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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 |
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 |
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 |
2014-11-28 | 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 |
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 |
2016-10-10 | 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 |
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 |
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 |
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 |
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 |
2016-08-30 | 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 |
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 |
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 |
2018-05-16 | 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 |
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 |
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 |
2016-07-06 | Damping of Alfven waves by Turbulence and its Consequences: from Cosmic-Rays Streaming to Launching Winds | This paper considers turbulent damping of Alfven waves in magnetized plasmas.
We identify two cases of damping, one related to damping of cosmic rays
streaming instability, the other related to damping of Alfven waves emitted by
a macroscopic wave source, e.g. stellar atmosphere. The physical difference
between the two cases is that in the former case the generated waves are
emitted in respect to the local direction of magnetic field, in the latter in
respect to the mean field. The scaling of damping is different in the two
cases. We the regimes of turbulence ranging from subAlfvenic to superAlfvenic
we obtain analytical expressions for the damping rates and define the ranges of
applicability of these expressions. Describing the damping of the streaming
instability, we find that for subAlfvenic turbulence the range of cosmic ray
energies influenced by weak turbulence is unproportionally large compared to
the range of scales that the weak turbulence is present. On the contrary, the
range of cosmic ray energies affected by strong Alfvenic turbulence is rather
limited. A number of astrophysical applications of the process ranging from
launching of stellar and galactic winds to propagation of cosmic rays in
galaxies and clusters of galaxies is considered. In particular, we discuss how
to reconcile the process of turbulent damping with the observed isotropy of the
Milky Way cosmic rays. | 1607.02042v1 |
2018-01-18 | Quantum Landau damping in dipolar Bose-Einstein condensates | We consider Landau damping of elementary excitations in Bose-Einstein
condensates (BECs) with dipolar interactions. We discuss quantum and
quasi-classical regimes of Landau damping. We use a generalized wave-kinetic
description of BECs which, apart from the long range dipolar interactions, also
takes into account the quantum fluctuations and the finite energy corrections
to short-range interactions. Such a description is therefore more general than
the usual mean field approximation. The present wave-kinetic approach is well
suited for the study of kinetic effects in BECs, such as those associated with
Landau damping, atom trapping and turbulent diffusion. The inclusion of quantum
fluctuations and energy corrections change the dispersion relation and the
damping rates, leading to possible experimental signatures of these effects.
Quantum Landau damping is described with generality, and particular examples
of dipole condensates in two and three dimensions are studied. The occurrence
of roton-maxon configurations, and their relevance to Landau damping is also
considered in detail, as well as the changes introduced by the three different
processes, associated with dipolar interactions, quantum fluctuations and
finite energy range collisions. The present approach is mainly based on a
linear perturbative procedure, but the nonlinear regime of Landau damping,
which includes atom trapping and atom diffusion, is also briefly discussed. | 1801.06256v1 |
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 |
2020-05-31 | Optimal decay rates of the compressible Euler equations with time-dependent damping in $\mathbb R^n$: (I) under-damping case | This paper is concerned with the multi-dimensional compressible Euler
equations with time-dependent damping of the form
$-\frac{\mu}{(1+t)^\lambda}\rho\boldsymbol u$ in $\mathbb R^n$, where $n\ge2$,
$\mu>0$, and $\lambda\in[0,1)$. When $\lambda>0$ is bigger, the damping effect
time-asymptotically gets weaker, which is called under-damping. We show the
optimal decay estimates of the solutions such that $\|\partial_x^\alpha
(\rho-1)\|_{L^2(\mathbb R^n)}\approx
(1+t)^{-\frac{1+\lambda}{2}(\frac{n}{2}+|\alpha|)}$, and $\|\partial_x^\alpha
\boldsymbol u\|_{L^2(\mathbb R^n)}\approx
(1+t)^{-\frac{1+\lambda}{2}(\frac{n}{2}+|\alpha|)-\frac{1-\lambda}{2}}$, and
see how the under-damping effect influences the structure of the Euler system.
Different from the traditional view that the stronger damping usually makes the
solutions decaying faster, here surprisingly we recognize that the weaker
damping with $0\le\lambda<1$ enhances the faster decay for the solutions. The
adopted approach is the technical Fourier analysis and the Green function
method. The main difficulties caused by the time-dependent damping lie in
twofold: non-commutativity of the Fourier transform of the linearized operator
precludes explicit expression of the fundamental solution; time-dependent
evolution implies that the Green matrix $G(t,s)$ is not translation invariant,
i.e., $G(t,s)\ne G(t-s,0)$. We formulate the exact decay behavior of the Green
matrices $G(t,s)$ with respect to $t$ and $s$ for both linear wave equations
and linear hyperbolic system, and finally derive the optimal decay rates for
the nonlinear Euler system. | 2006.00401v1 |
2022-08-17 | Anti-parity-time symmetry hidden in a damping linear resonator | Phase transition from the over-damping to under-damping states is a
ubiquitous phenomenon in physical systems. However, what kind of symmetry is
broken associated with this phase transition remains unclear. Here, we discover
that this phase transition is determined by an anti-parity-time
(anti-$\mathcal{PT}$) symmetry hidden in a single damping linear resonator,
which is significantly different from the conventional
anti-$\mathcal{PT}$-symmetric systems with two or more modes. We show that the
breaking of the anti-$\mathcal{PT}$ symmetry yields the phase transition from
the over-damping to under-damping states, with an exceptional point (EP)
corresponding to the critical-damping state. Moreover, we propose an
optomechanical scheme to show this anti-$\mathcal{PT}$ symmetry breaking by
using the optical spring effect in a quadratic optomechanical system. We also
suggest an optomechanical sensor with the sensitivity enhanced significantly
around the EPs for the anti-$\mathcal{PT}$ symmetry breaking. Our work unveils
the anti-$\mathcal{PT}$ symmetry hidden in damping oscillations and hence opens
up new possibilities for exploiting wide anti-$\mathcal{PT}$ symmetry
applications in single damping linear resonators. | 2208.08187v2 |
1996-12-10 | Collisional matter-phase damping in Bose-condensed gas | Collisional damping of the excitations in a Bose-condensed gas is
investigated over the wide range of energies and temperatures. Numerical
results for the damping rate are presented and a number of asymptotic and
interpolating expressions for it are derived. | 9612086v1 |
2001-11-29 | Tensor form of magnetization damping | A tensor form of phenomenological damping is derived for small magnetization
motions. This form reflects basic physical relaxation processes for a general
uniformly magnetized particle or film. Scalar Landau-Lifshitz damping is found
to occur only for two special cases of system symmetry. | 0111566v1 |
1999-07-28 | An effective relaxation-time approach to collisionless quark-gluon plasma | We present an effective relaxation-time theory to study the collisionless
quark-gluon plasma. Applying this method we calculate the damping rate to be of
order $g^2T$ and find plasmon scattering is the damping mechanism. The damping
for the transverse mode is stronger than the longitudinal one. | 9907526v1 |
1999-11-16 | Dynamical resummation and damping in the O(N) model | A general real-time formalism is developed to resum the self-energy operator
of broken symmetry scalar field theories in form of self-consistent gap
equations for the spectral function. The solution of the equations is
approximated with finite lifetime quasi-particles. In the Landau damping rates
viscosity terms, analogous to gauge theories, appear, what leads to a finite
damping rate for the long wavelength Goldstone modes. | 9911374v1 |
1993-03-24 | On the Quantizations of the Damped Systems | Based on a simple observation that a classical second order differential
equation may be decomposed into a set of two first order equations, we
introduce a Hamiltonian framework to quantize the damped systems. In
particular, we analyze the system of a linear damped harmonic oscillator and
demonstrate that the time evolution of the Schr\"odinger equation is
unambiguously determined. | 9303137v1 |
2006-01-09 | Energy decay for damped wave equations on partially rectangular domains | We consider the wave equation with a damping term on a partially rectangular
planar domain, assuming that the damping is concentrated close to the
non-rectangular part of the domain. Polynomial decay estimates for the energy
of the solution are established. | 0601195v1 |
2002-06-07 | Resonant states and classical damping | Using Koopman's approach to classical dynamical systems we show that the
classical damping may be interpreted as appearance of resonant states of the
corresponding Koopman's operator. It turns out that simple classical damped
systems give rise to discrete complex spectra. Therefore, the corresponding
generalized eigenvectors may be interpreted as classical resonant states. | 0206009v1 |
2004-03-12 | Factorization of damped wave equations with cubic nonlinearities | The recent factorization scheme that we introduced for nonlinear polynomial
ODEs in math-ph/0401040 is applied to the interesting case of damped wave
equations with cubic nonlinearities. Traveling kink solutions are possible in
the plane defined by the kink velocity versus the damping coefficient only
along hyperbolas that are plotted herein | 0403022v1 |
2002-08-07 | Toward a Universal Model of Damping--Modified Coulomb Friction | A modification of Coulomb's law of friction uses a variable coefficient of
friction that depends on a power law in the energy of mechanical oscillation.
Through the use of three different exponents: 0, 1/2 and 1; all commonly
encountered non-viscous forms of damping are accommodated. The nonlinear model
appears to yield good agreement with experiment in cases of surface, internal,
and amplitude dependent damping. | 0208025v1 |
2002-12-19 | Trapped particle bounds on stimulated scatter in the large k/kD regime | In the strongly damped regime, the convective gain rate for stimulated
scatter varies inversely with the plasma wave damping rate. Electron trapping
effects reduce the damping but also lead to loss of resonance for large enough
amplitude waves. This leads to a gain rate bound and corresponding optimum
scattered light frequency and plasma wave amplitude. | 0212071v1 |
2003-02-03 | Oscillator damping with more than one mechanism of internal friction dissipation | The author's modified Coulomb damping model has been generalized to
accommodate internal friction that derives from several dissipation mechanisms
acting simultaneously. Because of its fundamental nonlinear nature, internal
friction damping causes the quality factor Q of an oscillator in free-decay to
change in time. Examples are given which demonstrate reasonable agreement
between theory and experiment. | 0302003v1 |
2003-02-15 | Anisotropic Internal Friction Damping | The mechanical damping properties of sheet polaroid material have been
studied with a physical pendulum. The polaroid samples were placed under the
knife-edges of the pendulum, which was operated in free-decay at a period in
the vicinity of 10 s. With the edges oriented parallel to the direction of the
long molecular chains in the polaroid, it was found that the damping was more
than 10% smaller than when oriented perpendicular to the chains. | 0302055v1 |
2006-08-07 | Study of the Damped Pendulum | Experiments on the oscillatory motion of a suspended bar magnet throws light
on the damping effects acting on the pendulum. The viscous drag offered by air
was found the be the main contributor for slowing the pendulum down. The nature
and magnitude of the damping effects were shown to be strongly dependent on the
amplitude. | 0608071v1 |
1995-02-27 | Quantum Oscillator with Kronig-Penney Excitation in Different Regimes of Damping | There are discussed the exact solution of the time--dependent Schr\"{o}dinger
equation for a damped quantum oscillator subject to a periodical frequency
delta--kicks describing squeezed states which are expressed in terms of
Chebyshev polynomials. The cases of strong and weak damping are investigated in
the frame of Caldirola--Kanai model. | 9502023v1 |
2010-11-20 | Enhanced damping of ion acoustic waves in dense plasmas | A theory for the ion acoustic wave damping in dense plasmas and warm dense
matter, accounting for the Umklapp process, is presented. A higher decay rate
compared to the prediction from the Landau damping theory is predicted for
high-Z dense plasmas where the electron density ranges from $10^{21}$ to $
10^{24} \mathrm{cm^{-3}}$ and the electron temperature is moderately higher
than the Fermi energy. | 1011.4607v1 |
2012-05-16 | Enhanced coupling design of a detuned damped structure for clic | The key feature of the improved coupling design in the Damped Detuned
Structure (DDS) is focused on the four manifolds. Rectangular geometry slots
and rectangular manifolds are used. This results in a significantly stronger
coupling to the manifolds compared to the previous design. We describe the new
design together with its wakefield damping properties. | 1205.3590v1 |
2012-06-26 | On the $L^{2}$-critical nonlinear Schrödinger Equation with a nonlinear damping | We consider the Cauchy problem for the $L^{2}$-critical nonlinear
Schr\"{o}dinger equation with a nonlinear damping. According to the power of
the damping term, we prove the global existence or the existence of finite time
blowup dynamics with the log-log blow-up speed for $\|\nabla u(t)\|_{L^2}$. | 1206.6082v4 |
2012-12-08 | A note on the lifespan of solutions to the semilinear damped wave equation | This paper concerns estimates of the lifespan of solutions to the semilinear
damped wave equation. We give upper estimates of the lifespan for the
semilinear damped wave equation with variable coefficients in all space
dimensions. | 1212.1772v3 |
2012-12-10 | Strongly damped wave equation with exponential nonlinearities | In this paper, we study the initial boundary value problem for the two
dimensional strong damped wave equation with exponentially growing source and
damping terms. We first show the well-posedness of this problem and then prove
the existence of the global attractor in $(H_{0}^{1}(\Omega)\cap
L^{\infty}(\Omega))\times L^{2}(\Omega)$. | 1212.2180v2 |
2013-10-27 | Exponential decay of solutions for the plate equation with localized damping | In this paper, we give positive answer to the open question raised in [E.
Zuazua, Exponential decay for the semilinear wave equation with localized
damping in unbounded domains. J. Math. Pures Appl., 70 (1991) 513--529] on the
exponential decay of solutions for the semilinear plate equation with localized
damping. | 1310.7243v3 |
2014-03-07 | Landau damping in Sobolev spaces for the Vlasov-HMF model | We consider the Vlasov-HMF (Hamiltonian Mean-Field) model. We consider
solutions starting in a small Sobolev neighborhood of a spatially homogeneous
state satisfying a linearized stability criterion (Penrose criterion). We prove
that these solutions exhibit a scattering behavior to a modified state, which
implies a nonlinear Landau damping effect with polynomial rate of damping. | 1403.1668v2 |
2015-03-30 | Damping to prevent the blow-up of the Korteweg-de Vries equation | We study the behavior of the solution of a generalized damped KdV equation
$u_t + u_x + u_{xxx} + u^p u_x + \mathscr{L}_{\gamma}(u)= 0$. We first state
results on the local well-posedness. Then when $p \geq 4$, conditions on
$\mathscr{L}_{\gamma}$ are given to prevent the blow-up of the solution.
Finally, we numerically build such sequences of damping. | 1503.08559v1 |
2015-06-16 | Fast energy decay for wave equations with variable damping coefficients in the 1-D half line | We derive fast decay estimates of the total energy for wave equations with
localized variable damping coefficients, which are dealt with in the one
dimensional half line $(0,\infty)$. The variable damping coefficient vanishes
near the boundary $x = 0$, and is effective critically near spatial infinity $x
= \infty$. | 1506.04851v1 |
2015-11-25 | A Proposal of a Damping Term for the Relativistic Euler Equations | We introduce a damping term for the special relativistic Euler equations in
$3$-D and show that the equations reduce to the non-relativistic damped Euler
equations in the Newtonian limit. We then write the equations as a symmetric
hyperbolic system for which local-in-time existence of smooth solutions can be
shown. | 1511.08183v1 |
2016-01-27 | Concatenated Codes for Amplitude Damping | We discuss a method to construct quantum codes correcting amplitude damping
errors via code concatenation. The inner codes are chosen as asymmetric
Calderbank-Shor-Steane (CSS) codes. By concatenating with outer codes
correcting symmetric errors, many new codes with good parameters are found,
which are better than the amplitude damping codes obtained by any previously
known construction. | 1601.07423v1 |
2012-10-12 | Semi-linear wave equations with effective damping | We study the Cauchy problem for the semi-linear damped wave equation in any
space dimension. We assume that the time-dependent damping term is effective.
We prove the global existence of small energy data solutions in the
supercritical case. | 1210.3493v1 |
2018-03-20 | Stability of the wave equations on a tree with local Kelvin-Voigt damping | In this paper we study the stability problem of a tree of elastic strings
with local Kelvin-Voigt damping on some of the edges. Under the compatibility
condition of displacement and strain and continuity condition of damping
coefficients at the vertices of the tree, exponential/polynomial stability are
proved. | 1803.07280v1 |
2008-11-07 | Asymptotic stability of the wave equation on compact surfaces and locally distributed damping - A sharp result | This paper is concerned with the study of the wave equation on compact
surfaces and locally distributed damping. We study the case where the damping
is effective in a well-chosen subset of arbitrarily small measure. | 0811.1190v1 |
2008-11-07 | Uniform Stabilization of the wave equation on compact surfaces and locally distributed damping | This paper is concerned with the study of the wave equation on compact
surfaces and locally distributed damping. We study the case where the damping
is effective on the complement of visible umbilical sets. | 0811.1204v1 |
2016-03-29 | Generalized damped Milne-Pinney equation and Chiellini method | We adopt the Chiellini integrability method to find the solutions of various
generalizations of the damped Milne-Pinney equations. In particular, we find
the solution of the damped Ermakov-Painlev\'e II equation and generalized
dissipative Milne-Pinney equation. | 1603.08747v2 |
2018-09-10 | Logarithmic Decay of a Wave Equation with Kelvin-Voigt Damping | In this paper we analyze the long time behavior of a wave equation with local
Kelvin-Voigt Damping. Through introducing proper class symbol and
pseudo-differential calculus, we obtain a Carleman estimate, and then establish
an estimate on the corresponding resolvent operator. As a result, we show the
logarithmic decay rate for energy of the system without any geometric
assumption on the subdomain on which the damping is effective. | 1809.03196v1 |
2019-09-25 | Forced Coupled Duffing Oscillators with Nonlinear Damping: Resonance and Antiresonance | In this work, we investigate resonance and antiresonance behaviour in forced
coupled Duffing oscillators with nonlinear damping. Further, we will analyse
the parameter dependence of the frequency response and stability. In the course
of all the analysis, emphasis shall be on how different damping mechanisms
contrast against each other. | 1909.11390v1 |
2020-04-21 | Damping rate limitations for transverse dampers in large hadron colliders | The paper focuses on two issues important for design and operation of
bunch-by-bunch transverse damper in a very large hadron collider, where fast
damping is required to suppress beam instabilities and noise induced emittance
growth. The first issue is associated with kick variation along a bunch which
affects the damping of head-tail modes. The second issue is associated with
affect of damper noise on the instability threshold. | 2004.10249v2 |
2017-12-07 | Damped wave equations on compact hyperbolic surfaces | We prove exponential decay of energy for solutions of the damped wave
equation on compact hyperbolic surfaces with regular initial data as long as
the damping is nontrivial. The proof is based on a similar strategy as in
Dyatlov-Jin and in particular, uses the fractal uncertainty principle proved in
Bourgain-Dyatlov. | 1712.02692v1 |
2018-11-07 | Slow-dissipation limit of the harmonic oscillator with general power-law damping | An approximate solution is presented for simple harmonic motion in the
presence of damping by a force which is a general power-law function of the
velocity. The approximation is shown to be quite robust, allowing for a simple
way to investigate amplitude decay in the presence of general types of weak,
nonlinear damping. | 1811.02953v2 |
2021-08-17 | Spectral enclosures for the damped elastic wave equation | In this paper we investigate spectral properties of the damped elastic wave
equation. Deducing a correspondence between the eigenvalue problem of this
model and the one of Lam\'e operators with non self-adjoint perturbations, we
provide quantitative bounds on the location of the point spectrum in terms of
suitable norms of the damping coefficient. | 2108.07676v1 |
2022-02-10 | Stochastic optimal control for nonlinear damped network dynamics | We present a stochastic optimal control problem for a tree network. The
dynamics of the network are governed by transport equations with a special
emphasis on the non-linear damping function. Demand profiles at the network
sinks are modelled by a stochastic differential equations. An explicit optimal
inflow into the network is determined and numerical simulations are presented
to show the effects for different choices of the non-linear damping. | 2202.05114v1 |
2022-03-03 | Conformal symmetry in damped Pais-Uhlenbeck oscillator | Two Lagrangian formulations for describing of the damped harmonic oscillator
have been introduced by Bateman. For these models we construct higher
derivative generalization which enjoys the l-conformal Newton-Hooke symmetry.
The dynamics of generalized systems corresponds to the damped Pais-Uhlenbeck
oscillator for a particular choice of its frequencies. | 2203.01651v1 |
2022-05-26 | Ergodic results for the stochastic nonlinear Schrödinger equation with large damping | We study the nonlinear Schr\"odinger equation with linear damping, i.e. a
zero order dissipation, and additive noise. Working in $R^d$ with d = 2 or d =
3, we prove the uniqueness of the invariant measure when the damping
coefficient is sufficiently large. | 2205.13364v1 |
2022-10-31 | An adaptive damped Newton method for strongly monotone and Lipschitz continuous operator equations | We will consider the damped Newton method for strongly monotone and Lipschitz
continuous operator equations in a variational setting. We will provide a very
accessible justification why the undamped Newton method performs better than
its damped counterparts in a vicinity of a solution. Moreover, in the given
setting, an adaptive step-size strategy will be presented, which guarantees the
global convergence and favours an undamped update if admissible. | 2210.17107v1 |
2022-11-19 | Blow up and lifespan estimates for systems of semi-linear wave equations with damping and potential | In this paper, we consider the semi-linear wave systems with
power-nonlinearities and a large class of space-dependent damping and
potential. We obtain the same blow-up regions and the lifespan estimates for
three types wave systems, compared with the systems without damping and
potential. | 2211.10639v1 |
2023-08-10 | Pathwise uniqueness for stochastic heat and damped equations with Hölder continuous drift | In this paper, we prove pathwise uniqueness for stochastic differential
equations in infinite dimension. Under our assumptions, we are able to consider
the stochastic heat equation up to dimension $3$, the stochastic damped wave
equation in dimension $1$ and the stochastic Euler-Bernoulli damped beam
equation up to dimension $3$. We do not require that the so-called {\it
structure condition} holds true. | 2308.05415v1 |
2023-10-30 | Beliaev damping in Bose gas | According to the Bogoliubov theory the low energy behaviour of the Bose gas
at zero temperature can be described by non-interacting bosonic quasiparticles
called phonons. In this work the damping rate of phonons at low momenta, the
so-called Beliaev damping, is explained and computed with simple arguments
involving the Fermi Golden Rule and Bogoliubov's quasiparticles. | 2310.20070v1 |
2023-11-25 | Energy scattering for the unsteady damped nonlinear Schrodinger equation | We investigate the large time behavior of the solutions to the nonlinear
focusing Schr\"odinger equation with a time-dependent damping in the energy
sub-critical regime. Under non classical assumptions on the unsteady damping
term, we prove some scattering results in the energy space. | 2311.14980v2 |
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