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2018-08-19
|
Sharp lifespan estimates of blowup solutions to semilinear wave equations with time-dependent effective damping
|
We consider the initial value problem for the semilinear wave equation with
time-dependent effective damping. The interest is the behavior of lifespan of
solutions in view of the asymptotic profile of the damping as $t\to \infty$.
The result of this paper is the sharp lifespan estimates of blowup solutions
for general time-dependent damping including threshold cases between effective
and overdamping.
|
1808.06189v2
|
2018-09-05
|
Damping estimates for oscillatory integral operators with real-analytic phases and its applications
|
In this paper, we investigate sharp damping estimates for a class of one
dimensional oscillatory integral operators with real-analytic phases. By
establishing endpoint estimates for suitably damped oscillatory integral
operators, we are able to give a new proof of the sharp $L^p$ estimates which
have been proved by Xiao in Endpoint estimates for one-dimensional oscillatory
integral operators, \emph{Advances in Mathematics}, \textbf{316}, 255-291
(2017). The damping estimates obtained in this paper are of independent
interest.
|
1809.01298v2
|
2018-09-26
|
Global Attractor For Weakly Damped, Forced Mkdv Equation Below Energy Space
|
We prove the existence of the global attractor in $ \dot H^s$, $s > 11/12$
for the weakly damped and forced mKdV on the one dimensional torus. The
existence of global attractor below the energy space has not been known, though
the global well-posedness below the energy space is established. We directly
apply the I-method to the damped and forced mKdV, because the Miura
transformation does not work for the mKdV with damping and forcing terms. We
need to make a close investigation into the trilinear estimates involving
resonant frequencies, which are different from the bilinear estimates
corresponding to the KdV.
|
1809.09787v1
|
2018-10-03
|
Damped Oscillator with delta-kicked frequency in probability representation of quantum mechanic
|
We obtain the tomogram of squeezed correlated states of a quantum parametric
damped oscillator in an explicit form. We study the damping within the
framework of the Caldirola--Kanai model and chose the parametric excitation in
the form of a very short pulse simulated by a delta-kick of frequency; the
squeezing phenomenon is reviewed. The cases of strong and weak damping are
investigated.
|
1810.01672v1
|
2018-10-26
|
Drastic Reduction of Plasmon Damping in Two-Dimensional Electron Disks
|
The plasmon damping has been investigated using resonant microwave absorption
of two-dimensional electrons in disks with different diameters. We have found
an unexpected drastic reduction of the plasmon damping in the regime of strong
retardation. This finding implies large delocalization of retarded plasmon
field outside the plane of the two-dimensional electron system. A universal
relation between the damping of plasmon polariton waves and retardation
parameter is reported.
|
1811.01040v1
|
2019-01-05
|
Cauchy problem for thermoelastic plate equations with different damping mechanisms
|
In this paper we study Cauchy problem for thermoelastic plate equations with
friction or structural damping in $\mathbb{R}^n$, $n\geq1$, where the heat
conduction is modeled by Fourier's law. We explain some qualitative properties
of solutions influenced by different damping mechanisms. We show which damping
in the model has a dominant influence on smoothing effect, energy estimates,
$L^p-L^q$ estimates not necessary on the conjugate line, and on diffusion
phenomena. Moreover, we derive asymptotic profiles of solutions in a framework
of weighted $L^1$ data. In particular, sharp decay estimates for lower bound
and upper bound of solutions in the $\dot{H}^s$ norm ($s\geq0$) are shown.
|
1901.01423v2
|
2019-03-04
|
Damping of cosmological tensor modes in Horndeski theories after GW170817
|
This paper investigates the propagation of cosmological gravitational waves
interacting with free-streaming neutrinos within the context of Horndeski
theories of gravity constrained by the detection of GW170817. We apply the
theory of cosmological perturbations to explicitly derive the
Einstein-Boltzmann equation for the damped propagation of first-order
transverse traceless gravitational waves. In contrast to general relativity, we
argue that modified gravity can give rise to non-vanishing free-streaming
damping effects during the cosmological matter dominated era. We also provide
an analytic formula for the main multipole order with which modified gravity
and free-streaming neutrinos damp the variety of tensor correlation functions
of the cosmic microwave background.
|
1903.01502v2
|
2019-04-24
|
On the Energy Decay Rate of the Fractional Wave Equation on $\mathbb{R}$ with Relatively Dense Damping
|
We establish upper bounds for the decay rate of the energy of the damped
fractional wave equation when the averages of the damping coefficient on all
intervals of a fixed length are bounded below. If the power of the fractional
Laplacian, $s$, is between 0 and 2, the decay is polynomial. For $s \ge 2$, the
decay is exponential. Second, we show that our assumption on the damping is
necessary for the energy to decay exponentially.
|
1904.10946v3
|
2019-08-22
|
Damping of the Anderson-Bogolyubov mode by spin and mass imbalance in Fermi mixtures
|
We study the temporally nonlocal contributions to the gradient expansion of
the pair fluctuation propagator for spin- and mass-imbalanced Fermi mixtures.
These terms are related to damping processes of sound-like
(Anderson-Bogolyubov) collective modes and are relevant for the structure of
the complex pole of the pair fluctuation propagator. We derive conditions under
which damping occurs even at zero temperature for large enough mismatch of the
Fermi surfaces. We compare our analytical results with numerically computed
damping rates of the Anderson-Bogolyubov mode.
|
1908.08559v2
|
2019-11-05
|
On the Smallness Condition in Linear Inviscid Damping: Monotonicity and Resonance Chains
|
We consider the linearized Euler equations around a smooth, bilipschitz shear
profile $U(y)$ on $\mathbb{T}_L \times \mathbb{R}$. We construct an explicit
flow which exhibits linear inviscid damping for $L$ sufficiently small, but for
which damping fails if $L$ is large. In particular, similar to the instability
results for convex profiles for a shear flow being bilipschitz is not
sufficient for linear inviscid damping to hold. Instead of an eigenvalue-based
argument the underlying mechanism here is shown to be based on a new cascade of
resonances moving to higher and higher frequencies in $y$, which is distinct
from the echo chain mechanism in the nonlinear problem.
|
1911.02066v1
|
2020-01-02
|
On Echo Chains in Landau damping: Self-similar Solutions and Gevrey 3 as a Linear Stability Threshold
|
We show that the linearized Vlasov-Poisson equations around self-similar
non-homogeneous states near zero contain the full plasma echo mechanism,
yielding Gevrey 3 as a critical stability class. Moreover, here Landau damping
may persist despite blow-up: We construct a critical Gevrey regularity class in
which the force field converges in $L^2$. Thus, on the one hand, the physical
phenomenon of Landau damping holds. On the other hand, the density diverges to
infinity in Sobolev regularity. Hence, ``strong damping'' cannot hold.
|
2001.00513v1
|
2020-01-21
|
Pseudospectra of the damped wave equation with unbounded damping
|
We analyze pseudospectra of the generator of the damped wave equation with
unbounded damping. We show that the resolvent norm diverges as $\Re z \to -
\infty$. The highly non-normal character of the operator is a robust effect
preserved even when a strong potential is added. Consequently, spectral
instabilities and other related pseudospectral effects are present.
|
2001.07767v1
|
2020-02-09
|
The damped wave equation with singular damping
|
We analyze the spectral properties and peculiar behavior of solutions of a
damped wave equation on a finite interval with a singular damping of the form
$\alpha/x$, $\alpha>0$. We establish the exponential stability of the semigroup
for all positive $\alpha$, and determine conditions for the spectrum to consist
of a finite number of eigenvalues. As a consequence, we fully characterize the
set of initial conditions for which there is extinction of solutions in finite
time. Finally, we propose two open problems related to extremal decay rates of
solutions.
|
2002.03440v1
|
2020-03-12
|
Optimal nonlinear damping control of second-order systems
|
Novel nonlinear damping control is proposed for the second-order systems. The
proportional output feedback is combined with the damping term which is
quadratic to the output derivative and inverse to the set-point distance. The
global stability, passivity property, and convergence time and accuracy are
demonstrated. Also the control saturation case is explicitly analyzed. The
suggested nonlinear damping is denoted as optimal since requiring no design
additional parameters and ensuring a fast convergence, without transient
overshoots for a non-saturated and one transient overshoot for a saturated
control configuration.
|
2003.05670v3
|
2020-06-24
|
Stability of a star-shaped network with local Kelvin-Voigt damping and non-smooth coefficient at interface
|
In this paper, we study the stability problem of a star-shaped network of
elastic strings with a local Kelvin-Voigt damping. Under the assumption that
the damping coefficients have some singularities near the transmission point,
we prove that the semigroup corresponding to the system is polynomially stable
and the decay rates depends on the speed of the degeneracy. This result
improves the decay rate of the semigroup associated to the system on an earlier
result of Z.~Liu and Q.~Zhang in \cite{LZ} involving the wave equation with
local Kelvin-Voigt damping and non-smooth coefficient at interface.
|
2006.14949v1
|
2020-11-06
|
A generalized finite element method for the strongly damped wave equation with rapidly varying data
|
We propose a generalized finite element method for the strongly damped wave
equation with highly varying coefficients. The proposed method is based on the
localized orthogonal decomposition introduced and is designed to handle
independent variations in both the damping and the wave propagation speed
respectively. The method does so by automatically correcting for the damping in
the transient phase and for the propagation speed in the steady state phase.
Convergence of optimal order is proven in $L_2(H^1)$-norm, independent of the
derivatives of the coefficients. We present numerical examples that confirm the
theoretical findings.
|
2011.03311v1
|
2020-12-28
|
Nonlinear modal analysis of nonconservative systems: Extension of the periodic motion concept
|
As the motions of nonconservative autonomous systems are typically not
periodic, the definition of nonlinear modes as periodic motions cannot be
applied in the classical sense. In this paper, it is proposed 'make the motions
periodic' by introducing an additional damping term of appropriate sign and
magnitude. It is shown that this generalized definition is particularly suited
to reflect the periodic vibration behavior induced by harmonic external forcing
or negative linear damping. In a large range, the energy dependence of modal
frequency, damping ratio and stability is reproduced well. The limitation to
isolated or weakly-damped modes is discussed.
|
2101.00949v1
|
2021-04-12
|
Lp-asymptotic stability of 1D damped wave equations with localized and linear damping
|
In this paper, we study the $L^p$-asymptotic stability of the one-dimensional
linear damped wave equation with Dirichlet boundary conditions in $[0,1]$, with
$p\in (1,\infty)$. The damping term is assumed to be linear and localized to an
arbitrary open sub-interval of $[0,1]$. We prove that the semi-group
$(S_p(t))_{t\geq 0}$ associated with the previous equation is well-posed and
exponentially stable. The proof relies on the multiplier method and depends on
whether $p\geq 2$ or $1<p<2$.
|
2104.05679v1
|
2021-05-13
|
Sharp Polynomial Decay for Waves Damped from the Boundary in Cylindrical Waveguides
|
We study the decay of global energy for the wave equation with H\"older
continuous damping placed on the $C^{1,1}$-boundary of compact and non-compact
waveguides with star-shaped cross-sections. We show there is sharp
$t^{-1/2}$-decay when the damping is uniformly bounded from below on the
cylindrical wall of product cylinders where the Geometric Control Condition is
violated. On non-product cylinders, we also show that there is $t^{-1/3}$-decay
when the damping is uniformly bounded from below on the cylindrical wall.
|
2105.06566v1
|
2021-06-02
|
Stabilisation of the generalised Rao-Nakra beam by partial viscous damping
|
In this paper, we consider the stabilization of the generalized Rao-Nakra
beam equation, which consists of four wave equations for the longitudinal
displacements and the shear angle of the top and bottom layers and one
Euler-Bernoulli beam equation for the transversal displacement. Dissipative
mechanism are provided through viscous damping for two displacements. The
location of the viscous damping are divided into two groups, characterized by
whether both of the top and bottom layers are directly damped or otherwise.
Each group consists of three cases. We obtain the necessary and sufficient
conditions for the cases in group two to be strongly stable. Furthermore,
polynomial stability of certain orders are proved. The cases in group one are
left for future study
|
2106.01189v1
|
2021-09-01
|
Vibration damping platform for cavity quantum-electrodynamics experiments
|
We present a mechanical platform with enhanced vibration damping properties
for cavity quantum-electrodynamics experiments. It is based on a composite
design that combines a soft, vibration-damping core with a rigid shell
maintaining optical alignment. It passively damps the vibrations generated by
piezoelectric actuators controlling the mirror positions. The mechanical
resonances of the platform, which lead to a length change of the cavity are
efficiently suppressed up to 100 kHz. Our platform is ultra-high vacuum
compatible and can be used in most applications, in particular where long
cavities and optical access to the cavity center are required.
|
2109.00439v1
|
2021-09-05
|
Existence of a generalized polynomial attractor for the wave equation with nonlocal weak damping, anti-damping and critical nonlinearity
|
In this paper, we first establish a criterion based on contractive function
for the existence of polynomial attractors. This criterion only involves some
rather weak compactness associated with the repeated limit inferior and
requires no compactness, which makes it suitable for critical cases. Then by
this abstract theorem, we verify the existence of a polynomial attractor and
estimate its attractive speed for the wave equation with nonlocal weak damping,
anti-damping and critical nonlinearity.
|
2109.01967v2
|
2021-11-29
|
Stabilization of coupled wave equations with viscous damping on cylindrical and non-regular domains: Cases without the geometric control condition
|
In this paper, we investigate the direct and indirect stability of locally
coupled wave equations with local viscous damping on cylindrical and
non-regular domains without any geometric control condition. If only one
equation is damped, we prove that the energy of our system decays polynomially
with the rate $t^{-\frac{1}{2}}$ if the two waves have the same speed of
propagation, and with rate $t^{-\frac{1}{3}}$ if the two waves do not propagate
at the same speed. Otherwise, in case of two damped equations, we prove a
polynomial energy decay rate of order $t^{-1}$.
|
2111.14554v1
|
2022-01-25
|
Linear pair creation damping of high frequency plasma oscillation
|
We have studied the linear dispersion relation for Langmuir waves in plasmas
of very high density, based on the Dirac-Heisenberg-Wigner formalism. The
vacuum contribution to the physical observables leads to ultra-violet
divergences, that are removed by a charge renormalization. The remaining vacuum
contribution is small, and is in agreement with previously derived expressions
for the time-dependent vacuum polarization. The main new feature of the theory
is a damping mechanism similar to Landau damping, but where the plasmon energy
give rise to creation of electron-positron pairs. The dependence of the damping
rate (pair-creation rate) on wave-number, temperature, and density is analyzed.
Finally, the analytical results of linearized theory are compared.
|
2201.10370v1
|
2022-03-13
|
Continuum damping of topologically-protected edge modes at the boundary of a magnetized plasma
|
Recent extension of the topological ideas to continuous systems with broken
time-reversal symmetry, such as magnetized plasmas, provides new insights into
the nature of scattering-free topologically-protected surface plasma waves
(TSPWs). We demonstrate a unique characteristic of TSPWs propagating above the
electron cyclotron frequency: their collisionless damping via coupling to the
continuum of resonant modes localized inside a smooth plasma-vacuum interface.
Damped TSPWs retain their unidirectional nature and robustness against
backscattering. When sheared magnetic field creates a boundary between damped
and undamped TSPWs, the two refract into each other without reflections
|
2203.06693v2
|
2022-04-21
|
On scattering and damping of Toroidal Alfven eigenmode by drift wave turbulence
|
We demonstrate analytically that, in toroidal plasmas, scattering by drift
wave turbulence could lead to appreciable damping of toroidal Alfven eigenmodes
via generation of short-wavelength electron Landau damped kinetic Alfven waves.
A corresponding analytic expression of the damping rate is derived, and found
to be, typically, comparable to the linear drive by energetic particles. The
implications of this novel mechanism on the transport and heating processes in
burning plasmas are also discussed.
|
2204.09876v1
|
2022-10-30
|
Intrinsic polynomial squeezing for Balakrishnan-Taylor beam models
|
We explore the energy decay properties related to a model in extensible beams
with the so-called energy damping. We investigate the influence of the
nonloncal damping coefficient in the stability of the model. We prove, for the
first time, that the corresponding energy functional is squeezed by
polynomial-like functions involving the power of the damping coefficient, which
arises intrinsically from the Balakrishnan-Taylor beam models. As a
consequence, it is shown that such models with nonlocal energy damping are
never exponentially stable in its essence.
|
2210.16931v1
|
2023-02-13
|
Damping of gravitational waves in f(R) gravity
|
We study the damping of $f(R)$ gravitational waves by matter in flat
spacetime and in expanding universe. In the former case, we find that the
Landau damping of scalar mode in $f(R)$ theory exists, while that of the tensor
mode in general relativity does not; we also present the viscosity coefficients
and dispersion relations of the two modes. In the later case, we investigate
the evolution of tensor and scalar modes in Friedmann-Robertson-Walker (FRW)
cosmology with a matter distribution; by considering the case of $f(R)=R+\al
R^2$, we analysis the influence of parameter $\al$ on wave damping,and put
restrictions on its magnitude.
|
2302.06402v2
|
2023-07-11
|
Global smooth solution for the 3D generalized tropical climate model with partial viscosity and damping
|
The three-dimensional generalized tropical climate model with partial
viscosity and damping is considered in this paper. Global well-posedness of
solutions of the three-dimensional generalized tropical climate model with
partial viscosity and damping is proved for $\alpha\geq\frac{3}{2}$ and
$\beta\geq4$. Global smooth solution of the three-dimensional generalized
tropical climate model with partial viscosity and damping is proved in
$H^s(\mathbb R^3)$ $(s>2)$ for $\alpha\geq\frac{3}{2}$ and $4\leq\beta\leq5$.
|
2307.05145v3
|
2023-08-07
|
Reconstruction of the initial data from the solutions of damped wave equations
|
In this paper, we consider two types of damped wave equations: the weakly
damped equation and the strongly damped equation and show that the initial
velocity from the solution on the unit sphere. This inverse problem is related
to Photoacoustic Tomography (PAT), a hybrid medical imaging technique. PAT is
based on generating acoustic waves inside of an object of interest and one of
the mathematical problem in PAT is reconstructing the initial velocity from the
solution of the wave equation measured on the outside of object. Using the
spherical harmonics and spectral theorem, we demonstrate a way to recover the
initial velocity.
|
2308.03362v1
|
2023-09-26
|
Sharp conditions for exponential and non-exponential uniform stabilization of the time dependent damped wave equation
|
It is classical that uniform stabilization of solutions to the damped wave
equation is equivalent to the geometric control condition The author previously
showed that, when the damping depends on time, a generalization of the
geometric control condition implies uniform stabilization at an exponential
rate. In this paper, it is shown that this generalization of the geometric
control condition is necessary for uniform stabilization at an exponential
rate. Furthermore, when the damping does not satisfy this generalization, and
has some additional structure, upper and lower bounds on non-exponential
uniform stabilization are computed. The qualitative behavior of these upper and
lower bounds coincide.
|
2309.15005v1
|
2023-10-19
|
The damped focusing cubic wave equation on a bounded domain
|
For the focusing cubic wave equation on a compact Riemannian manifold of
dimension $3$, the dichotomy between global existence and blow-up for solutions
starting below the energy of the ground state is known since the work of Payne
and Sattinger. In the case of a damped equation, we prove that the dichotomy
between global existence and blow-up still holds. In particular, the damping
does not prevent blow-up. Assuming that the damping satisfies the geometric
control condition, we then prove that any global solution converges to a
stationary solution along a time sequence, and that global solutions below the
energy of the ground state can be stabilised, adapting the proof of a similar
result in the defocusing case.
|
2310.12644v2
|
2024-04-03
|
Damping Reveals Hidden Dimensions in Elastic Metastructures Through Induced Transparency
|
Damping typically results in attenuation of vibrations and elastic wave
propagation in mechanical systems. Contrary to this conventional understanding,
we demonstrate experimentally and explain theoretically the revival of an
elastic wave transmitted through a periodic metastructure when a weak
non-Hermitian defect (damping mechanism) induces violation of time-reversal
symmetry. Damping alters the nature of the system's resonant modes, instigating
interference in the scattering field. This leads to transmission revival,
revealing the presence of hidden modes which are otherwise masked by the
symmetry. Our findings offer an innovative approach for designing
dissipation-driven switches and controllers and non-destructive structural
health monitoring systems.
|
2404.02979v1
|
2000-03-16
|
Non-existence of radiation damping of gravitational motions
|
A rigorous, non-perturbative proof that there is no radiation damping of
gravitational motions.
|
0003230v1
|
2006-07-14
|
Lagrangian description of the radiation damping
|
We present a Lagrangian formalism to the dissipative system of a charge
interacting with its own radiation field, which gives rise to the radiation
damping \cite{Heitler}, by the indirect representation doubling the phase-space
dimensions.
|
0607370v1
|
1994-05-17
|
Damping Rate of a Hard Photon in a Relativistic Plasma
|
The damping rate of a hard photon in a hot relativistic QED and QCD plasma is
calculated using the resummation technique by Braaten and Pisarski.
|
9405309v1
|
1998-04-08
|
Evidence for xi- and t-dependent damping of the Pomeron Flux in the proton
|
We show that a triple-Regge parametrization of inclusive single diffraction
agrees with the data in the following two domains: (a) xi > 0.03 at all t, (b)
|t| > 1 GeV^2 at all xi. Since the triple-Regge parametrization fails when
applied to the full xi-t range of the total single-diffractive cross section,
we conclude that damping occurs only at low-xi and low-|t|. We give a (``toy'')
parametrization of the damping factor, D(xi), valid at low-|t|, which describes
the diffractive differential cross-section (dsig/dt) data at the ISR and
roughly accounts for the observed s-dependence of diffractive total
cross-section up to Tevatron energies. However, an effective damping factor
calculated for the CDF fitted function for dsig/dxidt at sqrt(s} = 1800 GeV and
|t| = 0.05 GeV^2, suggests that, at fixed-xi, damping increases as s increases.
We conjecture that, in the regions where the triple-Regge formalism describes
the data and there is no evidence of damping, factorization is valid and the
Pomeron-flux-factor may be universal. With the assumption that the observed
damping is due to multi-Pomeron exchange, our results imply that the recent UA8
demonstration that the effective Pomeron trajectory flattens for |t| > 1 GeV$^2
is evidence for the onset of the perturbative 2-gluon pomeron. Our damping
results may also shed some light on the self-consistency of recent measurements
of hard-diffractive jet production cross sections in the UA8, CDF and ZEUS
experiments.
|
9804257v1
|
2001-11-27
|
On the uniphase steady solutions of the nonlinear damped wave equation
|
We study the steady uniphase and multiphase solutions of the discretized
nonlinear damped wave equation.Conditions for the stability abd instability of
the steady solutions are given;in the instability case the linear stable and
unstable associated manifolds are described.
|
0111281v1
|
2006-09-05
|
Damping estimates for oscillatory integral operators with finite type singularities
|
We derive damping estimates and asymptotics of $L^p$ operator norms for
oscillatory integral operators with finite type singularities. The methods are
based on incorporating finite type conditions into $L^2$ almost orthogonality
technique of Cotlar-Stein.
|
0609145v1
|
2002-02-19
|
On "the authentic damping mechanism" of the phonon damping model. II
|
This article continues a discussion raised in previous publications (LANL
preprint server, nucl-th/0202006 and nucl-th/0202020). I try to convince my
opponents that general arguments are not "my case" and may be applied to their
model.
|
0202058v1
|
1996-12-27
|
Coherent and trajectory-coherent states of a damped harmonic oscillator
|
In this paper we construct the coherent and trajectory-coherent states of a
damped harmonic oscillator. We investigate the properties of this states.
|
9612051v2
|
2003-05-21
|
Probability representation of kinetic equation for open quantum system
|
The tomographic probability distribution is used to decribe the kinetic
equations for open quantum systems. Damped oscillator is studied. Purity
parameter evolution for different damping regime is considered.
|
0305119v1
|
2007-08-09
|
The resonant damping of fast magnetohydrodynamic oscillations in a system of two coronal slabs
|
Observations of transversal coronal loop oscillations very often show the
excitation and damping of oscillations in groups of coronal loops rather than
in individual and isolated structures. We present results on the oscillatory
properties (periods, damping rates, and spatial distribution of perturbations)
for resonantly damped oscillations in a system of two inhomogeneous coronal
slabs and compare them to the properties found in single slab loop models. A
system of two identical coronal loops is modeled, in Cartesian geometry, as
being composed by two density enhancements. The linear magnetohydrodynamic
(MHD) wave equations for oblique propagation of waves are solved and the
damping of the different solutions, due to the transversal inhomogeneity of the
density profile, is computed. The physics of the obtained results is analyzed
by an examination of the perturbed physical variables. We find that, due to the
interaction between the loops, the normal modes of oscillation present in a
single slab split into symmetric and antisymmetric oscillations when a system
of two identical slabs is considered. The frequencies of these solutions may
differ from the single slab results when the distance between the loops is of
the order of a few slab widths. Oblique propagation of waves weakens this
interaction, since solutions become more confined to the edges of the slabs.
The damping is strong for surface-like oscillations, while sausage body-like
solutions are unaffected. For some solutions, and small slab separations, the
damping in a system of two loops differs substantially from the damping of a
single loop.
|
0708.1251v1
|
2009-12-08
|
Exact Invariant Solutions for Generalized Invicid Burgers' Equation with Damping
|
In this work we study the Lie group analysis of a generalized invicid
Burgers' equations with damping. Seven inequivalent classes of this generalized
equation were classified and many exact and transformed solutions were obtained
for each class.
|
0912.1631v1
|
2011-07-28
|
Creating quantum discord through local generalized amplitude damping
|
We show that two qubits initially in completely classical state can create
quantum discord through a local generalized amplitude damping channel, but high
temperature will impede the creating of quantum discord.
|
1107.5670v1
|
2011-09-06
|
Damping of Alfven waves in solar partially ionized plasmas: effect of neutral helium in multi-fluid approach
|
Chromospheric and prominence plasmas contain neutral atoms, which may change
the plasma dynamics through collision with ions. Most of the atoms are neutral
hydrogen, but a significant amount of neutral helium may also be present in the
plasma with a particular temperature. Damping of MHD waves due to ion collision
with neutral hydrogen is well studied, but the effects of neutral helium are
largely unknown. We aim to study the effect of neutral helium in the damping of
Alfven waves in solar partially ionized plasmas. We consider three-fluid
magnetohydrodynamic (MHD) approximation, where one component is
electron-proton-singly ionized helium and other two components are the neutral
hydrogen and neutral helium atoms. We derive the dispersion relation of linear
Alfven waves in isothermal and homogeneous plasma. Then we solve the dispersion
relation and derive the damping rates of Alfven waves for different plasma
parameters. The presence of neutral helium significantly enhances the damping
of Alfven waves compared to the damping due to neutral hydrogen at certain
values of plasma temperature (10000-40000 K) and ionization. Damping rates have
a peak near the ion-neutral collision frequency, but decrease for the higher
part of wave spectrum. Collision of ions with neutral helium atoms can be of
importance for the damping of Alfven waves in chromospheric spicules and in
prominence-corona transition regions.
|
1109.1154v1
|
2012-03-08
|
Damping rates of solar-like oscillations across the HR diagram. Theoretical calculations confronted to CoRoT and Kepler observations
|
Space-borne missions CoRoT and {\it Kepler} are providing a rich harvest of
high-quality constraints on solar-like pulsators. Among the seismic parameters,
mode damping rates remains poorly understood and thus barely used to infer
physical properties of stars. Nevertheless, thanks to CoRoT and {\it Kepler}
space-crafts it is now possible to measure damping rates for hundreds of
main-sequence and thousands of red-giant stars with an unprecedented precision.
By using a non-adiabatic pulsation code including a time-dependent convection
treatment, we compute damping rates for stellar models representative for
solar-like pulsators from the main-sequence to the red-giant phase. This allows
us to reproduce the observations of both CoRoT and {\it Kepler}, which
validates our modeling of mode damping rates and thus the underlying physical
mechanisms included in the modeling. Actually, by considering the perturbations
of turbulent pressure and entropy (including perturbation of the dissipation
rate of turbulent energy into heat) by the oscillation in our computation, we
succeed in reproducing the observed relation between damping rates and
effective temperature.
Moreover, we discuss the physical reasons for mode damping rates to scale
with effective temperature, as observationally exhibited. Finally, this opens
the way for the use of mode damping rates to probe turbulent convection in
solar-like stars.
|
1203.1737v2
|
2012-09-14
|
Semi-linear structural damped waves
|
We study the global existence of small data solutions for Cauchy problem for
the semi-linear structural damped wave equation with source term.
|
1209.3204v2
|
2012-10-25
|
Decay rates for the damped wave equation on the torus
|
We address the decay rates of the energy for the damped wave equation when
the damping coefficient $b$ does not satisfy the Geometric Control Condition
(GCC). First, we give a link with the controllability of the associated
Schr\"odinger equation. We prove in an abstract setting that the observability
of the Schr\"odinger group implies that the semigroup associated to the damped
wave equation decays at rate $1/\sqrt{t}$ (which is a stronger rate than the
general logarithmic one predicted by the Lebeau Theorem).
Second, we focus on the 2-dimensional torus. We prove that the best decay one
can expect is $1/t$, as soon as the damping region does not satisfy GCC.
Conversely, for smooth damping coefficients $b$, we show that the semigroup
decays at rate $1/t^{1-\eps}$, for all $\eps >0$. The proof relies on a second
microlocalization around trapped directions, and resolvent estimates.
In the case where the damping coefficient is a characteristic function of a
strip (hence discontinuous), St\'{e}phane Nonnenmacher computes in an appendix
part of the spectrum of the associated damped wave operator, proving that the
semigroup cannot decay faster than $1/t^{2/3}$. In particular, our study shows
that the decay rate highly depends on the way $b$ vanishes.
|
1210.6879v1
|
2014-02-25
|
Asymptotic Profiles for wave equations with strong damping
|
We consider the Cauchy problem in ${\bf R}^{n}$ for strongly damped wave
equations. We derive asymptotic profiles of these solutions with weighted
$L^{1,1}({\bf R}^{n})$ data by using a method introduced in [10].
|
1402.6073v1
|
2014-04-17
|
Exponential stability of the wave equation with memory and time delay
|
We study the asymptotic behaviour of the wave equation with viscoelastic
damping in presence of a time-delayed damping. We prove exponential stability
if the amplitude of the time delay term is small enough.
|
1404.4456v1
|
2014-08-30
|
Marginalizing over the PageRank Damping Factor
|
In this note, we show how to marginalize over the damping parameter of the
PageRank equation so as to obtain a parameter-free version known as TotalRank.
Our discussion is meant as a reference and intended to provide a guided tour
towards an interesting result that has applications in information retrieval
and classification.
|
1409.0104v1
|
2014-10-29
|
Blowup for the nonlinear Schrödinger equation with an inhomogeneous damping term in the $L^2$ critical case
|
We consider the nonlinear Schr\"odinger equation with $L^2$-critical exponent
and an inhomogeneous damping term. By using the tools developed by Merle and
Raphael, we prove the existence of blowup phenomena in the energy space
$H^1(\mathbb{R})$.
|
1410.8011v1
|
2014-11-28
|
Landau damping
|
Landau damping is calculated using real variables, clarifying the physical
mechanism.
|
1411.7793v1
|
2014-12-16
|
Linear Collisionless Landau Damping in Hilbert Space
|
The equivalence between the Laplace transform [Landau L., J. Phys. USSR, 10
(1946), 25] and Hermite transform [Zocco and Schekochihin, Phys. Plasmas, 18,
102309 (2011)] solutions of the linear collisionless Landau damping problem is
proven.
|
1412.4913v1
|
2015-07-08
|
Calculation of continuum damping of Alfvén eigenmodes in 2D and 3D cases
|
In ideal MHD, shear Alfv\'{e}n eigenmodes may experience dissipationless
damping due to resonant interaction with the shear Alfv\'{e}n continuum. This
continuum damping can make a significant contribution to the overall
growth/decay rate of shear Alfv\'{e}n eigenmodes, with consequent implications
for fast ion transport. One method for calculating continuum damping is to
solve the MHD eigenvalue problem over a suitable contour in the complex plane,
thereby satisfying the causality condition. Such an approach can be implemented
in three-dimensional ideal MHD codes which use the Galerkin method. Analytic
functions can be fitted to numerical data for equilibrium quantities in order
to determine the value of these quantities along the complex contour. This
approach requires less resolution than the established technique of calculating
damping as resistivity vanishes and is thus more computationally efficient. The
complex contour method has been applied to the three-dimensional finite element
ideal MHD code CKA . In this paper we discuss the application of the complex
contour technique to calculate the continuum damping of global modes in tokamak
as well as torsatron, W7X and H1-NF stellarator cases. To the authors'
knowledge these stellarator calculations represent the first calculation of
continuum damping for eigenmodes in fully three-dimensional equilibria. The
continuum damping of global modes in W7X and H1-NF stellarator configurations
investigated is found to depend sensitively on coupling to numerous poloidal
and toroidal harmonics.
|
1507.02072v1
|
2015-08-16
|
Jeans instability and hydrodynamic roots of Landau damping
|
Landau damping of Langmuir waves is shown to have hydrodynamic roots, and, in
principle, might have been predicted (along with Langmuir waves) several
decades earlier, soon after Jeans (1902) paper appeared.
|
1508.03809v1
|
2015-12-07
|
Damped and zero-damped quasinormal modes of charged, nearly extremal black holes
|
Despite recent progress, the complete understanding of the perturbations of
charged, rotating black holes as described by the Kerr-Newman metric remains an
open and fundamental problem in relativity. In this study, we explore the
existence of families of quasinormal modes of Kerr-Newman black holes whose
decay rates limit to zero at extremality, called zero-damped modes in past
studies. We review the nearly extremal and WKB approximation methods for
spin-weighted scalar fields (governed by the Dudley-Finley equation) and give
an accounting of the regimes where scalar zero-damped and damped modes exist.
Using Leaver's continued fraction method, we verify that these approximations
give accurate predictions for the frequencies in their regimes of validity. In
the nonrotating limit, we argue that gravito-electromagnetic perturbations of
nearly extremal Reissner-Nordstr\"{o}m black holes have zero-damped modes in
addition to the well-known spectrum of damped modes. We provide an analytic
formula for the frequencies of these modes, verify their existence using a
numerical search, and demonstrate the accuracy of our formula. These results,
along with recent numerical studies, point to the existence of a simple
universal equation for the frequencies of zero-damped gravito-electromagnetic
modes of Kerr-Newman black holes, whose precise form remains an open question.
|
1512.02247v2
|
2016-09-24
|
Recovering the damping rates of cyclotron damped plasma waves from simulation data
|
Plasma waves with frequencies close to the particular gyrofrequencies of the
charged particles in the plasma lose energy due to cyclotron damping. We
briefly discuss the gyro-resonance of low frequency plasma waves and ions
particularly with regard to particle-in-cell (PiC) simulations. A setup is
outlined which uses artificially excited waves in the damped regime of the wave
mode's dispersion relation to track the damping of the wave's electromagnetic
fields. Extracting the damping rate directly from the field data in real or
Fourier space is an intricate and non-trivial task. We therefore present a
simple method of obtaining the damping rate {\Gamma} from the simulation data.
This method is described in detail, focusing on a step-by-step explanation of
the course of actions. In a first application to a test simulation we find that
the damping rates obtained from this simulation generally are in good agreement
with theoretical predictions. We then compare the results of one-, two- and
three-dimensional simulation setups and simulations with different physical
parameter sets.
|
1609.07646v2
|
2016-10-25
|
Quadratically damped oscillators with non-linear restoring force
|
In this paper we qualitatively analyse quadratically damped oscillators with
non-linear restoring force. In particular, we obtain Hamiltonian structure and
analytical form of the energy functions.
|
1610.07821v1
|
2016-11-24
|
Longitudinal Stability Study for the FACET-II e+ Damping Ring
|
This is an initial study of the longitudinal, single-bunch stability in the
proposed FACET-II e+ damping ring. It is preliminary because many vacuum
chamber objects of the ring have not yet been designed.
|
1611.08042v1
|
2017-08-25
|
On the entropy gain under the action of amplitude damping channel on qutrit
|
After realising qutrit in the form of bipartite system we estimate from below
the entropy gain under the action of the amplitude damping channel.
|
1708.07710v1
|
2017-10-24
|
Demonstration of a switchable damping system to allow low-noise operation of high-Q low-mass suspension systems
|
Low mass suspension systems with high-Q pendulum stages are used to enable
quantum radiation pressure noise limited experiments. Utilising multiple
pendulum stages with vertical blade springs and materials with high quality
factors provides attenuation of seismic and thermal noise, however damping of
these high-Q pendulum systems in multiple degrees of freedom is essential for
practical implementation. Viscous damping such as eddy-current damping can be
employed but introduces displacement noise from force noise due to thermal
fluctuations in the damping system. In this paper we demonstrate a passive
damping system with adjustable damping strength as a solution for this problem
that can be used for low mass suspension systems without adding additional
displacement noise in science mode. We show a reduction of the damping factor
by a factor of 8 on a test suspension and provide a general optimisation for
this system.
|
1710.08698v2
|
2017-11-30
|
Asymptotic for a second order evolution equation with vanishing damping term and Tikhonov regularization
|
We investigate the asymptotic behavior of solutions to a second order
differential equation with vanishing damping term, convex potential and
regularizing Tikhonov term.
|
1711.11241v1
|
2018-10-04
|
Damping of slow surface sausage modes in photospheric waveguides
|
There has been considerable interest in sausage modes in photospheric
waveguides like pores and sunspots, and slow surface sausage modes (SSSMs) have
been suggested to damp ufficiently rapidly to account for chromospheric
heating. Working in the framework of linear resistive magnetohydrodynamics, we
examine how efficient electric resistivity and resonant absorption in the cusp
continuum can be for damping SSSMs in a photospheric waveguide with equilibrium
parameters compatible with recent measurements of a photospheric pore. For
SSSMs with the measured wavelength, we find that the damping rate due to the
cusp resonance is substantially less strong than theoretically expected with
the thin-boundary approximation. The damping-time-to-period ratio ($\tau/P$) we
derive for standing modes, equivalent to the damping-length-to-wavelength ratio
for propagating modes given the extremely weak dispersion, can reach only $\sim
180$. However, the accepted values for electric resistivity ($\eta$) correspond
to a regime where both the cusp resonance and resistivity play a role. The
values for $\tau/P$ attained at the largest allowed $\eta$ may reach $\sim 30$.
We conclude that electric resistivity can be considerably more efficient than
the cusp resonance for damping SSSMs in the pore in question, and it needs to
be incorporated into future studies on the damping of SSSMs in photospheric
waveguides in general.
|
1810.02051v1
|
2018-10-20
|
Landau Damping in a weakly collisional regime
|
In this paper, we consider the nonlinear Vlasov-Poisson equations in a weakly
collisional regime and study the linear Boltzmann collision operator. We prove
that Landau damping still occurs in this case.
|
1810.10955v1
|
2018-10-26
|
Energy regenerative damping in variable impedance actuators for long-term robotic deployment
|
Energy efficiency is a crucial issue towards longterm deployment of compliant
robots in the real world. In the context of variable impedance actuators
(VIAs), one of the main focuses has been on improving energy efficiency through
reduction of energy consumption. However, the harvesting of dissipated energy
in such systems remains under-explored. 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 a reduction in the range of damping
achievable. A physical implementation on a simple VIA mechanism is presented in
which the regenerative properties of the proposed module are characterised and
compared against theoretical predictions. To investigate the role of variable
regenerative damping in terms of energy efficiency of longterm operation,
experiments are reported in which the VIA equipped with the proposed damping
module performs sequential reaching to a series of stochastic targets. The
results indicate that the combination of variable stiffness and variable
regenerative damping is preferable to achieve the optimal trade-off between
task performance and energy efficiency. Use of the latter results in a 25%
performance improvement on overall performance metrics (incorporating reaching
accuracy, settling time, energy consumption and regeneration), over comparable
schemes where either stiffness or damping are fixed.
|
1810.11246v3
|
2018-12-26
|
A class large solution of the 2D MHD equations with velocity and magnetic damping
|
In this paper, we construct a class global large solution to the
two-dimensional MHD equations with damp terms in the nonhomogeneous Sobolev
framework.
|
1812.10310v2
|
2019-02-19
|
Linear inviscid damping near monotone shear flows
|
We give an elementary proof of sharp decay rates and the linear inviscid
damping near monotone shear flow in a periodic channel, first obtained in [14].
We shall also obtain the precise asymptotics of the solutions, measured in the
space $L^{\infty}$.
|
1902.06849v1
|
2019-04-18
|
Damping of Propagating Kink Waves in the Solar Corona
|
Alfv\'enic waves have gained renewed interest since the existence of
ubiquitous propagating kink waves were discovered in the corona. {It has long
been suggested that Alfv\'enic} waves play an important role in coronal heating
and the acceleration of the solar wind. To this effect, it is imperative to
understand the mechanisms that enable their energy to be transferred to the
plasma. Mode conversion via resonant absorption is believed to be one of the
main mechanisms for kink wave damping, and is considered to play a key role in
the process of energy transfer. This study examines the damping of propagating
kink waves in quiescent coronal loops using the Coronal Multi-channel
Polarimeter (CoMP). A coherence-based method is used to track the Doppler
velocity signal of the waves, enabling us to investigate the spatial evolution
of velocity perturbations. The power ratio of outward to inward propagating
waves is used to estimate the associated damping lengths and quality factors.
To enable accurate estimates of these quantities, {we provide the first
derivation of a likelihood function suitable for fitting models to the ratio of
two power spectra obtained from discrete Fourier transforms. Maximum likelihood
estimation is used to fit an exponential damping model to the observed
variation in power ratio as a function of frequency.} We confirm earlier
indications that propagating kink waves are undergoing frequency dependent
damping. Additionally, we find that the rate of damping decreases, or
equivalently the damping length increases, for longer coronal loops that reach
higher in the corona.
|
1904.08834v1
|
2019-05-19
|
Finite time blow up for wave equations with strong damping in an exterior domain
|
We consider the initial boundary value problem in exterior domain for
strongly damped wave equations with power type nonlinearity |u|^p. We will
establish blow-up results under some conditions on the initial data and the
exponent p.
|
1905.07782v1
|
2019-12-15
|
A result for nonexistence of global solutions to semi-linear structural damped wave model
|
Main goal of this note is to give a result for nonexistence of global
solutions and determine the critical exponent as well to a semi-linear
structurally damped wave equation.
|
1912.07066v1
|
2020-09-23
|
Remark on the exponential decay of the solutions of the damped wave equation
|
A condition which guaranties the exponential decay of the solutions of the
initial-boundary value problem for the damped wave equation is proved. A method
for the effective computability of the coefficient of exponential decay is also
presented.
|
2009.11244v1
|
2020-10-13
|
The Impact of Damping in Second-Order Dynamical Systems with Applications to Power Grid Stability
|
We consider a broad class of second-order dynamical systems and study the
impact of damping as a system parameter on the stability, hyperbolicity, and
bifurcation in such systems. We prove a monotonic effect of damping on the
hyperbolicity of the equilibrium points of the corresponding first-order
system. This provides a rigorous formulation and theoretical justification for
the intuitive notion that damping increases stability. To establish this
result, we prove a matrix perturbation result for complex symmetric matrices
with positive semidefinite perturbations to their imaginary parts, which may be
of independent interest. Furthermore, we establish necessary and sufficient
conditions for the breakdown of hyperbolicity of the first-order system under
damping variations in terms of observability of a pair of matrices relating
damping, inertia, and Jacobian matrices, and propose sufficient conditions for
Hopf bifurcation resulting from such hyperbolicity breakdown. The developed
theory has significant applications in the stability of electric power systems,
which are one of the most complex and important engineering systems. In
particular, we characterize the impact of damping on the hyperbolicity of the
swing equation model which is the fundamental dynamical model of power systems,
and demonstrate Hopf bifurcations resulting from damping variations.
|
2010.06662v2
|
2020-10-26
|
Linear Predictive Coding for Acute Stress Prediction from Computer Mouse Movements
|
Prior work demonstrated the potential of using the Linear Predictive Coding
(LPC) filter to approximate muscle stiffness and damping from computer mouse
movements to predict acute stress levels of users. Theoretically, muscle
stiffness and damping in the arm can be estimated using a mass-spring-damper
(MSD) biomechanical model. However, the damping frequency (i.e., stiffness) and
damping ratio values derived using LPC were not yet compared with those from a
theoretical MSD model. This work demonstrates that the damping frequency and
damping ratio from LPC are significantly correlated with those from an MSD
model, thus confirming the validity of using LPC to infer muscle stiffness and
damping. We also compare the stress level binary classification performance
using the values from LPC and MSD with each other and with neural network-based
baselines. We found comparable performance across all conditions demonstrating
LPC and MSD model-based stress prediction efficacy, especially for longer mouse
trajectories. Clinical relevance: This work demonstrates the validity of the
LPC filter to approximate muscle stiffness and damping and predict acute stress
from computer mouse movements.
|
2010.13836v3
|
2020-11-01
|
Sharp dimension estimates of the attractor of the damped 2D Euler-Bardina equations
|
We prove existence of the global attractor of the damped and driven 2D
Euler--Bardina equations on the torus and give an explicit two-sided estimate
of its dimension that is sharp as $\alpha\to0^+$.
|
2011.00607v1
|
2021-03-30
|
Strong solution of 3D-NSE with exponential damping
|
In this paper we prove the existence and uniqueness of strong solution of the
incompressible Navier-Stokes equations with damping $\alpha
(e^{\beta|u|^2}-1)u$.
|
2103.16707v1
|
2021-06-22
|
Choice of Damping Coefficient in Langevin Dynamics
|
This article considers the application of Langevin dynamics to sampling and
investigates how to choose the damping parameter in Langevin dynamics for the
purpose of maximizing thoroughness of sampling. Also, it considers the
computation of measures of sampling thoroughness.
|
2106.11597v1
|
2021-09-27
|
Damping transition in an open generalized Aubry-André-Harper model
|
We study the damping dynamics of the single-particle correlation for an open
system under periodic and aperiodic order, which is dominated by the Lindblad
master equation. In the absence of the aperiodic order, the Liouvillian
superoperator exhibits the non-Hermitian skin effect, which leads to
unidirectional damping dynamics, dubbed as "chiral damping". Due to the
non-Hermitian skin effect, the damping dynamics is boundary sensitive: The
long-time damping of such open systems is algebraic under periodic boundary
conditions but exponential under open boundary conditions. We reveal the phase
transition with the inclusion of the hopping amplitude modulation. By using the
spectral topology and a finite-size scaling analysis in the commensurate case,
we show there exists a phase transition of the skin effect with non-Bloch
anti-parity-time symmetry breaking. For the incommensurate case, we find richer
phases with the coexistence of the non-Hermitian skin effect and the Anderson
localization, which are separated by a generalized mobility edge. We reveal the
transition of the damping dynamics as a consequence of the phase transition.
Furthermore, we propose a possible scheme with ultracold atoms in a dissipative
momentum lattice to realize and detect the damping dynamics.
|
2109.12958v2
|
2022-01-20
|
Long Time Decay of Leray Solution of 3D-NSE With Exponential Damping
|
We study the uniqueness, the continuity in $L^2$ and the large time decay for
the Leray solutions of the $3D$ incompressible Navier-Stokes equations with
nonlinear exponential damping term $a (e^{b |u|^{\bf 4}}-1)u$, ($a,b>0$).
|
2201.08292v1
|
2023-03-20
|
Nonlinear Damping and Field-aligned Flows of Propagating Shear Alfvén Waves with Braginskii Viscosity
|
Braginskii MHD provides a more accurate description of many plasma
environments than classical MHD since it actively treats the stress tensor
using a closure derived from physical principles. Stress tensor effects
nonetheless remain relatively unexplored for solar MHD phenomena, especially in
nonlinear regimes. This paper analytically examines nonlinear damping and
longitudinal flows of propagating shear Alfv\'en waves. Most previous studies
of MHD waves in Braginskii MHD considered the strict linear limit of vanishing
wave perturbations. We show that those former linear results only apply to
Alfv\'en wave amplitudes in the corona that are so small as to be of little
interest, typically a wave energy less than $10^{-11}$ times the energy of the
background magnetic field. For observed wave amplitudes, the Braginskii viscous
dissipation of coronal Alfv\'en waves is nonlinear and a factor around $10^9$
stronger than predicted by the linear theory. Furthermore, the dominant damping
occurs through the parallel viscosity coefficient $\eta_0$, rather than the
perpendicular viscosity coefficient $\eta_2$ in the linearized solution. This
paper develops the nonlinear theory, showing that the wave energy density
decays with an envelope $(1+z/L_d)^{-1}$. The damping length $L_d$ exhibits an
optimal damping solution, beyond which greater viscosity leads to lower
dissipation as the viscous forces self-organise the longitudinal flow to
suppress damping. Although the nonlinear damping greatly exceeds the linear
damping, it remains negligible for many coronal applications.
|
2303.11128v1
|
2023-09-04
|
Joint Oscillation Damping and Inertia Provision Service for Converter-Interfaced Generation
|
As renewable generation becomes more prevalent, traditional power systems
dominated by synchronous generators are transitioning to systems dominated by
converter-interfaced generation. These devices, with their weaker damping
capabilities and lower inertia, compromise the system's ability to withstand
disturbances, pose a threat to system stability, and lead to oscillations and
poor frequency response performance. While some new converter-interfaced
generations are capable of providing superior damping and fast frequency
control, there is a lack of effective measures to incentivize manufacturers to
adopt them. To address this gap, this paper defines the joint oscillation
damping and inertia provision services at the system level, seeking to
encourage converter-interfaced generation to provide enhanced damping and fast
frequency response capabilities. Our approach is anchored in a novel convex
parametric formulation that combines oscillation mode and frequency stability
constraints. These constraints ensure a sufficient damping ratio for all
oscillation modes and maintain transient frequency trajectories within
acceptable limits. They are designed to integrate smoothly into various
operational and planning optimization frameworks. Using this formulation, we
introduce a joint service for oscillation damping and inertia provision based
on a cost-minimization problem. This facilitates the optimal allocation of
damping and virtual inertia to converters, achieving both small-signal
stability and frequency stability. Furthermore, we investigate the economic
effects of introducing this service into a new ancillary service market,
assessing its impact on system operations and cost-efficiency. Numerical tests
highlight the service's efficacy in ensuring both small-signal stability and
frequency stability, and offer insights into potential economic benefits.
|
2309.01321v1
|
2024-01-09
|
Damping Separation of Finite Open Systems in Gravity-Related Experiments in the Free Molecular Flow Regime
|
The residual gas damping of the test mass (TM) in the free molecular flow
regime is studied in the finite open systems for high-precision gravity-related
experiments. Through strict derivation, we separate the damping coefficients
for two finite open systems, i.e., the bi-plate system and the sensor core
system, into base damping and diffusion damping. This elucidates the
relationship between the free damping in the infinite gas volume and the
proximity damping in the constrained volume, unifies them into one microscopic
picture, and allows us to point out three pathways of energy dissipation in the
bi-plate gap. We also provide the conditions that need to be met to achieve
this separation. In applications, for space gravitational wave detection, our
results for the residual gas damping coefficient for the 4TM torsion balance
experiment is the closest one to the experimental and simulation data compared
to previous models. For the LISA mission, our estimation for residual gas
acceleration noise at the sensitive axis is consistent with the simulation
result, within about $5\%$ difference. In addition, in the test of the
gravitational inverse-square law, our results suggest that the constraint on
the distance between TM and the conducting membrane can be reduced by about
$28\%$.
|
2401.04808v1
|
2024-01-30
|
The Velocity-Space Signature of Transit-Time Damping
|
Transit-time damping (TTD) is a process in which the magnetic mirror force --
induced by the parallel gradient of magnetic field strength -- interacts with
resonant plasma particles, leading to the collisionless damping of
electromagnetic waves and the resulting energization of those particles through
the perpendicular component of the electric field, $E_\perp$. In this study, we
utilize the recently developed field-particle correlation technique to analyze
gyrokinetic simulation data. This method enables the identification of the
velocity-space structure of the TTD energy transfer rate between waves and
particles during the damping of plasma turbulence. Our analysis reveals a
unique bipolar pattern of energy transfer in velocity space characteristic of
TTD. By identifying this pattern, we provide clear evidence of TTD's
significant role in the damping of strong plasma turbulence. Additionally, we
compare the TTD signature with that of Landau damping (LD). Although they both
produce a bipolar pattern of phase-space energy density loss and gain about the
parallel resonant velocity of the \Alfvenic waves, they are mediated by
different forces and exhibit different behaviors as $v_\perp \to 0$. We also
explore how the dominant damping mechanism varies with ion plasma beta
$\beta_i$, showing that TTD dominates over LD for $\beta_i > 1$. This work
deepens our understanding of the role of TTD in the damping of weakly
collisional plasma turbulence and paves the way to seek the signature of TTD
using in situ spacecraft observations of turbulence in space plasmas.
|
2401.16697v1
|
2024-03-04
|
How long will the quasar UV/optical flickering be damped?
|
The UV/optical light curves of Active Galactic Nuclei (AGNs) are commonly
described by the Damped Random Walk (DRW) model. However, the physical
interpretation of the damping timescale, a key parameter in the DRW model,
remains unclear. Particularly, recent observations indicate a weak dependence
of the damping timescale upon both wavelength and accretion rate, clearly being
inconsistent with the accretion-disk theory. In this study, we investigate the
damping timescale in the framework of the Corona Heated Accretion disk
Reprocessing (CHAR) model, a physical model that describes AGN variability. We
find that while the CHAR model can reproduce the observed power spectral
densities of the 20-year light curves for 190 sources from \cite{Stone2022},
the observed damping timescale, as well as its weak dependence on wavelength,
can also be well recovered through fitting the mock light curves with DRW. We
further demonstrate that such weak dependence is artificial due to the effect
of inadequate durations of light curves, which leads to best-fitting damping
timescales lower than the intrinsic ones. After eliminating this effect, the
CHAR model indeed yields a strong dependence of the intrinsic damping timescale
on the bolometric luminosity and rest-frame wavelength. Our results highlight
the demand for sufficiently long light curves in AGN variability studies and
important applications of the CHAR model in such studies.
|
2403.01691v1
|
2024-04-08
|
On the Stability of swelling porous elastic soils with a single internal fractional damping
|
We study polynomial stability to the one-dimensional system in the linear
isothermal theory of swelling porous elastic soils with an internal fractional
damping. We establish an optimal decay result by frequency domain method
|
2404.05577v1
|
2005-04-18
|
Chemical Abundances in SFG and DLA
|
We investigate the chemical abundances of local star-forming galaxies which
cause Damped Lyman Alpha lines. A metallicity versus redshift diagram is
constructed, on which the chemical abundances of low-redshift star-forming
galaxy populations are compared with those of high-redshift Damped Lyman Alpha
systems. We disucss two types of experiments on individual star-forming
galaxies. In the first, the Damped Lyman Alpha line is created against an
internal ultraviolet light source generated by a star-forming cluster or a
supernova explosion. In the second, the Damped Lyman Alpha line is seen against
a background Quasar. The metallicities measured from ionized gas in the
star-forming regions, and neutral gas in the Damped Lyman Alpha systems, are
compared with one another on a case-by-case basis. We highlight the occurrence
of the star-forming galaxy/Quasar pair SBS 1543+593/HS 1543+5921, where the
emission- and absorption-line derived abundances give the same result. We argue
that we therefore can in principle, interpret Damped Lyman Alpha system
metallicities as an extension of star-forming galaxy metallicities to higher
redshifts, supporting that gas-rich galaxies had lower chemical abundances when
the were younger.
|
0504389v2
|
1997-05-08
|
Topological asymmetry in the damping-pairing contribution of electron-boson scattering
|
We make a harmonic analysis of the pairing and damping contribution of a
finite $k$ range isotropic electron-phonon (or other boson) scattering in an
anisotropic two-dimensional electronic system. We show that the pairing
contribution of the anisotropic part of the electronic system can be much
larger than its damping contribution enhancing significantly T_c. The higher is
the order of the harmonic of the electronic anisotropy, smaller is its damping
contribution and higher can be the asymmetry in its damping-pairing
contribution. This could explain the puzzle of a much broader quasiparticle
peak in the n-doped than in the p-doped cuprates, their smaller T_c's being
also attributed to larger damping effects.
|
9705071v1
|
2000-03-29
|
Damping of condensate collective modes due to equilibration with the non-condensate
|
We consider the damping of condensate collective modes at finite temperatures
arising from lack of equilibrium between the condensate and the non-condensate
atoms, an effect that is ignored in the usual discussion of the collisionless
region. As a first approximation, we ignore the dynamics of the thermal cloud.
Our calculations should be applicable to collective modes of the condensate
which are oscillating out-of-phase with the thermal cloud. We obtain a
generalized Stringari equation of motion for the condensate at finite
temperatures, which includes a damping term associated with the fact that the
condensate is not in diffusive equilibrium with the static thermal cloud. This
inter-component collisional damping of the condensate modes is comparable in
magnitude to the Landau damping considered in the recent literature.
|
0003481v5
|
2007-02-01
|
Adiabatic Domain Wall Motion and Landau-Lifshitz Damping
|
Recent theory and measurements of the velocity of current-driven domain walls
in magnetic nanowires have re-opened the unresolved question of whether
Landau-Lifshitz damping or Gilbert damping provides the more natural
description of dissipative magnetization dynamics. In this paper, we argue that
(as in the past) experiment cannot distinguish the two, but that
Landau-Lifshitz damping nevertheless provides the most physically sensible
interpretation of the equation of motion. From this perspective, (i) adiabatic
spin-transfer torque dominates the dynamics with small corrections from
non-adiabatic effects; (ii) the damping always decreases the magnetic free
energy, and (iii) microscopic calculations of damping become consistent with
general statistical and thermodynamic considerations.
|
0702020v3
|
2001-02-09
|
Magnetic effects on the viscous boundary layer damping of the r-modes in neutron stars
|
This paper explores the effects that magnetic fields have on the viscous
boundary layers (VBLs) that can form in neutron stars at the crust-core
interface, and it investigates the VBL damping of the gravitational-radiation
driven r-mode instability. Approximate solutions to the magnetohydrodynamic
equations valid in the VBL are found for ordinary-fluid neutron stars. It is
shown that magnetic fields above 10^9 Gauss significantly change the structure
of the VBL, and that magnetic fields decrease the VBL damping time.
Furthermore, VBL damping completely suppresses the r-mode instability for B >=
10^{12} Gauss. Thus, magnetic fields will profoundly affect the VBL damping of
the r-mode instability in hot young pulsars (that are cool enough to have
formed a solid crust). One can speculate that magnetic fields can affect the
VBL damping of this instability in LMXBs and other cold old pulsars (if they
have sufficiently large internal fields).
|
0102042v1
|
2003-01-30
|
Dynamic effects of electromagnetic wave on a damped two-level atom
|
We studied the dynamic effects of an electromagnetic(EM) wave with circular
polarization on a two-level damped atom. The results demonstrate interesting ac
Stark split of energy levels of damped atom. The split levels have different
energies and lifetimes, both of which depend on the interaction and the damping
rate of atom. When the frequency of the EM wave is tuned to satisfy the
resonance condition in the strong coupling limit, the transition probability
exhibits Rabi oscillation. Momentum transfer between atom and EM wave shows
similar properties as the transition probability under resonance condition. For
a damped atom interacting with EM field, there exists no longer stable state.
More importantly, if the angular frequency of the EM wave is tuned the same as
the atomic transition frequency and its amplitude is adjusted appropriately
according to the damping coefficients, we can prepare a particular 'Dressed
State' of the coupled system between atom and EM field and can keep the system
coherently in this 'Dressed state' for a very long time. This opens another way
to prepare coherent atomic states.
|
0301166v1
|
2007-12-18
|
Spectroscopy of electronic defect states in Cu(In, Ga)(S, Se)$_2$-based heterojunctions and Schottky diodes under damp-heat exposure
|
The changes of defect characteristics induced by accelerated lifetime tests
on the heterostructure n-ZnO/i-ZnO/CdS/Cu(In, Ga)(S, Se)$_2$/Mo relevant for
photovoltaic energy conversion are investigated. We subject heterojunction and
Schottky devices to extended damp heat exposure at 85$^{\circ}$C ambient
temperature and 85% relative humidity for various time periods. In order to
understand the origin of the pronounced changes of the devices, we apply
current--voltage and capacitance--voltage measurements, admittance
spectroscopy, and deep-level transient spectroscopy. The fill factor and
open-circuit voltage of test devices are reduced after prolonged damp heat
treatment, leading to a reduced energy conversion efficiency. We observe the
presence of defect states in the vicinity of the CdS/chalcopyrite interface.
Their activation energy increases due to damp heat exposure, indicating a
reduced band bending at the Cu(In, Ga)(S, Se)$_2$ surface. The Fermi-level
pinning at the buffer/chalcopyrite interface, maintaining a high band bending
in as-grown cells, is lifted due to the damp-heat exposure. We also observe
changes in the bulk defect spectra due to the damp-heat treatment.
|
0712.2982v1
|
2008-05-07
|
Comparison Between Damping Coefficients of Measured Perforated Micromechanical Test Structures and Compact Models
|
Measured damping coefficients of six different perforated micromechanical
test structures are compared with damping coefficients given by published
compact models. The motion of the perforated plates is almost translational,
the surface shape is rectangular, and the perforation is uniform validating the
assumptions made for compact models. In the structures, the perforation ratio
varies from 24% - 59%. The study of the structure shows that the
compressibility and inertia do not contribute to the damping at the frequencies
used (130kHz - 220kHz). The damping coefficients given by all four compact
models underestimate the measured damping coefficient by approximately 20%. The
reasons for this underestimation are discussed by studying the various flow
components in the models.
|
0805.0893v1
|
2009-01-26
|
Dispersion of Waves in Relativistic Plasmas with Isotropic Particle Distributions
|
The dispersion laws of Langmuir and transverse waves are calculated in the
relativistic non-magnetized formalism for several isotropic particle
distributions: thermal, power-law, relativistic Lorentzian $\kappa,$ and hybrid
$\beta$. For Langmuir waves the parameters of superluminal undamped, subluminal
damped principal and higher modes are determined for a range of distribution
parameters. The undamped and principal damped modes are found to match
smoothly. Principal damped and second damped modes are found not to match
smoothly. The presence of maximum wavenumber is discovered above that no
longitudinal modes formally exist. The higher damped modes are discovered to be
qualitatively different for thermal and certain non-thermal distributions.
Consistently with the known results, the Landau damping is calculated to be
stronger for non-thermal power-law-like distributions. The dispersion law is
obtained for the single undamped transverse mode. The analytic results for the
simplest distributions are provided.
|
0901.4050v1
|
2009-03-28
|
Torsional waves propagation in an initially stressed dissipative cylinder
|
The present paper has been framed to show the effect of damping on the
propagation of torsional waves in an initially stressed, dissipative,
incompressible cylinder of infinite length. A governing equation has been
formulated on Biot's incremental deformation theory. The velocities of
torsional waves are obtained as complex ones, in which real part gives the
phase velocity of propagation and corresponding imaginary part gives the
damping. The study reveals that the damping of the medium has strong effect in
the propagation of torsional wave. Since every medium has damping so it is more
realistic to use the damped wave equation instead of the undamped wave
equation. The study also shows that the velocity of propagation of such waves
depend on the presence of initial stress. The influences of damping and initial
stresses are shown separately.
|
0903.4896v1
|
2009-04-09
|
Evaluating the locality of intrinsic precession damping in transition metals
|
The Landau-Lifshitz-Gilbert damping parameter is typically assumed to be a
local quantity, independent of magnetic configuration. To test the validity of
this assumption we calculate the precession damping rate of small amplitude
non-uniform mode magnons in iron, cobalt, and nickel. At scattering rates
expected near and above room temperature, little change in the damping rate is
found as the magnon wavelength is decreased from infinity to a length shorter
than features probed in recent experiments. This result indicates that
non-local effects due to the presence of weakly non-uniform modes, expected in
real devices, should not appreciably affect the dynamic response of the element
at typical operating temperatures. Conversely, at scattering rates expected in
very pure samples around cryogenic temperatures, non-local effects result in an
order of magnitude decrease in damping rates for magnons with wavelengths
commensurate with domain wall widths. While this low temperature result is
likely of little practical importance, it provides an experimentally testable
prediction of the non-local contribution of the spin-orbit torque-correlation
model of precession damping. None of these results exhibit strong dependence on
the magnon propagation direction.
|
0904.1455v1
|
2009-04-29
|
Atomistic theory for the damping of vibrational modes in mono-atomic gold chains
|
We develop a computational method for evaluating the damping of vibrational
modes in mono-atomic metallic chains suspended between bulk crystals under
external strain. The damping is due to the coupling between the chain and
contact modes and the phonons in the bulk substrates. The geometry of the atoms
forming the contact is taken into account. The dynamical matrix is computed
with density functional theory in the atomic chain and the contacts using
finite atomic displacements, while an empirical method is employed for the bulk
substrate. As a specific example, we present results for the experimentally
realized case of gold chains in two different crystallographic directions. The
range of the computed damping rates confirm the estimates obtained by fits to
experimental data [Frederiksen et al., Phys. Rev. B, 75, 205413(R)(2007)]. Our
method indicates that an order-of-magnitude variation in the damping is
possible even for relatively small changes in the strain. Such detailed insight
is necessary for a quantitative analysis of damping in metallic atomic chains,
and in explaining the rich phenomenology seen in the experiments.
|
0904.4627v2
|
2009-12-20
|
A Kinetic Alfven wave cascade subject to collisionless damping cannot reach electron scales in the solar wind at 1 AU
|
(Abridged) Turbulence in the solar wind is believed to generate an energy
cascade that is supported primarily by Alfv\'en waves or Alfv\'enic
fluctuations at MHD scales and by kinetic Alfv\'en waves (KAWs) at kinetic
scales $k_\perp \rho_i\gtrsim 1$. Linear Landau damping of KAWs increases with
increasing wavenumber and at some point the damping becomes so strong that the
energy cascade is completely dissipated. A model of the energy cascade process
that includes the effects of linear collisionless damping of KAWs and the
associated compounding of this damping throughout the cascade process is used
to determine the wavenumber where the energy cascade terminates. It is found
that this wavenumber occurs approximately when $|\gamma/\omega|\simeq 0.25$,
where $\omega(k)$ and $\gamma(k)$ are, respectively, the real frequency and
damping rate of KAWs and the ratio $\gamma/\omega$ is evaluated in the limit as
the propagation angle approaches 90 degrees relative to the direction of the
mean magnetic field.
|
0912.4026v2
|
2010-07-27
|
Alfvèn wave phase-mixing and damping in the ion cyclotron range of frequencies
|
Aims. To determine the effect of the Hall term in the generalised Ohm's law
on the damping and phase mixing of Alfven waves in the ion cyclotron range of
frequencies in uniform and non-uniform equilibrium plasmas. Methods. Wave
damping in a uniform plasma is treated analytically, whilst a Lagrangian remap
code (Lare2d) is used to study Hall effects on damping and phase mixing in the
presence of an equilibrium density gradient. Results. The magnetic energy
associated with an initially Gaussian field perturbation in a uniform resistive
plasma is shown to decay algebraically at a rate that is unaffected by the Hall
term to leading order in k^2di^2 where k is wavenumber and di is ion skin
depth. A similar algebraic decay law applies to whistler perturbations in the
limit k^2di^2>>1. In a non-uniform plasma it is found that the
spatially-integrated damping rate due to phase mixing is lower in Hall MHD than
it is in MHD, but the reduction in the damping rate, which can be attributed to
the effects of wave dispersion, tends to zero in both the weak and strong phase
mixing limits.
|
1007.4752v2
|
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