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1991-09-26 | The Damping of Energetic Gluons and Quarks in High-Temperature QCD | When a gluon or a quark is sent through the hot QCD plasma it can be absorbed
into the ambient heat bath and so can acquire an effective lifetime. At high
temperatures and for weak couplings the inverse lifetime, or damping rate, for
energetic quarks and transverse gluons, (those whose momenta satisfy $|\p| \gg
gT$) is given by $\gamma(\p) = c\; g^2 \log\left({1\over g}\right)\; T +
O(g^2T)$. We show that very simple arguments suffice both to fix the numerical
coefficient, $c$, in this expression and to show that the $O(g^2T)$
contribution is incalculable in perturbation theory without further
assumptions. For QCD with $N_c$ colours we find (expressed in terms of the
casimir invariants $C_a=N_c$ and $C_f=(N_c^2-1)/(2N_c)$): $c_g=+{C_a\over
4\pi}$ for gluons and $c_q=+{C_f\over 4\pi}$ for quarks. These numbers agree
with the more detailed calculations of Pisarski \etal\ but disagree with those
of Lebedev and Smilga. The simplicity of the calculation also permits a direct
verification of the gauge-invariance and physical sign of the result. | 9109051v1 |
2006-11-21 | Renormalization group study of damping in nonequilibrium field theory | In this paper we shall study whether dissipation in a $\lambda\phi^{4}$ may
be described, in the long wavelength, low frequency limit, with a simple Ohmic
term $\kappa\dot{\phi}$, as it is usually done, for example, in studies of
defect formation in nonequilibrium phase transitions. We shall obtain an
effective theory for the long wavelength modes through the coarse graining of
shorter wavelengths. We shall implement this coarse graining by iterating a
Wilsonian renormalization group transformation, where infinitesimal momentum
shells are coarse-grained one at a time, on the influence action describing the
dissipative dynamics of the long wavelength modes. To the best of our
knowledge, this is the first application of the nonequilibrium renormalization
group to the calculation of a damping coefficient in quantum field theory. | 0611222v1 |
1997-03-26 | A self-consistent treatment of damped motion for stable and unstable collective modes | We address the dynamics of damped collective modes in terms of first and
second moments. The modes are introduced in a self-consistent fashion with the
help of a suitable application of linear response theory. Quantum effects in
the fluctuations are governed by diffusion coefficients D_{\mu\nu}. The latter
are obtained through a fluctuation dissipation theorem generalized to allow for
a treatment of unstable modes. Numerical evaluations of the D_{\mu\nu} are
presented. We discuss briefly how this picture may be used to describe global
motion within a locally harmonic approximation. Relations to other methods are
discussed, like "dissipative tunneling", RPA at finite temperature and
generalizations of the "Static Path Approximation". | 9703056v1 |
1996-10-01 | Exact time evolution and master equations for the damped harmonic oscillator | Using the exact path integral solution for the damped harmonic oscillator it
is shown that in general there does not exist an exact dissipative Liouville
operator describing the dynamics of the oscillator for arbitrary initial bath
preparations. Exact non-stationary Liouville operators can be found only for
particular preparations. Three physically meaningful examples are examined. An
exact new master equation is derived for thermal initial conditions. Second,
the Liouville operator governing the time-evolution of equilibrium correlations
is obtained. Third, factorizing initial conditions are studied. Additionally,
one can show that there are approximate Liouville operators independent of the
initial preparation describing the long time dynamics under appropriate
conditions. The general form of these approximate master equations is derived
and the coefficients are determined for special cases of the bath spectral
density including the Ohmic, Drude and weak coupling cases. The connection with
earlier work is discussed. | 9610001v1 |
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 |
1999-10-05 | Uncertainty, entropy and decoherence of the damped harmonic oscillator in the Lindblad theory of open quantum systems | In the framework of the Lindblad theory for open quantum systems, expressions
for the density operator, von Neumann entropy and effective temperature of the
damped harmonic oscillator are obtained. The entropy for a state characterized
by a Wigner distribution function which is Gaussian in form is found to depend
only on the variance of the distribution function. We give a series of
inequalities, relating uncertainty to von Neumann entropy and linear entropy.
We analyze the conditions for purity of states and show that for a special
choice of the diffusion coefficients, the correlated coherent states (squeezed
coherent states) are the only states which remain pure all the time during the
evolution of the considered system. These states are also the most stable under
evolution in the presence of the environment and play an important role in the
description of environment induced decoherence. | 9910019v1 |
2007-12-11 | Neutrino oscillations in a stochastic model for space-time foam | We study decoherence models for flavour oscillations in four-dimensional
stochastically fluctuating space times and discuss briefly the sensitivity of
current neutrino experiments to such models. We pay emphasis on demonstrating
the model dependence of the associated decoherence-induced damping coefficients
in front of the oscillatory terms in the respective transition probabilities
between flavours. Within the context of specific models of foam, involving
point-like D-branes and leading to decoherence-induced damping which is
inversely proportional to the neutrino energies, we also argue that future
limits on the relevant decoherence parameters coming from TeV astrophysical
neutrinos, to be observed in ICE-CUBE, are not far from theoretically expected
values with Planck mass suppression. Ultra high energy neutrinos from Gamma Ray
Bursts at cosmological distances can also exhibit in principle sensitivity to
such effects. | 0712.1779v1 |
2008-06-06 | On the stability of shocks with particle pressure | We perform a linear stability analysis for corrugations of a Newtonian shock,
with particle pressure included, for an arbitrary diffusion coefficient. We
study first the dispersion relation for homogeneous media, showing that,
besides the conventional pressure waves and entropy/vorticity disturbances, two
new perturbation modes exist, dominated by the particles' pressure and damped
by diffusion. We show that, due to particle diffusion into the upstream region,
the fluid will be perturbed also upstream: we treat these perturbation in the
short wavelength (WKBJ) regime. We then show how to construct a corrugational
mode for the shock itself, one, that is, where the shock executes free
oscillations (possibly damped or growing) and sheds perturbations away from
itself: this global mode requires the new modes. Then, using the perturbed
Rankine-Hugoniot conditions, we show that this leads to the determination of
the corrugational eigenfrequency. We solve numerically the equations for the
eigenfrequency in the WKBJ regime for the models of Amato and Blasi (2005),
showing that they are stable. We then discuss the differences between our
treatment and previous work. | 0806.1113v1 |
2008-08-26 | Nonlinear regularization techniques for seismic tomography | The effects of several nonlinear regularization techniques are discussed in
the framework of 3D seismic tomography. Traditional, linear, $\ell_2$ penalties
are compared to so-called sparsity promoting $\ell_1$ and $\ell_0$ penalties,
and a total variation penalty. Which of these algorithms is judged optimal
depends on the specific requirements of the scientific experiment. If the
correct reproduction of model amplitudes is important, classical damping
towards a smooth model using an $\ell_2$ norm works almost as well as
minimizing the total variation but is much more efficient. If gradients (edges
of anomalies) should be resolved with a minimum of distortion, we prefer
$\ell_1$ damping of Daubechies-4 wavelet coefficients. It has the additional
advantage of yielding a noiseless reconstruction, contrary to simple $\ell_2$
minimization (`Tikhonov regularization') which should be avoided. In some of
our examples, the $\ell_0$ method produced notable artifacts. In addition we
show how nonlinear $\ell_1$ methods for finding sparse models can be
competitive in speed with the widely used $\ell_2$ methods, certainly under
noisy conditions, so that there is no need to shun $\ell_1$ penalizations. | 0808.3472v3 |
2010-03-31 | Non-Markovian master equation for a damped oscillator with time-varying parameters | We derive an exact non-Markovian master equation that generalizes the
previous work [Hu, Paz and Zhang, Phys. Rev. D {\bf 45}, 2843 (1992)] to damped
harmonic oscillators with time-varying parameters. This is achieved by
exploiting the linearity of the system and operator solution in Heisenberg
picture. Our equation governs the non-Markovian quantum dynamics when the
system is modulated by external devices. As an application, we apply our
equation to parity kick decoupling problems. The time-dependent dissipative
coefficients in the master equation are shown to be modified drastically when
the system is driven by $\pi$ pulses. For coherence protection to be effective,
our numerical results indicate that kicking period should be shorter than
memory time of the bath. The effects of using soft pulses in an ohmic bath are
also discussed. | 1003.5975v1 |
2011-06-06 | Weakly nonlinear stochastic CGL equations | We consider the linear Schr\"odinger equation under periodic boundary
condition, driven by a random force and damped by a quasilinear damping: $$
\frac{d}{dt}u+i\big(-\Delta+V(x)\big) u=\nu \Big(\Delta u-\gr |u|^{2p}u-i\gi
|u|^{2q}u \Big) +\sqrt\nu\, \eta(t,x).\qquad (*) $$ The force $\eta$ is white
in time and smooth in $x$. We are concerned with the limiting, as $\nu\to0$,
behaviour of its solutions on long time-intervals $0\le t\le\nu^{-1}T$, and
with behaviour of these solutions under the double limit $t\to\infty$ and
$\nu\to0$. We show that these two limiting behaviours may be described in terms
of solutions for the {\it system of effective equations for $(*)$} which is a
well posed semilinear stochastic heat equation with a non-local nonlinearity
and a smooth additive noise, written in Fourier coefficients. The effective
equations do not depend on the Hamiltonian part of the perturbation
$-i\gi|u|^{2q}u$ (but depend on the dissipative part $-\gr|u|^{2p}u$). If $p$
is an integer, they may be written explicitly. | 1106.1158v1 |
2011-07-13 | Increased Brownian force noise from molecular impacts in a constrained volume | We report on residual gas damping of the motion of a macroscopic test mass
enclosed in a nearby housing in the molecular flow regime. The damping
coefficient, and thus the associated thermal force noise, is found to increase
significantly when the distance between test mass and surrounding walls is
smaller than the test mass itself. The effect has been investigated with two
torsion pendulums of different geometry and has been modelled in a numerical
simulation whose predictions are in good agreement with the measurements.
Relevant to a wide variety of small-force experiments, the residual-gas force
noise power for the test masses in the LISA gravitational wave observatory is
roughly a factor 15 larger than in an infinite gas volume, though still
compatible with the target acceleration noise of 3 fm s^-2 Hz^-1/2 at the
foreseen pressure below 10^-6 Pa. | 1107.2520v1 |
2011-08-02 | PHENIX Measurements of Higher-order Flow Harmonics in Au+Au collisions at Root_s = 200 GeV | Flow coefficients $v_n$ for $n$ = 2, 3, 4, characterizing the anisotropic
collective flow in Au+Au collisions at $\sqrt{s_{NN}} = 200$ GeV, are
presented. They indicate the expected growth of viscous damping for sound
propagation in the quark gluon plasma (QGP) produced in these collisions.
Hydrodynamical model comparisons which include the effects of initial state
geometry fluctuations, highlight the role of higher harmonics ($v_{n, n>2}$) as
a constraint for disentangling the effects of viscosity and initial conditions,
and suggest a small specific viscosity for the QGP. This viscosity is
compatible with that obtained via a newly proposed technique
\cite{Lacey:2011ug} which employs the relative magnitudes of $v_n$ to estimate
the viscosity, and the "viscous horizon" or length-scale which characterizes
the highest harmonic that survives viscous damping. | 1108.0457v1 |
2011-12-02 | On the simulation of the energy transmission in the forbidden band-gap of a spatially discrete double sine-Gordon system | In this work, we present a numerical method to consistently approximate
solutions of a spatially discrete, double sine-Gordon chain which considers the
presence of external damping. In addition to the finite-difference scheme
employed to approximate the solution of the difference-differential equations
of the model under investigation, our method provides positivity-preserving
schemes to approximate the local and the total energy of the system, in such
way that the discrete rate of change of the total energy with respect to time
provides a consistent approximation of the corresponding continuous rate of
change. Simulations are performed, first of all, to assess the validity of the
computational technique against known qualitative solutions of coupled
sine-Gordon and coupled double sine-Gordon chains. Secondly, the method is used
in the investigation of the phenomenon of nonlinear transmission of energy in
double sine-Gordon systems; the qualitative effects of the damping coefficient
on the occurrence of the nonlinear process of supratransmission are briefly
determined in this work, too. | 1112.0595v1 |
2013-04-15 | Vibrational Resonance in the Morse Oscillator | We investigate the occurrence of vibrational resonance in both classical and
quantum mechanical Morse oscillators driven by a biharmonic force. The
biharmonic force consists of two forces of widely different frequencies \omega
and \Omega with \Omega>>\omega. In the damped and biharmonically driven
classical Morse oscillator applying a theoretical approach we obtain an
analytical expression for the response amplitude at the low-frequency \omega.
We identify the conditions on the parameters for the occurrence of the
resonance. The system shows only one resonance and moreover at resonance the
response amplitude is 1/(d\omega) where d is the coefficient of linear damping.
When the amplitude of the high-frequency force is varied after resonance the
response amplitude does not decay to zero but approaches a nonzero limiting
value. We have observed that vibrational resonance occurs when the sinusoidal
force is replaced by a square-wave force. We also report the occurrence of
resonance and anti-resonance of transition probability of quantum mechanical
Morse oscillator in the presence of the biharmonic external field. | 1304.3988v1 |
2013-11-27 | Encapsulated formulation of the Selective Frequency Damping method | We present an alternative "encapsulated" formulation of the Selective
Frequency Damping method for finding unstable equilibria of dynamical systems,
which is particularly useful when analysing the stability of fluid flows. The
formulation makes use of splitting methods, which means that it can be wrapped
around an existing time-stepping code as a "black box". The method is first
applied to a scalar problem in order to analyse its stability and highlight the
roles of the control coefficient $\chi$ and the filter width $\Delta$ in the
convergence (or not) towards the steady-state. Then the steady-state of the
incompressible flow past a two-dimensional cylinder at $Re=100$, obtained with
a code which implements the spectral/hp element method, is presented. | 1311.7000v1 |
2014-08-04 | Collective Dynamics of Interacting Particles in Unsteady Flows | We use the Fokker-Planck equation and its moment equations to study the
collective behavior of interacting particles in unsteady one-dimensional flows.
Particles interact according to a long-range attractive and a short-range
repulsive potential field known as Morse potential. We assume Stokesian drag
force between particles and their carrier fluid, and find analytic
single-peaked traveling solutions for the spatial density of particles in the
catastrophic phase. In steady flow conditions the streaming velocity of
particles is identical to their carrier fluid, but we show that particle
streaming is asynchronous with an unsteady carrier fluid. Using linear
perturbation analysis, the stability of traveling solutions is investigated in
unsteady conditions. It is shown that the resulting dispersion relation is an
integral equation of the Fredholm type, and yields two general families of
stable modes: singular modes whose eigenvalues form a continuous spectrum, and
a finite number of discrete global modes. Depending on the value of drag
coefficient, stable modes can be over-damped, critically damped, or decaying
oscillatory waves. The results of linear perturbation analysis are confirmed
through the numerical solution of the fully nonlinear Fokker-Planck equation. | 1408.0558v1 |
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 |
2014-12-05 | Adaptive Damping and Mean Removal for the Generalized Approximate Message Passing Algorithm | The generalized approximate message passing (GAMP) algorithm is an efficient
method of MAP or approximate-MMSE estimation of $x$ observed from a noisy
version of the transform coefficients $z = Ax$. In fact, for large zero-mean
i.i.d sub-Gaussian $A$, GAMP is characterized by a state evolution whose fixed
points, when unique, are optimal. For generic $A$, however, GAMP may diverge.
In this paper, we propose adaptive damping and mean-removal strategies that aim
to prevent divergence. Numerical results demonstrate significantly enhanced
robustness to non-zero-mean, rank-deficient, column-correlated, and
ill-conditioned $A$. | 1412.2005v1 |
2014-12-14 | An adaptive selective frequency damping method | The selective frequency damping (SFD) method is an alternative to classical
Newton's method to obtain unstable steady-state solutions of dynamical systems.
However this method has two main limitations: it does not converge for
arbitrary control parameters; and when it does converge, the time necessary to
reach the steady-state solution may be very long. In this paper we present an
adaptive algorithm to address these two issues. We show that by evaluating the
dominant eigenvalue of a "partially converged" steady flow, we can select a
control coefficient and a filter width that ensure an optimum convergence of
the SFD method. We apply this adaptive method to several classical test cases
of computational fluid dynamics and we show that a steady-state solution can be
obtained without any a priori knowledge of the flow stability properties. | 1412.4372v1 |
2015-04-29 | Wide-Range Tunable Dynamic Property of Carbon Nanotube-Based Fibers | Carbon nanotube (CNT) fiber is formed by assembling millions of individual
tubes. The assembly feature provides the fiber with rich interface structures
and thus various ways of energy dissipation, as reflected by the non-zero loss
tangent (>0.028--0.045) at low vibration frequencies. A fiber containing
entangled CNTs possesses higher loss tangents than a fiber spun from aligned
CNTs. Liquid densification and polymer infiltration, the two common ways to
increase the interfacial friction and thus the fiber's tensile strength and
modulus, are found to efficiently reduce the damping coefficient. This is
because the sliding tendency between CNT bundles can also be well suppressed by
the high packing density and the formation of covalent polymer cross-links
within the fiber. The CNT/bismaleimide composite fiber exhibited the smallest
loss tangent, nearly as the same as that of carbon fibers. At a higher level of
the assembly structure, namely a multi-ply CNT yarn, the inter-fiber friction
and sliding tendency obviously influence the yarn's damping performance, and
the loss tangent can be tuned within a wide range, as similar to carbon fibers,
nylon yarns, or cotton yarns. The wide-range tunable dynamic properties allow
new applications ranging from high quality factor materials to dissipative
systems. | 1504.07881v1 |
2015-05-13 | The effect of a reversible shear transformation on plastic deformation of an amorphous solid | Molecular dynamics simulations are performed to investigate the plastic
response of a model glass to a local shear transformation in a quiescent
system. The deformation of the material is induced by a spherical inclusion
that is gradually strained into an ellipsoid of the same volume and then
reverted back into the sphere. We show that the number of cage-breaking events
increases with increasing strain amplitude of the shear transformation. The
results of numerical simulations indicate that the density of cage jumps is
larger in the cases of weak damping or slow shear transformation. Remarkably,
we also found that, for a given strain amplitude, the peak value of the density
profiles is a function of the ratio of the damping coefficient and the time
scale of the shear transformation. | 1505.03488v1 |
2015-10-17 | Direct evidence for minority spin gap in the Co2MnSi Heusler alloy | Half Metal Magnets are of great interest in the field of spintronics because
of their potential full spin-polarization at the Fermi level and low
magnetization damping. The high Curie temperature and predicted 0.7eV minority
spin gap make the Heusler alloy Co2MnSi very promising for applications.We
investigated the half-metallic magnetic character of this alloy using
spin-resolved photoemission, ab initio calculation and ferromagnetic resonance.
At the surface of Co2MnSi, a gap in the minority spin channel is observed,
leading to 100% spin polarization. However, this gap is 0.3 eV below the Fermi
level and a minority spin state is observed at the Fermi level. We show that a
minority spin gap at the Fermi energy can nevertheless be recovered either by
changing the stoichiometry of the alloy or by covering the surface by Mn, MnSi
or MgO. This results in extremely small damping coefficients reaching values as
low as 7x 10-4. | 1510.05085v1 |
2016-04-06 | Brownian motion of a matter-wave bright soliton: realizing a quantum pollen grain | Taking an open quantum systems approach, we derive a collective equation of
motion for the dynamics of a matter-wave bright soliton moving through a
thermal cloud of a distinct atomic species. The reservoir interaction involves
energy transfer without particle transfer between the soliton and thermal
cloud, thus damping the soliton motion without altering its stability against
collapse. We derive a Langevin equation for the soliton centre of mass velocity
in the form of an Ornstein-Uhlenbeck process with analytical drift and
diffusion coefficients. This collective motion is confirmed by simulations of
the full stochastic projected Gross-Pitaevskii equation for the matter-wave
field. The system offers a pathway for experimentally observing the elusive
energy-damping reservoir interaction, and a clear realization of collective
Brownian motion for a mesoscopic superfluid droplet. | 1604.01487v1 |
2016-04-28 | Temperature Dependence of Viscosity in Normal Fluid $^3$He Below 800mK Determined by a Micro-electro-mechanical Oscillator | A micro-electro-mechanical system vibrating in its shear mode was used to
study the viscosity of normal liquid $^3$He from 20mK to 770mK at 3bar, 21bar,
and 29bar. The damping coefficient of the oscillator was determined by
frequency sweeps through its resonance at each temperature. Using a slide film
damping model, the viscosity of the fluid was obtained. Our viscosity values
are compared with previous measurements and with calculated values from Fermi
liquid theory. The crossover from the classical to the Fermi liquid regime is
manifest in the temperature dependence of viscosity. In the Fermi liquid
regime, the temperature dependence of viscosity changes from $T^{-1}$ to
$T^{-2}$ on cooling, indicating a transition from the Stokes flow to the
Couette flow regime. | 1604.08554v1 |
2016-06-11 | Parameter identification in a semilinear hyperbolic system | We consider the identification of a nonlinear friction law in a
one-dimensional damped wave equation from additional boundary measurements.
Well-posedness of the governing semilinear hyperbolic system is established via
semigroup theory and contraction arguments. We then investigte the inverse
problem of recovering the unknown nonlinear damping law from additional
boundary measurements of the pressure drop along the pipe. This coefficient
inverse problem is shown to be ill-posed and a variational regularization
method is considered for its stable solution. We prove existence of minimizers
for the Tikhonov functional and discuss the convergence of the regularized
solutions under an approximate source condition. The meaning of this condition
and some arguments for its validity are discussed in detail and numerical
results are presented for illustration of the theoretical findings. | 1606.03580v1 |
2016-09-15 | Low-damping sub-10-nm thin films of lutetium iron garnet grown by molecular-beam epitaxy | We analyze the structural and magnetic characteristics of (111)-oriented
lutetium iron garnet (Lu$_3$Fe$_5$O$_{12}$) films grown by molecular-beam
epitaxy, for films as thin as 2.8 nm. Thickness-dependent measurements of the
in- and out-of-plane ferromagnetic resonance allow us to quantify the effects
of two-magnon scattering, along with the surface anisotropy and the saturation
magnetization. We achieve effective damping coefficients of $11.1(9) \times
10^{-4}$ for 5.3 nm films and $32(3) \times 10^{-4}$ for 2.8 nm films, among
the lowest values reported to date for any insulating ferrimagnetic sample of
comparable thickness. | 1609.04753v1 |
2016-10-05 | Higher-Harmonic Collective Modes in a Trapped Gas from Second-Order Hydrodynamics | Utilizing a second-order hydrodynamics formalism, the dispersion relations
for the frequencies and damping rates of collective oscillations as well as
spatial structure of these modes up to the decapole oscillation in both two-
and three- dimensional gas geometries are calculated. In addition to
higher-order modes, the formalism also gives rise to purely damped
"non-hydrodynamic" modes. We calculate the amplitude of the various modes for
both symmetric and asymmetric trap quenches, finding excellent agreement with
an exact quantum mechanical calculation. We find that higher-order hydrodynamic
modes are more sensitive to the value of shear viscosity, which may be of
interest for the precision extraction of transport coefficients in Fermi gas
systems. | 1610.01611v2 |
2016-12-06 | Increased low-temperature damping in yttrium iron garnet thin films | We report measurements of the frequency and temperature dependence of
ferromagnetic resonance (FMR) for a 15-nm-thick yttrium iron garnet (YIG) film
grown by off-axis sputtering. Although the FMR linewidth is narrow at room
temperature (corresponding to a damping coefficient $\alpha$ = (9.0 $\pm$ 0.2)
$\times 10^{-4}$), comparable to previous results for high-quality YIG films of
similar thickness, the linewidth increases strongly at low temperatures, by a
factor of almost 30. This increase cannot be explained as due to two-magnon
scattering from defects at the sample interfaces. We argue that the increased
low-temperature linewidth is due to impurity relaxation mechanisms that have
been investigated previously in bulk YIG samples. We suggest that the
low-temperature linewidth is a useful figure of merit to guide the optimization
of thin-film growth protocols because it is a particularly sensitive indicator
of impurities. | 1612.01954v1 |
2016-12-09 | Slow motion for one-dimensional nonlinear damped hyperbolic Allen-Cahn systems | We consider a nonlinear damped hyperbolic reaction-diffusion system in a
bounded interval of the real line with homogeneous Neumann boundary conditions
and we study the metastable dynamics of the solutions. Using an "energy
approach" introduced by Bronsard and Kohn [CPAM 1990] to study slow motion for
Allen-Cahn equation and improved by Grant [SIAM J. Math. Anal. 1995] in the
study of Cahn-Morral systems, we improve and extend to the case of systems the
results valid for the hyperbolic Allen-Cahn equation. In particular, we study
the limiting behavior of the solutions as $\varepsilon\to0^+$, where
$\varepsilon^2$ is the diffusion coefficient, and we prove existence and
persistence of metastable states for a time
$T_\varepsilon>\exp(A/\varepsilon)$. Such metastable states have a transition
layer structure and the transition layers move with exponentially small
velocity. | 1612.03203v5 |
2017-02-20 | Resonant Scattering Characteristics of Homogeneous Dielectric Sphere | In the present article the classical problem of electromagnetic scattering by
a single homogeneous sphere is revisited. Main focus is the study of the
scattering behavior as a function of the material contrast and the size
parameters for all electric and magnetic resonances of a dielectric sphere.
Specifically, the Pad\'e approximants are introduced and utilized as an
alternative system expansion of the Mie coefficients. Low order Pad\'e
approximants can give compact and physically insightful expressions for the
scattering system and the enabled dynamic mechanisms. Higher order approximants
are used for predicting accurately the resonant pole spectrum. These results
are summarized into general pole formulae, covering up to fifth order magnetic
and forth order electric resonances of a small dielectric sphere. Additionally,
the connection between the radiative damping process and the resonant linewidth
is investigated. The results obtained reveal the fundamental connection of the
radiative damping mechanism with the maximum width occurring for each
resonance. Finally, the suggested system ansatz is used for studying the
resonant absorption maximum through a circuit-inspired perspective. | 1702.05883v1 |
2017-03-21 | Numerical Range and Quadratic Numerical Range for Damped Systems | We prove new enclosures for the spectrum of non-selfadjoint operator matrices
associated with second order linear differential equations $\ddot{z}(t) + D
\dot{z} (t) + A_0 z(t) = 0$ in a Hilbert space. Our main tool is the quadratic
numerical range for which we establish the spectral inclusion property under
weak assumptions on the operators involved; in particular, the damping operator
only needs to be accretive and may have the same strength as $A_0$. By means of
the quadratic numerical range, we establish tight spectral estimates in terms
of the unbounded operator coefficients $A_0$ and $D$ which improve earlier
results for sectorial and selfadjoint $D$; in contrast to numerical range
bounds, our enclosures may even provide bounded imaginary part of the spectrum
or a spectral free vertical strip. An application to small transverse
oscillations of a horizontal pipe carrying a steady-state flow of an ideal
incompressible fluid illustrates that our new bounds are explicit. | 1703.07447v1 |
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 |
2017-11-11 | Quantum Thermodynamics for Driven Dissipative Bosonic Systems | We investigate two prototypical dissipative bosonic systems under slow
driving and arbitrary system-bath coupling strength, recovering their dynamic
evolution as well as the heat and work rates, and we verify that thermodynamic
laws are respected. Specifically, we look at the damped harmonic oscillator and
the damped two-level system. For the former, we study independently the slow
time- dependent perturbation in the oscillator frequency and in the coupling
strength. For the latter, we concentrate on the slow modulation of the energy
gap between the two levels. Importantly, we are able to find the entropy
production rates for each case without explicitly defining nonequilibrium
extensions for the entropy functional. This analysis also permits the
definition of phenomenological friction coefficients in terms of structural
properties of the system-bath composite. | 1711.04077v1 |
2018-02-14 | Motion of interfaces for a damped hyperbolic Allen-Cahn equation | Consider the Allen-Cahn equation $u_t=\varepsilon^2\Delta u-F'(u)$, where $F$
is a double well potential with wells of equal depth, located at $\pm1$. There
are a lot of papers devoted to the study of the limiting behavior of the
solutions as the diffusion coefficient $\varepsilon\to0^+$, and it is well
known that, if the initial datum $u(\cdot,0)$ takes the values $+1$ and $-1$ in
the regions $\Omega_+$ and $\Omega_-$, then the "interface" connecting
$\Omega_+$ and $\Omega_-$ moves with normal velocity equal to the sum of its
principal curvatures, i.e. the interface moves by mean curvature flow.
This paper concerns with the motion of the inteface for a damped hyperbolic
Allen-Cahn equation, in a bounded domain of $\mathbb{R}^n$, for $n=2$ or $n=3$.
In particular, we focus the attention on radially simmetric solutions, studying
in detail the differences with the classic parabolic case, and we prove that,
under appropriate assumptions on the initial data $u(\cdot,0)$ and
$u_t(\cdot,0)$, the interface moves by mean curvature as $\varepsilon\to0^+$
also in the hyperbolic framework. | 1802.05038v1 |
2018-04-01 | Aggregated Momentum: Stability Through Passive Damping | Momentum is a simple and widely used trick which allows gradient-based
optimizers to pick up speed along low curvature directions. Its performance
depends crucially on a damping coefficient $\beta$. Large $\beta$ values can
potentially deliver much larger speedups, but are prone to oscillations and
instability; hence one typically resorts to small values such as 0.5 or 0.9. We
propose Aggregated Momentum (AggMo), a variant of momentum which combines
multiple velocity vectors with different $\beta$ parameters. AggMo is trivial
to implement, but significantly dampens oscillations, enabling it to remain
stable even for aggressive $\beta$ values such as 0.999. We reinterpret
Nesterov's accelerated gradient descent as a special case of AggMo and analyze
rates of convergence for quadratic objectives. Empirically, we find that AggMo
is a suitable drop-in replacement for other momentum methods, and frequently
delivers faster convergence. | 1804.00325v3 |
2018-09-27 | Non-equilibrium Quantum Langevin dynamics of orbital diamagnetic moment | We investigate the time dependent orbital diamagnetic moment of a charged
particle in a magnetic field in a viscous medium via the Quantum Langevin
Equation. We study how the interplay between the cyclotron frequency and the
viscous damping rate governs the dynamics of the orbital magnetic moment in the
high temperature classical domain and the low temperature quantum domain for an
Ohmic bath. These predictions can be tested via state of the art cold atom
experiments with hybrid traps for ions and neutral atoms. We also study the
effect of a confining potential on the dynamics of the magnetic moment. We
obtain the expected Bohr Van Leeuwen limit in the high temperature, asymptotic
time ($ \gamma t\longrightarrow \infty$, where $ \gamma $ is the viscous
damping coefficient) limit. | 1809.10370v1 |
2018-12-10 | Assessment of skin-friction-reduction techniques on a turbulent wing section | The scope of the present project is to quantify the effects of uniform
blowing and body-force damping on turbulent boundary layers subjected to a
non-uniform adverse-pressure-gradient distribution. To this end, well-resolved
large-eddy simulations are employed to describe the flow around the NACA4412
airfoil at moderate Reynolds number 200, 000 based on freestream velocity and
chord length. In the present paper we focus on uniform blowing and the
conference presentation will include a comparison with body-force damping
applied in the same region. The inner-scaled profiles of the mean velocity and
of selected components of the Reynolds-stress tensor are examined and compared
with the uncontrolled cases. It is known that uniform blowing and
adverse-pressure gradients share some similarities in their effect on the
boundary layers, and our results will show that these effects are not
independent. The behaviour of the skin-friction coefficient is analyzed through
the FIK decomposition, and the impact of this control strategy on the
aerodynamic efficiency of the airfoil is discussed. | 1812.03762v1 |
2018-12-19 | Rain Calms the Sea - The Impact of Entrained Air | We propose a mechanism for the damping of short ocean gravity waves during
rainstorms associated with the injection of air bubbles by rain drops. The
mechanism is proposed as one of the possible explanations that ascribe to rain
a calming effect on ocean surface waves. A model is developed that shows how
wave attenuation increases with the presence of air bubbles in the upper
reaches of the ocean. The model makes predictions of the effective wave
dissipation coefficient, as a function of the volumetric ratio of air to water,
as well as to the rainfall rate. The model predicts dissipation rates that are
in line with experimental estimates of the effective wave damping rate. | 1812.08200v2 |
2019-01-10 | Stability and Controllability results for a Timoshenko system | In this paper, we study the indirect boundary stability and exact
controllability of a one-dimensional Timoshenko system. In the first part of
the paper, we consider the Timoshenko system with only one boundary fractional
damping. We first show that the system is strongly stable but not uniformly
stable. Hence, we look for a polynomial decay rate for smooth initial data.
Using frequency domain arguments combined with the multiplier method, we prove
that the energy decay rate depends on coefficients appearing in the PDE and on
the order of the fractional damping. Moreover, under the equal speed
propagation condition, we obtain the optimal polynomial energy decay rate. In
the second part of this paper, we study the indirect boundary exact
controllability of the Timoshenko system with mixed Dirichlet-Neumann boundary
conditions and boundary control. Using non-harmonic analysis, we first
establish a weak observability inequality, which depends on the ratio of the
waves propagation speeds. Next, using the HUM method, we prove that the system
is exactly controllable in appropriate spaces and that the control time can be
small. | 1901.03303v2 |
2019-05-07 | Integral representation formulae for the solution of a wave equation with time-dependent damping and mass in the scale-invariant case | This paper is devoted to derive integral representation formulae for the
solution of an inhomogeneous linear wave equation with time-dependent damping
and mass terms, that are scale-invariant with respect to the so-called
hyperbolic scaling. Yagdjian's integral transform approach is employed for this
purpose. The main step in our argument consists in determining the kernel
functions for the different integral terms, which are related to the source
term and to initial data. We will start with the one dimensional case (in
space). We point out that we may not apply in a straightforward way Duhamel's
principle to deal with the source term since the coefficients of lower order
terms make our model not invariant by time translation. On the contrary, we
shall begin with the representation formula for the inhomogeneous equation with
vanishing data by using a revised Duhamel's principle. Then, we will derive the
representation of the solution in the homogeneous case with nontrivial data.
After deriving the formula in the one dimensional case, the classical approach
by spherical means is used in order to deal with the odd dimensional case.
Finally, using the method of descent, the representation formula in the even
dimensional case is proved. | 1905.02408v1 |
2019-05-20 | Short time blow-up by negative mass term for semilinear wave equations with small data and scattering damping | In this paper we study blow-up and lifespan estimate for solutions to the
Cauchy problem with small data for semilinear wave equations with scattering
damping and negative mass term. We show that the negative mass term will play a
dominant role when the decay of its coefficients is not so fast, thus the
solutions will blow up in a finite time. What is more, we establish a lifespan
estimate from above which is much shorter than the usual one. | 1905.08100v1 |
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 |
2019-09-19 | Blow-up for Strauss type wave equation with damping and potential | We study a kind of nonlinear wave equations with damping and potential, whose
coefficients are both critical in the sense of the scaling and depend only on
the spatial variables. Based on the earlier works, one may think there are two
kinds of blow-up phenomenons when the exponent of the nonlinear term is small.
It also means there are two kinds of law to determine the critical exponent. In
this paper, we obtain a blow-up result and get the estimate of the upper bound
of the lifespan in critical and sub-critical cases. All of the results support
such a conjecture, although for now, the existence part is still open. | 1909.08885v3 |
2019-12-10 | Stability of traveling waves in a driven Frenkel-Kontorova model | In this work we revisit a classical problem of traveling waves in a damped
Frenkel-Kontorova lattice driven by a constant external force. We compute these
solutions as fixed points of a nonlinear map and obtain the corresponding
kinetic relation between the driving force and the velocity of the wave for
different values of the damping coefficient. We show that the kinetic curve can
become non-monotone at small velocities, due to resonances with linear modes,
and also at large velocities where the kinetic relation becomes multivalued.
Exploring the spectral stability of the obtained waveforms, we identify, at the
level of numerical accuracy of our computations, a precise criterion for
instability of the traveling wave solutions: monotonically decreasing portions
of the kinetic curve always bear an unstable eigendirection. We discuss why the
validity of this criterion in the {\it dissipative} setting is a rather
remarkable feature offering connections to the Hamiltonian variant of the model
and of lattice traveling waves more generally. Our stability results are
corroborated by direct numerical simulations which also reveal the possible
outcomes of dynamical instabilities. | 1912.05052v2 |
2020-06-10 | Interpolation between Residual and Non-Residual Networks | Although ordinary differential equations (ODEs) provide insights for
designing network architectures, its relationship with the non-residual
convolutional neural networks (CNNs) is still unclear. In this paper, we
present a novel ODE model by adding a damping term. It can be shown that the
proposed model can recover both a ResNet and a CNN by adjusting an
interpolation coefficient. Therefore, the damped ODE model provides a unified
framework for the interpretation of residual and non-residual networks. The
Lyapunov analysis reveals better stability of the proposed model, and thus
yields robustness improvement of the learned networks. Experiments on a number
of image classification benchmarks show that the proposed model substantially
improves the accuracy of ResNet and ResNeXt over the perturbed inputs from both
stochastic noise and adversarial attack methods. Moreover, the loss landscape
analysis demonstrates the improved robustness of our method along the attack
direction. | 2006.05749v4 |
2020-06-24 | The Complex Permeability of Split-Ring Resonator Arrays Measured at Microwave Frequencies | We have measured the relative permeability of split-ring resonator (SRR)
arrays used in metamaterials designed to have $\mu^\prime< 0$ over a narrow
range of microwave frequencies. The SRR arrays were loaded into the bore of a
loop-gap resonator (LGR) and reflection coefficient measurements were used to
determine both the real and imaginary parts of the array's effective
permeability. Data were collected as a function of array size and SRR spacing.
The results were compared to those obtained from continuous extended split-ring
resonators (ESRRs). The arrays of planar SRRs exhibited enhanced damping and a
narrower range of frequencies with $\mu^\prime<0$ when compared to the ESRRs.
The observed differences in damping, however, were diminished considerably when
the array size was expanded from a one-dimensional array of $N$ SRRs to a
$2\times 2\times N$ array. Our method can also be used to experimentally
determine the effective permeability of other metamaterial designs. | 2006.13861v1 |
2020-12-28 | Reliability optimization of friction-damped systems using nonlinear modes | A novel probabilistic approach for the design of mechanical structures with
friction interfaces is proposed. The objective function is defined as the
probability that a specified performance measure of the forced vibration
response is achieved subject to parameter uncertainties. The practicability of
the approach regarding the extensive amount of required design evaluations is
strictly related to the computational efficiency of the nonlinear dynamic
analysis. Therefore, it is proposed to employ a recently developed parametric
reduced order model (ROM) based on nonlinear modes of vibration, which can
facilitate a decrease of the computational burden by several orders of
magnitude. The approach was applied to a rotationally periodic assembly of a
bladed disk with underplatform friction dampers. The robustness of the optimum
damper design was significantly improved compared to the deterministic
approach, taking into account uncertainties in the friction coefficient, the
excitation level and the linear damping. Moreover, a scale invariance for
piecewise linear contact constraints is proven, which can be very useful for
the reduction of the numerical effort for the analysis of such systems. | 2012.14466v1 |
2021-01-25 | A modified Kačanov iteration scheme with application to quasilinear diffusion models | The classical Ka\v{c}anov scheme for the solution of nonlinear variational
problems can be interpreted as a fixed point iteration method that updates a
given approximation by solving a linear problem in each step. Based on this
observation, we introduce a modified Ka\v{c}anov method, which allows for
(adaptive) damping, and, thereby, to derive a new convergence analysis under
more general assumptions and for a wider range of applications. For instance,
in the specific context of quasilinear diffusion models, our new approach does
no longer require a standard monotonicity condition on the nonlinear diffusion
coefficient to hold. Moreover, we propose two different adaptive strategies for
the practical selection of the damping parameters involved. | 2101.10137v3 |
2021-03-01 | Dynamics of a ring of three unidirectionally coupled Duffing oscillators with time-dependent damping | We study dynamics of a ring of three unidirectionally coupled double-well
Duffing oscillators for three different values of the damping coefficient:
fixed dumping, proportional to time, and inversely proportional to time. The
dynamics in all cases is analyzed through time series, Fourier and Hilbert
transforms, Poincar\'e sections, as well as bifurcation diagrams and Lyapunov
exponents with respect to the coupling strength. In the first case, we observe
a well-known route from a stable steady state to hyperchaos through Hopf
bifurcation and a series of torus bifurcations, as the coupling strength is
increased. In the second case, the system is highly dissipative and converges
into one of stable equilibria. Finally, in the third case, transient toroidal
hyperchaos takes place. | 2103.01297v1 |
2021-03-16 | On an inverse problem of nonlinear imaging with fractional damping | This paper considers the attenuated Westervelt equation in pressure
formulation. The attenuation is by various models proposed in the literature
and characterised by the inclusion of non-local operators that give power law
damping as opposed to the exponential of classical models. The goal is the
inverse problem of recovering a spatially dependent coefficient in the
equation, the parameter of nonlinearity $\kappa(x)$, in what becomes a
nonlinear hyperbolic equation with nonlocal terms. The overposed measured data
is a time trace taken on a subset of the domain or its boundary. We shall show
injectivity of the linearised map from $\kappa$ to the overposed data used to
recover it and from this basis develop and analyse Newton-type schemes for its
effective recovery. | 2103.08965v1 |
2021-04-22 | Dissipation and fluctuations in elongated bosonic Josephson junctions | We investigate the dynamics of bosonic atoms in elongated Josephson
junctions. We find that these systems are characterized by an intrinsic
coupling between the Josephson mode of macroscopic quantum tunneling and the
sound modes. This coupling of Josephson and sound modes gives rise to a damped
and stochastic Langevin dynamics for the Josephson degree of freedom. From a
microscopic Lagrangian, we deduce and investigate the damping coefficient and
the stochastic noise, which includes thermal and quantum fluctuations. Finally,
we study the time evolution of relative-phase and population-imbalance
fluctuations of the Josephson mode and their oscillating thermalization to
equilibrium. | 2104.11259v2 |
2022-04-07 | Pseudo Numerical Ranges and Spectral Enclosures | We introduce the new concepts of pseu\-do numerical range for operator
functions and families of sesquilinear forms as well as the pseu\-do block
numerical range for $n \times n$ operator matrix functions. While these notions
are new even in the bounded case, we cover operator polynomials with unbounded
coefficients, unbounded holomorphic form families of type (a) and associated
operator families of type (B). Our main results include spectral inclusion
properties of pseudo numerical ranges and pseudo block numerical ranges. For
diagonally dominant and off-diagonally dominant operator matrices they allow us
to prove spectral enclosures in terms of the pseudo numerical ranges of Schur
complements that no longer require dominance order $0$ and not even $<1$. As an
application, we establish a new type of spectral bounds for linearly damped
wave equations with possibly unbounded and/or singular damping. | 2204.03584v1 |
2022-04-14 | Stability of Exponentially Damped Oscillations under Perturbations of the Mori-Chain | There is an abundance of evidence that some relaxation dynamics, e.g.,
exponential decays, are much more common in nature than others. Recently, there
have been attempts to trace this dominance back to a certain stability of the
prevalent dynamics versus generic Hamiltonian perturbations. In the paper at
hand, we tackle this stability issue from yet another angle, namely in the
framework of the recursion method. We investigate the behavior of various
relaxation dynamics with respect to alterations of the so-called Lanczos
coefficients. All considered scenarios are set up in order to comply with the
"universal operator growth hypothesis". Our numerical experiments suggest the
existence of stability in a larger class of relaxation dynamics consisting of
exponentially damped oscillations. Further, we propose a criterion to identify
"pathological" perturbations that lead to uncommon dynamics. | 2204.06903v1 |
2022-05-09 | Mutual friction and diffusion of two-dimensional quantum vortices | We present a microscopic open quantum systems theory of thermally-damped
vortex motion in oblate atomic superfluids that includes previously neglected
energy-damping interactions between superfluid and thermal atoms. This
mechanism couples strongly to vortex core motion and causes dissipation of
vortex energy due to mutual friction, as well as Brownian motion of vortices
due to thermal fluctuations. We derive an analytic expression for the
dimensionless mutual friction coefficient that gives excellent quantitative
agreement with experimentally measured values, without any fitted parameters.
Our work closes an existing two orders of magnitude gap between dissipation
theory and experiments, previously bridged by fitted parameters, and provides a
microscopic origin for the mutual friction and diffusion of quantized vortices
in two-dimensional atomic superfluids. | 2205.04065v2 |
2022-05-12 | Global existence and stability of subsonic time-periodic solution to the damped compressible Euler equations in a bounded domain | In this paper, we consider the one-dimensional isentropic compressible Euler
equations with source term $\beta(t,x)\rho|u|^{\alpha}u$ in a bounded domain,
which can be used to describe gas transmission in a nozzle.~The model is
imposed a subsonic time-periodic boundary condition.~Our main results reveal
that the time-periodic boundary can trigger an unique subsonic time-periodic
smooth solution and this unique periodic solution is stable under small
perturbations on initial and boundary data.~To get the existence of subsonic
time-periodic solution, we use the linear iterative skill and transfer the
boundary value problem into two initial value ones by using the hyperbolic
property of the system. Then the corresponding linearized system can be
decoupled.~The uniqueness is a direct by-product of the stability. There is no
small assumptions on the damping coefficient. | 2205.05858v2 |
2022-09-11 | Approximation of Algebraic Riccati Equations with Generators of Noncompact Semigroups | In this work, we demonstrate that the Bochner integral representation of the
Algebraic Riccati Equations (ARE) are well-posed without any compactness
assumptions on the coefficient and semigroup operators. From this result, we
then are able to determine that, under some assumptions, the solution to the
Galerkin approximations to these equations are convergent to the infinite
dimensional solution. Going further, we apply this general result to
demonstrate that the finite element approximation to the ARE are optimal for
weakly damped wave semigroup processes in the $H^1(\Omega) \times L^2(\Omega)$
norm. Optimal convergence rates of the functional gain for a weakly damped wave
optimal control system in both the $H^1(\Omega) \times L^2(\Omega)$ and
$L^2(\Omega)\times L^2(\Omega)$ norms are demonstrated in the numerical
examples. | 2209.04769v5 |
2022-11-18 | Accelerated gradient methods with strong convergence to the minimum norm minimizer: a dynamic approach combining time scaling, averaging, and Tikhonov regularization | In a Hilbert framework, for convex differentiable optimization, we consider
accelerated gradient methods obtained by combining temporal scaling and
averaging techniques with Tikhonov regularization. We start from the continuous
steepest descent dynamic with an additional Tikhonov regularization term whose
coefficient vanishes asymptotically. We provide an extensive Lyapunov analysis
of this first-order evolution equation. Then we apply to this dynamic the
method of time scaling and averaging recently introduced by Attouch, Bot and
Nguyen. We thus obtain an inertial dynamic which involves viscous damping
associated with Nesterov's method, implicit Hessian damping and Tikhonov
regularization. Under an appropriate setting of the parameters, just using
Jensen's inequality, without the need for another Lyapunov analysis, we show
that the trajectories have at the same time several remarkable properties: they
provide a rapid convergence of values, fast convergence of the gradients to
zero, and strong convergence to the minimum norm minimizer. These results
complete and improve the previous results obtained by the authors. | 2211.10140v1 |
2022-12-21 | Global existence and Blow-up for the 1D damped compressible Euler equations with time and space dependent perturbation | In this paper, we consider the 1D Euler equation with time and space
dependent damping term $-a(t,x)v$. It has long been known that when $a(t,x)$ is
a positive constant or $0$, the solution exists globally in time or blows up in
finite time, respectively. We prove that those results are invariant with
respect to time and space dependent perturbations. We suppose that the
coefficient $a$ satisfies the following condition $$ |a(t,x)- \mu_0| \leq
a_1(t) + a_2 (x), $$ where $\mu_0 \geq 0$ and $a_1$ and $a_2$ are integrable
functions with $t$ and $x$. Under this condition, we show the global existence
and the blow-up with small initial data, when $\mu_0 >0$ and $\mu=0$
respectively. | 2212.11072v2 |
2023-07-19 | A spin-rotation mechanism of Einstein-de Haas effect based on a ferromagnetic disk | Spin-rotation coupling (SRC) is a fundamental phenomenon that connects
electronic spins with the rotational motion of a medium. We elucidate the
Einstein-de Haas (EdH) effect and its inverse with SRC as the microscopic
mechanism using the dynamic spin-lattice equations derived by elasticity theory
and Lagrangian formalism. By applying the coupling equations to an iron disk in
a magnetic field, we exhibit the transfer of angular momentum and energy
between spins and lattice, with or without damping. The timescale of the
angular momentum transfer from spins to the entire lattice is estimated by our
theory to be on the order of 0.01 ns, for the disk with a radius of 100 nm.
Moreover, we discover a linear relationship between the magnetic field strength
and the rotation frequency, which is also enhanced by a higher ratio of Young's
modulus to Poisson's coefficient. In the presence of damping, we notice that
the spin-lattice relaxation time is nearly inversely proportional to the
magnetic field. Our explorations will contribute to a better understanding of
the EdH effect and provide valuable insights for magneto-mechanical
manufacturing. | 2307.10390v1 |
2023-08-05 | The isometric immersion of surfaces with finite total curvature | In this paper, we study the smooth isometric immersion of a complete simply
connected surface with a negative Gauss curvature in the three-dimensional
Euclidean space. For a surface with a finite total Gauss curvature and
appropriate oscillations of the Gauss curvature, we prove the global existence
of a smooth solution to the Gauss-Codazzi system and thus establish a global
smooth isometric immersion of the surface into the three-dimensional Euclidean
space. Based on a crucial observation that some linear combinations of the
Riemann invariants decay faster than others, we reformulate the Gauss-Codazzi
system as a symmetric hyperbolic system with a partial damping. Such a damping
effect and an energy approach permit us to derive global decay estimates and
meanwhile control the non-integrable coefficients of nonlinear terms. | 2308.02832v2 |
2023-08-30 | Stochastic Thermodynamics of Brownian motion in Temperature Gradient | We study stochastic thermodynamics of a Brownian particle which is subjected
to a temperature gradient and is confined by an external potential. We first
formulate an over-damped Ito-Langevin theory in terms of local temperature,
friction coefficient, and steady state distribution, all of which are
experimentally measurable. We then study the associated stochastic
thermodynamics theory. We analyze the excess entropy production (EP) both at
trajectory level and at ensemble level, and derive the Clausius inequality as
well as the transient fluctuation theorem (FT). We also use molecular dynamics
to simulate a Brownian particle inside a Lennard-Jones fluid and verify the FT.
Remarkably we find that the FT remains valid even in the under-damped regime.
We explain the possible mechanism underlying this surprising result. | 2308.15764v3 |
2023-12-27 | Universal orbital and magnetic structures in infinite-layer nickelates | We conducted a comparative study of the rare-earth infinite-layer nickelates
films, RNiO2 (R = La, Pr, and Nd) using resonant inelastic X-ray scattering
(RIXS). We found that the gross features of the orbital configurations are
essentially the same, with minor variations in the detailed hybridization. For
low-energy excitations, we unambiguously confirm the presence of damped
magnetic excitations in all three compounds. By fitting to a linear spin-wave
theory, comparable spin exchange coupling strengths and damping coefficients
are extracted, indicating a universal magnetic structure in the infinite-layer
nickelates. Interestingly, while signatures of a charge order are observed in
LaNiO2 in the quasi-elastic region of the RIXS spectrum, it is absent in NdNiO2
and PrNiO2. This prompts further investigation into the universality and the
origins of charge order within the infinite-layer inickelates. | 2312.16444v1 |
2005-07-28 | Transverse spin waves in isotropic ferromagnets | The comparison of transverse spin wave spectra and its attenuation in
Heisenberg ferromagnet and in ferromagnetic Fermi liquid as well in polarized
Fermi liquid is undertaken. The transverse spin waves frequency in polarized
paramagnetic Fermi liquid as well in a Fermi liquid with spontaneous
magnetization is found to be proportional to the square of the wave vector with
complex diffusion coefficient such that the damping has a finite value
proportional to the scattering rate of quasiparticles at T=0.
This behavior of polarized Fermi liquid contrasts with the behavior of
Heisenberg ferromagnet in hydrodynamic regime where the transverse spin wave
attenuation appears in terms proportional to the wave vector in fourth power.
The reactive part of diffusion coefficient in paramagnetic state at T=0
proves to be inversely proportional to magnetization whereas in ferromagnetic
state it is directly proportional to magnetization. The dissipative part of
diffusion coefficient at T=0 in paramagnetic state is polarization independent,
whereas in ferromagnetic state it is proportional to square of magnetization.
Moreover, the spin wave spectrum in ferromagnetic Fermi liquid proves to be
unstable that demonstrates the difficulty of the Fermi liquid description of
itinerant ferromagnetism. | 0507676v1 |
1998-10-22 | Quantifying excitations of quasinormal mode systems | Computations of the strong field generation of gravitational waves by black
hole processes produce waveforms that are dominated by quasinormal (QN)
ringing, a damped oscillation characteristic of the black hole. We describe
here the mathematical problem of quantifying the QN content of the waveforms
generated. This is done in several steps: (i) We develop the mathematics of QN
systems that are complete (in a sense to be defined) and show that there is a
quantity, the ``excitation coefficient,'' that appears to have the properties
needed to quantify QN content. (ii) We show that incomplete systems can (at
least sometimes) be converted to physically equivalent complete systems. Most
notably, we give a rigorous proof of completeness for a specific modified model
problem. (iii) We evaluate the excitation coefficient for the model problem,
and demonstrate that the excitation coefficient is of limited utility. We
finish by discussing the general question of quantification of QN excitations,
and offer a few speculations about unavoidable differences between normal mode
and QN systems. | 9810074v1 |
2007-04-09 | Bulk viscosity of superfluid neutron stars | The hydrodynamics, describing dynamical effects in superfluid neutron stars,
essentially differs from the standard one-fluid hydrodynamics. In particular,
we have four bulk viscosity coefficients in the theory instead of one. In this
paper we calculate these coefficients, for the first time, assuming they are
due to non-equilibrium beta-processes (such as modified or direct Urca
process). The results of our analysis are used to estimate characteristic
damping times of sound waves in superfluid neutron stars. It is demonstrated
that all four bulk viscosity coefficients lead to comparable dissipation of
sound waves and should be considered on the same footing. | 0704.1071v2 |
2008-07-28 | Enhancement of thermal transport in the degenerate periodic Anderson model | The low-temperature transport coefficients of the degenerate periodic SU(N)
Anderson model are calculated in the limit of infinite correlation between {\it
f} electrons, within the framework of dynamical mean-field theory. We establish
the Fermi liquid (FL) laws in the clean limit, taking into account the
quasiparticle damping. The latter yields a reduced value of the Lorenz number
in the Wiedemann-Franz law. Our results indicate that the renormalization of
the thermal conductivity and of the Seebeck coefficient can lead to a
substantial enhancement of the electronic thermoelectric figure-of-merit at low
temperature.
Using the FL laws we discuss the low-temperature anomalies that show up in
the electrical resistance of the intermetallic compounds with Cerium and
Ytterbium ions, when studied as a function of pressure.
Our calculations explain the sharp maximum of the coefficient of the
$T^2$-term of the electrical resistance and the rapid variation of residual
resistance found in a number of Ce and Yb intermetallics at some critical
pressure. | 0807.4385v2 |
2012-06-09 | Non linearities in the harmonic spectrum of heavy ion collisions with ideal and viscous hydrodynamics | We determine the non-linear hydrodynamic response to geometrical fluctuations
in heavy ion collisions using ideal and viscous hydrodynamics. This response is
characterized with a set of non-linear response coefficients that determine,
for example, the $v_5$ that is produced by an $\epsilon_2$ and an $\epsilon_3$.
We analyze how viscosity damps both the linear and non-linear response
coefficients, and provide an analytical estimate that qualitatively explains
most of the trends observed in more complete simulations. Subsequently, we use
these nonlinear response coefficients to determine the linear and non-linear
contributions to $v_1$, $v_4$ and $v_5$. For viscous hydrodynamics the
nonlinear contribution is dominant for $v_4$, $v_5$ and higher harmonics. For
$v_1$, the nonlinear response constitutes an important $\sim 25%$ correction in
mid-central collisions. The nonlinear response is also analyzed as a function
of transverse momentum for $v_1$, $v_4$ and $v_5$. Finally, recent measurements
of correlations between event-planes of different harmonic orders are discussed
in the context of non-linear response. | 1206.1905v2 |
2014-10-05 | Finite-time stabilization of a network of strings | We investigate the finite-time stabilization of a tree-shaped network of
strings. Transparent boundary conditions are applied at all the external nodes.
At any internal node, in addition to the usual continuity conditions, a
modified Kirchhoff law incorporating a damping term $\alpha u_t$ with a
coefficient $\alpha$ that may depend on the node is considered. We show that
for a convenient choice of the sequence of coefficients $\alpha$, any solution
of the wave equation on the network becomes constant after a finite time. The
condition on the coefficients proves to be sharp at least for a star-shaped
tree. Similar results are derived when we replace the transparent boundary
condition by the Dirichlet (resp. Neumann) boundary condition at one external
node. | 1410.1122v1 |
2014-11-03 | Experimental Demonstration of the Co-existence of the Spin Hall and Rashba Effects in beta-Tantalum/Ferromagnet Bilayers | We have measured the spin torques of beta-Tantalum / Co20Fe60B20 bilayers
versus Ta thickness at room temperature using an FMR technique. The spin Hall
coefficient was calculated both from the observed change in damping coefficient
of the ferromagnet with Ta thickness, and from the ratio of the symmetric and
anti-symmetric components of the FMR signal. Results from these two methods
yielded values for the spin Hall coefficient of -0.090+/-0.005 and
-0.11+/-0.01, respectively. We have also identified a significant out-of-plane
spin torque originating from Ta, which is constant with Ta thickness. We
ascribe this to an interface spin orbit coupling, or Rashba effect, due to the
strength and constancy of the torque with Ta thickness. From fitting measured
data to a model including interface spin orbit coupling, we have determined the
spin diffusion length for beta-Tantalum to be ~2.5 nm. | 1411.0601v1 |
2017-11-05 | An entropy production based method for determining the position diffusion's coefficient of a quantum Brownian motion | Quantum Brownian motion of a harmonic oscillator in the Markovian
approximation is described by the respective Caldeira-Leggett master equation.
This master equation can be brought into Lindblad form by adding a position
diffusion term to it. The coefficient of this term is either customarily taken
to be the lower bound dictated by the Dekker inequality or determined by more
detailed derivations on the linearly damped quantum harmonic oscillator. In
this paper, we explore the theoretical possibilities of determining the
position diffusion term's coefficient by analyzing the entropy production of
the master equation. | 1711.01642v2 |
2019-03-25 | Bouncing behavior and dissipative characterization of a chain-filled granular damper | We have experimentally investigated the bouncing behavior and damping
performance of a container partially filled with granular chains, namely a
chain-filled damper. The motion of the chain-filled damper, recorded by a
particle tracing technology, demonstrates that the granular chains can
efficiently absorb the collisional energy of the damper. We extract both the
restitution coefficient of the first collision and the total flight time to
characterize the dissipation ability of the damper. Two containers and three
types of granular chains, different in size, stiffness and restitution
coefficient, are used to examine the experimental results. We find that the
restitution coefficient of the first collision of a single-chain-filled damper
can linearly tend to vanish with increasing the chain length and obtain a
minimum filling mass required to cease the container at the first collision (no
rebound). When the strong impact occurs, the collisional absorption efficiency
of a chain-filled damper is superior to a monodisperse-particle-filled damper.
Furthermore, the longer the chains are, the better the dissipative effect is. | 1903.10329v1 |
2020-02-06 | Measurement of resistance coefficients of pendulum motion with balls of various sizes | In order to obtain the damping and resistance coefficients of a pendulum, we
constructed an optical system containing a photogate for measuring the speed of
the pendulum at the lowest point of motion. The photogate consisted of a
photoresistor, a laser, a mechanical body, and a pendulum ball. A 3D printer
was used to produce the mechanical body and pendulum balls of various sizes.
Furthermore, we used Arduino to automate measurement of the speed at the lowest
point of motion and increase the precision. We found that the resistance
coefficient was proportional to the size of the balls, regardless of the ball
mass, in agreement with the drag equation for a small Reynolds number. | 2002.03796v1 |
2022-01-25 | Kinetics of hydrodynamic pions in chiral perturbation theory | We determine the kinetic coefficients of ultrasoft pions using chiral
perturbation theory at finite temperature close to the chiral limit. This is
used to compute the axial charge diffusion and damping coefficients in the
hydrodynamic effective theory for these pion waves. We show that to provide a
leading order answer for these coefficients one needs to explore the dynamics
of hard, soft, and ultrasoft pion modes, which are represented microscopically
by the appropriate kinetic and hydrodynamic descriptions.. | 2201.10495v2 |
2022-09-21 | Cross effects in spin hydrodynamics: A revisit Entropy analysis and statistical operator | We revisit the construction of first-order spin hydrodynamics and find that
the constitution relations receive the corrections from the cross effects
resulting from spin-orbit coupling. Starting from a routine entropy analysis,
we show how to identify cross effects and new cross transport coefficients from
the second law of thermodynamics. Interestingly, the conventional transport
coefficient heat conductivity $\kappa$ is bounded from below by the product of
cross transport coefficients, which means the threshold of heat conduction is
changed. With recourse to Zubarev's non-equilibrium statistical operator, we
reproduce the construction of first-order spin hydrodynamics and identification
of cross effects in a more rigorous way. By seeking the dispersion relations of
normal modes, we find that these cross effects suppress the attenuation of
sound modes and heat mode appearing in conventional hydrodynamics and also have
impacts on the damping of non-hydrodynamic spin modes. | 2209.10979v2 |
2024-02-14 | Global existence and long time behavior of solutions to some Oldroyd type models in hybrid Besov spaces | In this paper, we deal with some Oldroyd type models, which describe
incompressible viscoelastic fluids. There are 3 parameters in these models: the
viscous coefficient of fluid $\nu_{1}$, the viscous coefficient of the elastic
part of the stress tensor $\nu_{2}$, and the damping coefficient of the elastic
part of the stress tensor $\alpha$. In this paper, we assume at least one of
the parameters is zero: $(\nu_{1}, \nu_{2},\alpha)=(+,0,+), (+,0,0), (0,+,+),
(0,+,0), (0,0,+)$ and prove the global existence of unique solutions to all
these 5 cases in the framework of hybrid Besov spaces. We also derive decay
rates of the solutions except for the case $(\nu_{1}, \nu_{2},\alpha)=(+,0,0)$.
To the best of our knowledge, decay rates in this paper are the first results
in this framework, and can improve some previous works. | 2402.09175v1 |
2012-06-14 | On the Interpretation of the Foundations of Quantum Mechanics | This study discusses the quantum behavior of a particle, which is controlled
by fluctuations in the physical space-time (ST) variables, rather than provides
a novel interpretation of quantum theory. The fluctuations, i.e.,
inhomogeneities in a homogeneous phase ST, are prescribed by their probability.
They determine the reciprocal space and correlate with the correlation entropy
different from zero. Alongside with the minimum entropy, action, and the
presence of the Winn-Ehrenfest adiabatic invariant (AI), the fluctuations
require the Gilbert information (probabilistic) space linking the physical and
the reciprocal ST. Physical quantities in the information space are represented
by linear Hermitian operators, which is due to the entropy production in the
presence of an AI. Evolution of a quantum system is described by the wave
functions having the meaning of information concerning all virtually possible
states of a quantum particle. The wave functions are the solutions to the
Schrodinger equation and represent a navigation 'roadmap' for the particle to
follow. A quantum system is in fact a classical Hamiltonian system in the space
of coefficients of the wave function decomposition with respect to the operator
eigenfunctions. It is the linearity and the Hermitian nature of the operators
which determine the trajectory and the superposition principle in case of the
wave behavior of fluctuations. The uncertainty principle, reflects correlation
of the fluctuations and, hence, their nonlocality. This study discusses the
wave function phase, the Berry phase and its relationship to quantization,
discriminability of states and macroscopic quantum effects caused by
localization of the particle, followed by a possible entropy change during its
transition into a new thermodynamic state. | 1206.2998v1 |
2019-11-15 | A geometric look at MHD and the Braginsky dynamo | This paper considers magnetohydrodynamics (MHD) and some of its applications
from the perspective of differential geometry, considering the dynamics of an
ideal fluid flow and magnetic field on a general three-dimensional manifold,
equipped with a metric and an induced volume form. The benefit of this level of
abstraction is that it clarifies basic aspects of fluid dynamics such as how
certain quantities are transported, how they transform under the action of
mappings (for example the flow map between Lagrangian labels and Eulerian
positions), how conservation laws arise, and the origin of certain
approximations that preserve the mathematical structure of classical mechanics.
First, the governing equations for ideal MHD are derived in a general setting
by means of an action principle, and making use of Lie derivatives. The way in
which these equations transform under a pull back, by the map taking the
position of a fluid parcel to a background location, is detailed. This is then
used to parameterise Alfv\'en waves using concepts of pseudomomentum and
pseudofield, in parallel with the development of Generalised Lagrangian Mean
theory in hydrodynamics. Finally non-ideal MHD is considered with a sketch of
the development of the Braginsky $\alpha\omega$-dynamo in a general setting.
Expressions for the $\alpha$-tensor are obtained, including a novel geometric
formulation in terms of connection coefficients, and related to formulae found
elsewhere in the literature. | 1911.06592v2 |
2020-09-18 | Information- and Coding-Theoretic Analysis of the RLWE Channel | Several cryptosystems based on the \emph{Ring Learning with Errors} (RLWE)
problem have been proposed within the NIST post-quantum cryptography
standardization process, e.g., NewHope. Furthermore, there are systems like
Kyber which are based on the closely related MLWE assumption. Both previously
mentioned schemes result in a non-zero decryption failure rate (DFR). The
combination of encryption and decryption for these kinds of algorithms can be
interpreted as data transmission over a noisy channel. To the best of our
knowledge this paper is the first work that analyzes the capacity of this
channel. We show how to modify the encryption schemes such that the input
alphabets of the corresponding channels are increased. In particular, we
present lower bounds on their capacities which show that the transmission rate
can be significantly increased compared to standard proposals in the
literature. Furthermore, under the common assumption of stochastically
independent coefficient failures, we give lower bounds on achievable rates
based on both the Gilbert-Varshamov bound and concrete code constructions using
BCH codes. By means of our constructions, we can either increase the total
bitrate (by a factor of $1.84$ for Kyber and by factor of $7$ for NewHope)
while guaranteeing the same DFR or for the same bitrate, we can significantly
reduce the DFR for all schemes considered in this work (e.g., for NewHope from
$2^{-216}$ to $2^{-12769}$). | 2009.08681v3 |
2021-05-18 | Magnetic flux structuring of the quiet Sun internetwork. Center-to-limb analysis of solar-cycle variations | It is now well established that the quiet Sun contains in total more magnetic
flux than active regions and represents an important reservoir of magnetic
energy. But the nature and evolution of these fields remain largely unknown.
We investigate the solar-cycle and center-to-limb variations of magnetic-flux
structures at small scales in internetwork regions of the quiet Sun.
We used Hinode SOT/SP data from the irradiance program between 2008 and 2016.
Maps of the magnetic-flux density are derived from the center-of gravity method
applied to the FeI 630.15 nm and FeI 630.25 nm lines. To correct the maps from
the instrumental smearing, we applied a deconvolution method based on a
principal component analysis of the line profiles and on a Richardson-Lucy
deconvolution of their coefficients. We then performed a spectral analysis of
the spatial fluctuations of the magnetic-flux density in 10'' x 10''
internetwork regions spanning a wide range of latitudes.
At low and mid latitudes the power spectra do not vary significantly with the
solar cycle. However at solar maximum for one scan in the activity belt showing
an enhanced network, a marginal increase in the power of the magnetic
fluctuations is observed at granular and larger scales in the internetwork. At
high latitudes, we observe variations at granular and larger scales where the
power decreases at solar maximum. At all the latitudes the power of the
magnetic fluctuations at scales smaller than 0.5''remain constant throughout
the solar cycle.
Our results favor a small-scale dynamo that operates in the internetwork, but
they show that the global dynamo also contributes to the internetwork fields. | 2105.08657v1 |
2021-07-24 | Dual-Attention Enhanced BDense-UNet for Liver Lesion Segmentation | In this work, we propose a new segmentation network by integrating DenseUNet
and bidirectional LSTM together with attention mechanism, termed as
DA-BDense-UNet. DenseUNet allows learning enough diverse features and enhancing
the representative power of networks by regulating the information flow.
Bidirectional LSTM is responsible to explore the relationships between the
encoded features and the up-sampled features in the encoding and decoding
paths. Meanwhile, we introduce attention gates (AG) into DenseUNet to diminish
responses of unrelated background regions and magnify responses of salient
regions progressively. Besides, the attention in bidirectional LSTM takes into
account the contribution differences of the encoded features and the up-sampled
features in segmentation improvement, which can in turn adjust proper weights
for these two kinds of features. We conduct experiments on liver CT image data
sets collected from multiple hospitals by comparing them with state-of-the-art
segmentation models. Experimental results indicate that our proposed method
DA-BDense-UNet has achieved comparative performance in terms of dice
coefficient, which demonstrates its effectiveness. | 2107.11645v1 |
2023-12-03 | Heisenberg machines with programmable spin-circuits | We show that we can harness two recent experimental developments to build a
compact hardware emulator for the classical Heisenberg model in statistical
physics. The first is the demonstration of spin-diffusion lengths in excess of
microns in graphene even at room temperature. The second is the demonstration
of low barrier magnets (LBMs) whose magnetization can fluctuate rapidly even at
sub-nanosecond rates. Using experimentally benchmarked circuit models, we show
that an array of LBMs driven by an external current source has a steady-state
distribution corresponding to a classical system with an energy function of the
form $E = -1/2\sum_{i,j} J_{ij} (\hat{m}_i \cdot \hat{m}_j$). This may seem
surprising for a non-equilibrium system but we show that it can be justified by
a Lyapunov function corresponding to a system of coupled
Landau-Lifshitz-Gilbert (LLG) equations. The Lyapunov function we construct
describes LBMs interacting through the spin currents they inject into the spin
neutral substrate. We suggest ways to tune the coupling coefficients $J_{ij}$
so that it can be used as a hardware solver for optimization problems involving
continuous variables represented by vector magnetizations, similar to the role
of the Ising model in solving optimization problems with binary variables.
Finally, we implement a Heisenberg AND gate based on a network of three coupled
stochastic LLG equations, illustrating the concept of probabilistic computing
with a programmable Heisenberg model. | 2312.01477v1 |
2024-02-19 | Density estimation for elliptic PDE with random input by preintegration and quasi-Monte Carlo methods | In this paper, we apply quasi-Monte Carlo (QMC) methods with an initial
preintegration step to estimate cumulative distribution functions and
probability density functions in uncertainty quantification (UQ). The
distribution and density functions correspond to a quantity of interest
involving the solution to an elliptic partial differential equation (PDE) with
a lognormally distributed coefficient and a normally distributed source term.
There is extensive previous work on using QMC to compute expected values in UQ,
which have proven very successful in tackling a range of different PDE
problems. However, the use of QMC for density estimation applied to UQ problems
will be explored here for the first time. Density estimation presents a more
difficult challenge compared to computing the expected value due to
discontinuities present in the integral formulations of both the distribution
and density. Our strategy is to use preintegration to eliminate the
discontinuity by integrating out a carefully selected random parameter, so that
QMC can be used to approximate the remaining integral. First, we establish
regularity results for the PDE quantity of interest that are required for
smoothing by preintegration to be effective. We then show that an $N$-point
lattice rule can be constructed for the integrands corresponding to the
distribution and density, such that after preintegration the QMC error is of
order $\mathcal{O}(N^{-1+\epsilon})$ for arbitrarily small $\epsilon>0$. This
is the same rate achieved for computing the expected value of the quantity of
interest. Numerical results are presented to reaffirm our theory. | 2402.11807v1 |
2004-11-02 | Spurious contribution to CR scattering calculations | The quasilinear theory for cosmic ray propagation is a well known and widely
accepted theory. In this paper, we discuss the different contributions to the
pitch-angle Fokker-Planck coefficient from large and small scales for slab
geometry using the damping model of dynamical turbulence. These examinations
will give us a hint on the limitation range where quasilinear approximation is
a good approximation. | 0411074v1 |
2006-01-16 | Bistability in Interstellar Gas-Phase Chemistry | We present an analysis of "bistability" in gas-phase chemical models of dark
interstellar clouds. We identify the chemical mechanisms that allow high- and
low-ionization solutions to the chemical rate-equations to coexist. We derive
simple analytic scaling relations for the gas densities and ionization rates
for which the chemistry becomes bistable. We explain why bistability is
sensitive to the H3+ dissociative recombination rate coefficient, and why it is
damped by gas-grain neutralization. | 0601323v1 |
1995-03-17 | Motion of heavy particles coupled to fermionic and bosonic environments in one dimension | Making use of a simple unitary transformation we change the hamiltonian of a
particle coupled to an one dimensional gas of bosons or fermions to a new form
from which the many body degrees of freedom can be easily traced out. The
effective dynamics of the particle allows us to compute its damping constant in
terms of the reflection coefficient of the interaction potential and the
occupation number of the environmental particles. We apply our results to a
delta repulsive potential. | 9503089v2 |
1997-06-06 | Dynamics of viscous amphiphilic films supported by elastic solid substrates | The dynamics of amphiphilic films deposited on a solid surface is analyzed
for the case when shear oscillations of the solid surface are excited. The two
cases of surface- and bulk shear waves are studied with film exposed to gas or
to a liquid. By solving the corresponding dispersion equation and the wave
equation while maintaining the energy balance we are able to connect the
surface density and the shear viscocity of a fluid amphiphilic overlayer with
experimentally accessible damping coefficients, phase velocity, dissipation
factor and resonant frequency shifts of shear waves. | 9706058v1 |
1997-09-30 | AC transport with reservoirs of finite width | The linear response conductance coefficients are calculated in the scattering
approach at finite frequency, damping and magnetic field for a microstructure
in which the reservoirs are modeled as quantum wire leads of infinite length
but finite width. Independently of frequency, inelastic scattering causes
subbands with large group velocity to contribute more strongly to the
conductance than channels of comparable transmission but slower propagation. At
finite frequency and magnetic fields, additional correction terms appear, some
of which are sensitive to the phase of the S matrix. | 9709332v2 |
1999-12-08 | Thermodynamical fluctuations and photo-thermal shot noise in gravitational wave antennae | Thermodynamical fluctuations of temperature in mirrors of gravitational wave
antennae are transformed through thermal expansion coefficient into additional
noise. This source of noise, which may also be interpreted as fluctuations due
to thermoelastic damping, may not be neglected and leads to the necessity to
reexamine the choice of materials for the mirrors. Additional source of noise
are fluctuations of the mirrors' surfaces caused by optical power absorbed in
dielectrical reflective layers. | 9912139v1 |
2001-02-26 | Relaxation time of weakly interacting superparamagnets | The relaxation time of weakly interacting classical spins is calculated by
introducing the averages of the local dipolar field, obtained by thermodynamic
perturbation theory, in a rigorous expression for the single-spin
thermoactivation rate in a weak but arbitrarily oriented field. At low
temperatures the non-trivial dependence of the superparamagnetic blocking on
the damping coefficient, numerically found by Berkov and Gorn, is reproduced by
our model and interpreted in terms of the deviations from uniaxial anisotropy
associated to the transversal component of the dipolar field acting on each
spin. | 0102472v1 |
2001-08-11 | Spin dynamics from time-dependent spin density-functional theory | We derive the spin-wave dynamics of a magnetic material from the
time-dependent spin density functional theory in the linear response regime.
The equation of motion for the magnetization includes, besides the static spin
stiffness, a "Berry curvature" correction and a damping term. A gradient
expansion scheme based on the homogeneous spin-polarized electron gas is
proposed for the latter two quantities, and the first few coefficients of the
expansion are calculated to second order in the Coulomb interaction. | 0108193v1 |
2006-02-01 | Special frequencies in reflection spectra of Bragg multiple quantum well structures | We have studied theoretically optical reflection spectra from the Bragg
multiple quantum well structures. We give an analytical explanation of the
presence of two special frequencies in the spectra at which the reflection
coefficient weakly depends on the quantum well number. The influence of the
exciton nonradiative damping on the reflection spectra has been analyzed. It
has been shown that allowance for the dielectric contrast gives rise to the
third special frequency at which the contributions to the reflectivity related
to the dielectric contrast and the exciton resonance mutually compensate one
another. | 0602013v1 |
2007-02-05 | Diffusion in Modulated Media | We study the motion of Brownian particle in modulated media in the strong
damping limit by using {\em toy model}, with special emphasis on the transition
from localise to diffusive behavior. By using model potential we have seen the
localised behavior when the number of minima of the potential is finite in the
asymptotic time limit. In the limit of infinite number of minima we have seen
the diffusive behavior.We calculate exactly the diffusion coefficient in
periodic field of force. We have also studied the transport in commensurate and
incommensurate media. | 0702092v1 |
2004-09-10 | A Nonlinear Coupling Network to Simulate the Development of the r-mode Instablility in Neutron Stars I. Construction | R-modes of a rotating neutron star are unstable because of the emission of
gravitational radiation. We explore the saturation amplitudes of these modes
determined by nonlinear mode-mode coupling. Modelling the star as
incompressible allows the analytic computation of the coupling coefficients.
All couplings up to n=30 are obtained, and analytic values for the shear
damping and mode normalization are presented. In a subsequent paper we perform
numerical simulations of a large set of coupled modes. | 0409048v1 |
1996-03-25 | Fermion Scattering at a Phase Wave | We study fermion reflection at a phase wave which is formed during a bubble
collision in a first order phase transition. We calculate the reflection and
the transmission coefficients by solving the Dirac equation with the phase wave
background. Using the results we analyze the damping and the velocity of the
wave. | 9603401v2 |
2003-06-01 | Asymptotic Quasinormal Frequencies of d-dimensional Schwarzschild Black Holes | We determine the quasinormal frequencies for all gravitational perturbations
of the d-dimensional Schwarzschild black hole, in the infinite damping limit.
Using the potentials for gravitational perturbations derived recently by
Ishibashi and Kodama, we show that in all cases the asymptotic real part of the
frequency is proportional to the Hawking temperature with a coefficient of log
3. Via the correspondence principle, this leads directly to an equally spaced
entropy spectrum. We comment on the possible implications for the spacing of
eigenvalues of the Virasoro generator in the associated near-horizon conformal
algebra. | 0306004v2 |
2002-03-05 | Broken symmetries and pattern formation in two-frequency forced Faraday waves | We exploit the presence of approximate (broken) symmetries to obtain general
scaling laws governing the process of pattern formation in weakly damped
Faraday waves. Specifically, we consider a two-frequency forcing function and
trace the effects of time translation, time reversal and Hamiltonian structure
for three illustrative examples: hexagons, two-mode superlattices, and two-mode
rhomboids. By means of explicit parameter symmetries, we show how the size of
various three-wave resonant interactions depends on the frequency ratio m:n and
on the relative temporal phase of the two driving terms. These symmetry-based
predictions are verified for numerically calculated coefficients, and help
explain the results of recent experiments. | 0203004v1 |
1997-02-12 | A self-consistent treatment of the dynamics of stable and unstable collective modes | We address the dynamics of damped collective modes in terms of first and
second moments. The modes are introduced in a self-consistent fashion with the
help of a suitable application of linear response theory. Quantum effects in
the fluctuations are governed by diffusion coefficients D_{\mu\nu}. The latter
are obtained through a fluctuation dissipation theorem generalized to allow for
a treatment of unstable modes. Numerical evaluations of the D_{\mu\nu} are
presented. We discuss briefly how this picture may be used to describe global
motion within a locally harmonic approximation. | 9702029v1 |
2005-01-07 | Velocity-Space Diffusion in a Perpendicularly Propagating Electrostatic Wave | The motion of ions in the fields B = B_0 zhat and E = E_0 yhat cos(k_perp y -
omega t) is considered. When omega >> Omega_i and v_perp > omega/k_perp, the
equations of motion may be reduced to a set of difference equations. These
equations exhibit stochastic behavior when E_0 exceeds a threshold. The
diffusion coefficient above the threshold is determined. Far above the
threshold, ion Landau damping is recovered. Extension of the method to include
parallel propagation is outlined. | 0501035v1 |
2002-05-20 | Selection of Squeezed States via Decoherence | In the framework of Lindblad theory for open quantum systems, we calculate
the entropy of a damped quantum harmonic oscillator which is initially in a
quasi-free state. The maximally predictable states are identified as those
states producing the minimum entropy increase after a long enough time. In
general, the states with a squeezing parameter depending on the environment's
diffusion coefficients and friction constant are singled out, but if the
friction constant is much smaller than the oscillator's frequency, coherent
states
(or thermalized coherent states) are obtained as the preferred classical
states. | 0205127v1 |
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