanced gain and loss, it has been realized in photonic, acoustic,
and electronic structures. However, the observation of magnonic EP remains
elusive. The major challenge is to experimentally generate the negative Gilbert
damping, which was thought to be highly unlikely but is demanded by the PT
symmetry. In this work, we study the magneto-optical interaction of
circularly-polarized lasers with a submicron magnet placed in an optical
cavity. We show that the off-resonant coupling between the driving laser and
cavity photon in the far-blue detuning can induce the magnetic gain (or
negative damping) exactly of the Gilbert type. A hyperbolic-tangent function
ansatz is found to well describe the time-resolved spin switching as the
intrinsic magnetization dissipation is overcome. When the optically pumped
magnet interacts with a purely lossy one, we observe a phase transition from
the imbalanced to passive PT symmetries by varying the detuning coeffcient. Our
findings provide a feasible way to manipulate the sign of the magnetic damping
parameter and to realize the EP in cavity optomagnonics.
|
2006.16510v1
|
2020-07-10
|
Decentralized Frequency Control using Packet-based Energy Coordination
|
This paper presents a novel frequency-responsive control scheme for
demand-side resources, such as electric water heaters. A frequency-dependent
control law is designed to provide damping from distributed energy resources
(DERs) in a fully decentralized fashion. This local control policy represents a
frequency-dependent threshold for each DER that ensures that the aggregate
response provides damping during frequency deviations. The proposed
decentralized policy is based on an adaptation of a packet-based DER
coordination scheme where each device send requests for energy access (also
called an "energy packet") to an aggregator. The number of previously accepted
active packets can then be used a-priori to form an online estimate of the
aggregate damping capability of the DER fleet in a dynamic power system. A
simple two-area power system is used to illustrate and validate performance of
the decentralized control policy and the accuracy of the online damping
estimating for a fleet of 400,000 DERs.
|
2007.05624v1
|
2020-07-30
|
Origin of micron-scale propagation lengths of heat-carrying acoustic excitations in amorphous silicon
|
The heat-carrying acoustic excitations of amorphous silicon are of interest
because their mean free paths may approach micron scales at room temperature.
Despite extensive investigation, the origin of the weak acoustic damping in the
heat-carrying frequencies remains a topic of debate. Here, we report
measurements of the thermal conductivity mean free path accumulation function
in amorphous silicon thin films from 60 - 315 K using transient grating
spectroscopy. With additional picosecond acoustics measurements and considering
the known frequency-dependencies of damping mechanisms in glasses, we
reconstruct the mean free paths from $\sim 0.1-3$ THz. The mean free paths are
independent of temperature and exhibit a Rayleigh scattering trend over most of
this frequency range. The observed trend is inconsistent with the predictions
of numerical studies based on normal mode analysis but agrees with diverse
measurements on other glasses. The micron-scale MFPs in amorphous Si arise from
the absence of anharmonic or two-level system damping in the sub-THz
frequencies, leading to heat-carrying acoustic excitations with
room-temperature damping comparable to that of other glasses at cryogenic
temperatures.
|
2007.15777v2
|
2020-08-07
|
Quantifying the evidence for resonant damping of coronal waves with foot-point wave power asymmetry
|
We use Coronal Multi-channel Polarimeter (CoMP) observations of propagating
waves in the solar corona and Bayesian analysis to assess the evidence of
models with resonant damping and foot-point wave power asymmetries. Two nested
models are considered. The reduced model considers resonant damping as the sole
cause of the measured discrepancy between outward and inward wave power. The
larger model contemplates an extra source of asymmetry with origin at the
foot-points. We first compute probability distributions of parameters
conditional on the models and the observed data. The obtained constraints are
then used to calculate the evidence for each model in view of data. We find
that we need to consider the larger model to explain CoMP data and to
accurately infer the damping ratio, hence, to better assess the possible
contribution of the waves to coronal heating.
|
2008.03004v1
|
2020-08-22
|
Sound damping in frictionless granular materials: The interplay between configurational disorder and inelasticity
|
We numerically investigate sound damping in a model of granular materials in
two dimensions. We simulate evolution of standing waves in disordered
frictionless disks and analyze their damped oscillations by velocity
autocorrelation functions and power spectra. We control the strength of
inelastic interactions between the disks in contact to examine the effect of
energy dissipation on sound characteristics of disordered systems. Increasing
the strength of inelastic interactions, we find that (i) sound softening
vanishes and (ii) sound attenuation due to configurational disorder, i.e. the
Rayleigh scattering at low frequencies and disorder-induced broadening at high
frequencies, is completely dominated by the energy dissipation. Our findings
suggest that sound damping in granular media is determined by the interplay
between elastic heterogeneities and inelastic interactions.
|
2008.09760v1
|
2020-09-27
|
Squeezed comb states
|
Continuous-variable codes are an expedient solution for quantum information
processing and quantum communication involving optical networks. Here we
characterize the squeezed comb, a finite superposition of equidistant squeezed
coherent states on a line, and its properties as a continuous-variable encoding
choice for a logical qubit. The squeezed comb is a realistic approximation to
the ideal code proposed by Gottesman, Kitaev, and Preskill [Phys. Rev. A 64,
012310 (2001)], which is fully protected against errors caused by the
paradigmatic types of quantum noise in continuous-variable systems: damping and
diffusion. This is no longer the case for the code space of finite squeezed
combs, and noise robustness depends crucially on the encoding parameters. We
analyze finite squeezed comb states in phase space, highlighting their
complicated interference features and characterizing their dynamics when
exposed to amplitude damping and Gaussian diffusion noise processes. We find
that squeezed comb state are more suitable and less error-prone when exposed to
damping, which speaks against standard error correction strategies that employ
linear amplification to convert damping into easier-to-describe isotropic
diffusion noise.
|
2009.12888v2
|
2020-11-16
|
Switchable Damping for a One-Particle Oscillator
|
The possibility to switch the damping rate for a one-electron oscillator is
demonstrated, for an electron that oscillates along the magnetic field axis in
a Penning trap. Strong axial damping can be switched on to allow this
oscillation to be used for quantum nondemolition detection of the cyclotron and
spin quantum state of the electron. Weak axial damping can be switched on to
circumvent the backaction of the detection motion that has limited past
measurements. The newly developed switch will reduce the linewidth of the
cyclotron transition of one-electron by two orders of magnitude.
|
2011.08136v2
|
2020-11-17
|
Challenging an experimental nonlinear modal analysis method with a new strongly friction-damped structure
|
In this work, we show that a recently proposed method for experimental
nonlinear modal analysis based on the extended periodic motion concept is well
suited to extract modal properties for strongly nonlinear systems (i.e. in the
presence of large frequency shifts, high and nonlinear damping, changes of the
mode shape, and higher harmonics). To this end, we design a new test rig that
exhibits a large extent of friction-induced damping (modal damping ratio up to
15 %) and frequency shift by 36 %. The specimen, called RubBeR, is a
cantilevered beam under the influence of dry friction, ranging from full stick
to mainly sliding. With the specimen's design, the measurements are well
repeatable for a system subjected to dry frictional force. Then, we apply the
method to the specimen and show that single-point excitation is sufficient to
track the modal properties even though the deflection shape changes with
amplitude. Computed frequency responses using a single nonlinear-modal
oscillator with the identified modal properties agree well with measured
reference curves of different excitation levels, indicating the modal
properties' significance and accuracy.
|
2011.08527v1
|
2020-11-27
|
Thermal damping of Weak Magnetosonic Turbulence in the Interstellar Medium
|
We present a generic mechanism for the thermal damping of compressive waves
in the interstellar medium (ISM), occurring due to radiative cooling. We solve
for the dispersion relation of magnetosonic waves in a two-fluid (ion-neutral)
system in which density- and temperature-dependent heating and cooling
mechanisms are present. We use this dispersion relation, in addition to an
analytic approximation for the nonlinear turbulent cascade, to model
dissipation of weak magnetosonic turbulence. We show that in some ISM
conditions, the cutoff wavelength for magnetosonic turbulence becomes tens to
hundreds of times larger when the thermal damping is added to the regular
ion-neutral damping. We also run numerical simulations which confirm that this
effect has a dramatic impact on cascade of compressive wave modes.
|
2011.13879v3
|
2021-02-10
|
WAMS-Based Model-Free Wide-Area Damping Control by Voltage Source Converters
|
In this paper, a novel model-free wide-area damping control (WADC) method is
proposed, which can achieve full decoupling of modes and damp multiple critical
inter-area oscillations simultaneously using grid-connected voltage source
converters (VSCs). The proposed method is purely measurement based and requires
no knowledge of the network topology and the dynamic model parameters. Hence,
the designed controller using VSCs can update the control signals online as the
system operating condition varies. Numerical studies in the modified IEEE
68-bus system with grid-connected VSCs show that the proposed method can
estimate the system dynamic model accurately and can damp inter-area
oscillations effectively under different working conditions and network
topologies.
|
2102.05494v1
|
2021-03-11
|
Magnetoelastic Gilbert damping in magnetostrictive Fe$_{0.7}$Ga$_{0.3}$ thin films
|
We report an enhanced magnetoelastic contribution to the Gilbert damping in
highly magnetostrictive Fe$_{0.7}$Ga$_{0.3}$ thin films. This effect is
mitigated for perpendicular-to-plane fields, leading to a large anisotropy of
the Gilbert damping in all of the films (up to a factor of 10 at room
temperature). These claims are supported by broadband measurements of the
ferromagnetic resonance linewidths over a range of temperatures (5 to 400 K),
which serve to elucidate the effect of both the magnetostriction and phonon
relaxation on the magnetoelastic Gilbert damping.
|
2103.07008v1
|
2021-04-08
|
Fast optimization of viscosities for frequency-weighted damping of second-order systems
|
We consider frequency-weighted damping optimization for vibrating systems
described by a second-order differential equation. The goal is to determine
viscosity values such that eigenvalues are kept away from certain undesirable
areas on the imaginary axis. To this end, we present two complementary
techniques. First, we propose new frameworks using nonsmooth constrained
optimization problems, whose solutions both damp undesirable frequency bands
and maintain stability of the system. These frameworks also allow us to weight
which frequency bands are the most important to damp. Second, we also propose a
fast new eigensolver for the structured quadratic eigenvalue problems that
appear in such vibrating systems. In order to be efficient, our new eigensolver
exploits special properties of diagonal-plus-rank-one complex symmetric
matrices, which we leverage by showing how each quadratic eigenvalue problem
can be transformed into a short sequence of such linear eigenvalue problems.
The result is an eigensolver that is substantially faster than standard
techniques. By combining this new solver with our new optimization frameworks,
we obtain our overall algorithm for fast computation of optimal viscosities.
The efficiency and performance of our new methods are verified and illustrated
on several numerical examples.
|
2104.04035v1
|
2021-04-09
|
Nonexistence result for the generalized Tricomi equation with the scale-invariant damping, mass term and time derivative nonlinearity
|
In this article, we consider the damped wave equation in the
\textit{scale-invariant case} with time-dependent speed of propagation, mass
term and time derivative nonlinearity. More precisely, we study the blow-up of
the solutions to the following equation: $$ (E) \quad u_{tt}-t^{2m}\Delta
u+\frac{\mu}{t}u_t+\frac{\nu^2}{t^2}u=|u_t|^p, \quad \mbox{in}\
\mathbb{R}^N\times[1,\infty), $$ that we associate with small initial data.
Assuming some assumptions on the mass and damping coefficients, $\nu$ and
$\mu>0$, respectively, that the blow-up region and the lifespan bound of the
solution of $(E)$ remain the same as the ones obtained for the case without
mass, {\it i.e.} $\nu=0$ in $(E)$. The latter case constitutes, in fact, a
shift of the dimension $N$ by $\frac{\mu}{1+m}$ compared to the problem without
damping and mass. Finally, we think that the new bound for $p$ is a serious
candidate to the critical exponent which characterizes the threshold between
the blow-up and the global existence regions.
|
2104.04393v2
|
2021-04-12
|
Slow periodic oscillation without radiation damping: New evolution laws for rate and state friction
|
The dynamics of sliding friction is mainly governed by the frictional force.
Previous studies have shown that the laboratory-scale friction is well
described by an empirical law stated in terms of the slip velocity and the
state variable. The state variable represents the detailed physicochemical
state of the sliding interface. Despite some theoretical attempts to derive
this friction law, there has been no unique equation for time evolution of the
state variable. Major equations known to date have their own merits and
drawbacks. To shed light on this problem from a new aspect, here we investigate
the feasibility of periodic motion without the help of radiation damping.
Assuming a patch on which the slip velocity is perturbed from the rest of the
sliding interface, we prove analytically that three major evolution laws fail
to reproduce stable periodic motion without radiation damping. Furthermore, we
propose two new evolution equations that can produce stable periodic motion
without radiation damping. These two equations are scrutinized from the
viewpoint of experimental validity and the relevance to slow earthquakes.
|
2104.05398v2
|
2021-04-27
|
Absence of a boson peak in anharmonic phonon models with Akhiezer-type damping
|
In a recent article M. Baggioli and A. Zaccone (Phys. Rev. Lett. {\bf 112},
145501 (2019)) claimed that an anharmonic damping, leading to a sound
attenuation proportional to $\omega^2$ (Akhiezer-type damping) would imply a
boson peak, i.e.\ a maximum in the vibrational density of states, divided by
the frequency squared (reduced density of states). This would apply both to
glasses and crystals.Here we show that this is not the case. In a
mathematically correct treatment of the model the reduced density of states
monotonously decreases, i.e.\ there is no boson peak. We further show that the
formula for the would-be boson peak, presented by the authors, corresponds to a
very short one-dimensional damped oscillator system. The peaks they show
correspond to resonances, which vanish in the thermodynamic limit.
|
2104.13076v1
|
2021-05-03
|
Damping and polarization rates in near equilibrium state
|
The collision terms in spin transport theory are analyzed in Kadanoff-Baym
formalism for systems close to equilibrium. The non-equilibrium fluctuations in
spin distribution include both damping and polarization, with the latter
arising from the exchange between orbital and spin angular momenta. The damping
and polarization rates or the relaxation times are expressed in terms of
various Dirac components of the self-energy. Unlike the usually used
Anderson-Witting relaxation time approximation assuming a single time scale for
different degrees of freedom, the polarization effect is induced by the thermal
vorticity and its time scale of thermalization is different from the damping.
The numerical calculation in the Nambu--Jona-Lasinio model shows that, charge
is thermalized earlier and spin is thermalized later.
|
2105.00915v1
|
2021-05-14
|
Exact solution of damped harmonic oscillator with a magnetic field in a time dependent noncommutative space
|
In this paper we have obtained the exact eigenstates of a two dimensional
damped harmonic oscillator in the presence of an external magnetic field
varying with respect to time in time dependent noncommutative space. It has
been observed that for some specific choices of the damping factor, the time
dependent frequency of the oscillator and the time dependent external magnetic
field, there exists interesting solutions of the time dependent noncommutative
parameters following from the solutions of the Ermakov-Pinney equation.
Further, these solutions enable us to get exact analytic forms for the phase
which relates the eigenstates of the Hamiltonian with the eigenstates of the
Lewis invariant. Then we compute the expectation value of the Hamiltonian. The
expectation values of the energy are found to vary with time for different
solutions of the Ermakov-Pinney equation corresponding to different choices of
the damping factor, the time dependent frequency of the oscillator and the time
dependent applied magnetic field. We also compare our results with those in the
absence of the magnetic field obtained earlier.
|
2106.05182v1
|
2021-06-21
|
Self-stabilization of light sails by damped internal degrees of freedom
|
We consider the motion of a light sail that is accelerated by a powerful
laser beam. We derive the equations of motion for two proof-of-concept sail
designs with damped internal degrees of freedom. Using linear stability
analysis we show that perturbations of the sail movement in all lateral degrees
of freedom can be damped passively. This analysis also shows complicated
behaviour akin to that associated with exceptional points in PT-symmetric
systems in optics and quantum mechanics. The excess heat that is produced by
the damping mechanism is likely to be substantially smaller than the expected
heating due to the partial absorption of the incident laser beam by the sail.
|
2106.10961v1
|
2021-07-14
|
Determining the source of phase noise: Response of a driven Duffing oscillator to low-frequency damping and resonance frequency fluctuations
|
We present an analytical calculation of the response of a driven Duffing
oscillator to low-frequency fluctuations in the resonance frequency and
damping. We find that fluctuations in these parameters manifest themselves
distinctively, allowing them to be distinguished. In the strongly nonlinear
regime, amplitude and phase noise due to resonance frequency fluctuations and
amplitude noise due to damping fluctuations are strongly attenuated, while the
transduction of damping fluctuations into phase noise remains of order $1$. We
show that this can be seen by comparing the relative strengths of the amplitude
fluctuations to the fluctuations in the quadrature components, and suggest that
this provides a means to determine the source of low-frequency noise in a
driven Duffing oscillator.
|
2107.06879v1
|
2021-07-27
|
Spin transport-induced damping of coherent THz spin dynamics in iron
|
We study the damping of perpendicular standing spin-waves (PSSWs) in
ultrathin Fe films at frequencies up to 2.4 THz. The PSSWs are excited by
optically generated ultrashort spin current pulses, and probed optically in the
time domain. Analyzing the wavenumber and thickness dependence of the damping,
we demonstrate that at sufficiently large wave vectors $k$ the damping is
dominated by spin transport effects scaling with k^4 and limiting the frequency
range of observable PSSWs. Although this contribution is known to originate in
the spin diffusion, we argue that at moderate and large k a more general
description is necessary and develop a model where the 'transverse spin mean
free path' is the a key parameter, and estimate it to be ~0.5 nm.
|
2107.12812v2
|
2021-07-29
|
A N-dimensional elastic\viscoelastic transmission problem with Kelvin-Voigt damping and non smooth coefficient at the interface
|
We investigate the stabilization of a multidimensional system of coupled wave
equations with only one Kelvin Voigt damping. Using a unique continuation
result based on a Carleman estimate and a general criteria of Arendt Batty, we
prove the strong stability of the system in the absence of the compactness of
the resolvent without any geometric condition. Then, using a spectral analysis,
we prove the non uniform stability of the system. Further, using frequency
domain approach combined with a multiplier technique, we establish some
polynomial stability results by considering different geometric conditions on
the coupling and damping domains. In addition, we establish two polynomial
energy decay rates of the system on a square domain where the damping and the
coupling are localized in a vertical strip.
|
2107.13785v1
|
2021-09-03
|
Stabilization of the damped plate equation under general boundary conditions
|
We consider a damped plate equation on an open bounded subset of R^d, or a
smooth manifold, with boundary, along with general boundary operators
fulfilling the Lopatinskii-Sapiro condition. The damping term acts on a region
without imposing a geometrical condition. We derive a resolvent estimate for
the generator of the damped plate semigroup that yields a logarithmic decay of
the energy of the solution to the plate equation. The resolvent estimate is a
consequence of a Carleman inequality obtained for the bi-Laplace operator
involving a spectral parameter under the considered boundary conditions. The
derivation goes first though microlocal estimates, then local estimates, and
finally a global estimate.
|
2109.01521v2
|
2021-09-07
|
Fluid energy cascade rate and kinetic damping: new insight from 3D Landau-fluid simulations
|
Using an exact law for incompressible Hall magnetohydrodynamics (HMHD)
turbulence, the energy cascade rate is computed from three-dimensional HMHD-CGL
(bi-adiabatic ions and isothermal electrons) and Landau fluid (LF) numerical
simulations that feature different intensities of Landau damping over a broad
range of wavenumbers, typically $0.05\lesssim k_\perp d_i \lesssim100$. Using
three sets of cross-scale simulations where turbulence is initiated at large,
medium and small scales, the ability of the fluid energy cascade to "sense" the
kinetic Landau damping at different scales is tested. The cascade rate
estimated from the exact law and the dissipation calculated directly from the
simulation are shown to reflect the role of Landau damping in dissipating
energy at all scales, with an emphasis on the kinetic ones. This result
provides new prospects on using exact laws for simplified fluid models to
analyze dissipation in kinetic simulations and spacecraft observations, and new
insights into theoretical description of collisionless magnetized plasmas.
|
2109.03123v2
|
2021-09-24
|
Effect of nonlocal transformations on the linearizability and exact solvability of the nonlinear generalized modified Emden type equations
|
The nonlinear generalized modified Emden type equations (GMEE) are known to
be linearizable into simple harmonic oscillator (HO) or damped harmonic
oscillators (DHO) via some nonlocal transformations. Hereby, we show that the
structure of the nonlocal transformation and the linearizability into HO or DHO
determine the nature/structure of the dynamical forces involved (hence,
determine the structure of the dynamical equation). Yet, a reverse engineering
strategy is used so that the exact solutions of the emerging GMEE are
nonlocally transformed to find the exact solutions of the HO and DHO dynamical
equations. Consequently, whilst the exact solution for the HO remains a
textbook one, the exact solution for the DHO (never reported elsewhere, to the
best of our knowledge) turns out to be manifestly the most explicit and general
solution that offers consistency and comprehensive coverage for the associated
under-damping, critical-damping, and over-damping cases (i.e., no complex
settings for the coordinates and/or the velocities are eminent/feasible).
Moreover, for all emerging dynamical system, we report illustrative figures for
each solution as well as the corresponding phase-space trajectories as they
evolve in time.
|
2109.12059v1
|
2021-12-27
|
Trajectory attractors for 3D damped Euler equations and their approximation
|
We study the global attractors for the damped 3D Euler--Bardina equations
with the regularization parameter $\alpha>0$ and Ekman damping coefficient
$\gamma>0$ endowed with periodic boundary conditions as well as their damped
Euler limit $\alpha\to0$. We prove that despite the possible non-uniqueness of
solutions of the limit Euler system and even the non-existence of such
solutions in the distributional sense, the limit dynamics of the corresponding
dissipative solutions introduced by P.\,Lions can be described in terms of
attractors of the properly constructed trajectory dynamical system. Moreover,
the convergence of the attractors $\Cal A(\alpha)$ of the regularized system to
the limit trajectory attractor $\Cal A(0)$ as $\alpha\to0$ is also established
in terms of the upper semicontinuity in the properly defined functional space.
|
2112.13691v1
|
2022-01-12
|
Implicit Bias of MSE Gradient Optimization in Underparameterized Neural Networks
|
We study the dynamics of a neural network in function space when optimizing
the mean squared error via gradient flow. We show that in the
underparameterized regime the network learns eigenfunctions of an integral
operator $T_{K^\infty}$ determined by the Neural Tangent Kernel (NTK) at rates
corresponding to their eigenvalues. For example, for uniformly distributed data
on the sphere $S^{d - 1}$ and rotation invariant weight distributions, the
eigenfunctions of $T_{K^\infty}$ are the spherical harmonics. Our results can
be understood as describing a spectral bias in the underparameterized regime.
The proofs use the concept of "Damped Deviations", where deviations of the NTK
matter less for eigendirections with large eigenvalues due to the occurence of
a damping factor. Aside from the underparameterized regime, the damped
deviations point-of-view can be used to track the dynamics of the empirical
risk in the overparameterized setting, allowing us to extend certain results in
the literature. We conclude that damped deviations offers a simple and unifying
perspective of the dynamics when optimizing the squared error.
|
2201.04738v1
|
2022-01-19
|
Variance-Reduced Stochastic Quasi-Newton Methods for Decentralized Learning: Part II
|
In Part I of this work, we have proposed a general framework of decentralized
stochastic quasi-Newton methods, which converge linearly to the optimal
solution under the assumption that the local Hessian inverse approximations
have bounded positive eigenvalues. In Part II, we specify two fully
decentralized stochastic quasi-Newton methods, damped regularized
limited-memory DFP (Davidon-Fletcher-Powell) and damped limited-memory BFGS
(Broyden-Fletcher-Goldfarb-Shanno), to locally construct such Hessian inverse
approximations without extra sampling or communication. Both of the methods use
a fixed moving window of $M$ past local gradient approximations and local
decision variables to adaptively construct positive definite Hessian inverse
approximations with bounded eigenvalues, satisfying the assumption in Part I
for the linear convergence. For the proposed damped regularized limited-memory
DFP, a regularization term is added to improve the performance. For the
proposed damped limited-memory BFGS, a two-loop recursion is applied, leading
to low storage and computation complexity. Numerical experiments demonstrate
that the proposed quasi-Newton methods are much faster than the existing
decentralized stochastic first-order algorithms.
|
2201.07733v1
|
2022-01-19
|
Active tuning of plasmon damping via light induced magnetism
|
Circularly polarized optical excitation of plasmonic nanostructures causes
coherent circulating motion of their electrons, which in turn, gives rise to
strong optically induced magnetization - a phenomenon known as the inverse
Faraday effect (IFE). In this study we report how the IFE also significantly
decreases plasmon damping. By modulating the optical polarization state
incident on achiral plasmonic nanostructures from linear to circular, we
observe reversible increases of reflectance by 78% as well as simultaneous
increases of optical field concentration by 35.7% under 10^9 W/m^2 continuous
wave (CW) optical excitation. These signatures of decreased plasmon damping
were also monitored in the presence of an externally applied magnetic field
(0.2 T). The combined interactions allow an estimate of the light-induced
magnetization, which corresponds to an effective magnetic field of ~1.3 T
during circularly polarized CW excitation (10^9 W/m^2). We rationalize the
observed decreases in plasmon damping in terms of the Lorentz forces acting on
the circulating electron trajectories. Our results outline strategies for
actively modulating intrinsic losses in the metal, and thereby, the optical
mode quality and field concentration via opto-magnetic effects encoded in the
polarization state of incident light.
|
2201.07842v1
|
2022-01-27
|
Effect of vertex corrections on the enhancement of Gilbert damping in spin pumping into a two-dimensional electron gas
|
We theoretically consider the effect of vertex correction on spin pumping
from a ferromagnetic insulator (FI) into a two-dimensional electron gas (2DEG)
in which the Rashba and Dresselhaus spin-orbit interactions coexist. The
Gilbert damping in the FI is enhanced by elastic spin-flipping or magnon
absorption. We show that the Gilbert damping due to elastic spin-flipping is
strongly enhanced by the vertex correction when the ratio of the two spin-orbit
interactions is near a special value at which the spin relaxation time diverges
while that due to magnon absorption shows only small modification. We also show
that the shift in the resonant frequency due to elastic spin-flipping is
strongly enhanced in a similar way as the Gilbert damping.
|
2201.11498v3
|
2022-03-02
|
Simplified Stability Assessment of Power Systems with Variable-Delay Wide-Area Damping Control
|
Power electronic devices such as HVDC and FACTS can be used to improve the
damping of poorly damped inter-area modes in large power systems. This involves
the use of wide-area feedback signals, which are transmitted via communication
networks. The performance of the closed-loop system is strongly influenced by
the delay associated with wide-area signals. The random nature of this delay
introduces a switched linear system model. The stability assessment of such a
system requires linear matrix inequality based approaches. This makes the
stability analysis more complicated as the system size increases. To address
this challenge, this paper proposes a delay-processing strategy that simplifies
the modelling and analysis in discrete-domain. In contrast to the existing
stability assessment techniques, the proposed approach is advantageous because
the stability, as well as damping performance, can be accurately predicted by a
simplified analysis. The proposed methodology is verified with a case study on
the 2-area 4-machine power system with a series compensated tie-line. The
results are found to be in accordance with the predictions of the proposed
simplified analysis.
|
2203.01362v1
|
2022-03-03
|
Forward-modulated damping estimates and nonlocalized stability of periodic Lugiato-Lefever wave
|
In an interesting recent analysis, Haragus-Johnson-Perkins-de Rijk have shown
modulational stability under localized perturbations of steady periodic
solutions of the Lugiato-Lefever equation (LLE), in the process pointing out a
difficulty in obtaining standard "nonlinear damping estimates" on modulated
perturbation variables to control regularity of solutions. Here, we point out
that in place of standard "inverse-modulated" damping estimates, one can
alternatively carry out a damping estimate on the "forward-modulated"
perturbation, noting that norms of forward- and inverse-modulated variables are
equivalent modulo absorbable errors, thus recovering the classical argument
structure of Johnson-Noble-Rodrigues-Zumbrun for parabolic systems. This
observation seems of general use in situations of delicate regularity.
Applied in the context of (LLE) it gives the stronger result of stability and
asymptotic behavior with respect to nonlocalized perturbations.
|
2203.01770v3
|
2022-03-31
|
Observing Particle Energization above the Nyquist Frequency: An Application of the Field-Particle Correlation Technique
|
The field-particle correlation technique utilizes single-point measurements
to uncover signatures of various particle energization mechanisms in turbulent
space plasmas. The signature of Landau damping by electrons has been found in
both simulations and observations from Earth's magnetosheath using this
technique, but instrumental limitations of spacecraft sampling rates present a
challenge to discovering the full extent of the presence of Landau damping in
the solar wind. Theory predicts that field-particle correlations can recover
velocity-space energization signatures even from data that is undersampled with
respect to the characteristic frequencies at which the wave damping occurs. To
test this hypothesis, we perform a high-resoluation gyrokinetic simulation of
space plasma turbulence, confirm that it contains signatures of electron Landau
damping, and then systematically reduce the time resolution of the data to
identify the point at which the signatures become impossible to recover. We
find results in support of our theoretical prediction and look for a rule of
thumb that can be compared with the measurement capabilities of spacecraft
missions to inform the process of applying field-particle correlations to low
time resolution data.
|
2204.00104v1
|
2022-04-06
|
A Potential Based Quantization Procedure of the Damped Oscillator
|
Nowadays, two of the most prospering fields of physics are quantum computing
and spintronics. In both, the loss of information and dissipation plays a
crucial role. In the present work we formulate the quantization of the
dissipative oscillator, which aids understanding of the above mentioned, and
creates a theoretical frame to overcome these issues in the future. Based on
the Lagrangian framework of the damped spring system, the canonically
conjugated pairs and the Hamiltonian of the system are obtained, by which the
quantization procedure can be started and consistently applied. As a result,
the damping quantum wave equation of the dissipative oscillator is deduced, by
which an exact damping wave solution of this equation is obtained.
Consequently, we arrive at such an irreversible quantum theory by which the
quantum losses can be described.
|
2204.02893v2
|
2022-04-19
|
Role of shape anisotropy on thermal gradient-driven domain wall dynamics in magnetic nanowires
|
We investigate the magnetic domain wall (DW) dynamics in uniaxial/biaxial
nanowires under a thermal gradient (TG). The findings reveal that the DW
propagates toward the hotter region in both nanowires. The main physics of such
observations is the magnonic angular momentum transfer to the DW. The hard
(shape) anisotropy exists in biaxial nanowire, which contributes an additional
torque, hence DW speed is larger than that in uniaxial nanowire. With lower
damping, the DW velocity is smaller and DW velocity increases with damping
which is opposite to usual expectation. To explain this, it is predicted that
there is a probability to form the standing spin-waves (which do not carry net
energy/momentum) together with travelling spin-waves if the propagation length
of thermally-generated spin-waves is larger than the nanowire length. For
larger-damping, DW decreases with damping since the magnon propagation length
decreases. Therefore, the above findings might be useful in realizing the
spintronic (racetrack memory) devices.
|
2204.09101v2
|
2022-04-25
|
Energy decay estimates for the wave equation with supercritical nonlinear damping
|
We consider a damped wave equation in a bounded domain. The damping is
nonlinear and is homogeneous with degree p -- 1 with p > 2. First, we show that
the energy of the strong solution in the supercritical case decays as a
negative power of t; the rate of decay is the same as in the subcritical or
critical cases, provided that the space dimension does not exceed ten. Next,
relying on a new differential inequality, we show that if the initial
displacement is further required to lie in L p , then the energy of the
corresponding weak solution decays logarithmically in the supercritical case.
Those new results complement those in the literature and open an important
breach in the unknown land of super-critical damping mechanisms.
|
2204.11494v1
|
2022-05-07
|
Proposal for a Damping-Ring-Free Electron Injector for Future Linear Colliders
|
The current designs of future electron-positron linear colliders incorporate
large and complex damping rings to produce asymmetric beams for beamstrahlung
suppression. Here we present the design of an electron injector capable of
delivering flat electron beams with phase-space partition comparable to the
electron-beam parameters produced downstream of the damping ring in the
proposed international linear collider (ILC) design. Our design does not employ
a damping ring but is instead based on cross-plane phase-space-manipulation
techniques. The performance of the proposed configuration, its sensitivity to
jitter along with its impact on spin-polarization is investigated. The proposed
paradigm could be adapted to other linear collider concepts under consideration
and offers a path toward significant cost and complexity reduction.
|
2205.03736v1
|
2022-06-02
|
Optimal Control of the 3D Damped Navier-Stokes-Voigt Equations with Control Constraints
|
In this paper, we consider the 3D Navier-Stokes-Voigt (NSV) equations with
nonlinear damping $|u|^{r-1}u, r\in[1,\infty)$ in bounded and space-periodic
domains. We formulate an optimal control problem of minimizing the curl of the
velocity field in the energy norm subject to the flow velocity satisfying the
damped NSV equation with a distributed control force. The control also needs to
obey box-type constraints. For any $r\geq 1,$ the existence and uniqueness of a
weak solution is discussed when the domain $\Omega$ is periodic/bounded in
$\mathbb R^3$ while a unique strong solution is obtained in the case of
space-periodic boundary conditions. We prove the existence of an optimal pair
for the control problem. Using the classical adjoint problem approach, we show
that the optimal control satisfies a first-order necessary optimality condition
given by a variational inequality. Since the optimal control problem is
non-convex, we obtain a second-order sufficient optimality condition showing
that an admissible control is locally optimal. Further, we derive optimality
conditions in terms of adjoint state defined with respect to the growth of the
damping term for a global optimal control.
|
2206.00988v2
|
2022-06-05
|
Stationary measures for stochastic differential equations with degenerate damping
|
A variety of physical phenomena involve the nonlinear transfer of energy from
weakly damped modes subjected to external forcing to other modes which are more
heavily damped. In this work we explore this in (finite-dimensional) stochastic
differential equations in $\mathbb R^n$ with a quadratic, conservative
nonlinearity $B(x,x)$ and a linear damping term $-Ax$ which is degenerate in
the sense that $\mathrm{ker} A \neq \emptyset$. We investigate sufficient
conditions to deduce the existence of a stationary measure for the associated
Markov semigroups. Existence of such measures is straightforward if $A$ is full
rank, but otherwise, energy could potentially accumulate in $\mathrm{ker} A$
and lead to almost-surely unbounded trajectories, making the existence of
stationary measures impossible. We give a relatively simple and general
sufficient condition based on time-averaged coercivity estimates along
trajectories in neighborhoods of $\mathrm{ker} A$ and many examples where such
estimates can be made.
|
2206.02240v1
|
2022-07-13
|
Energy decay for the time dependent damped wave equation
|
Energy decay is established for the damped wave equation on compact
Riemannian manifolds where the damping coefficient is allowed to depend on
time. Using a time dependent observability inequality, it is shown that the
energy of solutions decays at an exponential rate if the damping coefficient
satisfies a time dependent analogue of the classical geometric control
condition. Existing time dependent observability inequalities are improved by
removing technical assumptions on the permitted initial data.
|
2207.06260v4
|
2022-08-04
|
Lp-asymptotic stability of 1D damped wave equations with localized and nonlinear damping
|
In this paper, we study the $L^p$-asymptotic stability with $p\in (1,\infty)$
of the one-dimensional nonlinear damped wave equation with a localized damping
and Dirichlet boundary conditions in a bounded domain $(0,1)$. We start by
addressing the well-posedness problem. We prove the existence and the
uniqueness of weak solutions for $p\in [2,\infty)$ and the existence and the
uniqueness of strong solutions for all $p\in [1,\infty)$. The proofs rely on
the well-posedness already proved in the $L^\infty$ framework by [4] combined
with a density argument. Then we prove that the energy of strong solutions
decays exponentially to zero. The proof relies on the multiplier method
combined with the work that has been done in the linear case in [8].
|
2208.02779v1
|
2022-08-07
|
Damping of neutrino oscillations, decoherence and the lengths of neutrino wave packets
|
Spatial separation of the wave packets (WPs) of neutrino mass eigenstates
leads to decoherence and damping of neutrino oscillations. Damping can also be
caused by finite energy resolution of neutrino detectors or, in the case of
experiments with radioactive neutrino sources, by finite width of the emitted
neutrino line. We study in detail these two types of damping effects using
reactor neutrino experiments and experiments with radioactive $^{51}$Cr source
as examples. We demonstrate that the effects of decoherence by WP separation
can always be incorporated into a modification of the energy resolution
function of the detector and so are intimately entangled with it. We estimate
for the first time the lengths $\sigma_x$ of WPs of reactor neutrinos and
neutrinos from a radioactive $^{51}$Cr source. The obtained values, $\sigma_x =
(2\times 10^{-5} - 1.4\times 10^{-4})$ cm, are at least six orders of magnitude
larger than the currently available experimental lower bounds. We conclude that
effects of decoherence by WP separation cannot be probed in reactor and
radioactive source experiments.
|
2208.03736v2
|
2022-08-23
|
Fate of exceptional points in the presence of nonlinearities
|
The non-Hermitian dynamics of open systems deal with how intricate coherent
effects of a closed system intertwine with the impact of coupling to an
environment. The system-environment dynamics can then lead to so-called
exceptional points, which are the open-system marker of phase transitions,
i.e., the closing of spectral gaps in the complex spectrum. Even in the
ubiquitous example of the damped harmonic oscillator, the dissipative
environment can lead to an exceptional point, separating between under-damped
and over-damped dynamics at a point of critical damping. Here, we examine the
fate of this exceptional point in the presence of strong correlations, i.e.,
for a nonlinear oscillator. By employing a functional renormalization group
approach, we identify non-perturbative regimes of this model where the
nonlinearity makes the system more robust against the influence of dissipation
and can remove the exceptional point altogether. The melting of the exceptional
point occurs above a critical nonlinearity threshold. Interestingly, the
exceptional point melts faster with increasing temperatures, showing a
surprising flow to coherent dynamics when coupled to a warm environment.
|
2208.11205v2
|
2022-09-10
|
Data-driven, multi-moment fluid modeling of Landau damping
|
Deriving governing equations of complex physical systems based on first
principles can be quite challenging when there are certain unknown terms and
hidden physical mechanisms in the systems. In this work, we apply a deep
learning architecture to learn fluid partial differential equations (PDEs) of a
plasma system based on the data acquired from a fully kinetic model. The
learned multi-moment fluid PDEs are demonstrated to incorporate kinetic effects
such as Landau damping. Based on the learned fluid closure, the data-driven,
multi-moment fluid modeling can well reproduce all the physical quantities
derived from the fully kinetic model. The calculated damping rate of Landau
damping is consistent with both the fully kinetic simulation and the linear
theory. The data-driven fluid modeling of PDEs for complex physical systems may
be applied to improve fluid closure and reduce the computational cost of
multi-scale modeling of global systems.
|
2209.04726v1
|
2022-09-25
|
Formation of the cosmic-ray halo: The role of nonlinear Landau damping
|
We present a nonlinear model of self-consistent Galactic halo, where the
processes of cosmic ray (CR) propagation and excitation/damping of MHD waves
are included. The MHD-turbulence, which prevents CR escape from the Galaxy, is
entirely generated by the resonant streaming instability. The key mechanism
controlling the halo size is the nonlinear Landau (NL) damping, which
suppresses the amplitude of MHD fluctuations and, thus, makes the halo larger.
The equilibrium turbulence spectrum is determined by a balance of CR excitation
and NL damping, which sets the regions of diffusive and advective propagation
of CRs. The boundary $z_{cr}(E)$ between the two regions is the halo size,
which slowly increases with the energy. For the vertical magnetic field of
$\sim 1~\mu G$, we estimate $z_{cr} \sim 1$ kpc for GeV protons. The derived
proton spectrum is in a good agreement with observational data.
|
2209.12302v1
|
2022-10-10
|
Finite time extinction for a critically damped Schr{ö}dinger equation with a sublinear nonlinearity
|
This paper completes some previous studies by several authors on the finite
time extinction for nonlinear Schr{\"o}dinger equation when the nonlinear
damping term corresponds to the limit cases of some ``saturating non-Kerr law''
$F(|u|^2)u=\frac{a}{\varepsilon+(|u|^2)^\alpha}u,$ with $a\in\mathbb{C},$
$\varepsilon\geqslant0,$ $2\alpha=(1-m)$ and $m\in[0,1).$ Here we consider the
sublinear case $0<m<1$ with a critical damped coefficient: $a\in\mathbb{C}$ is
assumed to be in the set $D(m)=\big\{z\in\mathbb{C}; \; \mathrm{Im}(z)>0 \text{
and } 2\sqrt{m}\mathrm{Im}(z)=(1-m)\mathrm{Re}(z)\big\}.$ Among other things,
we know that this damping coefficient is critical, for instance, in order to
obtain the monotonicity of the associated operator (see the paper by Liskevich
and Perel'muter [16] and the more recent study by Cialdea and Maz'ya [14]). The
finite time extinction of solutions is proved by a suitable energy method after
obtaining appropiate a priori estimates. Most of the results apply to
non-necessarily bounded spatial domains.
|
2210.04493v4
|
2022-10-14
|
Landau damping for gravitational waves in parity-violating theories
|
We discuss how tensor polarizations of gravitational waves can suffer Landau
damping in the presence of velocity birefringence, when parity symmetry is
explicitly broken. In particular, we analyze the role of the Nieh-Yan and
Chern-Simons terms in modified theories of gravity, showing how the
gravitational perturbation in collisionless media can be characterized by a
subluminal phase velocity, circumventing the well-known results of General
Relativity and allowing for the appearance of the kinematic damping. We
investigate in detail the connection between the thermodynamic properties of
the medium, such as temperature and mass of the particles interacting with the
gravitational wave, and the parameters ruling the parity violating terms of the
models. In this respect, we outline how the dispersion relations can give rise
in each model to different regions of the wavenumber space, where the phase
velocity is subluminal, superluminal or does not exist. Quantitative estimates
on the considered models indicate that the phenomenon of Landau damping is not
detectable given the sensitivity of present-day instruments.
|
2210.07673v2
|
2022-10-25
|
Formation of shifted shock for the 3D compressible Euler equations with damping
|
In this paper, we show the shock formation of the solutions to the
3-dimensional (3D) compressible isentropic and irrotational Euler equations
with damping for the initial short pulse data which was first introduced by
D.Christodoulou\cite{christodoulou2007}. Due to the damping effect, the
largeness of the initial data is necessary for the shock formation and we will
work on the class of large data (in energy sense). Similar to the undamped
case, the formation of shock is characterized by the collapse of the
characteristic hypersurfaces and the vanishing of the inverse foliation density
function $\mu$, at which the first derivatives of the velocity and the density
blow up. However, the damping effect changes the asymptotic behavior of the
inverse foliation density function $\mu$ and then shifts the time of shock
formation compared with the undamped case. The methods in the paper can also be
extended to a class of $3D$ quasilinear wave equations for the short pulse
initial data.
|
2210.13796v1
|
2022-10-30
|
Dynamics of a class of extensible beams with degenerate and non-degenerate nonlocal damping
|
This work is concerned with new results on long-time dynamics of a class of
hyperbolic evolution equations related to extensible beams with three
distinguished nonlocal nonlinear damping terms. In the first possibly
degenerate case, the results feature the existence of a family of compact
global attractors and a thickness estimate for their Kolmogorov's
$\varepsilon$-entropy. Then, in the non-degenerate context, the structure of
the helpful nonlocal damping leads to the existence of finite-dimensional
compact global and exponential attractors. Lastly, in a degenerate and critical
framework, it is proved the existence of a bounded closed global attractor but
not compact. To the proofs, we provide several new technical results by means
of refined estimates that open up perspectives for a new branch of nonlinearly
damped problems.
|
2210.16851v1
|
2022-11-11
|
Nonlinear fractional damped wave equation on compact Lie groups
|
In this paper, we deal with the initial value fractional damped wave equation
on $G$, a compact Lie group, with power-type nonlinearity. The aim of this
manuscript is twofold. First, using the Fourier analysis on compact Lie groups,
we prove a local in-time existence result in the energy space for the
fractional damped wave equation on $G$. Moreover, a finite time blow-up result
is established under certain conditions on the initial data. In the next part
of the paper, we consider fractional wave equation with lower order terms, that
is, damping and mass with the same power type nonlinearity on compact Lie
groups, and prove the global in-time existence of small data solutions in the
energy evolution space.
|
2211.06155v1
|
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