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2007-08-28
|
Ising Dynamics with Damping
|
We show for the Ising model that is possible construct a discrete time
stochastic model analogous to the Langevin equation that incorporates an
arbitrary amount of damping. It is shown to give the correct equilibrium
statistics and is then used to investigate nonequilibrium phenomena, in
particular, magnetic avalanches. The value of damping can greatly alter the
shape of hysteresis loops, and for small damping and high disorder, the
morphology of large avalanches can be drastically effected. Small damping also
alters the size distribution of avalanches at criticality.
|
0708.3855v1
|
2008-02-08
|
On the scaling of the damping time for resonantly damped oscillations in coronal loops
|
There is not as yet full agreement on the mechanism that causes the rapid
damping of the oscillations observed by TRACE in coronal loops. It has been
suggested that the variation of the observed values of the damping time as
function of the corresponding observed values of the period contains
information on the possible damping mechanism. The aim of this Letter is to
show that, for resonant absorption, this is definitely not the case unless
detailed a priori information on the individual loops is available.
|
0802.1143v1
|
2008-10-02
|
Critically damped quantum search
|
Although measurement and unitary processes can accomplish any quantum
evolution in principle, thinking in terms of dissipation and damping can be
powerful. We propose a modification of Grover's algorithm in which the idea of
damping plays a natural role. Remarkably, we have found that there is a
critical damping value that divides between the quantum $O(\sqrt{N})$ and
classical O(N) search regimes. In addition, by allowing the damping to vary in
a fashion we describe, one obtains a fixed-point quantum search algorithm in
which ignorance of the number of targets increases the number of oracle queries
only by a factor of 1.5.
|
0810.0470v1
|
2009-07-01
|
Modal approximations to damped linear systems
|
We consider a finite dimensional damped second order system and obtain
spectral inclusion theorems for the related quadratic eigenvalue problem. The
inclusion sets are the 'quasi Cassini ovals' which may greatly outperform
standard Gershgorin circles. As the unperturbed system we take a modally damped
part of the system; this includes the known proportionally damped models, but
may give much sharper estimates. These inclusions are then applied to derive
some easily calculable sufficient conditions for the overdampedness of a given
damped system.
|
0907.0167v1
|
2010-01-14
|
Multi-Error-Correcting Amplitude Damping Codes
|
We construct new families of multi-error-correcting quantum codes for the
amplitude damping channel. Our key observation is that, with proper encoding,
two uses of the amplitude damping channel simulate a quantum erasure channel.
This allows us to use concatenated codes with quantum erasure-correcting codes
as outer codes for correcting multiple amplitude damping errors. Our new codes
are degenerate stabilizer codes and have parameters which are better than the
amplitude damping codes obtained by any previously known construction.
|
1001.2356v1
|
2011-09-05
|
Spectral theory of damped quantum chaotic systems
|
We investigate the spectral distribution of the damped wave equation on a
compact Riemannian manifold, especially in the case of a metric of negative
curvature, for which the geodesic flow is Anosov. The main application is to
obtain conditions (in terms of the geodesic flow on $X$ and the damping
function) for which the energy of the waves decays exponentially fast, at least
for smooth enough initial data. We review various estimates for the high
frequency spectrum in terms of dynamically defined quantities, like the value
distribution of the time-averaged damping. We also present a new condition for
a spectral gap, depending on the set of minimally damped trajectories.
|
1109.0930v1
|
2012-06-07
|
From resolvent estimates to damped waves
|
In this paper we show how to obtain decay estimates for the damped wave
equation on a compact manifold without geometric control via knowledge of the
dynamics near the un-damped set. We show that if replacing the damping term
with a higher-order \emph{complex absorbing potential} gives an operator
enjoying polynomial resolvent bounds on the real axis, then the "resolvent"
associated to our damped problem enjoys bounds of the same order. It is known
that the necessary estimates with complex absorbing potential can also be
obtained via gluing from estimates for corresponding non-compact models.
|
1206.1565v1
|
2012-12-03
|
Inviscid limit of stochastic damped 2D Navier-Stokes equations
|
We consider the inviscid limit of the stochastic damped 2D Navier- Stokes
equations. We prove that, when the viscosity vanishes, the stationary solution
of the stochastic damped Navier-Stokes equations converges to a stationary
solution of the stochastic damped Euler equation and that the rate of
dissipation of enstrophy converges to zero. In particular, this limit obeys an
enstrophy balance. The rates are computed with respect to a limit measure of
the unique invariant measure of the stochastic damped Navier-Stokes equations.
|
1212.0509v3
|
2014-01-13
|
NLSE for quantum plasmas with the radiation damping
|
We consider contribution of the radiation damping in the quantum hydrodynamic
equations for spinless particles. We discuss possibility of obtaining of
corresponding non-linear Schrodinger equation (NLSE) for the macroscopic wave
function. We compare contribution of the radiation damping with weakly (or
semi-) relativistic effects appearing in the second order by v/c. The radiation
damping appears in the third order by v/c. So it might be smaller than weakly
relativistic effects, but it gives damping of the Langmuir waves which can be
considerable.
|
1401.2829v1
|
2014-09-26
|
An ultimate storage ring lattice with vertical emittance generated by damping wigglers
|
We discuss the approach of generating round beams for ultimate storage rings
using vertical damping wigglers (with horizontal magnetic field). The vertical
damping wigglers provide damping and excite vertical emittance. This eliminates
the need to generate large linear coupling that is impractical with traditional
off-axis injection. We use a PEP-X compatible lattice to demonstrate the
approach. This lattice uses separate quadrupole and sextupole magnets with
realistic gradient strengths. Intrabeam scattering effects are calculated. The
horizontal and vertical emittances are 22.3 pm and 10.3 pm, respectively, for a
200 mA, 4.5 GeV beam, with a vertical damping wiggler of a total length of 90
meters, peak field of 1.5 T and wiggler period of 100 mm.
|
1409.7452v2
|
2016-08-14
|
Mechanical energy and mean equivalent viscous damping for SDOF fractional oscillators
|
This paper addresses the total mechanical energy of a single degree of
freedom fractional oscillator. Based on the energy storage and dissipation
properties of the Caputo fractional derivatives, the expression for total
mechanical energy in the single degree of freedom fractional oscillator is
firstly presented. The energy regeneration due to the external exciting force
and the energy loss due to the fractional damping force during the vibratory
motion are analyzed. Furthermore, based on the mean energy dissipation of the
fractional damping element in steady-state vibration, a new concept of mean
equivalent viscous damping is suggested and the value of the damping
coefficient is evaluated.
|
1608.04071v1
|
2017-03-01
|
Behaviors of the energy of solutions of two coupled wave equations with nonlinear damping on a compact manifold with boundary
|
In this paper we study the behaviors of the the energy of solutions of
coupled wave equations on a compact manifold with boundary in the case of
indirect nonlinear damping . Only one of the two equations is directly damped
by a localized nonlinear damping term. Under geometric conditions on both the
coupling and the damping regions we prove that the rate of decay of the energy
of smooth solutions of the system is determined from a first order differential
equation .
|
1703.00172v1
|
2017-06-02
|
Vanishing viscosity limit for global attractors for the damped Navier--Stokes system with stress free boundary conditions
|
We consider the damped and driven Navier--Stokes system with stress free
boundary conditions and the damped Euler system in a bounded domain
$\Omega\subset\mathbf{R}^2$. We show that the damped Euler system has a
(strong) global attractor in~$H^1(\Omega)$. We also show that in the vanishing
viscosity limit the global attractors of the Navier--Stokes system converge in
the non-symmetric Hausdorff distance in $H^1(\Omega)$ to the the strong global
attractor of the limiting damped Euler system (whose solutions are not
necessarily unique).
|
1706.00607v1
|
2018-01-20
|
Long time dynamics for weakly damped nonlinear Klein-Gordon equations
|
We continue our study of damped nonlinear Klein-Gordon equations. In our
previous work we considered fixed positive damping and proved a form of the
soliton resolution conjecture for radial solutions. In contrast, here we
consider damping which decreases in time to 0. In the class of radial data we
again establish soliton resolution provided the damping goes to 0 sufficiently
slowly. While our previous work relied on invariant manifold theory, here we
use the Lojasiewicz-Simon inequality applied to a suitable Lyapunov functional.
|
1801.06735v1
|
2018-02-28
|
Nonexistence of global solutions of wave equations with weak time-dependent damping and combined nonlinearity
|
In our previous two works, we studied the blow-up and lifespan estimates for
damped wave equations with a power nonlinearity of the solution or its
derivative, with scattering damping independently. In this work, we are devoted
to establishing a similar result for a combined nonlinearity. Comparing to the
result of wave equation without damping, one can say that the scattering
damping has no influence.
|
1802.10273v1
|
2018-11-12
|
Choking non-local magnetic damping in exchange biased ferromagnets
|
We investigated the temperature dependence of the magnetic damping in the
exchange biased Pt/ Fe50Mn50 /Fe20Ni80 /SiOx multilayers. In samples having a
strong exchange bias, we observed a drastic decrease of the magnetic damping of
the FeNi with increasing temperature up to the blocking temperature. The
results essentially indicate that the non-local enhancement of the magnetic
damping can be choked by the adjacent antiferromagnet and its temperature
dependent exchange bias. We also pointed out that such a strong temperature
dependent damping may be very beneficial for spintronic applications.
|
1811.04821v1
|
2019-05-23
|
Escaping Locally Optimal Decentralized Control Polices via Damping
|
We study the evolution of locally optimal decentralized controllers with the
damping of the control system. Empirically it is shown that even for instances
with an exponential number of connected components, damping merges all local
solutions to the one global solution. We characterize the evolution of locally
optimal solutions with the notion of hemi-continuity and further derive
asymptotic properties of the objective function and of the locally optimal
controllers as the damping becomes large. Especially, we prove that with enough
damping, there is no spurious locally optimal controller with favorable control
structures. The convoluted behavior of the locally optimal trajectory is
illustrated with numerical examples.
|
1905.09915v1
|
2019-08-22
|
Some remarks on the asymptotic profile of solutions to structurally damped $σ$-evolution equations
|
In this paper, we are interested in analyzing the asymptotic profiles of
solutions to the Cauchy problem for linear structurally damped
$\sigma$-evolution equations in $L^2$-sense. Depending on the parameters
$\sigma$ and $\delta$ we would like to not only indicate approximation formula
of solutions but also recognize the optimality of their decay rates as well in
the distinct cases of parabolic like damping and $\sigma$-evolution like
damping. Moreover, such results are also discussed when we mix these two kinds
of damping terms in a $\sigma$-evolution equation to investigate how each of
them affects the asymptotic profile of solutions.
|
1908.08492v1
|
2019-09-18
|
Global smooth solutions of the damped Boussinesq equations with a class of large initial data
|
The global regularity problem concerning the inviscid Boussinesq equations
remains an open problem. In an attempt to understand this problem, we examine
the damped Boussinesq equations and study how damping affects the regularity of
solutions. In this paper, we consider the global existence to the damped
Boussinesq equations with a class of large initial data, whose $B^{s}_{p,r}$ or
$\dot{B}^{s}_{p,r}$ norms can be arbitrarily large. The idea is splitting the
linear Boussinesq equations from the damped Boussinesq equations, the
exponentially decaying solution of the former equations together with the
structure of the Boussinesq equations help us to obtain the global smooth
solutions.
|
1909.08360v1
|
2020-02-15
|
Asymptotic profile and optimal decay of solutions of some wave equations with logarithmic damping
|
We introduce a new model of the nonlocal wave equations with a logarithmic
damping mechanism. We consider the Cauchy poroblem for the new model in the
whole space. We study the asymptotic profile and optimal decay and blowup rates
of solutions as time goes to infinity. The damping terms considered in this
paper is not studied so far, and in the low frequency parameters the damping is
rather weakly effective than that of well-studied fractional type of nonlocal
damping. In order to get the optimal estimates in time we meet the so-called
hypergeometric functions with special parameters.
|
2002.06319v1
|
2020-05-13
|
Weak Input to state estimates for 2D damped wave equations with localized and non-linear damping
|
In this paper, we study input-to-state (ISS) issues for damped wave equations
with Dirichlet boundary conditions on a bounded domain of dimension two. The
damping term is assumed to be non-linear and localized to an open subset of the
domain. In a first step, we handle the undisturbed case as an extension of a
previous work, where stability results are given with a damping term active on
the full domain. Then, we address the case with disturbances and provide
input-to-state types of results.
|
2005.06206v3
|
2020-07-25
|
Decay for the Kelvin-Voigt damped wave equation: Piecewise smooth damping
|
We study the energy decay rate of the Kelvin-Voigt damped wave equation with
piecewise smooth damping on the multi-dimensional domain. Under suitable
geometric assumptions on the support of the damping, we obtain the optimal
polynomial decay rate which turns out to be different from the one-dimensional
case studied in \cite{LR05}. This optimal decay rate is saturated by high
energy quasi-modes localised on geometric optics rays which hit the interface
along non orthogonal neither tangential directions. The proof uses
semi-classical analysis of boundary value problems.
|
2007.12994v2
|
2020-08-12
|
From Lieb-Thirring inequalities to spectral enclosures for the damped wave equation
|
Using a correspondence between the spectrum of the damped wave equation and
non-self-adjoint Schroedinger operators, we derive various bounds on complex
eigenvalues of the former. In particular, we establish a sharp result that the
one-dimensional damped wave operator is similar to the undamped one provided
that the L^1 norm of the (possibly complex-valued) damping is less than 2. It
follows that these small dampings are spectrally undetectable.
|
2008.05176v1
|
2021-08-02
|
Wide-Area Damping Control for Interarea Oscillations in Power Grids Based on PMU Measurements
|
In this paper, a phasor measurement unit (PMU)-based wide-area damping
control method is proposed to damp the interarea oscillations that threaten the
modern power system stability and security. Utilizing the synchronized PMU
data, the proposed almost model-free approach can achieve an effective damping
for the selected modes using a minimum number of synchronous generators.
Simulations are performed to show the validity of the proposed wide-area
damping control scheme.
|
2108.01193v1
|
2021-09-05
|
Regularity of the semigroups associated with some damped coupled elastic systems II: a nondegenerate fractional damping case
|
In this paper, we examine regularity issues for two damped abstract elastic
systems; the damping and coupling involve fractional powers $\mu, \theta$, with
$0 \leq \mu , \theta \leq 1$, of the principal operators. The matrix defining
the coupling and damping is nondegenerate. This new work is a sequel to the
degenerate case that we discussed recently in \cite{kfl}. First, we prove that
for $1/2 \leq \mu , \theta \leq 1$, the underlying semigroup is analytic. Next,
we show that for $\min(\mu,\theta) \in (0,1/2)$, the semigroup is of certain
Gevrey classes. Finally, some examples of application are provided.
|
2109.02044v1
|
2021-09-28
|
A robust and efficient line search for self-consistent field iterations
|
We propose a novel adaptive damping algorithm for the self-consistent field
(SCF) iterations of Kohn-Sham density-functional theory, using a backtracking
line search to automatically adjust the damping in each SCF step. This line
search is based on a theoretically sound, accurate and inexpensive model for
the energy as a function of the damping parameter. In contrast to usual damped
SCF schemes, the resulting algorithm is fully automatic and does not require
the user to select a damping. We successfully apply it to a wide range of
challenging systems, including elongated supercells, surfaces and
transition-metal alloys.
|
2109.14018v3
|
2021-11-17
|
Spectral asymptotics for the vectorial damped wave equation
|
The eigenfrequencies associated to a scalar damped wave equation are known to
belong to a band parallel to the real axis. In [Sj{\"o}00] J. Sj{\"o}strand
showed that up to a set of density 0, the eigenfrequencies are confined in a
thinner band determined by the Birkhoff limits of the damping term. In this
article we show that this result is still true for a vectorial damped wave
equation. In this setting the Lyapunov exponents of the cocycle given by the
damping term play the role of the Birkhoff limits of the scalar setting.
|
2111.08982v1
|
2021-12-13
|
Rotons and their damping in elongated dipolar Bose-Einstein condensates
|
We discuss finite temperature damping of rotons in elongated Bose-condensed
dipolar gases, which are in the Thomas-Fermi regime in the tightly confined
directions. The presence of many branches of excitations which can participate
in the damping process, is crucial for the Landau damping and results in
significant increase of the damping rate. It is found, however, that even
rotons with energies close to the roton gap may remain fairly stable in systems
with the roton gap as small as 1nK.
|
2112.06835v2
|
2022-03-03
|
Stability results of locally coupled wave equations with local Kelvin-Voigt damping: Cases when the supports of damping and coupling coefficients are disjoint
|
In this paper, we study the direct/indirect stability of locally coupled wave
equations with local Kelvin-Voigt dampings/damping and by assuming that the
supports of the dampings and the coupling coefficients are disjoint. First, we
prove the well-posedness, strong stability, and polynomial stability for some
one dimensional coupled systems. Moreover, under some geometric control
condition, we prove the well-posedness and strong stability in the
multi-dimensional case.
|
2203.01632v1
|
2022-03-12
|
Asymptotic expansion of solutions to the wave equation with space-dependent damping
|
We study the large time behavior of solutions to the wave equation with
space-dependent damping in an exterior domain. We show that if the damping is
effective, then the solution is asymptotically expanded in terms of solutions
of corresponding parabolic equations. The main idea to obtain the asymptotic
expansion is the decomposition of the solution of the damped wave equation into
the solution of the corresponding parabolic problem and the time derivative of
the solution of the damped wave equation with certain inhomogeneous term and
initial data. The estimate of the remainder term is an application of weighted
energy method with suitable supersolutions of the corresponding parabolic
problem.
|
2203.06360v1
|
2022-10-27
|
Sharp polynomial decay for polynomially singular damping on the torus
|
We study energy decay rates for the damped wave equation with unbounded
damping, without the geometric control condition. Our main decay result is
sharp polynomial energy decay for polynomially controlled singular damping on
the torus. We also prove that for normally $L^p$-damping on compact manifolds,
the Schr\"odinger observability gives $p$-dependent polynomial decay, and
finite time extinction cannot occur. We show that polynomially controlled
singular damping on the circle gives exponential decay.
|
2210.15697v3
|
2023-09-26
|
Qualitative properties of solutions to a nonlinear transmission problem for an elastic Bresse beam
|
We consider a nonlinear transmission problem for a Bresse beam, which
consists of two parts, damped and undamped. The mechanical damping in the
damped part is present in the shear angle equation only, and the damped part
may be of arbitrary positive length. We prove well-posedness of the
corresponding PDE system in energy space and establish existence of a regular
global attractor under certain conditions on nonlinearities and coefficients of
the damped part only. Moreover, we study singular limits of the problem when
$l\to 0$ or $l\to 0$ simultaneously with $k_i\to +\infty$ and perform numerical
modelling for these processes.
|
2309.15171v2
|
2023-09-27
|
Dispersion and damping of ion-acoustic waves in the plasma with a regularized kappa-distribution
|
The dispersion and damping of ion-acoustic waves in the plasma with a
regularized kappa-distribution are studied. The generalized dispersion relation
and damping rate are derived, which both depend significantly on the parameters
alpha and kappa. The numerical analyses show that the wave frequency and the
damping rate of ion-acoustic waves in the plasma with the regularized
kappa-distribution are both generally less than those in the plasma with the
kappa-distribution, and if kappa is less than a value, the ion-acoustic waves
and their damping rate exist in the plasma with the regularized
kappa-distribution.
|
2309.15885v1
|
2023-11-16
|
Near-optimal Closed-loop Method via Lyapunov Damping for Convex Optimization
|
We introduce an autonomous system with closed-loop damping for first-order
convex optimization. While, to this day, optimal rates of convergence are only
achieved by non-autonomous methods via open-loop damping (e.g., Nesterov's
algorithm), we show that our system is the first one featuring a closed-loop
damping while exhibiting a rate arbitrarily close to the optimal one. We do so
by coupling the damping and the speed of convergence of the system via a
well-chosen Lyapunov function. We then derive a practical first-order algorithm
called LYDIA by discretizing our system, and present numerical experiments
supporting our theoretical findings.
|
2311.10053v1
|
2024-02-05
|
Fractional damping induces resonant behavior in the Duffing oscillator
|
The interaction between the fractional order parameter and the damping
parameter can play a relevant role for introducing different dynamical
behaviors in a physical system. Here, we study the Duffing oscillator with a
fractional damping term. Our findings show that for certain values of the
fractional order parameter, the damping parameter, and the forcing amplitude
high oscillations amplitude can be induced. This phenomenon is due to the
appearance of a resonance in the Duffing oscillator only when the damping term
is fractional.
|
2402.02940v1
|
2024-03-13
|
Impact of Decoherence on Average Correlation
|
This article presents a comprehensive study of the impact of decoherence on
the average correlation for pure quantum states. We explore two primary
mechanisms of decoherence: phase damping and amplitude damping, each having
distinct effects on quantum systems. Phase damping, which describes the loss of
quantum coherence without energy loss, primarily affects the phase
relationships between the components of a quantum system while amplitude
damping involves energy dissipation and also affects the state's occupation
probabilities. We show that the average correlation follows a predictable
decaying pattern in both scenarios. Our analysis can be understood in the
context of quantum computing, by focusing on how phase damping influences the
entanglement and correlation between qubits, key factors in quantum
computational efficiency and error correction protocols.
|
2403.10551v1
|
1998-02-18
|
Damping rates of hot Giant Dipole Resonances
|
The damping rate of hot giant dipole resonances (GDR) is investigated.
Besides Landau damping we consider collisions and density fluctuations as
contributions to the damping of GDR. Within the nonequilibrium Green's function
method we derive a non-Markovian kinetic equation. The linearization of the
latter one leads to complex dispersion relations. The complex solution provides
the centroid energy and the damping width of giant resonances. The experimental
damping widths are the full width half maximum (FWHM) and can be reproduced by
the full width of the structure function. Within simple finite size scaling we
give a relation between the minimal interaction strength which is required for
a collective oscillation and the clustersize. We investigate the damping of
giant dipole resonances within a Skyrme type of interaction. Different
collision integrals are compared with each other in order to incorporate
correlations. The inclusion of a conserving relaxation time approximation
allows to find the $T^2$-dependence of the damping rate with a temperature
known from the Fermi-liquid theory. However, memory effects turn out to be
essential for a proper treatment of the damping of collective modes. We derive
a Landau like formula for the one--particle relaxation time similar to the
damping of zero sound.
|
9802052v2
|
2015-12-11
|
Ultra-low magnetic damping of a metallic ferromagnet
|
The phenomenology of magnetic damping is of critical importance for devices
that seek to exploit the electronic spin degree of freedom since damping
strongly affects the energy required and speed at which a device can operate.
However, theory has struggled to quantitatively predict the damping, even in
common ferromagnetic materials. This presents a challenge for a broad range of
applications in spintronics and spin-orbitronics that depend on materials and
structures with ultra-low damping. Such systems enable many experimental
investigations that further our theoretical understanding of numerous magnetic
phenomena such as damping and spin-transport mediated by chirality and the
Rashba effect. Despite this requirement, it is believed that achieving
ultra-low damping in metallic ferromagnets is limited due to the scattering of
magnons by the conduction electrons. However, we report on a binary alloy of Co
and Fe that overcomes this obstacle and exhibits a damping parameter
approaching 0.0001, which is comparable to values reported only for
ferrimagnetic insulators. We explain this phenomenon by a unique feature of the
bandstructure in this system: The density of states exhibits a sharp minimum at
the Fermi level at the same alloy concentration at which the minimum in the
magnetic damping is found. This discovery provides both a significant
fundamental understanding of damping mechanisms as well as a test of
theoretical predictions.
|
1512.03610v1
|
2020-05-12
|
Effective Viscous Damping Enables Morphological Computation in Legged Locomotion
|
Muscle models and animal observations suggest that physical damping is
beneficial for stabilization. Still, only a few implementations of mechanical
damping exist in compliant robotic legged locomotion. It remains unclear how
physical damping can be exploited for locomotion tasks, while its advantages as
sensor-free, adaptive force- and negative work-producing actuators are
promising. In a simplified numerical leg model, we studied the energy
dissipation from viscous and Coulomb damping during vertical drops with
ground-level perturbations. A parallel spring-damper is engaged between
touch-down and mid-stance, and its damper auto-disengages during mid-stance and
takeoff. Our simulations indicate that an adjustable and viscous damper is
desired. In hardware we explored effective viscous damping and adjustability
and quantified the dissipated energy. We tested two mechanical, leg-mounted
damping mechanisms; a commercial hydraulic damper, and a custom-made pneumatic
damper. The pneumatic damper exploits a rolling diaphragm with an adjustable
orifice, minimizing Coulomb damping effects while permitting adjustable
resistance. Experimental results show that the leg-mounted, hydraulic damper
exhibits the most effective viscous damping. Adjusting the orifice setting did
not result in substantial changes of dissipated energy per drop, unlike
adjusting damping parameters in the numerical model. Consequently, we also
emphasize the importance of characterizing physical dampers during real legged
impacts to evaluate their effectiveness for compliant legged locomotion.
|
2005.05725v2
|
2022-02-10
|
Non-stationary Anderson acceleration with optimized damping
|
Anderson acceleration (AA) has a long history of use and a strong recent
interest due to its potential ability to dramatically improve the linear
convergence of the fixed-point iteration. Most authors are simply using and
analyzing the stationary version of Anderson acceleration (sAA) with a constant
damping factor or without damping. Little attention has been paid to
nonstationary algorithms. However, damping can be useful and is sometimes
crucial for simulations in which the underlying fixed-point operator is not
globally contractive. The role of this damping factor has not been fully
understood. In the present work, we consider the non-stationary Anderson
acceleration algorithm with optimized damping (AAoptD) in each iteration to
further speed up linear and nonlinear iterations by applying one extra
inexpensive optimization. We analyze this procedure and develop an efficient
and inexpensive implementation scheme. We also show that, compared with the
stationary Anderson acceleration with fixed window size sAA(m), optimizing the
damping factors is related to dynamically packaging sAA(m) and sAA(1) in each
iteration (alternating window size $m$ is another direction of producing
non-stationary AA). Moreover, we show by extensive numerical experiments that
the proposed non-stationary Anderson acceleration with optimized damping
procedure often converges much faster than stationary AA with constant damping
or without damping.
|
2202.05295v1
|
2023-06-30
|
A finite element method to compute the damping rate of oscillating fluids inside microfluidic nozzles
|
We introduce a finite element method for computing the damping rate of fluid
oscillations in nozzles of drop-on-demand (DoD) microfluidic devices. Accurate
knowledge of the damping rates for the least-damped oscillation modes following
droplet ejection is paramount for assessing jetting stability at higher jetting
frequencies, as ejection from a non-quiescent meniscus can result in deviations
from nominal droplet properties. Computational fluid dynamics (CFD) simulations
often struggle to accurately predict meniscus damping in the limit of low
viscosity and high surface tension. Moreover, their use in design loops aimed
at optimizing the nozzle geometry for stable jetting is slow and
computationally expensive. The faster alternative we adopt here is to compute
the damping rate directly from the eigenvalues of the linearized problem.
Starting from a variational formulation of the linearized governing equations,
we obtain a generalized eigenvalue problem for the oscillation modes, and
approximate its solutions with a finite element method that uses Taylor-Hood
elements. We solve the matrix eigenvalue problem with a sparse, parallelized
implementation of the Krylov-Schur algorithm. The spatial shape and temporal
evolution (angular frequency and damping rate) of the set of least-damped
oscillation modes are obtained in a matter of minutes, compared to days for a
CFD simulation. We verify that the method can reproduce an analytical benchmark
problem, and then determine numerical convergence rates on two examples with
axisymmetric geometry. We also prove that the method is free of spurious modes
with zero or positive damping rates. The method's ability to quickly generate
accurate estimates of fluid oscillation damping rates makes it suitable for
integration into design loops for prototyping microfluidic nozzles.
|
2307.00094v1
|
2023-07-05
|
Optimal damping of vibrating systems: dependence on initial conditions
|
Common criteria used for measuring performance of vibrating systems have one
thing in common: they do not depend on initial conditions of the system. In
some cases it is assumed that the system has zero initial conditions, or some
kind of averaging is used to get rid of initial conditions. The aim of this
paper is to initiate rigorous study of the dependence of vibrating systems on
initial conditions in the setting of optimal damping problems. We show that,
based on the type of initial conditions, especially on the ratio of potential
and kinetic energy of the initial conditions, the vibrating system will have
quite different behavior and correspondingly the optimal damping coefficients
will be quite different. More precisely, for single degree of freedom systems
and the initial conditions with mostly potential energy, the optimal damping
coefficient will be in the under-damped regime, while in the case of the
predominant kinetic energy the optimal damping coefficient will be in the
over-damped regime. In fact, in the case of pure kinetic initial energy, the
optimal damping coefficient is $+\infty$! Qualitatively, we found the same
behavior in multi degree of freedom systems with mass proportional damping. We
also introduce a new method for determining the optimal damping of vibrating
systems, which takes into account the peculiarities of initial conditions and
the fact that, although in theory these systems asymptotically approach
equilibrium and never reach it exactly, in nature and in experiments they
effectively reach equilibrium in some finite time.
|
2307.02352v2
|
2024-01-18
|
Multithermal apparent damping of slow waves due to strands with a Gaussian temperature distribution
|
Context. Slow waves in solar coronal loops are strongly damped. The current
theory of damping by thermal conduction cannot explain some observational
features.\n Aims. We investigate the propagation of slow waves in a coronal
loop built up from strands of different temperatures. \n Methods. We consider
the loop to have a multithermal, Gaussian temperature distribution. The
different propagation speeds in different strands lead to an multithermal
apparent damping of the wave, similar to observational phase mixing. We use an
analytical model to predict the damping length and propagation speed for the
slow waves, including in imaging with filter telescopes. \n Results. We compare
the damping length due to this multithermal apparent damping with damping due
to thermal conduction and find that the multithermal apparent damping is more
important for shorter period slow waves. We have found the influence of
instrument filters on the wave's propagation speed and damping. This allows us
to compare our analytical theory to forward models of numerical simulations. \n
Conclusions. We find that our analytical model matches the numerical
simulations very well. Moreover, we offer an outlook for using the slow wave
properties to infer the loop's thermal properties.
|
2401.09803v1
|
1996-06-07
|
Abundances at High Redshifts: the Chemical Enrichment History of Damped Lyman-alpha Galaxies
|
Damped Lyman-alpha absorption systems found in the spectra of high redshift
quasars are believed to trace the interstellar gas in high redshift galaxies.
In this paper, we study the elemental abundances of C, N, O, Al, Si, S, Cr, Mn,
Fe, Ni, and Zn in a sample of 14 damped Lyman-alpha systems using high quality
echelle spectra of quasars obtained with the 10m Keck telescope. These
abundances are combined with similar measurements in the literature in order to
investigate the chemical evolution of damped Lyman-alpha galaxies in the
redshift range 0.7<z<4.4. Among the things investigated are: the metallicity
distribution of damped Lyman-alpha galaxy, its evolution with redshift (ie,
age-metallicity relation), the relative abundance patterns of the heavy metals
and implications for their nucleosynthetic origin, the effects of dust, the
nature of the star formation process in damped Lyman-alpha galaxies, and the
nature of damped Lyman-alpha galaxies themselves.
|
9606044v1
|
1998-07-17
|
Chaotic scattering on surfaces and collisional damping of collective modes
|
The damping of hot giant dipole resonances is investigated. The contribution
of surface scattering is compared with the contribution from interparticle
collisions. A unified response function is presented which includes surface
damping as well as collisional damping. The surface damping enters the response
via the Lyapunov exponent and the collisional damping via the relaxation time.
The former is calculated for different shape deformations of quadrupole and
octupole type. The surface as well as the collisional contribution each
reproduce almost the experimental value, therefore we propose a proper
weighting between both contributions related to their relative occurrence due
to collision frequencies between particles and of particles with the surface.
We find that for low and high temperatures the collisional contribution
dominates whereas the surface damping is dominant around the temperatures
$\sqrt{3}/2\pi$ of the centroid energy.
|
9807185v4
|
2000-09-08
|
Probing High-Redshift Disks with Damped Lyman Alpha Systems
|
Evidence is presented that the damped Lyman alpha absorption systems are the
high-redshift (z > 3) progenitors of galaxy disks. I discuss kinematic evidence
that the damped Lyman Alpha systems are rotating disks. I also discuss
implications of the lack of metal-poor damped Lyman alpha systems with line
width Delta v > 100 {\kms}. I then present new evidence stemming from
correlations between element-abundance ratios and [Fe/H], which connects damped
systems to the thick stellar disk of the Galaxy. I discuss the connections
between damped Lyman alpha systems and Lyman break galaxies, and how [CII] 158
micron emission from damped Lyman alpha systems discriminates among competing
theories of galaxy formation. ~
|
0009126v1
|
2006-09-10
|
Damping of Compressional MHD Waves In Quiescent Prominences and Prominence-Corona Transition Region (PCTR)
|
The effects of radiative losses due to Newtonian cooling and MHD turbulence
have been considered to examine the spatial damping of linear compressional
waves in quiescent prominences and prominence-corona transition region (PCTR).
The radiative losses give acceptable damping lengths for the slow mode wave for
the radiative relaxation time in the range (10-1000s). From prominence
seismology, the values of opacity and turbulent kinematic viscosity have been
inferred. It has been found that for a given value of radiative relaxation
time, the high frequency slow mode waves are highly damped. We have also
investigated the possible role of MHD turbulence in damping of MHD waves and
found a turbulent viscosity can re-produce the observed damping time and
damping length in prominences, especially in PCTR.
|
0609266v1
|
1997-10-14
|
Damping of low-energy excitations of a trapped Bose condensate at finite temperatures
|
We present the theory of damping of low-energy excitations of a trapped Bose
condensate at finite temperatures, where the damping is provided by the
interaction of these excitations with the thermal excitations. We emphasize the
key role of stochastization in the behavior of the thermal excitations for
damping in non-spherical traps. The damping rates of the lowest excitations,
following from our theory, are in fair agreement with the data of recent JILA
and MIT experiments. The damping of quasiclassical excitations is determined by
the condensate boundary region, and the result for the damping rate is
drastically different from that in a spatially homogeneous gas.
|
9710128v3
|
2001-12-09
|
Soliton dynamics in damped and forced Boussinesq equations
|
We investigate the dynamics of a lattice soliton on a monatomic chain in the
presence of damping and external forces. We consider Stokes and hydrodynamical
damping. In the quasi-continuum limit the discrete system leads to a damped and
forced Boussinesq equation. By using a multiple-scale perturbation expansion up
to second order in the framework of the quasi-continuum approach we derive a
general expression for the first-order velocity correction which improves
previous results. We compare the soliton position and shape predicted by the
theory with simulations carried out on the level of the monatomic chain system
as well as on the level of the quasi-continuum limit system. For this purpose
we restrict ourselves to specific examples, namely potentials with cubic and
quartic anharmonicities as well as the truncated Morse potential, without
taking into account external forces. For both types of damping we find a good
agreement with the numerical simulations both for the soliton position and for
the tail which appears at the rear of the soliton. Moreover we clarify why the
quasi-continuum approximation is better in the hydrodynamical damping case than
in the Stokes damping case.
|
0112148v1
|
2006-04-17
|
The Highly Damped Quasinormal Modes of $d$-dimensional Reissner-Nordstrom Black Holes in the Small Charge Limit
|
We analyze in detail the highly damped quasinormal modes of $d$-dimensional
Reissner-Nordstr$\ddot{\rm{o}}$m black holes with small charge, paying
particular attention to the large but finite damping limit in which the
Schwarzschild results should be valid. In the infinite damping limit, we
confirm using different methods the results obtained previously in the
literature for higher dimensional Reissner-Nordstr$\ddot{\rm{o}}$m black holes.
Using a combination of analytic and numerical techniques we also calculate the
transition of the real part of the quasinormal mode frequency from the
Reissner-Nordstr$\ddot{\rm{o}}$m value for very large damping to the
Schwarzschild value of $\ln(3) T_{bh}$ for intermediate damping. The real
frequency does not interpolate smoothly between the two values. Instead there
is a critical value of the damping at which the topology of the
Stokes/anti-Stokes lines change, and the real part of the quasinormal mode
frequency dips to zero.
|
0604073v2
|
2005-02-16
|
Damping signatures in future neutrino oscillation experiments
|
We discuss the phenomenology of damping signatures in the neutrino
oscillation probabilities, where either the oscillating terms or the
probabilities can be damped. This approach is a possibility for tests of
non-oscillation effects in future neutrino oscillation experiments, where we
mainly focus on reactor and long-baseline experiments. We extensively motivate
different damping signatures due to small corrections by neutrino decoherence,
neutrino decay, oscillations into sterile neutrinos, or other mechanisms, and
classify these signatures according to their energy (spectral) dependencies. We
demonstrate, at the example of short baseline reactor experiments, that damping
can severely alter the interpretation of results, e.g., it could fake a value
of $\sin(2\theta_{13})$ smaller than the one provided by Nature. In addition,
we demonstrate how a neutrino factory could constrain different damping models
with emphasis on how these different models could be distinguished, i.e., how
easily the actual non-oscillation effects could be identified. We find that the
damping models cluster in different categories, which can be much better
distinguished from each other than models within the same cluster.
|
0502147v2
|
1997-07-23
|
Riccati parameter modes from Newtonian free damping motion by supersymmetry
|
We determine the class of damped modes \tilde{y} which are related to the
common free damping modes y by supersymmetry. They are obtained by employing
the factorization of Newton's differential equation of motion for the free
damped oscillator by means of the general solution of the corresponding Riccati
equation together with Witten's method of constructing the supersymmetric
partner operator. This procedure leads to one-parameter families of (transient)
modes for each of the three types of free damping, corresponding to a
particular type of %time-dependent angular frequency. %time-dependent,
antirestoring acceleration (adding up to the usual Hooke restoring
acceleration) of the form a(t)=\frac{2\gamma ^2}{(\gamma t+1)^{2}}\tilde{y},
where \gamma is the family parameter that has been chosen as the inverse of the
Riccati integration constant. In supersymmetric terms, they represent all those
one Riccati parameter damping modes having the same Newtonian free damping
partner mode
|
9707019v4
|
2000-08-22
|
Local and Fundamental Mode Coupler Damping of the Transverse Wakefield in RDDS1 Linacs
|
In damping the wakefield generated by an electron beam traversing several
thousand X-band linacs in the NLC we utilise a Gaussian frequency distribution
of dipole modes to force the modes to deconstructively interfere, supplemented
with moderate damping achieved by coupling these modes to four attached
manifolds. Most of these modes are adequately damped by the manifolds. However,
the modes towards the high frequency end of the lower dipole band are not
adequately damped because the last few cells are, due to mechanical fabrication
requirements, not coupled to the manifolds. To mitigate this problem in the
present RDDS1 design, the output coupler for the accelerating mode has been
designed so as to also couple out those dipole modes which reach the output
coupler cell. In order to couple out both dipole mode polarizations, the output
coupler has four ports. We also report on the results of a study of the
benefits which can be achieved by supplementing manifold damping with local
damping for a limited number of cells at the downstream end of the structure.
|
0008211v1
|
2007-10-25
|
Damping of Condensate Oscillation of a Trapped Bose Gas in a One-Dimensional Optical Lattice at Finite Temperatures
|
We study damping of a dipole oscillation in a Bose-Condensed gas in a
combined cigar-shaped harmonic trap and one-dimensional (1D) optical lattice
potential at finite temperatures. In order to include the effect of thermal
excitations in the radial direction, we derive a quasi-1D model of the
Gross-Pitaeavskii equation and the Bogoliubov equations. We use the Popov
approximation to calculate the temperature dependence of the condensate
fraction with varying lattice depth. We then calculate the Landau damping rate
of a dipole oscillation as a function of the lattice depth and temperature. The
damping rate increases with increasing lattice depth, which is consistent with
experimental observations. The magnitude of the damping rate is in reasonable
agreement with experimental data. We also find that the damping rate has a
strong temperature dependence, showing a sharp increase with increasing
temperature. Finally, we emphasize the importance of the radial thermal
excitations in both equilibrium properties and the Landau damping.
|
0710.4610v1
|
2008-01-03
|
Spin orbit precession damping in transition metal ferromagnets
|
We provide a simple explanation, based on an effective field, for the
precession damping rate due to the spin-orbit interaction. Previous effective
field treatments of spin-orbit damping include only variations of the state
energies with respect to the magnetization direction, an effect referred to as
the breathing Fermi surface. Treating the interaction of the rotating spins
with the orbits as a perturbation, we include also changes in the state
populations in the effective field. In order to investigate the quantitative
differences between the damping rates of iron, cobalt, and nickel, we compute
the dependence of the damping rate on the density of states and the spin-orbit
parameter. There is a strong correlation between the density of states and the
damping rate. The intraband terms of the damping rate depend on the spin-orbit
parameter cubed while the interband terms are proportional to the spin-orbit
parameter squared. However, the spectrum of band gaps is also an important
quantity and does not appear to depend in a simple way on material parameters.
|
0801.0549v1
|
2009-02-03
|
Damping of filament thread oscillations: effect of the slow continuum
|
Transverse oscillations of small amplitude are commonly seen in
high-resolution observations of filament threads, i.e. the fine-structures of
solar filaments/prominences, and are typically damped in a few periods. Kink
wave modes supported by the thread body offer a consistent explanation of these
observed oscillations. Among the proposed mechanisms to explain the kink mode
damping, resonant absorption in the Alfven continuum seems to be the most
efficient as it produces damping times of about 3 periods. However, for a
nonzero-beta plasma and typical prominence conditions, the kink mode is also
resonantly coupled to slow (or cusp) continuum modes, which could further
reduce the damping time. In this Letter, we explore for the first time both
analytically and numerically the effect of the slow continuum on the damping of
transverse thread oscillations. The thread model is composed of a homogeneous
and straight cylindrical plasma, an inhomogeneous transitional layer, and the
homogeneous coronal plasma. We find that the damping of the kink mode due to
the slow resonance is much less efficient than that due to the Alfven
resonance.
|
0902.0572v2
|
2010-11-23
|
Magnetohydrodynamic kink waves in two-dimensional non-uniform prominence threads
|
We analyse the oscillatory properties of resonantly damped transverse kink
oscillations in two-dimensional prominence threads. The fine structures are
modelled as cylindrically symmetric magnetic flux tubes with a dense central
part with prominence plasma properties and an evacuated part, both surrounded
by coronal plasma. The equilibrium density is allowed to vary non-uniformly in
both the transverse and the longitudinal directions.We examine the influence of
longitudinal density structuring on periods, damping times, and damping rates
for transverse kink modes computed by numerically solving the linear resistive
magnetohydrodynamic (MHD) equations. The relevant parameters are the length of
the thread and the density in the evacuated part of the tube, two quantities
that are difficult to directly estimate from observations. We find that both of
them strongly influence the oscillatory periods and damping times, and to a
lesser extent the damping ratios. The analysis of the spatial distribution of
perturbations and of the energy flux into the resonances allows us to explain
the obtained damping times. Implications for prominence seismology, the physics
of resonantly damped kink modes in two-dimensional magnetic flux tubes, and the
heating of prominence plasmas are discussed.
|
1011.5175v2
|
2011-04-04
|
Plasmonic abilities of gold and silver spherical nanoantennas in terms of size dependent multipolar resonance frequencies and plasmon damping rates
|
Absorbing and emitting optical properties of a spherical plasmonic
nanoantenna are described in terms of the size dependent resonance frequencies
and damping rates of the multipolar surface plasmons (SP). We provide the
plasmon size characteristics for gold and silver spherical particles up to the
large size retardation regime where the plasmon radiative damping is
significant. We underline the role of the radiation damping in comparison with
the energy dissipation damping in formation of receiving and transmitting
properties of a plasmonic particle. The size dependence of both: the multipolar
SP resonance frequencies and corresponding damping rates can be a convenient
tool in tailoring the characteristics of plasmonic nanoantennas for given
application. Such characteristics enable to control an operation frequency of a
plasmonic nanoantenna and to change the operation range from the spectrally
broad to spectrally narrow and vice versa. It is also possible to switch
between particle receiving (enhanced absorption) and emitting (enhanced
scattering) abilities. Changing the polarization geometry of observation it is
possible to effectively separate the dipole and the quadrupole plasmon
radiation from all the non-plasmonic contributions to the scattered light.
Keywords: surface plasmon (SP) resonance, plasmon damping rates, multipolar
plasmon
|
1104.0565v1
|
2011-11-16
|
Three-player quantum Kolkata restaurant problem under decoherence
|
Effect of quantum decoherence in a three-player quantum Kolkata restaurant
problem is investigated using tripartite entangled qutrit states. Amplitude
damping, depolarizing, phase damping, trit-phase flip and phase flip channels
are considered to analyze the behaviour of players payoffs. It is seen that
Alice's payoff is heavily influenced by the amplitude damping channel as
compared to the depolarizing and flipping channels. However, for higher level
of decoherence, Alice's payoff is strongly affected by depolarizing noise.
Whereas the behaviour of phase damping channel is symmetrical around 50 %
decoherence. It is also seen that for maximum decoherence (p=1), the influence
of amplitude damping channel dominates over depolarizing and flipping channels.
Whereas, phase damping channel has no effect on the Alice's payoff. Therefore,
the problem becomes noiseless one at maximum decoherence in case of phase
damping channel. Furthermore, the Nash equilibrium of the problem does not
change under decoherence.
|
1111.3913v2
|
2012-07-27
|
The effect of non-uniform damping on flutter in axial flow and energy harvesting strategies
|
The problem of energy harvesting from flutter instabilities in flexible
slender structures in axial flows is considered. In a recent study, we used a
reduced order theoretical model of such a system to demonstrate the feasibility
for harvesting energy from these structures. Following this preliminary study,
we now consider a continuous fluid-structure system. Energy harvesting is
modelled as strain-based damping and the slender structure under investigation
lies in a moderate fluid loading range, for which {the flexible structure} may
be destabilised by damping. The key goal of this work is to {analyse the effect
of damping distribution and intensity on the amount of energy harvested by the
system}. The numerical results {indeed} suggest that non-uniform damping
distributions may significantly improve the power harvesting capacity of the
system. For low damping levels, clustered dampers at the position of peak
curvature are shown to be optimal. Conversely for higher damping, harvesters
distributed over the whole structure are more effective.
|
1207.6484v1
|
2012-11-20
|
Damping rates of surface plasmons for particles of size from nano- to micrometers; reduction of the nonradiative decay
|
Damping rates of multipolar, localized surface plasmons (SP) of gold and
silver nanospheres of radii up to $1000nm$ were found with the tools of
classical electrodynamics. The significant increase in damping rates followed
by noteworthy decrease for larger particles takes place along with substantial
red-shift of plasmon resonance frequencies as a function of particle size. We
also introduced interface damping into our modeling, which substantially
modifies the plasmon damping rates of smaller particles. We demonstrate
unexpected reduction of the multipolar SP damping rates in certain size ranges.
This effect can be explained by the suppression of the nonradiative decay
channel as a result of the lost competition with the radiative channel. We show
that experimental dipole damping rates [H. Baida, et al., Nano Lett. 9(10)
(2009) 3463, and C. S\"onnichsen, et al., Phys. Rev. Lett. 88 (2002) 077402],
and the resulting resonance quality factors can be described in a consistent
and straightforward way within our modeling extended to particle sizes still
unavailable experimentally.
|
1211.4781v1
|
2013-10-23
|
Landau damping in a collisionless dipolar Bose gas
|
We present a theory for the Landau damping of low energy quasi-particles in a
collisionless, quasi-2D dipolar Bose gas and produce expressions for the
damping rate in uniform and non-uniform systems. Using simple energy-momentum
conservation arguments, we show that in the homogeneous system, the nature of
the low energy dispersion in a dipolar Bose gas severely inhibits Landau
damping of long wave-length excitations. For a gas with contact and dipolar
interactions, the damping rate for phonons tends to decrease with increasing
dipolar interactions; for strong dipole-dipole interactions, phonons are
virtually undamped over a broad range of temperature. The damping rate for
maxon-roton excitations is found to be significantly larger than the damping
rate for phonons.
|
1310.6386v1
|
2014-01-15
|
Damping of Terahertz Plasmons in Graphene Coupled with Surface Plasmons in Heavily-Doped Substrate
|
Coupling of plasmons in graphene at terahert (THz) frequencies with surface
plasmons in a heavily-doped substrate is studied theoretically. We reveal that
a huge scattering rate may completely damp out the plasmons, so that proper
choices of material and geometrical parameters are essential to suppress the
coupling effect and to obtain the minimum damping rate in graphene. Even with
the doping concentration 10^{19} - 10^{20} cm^{-3} and the thickness of the
dielectric layer between graphene and the substrate 100 nm, which are typical
values in real graphene samples with a heavily-doped substrate, the increase in
the damping rate is not negligible in comparison with the
acoustic-phonon-limited damping rate. Dependence of the damping rate on
wavenumber, thicknesses of graphene-to-substrate and gate-to-graphene
separation, substrate doping concentration, and dielectric constants of
surrounding materials are investigated. It is shown that the damping rate can
be much reduced by the gate screening, which suppresses the field spread of the
graphene plasmons into the substrate.
|
1401.3396v1
|
2014-11-28
|
Non-equilibrium thermodynamics of damped Timoshenko and damped Bresse systems
|
In this paper, we cast damped Timoshenko and damped Bresse systems into a
general framework for non-equilibrium thermodynamics, namely the GENERIC
(General Equation for Non-Equilibrium Reversible-Irreversible Coupling)
framework. The main ingredients of GENERIC consist of five building blocks: a
state space, a Poisson operator, a dissipative operator, an energy functional,
and an entropy functional. The GENERIC formulation of damped Timoshenko and
damped Bresse systems brings several benefits. First, it provides alternative
ways to derive thermodynamically consistent models of these systems by
construct- ing building blocks instead of invoking conservation laws and
constitutive relations. Second, it reveals clear physical and geometrical
structures of these systems, e.g., the role of the energy and the entropy as
the driving forces for the reversible and irreversible dynamics respectively.
Third, it allows us to introduce a new GENERIC model for damped Timoshenko
systems that is not existing in the literature.
|
1412.0038v2
|
2014-12-08
|
Bi-$\cal{PT}$ symmetry in nonlinearly damped dynamical systems and tailoring $\cal{PT}$ regions with position dependent loss-gain profiles
|
We investigate the remarkable role of position dependent damping in
determining the parametric regions of symmetry breaking in nonlinear
$\cal{PT}$-symmetric systems. We illustrate the nature of $\cal{PT}$-symmetry
preservation and breaking with reference to a remarkable integrable scalar
nonlinear system. In the two dimensional cases of such position dependent
damped systems, we unveil the existence of a class of novel
bi-$\cal{PT}$-symmetric systems which have two fold $\cal{PT}$ symmetries. We
analyze the dynamics of these systems and show how symmetry breaking occurs,
that is whether the symmetry breaking of the two $\cal{PT}$ symmetries occurs
in pair or occurs one by one. The addition of linear damping in these
nonlinearly damped systems induces competition between the two types of
damping. This competition results in a $\cal{PT}$ phase transition in which the
$\cal{PT}$ symmetry is broken for lower loss/gain strength and is restored by
increasing the loss/gain strength. We also show that by properly designing the
form of the position dependent damping, we can tailor the $\cal{PT}$-symmetric
regions of the system.
|
1412.2574v3
|
2015-09-04
|
Damped transverse oscillations of interacting coronal loops
|
Damped transverse oscillations of magnetic loops are routinely observed in
the solar corona. This phenomenon is interpreted as standing kink
magnetohydrodynamic waves, which are damped by resonant absorption owing to
plasma inhomogeneity across the magnetic field. The periods and damping times
of these oscillations can be used to probe the physical conditions of the
coronal medium. Some observations suggest that interaction between neighboring
oscillating loops in an active region may be important and can modify the
properties of the oscillations compared to those of an isolated loop. Here we
theoretically investigate resonantly damped transverse oscillations of
interacting non-uniform coronal loops. We provide a semi-analytic method, based
on the T-matrix theory of scattering, to compute the frequencies and damping
rates of collective oscillations of an arbitrary configuration of parallel
cylindrical loops. The effect of resonant damping is included in the T-matrix
scheme in the thin boundary approximation. Analytic and numerical results in
the specific case of two interacting loops are given as an application.
|
1509.01487v1
|
2015-09-14
|
Beliaev damping in quasi-2D dipolar condensates
|
We study the effects of quasiparticle interactions in a quasi-two dimensional
(quasi-2D), zero-temperature Bose-Einstein condensate of dipolar atoms, which
can exhibit a roton-maxon feature in its quasiparticle spectrum. Our focus is
the Beliaev damping process, in which a quasiparticle collides with the
condensate and resonantly decays into a pair of quasiparticles. Remarkably, the
rate for this process exhibits a highly non-trivial dependence on the
quasiparticle momentum and the dipolar interaction strength. For weak
interactions, the low energy phonons experience no damping, and the higher
energy quasiparticles undergo anomalously weak damping. In contrast, the
Beliaev damping rates become anomalously large for stronger dipolar
interactions, as rotons become energetically accessible as final states.
Further, we find a qualitative anisotropy in the damping rates when the dipoles
are tilted off the axis of symmetry. Our study reveals the unconventional
nature of Beliaev damping in dipolar condensates, and has important
implications for ongoing studies of equilibrium and non-equilibrium dynamics in
these systems.
|
1509.04217v1
|
2015-12-08
|
Thermal energies of classical and quantum damped oscillators coupled to reservoirs
|
We consider the global thermal state of classical and quantum harmonic
oscillators that interact with a reservoir. Ohmic damping of the oscillator can
be exactly treated with a 1D scalar field reservoir, whereas general non-Ohmic
damping is conveniently treated with a continuum reservoir of harmonic
oscillators. Using the diagonalized Hamiltonian of the total system, we
calculate a number of thermodynamic quantities for the damped oscillator: the
mean force internal energy, mean force free energy, and another internal energy
based on the free-oscillator Hamiltonian. The classical mean force energy is
equal to that of a free oscillator, for both Ohmic and non-Ohmic damping and no
matter how strong the coupling to the reservoir. In contrast, the quantum mean
force energy depends on the details of the damping and diverges for strictly
Ohmic damping. These results give additional insight into the steady-state
thermodynamics of open systems with arbitrarily strong coupling to a reservoir,
complementing results for energies derived within dynamical approaches (e.g.
master equations) in the weak-coupling regime.
|
1512.02551v2
|
2016-05-17
|
Simultaneous Identification of Damping Coefficient and Initial Value in PDEs from boundary measurement
|
In this paper, the simultaneous identification of damping or anti-damping
coefficient and initial value for some PDEs is considered. An identification
algorithm is proposed based on the fact that the output of system happens to be
decomposed into a product of an exponential function and a periodic function.
The former contains information of the damping coefficient, while the latter
does not. The convergence and error analysis are also developed. Three
examples, namely an anti-stable wave equation with boundary anti-damping, the
Schr\"odinger equation with internal anti-damping, and two connected strings
with middle joint anti-damping, are investigated and demonstrated by numerical
simulations to show the effectiveness of the proposed algorithm.
|
1605.05063v1
|
2016-08-30
|
Optimal damping ratios of multi-axial perfectly matched layers for elastic-wave modeling in general anisotropic media
|
The conventional Perfectly Matched Layer (PML) is unstable for certain kinds
of anisotropic media. This instability is intrinsic and independent of PML
formulation or implementation. The Multi-axial PML (MPML) removes such
instability using a nonzero damping coefficient in the direction parallel with
the interface between a PML and the investigated domain. The damping ratio of
MPML is the ratio between the damping coefficients along the directions
parallel with and perpendicular to the interface between a PML and the
investigated domain. No quantitative approach is available for obtaining these
damping ratios for general anisotropic media. We develop a quantitative
approach to determining optimal damping ratios to not only stabilize PMLs, but
also minimize the artificial reflections from MPMLs. Numerical tests based on
finite-difference method show that our new method can effectively provide a set
of optimal MPML damping ratios for elastic-wave propagation in 2D and 3D
general anisotropic media.
|
1608.08326v3
|
2016-10-10
|
A Five-Freedom Active Damping and Alignment Device Used in the Joule Balance
|
Damping devices are necessary for suppressing the undesired coil motions in
the watt/joule balance. In this paper, an active electromagnetic damping
device, located outside the main magnet, is introduced in the joule balance
project. The presented damping device can be used in both dynamic and static
measurement modes. With the feedback from a detection system, five degrees of
freedom of the coil, i.e. the horizontal displacement $x$, $y$ and the rotation
angles $\theta_x$, $\theta_y$, $\theta_z$, can be controlled by the active
damping device. Hence, two functions, i.e. suppressing the undesired coil
motions and reducing the misalignment error, can be realized with this active
damping device. The principle, construction and performance of the proposed
active damping device are presented.
|
1610.02799v1
|
2016-10-01
|
The destabilizing effect of external damping: Singular flutter boundary for the Pfluger column with vanishing external dissipation
|
Elastic structures loaded by nonconservative positional forces are prone to
instabilities induced by dissipation: it is well-known in fact that internal
viscous damping destabilizes the marginally stable Ziegler's pendulum and
Pfluger column (of which the Beck's column is a special case), two structures
loaded by a tangential follower force. The result is the so-called
'destabilization paradox', where the critical force for flutter instability
decreases by an order of magnitude when the coefficient of internal damping
becomes infinitesimally small. Until now external damping, such as that related
to air drag, is believed to provide only a stabilizing effect, as one would
intuitively expect. Contrary to this belief, it will be shown that the effect
of external damping is qualitatively the same as the effect of internal
damping, yielding a pronounced destabilization paradox. Previous results
relative to destabilization by external damping of the Ziegler's and Pfluger's
elastic structures are corrected in a definitive way leading to a new
understanding of the destabilizating role played by viscous terms.
|
1611.03886v1
|
2017-10-10
|
A four-field gyrofluid model with neoclassical effects for the study of the rotation velocity of magnetic islands in tokamaks
|
A four-field system of equations which includes the neoclassical flow damping
effects and the lowest-order finite-Larmor-radius (FLR) corrections is deduced
from a system of gyrofluid equations. The FLR corrections to the poloidal flow
damping are calculated by solving a simplified version of the gyrokinetic
equation. This system of equations is applied to the study of a chain of freely
rotating magnetic islands in a tokamak, resulting from the nonlinear evolution
of a resistive tearing mode, to determine the islands rotation velocity
consistently with the fields radial profiles close to the resonant surface. The
island rotation velocity is determined by imposing the torque-balance
condition. The equations thus deduced are applied to the study of two different
collisional regimes, namely the weak-damping regime and the intermediate
damping regime. The equations reduce, in the weak damping regime, to a form
already obtained in previous works, while an additional term, containing the
lowest order FLR corrections to the poloidal flow damping, appears in the
intermediate damping regime. The numerical integration of the final system of
equations permits to determine the dependence of the island rotation velocity
on the plasma collisionality and the islands width compared to the ion Larmor
radius.
|
1710.03585v1
|
2017-10-13
|
Mode-Dependent Damping in Metallic Antiferromagnets Due to Inter-Sublattice Spin Pumping
|
Damping in magnetization dynamics characterizes the dissipation of magnetic
energy and is essential for improving the performance of spintronics-based
devices. While the damping of ferromagnets has been well studied and can be
artificially controlled in practice, the damping parameters of
antiferromagnetic materials are nevertheless little known for their physical
mechanisms or numerical values. Here we calculate the damping parameters in
antiferromagnetic dynamics using the generalized scattering theory of
magnetization dissipation combined with the first-principles transport
computation. For the PtMn, IrMn, PdMn and FeMn metallic antiferromagnets, the
damping coefficient associated with the motion of magnetization ($\alpha_m$) is
one to three orders of magnitude larger than the other damping coefficient
associated with the variation of the N\'eel order ($\alpha_n$), in sharp
contrast to the assumptions made in the literature.
|
1710.04766v1
|
2017-12-04
|
Resonance oscillation of a damped driven simple pendulum
|
The resonance characteristics of a driven damped harmonic oscillator are well
known. Unlike harmonic oscillators which are guided by parabolic potentials, a
simple pendulum oscillates under sinusoidal potentials. The problem of an
undamped pendulum has been investigated to a great extent. However, the
resonance characteristics of a driven damped pendulum have not been re- ported
so far due to the difficulty in solving the problem analytically. In the
present work we report the resonance characteristics of a driven damped
pendulum calculated numerically. The results are compared with the resonance
characteristics of a damped driven harmonic oscillator. The work can be of
pedagogic interest too as it reveals the richness of driven damped motion of a
simple pendulum in comparison to and how strikingly it differs from the motion
of a driven damped harmonic oscillator. We confine our work only to the
nonchaotic regime of pendulum motion.
|
1712.01032v1
|
2018-01-17
|
On Global Existence and Blow-up for Damped Stochastic Nonlinear Schrödinger Equation
|
In this paper, we consider the well-posedness of the weakly damped stochastic
nonlinear Schr\"odinger(NLS) equation driven by multiplicative noise. First, we
show the global existence of the unique solution for the damped stochastic NLS
equation in critical case. Meanwhile, the exponential integrability of the
solution is proved, which implies the continuous dependence on the initial
data. Then, we analyze the effect of the damped term and noise on the blow-up
phenomenon. By modifying the associated energy, momentum and variance identity,
we deduce a sharp blow-up condition for damped stochastic NLS equation in
supercritical case. Moreover, we show that when the damped effect is large
enough, the damped effect can prevent the blow-up of the solution with high
probability.
|
1801.05630v1
|
2018-03-29
|
Giant resonant nonlinear damping in nanoscale ferromagnets
|
Magnetic damping is a key metric for emerging technologies based on magnetic
nanoparticles, such as spin torque memory and high-resolution biomagnetic
imaging. Despite its importance, understanding of magnetic dissipation in
nanoscale ferromagnets remains elusive, and the damping is often treated as a
phenomenological constant. Here we report the discovery of a giant
frequency-dependent nonlinear damping that strongly alters the response of a
nanoscale ferromagnet to spin torque and microwave magnetic field. This novel
damping mechanism originates from three-magnon scattering that is strongly
enhanced by geometric confinement of magnons in the nanomagnet. We show that
the giant nonlinear damping can invert the effect of spin torque on a
nanomagnet leading to a surprising current-induced enhancement of damping by an
antidamping torque. Our work advances understanding of magnetic dynamics in
nanoscale ferromagnets and spin torque devices.
|
1803.10925v1
|
2018-05-16
|
Stabilization rates for the damped wave equation with Hölder-regular damping
|
We study the decay rate of the energy of solutions to the damped wave
equation in a setup where the geometric control condition is violated. We
consider damping coefficients which are $0$ on a strip and vanish like
polynomials, $x^{\beta}$. We prove that the semigroup cannot be stable at rate
faster than $1/t^{(\beta+2)/(\beta+3)}$ by producing quasimodes of the
associated stationary damped wave equation. We also prove that the semigroup is
stable at rate at least as fast as $1/t^{(\beta+2)/(\beta+4)}$. These two
results establish an explicit relation between the rate of vanishing of the
damping and rate of decay of solutions. Our result partially generalizes a
decay result of Nonnemacher in which the damping is an indicator function on a
strip.
|
1805.06535v3
|
2019-03-01
|
Comprehensive Study of Neutrino-Dark Matter Mixed Damping
|
Mixed damping is a physical effect that occurs when a heavy species is
coupled to a relativistic fluid which is itself free streaming. As a cross-case
between collisional damping and free-streaming, it is crucial in the context of
neutrino-dark matter interactions. In this work, we establish the parameter
space relevant for mixed damping, and we derive an analytical approximation for
the evolution of dark matter perturbations in the mixed damping regime to
illustrate the physical processes responsible for the suppression of
cosmological perturbations. Although extended Boltzmann codes implementing
neutrino-dark matter scattering terms automatically include mixed damping, this
effect has not been systematically studied. In order to obtain reliable
numerical results, it is mandatory to reconsider several aspects of
neutrino-dark matter interactions, such as the initial conditions, the
ultra-relativistic fluid approximation and high order multiple moments in the
neutrino distribution. Such a precise treatment ensures the correct assessment
of the relevance of mixed damping in neutrino-dark matter interactions.
|
1903.00540v2
|
2019-08-04
|
Efficient spin excitation via ultrafast damping-like torques in antiferromagnets
|
Damping effects form the core of many emerging concepts for high-speed
spintronic applications. Important characteristics such as device switching
times and magnetic domain-wall velocities depend critically on the damping
rate. While the implications of spin damping for relaxation processes are
intensively studied, damping effects during impulsive spin excitations are
assumed to be negligible because of the shortness of the excitation process.
Herein, we show that, unlike in ferromagnets, ultrafast damping plays a crucial
role in antiferromagnets because of their strongly elliptical spin precession.
In time-resolved measurements, we find that ultrafast damping results in an
immediate spin canting along the short precession axis. The interplay between
antiferromagnetic exchange and magnetic anisotropy amplifies this canting by
several orders of magnitude towards large-amplitude modulations of the
antiferromagnetic order parameter. This leverage effect discloses a highly
efficient route towards the ultrafast manipulation of magnetism in
antiferromagnetic spintronics.
|
1908.01359v3
|
2019-10-31
|
Gyrokinetic investigation of the damping channels of Alfvén modes in ASDEX Upgrade
|
The linear destabilization and nonlinear saturation of energetic-particle
driven Alfv\'enic instabilities in tokamaks strongly depend on the damping
channels. In this work, the collisionless damping mechanisms of Alfv\'enic
modes are investigated within a gyrokinetic framework, by means of global
simulations with the particle-in-cell code ORB5, and compared with the
eigenvalue code LIGKA and reduced models. In particular, the continuum damping
and the Landau damping (of ions and electrons) are considered. The electron
Landau damping is found to be dominant on the ion Landau damping for
experimentally relevant cases. As an application, the linear and nonlinear
dynamics of toroidicity induced Alfv\'en eigenmodes and energetic-particle
driven modes in ASDEX Upgrade is investigated theoretically and compared with
experimental measurements.
|
1910.14489v1
|
2020-03-13
|
Anharmonic phonon damping enhances the $T_c$ of BCS-type superconductors
|
A theory of superconductivity is presented where the effect of anharmonicity,
as entailed in the acoustic, or optical, phonon damping, is explicitly
considered in the pairing mechanism. The gap equation is solved including
diffusive Akhiezer damping for longitudinal acoustic phonons or Klemens damping
for optical phonons, with a damping coefficient which, in either case, can be
directly related to the Gruneisen parameter and hence to the anharmonic
coefficients in the interatomic potential. The results show that the increase
of anharmonicity has a strikingly non-monotonic effect on the critical
temperature $T_{c}$. The optimal damping coefficient yielding maximum $T_c$ is
set by the velocity of the bosonic mediator. This theory may open up
unprecedented opportunities for material design where $T_{c}$ may be tuned via
the anharmonicity of the interatomic potential, and presents implications for
the superconductivity in the recently discovered hydrides, where anharmonicity
is very strong and for which the anharmonic damping is especially relevant.
|
2003.06220v2
|
2020-03-29
|
Stability results for an elastic-viscoelastic waves interaction systems with localized Kelvin-Voigt damping and with an internal or boundary time delay
|
We investigate the stability of a one-dimensional wave equation with non
smooth localized internal viscoelastic damping of Kelvin-Voigt type and with
boundary or localized internal delay feedback. The main novelty in this paper
is that the Kelvin-Voigt and the delay damping are both localized via non
smooth coefficients. In the case that the Kelvin-Voigt damping is localized
faraway from the tip and the wave is subjected to a locally distributed
internal or boundary delay feedback, we prove that the energy of the system
decays polynomially of type t^{-4}. However, an exponential decay of the energy
of the system is established provided that the Kelvin-Voigt damping is
localized near a part of the boundary and a time delay damping acts on the
second boundary. While, when the Kelvin-Voigt and the internal delay damping
are both localized via non smooth coefficients near the tip, the energy of the
system decays polynomially of type t^{-4}. Frequency domain arguments combined
with piecewise multiplier techniques are employed.
|
2003.12967v1
|
2020-09-16
|
Fast convex optimization via inertial dynamics combining viscous and Hessian-driven damping with time rescaling
|
In a Hilbert setting, we develop fast methods for convex unconstrained
optimization. We rely on the asymptotic behavior of an inertial system
combining geometric damping with temporal scaling. The convex function to
minimize enters the dynamic via its gradient. The dynamic includes three
coefficients varying with time, one is a viscous damping coefficient, the
second is attached to the Hessian-driven damping, the third is a time scaling
coefficient. We study the convergence rate of the values under general
conditions involving the damping and the time scale coefficients. The obtained
results are based on a new Lyapunov analysis and they encompass known results
on the subject. We pay particular attention to the case of an asymptotically
vanishing viscous damping, which is directly related to the accelerated
gradient method of Nesterov. The Hessian-driven damping significantly reduces
the oscillatory aspects. As a main result, we obtain an exponential rate of
convergence of values without assuming the strong convexity of the objective
function. The temporal discretization of these dynamics opens the gate to a
large class of inertial optimization algorithms.
|
2009.07620v1
|
2020-12-27
|
Quantum speed limit time in relativistic frame
|
We investigate the roles of the relativistic effect on the speed of evolution
of a quantum system coupled with amplitude damping channels. We find that the
relativistic effect speed-up the quantum evolution to a uniform evolution speed
of open quantum systems for the damping parameter $p_{\tau}\lesssim
p_{\tau_{c0}}.$ Moreover, we point out a non-monotonic behavior of the quantum
speed limit time (QSLT) with acceleration in the damping limit
$p_{\tau_{c0}}\lesssim p_{\tau}\lesssim p_{\tau_{c1}},$ where the relativistic
effect first speed-up and then slow down the quantum evolution process of the
damped system. For the damping strength $p_{\tau_{c1}}\lesssim p_{\tau}$, we
observe a monotonic increasing behavior of QSLT, leads to slow down the quantum
evolution of the damped system. In addition, we examine the roles of the
relativistic effect on the speed limit time for a system coupled with the phase
damping channels.
|
2012.13859v2
|
2021-06-23
|
Regularization of central forces with damping in two and three-dimensions
|
Regularization of damped motion under central forces in two and
three-dimensions are investigated and equivalent, undamped systems are
obtained. The dynamics of a particle moving in $\frac{1}{r}$ potential and
subjected to a damping force is shown to be regularized a la Levi-Civita. We
then generalize this regularization mapping to the case of damped motion in the
potential $r^{-\frac{2N}{N+1}}$. Further equation of motion of a damped Kepler
motion in 3-dimensions is mapped to an oscillator with inverted sextic
potential and couplings, in 4-dimensions using Kustaanheimo-Stiefel
regularization method. It is shown that the strength of the sextic potential is
given by the damping co-efficient of the Kepler motion. Using homogeneous
Hamiltonian formalism, we establish the mapping between the Hamiltonian of
these two models. Both in 2 and 3-dimensions, we show that the regularized
equation is non-linear, in contrast to undamped cases. Mapping of a particle
moving in a harmonic potential subjected to damping to an undamped system with
shifted frequency is then derived using Bohlin-Sudman transformation.
|
2106.12134v1
|
2021-07-06
|
Theory of vibrators with variable-order fractional forces
|
In this paper, we present a theory of six classes of vibrators with
variable-order fractional forces of inertia, damping, and restoration. The
novelty and contributions of the present theory are reflected in six aspects.
1) Equivalent motion equations of those variable-order fractional vibrators are
proposed. 2) The analytical expressions of the effective mass, damping, and
stiffness of those variable-order fractional vibrators are presented. 3) The
asymptotic properties of the effective mass, damping, and stiffness of a class
of variable-order fractional vibrators are given. 4) The restricted effective
parameters (damping ratio, damping free natural frequency, damped natural
frequency, frequency ratio) of the variable-order fractional vibrators are put
forward. 5) We bring forward the analytical representations of the free
responses, the impulse responses, and the frequency transfer functions of those
variable-order fractional vibrators. 6) We propose a solution to an open
problem of how to mathematically explain the Rayleigh damping assumption based
on the present theory of variable-order fractional vibrations.
|
2107.02340v2
|
2021-08-15
|
Exponential stability of a damped beam-string-beam transmission problem
|
We consider a beam-string-beam transmission problem, where two structurally
damped or undamped beams are coupled with a frictionally damped string by
transmission conditions. We show that for this type of structure, the
dissipation produced by the frictional part is strong enough to produce
exponential decay of the solution no matter how small is its size: for the
exponential stability in the damped-damped-damped situation we use energy
method and in the undamped-damped-undamped situation we use a frequency domain
method from the semigroups theory, which combines a contradiction argument with
the multiplier technique to carry out a special analysis for the resolvent.
Additionally, we show that the solution first defined by the weak formulation,
in fact, has higher Sobolev space regularity.
|
2108.06749v1
|
2021-09-10
|
Fourth-order dynamics of the damped harmonic oscillator
|
It is shown that the classical damped harmonic oscillator belongs to the
family of fourth-order Pais-Uhlenbeck oscillators. It follows that the
solutions to the damped harmonic oscillator equation make the Pais-Uhlenbeck
action stationary. Two systematic approaches are given for deriving the
Pais-Uhlenbeck action from the damped harmonic oscillator equation, and it may
be possible to use these methods to identify stationary action principles for
other dissipative systems which do not conform to Hamilton's principle. It is
also shown that for every damped harmonic oscillator $x$, there exists a
two-parameter family of dual oscillators $y$ satisfying the Pais-Uhlenbeck
equation. The damped harmonic oscillator and any of its duals can be
interpreted as a system of two coupled oscillators with atypical spring
stiffnesses (not necessarily positive and real-valued). For overdamped systems,
the resulting coupled oscillators should be physically achievable and may have
engineering applications. Finally, a new physical interpretation is given for
the optimal damping ratio $\zeta=1/\sqrt{2}$ in control theory.
|
2109.06034v1
|
2022-01-13
|
Damping of Alfvén waves in MHD turbulence and implications for cosmic ray streaming instability and galactic winds
|
Alfv\'{e}nic component of MHD turbulence damps Alfv\'{e}nic waves. The
consequences of this effect are important for many processes, from cosmic ray
(CR) propagation to launching outflows and winds in galaxies and other
magnetized systems. We discuss the differences in the damping of the streaming
instability by turbulence and the damping of a plane parallel wave. The former
takes place in the system of reference aligned with the local direction of
magnetic field along which CRs stream. The latter is in the reference frame of
the mean magnetic field and traditionally considered in plasma studies. We also
compare the turbulent damping of streaming instability with ion-neutral
collisional damping, which becomes the dominant damping effect at a
sufficiently low ionization fraction. Numerical testing and astrophysical
implications are also discussed.
|
2201.05168v1
|
2022-03-14
|
Investigation of nonlinear squeeze-film damping involving rarefied gas effect in micro-electro-mechanical-systems
|
In this paper, the nonlinear squeeze-film damping (SFD) involving rarefied
gas effect in the micro-electro-mechanical-systems (MEMS) is investigated.
Considering the motion of structures (beam, cantilever, and membrane) in MEMS,
the dynamic response of structure will be influenced largely by the
squeeze-film damping. In the traditional model, a viscous damping assumption
that damping force is linear with moving velocity is used. As the nonlinear
damping phenomenon is observed for a micro-structure oscillating with a
high-velocity, this assumption is invalid and will generates error result for
predicting the response of micro-structure. In addition, due to the small size
of device and the low pressure of encapsulation, the gas in MEMS usually is
rarefied gas. Therefore, to correctly predict the damping force, the rarefied
gas effect must be considered. To study the nonlinear SFD phenomenon involving
the rarefied gas effect, a kinetic method, namely discrete unified gas kinetic
scheme (DUGKS), is introduced. And based on DUGKS, two solving methods, a
traditional decoupled method (Eulerian scheme) and a coupled framework
(arbitrary Lagrangian-Eulerian scheme), are adopted. With these two methods,
two basic motion forms, linear (perpendicular) and tilting motions of a rigid
micro-beam, are studied with forced and free oscillations.
|
2203.06902v1
|
2022-05-21
|
Noether symmetries and first integrals of damped harmonic oscillator
|
Noether theorem establishes an interesting connection between symmetries of
the action integral and conservation laws of a dynamical system. The aim of the
present work is to classify the damped harmonic oscillator problem with respect
to Noether symmetries and to construct corresponding conservation laws for all
over-damped, under damped and critical damped cases. For each case we obtain
maximum five linearly independent group generators which provide related five
conserved quantities. Remarkably, after obtaining complete set of invariant
quantities we obtain analytical solutions for each case. In the current work,
we also introduce a new Lagrangian for the damped harmonic oscillator. Though
the form of this new Lagrangian and presented by Bateman are completely
different, yet it generates same set of Noether symmetries and conserved
quantities. So, this new form of Lagrangian we are presenting here may be
seriously interesting for the physicists. Moreover, we also find the Lie
algebras of Noether symmetries and point out some interesting aspects of
results related to Noether symmetries and first integrals of damped harmonic
oscillator which perhaps not reported in the earlier studies.
|
2205.10525v1
|
2023-01-31
|
The emergence of soft-glassy mechanics in simulated foams
|
Several seemingly different soft materials, including foams, cells, and many
complex fluids, exhibit remarkably similar rheological properties and
microscopic dynamics, termed soft glassy mechanics. Here, we show that such
behavior emerges from a simple model of a damped ripening foam, for
sufficiently weak damping. In particular, we observe intermittent avalanchey
dynamics, bubble super-diffusion, and power-law rheology that vary as the
damping factor is changed. In the limit of weak damping, the dynamics are
determined by the tortuous low-lying portions of the energy landscape, as
described in a recent study. For strong damping the viscous stresses cause the
system configuration to evolve along higher energy paths, washing out
small-scale tortuosity and producing motion with an increasingly ballistic
character. Using a microrheological approach, the linear viscoelastic response
of the model can be efficiently calculated. This resembles the power-law
rheology expected for soft glassy mechanics, but unexpectedly, is only weakly
sensitive to the damping parameter. Lastly, we study the reported memory effect
in foams after large perturbations and find that the timescale of the memory
goes to zero as the damping parameter vanishes, suggesting that the effect is
due to viscous stress relaxation rather than slow structural changes stabilized
by the energy landscape.
|
2301.13400v1
|
2023-02-13
|
Thickness and temperature dependent damping in La$_{0.67}$Sr$_{0.33}$MnO$_{3}$ epitaxial films
|
The damping of La0.67Sr0.33MnO3 (LSMO) epitaxial films as a function of
thickness at different temperatures was studied. The competition between two
scattering types (\r{ho}-like and {\sigma}-like) with entirely distinct
thickness and temperature dependencies resulted in complicated damping
behavior. The behavior of {\sigma}-like damping in LSMO films is consistent
with the behavior in magnetic metal films. However, because \r{ho}-like damping
is sensitive to the fine electron structure near the Fermi surface, the
distortion of the oxygen octahedra controlled by the film thickness is an
important factor in controlling the damping. Our study demonstrates that the
complexity of damping in LSMO epitaxial films is a consequence of
strong-correlation effects, which are characteristic of complex
transition-metal oxides.
|
2302.06099v3
|
2023-09-15
|
On the formation of singularities for the slightly supercritical NLS equation with nonlinear damping
|
We consider the focusing, mass-supercritical NLS equation augmented with a
nonlinear damping term. We provide sufficient conditions on the nonlinearity
exponents and damping coefficients for finite-time blow-up. In particular,
singularities are formed for focusing and dissipative nonlinearities of the
same power, provided that the damping coefficient is sufficiently small. Our
result thus rigorously proves the non-regularizing effect of nonlinear damping
in the mass-supercritical case, which was suggested by previous numerical and
formal results.
We show that, under our assumption, the damping term may be controlled in
such a way that the self-similar blow-up structure for the focusing NLS is
approximately retained even within the dissipative evolution. The nonlinear
damping contributes as a forcing term in the equation for the perturbation
around the self-similar profile, that may produce a growth over finite time
intervals. We estimate the error terms through a modulation analysis and a
careful control of the time evolution of total momentum and energy functionals.
|
2309.08281v1
|
1998-05-07
|
Discovery of z=0.0912 and z=0.2212 Damped Lyman-alpha Absorption Line Systems Toward the Quasar OI 363: Limits on the Nature of Damped Lyman-alpha Galaxies
|
The discovery of a z_abs = 0.0912 damped Lyman-alpha absorption-line system
in the HST-FOS ultraviolet spectrum of the quasar OI 363 (0738+313) is
reported. This is the lowest redshift quasar damped Lyman-alpha system known.
Its neutral hydrogen column density is N(HI) = 1.5(+/- 0.2) E21 atoms/cm^2,
which easily exceeds the classical criterion for damped Lyman-alpha of N(HI)
greater than or equal to 2E20 atoms/cm^2. Remarkably, a z_abs = 0.2212 damped
system with N(HI) = 7.9(+/- 1.4) E20 atoms/cm^2 has also been discovered in the
same spectrum.
In the past, the standard paradigm for damped Lyman-alpha systems has been
that they arise in galactic or protogalactic HI disks with low impact
parameters in luminous galaxies. However, WIYN imaging of the OI 363 field
shows that none of the galaxies visible in the vicinity of the quasar is a
luminous gas-rich spiral with low impact parameter, either at z = 0.0912 or z =
0.2212. Thus, these damped systems are among the clearest examples yet of cases
that are inconsistent with the standard damped Lyman-alpha - HI-disk paradigm.
|
9805093v1
|
2008-01-24
|
Attenuation of small-amplitude oscillations in a prominence-corona model with a transverse magnetic field
|
Small-amplitude prominence oscillations are usually damped after a few
periods. We study the attenuation of non-adiabatic magnetoacoustic waves in a
slab prominence embedded in the coronal medium. We assume an equilibrium
configuration with a transverse magnetic field to the slab axis and investigate
wave damping by thermal conduction and radiative losses. The differential MHD
equations that govern linear slow and fast modes are numerically solved to
obtain the complex oscillatory frequency and the corresponding eigenfunctions.
We find that coronal thermal conduction and radiative losses from the
prominence plasma reveal as the most relevant damping mechanisms. Both
mechanisms govern together the attenuation of hybrid modes, whereas prominence
radiation is responsible for the damping of internal modes and coronal
conduction essentially dominates the attenuation of external modes. In
addition, the energy transfer between the prominence and the corona caused by
thermal conduction has a noticeable effect on the wave stability, radiative
losses from the prominence plasma being of paramount importance for the thermal
stability of fast modes. We conclude that slow modes are efficiently damped,
with damping times compatible with observations. On the contrary, fast modes
are less attenuated by non-adiabatic effects and their damping times are
several orders of magnitude larger than those observed. The presence of the
corona causes a decrease of the damping times with respect to those of an
isolated prominence slab, but its effect is still insufficient to obtain
damping times of the order of the period in the case of fast modes.
|
0801.3744v2
|
2010-04-26
|
Selective spatial damping of propagating kink waves due to resonant absorption
|
There is observational evidence of propagating kink waves driven by
photospheric motions. These disturbances, interpreted as kink
magnetohydrodynamic (MHD) waves are attenuated as they propagate upwards in the
solar corona. In this paper we show that resonant absorption provides a simple
explanation to the spatial damping of these waves. Kink MHD waves are studied
using a cylindrical model of solar magnetic flux tubes which includes a
non-uniform layer at the tube boundary. Assuming that the frequency is real and
the longitudinal wavenumber complex, the damping length and damping per
wavelength produced by resonant absorption are analytically calculated. The
damping length of propagating kink waves due resonant absorption is a
monotonically decreasing function of frequency. For kink waves with low
frequencies the damping length is exactly inversely proportional to frequency
and we denote this as the TGV relation. When moving to high frequencies the TGV
relation continues to be an exceptionally good approximation of the actual
dependency of the damping length on frequency. This dependency means that
resonant absorption is selective as it favours low frequency waves and can
efficiently remove high frequency waves from a broad band spectrum of kink
waves. It is selective as the damping length is inversely proportional to
frequency so that the damping becomes more severe with increasing frequency.
This means that radial inhomogeneity can cause solar waveguides to be a natural
low-pass filter for broadband disturbances. Hence kink wave trains travelling
along, e.g., coronal loops, will have a greater proportion of the high
frequency components dissipated lower down in the atmosphere. This could have
important consequences with respect to the spatial distribution of wave heating
in the solar atmosphere.
|
1004.4468v1
|
2011-04-10
|
Spatial Damping of Propagating Kink Waves Due to Resonant Absorption: Effect of Background Flow
|
Observations show the ubiquitous presence of propagating magnetohydrodynamic
(MHD) kink waves in the solar atmosphere. Waves and flows are often observed
simultaneously. Due to plasma inhomogeneity in the perpendicular direction to
the magnetic field, kink waves are spatially damped by resonant absorption. The
presence of flow may affect the wave spatial damping. Here, we investigate the
effect of longitudinal background flow on the propagation and spatial damping
of resonant kink waves in transversely nonuniform magnetic flux tubes. We
combine approximate analytical theory with numerical investigation. The
analytical theory uses the thin tube (TT) and thin boundary (TB) approximations
to obtain expressions for the wavelength and the damping length. Numerically,
we verify the previously obtained analytical expressions by means of the full
solution of the resistive MHD eigenvalue problem beyond the TT and TB
approximations. We find that the backward and forward propagating waves have
different wavelengths and are damped on length scales that are inversely
proportional to the frequency as in the static case. However, the factor of
proportionality depends on the characteristics of the flow, so that the damping
length differs from its static analogue. For slow, sub-Alfvenic flows the
backward propagating wave gets damped on a shorter length scale than in the
absence of flow, while for the forward propagating wave the damping length is
longer. The different properties of the waves depending on their direction of
propagation with respect to the background flow may be detected by the
observations and may be relevant for seismological applications.
|
1104.1791v1
|
2013-02-08
|
On the Damping-Induced Self-Recovery Phenomenon in Mechanical Systems with Several Unactuated Cyclic Variables
|
The damping-induced self-recovery phenomenon refers to the fundamental
property of underactuated mechanical systems: if an unactuated cyclic variable
is under a viscous damping-like force and the system starts from rest, then the
cyclic variable will always move back to its initial condition as the actuated
variables come to stop. The regular momentum conservation phenomenon can be
viewed as the limit of the damping-induced self-recovery phenomenon in the
sense that the self-recovery phenomenon disappears as the damping goes to zero.
This paper generalizes the past result on damping-induced self-recovery for the
case of a single unactuated cyclic variable to the case of multiple unactuated
cyclic variables. We characterize a class of external forces that induce new
conserved quantities, which we call the damping-induced momenta. The
damping-induced momenta yield first-order asymptotically stable dynamics for
the unactuated cyclic variables under some conditions, thereby inducing the
self-recovery phenomenon. It is also shown that the viscous damping-like forces
impose bounds on the range of trajectories of the unactuated cyclic variables.
Two examples are presented to demonstrate the analytical discoveries: the
planar pendulum with gimbal actuators and the three-link planar manipulator on
a horizontal plane.
|
1302.2109v1
|
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