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2020-06-08 | Hysteretic depinning of a particle in a periodic potential: Phase diagram and criticality | We consider a massive particle driven with a constant force in a periodic
potential and subjected to a dissipative friction. As a function of the drive
and damping, the phase diagram of this paradigmatic model is well known to
present a pinned, a sliding, and a bistable regime separated by three distinct
bifurcation lines. In physical terms, the average velocity $v$ of the particle
is nonzero only if either (i) the driving force is large enough to remove any
stable point, forcing the particle to slide, or (ii) there are local minima but
the damping is small enough, below a critical damping, for the inertia to allow
the particle to cross barriers and follow a limit cycle; this regime is
bistable and whether $v > 0$ or $v = 0$ depends on the initial state. In this
paper, we focus on the asymptotes of the critical line separating the bistable
and the pinned regimes. First, we study its behavior near the "triple point"
where the pinned, the bistable, and the sliding dynamical regimes meet. Just
below the critical damping we uncover a critical regime, where the line
approaches the triple point following a power-law behavior. We show that its
exponent is controlled by the normal form of the tilted potential close to its
critical force. Second, in the opposite regime of very low damping, we revisit
existing results by providing a simple method to determine analytically the
exact behavior of the line in the case of a generic potential. The analytical
estimates, accurately confirmed numerically, are obtained by exploiting exact
soliton solutions describing the orbit in a modified tilted potential which can
be mapped to the original tilted washboard potential. Our methods and results
are particularly useful for an accurate description of underdamped nonuniform
oscillators driven near their triple point. | 2006.04912v2 |
2021-06-18 | Sloshing dynamics of liquid tank with built-in buoys for wave energy harvesting | This paper proposes a novel design of liquid tank with built-in buoys for
wave energy harvesting, named the 'sloshing wave energy converter (S-WEC)'.
When the tank is oscillated by external loads (such as ocean waves), internal
liquid sloshing is activated, and the mechanical energy of sloshing waves can
be absorbed by the power take-off (PTO) system attached to these buoys. A
fully-nonlinear numerical model is established based on the boundary element
method for a systematic investigation on dynamic properties of the proposed
S-WEC. A motion decoupling algorithm based on auxiliary functions is developed
to solve the nonlinear interaction of sloshing waves and floating buoys in the
tank. An artificial damping model is introduced to reflect viscous effects of
the sloshing liquid. Physical experiments are carried out on a scaled S-WEC
model to validate the mathematical and numerical methodologies. Natural
frequencies of the S-WEC system are first investigated through spectrum
analyses on motion histories of the buoy and sloshing liquid. The viscous
damping strength is identified through comparisons with experimental
measurements. Effects of the PTO damping on power generation characteristics of
S-WEC is further explored. An optimal PTO damping can be found for each
excitation frequency, leading to the maximisation of both the power generation
and conversion efficiency of the buoy. To determine a constant PTO damping for
engineering design, a practical approach based on diagram analyses is proposed.
Effects of the buoy's geometry on power generation characteristics of the S-WEC
are also investigated. In engineering practice, the present design of S-WEC can
be a promising technical solution of ocean wave energy harvesting, based on its
comprehensive advantages on survivability enhancement, metal corrosion or
fouling organism inhibition, power generation stability and efficiency, and so
on. | 2106.10005v1 |
2021-06-11 | Cosmology with Love: Measuring the Hubble constant using neutron star universal relations | Gravitational-wave cosmology began in 2017 with the observation of the
gravitational waves emitted in the merger of two neutron stars, and the
coincident observation of the electromagnetic emission that followed. Although
only a $30\%$ measurement of the Hubble constant was achieved, future
observations may yield more precise measurements either through other
coincident events or through cross correlation of gravitational-wave events
with galaxy catalogs. Here, we implement a new way to measure the Hubble
constant without an electromagnetic counterpart and through the use of the
binary Love relations. These relations govern the tidal deformabilities of
neutron stars in an equation-of-state insensitive way. Importantly, the Love
relations depend on the component masses of the binary in the source frame.
Since the gravitational-wave phase and amplitude depend on the chirp mass in
the observer (and hence redshifted) frame, one can in principle combine the
binary Love relations with the gravitational-wave data to directly measure the
redshift, and thereby infer the value of the Hubble constant. We implement this
approach in both real and synthetic data through a Bayesian parameter
estimation study in a range of observing scenarios. We find that for the
LIGO/Virgo/KAGRA design sensitivity era, this method results in a similar
measurement accuracy of the Hubble constant to those of current-day, dark-siren
measurements. For third generation detectors, this accuracy improves to
$\lesssim 10\%$ when combining measurements from binary neutron star events in
the LIGO Voyager era, and to $\lesssim 2\%$ in the Cosmic Explorer era. | 2106.06589v2 |
2017-04-13 | Stochastic Gradient Descent as Approximate Bayesian Inference | Stochastic Gradient Descent with a constant learning rate (constant SGD)
simulates a Markov chain with a stationary distribution. With this perspective,
we derive several new results. (1) We show that constant SGD can be used as an
approximate Bayesian posterior inference algorithm. Specifically, we show how
to adjust the tuning parameters of constant SGD to best match the stationary
distribution to a posterior, minimizing the Kullback-Leibler divergence between
these two distributions. (2) We demonstrate that constant SGD gives rise to a
new variational EM algorithm that optimizes hyperparameters in complex
probabilistic models. (3) We also propose SGD with momentum for sampling and
show how to adjust the damping coefficient accordingly. (4) We analyze MCMC
algorithms. For Langevin Dynamics and Stochastic Gradient Fisher Scoring, we
quantify the approximation errors due to finite learning rates. Finally (5), we
use the stochastic process perspective to give a short proof of why Polyak
averaging is optimal. Based on this idea, we propose a scalable approximate
MCMC algorithm, the Averaged Stochastic Gradient Sampler. | 1704.04289v2 |
2004-04-13 | The Fine-structure Constant as a Probe of Chemical Evolution and AGB Nucleosynthesis in Damped Lyman-alpha Systems | Evidence from a large sample of quasar absorption-line spectra in damped
Lyman-alpha systems has suggested a possible time variation of the fine
structure constant alpha. The most statistically significant portion of this
sample involves the comparison of Mg and Fe wavelength shifts using the
many-multiplet (MM) method. However, the sensitivity of this method to the
abundance of heavy isotopes, especially Mg, is enough to imitate an apparent
variation in alpha in the redshift range 0.5 < z < 1.8. We implement recent
yields of intermediate mass (IM) stars into a chemical evolution model and show
that the ensuing isotope distribution of Mg can account for the observed
variation in alpha provided the early IMF was particularly rich in intermediate
mass stars (or the heavy Mg isotope yields from AGB stars are even higher than
in present-day models). As such, these observations of quasar absorption
spectra can be used to probe the nucleosynthetic history of low-metallicity
damped Lyman-alpha systems in the redshift range 0.5 < z < 1.8. This analysis,
in conjunction with other abundance measurements of low-metallicity systems,
reinforces the mounting evidence that star formation at low metallicities may
have been strongly influenced by a population of IM stars. Such IM stars have a
significant influence on other abundances, particularly nitrogen. We constrain
our models with independent measurements of N, Si, and Fe in damped Lyman-alpha
systems as well as C/O in low-metallicity stars. In this way, we obtain
consistent model parameters for this chemical-evolution interpretation of the
MM method results. | 0404257v2 |
2017-12-05 | Harnessing Electrical Power from Vortex-Induced Vibration of a Circular Cylinder | The generation of electrical power from Vortex-Induced Vibration (VIV) of a
cylinder is investigated numerically. The cylinder is free to oscillate in the
direction transverse to the incoming flow. The cylinder is attached to a magnet
that can move along the axis of a coil made from conducting wire. The magnet
and the coil together constitute a basic electrical generator. When the
cylinder undergoes VIV, the motion of the magnet creates a voltage across the
coil, which is connected to a resistive load. By Lenz's law, induced current in
the coil applies a retarding force to the magnet. Effectively, the electrical
generator applies a damping force on the cylinder with a spatially varying
damping coefficient. For the initial investigation reported here, the Reynolds
number is restricted to Re < 200, so that the flow is laminar and
two-dimensional (2D). The incompressible 2D Navier-Stokes equations are solved
using an extensively validated spectral-element based solver. The effects of
the electromagnetic (EM) damping constant xi_m, coil dimensions (radius a,
length L), and mass ratio on the electrical power extracted are quantified. It
is found that there is an optimal value of xi_m (xi_opt) at which maximum
electrical power is generated. As the radius or length of the coil is
increased, the value of xi_opt is observed to increase. Although the maximum
average power remains the same, a larger coil radius or length results in a
more robust system in the sense that a relatively large amount of power can be
extracted when xi_m is far from xi_opt, unlike the constant damping ratio case.
The average power output is also a function of Reynolds number, primarily
through the increased maximum oscillation amplitude that occurs with increased
Reynolds number at least within the laminar range, although the general
qualitative findings seem likely to carry across to high Reynolds number VIV. | 1712.01588v1 |
2023-12-25 | IMEX-RK methods for Landau-Lifshitz equation with arbitrary damping | Magnetization dynamics in ferromagnetic materials is modeled by the
Landau-Lifshitz (LL) equation, a nonlinear system of partial differential
equations. Among the numerical approaches, semi-implicit schemes are widely
used in the micromagnetics simulation, due to a nice compromise between
accuracy and efficiency. At each time step, only a linear system needs to be
solved and a projection is then applied to preserve the length of
magnetization. However, this linear system contains variable coefficients and a
non-symmetric structure, and thus an efficient linear solver is highly desired.
If the damping parameter becomes large, it has been realized that efficient
solvers are only available to a linear system with constant, symmetric, and
positive definite (SPD) structure. In this work, based on the implicit-explicit
Runge-Kutta (IMEX-RK) time discretization, we introduce an artificial damping
term, which is treated implicitly. The remaining terms are treated explicitly.
This strategy leads to a semi-implicit scheme with the following properties:
(1) only a few linear system with constant and SPD structure needs to be solved
at each time step; (2) it works for the LL equation with arbitrary damping
parameter; (3) high-order accuracy can be obtained with high-order IMEX-RK time
discretization. Numerically, second-order and third-order IMEX-RK methods are
designed in both the 1-D and 3-D domains. A comparison with the backward
differentiation formula scheme is undertaken, in terms of accuracy and
efficiency. The robustness of both numerical methods is tested on the first
benchmark problem from National Institute of Standards and Technology. The
linearized stability estimate and optimal rate convergence analysis are
provided for an alternate IMEX-RK2 numerical scheme as well. | 2312.15654v1 |
2017-07-28 | Measurements of the Temperature and E-Mode Polarization of the CMB from 500 Square Degrees of SPTpol Data | We present measurements of the $E$-mode polarization angular auto-power
spectrum ($EE$) and temperature-$E$-mode cross-power spectrum ($TE$) of the
cosmic microwave background (CMB) using 150 GHz data from three seasons of
SPTpol observations. We report the power spectra over the spherical harmonic
multipole range $50 < \ell \leq 8000$, and detect nine acoustic peaks in the
$EE$ spectrum with high signal-to-noise ratio. These measurements are the most
sensitive to date of the $EE$ and $TE$ power spectra at $\ell > 1050$ and $\ell
> 1475$, respectively. The observations cover 500 deg$^2$, a fivefold increase
in area compared to previous SPTpol analyses, which increases our sensitivity
to the photon diffusion damping tail of the CMB power spectra enabling tighter
constraints on \LCDM model extensions. After masking all sources with
unpolarized flux $>50$ mJy we place a 95% confidence upper limit on residual
polarized point-source power of $D_\ell = \ell(\ell+1)C_\ell/2\pi
<0.107\,\mu{\rm K}^2$ at $\ell=3000$, suggesting that the $EE$ damping tail
dominates foregrounds to at least $\ell = 4050$ with modest source masking. We
find that the SPTpol dataset is in mild tension with the $\Lambda CDM$ model
($2.1\,\sigma$), and different data splits prefer parameter values that differ
at the $\sim 1\,\sigma$ level. When fitting SPTpol data at $\ell < 1000$ we
find cosmological parameter constraints consistent with those for $Planck$
temperature. Including SPTpol data at $\ell > 1000$ results in a preference for
a higher value of the expansion rate ($H_0 = 71.3 \pm
2.1\,\mbox{km}\,s^{-1}\mbox{Mpc}^{-1}$ ) and a lower value for present-day
density fluctuations ($\sigma_8 = 0.77 \pm 0.02$). | 1707.09353v3 |
2023-02-15 | Fully Energy-Efficient Randomized Backoff: Slow Feedback Loops Yield Fast Contention Resolution | Contention resolution addresses the problem of coordinating access to a
shared channel. Time proceeds in slots, and a packet transmission can be made
in any slot. A packet is successfully sent if no other packet is also
transmitted during that slot. If two or more packets are sent in the same slot,
then none of these transmissions succeed. Listening during a slot gives ternary
feedback, indicating if that slot had (0) silence, (1) a successful
transmission, or (2+) noise. No other feedback is available. Packets are
(adversarially) injected into the system over time. A packet departs the system
once it is successful. The goal is to send all packets while optimizing
throughput, which is roughly the fraction of successful slots.
Most prior algorithms with constant throughput require a short feedback loop,
in the sense that a packet's sending probability in slot t+1 is fully
determined by its internal state at slot t and the channel feedback at slot t.
An open question is whether these short feedback loops are necessary; that is,
how often must listening and updating occur in order to achieve constant
throughput? This question addresses energy efficiency, since both listening and
sending consume significant energy. The channel can also suffer adversarial
noise ("jamming"), which causes any listener to hear noise, even when no
packets are sent. How does jamming affect our goal of long feedback
loops/energy efficiency?
Connecting these questions, we ask: what does a contention-resolution
algorithm have to sacrifice to reduce channel accesses? Must we give up on
constant throughput or robustness to noise? Here, we show that we need not
concede anything. Suppose there are N packets and J jammed slots, where the
input is determined by an adaptive adversary. We give an algorithm that, with
high probability in N+J, has constant throughput and polylog(N+J) channel
accesses per packet. | 2302.07751v2 |
2006-11-01 | Ferromagnetic resonance study of sputtered Co|Ni multilayers | We report on room temperature ferromagnetic resonance (FMR) studies of [$t$
Co$|2t$ Ni]$\times$N sputtered films, where $0.1 \leq t \leq 0.6$ nm. Two
series of films were investigated: films with same number of Co$|$Ni bilayer
repeats (N=12), and samples in which the overall magnetic layer thickness is
kept constant at 3.6 nm (N=1.2/$t$). The FMR measurements were conducted with a
high frequency broadband coplanar waveguide up to 50 GHz using a flip-chip
method. The resonance field and the full width at half maximum were measured as
a function of frequency for the field in-plane and field normal to the plane,
and as a function of angle to the plane for several frequencies. For both sets
of films, we find evidence for the presence of first and second order
anisotropy constants, $K_1$ and $K_2$. The anisotropy constants are strongly
dependent on the thickness $t$, and to a lesser extent on the total thickness
of the magnetic multilayer. The Land\'e g-factor increases with decreasing $t$
and is practically independent of the multilayer thickness. The magnetic
damping parameter $\alpha$, estimated from the linear dependence of the
linewidth, $\triangle H$, on frequency, in the field in-plane geometry,
increases with decreasing $t$. This behaviour is attributed to an enhancement
of spin-orbit interactions with $t$ decreasing and in thinner films, to a
spin-pumping contribution to the damping. | 0611027v2 |
1996-04-10 | A Keck HIRES Investigation of the Metal Abundances and Kinematics of the z=2.46 Damped Lya System Toward Q0201+365 | We present high resolution ($\approx 8$ \kms) spectra of the QSO Q0201+365
obtained with HIRES, the echelle spectrograph on the 10m W.M. Keck Telescope.
Although we identify over $80\%$ of the absorption features and analyze several
of the more complex metal-line systems, we focus our analysis on the damped
\Lya system at $z=2.462$. Ionization simulations suggest the hydrogen in this
system is significantly neutral and all of the observed metals are
predominantly singly ionized. We measure accurate abundances for Fe, Cr, Si, Ni
and place a lower limit on the abundance of Zn: [Fe/H] = $-0.830 \pm 0.051$,
[Cr/H] = $-0.902 \pm 0.064$, [Si/H] = $-0.376 \pm 0.052$, [Ni/H] = $-1.002 \pm
0.054$ and [Zn/H] $> -0.562 \pm 0.064$. We give evidence suggesting the actual
Zn abundance is [Zn/H] $\approx -0.262$, implying the highest metallicity
observed at a redshift $z \geq 2$. The relative abundances of these elements
remains constant over essentially the entire system ($\approx 150$ \kms in
velocity space), suggesting it is well mixed. Furthermore, we use the lack of
abundance variations to infer properties of the dust responsible for element
depletion. Finally, we discuss the kinematic characteristics of this damped
\Lya system, comparing and contrasting it with other systems. The low-ion line
profiles span $\approx 200$ \kms in velocity space and have an asymmetric shape
with the strongest feature on the red edge. These kinematic characteristics are
consistent with a rotating disk model. | 9604042v1 |
2005-07-06 | The free precession and libration of Mercury | An analysis based on the direct torque equations including tidal dissipation
and a viscous core-mantle coupling is used to determine the damping time scales
of O(10^5) years for free precession of the spin about the Cassini state and
free libration in longitude for Mercury. The core-mantle coupling dominates the
damping over the tides by one to two orders of magnitude for the plausible
parameters chosen. The short damping times compared with the age of the solar
system means we must find recent or on-going excitation mechanisms if such free
motions are found by the current radar experiments or the future measurement by
the MESSENGER and BepiColombo spacecraft that will orbit Mercury. We also show
that the average precession rate is increased by about 30% over that obtained
from the traditional precession constant because of a spin-orbit resonance
induced contribution by the C_{22} term in the expansion of the gravitational
field. The C_{22} contribution also causes the path of the spin during the
precession to be slightly elliptical with a variation in the precession rate
that is a maximum when the obliquity is a minimum. An observable free
precession will compromise the determination of obliquity of the Cassini state
and hence of C/MR^2 for Mercury, but a detected free libration will not
compromise the determination of the forced libration amplitude and thus the
verification of a liquid core | 0507117v1 |
1994-09-29 | Avalanches in the Weakly Driven Frenkel-Kontorova Model | A damped chain of particles with harmonic nearest-neighbor interactions in a
spatially periodic, piecewise harmonic potential (Frenkel-Kontorova model) is
studied numerically. One end of the chain is pulled slowly which acts as a weak
driving mechanism. The numerical study was performed in the limit of infinitely
weak driving. The model exhibits avalanches starting at the pulled end of the
chain. The dynamics of the avalanches and their size and strength distributions
are studied in detail. The behavior depends on the value of the damping
constant. For moderate values a erratic sequence of avalanches of all sizes
occurs. The avalanche distributions are power-laws which is a key feature of
self-organized criticality (SOC). It will be shown that the system selects a
state where perturbations are just able to propagate through the whole system.
For strong damping a regular behavior occurs where a sequence of states
reappears periodically but shifted by an integer multiple of the period of the
external potential. There is a broad transition regime between regular and
irregular behavior, which is characterized by multistability between regular
and irregular behavior. The avalanches are build up by sound waves and shock
waves. Shock waves can turn their direction of propagation, or they can split
into two pulses propagating in opposite directions leading to transient
spatio-temporal chaos. PACS numbers: 05.70.Ln,05.50.+q,46.10.+z | 9409006v1 |
2009-04-29 | Synthetic electric fields and phonon damping in carbon nanotubes and graphene | Smoothly varying lattice strain in graphene affects the Dirac carriers
through a synthetic gauge field. When the lattice strain is time dependent, as
in connection with phononic excitations, the gauge field becomes time dependent
and the synthetic vector potential is also associated with an electric field.
We show that this synthetic electric field has observable consequences. Joule
heating associated with the currents driven by the synthetic electric field
dominates the intrinsic damping, caused by the electron-phonon interaction, of
many acoustic phonon modes of graphene and metallic carbon nanotubes when
including the effects of disorder and Coulomb interactions. Several important
consequences follow from the observation that by time-reversal symmetry, the
synthetic electric field associated with the vector potential has opposite
signs for the two valleys. First, this implies that the synthetic electric
field drives charge-neutral valley currents and is therefore unaffected by
screening. This frequently makes the effects of the synthetic vector potential
more relevant than a competing effect of the scalar deformation potential which
has a much larger bare coupling constant. Second, valley currents decay by
electron-electron scattering (valley Coulomb drag) which causes interesting
temperature dependence of the damping rates. While our theory pertains first
and foremost to metallic systems such as doped graphene and metallic carbon
nanotubes, the underlying mechanisms should also be relevant for semiconducting
carbon nanotubes when they are doped. | 0904.4660v1 |
2010-08-12 | Dynamical damping terms for symmetry-seeking shift conditions | Suitable gauge conditions are fundamental for stable and accurate
numerical-relativity simulations of inspiralling compact binaries. A number of
well-studied conditions have been developed over the last decade for both the
lapse and the shift and these have been successfully used both in vacuum and
non-vacuum spacetimes when simulating binaries with comparable masses. At the
same time, recent evidence has emerged that the standard "Gamma-driver" shift
condition requires a careful and non-trivial tuning of its parameters to ensure
long-term stable evolutions of unequal-mass binaries. We present a novel gauge
condition in which the damping constant is promoted to be a dynamical variable
and the solution of an evolution equation. We show that this choice removes the
need for special tuning and provides a shift damping term which is free of
instabilities in our simulations and dynamically adapts to the individual
positions and masses of the binary black-hole system. Our gauge condition also
reduces the variations in the coordinate size of the apparent horizon of the
larger black hole and could therefore be useful when simulating binaries with
very small mass ratios. | 1008.2212v2 |
2011-11-06 | The various manifestations of collisionless dissipation in wave propagation | The propagation of an electrostatic wave packet inside a collisionless and
initially Maxwellian plasma is always dissipative because of the irreversible
acceleration of the electrons by the wave. Then, in the linear regime, the wave
packet is Landau damped, so that in the reference frame moving at the group
velocity, the wave amplitude decays exponentially with time. In the nonlinear
regime, once phase mixing has occurred and when the electron motion is nearly
adiabatic, the damping rate is strongly reduced compared to the Landau one, so
that the wave amplitude remains nearly constant along the characteristics. Yet,
we show here that the electrons are still globally accelerated by the wave
packet, and, in one dimension, this leads to a non local amplitude dependence
of the group velocity. As a result, a freely propagating wave packet would
shrink, and, therefore, so would its total energy. In more than one dimension,
not only does the magnitude of the group velocity nonlinearly vary, but also
its direction. In the weakly nonlinear regime, when the collisionless damping
rate is still significant compared to its linear value, this leads to an
effective defocussing effect which we quantify, and which we compare to the
self-focussing induced by wave front bowing. | 1111.1391v2 |
2014-08-20 | Josephson junction ratchet: effects of finite capacitances | We study transport in an asymmetric SQUID which is composed of a loop with
three capacitively and resistively shunted Josephson junctions: two in series
in one arm and the remaining one in the other arm. The loop is threaded by an
external magnetic flux and the system is subjected to both a time-periodic and
a constant current. We formulate the deterministic and, as well, the stochastic
dynamics of the SQUID in terms of the Stewart-McCumber model and derive an
equation for the phase difference across one arm, in which an effective
periodic potential is of the ratchet type, i.e. its reflection symmetry is
broken. In doing so, we extend and generalize earlier study by Zapata et al.
[Phys. Rev. Lett. 77, 2292 (1996)] and analyze directed transport in wide
parameter regimes: covering the over-damped to moderate damping regime up to
its fully under-damped regime. As a result we detect the intriguing features of
a negative (differential) conductance, repeated voltage reversals, noise
induced voltage reversals and solely thermal noise-induced ratchet currents. We
identify a set of parameters for which the ratchet effect is most pronounced
and show how the direction of transport can be controlled by tailoring the
external magnetic flux. | 1408.4607v1 |
2015-09-07 | Spectral inequality and resolvent estimate for the bi-Laplace operator | On a compact Riemannian manifold with boundary, we prove a spectral
inequality for the bi-Laplace operator in the case of so-called "clamped"
boundary conditions , that is, homogeneous Dirichlet and Neumann conditions
simultaneously. We also prove a resolvent estimate for the generator of the
damped plate semigroup associated with these boundary conditions. The spectral
inequality allows one to observe finite sums of eigenfunctions for this
fourth-order elliptic operator, from an arbitrary open subset of the manifold.
Moreover, the constant that appears in the inequality grows as exp(C$\mu$ 1/4)
where $\mu$ is the largest eigenvalue associated with the eigenfunctions
appearing in the sum. This type of inequality is known for the Laplace
operator. As an application, we obtain a null-controllability result for a
higher-order parabolic equation. The resolvent estimate provides the spectral
behavior of the plate semigroup generator on the imaginary axis. This type of
estimate is known in the case of the damped wave semigroup. As an application ,
we deduce a stabilization result for the damped plate equation, with a log-type
decay. The proofs of both the spectral inequality and the resolvent estimate
are based on the derivation of different types of Carleman estimates for an
elliptic operator related to the bi-Laplace operator: in the interior and at
some boundaries. One of these estimates exhibits a loss of one full derivative.
Its proof requires the introduction of an appropriate semi-classical calculus
and a delicate microlocal argument. | 1509.02098v5 |
2017-02-16 | Effects of Landau damping on ion-acoustic solitary waves in a semiclassical plasma | We study the nonlinear propagation of ion-acoustic waves (IAWs) in an
unmagnetized collisionless plasma with the effects of electron and ion Landau
damping in the weak quantum (semiclassical) regime, i.e., when the typical
ion-acoustic (IA) length scale is larger than the thermal de Broglie
wavelength. Starting from a set of classical and semiclassical Vlasov equations
for ions and electrons, coupled to the Poisson equation, we derive a modified
(by the particle dispersion) Korteweg-de Vries (KdV) equation which governs the
evolution of IAWs with the effects of wave-particle resonance. It is found that
in contrast to the classical results, the nonlinear IAW speed $(\lambda)$ and
the linear Landau damping rate $(\gamma)$ are no longer constants, but can vary
with the wave number $(k)$ due to the quantum particle dispersion. The effects
of the quantum parameter $H$ (the ratio of the plasmon energy to the thermal
energy) and the electron to ion temperature ratio $(T)$ on the profiles of
$\lambda$, $\gamma$ and the solitary wave amplitude are also studied. It is
shown that the decay rate of the wave amplitude is reduced by the effects of
$H$. | 1702.05035v2 |
2017-08-16 | Effects of group velocity and multi-plasmon resonances on the modulation of Langmuir waves in a degenerate plasma | We study the nonlinear wave modulation of Langmuir waves (LWs) in a fully
degenerate plasma. Using the Wigner-Moyal equation coupled to the Poisson
equation and the multiple scale expansion technique, a modified nonlocal
nonlinear Schr{\"{o}}dinger (NLS) equation is derived which governs the
evolution of LW envelopes in degenerate plasmas. The nonlocal nonlinearity in
the NLS equation appears due to the group velocity and multi-plasmon
resonances, i.e., resonances induced by the simultaneous particle absorption of
multiple wave quanta. We focus on the regime where the resonant velocity of
electrons is larger than the Fermi velocity and thereby the linear Landau
damping is forbidden. As a result, the nonlinear wave-particle resonances due
to the group velocity and multi-plasmon processes are the dominant mechanisms
for wave-particle interaction. It is found that in contrast to classical or
semiclassical plasmas, the group velocity resonance does not necessarily give
rise the wave damping in the strong quantum regime where $ \hbar k\sim mv_{F}$
with $\hbar$ denoting the reduced Planck's constant, $m$ the electron mass and
$v_F$ the Fermi velocity, however, the three-plasmon process plays a dominant
role in the nonlinear Landau damping of wave envelopes. In this regime, the
decay rate of the wave amplitude is also found to be higher compared to that in
the modest quantum regime where the multi-plasmon effects are forbidden. | 1708.04965v3 |
2012-11-14 | New algorithm for footstep localization using seismic sensors in an indoor environment | In this study, we consider the use of seismic sensors for footstep
localization in indoor environments. A popular strategy of localization is to
use the measured differences in arrival times of source signals at multiple
pairs of receivers. In the literature, most algorithms that are based on time
differences of arrival (TDOA) assume that the propagation velocity is a
constant as a function of the source position, which is valid for air
propagation or even for narrow band signals. However a bounded medium such as a
concrete slab (encountered in indoor environement) is usually dispersive and
damped. In this study, we demonstrate that under such conditions, the concrete
slab can be assimilated to a thin plate; considering a Kelvin-Voigt damping
model, we introduce the notion of {\em perceived propagation velocity}, which
decreases when the source-sensor distance increases. This peculiar behaviour
precludes any possibility to rely on existing localization methods in indoor
environment. Therefore, a new localization algorithm that is adapted to a
damped and dispersive medium is proposed, using only on the sign of the
measured TDOA (SO-TDOA). A simulation and some experimental results are
included, to define the performance of this SO-TDOA algorithm. | 1211.3233v2 |
2020-03-03 | Linear stability analysis for 2D shear flows near Couette in the isentropic Compressible Euler equations | In this paper, we investigate linear stability properties of the 2D
isentropic compressible Euler equations linearized around a shear flow given by
a monotone profile, close to the Couette flow, with constant density, in the
domain $\mathbb{T}\times \mathbb{R}$. We begin by directly investigating the
Couette shear flow, where we characterize the linear growth of the compressible
part of the fluid while proving time decay for the incompressible part
(inviscid damping with slower rates). Then we extend the analysis to monotone
shear flows near Couette, where we are able to give an upper bound, superlinear
in time, for the compressible part of the fluid. The incompressible part enjoys
an inviscid damping property, analogous to the Couette case. In the pure
Couette case, we exploit the presence of an additional conservation law (which
connects the vorticity and the density on the moving frame) in order to reduce
the number of degrees of freedom of the system. The result then follows by
using weighted energy estimates. In the general case, unfortunately, this
conservation law no longer holds. Therefore we define a suitable weighted
energy functional for the whole system, which can be used to estimate the
irrotational component of the velocity but does not provide sharp bounds on the
solenoidal component. However, even in the absence of the aforementioned
additional conservation law, we are still able to show the existence of a
functional relation which allows us to recover somehow the vorticity from the
density, on the moving frame. By combining the weighted energy estimates with
the functional relation we also recover the inviscid damping for the solenoidal
component of the velocity. | 2003.01694v1 |
2016-06-29 | On the global existence and blowup of smooth solutions to the multi-dimensional compressible Euler equations with time-depending damping | In this paper, we are concerned with the global existence and blowup of
smooth solutions to the multi-dimensional compressible Euler equations with
time-depending damping \begin{equation*}
\partial_t\rho+\operatorname{div}(\rho u)=0, \quad
\partial_t(\rho u)+\operatorname{div}\left(\rho u\otimes
u+p\,I_d\right)=-\alpha(t)\rho u, \quad
\rho(0,x)=\bar \rho+\varepsilon\rho_0(x),\quad u(0,x)=\varepsilon u_0(x),
\end{equation*} where $x=(x_1, \cdots, x_d)\in\Bbb R^d$ $(d=2,3)$, the
frictional coefficient is $\alpha(t)=\frac{\mu}{(1+t)^\lambda}$ with
$\lambda\ge0$ and $\mu>0$, $\bar\rho>0$ is a constant, $\rho_0,u_0 \in
C_0^\infty(\Bbb R^d)$, $(\rho_0,u_0)\not\equiv 0$, $\rho(0,x)>0$, and
$\varepsilon>0$ is sufficiently small. One can totally divide the range of
$\lambda\ge0$ and $\mu>0$ into the following four cases:
Case 1: $0\le\lambda<1$, $\mu>0$ for $d=2,3$;
Case 2: $\lambda=1$, $\mu>3-d$ for $d=2,3$;
Case 3: $\lambda=1$, $\mu\le 3-d$ for $d=2$;
Case 4: $\lambda>1$, $\mu>0$ for $d=2,3$.
\noindent We show that there exists a global $C^{\infty}-$smooth solution
$(\rho, u)$ in Case 1, and Case 2 with $\operatorname{curl} u_0\equiv 0$, while
in Case 3 and Case 4, in general, the solution $(\rho, u)$ blows up in finite
time. Therefore, $\lambda=1$ and $\mu=3-d$ appear to be the critical power and
critical value, respectively, for the global existence of small amplitude
smooth solution $(\rho, u)$ in $d-$dimensional compressible Euler equations
with time-depending damping. | 1606.08935v1 |
2020-01-13 | Modelling Stochastic Signatures in Classical Pulsators | We consider the impact of stochastic perturbations on otherwise coherent
oscillations of classical pulsators. The resulting dynamics are modelled by a
driven damped harmonic oscillator subject to either an external or an internal
forcing and white noise velocity fluctuations. We characterize the phase and
relative amplitude variations using analytical and numerical tools. When the
forcing is internal the phase variation displays a random walk behaviour and a
red noise power spectrum with a ragged erratic appearance. We determine the
dependence of the root mean square phase and relative amplitude variations
($\sigma_{\Delta \varphi}$ and $\sigma_{\Delta A/A}$, respectively) on the
amplitude of the stochastic perturbations, the damping constant $\eta$, and the
total observation time $t_{\rm obs}$ for this case, under the assumption that
the relative amplitude variations remain small, showing that $\sigma_{\Delta
\varphi}$ increases with $t_{\rm obs}^{1/2}$ becoming much larger than
$\sigma_{\Delta A/A}$ for $t_{\rm obs} \gg \eta^{-1}$. In the case of an
external forcing the phase and relative amplitude variations remain of the same
order, independent of the observing time. In the case of an internal forcing,
we find that $\sigma_{\Delta \varphi}$ does not depend on $\eta$. Hence, the
damping time cannot be inferred from fitting the power of the signal, as done
for solar-like pulsators, but the amplitude of the stochastic perturbations may
be constrained from the observations. Our results imply that, given sufficient
time, the variation of the phase associated to the stochastic perturbations in
internally driven classical pulsators will become sufficiently large to be
probed observationally. | 2001.04558v1 |
2020-05-27 | Role of diffusive surface scattering in nonlocal plasmonics | The recent generalised nonlocal optical response (GNOR) theory for plasmonics
is analysed, and its main input parameter, namely the complex hydrodynamic
convection-diffusion constant, is quantified in terms of enhanced Landau
damping due to diffusive surface scattering of electrons at the surface of the
metal. GNOR has been successful in describing plasmon damping effects, in
addition to the frequency shifts originating from induced-charge screening,
through a phenomenological electron diffusion term implemented into the
traditional hydrodynamic Drude model of nonlocal plasmonics. Nevertheless, its
microscopic derivation and justification is still missing. Here we discuss how
the inclusion of a diffusion-like term in standard hydrodynamics can serve as
an efficient vehicle to describe Landau damping without resorting to
computationally demanding quantum-mechanical calculations, and establish a
direct link between this term and the Feibelman $d$ parameter for the centroid
of charge. Our approach provides a recipe to connect the phenomenological
fundamental GNOR parameter to a frequency-dependent microscopic
surface-response function. We therefore tackle one of the principal limitations
of the model, and further elucidate its range of validity and limitations, thus
facilitating its proper application in the framework of nonclassical
plasmonics. | 2005.13218v2 |
2021-01-28 | Vortex-induced Vibrations of a Confined Circular Cylinder for Efficient Flow Power Extraction | A simple method to increase the flow power extraction efficiency of a
circular cylinder, undergoing vortex-induced vibration (VIV), by confining it
between two parallel plates is proposed. A two-dimensional numerical study was
performed on VIV of a circular cylinder inside a parallel plate channel of
height H at Reynolds number 150 to quantify the improvement. The cylinder is
elastically mounted with a spring such that it is only free to vibrate in the
direction transverse to the channel flow and has a fixed mass ratio (m*) of 10.
The energy extraction process is modelled as a damper, with spatially constant
damping ration ((), attached to the cylinder. The simulations are performed by
varying the reduced velocity for a set of fixed mass-damping ({\alpha} = m*()
values ranging between 0 to 1. The blockage ratio (b = D/H) is varied from 0.25
to 0.5 by changing the channel height. The quasi-periodic initial branch found
for the unconfined cylinder shrinks with the increasing blockage. The extracted
power is found to increase rapidly with the blockage. For maximum blockage (b =
0.2), the maximum flow power extracted by the cylinder is an order of magnitude
larger as compared to what it would extract in an open domain with free stream
velocity equal to the channel mean velocity. The optimal mass-damping
({\alpha}c ) for extracting maximum power is found to lie between 0.2 to 0.3.
An expression is derived to predict the maximum extracted power from the
undamped response of a confined/unconfined cylinder. With the assumption
{\alpha}c = 0.25, the derived expression can predict the maximum power
extraction within +-20% of the actual values obtained from present and previous
numerical and experimental studies. | 2101.11803v1 |
2021-03-26 | First-order strong-field QED processes including the damping of particles states | Volkov states are exact solutions of the Dirac equation in the presence of an
arbitrary plane wave. Volkov states, as well as free photon states, are not
stable in the presence of the background plane-wave field but "decay" as
electrons/positrons can emit photons and photons can transform into
electron-positron pairs. By using the solutions of the corresponding
Schwinger-Dyson equations within the locally-constant field approximation, we
compute the probabilities of nonlinear single Compton scattering and nonlinear
Breit-Wheeler pair production by including the effects of the decay of
electron, positron, and photon states. As a result, we find that the
probabilities of these processes can be expressed as the integral over the
light-cone time of the known probabilities valid for stable states per unit of
light-cone time times a light-cone time-dependent exponential damping function
for each interacting particle. The exponential function for an incoming
(outgoing) either electron/positron or photon at each light-cone time
corresponds to the total probability that either the electron/positron emits a
photon via nonlinear Compton scattering or the photon transforms into an
electron-positron pair via nonlinear Breit-Wheeler pair production until that
light-cone time (from that light-cone time on). It is interesting that the
exponential damping terms depend not only on the particles momentum but also on
their spin (for electrons/positrons) and polarization (for photons). This
additional dependence on the discrete quantum numbers prevents the application
of the electron/positron spin and photon polarization sum-rules, which
significantly simplify the computations in the perturbative regime. | 2103.14637v1 |
2021-08-11 | Numerical investigation of the formation and stability of homogeneous pairs of soft particles in inertial microfluidics | We investigate the formation and stability of a pair of identical soft
capsules in channel flow under mild inertia. We employ a combination of the
lattice Boltzmann, finite element and immersed boundary methods to simulate the
elastic particles in flow. Validation tests show excellent agreement with
numerical results obtained by other research groups. Our results reveal new
trajectory types that have not been observed for pairs of rigid particles.
While particle softness increases the likelihood of a stable pair forming, the
pair stability is determined by the lateral position of the particles. A key
finding is that stabilisation of the axial distance occurs after lateral
migration of the particles. During the later phase of pair formation, particles
undergo damped oscillations that are independent of initial conditions. These
damped oscillations are driven by a strong hydrodynamic coupling of the
particle dynamics, particle inertia and viscous dissipation. While the
frequency and damping coefficient of the oscillations depend on particle
softness, the pair formation time is largely determined by the initial particle
positions: the time to form a stable pair grows exponentially with the initial
axial distance. Our results demonstrate that particle softness has a strong
impact on the behaviour of particle pairs. The findings could have significant
ramifications for microfluidic applications where a constant and reliable axial
distance between particles is required, such as flow cytometry. | 2108.05277v1 |
2021-11-27 | Rate of Entropy Production in Stochastic Mechanical Systems | Entropy production in stochastic mechanical systems is examined here with
strict bounds on its rate. Stochastic mechanical systems include pure
diffusions in Euclidean space or on Lie groups, as well as systems evolving on
phase space for which the fluctuation-dissipation theorem applies, i.e.,
return-to-equilibrium processes. Two separate ways for ensembles of such
mechanical systems forced by noise to reach equilibrium are examined here.
First, a restorative potential and damping can be applied, leading to a
classical return-to-equilibrium process wherein energy taken out by damping can
balance the energy going in from the noise. Second, the process evolves on a
compact configuration space (such as random walks on spheres, torsion angles in
chain molecules, and rotational Brownian motion) lead to long-time solutions
that are constant over the configuration space, regardless of whether or not
damping and random forcing balance. This is a kind of potential-free
equilibrium distribution resulting from topological constraints. Inertial and
noninertial (kinematic) systems are considered. These systems can consist of
unconstrained particles or more complex systems with constraints, such as
rigid-bodies or linkages. These more complicated systems evolve on Lie groups
and model phenomena such as rotational Brownian motion and nonholonomic robotic
systems. In all cases, it is shown that the rate of entropy production is
closely related to the appropriate concept of Fisher information matrix of the
probability density defined by the Fokker-Planck equation. Classical results
from information theory are then repurposed to provide computable bounds on the
rate of entropy production in stochastic mechanical systems. | 2111.13930v1 |
2022-04-20 | Ferrimagnet GdFeCo characterization for spin-orbitronics: large field-like and damping-like torques | Spintronics is showing promising results in the search for new materials and
effects to reduce energy consumption in information technology. Among these
materials, ferrimagnets are of special interest, since they can produce large
spin currents that trigger the magnetization dynamics of adjacent layers or
even their own magnetization. Here, we present a study of the generation of
spin current by GdFeCo in a GdFeCo/Cu/NiFe trilayer where the FeCo sublattice
magnetization is dominant at room temperature. Magnetic properties such as the
saturation magnetization are deduced from magnetometry measurements while
damping constant is estimated from spin-torque ferromagnetic resonance
(ST-FMR). We show that the overall damping-like (DL) and field-like (FL)
effective fields as well as the associated spin Hall angles can be reliably
obtained by performing the dependence of ST-FMR by an added dc current. The sum
of the spin Hall angles for both the spin Hall effect (SHE) and the spin
anomalous Hall effect (SAHE) symmetries are: $\theta_{DL}^{SAHE} +
\theta_{DL}^{SHE}=-0.15 \pm 0.05$ and $\theta_{FL}^{SAHE} +
\theta_{FL}^{SHE}=0.026 \pm 0.005$. From the symmetry of ST-FMR signals we find
that $\theta_{DL}^{SHE}$ is positive and dominated by the negative
$\theta_{DL}^{SAHE}$. The present study paves the way for tuning the different
symmetries in spin conversion in highly efficient ferrimagnetic systems. | 2204.09776v1 |
2022-11-28 | Exciting the TTV Phases of Resonant Sub-Neptunes | There are excesses of sub-Neptunes just wide of period commensurabilities
like the 3:2 and 2:1, and corresponding deficits narrow of them. Any theory
that explains this period ratio structure must also explain the strong transit
timing variations (TTVs) observed near resonance. Besides an amplitude and a
period, a sinusoidal TTV has a phase. Often overlooked, TTV phases are
effectively integration constants, encoding information about initial
conditions or the environment. Many TTVs near resonance exhibit non-zero
phases. This observation is surprising because dissipative processes that
capture planets into resonance also damp TTV phases to zero. We show how both
the period ratio structure and the non-zero TTV phases can be reproduced if
pairs of sub-Neptunes capture into resonance in a gas disc while accompanied by
a third eccentric non-resonant body. Convergent migration and eccentricity
damping by the disc drives pairs to orbital period ratios wide of
commensurability; then, after the disc clears, secular forcing by the third
body phase-shifts the TTVs. The scenario predicts that resonant planets are
apsidally aligned and possess eccentricities up to an order of magnitude larger
than previously thought. | 2211.15701v2 |
2023-01-23 | Estimation of turbulent proton and electron heating rates via Landau damping constrained by Parker Solar Probe observations | The heating of ions and electrons due to turbulent dissipation plays a
crucial role in the thermodynamics of the solar wind and other plasma
environments. Using magnetic field and thermal plasma observations from the
first two perihelia of the Parker Solar Probe (PSP), we model the relative
heating rates as a function of radial distance, magnetic spectra, and plasma
conditions, enabling us to better characterize the thermodynamics of the inner
heliosphere. We employ the Howes et al. 2008 steady-state cascade model, which
considers the behavior of turbulent, low-frequency, wavevector-anisotropic,
critically balanced Alfv\'enic fluctuations that dissipate via Landau damping
to determine proton-to-electron heating rates $Q_p/Q_e$. We distinguish
ion-cyclotron frequency circularly polarized waves from low-frequency
turbulence and constrain the cascade model using spectra constructed from the
latter. We find that the model accurately describes the observed energy
spectrum from over 39.4 percent of the intervals from Encounters 1 and 2,
indicating the possibility for Landau damping to heat the young solar wind. The
ability of the model to describe the observed turbulent spectra increases with
the ratio of thermal-to-magnetic pressure, $\beta_p$, indicating that the model
contains the necessary physics at higher $\beta_p$. We estimate high magnitudes
for the Kolmogorov constant which is inversely proportional to the non-linear
energy cascade rate. We verify the expected strong dependency of $Q_p/Q_e$ on
$\beta_p$ and the consistency of the critical balance assumption. | 2301.09713v1 |
2024-02-02 | Controllable frequency tunability and parabolic-like threshold current behavior in spin Hall nano-oscillators | We investigate the individual impacts of critical magnetodynamical
parameters-effective magnetization and magnetic damping-on the auto-oscillation
characteristics of nano-constriction-based Spin Hall Nano-Oscillators (SHNOs).
Our micromagnetic simulations unveil a distinctive non-monotonic relationship
between current and auto-oscillation frequency in out-of-plane magnetic fields.
The influence of effective magnetization on frequency tunability varies with
out-of-plane field strengths. At large out-of-plane fields, the frequency
tunability is predominantly governed by effective magnetization, achieving a
current tunability of 1 GHz/mA-four times larger than that observed at the
lowest effective magnetization. Conversely, at low out-of-plane fields,
although a remarkably high-frequency tunability of 4 GHz/mA is observed, the
effective magnetization alters the onset of the transition from a linear-like
mode to a spin-wave bullet mode. Magnetic damping primarily affects the
threshold current with negligible impact on auto-oscillation frequency
tunability. The threshold current scales linearly with increased magnetic
damping at a constant out-of-plane field but exhibits a parabolic behavior with
variations in out-of-plane fields. This behavior is attributed to the
qualitatively distinct evolution of the auto-oscillation mode across different
out-of-plane field values. Our study not only extends the versatility of SHNOs
for oscillator-based neuromorphic computing with controllable frequency
tunability but also unveils the intricate auto-oscillation dynamics in
out-of-plane fields. | 2402.01570v1 |
2024-03-18 | Radiative loss and ion-neutral collisional effects in astrophysical plasmas | In this paper we study the role of radiative cooling in a two-fluid model
consisting of coupled neutrals and charged particles. We first analyze the
linearized two-fluid equations where we include radiative losses in the energy
equation for the charged particles. In a 1D geometry for parallel propagation
and in the limiting cases of weak and strong coupling, it can be shown
analytically that the instability conditions for the thermal mode and the sound
waves, the isobaric and isentropic criteria, respectively, remain unchanged
with respect to one-fluid radiative plasmas. For the parameters considered in
this paper, representative for the solar corona, the radiative cooling produces
growth of the thermal mode and damping of the sound waves. When neutrals are
included and are sufficiently coupled to the charges, the thermal mode growth
rate and the wave damping both reduce by the same factor, which depends on the
ionization fraction only. For a heating function which is constant in time, we
find that the growth of the thermal mode and the damping of the sound waves are
slightly larger. The numerical calculation of the eigenvalues of the general
system of equations in a 3D geometry confirm the analytic results. We then run
2D fully nonlinear simulations which give consistent results: a higher
ionization fraction or lower coupling will increase the growth rate. The
magnetic field contribution is negligible in the linear phase.
Ionization-recombination effects might play an important role because the
radiative cooling produces a large range of temperatures in the system. In the
numerical simulation, after the first condensation phase, when the minimum
temperature is reached, the fraction of neutrals increases four orders of
magnitude because of the recombination. | 2403.11900v1 |
2001-01-12 | Spatial gradients in the cosmological constant | It is possible that there may be differences in the fundamental physical
parameters from one side of the observed universe to the other. I show that the
cosmological constant is likely to be the most sensitive of the physical
parameters to possible spatial variation, because a small variation in any of
the other parameters produces a huge variation of the cosmological constant. It
therefore provides a very powerful {\em indirect} evidence against spatial
gradients or temporal variation in the other fundamental physical parameters,
at least 40 orders of magnitude more powerful than direct experimental
constraints. Moreover, a gradient may potentially appear in theories where the
variability of the cosmological constant is connected to an anthropic selection
mechanism, invoked to explain the smallness of this parameter. In the Hubble
damping mechanism for anthropic selection, I calculate the possible gradient.
While this mechanism demonstrates the existence of this effect, it is too small
to be seen experimentally, except possibly if inflation happens around the
Planck scale. | 0101130v1 |
1999-01-22 | Longitudinal wavevector- and frequency-dependent dielectric constant of the TIP4P water model | A computer adapted theory for self-consistent calculations of the wavevector-
and frequency-dependent dielectric constant for interaction site models of
polar systems is proposed. A longitudinal component of the dielectric constant
is evaluated for the TIP4P water model in a very wide scale of wavenumbers and
frequencies using molecular dynamics simulations. It is shown that values for
the dielectric permittivity, calculated within the exact interaction site
description, differ in a characteristic way from those obtained by the point
dipole approximation which is usually used in computer experiment. It is also
shown that the libration oscillations, existing in the shape of longitudinal
time-dependent polarization fluctuations at small and intermediate wavevector
values, vanish however for bigger wavenumbers. A comparison between the
wavevector and frequency behaviour of the dielectric constant for the TIP4P
water and the Stockmayer model is made. The static screening of external
charges and damping of longitudinal electric excitations in water are
considered as well. A special investigation is devoted to the time dependence
of dielectric quantities in the free motion regime. | 9901036v1 |
2010-07-05 | On the Karman constant | Numerous studies in the past 40 years have established that turbulent flow
fields are populated by transient coherent structures that represent patches of
fluids moving cohesively for significant distances before they are worn out by
momentum exchange with the surrounding fluid. Two particular well-documented
structures are the hairpin vortices that move longitudinally above the wall and
ejections inclined with respect to the wall that bring the fluid from the
transient viscous layers underneath these vortices into the outer region of the
boundary layer.
It is proposed that the Karman universal constant in the logarithmic law the
sine of the angle between the transient ejections and the direction normal to
the wall. The edge of the buffer layer is represented by a combination of the
Karman constant and the damping function in the wall layer.
Computation of this angle from experimental data of velocity distributions in
turbulent shear flows matches published traces of fronts of turbulence obtained
from the time shifts in the peak of the correlation function of the velocity.
Key works: Turbulence, coherent structures, Karman constant, mixing-length,
shear layers | 1007.0605v1 |
2021-05-19 | Sound attenuation derived from quenched disorder in solids | In scattering experiments, the dynamical structure factor (DSF) characterizes
inter-particle correlations and their time evolution. We analytically evaluated
the DSF of disordered solids with disorder in the spring constant, by averaging
over quenched disorder in the values of lattice bond strength, along the
acoustic branch. The width of the resulting acoustic excitation peak is treated
as the effective damping constant $\Gamma(q)$, which we found to grow linearly
with exchanged momentum $q$. This is verified by numerically calculating a
model system consisting of harmonic linear chains with disorder in spring
constant. We also found that the quenched averaging of the vibrational density
of states produces a characteristic peak at a frequency related to the average
acoustic resonance. Such a peak (the excess over Debye law) may be related to
the "boson peak" frequently discussed in disordered solids, in our case
explicitly arising from the quenched disorder in the distribution of spring
constants. | 2105.09393v1 |
2020-01-08 | Assessing different approaches to ab initio calculations of spin wave stiffness | Ab initio calculations of the spin wave stiffness constant $D$ for elemental
Fe and Ni performed by different groups in the past have led to values with a
considerable spread of 50-100 %. We present results for the stiffness constant
$D$ of Fe, Ni, and permalloy Fe$_{0.19}$Ni$_{0.81}$ obtained by three different
approaches: (i) by finding the quadratic term coefficient of the power
expansion of the spin wave energy dispersion, (ii) by a damped real-space
summation of weighted exchange coupling constants, and (iii) by integrating the
appropriate expression in reciprocal space. All approaches are implemented by
means of the same Korringa-Kohn-Rostoker (KKR) Green function formalism. We
demonstrate that if properly converged, all procedures yield comparable values,
with uncertainties of 5-10 % remaining. By a careful analysis of the influence
of various technical parameters we estimate the margin of errors for the
stiffness constants evaluated by different approaches and suggest procedures to
minimize the risk of getting incorrect results. | 2001.02558v2 |
2022-05-17 | Acoustic gravitational interaction revised | In this paper, we deduce the expression of the gravito-acoustic force between
two oscillating bubbles using the hypothesis that this type of force is a force
of scattering-absorption of the energy of excitatory waves. The expression of
the gravito-acoustic force at resonance highlights the dependence of this force
on the product of the virtual masses of the two bubbles and on an acoustic
gravitational constant. The acoustic gravitational constant depends on the
absorption damping coefficient. We may say also that the expression of the
acoustic gravitational constant is analogous to the expression of the
gravitational constant in the electromagnetic world, that one obtained in the
Einstein-Sciama model and the Dirac-Eddington large numbers hypothesis. The
results obtained for this type of phenomenon in the acoustic world support the
similarity between the acoustic world and the electromagnetic world. | 2206.00435v1 |
2021-02-09 | Binet's factorial series and extensions to Laplace transforms | We investigate a generalization of Binet's factorial series in the parameter
$\alpha$ \[ \mu\left( z\right) =\sum_{m=1}^{\infty}\frac{b_{m}\left(
\alpha\right) }{\prod_{k=0}^{m-1}(z+\alpha+k)}% \] due to Gilbert, for the
Binet function \[ \mu\left( z\right) =\log\Gamma\left( z\right) -\left(
z-\frac{1} {2}\right) \log z+z-\frac{1}{2}\log\left( 2\pi\right) \] After a
review of the Binet function $\mu\left( z\right) $ and Gilbert's investigations
of $\mu\left( z\right) $, several properties of the Binet polynomials
$b_{m}\left( \alpha\right) $ are presented. We compare Gilbert's generalized
factorial series with Stirling's asymptotic expansion and demonstrate by a
numerical example that, with a same number of terms evaluated, the Gilbert
generalized factorial series with an optimized value of $\alpha$ can beat the
best possible accuracy of Stirling's expansion. Finally, we extend Binet's
method to factorial series of Laplace transforms. | 2102.04891v7 |
2022-07-27 | Determination of Thickness-dependent Damping Constant and Plasma Frequency for Ultrathin Ag and Au Films: Nanoscale Dielectric Function | There is an ever increasing interest in the development of plasmonic 2D
nanomaterials, with widespread applications in optoelectronics, high resolution
microscopy, imaging and sensing, among others. With the current ability of
ultrathin noble metal film deposition down to a few monolayers in thickness,
there is a need for an analytical expression of the thickness dependent complex
dielectric function for predicting optical properties for arbitrary
thicknesses. The free and bound electron contributions to the dielectric
function are dealt with independently, since their influences affect separate
wavelengths ranges. The former is dealt within the Drude model framework for
large wavelengths with appropriately addressed damping constant and plasma
frequency parameters to account for thickness dependence. Applying our
previously developed method, we determine these parameters for specific film
thicknesses, based on refractive index experimental values for Ag and Au thin
films. Fitting separately each one of these parameters allowed us to find an
analytical expression for their dependence on arbitrary film thickness and
consequently for the free electron contribution. Concerning bound electrons, it
is seen that its contribution for small wavelengths is the same for all
analyzed thicknesses and may be set equal to the bulk bound contribution.
Taking all these facts into account, the complex dielectric function can be
rewritten analytically, in terms of the bulk dielectric function plus
corrective film thickness dependent terms. In particular, the fitting process
for the damping constant allows us to determine that the electron scattering at
the film boundary is mainly diffusive (inelastic) for both silver and gold thin
films. It is also shown that, in accordance with theoretical studies, plasma
frequency shows a red shift as the film thickness decreases. | 2207.13580v1 |
1999-11-03 | Tensor Microwave Anisotropies from a Stochastic Magnetic Field | We derive an expression for the angular power spectrum of cosmic microwave
background anisotropies due to gravity waves generated by a stochastic magnetic
field and compare the result with current observations; we take into account
the non-linear nature of the stress energy tensor of the magnetic field.
For almost scale invariant spectra, the amplitude of the magnetic field at
galactic scales is constrained to be of order 10^{-9} Gauss. If we assume that
the magnetic field is damped below the Alfven damping scale, we find that its
amplitude at
0.1 h^{-1}Mpc, B_\lambda, is constrained to be B_\lambda<7.9 x10^{-6} e^{3n}
Gauss, for n<-3/2, and B_\lambda<9.5x10^{-8} e^{0.37n} Gauss, for n>-3/2, where
n is the spectral index of the magnetic field and H_0=100h km s^{-1}Mpc^{-1} is
the Hubble constant today. | 9911040v1 |
2002-07-15 | On the Structure of the Iron K-Edge | It is shown that the commonly held view of a sharp Fe K edge must be modified
if the decay pathways of the series of resonances converging to the K
thresholds are adequately taken into account. These resonances display damped
Lorentzian profiles of nearly constant widths that are smeared to impose
continuity across the threshold. By modeling the effects of K damping on
opacities, it is found that the broadening of the K edge grows with the
ionization level of the plasma and that the appearance at high ionization of a
localized absorption feature at 7.2 keV is identified as the K-beta unresolved
transition array. | 0207324v2 |
2006-12-15 | Damp Mergers: Recent Gaseous Mergers without Significant Globular Cluster Formation? | Here we test the idea that new globular clusters (GCs) are formed in the same
gaseous ("wet") mergers or interactions that give rise to the young stellar
populations seen in the central regions of many early-type galaxies. We compare
mean GC colors with the age of the central galaxy starburst. The red GC
subpopulation reveals remarkably constant mean colors independent of galaxy
age. A scenario in which the red GC subpopulation is a combination of old and
new GCs (formed in the same event as the central galaxy starburst) can not be
ruled out; although this would require an age-metallicity relation for the
newly formed GCs that is steeper than the Galactic relation. However, the data
are also well described by a scenario in which most red GCs are old, and few,
if any, are formed in recent gaseous mergers. This is consistent with the old
ages inferred from some spectroscopic studies of GCs in external systems. The
event that induced the central galaxy starburst may have therefore involved
insufficient gas mass for significant GC formation. We term such gas-poor
events "damp" mergers. | 0612415v1 |
1998-02-24 | Resonant steps and spatiotemporal dynamics in the damped dc-driven Frenkel-Kontorova chain | Kink dynamics of the damped Frenkel-Kontorova (discrete sine-Gordon) chain
driven by a constant external force are investigated. Resonant steplike
transitions of the average velocity occur due to the competitions between the
moving kinks and their radiated phasonlike modes. A mean-field consideration is
introduced to give a precise prediction of the resonant steps. Slip-stick
motion and spatiotemporal dynamics on those resonant steps are discussed. Our
results can be applied to studies of the fluxon dynamics of 1D
Josephson-junction arrays and ladders, dislocations, tribology and other
fields. | 9802251v1 |
1999-03-11 | Thermally activated escape rates of uniaxial spin systems with transverse field | Classical escape rates of uniaxial spin systems are characterized by a
prefactor differing from and much smaller than that of the particle problem,
since the maximum of the spin energy is attained everywhere on the line of
constant latitude: theta=const, 0 =< phi =< 2*pi. If a transverse field is
applied, a saddle point of the energy is formed, and high, moderate, and low
damping regimes (similar to those for particles) appear. Here we present the
first analytical and numerical study of crossovers between the uniaxial and
other regimes for spin systems. It is shown that there is one HD-Uniaxial
crossover, whereas at low damping the uniaxial and LD regimes are separated by
two crossovers. | 9903192v2 |
2006-11-18 | Distributions of switching times of single-domain particles using a time quantified Monte Carlo method | Using a time quantified Monte Carlo scheme we performed simulations of the
switching time distribution of single mono-domain particles in the
Stoner-Wohlfarth approximation. We considered uniaxial anisotropy and different
conditions for the external applied field. The results obtained show the
switching time distribution can be well described by two relaxation times,
either when the applied field is parallel to the easy axis or for an oblique
external field and a larger damping constant. We found that in the low barrier
limit these relaxation times are in very good agreement with analytical results
obtained from solutions of the Fokker-Planck equation related to this problem.
When the damping is small and the applied field is oblique the shape of the
distribution curves shows several peaks and resonance effects. | 0611494v2 |
2004-01-13 | Highly Damped Quasinormal Modes of Kerr Black Holes: A Complete Numerical Investigation | We compute for the first time very highly damped quasinormal modes of the
(rotating) Kerr black hole. Our numerical technique is based on a decoupling of
the radial and angular equations, performed using a large-frequency expansion
for the angular separation constant_{s}A_{l m}. This allows us to go much
further in overtone number than ever before. We find that the real part of the
quasinormal frequencies approaches a non-zero constant value which does not
depend on the spin s of the perturbing field and on the angular index l:
\omega_R=m\varpi(a). We numerically compute \varpi(a). Leading-order
corrections to the asymptotic frequency are likely to be of order 1/\omega_I.
The imaginary part grows without bound, the spacing between consecutive modes
being a monotonic function of a. | 0401052v1 |
1992-06-21 | Gauge Dependence of the Resummed Thermal Gluon Self Energy | The gauge dependence of the hot gluon self energy is examined in the context
of Pisarski's method for resumming hard thermal loops. Braaten and Pisarski
have used the Ward identities satisfied by the hard corrections to the n-point
functions to argue the gauge fixing independence of the leading order resummed
QCD plasma damping rate in covariant and strict Coulomb gauges. We extend their
analysis to include all linear gauges that preserve rotational invariance and
display explicitly the conditions required for gauge fixing independence. It is
shown that in covariant gauges the resummed damping constant is gauge fixing
independent only if an infrared regulator is explicitly maintained throughout
the calculation. | 9206239v1 |
1993-05-07 | Thermal quark production in pure glue and quark gluon plasmas | We calculate production rates for massless $(u,d)$ and massive $(s,c,b)$
quarks in pure glue and quark gluon plasmas to leading order in the strong
coupling constant $g$. The leading contribution comes from gluon decay into
$q\bar q$ pairs, using a thermal gluon propagator with finite thermal mass and
damping rate. The rate behaves as $\alpha_S^2(\ln 1/\alpha_S)^2 T^4$ when $m,
\alpha_S \rightarrow 0$ and depends linearly on the transverse gluon damping
rate for all values of the quark mass $m$. The light quark ($u$, $d$, $s$)
chemical equilibration time is approximately 10-100 $T^{-1}$ for $g=$2-3, so
that quarks are likely to remain far from chemical equilibrium in
ultrarelativistic nuclear collisions. | 9305227v1 |
2005-06-28 | Liouville Decoherence in a Model of Flavour Oscillations in the presence of Dark Energy | We study in some detail the master equation, and its solution in a simplified
case modelling flavour oscillations of a two-level system, stemming from the
Liouville-string approach to quantum space time foam. In this framework we
discuss the appearance of diffusion terms and decoherence due to the
interaction of low-energy string matter with space-time defects, such as
D-particles in the specific model of ``D-particle foam'', as well as dark
energy contributions. We pay particular attention to contrasting the decoherent
role of a cosmological constant in inducing exponential quantum damping in the
evolution of low-energy observables, such as the probability of flavour
oscillations, with the situation where the dark energy relaxes to zero for
asymptotically large times, in which case such a damping is absent. Our
findings may be of interest to (astrophysical) tests of quantum space-time foam
models in the not-so-distant future. | 0506242v1 |
2006-04-07 | Quasi-periodic attractors, Borel summability and the Bryuno condition for strongly dissipative systems | We consider a class of ordinary differential equations describing
one-dimensional analytic systems with a quasi-periodic forcing term and in the
presence of damping. In the limit of large damping, under some generic
non-degeneracy condition on the force, there are quasi-periodic solutions which
have the same frequency vector as the forcing term. We prove that such
solutions are Borel summable at the origin when the frequency vector is either
any one-dimensional number or a two-dimensional vector such that the ratio of
its components is an irrational number of constant type. In the first case the
proof given simplifies that provided in a previous work of ours. We also show
that in any dimension $d$, for the existence of a quasi-periodic solution with
the same frequency vector as the forcing term, the standard Diophantine
condition can be weakened into the Bryuno condition. In all cases, under a
suitable positivity condition, the quasi-periodic solution is proved to
describe a local attractor. | 0604162v1 |
1998-02-27 | New collective mode due to collisional coupling | Starting from a nonmarkovian conserving relaxation time approximation for
collisions we derive coupled dispersion relations for asymmetric nuclear
matter. The isovector and isoscalar modes are coupled due to asymmetric nuclear
meanfield acting on neutrons and protons differently. A further coupling is
observed by collisional correlations. The latter one leads to the appearance of
a new soft mode besides isoscalar and isovector modes in the system. We suggest
that this mode might be observable in asymmetric systems. This soft mode
approaches the isovector mode for high temperatures. At the same time the
isovector mode remains finite and approaches a constant value at higher
temperatures showing a transition from zero sound like damping to first sound.
The damping of the new soft mode is first sound like at all temperatures. | 9802083v1 |
2000-08-14 | Design of a 3 GHz Accelerator Structure for the CLIC Test Facility (CTF 3) Drive Beam | For the CLIC two-beam scheme, a high-current, long-pulse drive beam is
required for RF power generation. Taking advantage of the 3 GHz klystrons
available at the LEP injector once LEP stops, a 180 MeV electron accelerator is
being constructed for a nominal beam current of 3.5 A and 1.5 microsecond pulse
length. The high current requires highly effective suppression of dipolar
wakes. Two concepts are investigated for the accelerating structure design: the
"Tapered Damped Structure" developed for the CLIC main beam, and the "Slotted
Iris - Constant Aperture" structure. Both use 4 SiC loads per cell for
effective higher-order mode damping. A full-size prototype of the TDS structure
has been built and tested successfully at full power. A first prototype of the
SICA structure is being built. | 0008052v1 |
2004-11-02 | Supersymmetric free-damped oscillators: Adaptive observer estimation of the Riccati parameter | A supersymmetric class of free damped oscillators with three parameters has
been obtained in 1998 by Rosu and Reyes through the factorization of the Newton
equation. The supplementary parameter is the integration constant of the
general Riccati solution. The estimation of the latter parameter is performed
here by employing the recent adaptive observer scheme of Besancon et al., but
applied in a nonstandard form in which a time-varying quantity containing the
unknown Riccati parameter is estimated first. Results of computer simulations
are presented to illustrate the good feasibility of this approach for a case in
which the estimation is not easily accomplished by other means | 0411019v2 |
2007-01-30 | Charge Fluctuation of Dust Grain and Its Impact on Dusty-Acoustic Wave Damping | We consider the influence of dust charge fluctuations on damping of the
dust-ion-acoustic waves. It is assumed that all grains have equal masses but
charges are not constant in time - they may fluctuate in time. The dust charges
are not really independent of the variations in the plasma potentials. All
modes will influence the charging mechanism, and feedback will lead to several
new interesting and unexpected phenomena. The charging of the grains depends on
local plasma characteristics. If the waves disturb these characteristic, then
charging of the grains is affected and the grain charge is modified, with a
resulting feedback on the wave mode. In the case considered here, when the
temperature of electrons is much greater than the temperature of the ions and
the temperature of electrons is not great enough for further ionization of the
ions, we show that attenuation of the acoustic wave depends only on one
phenomenological coefficient | 0701336v1 |
2004-01-28 | Bloch Equations and Completely Positive Maps | The phenomenological dissipation of the Bloch equations is reexamined in the
context of completely positive maps. Such maps occur if the dissipation arises
from a reduction of a unitary evolution of a system coupled to a reservoir. In
such a case the reduced dynamics for the system alone will always yield
completely positive maps of the density operator. We show that, for Markovian
Bloch maps, the requirement of complete positivity imposes some Bloch
inequalities on the phenomenological damping constants. For non-Markovian Bloch
maps some kind of Bloch inequalities involving eigenvalues of the damping basis
can be established as well. As an illustration of these general properties we
use the depolarizing channel with white and colored stochastic noise. | 0401177v1 |
2006-01-10 | Quantum Brownian motion and the Third Law of thermodynamics | The quantum thermodynamic behavior of small systems is investigated in
presence of finite quantum dissipation. We consider the archetype cases of a
damped harmonic oscillator and a free quantum Brownian particle. A main finding
is that quantum dissipation helps to ensure the validity of the Third Law. For
the quantum oscillator, finite damping replaces the zero-coupling result of an
exponential suppression of the specific heat at low temperatures by a power-law
behavior. Rather intriguing is the behavior of the free quantum Brownian
particle. In this case, quantum dissipation is able to restore the Third Law:
Instead of being constant down to zero temperature, the specific heat now
vanishes proportional to temperature with an amplitude that is inversely
proportional to the ohmic dissipation strength. A distinct subtlety of finite
quantum dissipation is the result that the various thermodynamic functions of
the sub-system do not only depend on the dissipation strength but depend as
well on the prescription employed in their definition. | 0601056v1 |
2007-08-26 | Geodesic plasma flows instabilities of Riemann twisted solar loops | Riemann and sectional curvatures of magnetic twisted flux tubes in Riemannian
manifold are computed to investigate the stability of the plasma astrophysical
tubes. The geodesic equations are used to show that in the case of thick
magnetic tubes, the curvature of planar (Frenet torsion-free) tubes have the
effect ct of damping the flow speed along the tube. Stability of geodesic flows
in the Riemannian twisted thin tubes (almost filaments), against constant
radial perturbations is investigated by using the method of negative sectional
curvature for unstable flows. No special form of the flow like Beltrami flows
is admitted, and the proof is general for the case of thin magnetic flux tubes.
In the magnetic equilibrium state, the twist of the tube is shown to display
also a damping effect on the toroidal velocity of the plasma flow. It is found
that for positive perturbations and angular speed of the flow, instability is
achieved, since the sectional Ricci curvature of the magnetic twisted tube
metric is negative. Solar flare production may appear from these geometrical
instabilities of the twisted solar loops. | 0708.3473v1 |
2009-01-28 | Location- and observation time-dependent quantum-tunneling | We investigate quantum tunneling in a translation invariant chain of
particles. The particles interact harmonically with their nearest neighbors,
except for one bond, which is anharmonic. It is described by a symmetric double
well potential. In the first step, we show how the anharmonic coordinate can be
separated from the normal modes. This yields a Lagrangian which has been used
to study quantum dissipation. Elimination of the normal modes leads to a
nonlocal action of Caldeira-Leggett type. If the anharmonic bond defect is in
the bulk, one arrives at Ohmic damping, i.e. there is a transition of a
delocalized bond state to a localized one if the elastic constant exceeds a
critical value $C_{crit}$. The latter depends on the masses of the bond defect.
Superohmic damping occurs if the bond defect is in the site $M$ at a finite
distance from one of the chain ends. If the observation time $T$ is smaller
than a characteristic time $\tau_M \sim M$, depending on the location M of the
defect, the behavior is similar to the bulk situation. However, for $T \gg
\tau_M$ tunneling is never suppressed. | 0901.4518v1 |
2010-01-06 | Freezing of spin dynamics and omega/T scaling in underdoped cuprates | The memory function approach to spin dynamics in doped antiferromagnetic
insulator combined with the assumption of temperature independent static spin
correlations and constant collective mode damping leads to omega/T scaling in a
broad range. The theory involving a non universal scaling parameter is used to
analyze recent inelastic neutron scattering results for underdoped cuprates.
Adopting modified damping function also the emerging central peak in low-doped
cuprates at low temperatures can be explained within the same framework. | 1001.0837v1 |
2010-02-02 | Inertial Oscillations of Pinned Dislocations | Dislocation pinning plays a vital role in the plastic behaviour of a
crystalline solid. Here we report the first observation of the damped
oscillations of a mobile dislocation after it gets pinned at an obstacle in the
presence of a constant static shear load. These oscillations are found to be
inertial, instead of forced as obtained in the studies of internal friction of
solid. The rate of damping enables us to determine the effective mass of the
dislocation. Nevertheless, the observed relation between the oscillation
frequency and the link length is found to be anomalous, when compared with the
theoretical results in the framework of Koehler's vibrating string model. We
assign this anomaly to the improper boundary conditions employed in the
treatment. Finally, we propose that the inertial oscillations may offer a
plausible explanation of the electromagnetic emissions during material
deformation and seismic activities. | 1002.0422v1 |
2010-05-20 | Line Solutions for the Euler and Euler-Poisson Equations with Multiple Gamma Law | In this paper, we study the Euler and Euler-Poisson equations in $R^{N}$,
with multiple $\gamma$-law for pressure function: \begin{equation}
P(\rho)=e^{s}\sum_{j=1}^{m}\rho^{\gamma_{j}}, \end{equation} where all
$\gamma_{i+1}>\gamma_{i}\geq1$, is the constants. The analytical line solutions
are constructed for the systems. It is novel to discover the analytical
solutions to handle the systems with mixed pressure function. And our solutions
can be extended to the systems with the generalized multiple damping and
pressure function. | 1005.3651v1 |
2010-07-12 | Ferromagnetic Excitations in La$_{0.82}$Sr$_{0.18}$CoO$_{3}$ Observed Using Neutron Inelastic Scattering | Polarized neutron inelastic scattering has been used to measure spin
excitations in ferromagnetic La$_{0.82}$Sr$_{0.18}$CoO$_{3}$. The magnon
spectrum of these spin excitations is well defined at low energies but becomes
heavily damped at higher energies, and can be modeled using a quadratic
dispersion. We determined a spin wave stiffness constant of $D=94\pm
3$\,meV\,\AA$^{2}$. Assuming a nearest-neighbor Heisenberg model we find
reasonable agreement between the exchange determined from D and the bulk Curie
temperature. Several possible mechanisms to account for the observed spin-wave
damping are discussed. | 1007.1919v1 |
2010-10-03 | Measurement of damping and temperature: Precision bounds in Gaussian dissipative channels | We present a comprehensive analysis of the performance of different classes
of Gaussian states in the estimation of Gaussian phase-insensitive dissipative
channels. In particular, we investigate the optimal estimation of the damping
constant and reservoir temperature. We show that, for two-mode squeezed vacuum
probe states, the quantum-limited accuracy of both parameters can be achieved
simultaneously. Moreover, we show that for both parameters two-mode squeezed
vacuum states are more efficient than either coherent, thermal or single-mode
squeezed states. This suggests that at high energy regimes two-mode squeezed
vacuum states are optimal within the Gaussian setup. This optimality result
indicates a stronger form of compatibility for the estimation of the two
parameters. Indeed, not only the minimum variance can be achieved at fixed
probe states, but also the optimal state is common to both parameters.
Additionally, we explore numerically the performance of non-Gaussian states for
particular parameter values to find that maximally entangled states within
D-dimensional cutoff subspaces perform better than any randomly sampled states
with similar energy. However, we also find that states with very similar
performance and energy exist with much less entanglement than the maximally
entangled ones. | 1010.0442v1 |
2010-10-18 | K-shell photoionization of Na-like to Cl-like ions of Mg, Si, S, Ar, and Ca | We present $R$-matrix calculations of photoabsorption and photoionization
cross sections across the K-edge of Mg, Si, S, Ar, and Ca ions with more than
10 electrons. The calculations include the effects of radiative and Auger
damping by means of an optical potential. The wave functions are constructed
from single-electron orbital bases obtained using a Thomas--Fermi--Dirac
statistical model potential. Configuration interaction is considered among all
states up to $n=3$. The damping processes affect the resonances converging to
the K-thresholds causing them to display symmetric profiles of constant width
that smear the otherwise sharp edge at the photoionization threshold. These
data are important for modeling of features found in photoionized plasmas. | 1010.3734v1 |
2010-10-19 | A possible signature of cosmic neutrino decoupling in the nHz region of the spectrum of primordial gravitational waves | In this paper we study the effect of cosmic neutrino decoupling on the
spectrum of cosmological gravitational waves (GWs). At temperatures T>>1 MeV,
neutrinos constitute a perfect fluid and do not hinder GW propagation, while
for T<<1 MeV they free-stream and have an effective viscosity that damps
cosmological GWs by a constant amount. In the intermediate regime,
corresponding to neutrino decoupling, the damping is frequency-dependent. GWs
entering the horizon during neutrino decoupling have a frequency f ~ 1 nHz,
corresponding to a frequency region that will be probed by Pulsar Timing Arrays
(PTAs). In particular, we show how neutrino decoupling induces a spectral
feature in the spectrum of cosmological GWs just below 1 nHz. We briefly
discuss the conditions for a detection of this feature and conclude that it is
unlikely to be observed by PTAs. | 1010.3849v2 |
2011-04-25 | Exactly Solvable Nonhomogeneous Burgers Equations with Variable Coefficients | We consider a nonhomogeneous Burgers equation with time variable
coefficients, and obtain an explicit solution of the general initial value
problem in terms of solution to a corresponding linear ODE. Special exact
solutions such as generalized shock and multi-shock solitary waves, triangular
wave, N-wave and rational type solutions are found and discussed. As exactly
solvable models, we study forced Burgers equations with constant damping and an
exponentially decaying diffusion coefficient. Different type of exact solutions
are obtained for the critical, over and under damping cases, and their behavior
is illustrated explicitly. In particular, the existence of inelastic type of
collisions is observed by constructing multi-shock solitary wave solutions, and
for the rational type solutions the motion of the pole singularities is
described. | 1104.4717v1 |
2011-07-15 | K-shell photoionization of Nickel ions using R-matrix | We present R-matrix calculations of photoabsorption and photoionization cross
sections across the K edge of the Li-like to Ca-like ions stages of Ni.
Level-resolved, Breit-Pauli calculations were performed for the Li-like to
Na-like stages. Term-resolved calculations, which include the mass-velocity and
Darwin relativistic corrections, were performed for the Mg-like to Ca-like ion
stages. This data set is extended up to Fe-like Ni using the distorted wave
approximation as implemented by AUTOSTRUCTURE. The R-matrix calculations
include the effects of radiative and Auger dampings by means of an optical
potential. The damping processes affect the absorption resonances converging to
the K thresholds causing them to display symmetric profiles of constant width
that smear the otherwise sharp edge at the K-shell photoionization threshold.
These data are important for the modeling of features found in photoionized
plasmas. | 1107.3146v1 |
2011-12-21 | A numerical method for computing radially symmetric solutions of a dissipative nonlinear modified Klein-Gordon equation | In this paper we develop a finite-difference scheme to approximate radially
symmetric solutions of the initial-value problem with smooth initial conditions
in an open sphere around the origin, where the internal and external damping
coefficients are constant, and the nonlinear term follows a power law. We prove
that our scheme is consistent of second order when the nonlinearity is
identically equal to zero, and provide a necessary condition for it to be
stable order n. Part of our study will be devoted to compare the physical
effects of the damping coefficients. | 1112.4921v1 |
2012-07-18 | Attractiveness of periodic orbits in parametrically forced systemswith time-increasing friction | We consider dissipative one-dimensional systems subject to a periodic force
and study numerically how a time-varying friction affects the dynamics. As a
model system, particularly suited for numerical analysis, we investigate the
driven cubic oscillator in the presence of friction. We find that, if the
damping coefficient increases in time up to a final constant value, then the
basins of attraction of the leading resonances are larger than they would have
been if the coefficient had been fixed at that value since the beginning. From
a quantitative point of view, the scenario depends both on the final value and
the growth rate of the damping coefficient. The relevance of the results for
the spin-orbit model are discussed in some detail. | 1207.4319v1 |
2012-07-19 | Acoustic damping and dispersion in vitreous germanium oxide | New Brillouin scattering measurements of velocity and attenuation of sound in
the hypersonic regime are presented. The data are analyzed together with the
literature results at sonic and ultrasonic frequencies. As usual, thermally
activated relaxation of structural entities describes the attenuation at sonic
and ultrasonic frequencies. As already shown in vitreous silica, we conclude
that the damping by network viscosity, resulting from relaxation of thermal
phonons, must be taken into account to describe the attenuation at hypersonic
frequencies. In addition, the bare velocity obtained by subtracting to the
experimental data the effect of the two above mechanisms is constant for
temperatures below 250 K, but increases almost linearly above, up to the glass
transition temperature. This might indicate the presence of a progressive local
polyamorphic transition, as already suggested for vitreous silica. | 1207.4582v1 |
2012-08-21 | Brownian transport in corrugated channels with inertia | The transport of suspended Brownian particles dc-driven along corrugated
narrow channels is numerically investigated in the regime of finite damping. We
show that inertial corrections cannot be neglected as long as the width of the
channel bottlenecks is smaller than an appropriate particle diffusion length,
which depends on the the channel corrugation and the drive intensity. Being
such a diffusion length inversely proportional to the damping constant,
transport through sufficiently narrow obstructions turns out to be always
sensitive to the viscosity of the suspension fluid. The inertia corrections to
the transport quantifiers, mobility and diffusivity, markedly differ for
smoothly and sharply corrugated channels. | 1208.4401v2 |
2013-01-23 | Characterization of magnetostatic surface spin waves in magnetic thin films: evaluation for microelectronic applications | The authors have investigated the possibility of utilizing spin waves for
inter- and intra-chip communications, and as logic elements using both
simulations and experimental techniques. Through simulations it has been shown
that the decay lengths of magnetostatic spin waves are affected most by the
damping parameter, and least by the exchange stiffness constant. The damping
and dispersion properties of spin waves limit the attenuation length to several
tens of microns. Thus, we have ruled out the possibility of inter-chip
communications via spin waves. Experimental techniques for the extraction of
the dispersion relationship have also been demonstrated, along with
experimental demonstrations of spin wave interference for amplitude modulation.
The effectiveness of spin wave modulation through interference, along with the
capability of determining the spin wave dispersion relationships electrically
during manufacturing and testing phase of chip production may pave the way for
using spin waves in analog computing wherein the circuitry required for
performing similar functionality becomes prohibitive. | 1301.5395v1 |
2013-04-15 | Energy dissipation in DC-field driven electron lattice coupled to fermion baths | Electron transport in electric-field-driven tight-binding lattice coupled to
fermion baths is comprehensively studied. We reformulate the problem by using
the scattering state method within the Coulomb gauge. Calculations show that
the formulation justifies direct access to the steady-state bypassing the
time-transient calculations, which then makes the steady-state methods
developed for quantum dot theories applicable to lattice models. We show that
the effective temperature of the hot-electron induced by a DC electric field
behaves as $T_{\rm eff}=C\gamma(\Omega/\Gamma)$ with a numerical constant $C$,
tight-binding parameter $\gamma$, the Bloch oscillation frequency $\Omega$ and
the damping parameter $\Gamma$. In the small damping limit $\Gamma/\Omega\to
0$, the steady-state has a singular property with the electron becoming
extremely hot in an analogy to the short-circuit effect. This leads to the
conclusion that the dissipation mechanism cannot be considered as an implicit
process, as treated in equilibrium theories. Finally, using the energy flux
relation, we derive a steady-state current for interacting models where only
on-site Green's functions are necessary. | 1304.4269v1 |
2013-05-07 | Micromagnetic modelling of anisotropic damping in ferromagnet | We report a numerical implementation of the Landau-Lifshitz-Baryakhtar
theory, which dictates that the micromagnetic relaxation term obeys the
symmetry of the magnetic crystal, i. e. replacing the single intrinsic damping
constant with a tensor of corresponding symmetry. The effect of anisotropic
relaxation is studied in thin saturated ferromagnetic disk and ellipse with and
without uniaxial magneto-crystalline anisotropy. We investigate the angular
dependency of the linewidth of magnonic resonances with respect to the given
structure of the relaxation tensor. The simulations suggest that the anisotropy
of the magnonic linewidth is determined by only two factors: the projection of
the relaxation tensor onto the plane of precession and the ellipticity of the
later. | 1305.1641v2 |
2013-07-14 | Asteroseismic effects in close binary stars | Turbulent processes in the convective envelopes of the sun and stars have
been shown to be a source of internal acoustic excitations. In single stars,
acoustic waves having frequencies below a certain cutoff frequency propagate
nearly adiabatically and are effectively trapped below the photosphere where
they are internally reflected. This reflection essentially occurs where the
local wavelength becomes comparable to the pressure scale height. In close
binary stars, the sound speed is a constant on equipotentials, while the
pressure scale height, which depends on the local effective gravity, varies on
equipotentials and may be much greater near the inner Lagrangian point (L_1).
As a result, waves reaching the vicinity of L_1 may propagate unimpeded into
low density regions, where they tend to dissipate quickly due to non-linear and
radiative effects. We study the three dimensional propagation and enhanced
damping of such waves inside a set of close binary stellar models using a WKB
approximation of the acoustic field. We find that these waves can have much
higher damping rates in close binaries, compared to their non-binary
counterparts. We also find that the relative distribution of acoustic energy
density at the visible surface of close binaries develops a ring-like feature
at specific acoustic frequencies and binary separations. | 1307.3709v1 |
2013-07-31 | Dynamics of ions in the selectivity filter of the KcsA channel: Towards a coupled Brownian particle description | The statistical and dynamical properties of ions in the selectivity filter of
the KcsA ion channel are considered on the basis of molecular dynamics (MD)
simulations of the KcsA protein embedded in a lipid membrane surrounded by an
ionic solution. A new approach to the derivation of a Brownian dynamics (BD)
model of ion permeation through the filter is discussed, based on unbiased MD
simulations. It is shown that depending on additional assumptions, ion's
dynamics can be described either by under-damped Langevin equation with
constant damping and white noise or by Langevin equation with a fractional
memory kernel. A comparison of the potential of the mean force derived from
unbiased MD simulations with the potential produced by the umbrella sampling
method demonstrates significant differences in these potentials. The origin of
these differences is an open question that requires further clarifications. | 1307.8298v1 |
2013-10-09 | Improved Coincident and Coherent Detection Statistics for Searches for Gravitational Wave Ringdown Signals | We study an improved method for detecting gravitational wave (GW) signals
from perturbed black holes by earth-based detectors in the quest for searching
for intermediate-mass black holes (IMBHs). Such signals, called ringdowns, are
damped sinusoids whose frequency and damping constant can be used to measure a
black hole's mass and spin. Utilizing the output from a matched filter analysis
pipeline, we present an improved statistic for the detection of a ringdown
signal that is found to be coincident in multiple detectors. The statistic
addresses the non-Gaussianity of the data without the use of an additional
signal-based waveform consistency test. We also develop coherent network
statistics to check for consistency of signal amplitudes and phases in the
different detectors with their different orientations and signal arrival times.
We find that the detection efficiency can be improved at least by a few tens of
percent by applying these multi-detector statistics primarily because of the
ineffectiveness of single-detector based discriminators of non-stationary
noise, such as the chi-square test, in the case of ringdown signals studied
here. | 1310.2341v2 |
2014-09-01 | Damping of Bloch oscillations: Variational solutions of the Boltzmann equation beyond linear response | Variational solutions of the Boltzmann equation usually rely on the concept
of linear response. We extend the variational approach for tight-binding models
at high entropies to a regime far beyond linear response. We analyze both
weakly interacting fermions and incoherent bosons on a lattice. We consider a
case where the particles are driven by a constant force, leading to the
well-known Bloch oscillations, and we consider interactions that are weak
enough not to overdamp these oscillations. This regime is computationally
demanding and relevant for ultracold atoms in optical lattices. We derive a
simple theory in terms of coupled dynamic equations for the particle density,
energy density, current and heat current, allowing for analytic solutions. As
an application, we identify damping coefficients for Bloch oscillations in the
Hubbard model at weak interactions and compute them for a one-dimensional toy
model. We also approximately solve the long-time dynamics of a weakly
interacting, strongly Bloch-oscillating cloud of fermionic particles in a
tilted lattice, leading to a subdiffusive scaling exponent. | 1409.0560v2 |
2015-10-01 | Production of charged Higgs boson pairs in the $pp \to ppH^{+}H^{-}$ reaction at the LHC and FCC | We present differential cross sections for the $pp \to ppH^{+}H^{-}$ reaction
via photon-photon fusion with exact kinematics. We show predictions for
$\sqrt{s}$ = 14 TeV (LHC) and at the Future Circular Collider (FCC) for
$\sqrt{s}$ = 100 TeV. The integrated cross section for $\sqrt{s}$ = 14~TeV
(LHC) is about 0.1~fb and about 0.9~fb at the FCC for $\sqrt{s}$ = 100~TeV when
assuming $m_{H^{\pm}} = 150$~GeV. We present distributions in diHiggs boson
invariant mass. The results are compared with those obtained within
equivalent-photon approximation. We discuss also first calculations of cross
section for exclusive diffractive pQCD mechanism with estimated limits on the
$g_{hH^{+}H^{-}}$ coupling constant within 2HDM based on the LHC experimental
data. The diffractive contribution is much smaller than the $\gamma \gamma$
one. Absorption corrections are calculated differentially for various
distributions. In general, they lead to a damping of the cross section. The
damping depends on $M_{H^{+}H^{-}}$ invariant mass and on four-momentum
transfers squared in the proton line. We discuss a possibility to measure the
exclusive production of $H^{\pm}$ bosons. | 1510.00171v1 |
2015-10-15 | On the global existence and blowup of smooth solutions of 3-D compressible Euler equations with time-depending damping | In this paper, we are concerned with the global existence and blowup of
smooth solutions of the 3-D compressible Euler equation with time-depending
damping $$
\partial_t\rho+\operatorname{div}(\rho u)=0, \quad
\partial_t(\rho u)+\operatorname{div}\left(\rho u\otimes
u+p\,I_{3}\right)=-\,\frac{\mu}{(1+t)^{\lambda}}\,\rho u, \quad
\rho(0,x)=\bar \rho+\varepsilon\rho_0(x),\quad u(0,x)=\varepsilon u_0(x), $$
where $x\in\mathbb R^3$, $\mu>0$, $\lambda\geq 0$, and $\bar\rho>0$ are
constants, $\rho_0,\, u_0\in C_0^{\infty}(\mathbb R^3)$, $(\rho_0,
u_0)\not\equiv 0$, $\rho(0,\cdot)>0$, and $\varepsilon>0$ is sufficiently
small. For $0\leq\lambda\leq1$, we show that there exists a global smooth
solution $(\rho, u)$ when $\operatorname{curl} u_0\equiv 0$, while for
$\lambda>1$, in general, the solution $(\rho, u)$ will blow up in finite time.
Therefore, $\lambda=1$ appears to be the critical value for the global
existence of small amplitude smooth solutions. | 1510.04613v1 |
2016-05-01 | Optical trapping by Laguerre-Gaussian beams: Symmetries, stability and equilibria | We use the T-matrix formalism in combination with the method of far-field
matching to evaluate the optical force exerted by Laguerre-Gaussian (LG) light
beams on a spherical (Mie) particle. For both non-vortex and optical vortex LG
beams, the theoretical results are used to analyze the optical-force-induced
dynamics of the scatterer near the trapping points represented by the
equilibrium (zero-force) positions. The regimes of linearized dynamics are
described in terms of the stiffness matrix spectrum and the damping constant of
the ambient medium. For the purely azimuthal LG beams, the dynamics is found to
be locally non-conservative and is characterized by the presence of
conditionally stable equilibria (unstable zero-force points that can be
stabilized by the ambient damping). The effects related to the Mie resonances
that under certain conditions manifest themselves as the points changing the
trapping properties of the particles are discussed. | 1605.00243v2 |
2016-05-05 | Relaxation of Ferroelectric States in 2D Distributions of quantum Dots:EELS Simulation | The relaxation time of collective electronic states in a 2D distribution of
quantum dots is investigated theoretically by simulating EELS experiments. From
the numerical calculation of the probability of energy loss of an electron
beam, traveling parallel to the distribution, it is possible to estimate the
damping time of ferroelectric-like states. We generate this collective response
of the distribution by introducing a mean field interaction among the quantum
dots, and then, the model is extended incorporating effects of long-range
correlations through a Bragg-Williams approximation. The behavior of the
dielectric function, the energy loss function, and the relaxation time of
ferroelectric-like states is then investigated as a function of the temperature
of the distribution and the damping constant of the electronic states in the
single quantum dots. The robustness of the trends and tendencies of our results
indicate that this scheme of analysis can guide experimentalists to develop
tailored quantum dots distributions for specific applications. | 1605.01642v1 |
2016-07-27 | Linear and nonlinear viscoelastic arterial wall models: application on animals | This work deals with the viscoelasticity of the arterial wall and its
influence on the pulse waves. We describe the viscoelasticity by a non-linear
Kelvin-Voigt model in which the coefficients are fitted using experimental time
series of pressure and radius measured on a sheep's arterial network. We
obtained a good agreement between the results of the nonlinear Kelvin-Voigt
model and the experimental measurements. We found that the viscoelastic
relaxation time-defined by the ratio between the viscoelastic coefficient and
the Young's modulus-is nearly constant throughout the network. Therefore, as it
is well known that smaller arteries are stiffer, the viscoelastic coefficient
rises when approaching the peripheral sites to compensate the rise of the
Young's modulus, resulting in a higher damping effect. We incorporated the
fitted viscoelastic coefficients in a nonlinear 1D fluid model to compute the
pulse waves in the network. The damping effect of viscoelasticity on the high
frequency waves is clear especially at the peripheral sites. | 1607.07973v1 |
2016-09-30 | Origin of the effective mobility in non-linear active micro-rheology | The distinction between the damping coefficient and the effective non-linear
mobility of driven particles in active micro-rheology of supercooled liquids is
explained in terms of individual and collective dynamics. The effective
mobility arises as a collective effect which gives insight into the energy
landscape of the system. On the other hand, the damping coefficient is a
constant that modulates the effect of external forces over the thermal energy
which particles have at their disposition to perform Brownian motion. For long
times, these thermal fluctuations become characterized in terms of an effective
temperature that is a consequence of the dynamic coupling between kinetic and
configurational degrees of freedom induced by the presence of the strong
external force. The interplay between collective mobility and effective
temperature allows to formulate a generalized Stokes-Einstein relation that may
be used to determine the collective diffusion coefficient. The explicit
relations we deduce reproduce simulation data remarkably well. | 1609.09853v1 |
2016-10-16 | Pulse-noise approach for classical spin systems | For systems of classical spins interacting with the bath via damping and
thermal noise, the approach is suggested to replace the white noise by a pulse
noise acting at regular time intervals $\Delta t$, within which the system
evolves conservatively. The method is working well in the typical case of a
small dimensionless damping constant $\lambda$ and allows a considerable
speed-up of computations by using high-order numerical integrators with a large
time step $\delta t$ (up to a fraction of the precession period), while keeping
$\delta t\ll\Delta t$ to reduce the relative contribution of noise-related
operations. In cases when precession can be discarded, $\delta t$ can be
increased up to a fraction of the relaxation time $\propto1/\lambda$ that leads
to a further speed-up. This makes equilibration speed comparable with that of
Metropolis Monte Carlo. The pulse-noise approach is tested on single-spin and
multi-spin models. | 1610.04914v2 |
2017-05-21 | Plasmon modes in graphene-GaAs heterostructures | We investigate the plasmon dispersion relation and damping rate of collective
excitations in a double-layer system consisting of bilayer graphene and GaAs
quantum well, separated by a distance, at zero temperature with no interlayer
tunneling. We use the random-phase-approximation dielectric function and take
into account the nonhomogeneity of the dielectric background of the system. We
show that the plasmon frequencies and damping rates depend considerably on
interlayer correlation parameters, electron densities and dielectric constants
of the contacting media. | 1705.07389v1 |
2017-08-02 | Global existence of solutions for semi-linear wave equation with scale-invariant damping and mass in exponentially weighted spaces | In this paper we consider the following Cauchy problem for the semi-linear
wave equation with scale-invariant dissipation and mass and power
non-linearity: \begin{align}\label{CP abstract} \begin{cases} u_{tt}-\Delta
u+\dfrac{\mu_1}{1+t} u_t+\dfrac{\mu_2^2}{(1+t)^2}u=|u|^p, \\ u(0,x)=u_0(x),
\,\, u_t(0,x)=u_1(x), \end{cases}\tag{$\star$} \end{align} where $\mu_1,
\mu_2^2$ are nonnegative constants and $p>1$. On the one hand we will prove a
global (in time) existence result for \eqref{CP abstract} under suitable
assumptions on the coefficients $\mu_1, \mu_2^2$ of the damping and the mass
term and on the exponent $p$, assuming the smallness of data in exponentially
weighted energy spaces. On the other hand a blow-up result for \eqref{CP
abstract} is proved for values of $p$ below a certain threshold, provided that
the data satisfy some integral sign conditions. Combining these results we find
the critical exponent for \eqref{CP abstract} in all space dimensions under
certain assumptions on $\mu_1$ and $\mu_2^2$. Moreover, since the global
existence result is based on a contradiction argument, it will be shown firstly
a local (in time) existence result. | 1708.00738v1 |
2017-08-21 | Solar Line Asymmetries: Modelling the Effect of Granulation on the Solar Spectrum | A parametric model of granulation employing a small number of parameters was
developed. Synthetic spectra calculated using this model closely match observed
spectra and, in particular, reproduce the asymmetries observed in spectral
lines. Both the microturbulent motions and the large-scale flow velocity
decrease exponentially with a scale height of 368 km as the height within the
photosphere increases. The model agrees with observations of the solar
granulation (from which it was derived).
The horizontal motions associated with granulation were found and used to
calculate spectra emergent away from disk centre. These calculated spectra were
compared to observed spectra, with the agreement supporting the accuracy of the
granular model.
Also in the course of this work, the Brueckner-O'Mara damping theory was
found to predict damping constants accurately. The photospheric abundances of a
number of elements were determined. The abundance obtained for iron agrees with
the meteoric iron abundance. Astrophysical f-values for some lines were also
determined. | 1708.06408v1 |
2017-11-01 | Plasmon modes in bilayer-monolayer graphene heterostructures | We investigate the dispersion relation and damping of plasmon modes in a
bilayer-monolayer graphene heterostructure with carrier densities and at zero
temperature within the random-phase-approximation taking into account the
nonhomogeneity of the dielectric background of the system. We derive analytical
expressions for plasmon frequencies by using long wavelength expansion of
response and bare Coulomb interaction functions. We show that optical plasmon
dispersion curve of the bilayer-monolayer system lies slightly below that of
double-layer graphene (DLG) and the acoustic one lies much lower than that of
DLG. We find that while decay rates of acoustic modes of the system and DLG are
remarkably different, those of optical modes in both double-layer systems are
similar. Except the damping rate of acoustic mode, properties of plasmon
excitations in considered system depend remarkably on the interlayer distance,
inhomogeneity of the background, density ratio and spacer dielectric constant,
especially at large wave-vectors. | 1711.00334v1 |
2018-07-15 | Asymptotic profile of solutions for semilinear wave equations with structural damping | This paper is concerned with the initial value problem for semilinear wave
equation with structural damping $u_{tt}+(-\Delta)^{\sigma}u_t -\Delta u
=f(u)$, where $\sigma \in (0,\frac{1}{2})$ and $f(u) \sim |u|^p$ or $u
|u|^{p-1}$ with $p> 1 + {2}/(n - 2 \sigma)$. We first show the global existence
for initial data small in some weighted Sobolev spaces on $\mathcal R^n$ ($n
\ge 2$). Next, we show that the asymptotic profile of the solution above is
given by a constant multiple of the fundamental solution of the corresponding
parabolic equation, provided the initial data belong to weighted $L^1$ spaces. | 1807.05509v3 |
2019-06-21 | Control of eigenfunctions on surfaces of variable curvature | We prove a microlocal lower bound on the mass of high energy eigenfunctions
of the Laplacian on compact surfaces of negative curvature, and more generally
on surfaces with Anosov geodesic flows. This implies controllability for the
Schr\"odinger equation by any nonempty open set, and shows that every
semiclassical measure has full support. We also prove exponential energy decay
for solutions to the damped wave equation on such surfaces, for any nontrivial
damping coefficient. These results extend previous works [arXiv:1705.05019],
[arXiv:1712.02692], which considered the setting of surfaces of constant
negative curvature.
The proofs use the strategy of [arXiv:1705.05019], [arXiv:1712.02692] and
rely on the fractal uncertainty principle of [arXiv:1612.09040]. However, in
the variable curvature case the stable/unstable foliations are not smooth, so
we can no longer associate to these foliations a pseudodifferential calculus of
the type used in [arXiv:1504.06589]. Instead, our argument uses Egorov's
Theorem up to local Ehrenfest time and the hyperbolic parametrix of
[arXiv:0706.3242], together with the $C^{1+}$ regularity of the stable/unstable
foliations. | 1906.08923v2 |
2012-10-12 | Threshold current for switching of a perpendicular magnetic layer induced by spin Hall effect | We theoretically investigate the switching of a perpendicular magnetic layer
by in-plane charge current due to the spin Hall effect. We find that, in the
high damping regime, the threshold switching current is independent of the
damping constant, and is almost linearly proportional to both effective
perpendicular magnetic anisotropy field and external in-plane field applied
along the current direction. We obtain an analytic expression of the threshold
current, in excellent agreement with numerical results. This expression can be
used to determine the physical quantities associated with spin Hall effect, and
to design relevant magnetic devices based on the switching of perpendicular
magnetic layers. | 1210.3442v2 |
2012-10-15 | Symmetries of the quantum damped harmonic oscillator | For the non-conservative Caldirola-Kanai system, describing a quantum damped
harmonic oscillator, a couple of constant-of-motion operators generating the
Heisenberg-Weyl algebra can be found. The inclusion of the standard time
evolution generator (which is not a symmetry) as a symmetry in this algebra, in
a unitary manner, requires a non-trivial extension of this basic algebra and
hence of the physical system itself. Surprisingly, this extension leads
directly to the so-called Bateman dual system, which now includes a new
particle acting as an energy reservoir. In addition, the Caldirola-Kanai
dissipative system can be retrieved by imposing constraints. The algebra of
symmetries of the dual system is presented, as well as a quantization that
implies, in particular, a first-order Schr\"odinger equation. As opposed to
other approaches, where it is claimed that the spectrum of the Bateman
Hamiltonian is complex and discrete, we obtain that it is real and continuous,
with infinite degeneracy in all regimes. | 1210.4058v1 |
2012-09-26 | Damping of giant dipole resonance in highly excited nuclei | The giant dipole resonance's (GDR) width and shape at finite temperature and
angular momentum are described within the phonon damping model (PDM), which
predicts an overall increase in the GDR's total width at low and moderate
temperature T, and its saturation at high T. At T< 1 MeV the GDR width remains
nearly constant because of thermal pairing. The PDM description is compared
with the experimental systematics obtained from heavy-ion fusion, inelastic
scattering of light particles on heavy targets, and alpha induced fusion
reactions, as well as with predictions by other theoretical approaches. The
results obtained within the PDM and GDR's experimental data are also employed
to predict the viscosity of hot medium and heavy nuclei. | 1209.5820v2 |
2015-12-16 | Back to Maupertuis' least action principle for dissipative systems: not all motions in Nature are most energy economical | It is shown that an oldest form of variational calculus of mechanics, the
Maupertuis least action principle, can be used as a simple and powerful
approach for the formulation of the variational principle for damped motions,
allowing a simple derivation of the Lagrangian mechanics for any dissipative
systems and an a connection of the optimization of energy dissipation to the
least action principles. On this basis, it is shown that not all motions of
classical mechanics obey the rule of least energy dissipation or follow the
path of least resistance, and that the least action is equivalent to least
dissipation for two kinds of motions : all stationary motions with constant
velocity and all motions damped by Stokes drag. | 1512.05339v1 |
2016-08-19 | Cooling a harmonic oscillator by optomechanical modification of its bath | Optomechanical systems show tremendous promise for high sensitivity sensing
of forces and modification of mechanical properties via light. For example,
similar to neutral atoms and trapped ions, laser cooling of mechanical motion
by radiation pressure can take single mechanical modes to their ground state.
Conventional optomechanical cooling is able to introduce additional damping
channel to mechanical motion, while keeping its thermal noise at the same
level, and as a consequence, the effective temperature of the mechanical mode
is lowered. However, the ratio of temperature to quality factor remains roughly
constant, preventing dramatic advances in quantum sensing using this approach.
Here we propose an approach for simultaneously reducing the thermal load on a
mechanical resonator while improving its quality factor. In essence, we use the
optical interaction to dynamically modify the dominant damping mechanism,
providing an optomechanically-induced effect analogous to a phononic band gap.
The mechanical mode of interest is assumed to be weakly coupled to its heat
bath but strongly coupled to a second mechanical mode, which is cooled by
radiation pressure coupling to a red detuned cavity field. We also identify a
realistic optomechanical design that has the potential to realize this novel
cooling scheme. | 1608.05717v1 |
2018-12-28 | Axion Misalignment Driven to the Bottom | Several theoretical motivations point to ultralight QCD axions with large
decay constants $f_a \simeq \mathcal{O}(10^{16}-10^{17})$ GeV, to which
experimental proposals are dedicated. This regime is known to face the problem
of overproduction of axion dark matter from the misalignment mechanism unless
the misalignment angle $\theta_{\rm mis}$ is as small as
$\mathcal{O}(10^{-3}-10^{-4})$, which is generally considered a fine-tuning
problem. We investigate a dynamical explanation for a small $\theta_{\rm mis}$.
The axion mass arises from strong dynamics and may be sufficiently enhanced by
early dynamics so as to overcome Hubble friction and drive the field value to
the bottom of the potential long before the QCD phase transition. Together with
an approximate CP symmetry in the theory, this minimum is very closely related
to today's value and thus $\theta_{\rm mis}$ can automatically be well under
unity. Owing to such efficient relaxation, the isocurvature perturbations are
essentially damped. As an existence proof, using supersymmetric theories we
illustrate that the Higgs coupling with the inflaton energy can successfully
achieve this axion damping in a consistent inflationary cosmology. | 1812.11186v2 |
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