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2002-06-17 | Damped Bloch oscillations of cold atoms in optical lattices | The paper studies Bloch oscillations of cold neutral atoms in the optical
lattice. The effect of spontaneous emission on the dynamics of the system is
analyzed both analytically and numerically. The spontaneous emission is shown
to cause (i) the decay of Bloch oscillations with the decrement given by the
rate of spontaneous emission and (ii) the diffusive spreading of the atoms with
a diffusion coefficient depending on {\em both} the rate of spontaneous
emission and the Bloch frequency. | 0206108v1 |
2005-06-22 | A degenerate three-level laser with a parametric amplifier | The aim of this paper is to study the squeezing and statistical properties of
the light produced by a degenerate three-level laser whose cavity contains a
degenerate parametric amplifier. In this quantum optical system the top and
bottom levels of the three-level atoms injected into the laser cavity are
coupled by the pump mode emerging from the parametric amplifier. For a linear
gain coefficient of 100 and for a cavity damping constant of 0.8, the maximum
intracavity squeezing is found at steady state and at threshold to be 93%. | 0506178v3 |
2006-04-28 | Purity of states in the theory of open quantum systems | The condition of purity of states for a damped harmonic oscillator is
considered in the framework of Lindblad theory for open quantum systems. For a
special choice of the environment coefficients, the correlated coherent states
are shown to be 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. | 0604212v1 |
2007-05-08 | Theoretical Analysis of Subthreshold Oscillatory Behaviors in Nonlinear Autonomous Systems | We have developed a linearization method to investigate the subthreshold
oscillatory behaviors in nonlinear autonomous systems. By considering firstly
the neuronal system as an example, we show that this theoretical approach can
predict quantitatively the subthreshold oscillatory activities, including the
damping coefficients and the oscillatory frequencies which are in good
agreement with those observed in experiments. Then we generalize the
linearization method to an arbitrary autonomous nonlinear system. The detailed
extension of this theoretical approach is also presented and further discussed. | 0705.1019v1 |
2007-06-03 | A class of series acceleration formulae for Catalan's constant | In this note, we develop transformation formulae and expansions for the log
tangent integral, which are then used to derive series acceleration formulae
for certain values of Dirichlet L-functions, such as Catalan's constant. The
formulae are characterized by the presence of an infinite series whose general
term consists of a linear recurrence damped by the central binomial coefficient
and a certain quadratic polynomial. Typically, the series can be expressed in
closed form as a rational linear combination of Catalan's constant and pi times
the logarithm of an algebraic unit. | 0706.0356v1 |
2007-08-21 | Dimer diffusion in a washboard potential | The transport of a dimer, consisting of two Brownian particles bounded by a
harmonic potential, moving on a periodic substrate is investigated both
numerically and analytically. The mobility and diffusion of the dimer center of
mass present distinct properties when compared with those of a monomer under
the same transport conditions. Both the average current and the diffusion
coefficient are found to be complicated non-monotonic functions of the driving
force. The influence of dimer equilibrium length, coupling strength and damping
constant on the dimer transport properties are also examined in detail. | 0708.2858v2 |
2007-10-25 | Casimir energy and entropy between dissipative mirrors | We discuss the Casimir effect between two identical, parallel slabs,
emphasizing the role of dissipation and temperature. Starting from quite
general assumptions, we analyze the behavior of the Casimir entropy in the
limit T->0 and link it to the behavior of the slab's reflection coefficients at
low frequencies. We also derive a formula in terms of a sum over modes, valid
for dissipative slabs that can be interpreted in terms of a damped quantum
oscillator. | 0710.4915v2 |
2007-12-19 | Hyperon bulk viscosity in the presence of antikaon condensate | We investigate the hyperon bulk viscosity due to the non-leptonic process $n
+ p \rightleftharpoons p + \Lambda $ in $K^-$ condensed matter and its effect
on the r-mode instability in neutron stars. We find that the hyperon bulk
viscosity coefficient in the presence of antikaon condensate is suppressed
compared with the case without the condensate. The suppressed hyperon bulk
viscosity in the superconducting phase is still an efficient mechanism to damp
the r-mode instability in neutron stars. | 0712.3171v2 |
2008-06-24 | A Gear-like Predictor-Corrector method for Brownian Dynamics Simulation | We introduce a Predictor-Corrector type method suitable for performing
many-particle Brownian Dynamics simulations. Since the method goes over to the
Gear's method for Molecular Dynamics simulation in the limit of vanishing
friction, we refer to it as a Gear-like algorithm. The algorithm has been
tested on a one-dimensional, stochastically damped harmonic oscillator model,
showing that it can cover a wide range of friction coefficients with a
high-order accuracy, excellent stability, and a very small energy drift on the
long time scales. | 0806.3912v2 |
2008-08-29 | Kramers Theory for Conformational Transitions of Macromolecules | We consider the application of Kramers theory to the microscopic calculation
of rates of conformational transitions of macromolecules. The main difficulty
in such an approach is to locate the transition state in a huge configuration
space. We present a method which identifies the transition state along the most
probable reaction pathway. It is then possible to microscopically compute the
activation energy, the damping coefficient, the eigenfrequencies at the
transition state and obtain the rate, without any a-priori choice of a reaction
coordinate. Our theoretical results are tested against the results of Molecular
Dynamics simulations for transitions in a 2-dimensional double well and for the
cis-trans isomerization of a linear molecule. | 0809.0027v1 |
2008-12-30 | Bulk viscosity of strange matter and r-modes in neutron stars | We discuss bulk viscosity due to non-leptonic processes involving hyperons
and Bose-Einstein condensate of negatively charged kaons in neutron stars. It
is noted that the hyperon bulk viscosity coefficient is a few order of
magnitude larger than that of the case with the condensate. Further it is found
that the hyperon bulk viscosity is suppressed in a superconducting phase. The
hyperon bulk viscosity efficiently damps the r-mode instability in neutron
stars irrespective of whether a superconducting phase is present or not in
neutron star interior. | 0812.5021v1 |
2009-05-01 | Asymptotic behavior of second-order dissipative evolution equations combining potential with non-potential effects | We study the asymptotic convergence properties, as the time variable goes to
infinity, of trajectories of second-order dissipative evolution equations
combining potential with non-potential effects. We exhibit a sharp condition,
involving the damping parameter and the cocoercive coefficient of the
non-potential operator, which guarantees convergence to equilibria of the
trajectories. Applications are given to constrained optimization, fixed point
problems, dynamical approach to Nash equilibria, and asymptotic stabilization
in the case of a continuum of equilibria. | 0905.0092v1 |
2010-02-09 | The pulse and monochromatic light stimulation of semiconductor quantum wells | The light reflectance and absorbance are calculated for a quantum well (QW)
the width of which is comparable with the light wave length. The difference of
the refraction coefficients of the quantum well and barriers is taken into
account. The stimulating pulse form is arbitrary. An existence of two closely
situated discrete excitation energy levels is supposed. Such energy level pare
may correspond to two magnetopolaron states in a quantizing magnetic field
perpendicular to the QW plane. The relationship of the radiative and
non-radiative damping is arbitrary. The final results does not use the
approximation of the weak Coulomb interaction of electrons and holes. | 1002.1780v1 |
2010-02-09 | Asymptotical photon distributions in the dissipative Dynamical Casimir Effect | Asymptotical formulas for the photon distribution function of a quantum
oscillator with time-dependent frequency and damping coefficients, interacting
with a thermal reservoir, are derived in the case of a large mean number of
quanta. Different regimes of excitation of an initial thermal state with an
arbitrary temperature are considered. New formulas are used to predict the
statistical properties of the electromagnetic field created in the experiments
on the Dynamical Casimir Effect which are now under preparation. | 1002.1861v1 |
2010-03-12 | Symmetry Analysis of 2+1 dimensional Burgers equation with variable damping | The symmetry classification of the two dimensional Burgers equation with
variable coefficient is considered. Symmetry algebra is found and a
classification of its subalgebras, up to conjugacy, is obtained. Similarity
reductions are performed for each class. | 1003.2511v1 |
2010-06-14 | Transport parameters in neutron stars from in-medium NN cross sections | We present a numerical study of shear viscosity and thermal conductivity of
symmetric nuclear matter, pure neutron matter and $\beta$-stable nuclear
matter, in the framework of the Brueckner theory. The calculation of in-medium
cross sections and nucleon effective masses is performed with a consistent two
and three body interaction. The investigation covers a wide baryon density
range as requested in the applications to neutron stars. The results for the
transport coefficients in $\beta$-stable nuclear matter are used to make
preliminary predictions on the damping time scales of non radial modes in
neutron stars. | 1006.2656v1 |
2010-12-10 | Spin-orbit driven ferromagnetic resonance: A nanoscale magnetic characterisation technique | We demonstrate a scalable new ferromagnetic resonance (FMR) technique based
on the spin-orbit interaction. An alternating current drives FMR in uniform
ferromagnetic structures patterned from the dilute magnetic semiconductors
(Ga,Mn)As and (Ga,Mn)(As,P). This allows the direct measurement of magnetic
anisotropy coefficients and damping parameters for individual nano-bars. By
analysing the ferromagnetic resonance lineshape, we perform vector magnetometry
on the current-induced driving field, observing contributions with symmetries
of both the Dresselhaus and Rashba spin-orbit interactions. | 1012.2397v1 |
2011-09-28 | Local solvability and loss of smoothness of the Navier-Stokes-Maxwell equations with large initial data | Existence of local-in-time unique solution and loss of smoothness of full
Magnet-Hydro-Dynamics system (MHD) is considered for periodic initial data. The
result is proven using Fujita-Kato's method in $\ell^1$ based (for the Fourier
coefficients) functional spaces enabling us to easily estimate nonlinear terms
in the system as well as solutions to Maxwells's equations. A loss of
smoothness result is shown for the velocity and magnetic field. It comes from
the damped-wave operator which does not have any smoothing effect. | 1109.6089v1 |
2011-12-12 | On the vanishing electron-mass limit in plasma hydrodynamics in unbounded media | We consider the zero-electron-mass limit for the Navier-Stokes-Poisson system
in unbounded spatial domains. Assuming smallness of the viscosity coefficient
and ill-prepared initial data, we show that the asymptotic limit is represented
by the incompressible Navier-Stokes system, with a Brinkman damping, in the
case when viscosity is proportional to the electron-mass, and by the
incompressible Euler system provided the viscosity is dominated by the electron
mass. The proof is based on the RAGE theorem and dispersive estimates for
acoustic waves, and on the concept of suitable weak solutions for the
compressible Navier-Stokes system. | 1112.2562v1 |
2014-05-03 | Lie Symmetry Classification and Numerical Analysis of KdV Equation with Power-law Nonlinearity | In this paper, a complete Lie symmetry analysis of the damped wave equation
with time-dependent coefficients is investigated. Then the invariant solutions
and the exact solutions generated from the symmetries are presented. Moreover,
a Lie algebraic classifications and the optimal system are discussed. Finally,
using Chebyshev pseudo-spectral method (CPSM), a numerical analysis to solve
the invariant solutions corresponded the Lie symmetries of main equation is
presented. This method applies the Chebyshev-Gauss-Lobatto points as
collocation points. | 1405.0592v3 |
2015-02-22 | Fractional extension of Kramers rate and barrier escaping from metastable potential well | The reactive process of barrier escaping from the metastable potential well
is studied together with the extension of Kramers' rate formula to the
fractional case. Characteristic quantities are computed for an thimbleful of
insight into the near barrier escaping and recrossing dynamics. Where the
stationary transmission coefficient is revealed to be larger than the usual
cases which implies less barrier recrossing. And the non-monotonic varying of
it reveals a close dependence to the fractional exponent $\alpha$. In most
cases, the near barrier behavior of the escaping dynamics is equivalent to the
diffusion in the two-dimensional non-Ohmic damping system. | 1502.06184v1 |
2016-02-20 | Synchronization of two couple pendula in absence of escapement | A model of two oscillating pendula placed on a mobile support is studied.
Once an overall scheme of equations, under general assumptions, is formulated
via the Lagrangian equations of motion, the specific case of absence of
escapement is examined. The mechanical models consists of two coupled pendula
both oscillating on a moving board attached to a spring. The final result
performs a selection among the peculiar parameters of the physical process
(lenghts, ratio of masses, friction and damping coefficients, stiffness of the
spring) which provide a tendency to synchronization. | 1602.06382v1 |
2016-06-06 | Weak invariants of time-dependent quantum dissipative systems | The concept of weak invariant is introduced. Then, the weak invariants
associated with time-dependent quantum dissipative systems are discussed in the
context of master equations of the Lindblad type. In particular, with the help
of the su(1,1) Lie-algebraic structure, the weak invariant is explicitly
constructed for the quantum damped harmonic oscillator with the time-dependent
frequency and friction coefficient. This generalizes the Lewis-Riesenfeld
invariant to the case of nonunitary dynamics in the Markovian approximation. | 1606.01767v4 |
2017-06-25 | Influence of qubits' nonradiative decay into a common bath on the transport properties of microwave photons | We consider the influence of nonradiative damping of qubits on the microwave
transport of photons, propagating in an open one-dimensional microstrip line.
Within the framework of the formalism of a non-Hermitian Hamiltonian we
obtained the expressions for the transmission and reflection coefficients for
two qubits which explicitly account for the indirect interaction between qubits
due to nonradiative decay into common bath. It is shown that this interaction
leads to the results that are significantly different from those already known | 1706.08028v2 |
2018-07-17 | Energy decay for evolution equations with delay feedbacks | We study abstract linear and nonlinear evolutionary systems with single or
multiple delay feedbacks, illustrated by several concrete examples. In
particular, we assume that the operator associated with the undelayed part of
the system generates an exponentially stable semigroup and that the delay
damping coefficients are locally integrable in time. A step by step procedure
combined with Gronwall's inequality allows us to prove the existence and
uniqueness of solutions. Furthermore, under appropriate conditions we obtain
exponential decay estimates. | 1807.06445v2 |
2018-08-22 | Weak convergence of Euler-Maruyama's approximation for SDEs under integrability condition | This work establishes the weak convergence of Euler-Maruyama's approximation
for stochastic differential equations (SDEs) with singular drifts under the
integrability condition in lieu of the widely used growth condition. This
method is based on a skillful application of the dimension-free Harnack
inequality. Moreover, when the drifts satisfy certain regularity conditions,
the convergence rate is estimated. This method is also applicable when the
diffusion coefficients are degenerate. A stochastic damping Hamiltonian system
is studied as an illustrative example. | 1808.07250v1 |
2019-11-30 | Robustness Evaluation of the Butterfly Optimization Algorithm on a Control System | In this paper, the Butterfly Optimization Algorithm (BOA) proposed by [1] is
adopted to optimize the parameters of a designed Lead-Lad Controller so as to
obtain a stabilized control system. Numerical analysis was carried out for BOA
on the control problem and the results are compared to those obtained from the
well known Genetic Algorithm (GA) and Differential Evolution (DE) Algorithm.
BOA performs better in terms of eigenvalue analysis but similar to GA and DE in
terms of optimizing the minimum damping coefficient for the control system | 1912.00185v1 |
2019-12-05 | Blow up for small-amplitude semilinear wave equations with mixed nonlinearities on asymptotically Euclidean manifolds | In this work, we investigate the problem of finite time blow up as well as
the upper bound estimates of lifespan for solutions to small-amplitude
semilinear wave equations with mixed nonlinearities $a |u_t|^p+b |u|^q$, posed
on asymptotically Euclidean manifolds, which is related to both the Strauss
conjecture and Glassey conjecture. In some cases, we obtain existence results,
where the lower bound of the lifespan agrees with the upper bound in order. In
addition, our results apply for semilinear damped wave equations, when the
coefficient of the dissipation term is integrable (without sign condition) and
space-independent. | 1912.02561v1 |
2020-03-16 | Extreme Hawking Radiation | Modeling the collapse of an extreme Reissner-Nordstr\"om (ERN) black hole by
solving the corresponding moving mirror model for the trajectory that
asymptotically approaches uniform acceleration, we obtain the non-zero beta
coefficients for all times. Finite energy is emitted, the radiation spectra is
non-thermal (non-steady / not Planck), soft particles characterize the
evaporation, and particle production at ultra-late times is damped.
Entanglement entropy diverges with no Page curve turn-over, demonstrating
non-thermal information loss. The radiation obeys time-reversal symmetry. | 2003.07016v1 |
2021-02-01 | Comment on "Deformed Fokker-Planck equation: inhomogeneous medium with a position-dependent mass" | In a recent paper by B. G. da Costa {\it et al.} [Phys. Rev. E 102,
062105(2020)], the phenomenological Langevin equation and the corresponding
Fokker-Planck equation for an inhomogeneous medium with a position-dependent
particle mass and position-dependent damping coefficient have been studied. The
aim of this comment is to present a microscopic derivation of the Langevin
equation for such a system. It is not equivalent to that in the commented
paper. | 2102.00699v1 |
2021-02-05 | Nonequilibrium statistical mechanics of crystals | The local equilibrium approach previously developed by the Authors [J.
Mabillard and P. Gaspard, J. Stat. Mech. (2020) 103203] for matter with broken
symmetries is applied to crystalline solids. The macroscopic hydrodynamics of
crystals and their local thermodynamic and transport properties are deduced
from the microscopic Hamiltonian dynamics. In particular, the Green-Kubo
formulas are obtained for all the transport coefficients. The eight
hydrodynamic modes and their dispersion relation are studied for general and
cubic crystals. In the same twenty crystallographic classes as those compatible
with piezoelectricity, cross effects coupling transport between linear momentum
and heat or crystalline order are shown to split the degeneracy of damping
rates for modes propagating in opposite generic directions. | 2102.03096v1 |
2021-03-14 | A note on damped wave equations with a nonlinear dissipation in non-cylindrical domains | In this paper, we study the large time behavior of a class of wave equation
with a nonlinear dissipation in non-cylindrical domains. The result we obtained
here relaxes the conditions for the nonlinear term coefficients (in precise,
that is $\beta(t)|u|^\rho u$) in \cite{alb} and \cite{ha} (which require
$\beta(t)$ to be a constant or $\beta(t)$ to be decreasing with time $t$) and
has less restriction for the defined regions. | 2103.09678v2 |
2021-03-28 | Skyrmion elongation, duplication and rotation by spin-transfer torque under spatially varying spin current | The effect of the spatially varying spin current on a skyrmion is numerically
investigated. It is shown that an inhomogeneous current density induces an
elongation of the skyrmion. This elongation can be controlled using current
pulses of different strength and duration. Long current pulses lead to a
splitting that forms two replicas of the initial skyrmion while for short
pulses the elongated skyrmion relaxes back to its initial circular state
through rotation in the MHz-GHz frequency range. The frequency is dependent on
the strength of the damping coefficient. | 2103.15094v1 |
2021-05-13 | Thermal instability in a ferrimagnetic resonator strongly coupled to a loop-gap microwave cavity | We study nonlinear response of a ferrimagnetic sphere resonator (FSR)
strongly coupled to a microwave loop gap resonator (LGR). The measured response
in the regime of weak nonlinearity allows the extraction of the FSR Kerr
coefficient and its cubic damping rate. We find that there is a certain range
of driving parameters in which the system exhibits instability. In that range,
self-sustained modulation of the reflected power off the system is generated.
The instability is attributed to absorption-induced heating of the FSR above
its Curie temperature. | 2105.06102v2 |
2022-01-25 | A fully adaptive explicit stabilized integrator for advection-diffusion-reaction problems | A novel second order family of explicit stabilized Runge-Kutta-Chebyshev
methods for advection-diffusion-reaction equations is introduced. The new
methods outperform existing schemes for relatively high Peclet number due to
their favorable stability properties and explicitly available coefficients. The
construction of the new schemes is based on stabilization using second kind
Chebyshev polynomials first used in the construction of the stochastic
integrator SK-ROCK. An adaptive algorithm to implement the new scheme is
proposed. This algorithm is able to automatically select the suitable step
size, number of stages, and damping parameter at each integration step.
Numerical experiments that illustrate the efficiency of the new algorithm are
presented. | 2201.10206v2 |
2022-11-08 | Current and diffusion of Overdamped Active Brownian Particles in a Ratchet Potential | The transport properties of a spherical active Brownian particle in a
periodic potential under heavy damping are considered. The self-propelled
particle is subjected to the asymmetric potential, detailed balance is lost and
the particles generate a non-zero drift speed.
The average current is calculated and the diffusivity of the particle is
analyzed from the effective diffusion coefficient. For chiral active particles,
the diffusivity decreases with increasing the angular velocity, confining the
particle near the initial position, and reducing the average current. | 2211.04298v1 |
2022-12-24 | Anisotropic acoustics in dipolar Fermi gases | We consider plane wave modes in ultracold, but not quantum degenerate,
dipolar Fermi gases in the hydrodynamic limit. Longitudinal waves present
anisotropies in both the speed of sound and their damping, and experience a
small, undulatory effect in their flow velocity. Two distinct types of shear
waves appear, a ``familiar" one, and another that is accompanied by nontrivial
density and temperature modulations. We propose these shear modes as an
experimental means to measure the viscosity coefficients, including their
anisotropies. | 2212.12659v1 |
2023-02-09 | Two-loop hard thermal loops for any model | Hard thermal loops describe how soft gauge fields are screened and damped in
hot plasmas. As such they are used to calculate transport coefficients,
Sphaleron rates, equations of state, and particle production. However, most
calculations are done using one-loop self-energies. And two-loop contributions
can be large. To that end this paper provides vector two-loop self-energies for
generic models: Any scalar, fermion, or vector representation; and all possible
renormalizable terms. Several examples are given to showcase the results.
Two-loop results for higher-point functions are also given. | 2302.04894v1 |
2024-01-29 | Dissipative effects on the propagation of spin modes | In relativistic hydrodynamics with spin, following de Groot--van Leeuwen--van
Weert's energy-momentum and spin tensor definitions, we analyze the propagation
of spin degrees of freedom. We deduce an analytical formula for spin wave
velocity, finding that it approaches half the speed of light in the
ultra-relativistic limit. Only transverse degrees of freedom propagate, similar
to electromagnetic waves. Additionally, we explore dissipative effects and
determine the damping coefficients for Maxwell-J\"uttner statistics. | 2401.16007v1 |
2024-03-05 | Microscopic parametrization of the near threshold oscillations of the nucleon time-like effective electromagnetic form factors | We present an analysis of the recent near threshold BESIII data for the
nucleon time-like effective form factors. The damped oscillation emerging from
the subtraction of the dipole formula is treated in non-perturbative-QCD,
making use of the light cone distribution amplitudes expansion.
Non-perturbative effects are accounted for by considering Q2-dependent
coefficients in such expansions, whose free parameters are determined by
fitting to the proton and neutron data. Possible implications and future
analysis have been discussed. | 2403.02916v1 |
2017-07-28 | Measurements of the Temperature and E-Mode Polarization of the CMB from 500 Square Degrees of SPTpol Data | We present measurements of the $E$-mode polarization angular auto-power
spectrum ($EE$) and temperature-$E$-mode cross-power spectrum ($TE$) of the
cosmic microwave background (CMB) using 150 GHz data from three seasons of
SPTpol observations. We report the power spectra over the spherical harmonic
multipole range $50 < \ell \leq 8000$, and detect nine acoustic peaks in the
$EE$ spectrum with high signal-to-noise ratio. These measurements are the most
sensitive to date of the $EE$ and $TE$ power spectra at $\ell > 1050$ and $\ell
> 1475$, respectively. The observations cover 500 deg$^2$, a fivefold increase
in area compared to previous SPTpol analyses, which increases our sensitivity
to the photon diffusion damping tail of the CMB power spectra enabling tighter
constraints on \LCDM model extensions. After masking all sources with
unpolarized flux $>50$ mJy we place a 95% confidence upper limit on residual
polarized point-source power of $D_\ell = \ell(\ell+1)C_\ell/2\pi
<0.107\,\mu{\rm K}^2$ at $\ell=3000$, suggesting that the $EE$ damping tail
dominates foregrounds to at least $\ell = 4050$ with modest source masking. We
find that the SPTpol dataset is in mild tension with the $\Lambda CDM$ model
($2.1\,\sigma$), and different data splits prefer parameter values that differ
at the $\sim 1\,\sigma$ level. When fitting SPTpol data at $\ell < 1000$ we
find cosmological parameter constraints consistent with those for $Planck$
temperature. Including SPTpol data at $\ell > 1000$ results in a preference for
a higher value of the expansion rate ($H_0 = 71.3 \pm
2.1\,\mbox{km}\,s^{-1}\mbox{Mpc}^{-1}$ ) and a lower value for present-day
density fluctuations ($\sigma_8 = 0.77 \pm 0.02$). | 1707.09353v3 |
1999-04-13 | Damping of Collective Nuclear Motion and Thermodynamic Properties of Nuclei beyond Mean Field | The dynamical description of correlated nuclear motion is based on a set of
coupled equations of motion for the one-body density matrix $\rho (11';t)$ and
the two-body correlation function $c_2(12,1'2';t)$, which is obtained from the
density-matrix hierarchy beyond conventional mean-field approaches by
truncating 3-body correlations. The resulting equations nonperturbatively
describe particle-particle collisions (short-range correlations) as well as
particle-hole interactions (long-range correlations). Within a basis of
time-dependent Hartree-Fock states these equations of motion are solved for
collective vibrations of $^{40}Ca$ at several finite thermal excitation
energies corresponding to temperatures $T=0-6$ MeV. Transport coefficients for
friction and diffusion are extracted from the explicit solutions in comparison
to the solutions of the associated TDHF, VUU, Vlasov or damped quantum
oscillator equations of motion. We find that the actual magnitude of the
transport coefficients is strongly influenced by partlicle-hole correlations at
low temperature which generate large fluctuations in the nuclear shape degrees
of freedom. Thermodynamically, the specific heat and the entropy of the system
as a function of temperature does not differ much from the mean-field limit
except for a bump in the specific heat around $T\simeq 4$ MeV which we
attribute to the melting of shell effects in the correlated system. | 9904034v1 |
2010-09-30 | An efficient numerical algorithm for the L2 optimal transport problem with applications to image processing | We present a numerical method to solve the optimal transport problem with a
quadratic cost when the source and target measures are periodic probability
densities. This method is based on a numerical resolution of the corresponding
Monge-Amp\`ere equation. We extend the damped Newton algorithm of Loeper and
Rapetti \cite{LR} to the more general case of a non uniform density which is
relevant to the optimal transport problem, and we show that our algorithm
converges for sufficiently large damping coefficients. The main idea consists
of designing an iterative scheme where the fully nonlinear equation is
approximated by a non-constant coefficient linear elliptic PDE that we solve
numerically. We introduce several improvements and some new techniques for the
numerical resolution of the corresponding linear system. Namely, we use a Fast
Fourier Transform (FFT) method by Strain \cite{St}, which allows to increase
the efficiency of our algorithm against the standard finite difference method.
Moreover, we use a fourth order finite difference scheme to approximate the
partial derivatives involved in the nonlinear terms of the Newton algorithm,
which are evaluated once at each iteration; this leads to a significant
improvement of the accuracy of the method, but does not sacrifice its
efficiency. Finally, we present some numerical experiments which demonstrate
the robustness and efficiency of our method on several examples of image
processing, including an application to multiple sclerosis disease detection. | 1009.6039v2 |
2010-10-13 | Global Uniqueness and Stability in Determining the Damping Coefficient of an Inverse Hyperbolic Problem with Non-Homogeneous Neumann B.C. through an Additional Dirichlet Boundary Trace | We consider a second-order hyperbolic equation on an open bounded domain
$\Omega$ in $\mathbb{R}^n$ for $n\geq2$, with $C^2$-boundary
$\Gamma=\pa\Omega=\bar{\Gamma_0\cup\Gamma_1}$,
$\Gamma_0\cap\Gamma_1=\emptyset$, subject to non-homogeneous Neumann boundary
conditions on the entire boundary $\Gamma$. We then study the inverse problem
of determining the interior damping coefficient of the equation by means of an
additional measurement of the Dirichlet boundary trace of the solution, in a
suitable, explicit sub-portion $\Gamma_1$ of the boundary $\Gamma$, and over a
computable time interval $T>0$. Under sharp conditions on the complementary
part $\Gamma_0= \Gamma\backslash\Gamma_1$, $T>0$, and under weak regularity
requirements on the data, we establish the two canonical results in inverse
problems: (i) uniqueness and (ii) stability (at the $L^2$-level). The latter
(ii) is the main result of the paper. Our proof relies on three main
ingredients: (a) sharp Carleman estimates at the $H^1 \times L_2$-level for
second-order hyperbolic equations \cite{L-T-Z.1}; (b) a correspondingly implied
continuous observability inequality at the same energy level \cite{L-T-Z.1};
(c) sharp interior and boundary regularity theory for second-order hyperbolic
equations with Neumann boundary data \cite{L-T.4}, \cite{L-T.5}, \cite{L-T.6},
\cite{Ta.3}. The proof of the linear uniqueness result (Section 4, step 5) also
takes advantage of a convenient tactical route "post-Carleman estimates"
suggested by V.Isakov in \cite[Thm.\,8.2.2, p.\,231]{Is.2}. | 1010.2696v2 |
2013-10-31 | Impurity Screening and Surface Acoustic Wave Absorption in a Dipolar Exciton Condensate at Finite Temperatures | We describe the behavior of a repulsively interacting Bose-Einstein
condensate of indirect dipolar exciton gas in a double quantum well (QW) system
under external static or dynamic electric fields at finite temperatures.
Electrostatic perturbation is considered to be created by an impurity atom or
shot-range defect of QW fluctuation. The screening of this defect potential by
an exciton condensate is studied. We find asymptotic spatial dependence of the
screened potential and analyse its dependence on the temperature and exciton
concentration. It is shown that the asymptotic of the screened potential has a
steep power law dependence in contrast to the well known results of electron
gas. This peculiarity reflects the bosonic nature of the exciton condensate.
The behavior of exciton condensate under external alternative field created by
a surface acoustic wave (SAW) is examined in detail. We focus our attention on
the dependence of SAW absorption coefficient on temperature and exciton
concentration. We found that at zero temperatures Landau damping does not
contribute to the SAW absorption, but the Belyaev mechanism produces unusual
behavior of SAW absorption coefficient on exciton concentration: if the exciton
concentration exceeds some critical value, the SAW absorption vanishes. At
finite temperatures Landau damping comes into action and results in washing out
the sharp absorption behavior. Such unusual SAW absorption properties can be
used for experimental evidence of the exciton condensation. This method is also
applicable to the experimental testing of both dark and bright exciton
condensates, that is impossible to do with the optical luminescence technique. | 1310.8394v1 |
2015-04-05 | Stability of non-autonomous difference equations with applications to transport and wave propagation on networks | In this paper, we address the stability of transport systems and wave
propagation on networks with time-varying parameters. We do so by reformulating
these systems as non-autonomous difference equations and by providing a
suitable representation of their solutions in terms of their initial conditions
and some time-dependent matrix coefficients. This enables us to characterize
the asymptotic behavior of solutions in terms of such coefficients. In the case
of difference equations with arbitrary switching, we obtain a delay-independent
generalization of the well-known criterion for autonomous systems due to Hale
and Silkowski. As a consequence, we show that exponential stability of
transport systems and wave propagation on networks is robust with respect to
variations of the lengths of the edges of the network preserving their rational
dependence structure. This leads to our main result: the wave equation on a
network with arbitrarily switching damping at external vertices is
exponentially stable if and only if the network is a tree and the damping is
bounded away from zero at all external vertices but at most one. | 1504.01116v4 |
2016-11-24 | Zero-Point Energy Leakage in Quantum Thermal Bath Molecular Dynamics Simulations | The quantum thermal bath (QTB) has been presented as analternative to
path-integral-based methods to introduce nuclear quantumeffects in molecular
dynamics simulations. The method has proved to beefficient, yielding accurate
results for various systems. However, the QTBmethod is prone to zero-point
energy leakage (ZPEL) in highly anharmonicsystems. This is a well-known problem
in methods based on classicaltrajectories where part of the energy of the
high-frequency modes istransferred to the low-frequency modes leading to a
wrong energydistribution. In some cases, the ZPEL can have dramatic
consequences onthe properties of the system. Thus, we investigate the ZPEL by
testing theQTB method on selected systems with increasing complexity in order
to studythe conditions and the parameters that influence the leakage. We also
analyze the consequences of the ZPEL on the structuraland vibrational
properties of the system. We find that the leakage is particularly dependent on
the damping coefficient and thatincreasing its value can reduce and, in some
cases, completely remove the ZPEL. When using sufficiently high values for
thedamping coefficient, the expected energy distribution among the vibrational
modes is ensured. In this case, the QTB methodgives very encouraging results.
In particular, the structural properties are well-reproduced. The dynamical
properties should beregarded with caution although valuable information can
still be extracted from the vibrational spectrum, even for large values ofthe
damping term. | 1611.08221v1 |
2016-12-11 | Temperature dependence of the plastic scintillator detector for DAMPE | The Plastic Scintillator Detector (PSD) is one of the main sub-detectors in
the DArk Matter Particle Explorer (DAMPE) project. It will be operated over a
large temperature range from -$10$ to $30^{\circ}$C, so the temperature effect
of the whole detection system should be studied in detail. The temperature
dependence of the PSD system is mainly contributed by the three parts: the
plastic scintillator bar, the photomultiplier tube (PMT), and the Front End
Electronics (FEE). These three parts have been studied in detail and the
contribution of each part has been obtained and discussed. The temperature
coefficient of the PMT is $-0.320(\pm0.033)\%/^{\circ}$C, and the coefficient
of the plastic scintillator bar is $-0.036(\pm0.038)\%/^{\circ}$C. This result
means that after subtracting the FEE pedestal, the variation of the signal
amplitude of the PMT-scintillator system due to temperature mainly comes from
the PMT, and the plastic scintillator bar is not sensitive to temperature over
the operating range. Since the temperature effect cannot be ignored, the
temperature dependence of the whole PSD has been also studied and a correction
has been made to minimize this effect. The correction result shows that the
effect of temperature on the signal amplitude of the PSD system can be
suppressed. | 1612.03398v1 |
2017-05-09 | Recovery of mechanical pressure in a gas of underdamped active dumbbells with Brownian noise | In contrast with a gas at thermodynamic equilibrium, the mean force exerted
on a wall by a gas of active particles usually depends on the confining
potential, thereby preventing a proper definition of mechanical pressure. In
this paper, we investigate numerically the properties of a gas of underdamped
self-propelled dumbbells subject to Brownian noise of increasing intensity, in
order to understand how the notion of pressure is recovered as noise
progressively masks the effects of self-propulsion and the system approaches
thermodynamic equilibrium. The simulations performed for a mobile asymmetric
wall separating two chambers containing an equal number of active dumbbells
highlight some subtle and unexpected properties of the system. First, Brownian
noise of moderate intensity is sufficient to let mean forces equilibrate for
small values of the damping coefficient, while much stronger noise is required
for larger values of the damping coefficient. Moreover, the displacement of the
mean position of the wall upon increase of the intensity of the noise is not
necessarily monotonous and may instead display changes of direction. Both facts
actually reflect the existence of several mechanisms leading to the rupture of
force balance, which tend to displace the mean position of the wall towards
different directions and display different robustness against an increase of
the intensity of Brownian noise. This work therefore provides a clear
illustration of the fact that driving an autonomous system towards (or away
from) thermodynamic equilibrium may not be a straightforward process, but may
instead proceed through the variations of the relative weights of several
conflicting mechanisms. | 1705.03291v1 |
2017-11-27 | Colloidal particle adsorption at water/water interfaces with ultra-low interfacial tension | Using fluorescence microscopy we study the adsorption of single latex
microparticles at a water/water interface between demixing aqueous solutions of
polymers, generally known as a water-in-water emulsion. Similar microparticles
at the interface between molecular liquids have exhibited an extremely slow
relaxation preventing the observation of expected equilibrium states. This
phenomenon has been attributed to "long-lived" metastable states caused by
significant energy barriers $\Delta{\cal F}\sim \gamma A_d\gg k_B T$ induced by
high interfacial tension ($\gamma \sim 10^{-2}$ N/m) and nanoscale surface
defects with characteristic areas $A_d \simeq$ 10--30 nm$^2$. For the studied
water/water interface with ultra-low surface tension ($\gamma \sim 10^{-4}$
N/m) we are able to characterize the entire adsorption process and observe
equilibrium states prescribed by a single equilibrium contact angle independent
of the particle size. Notably, we observe crossovers from fast initial dynamics
to slower kinetic regimes analytically predicted for large surface defects
($A_d \simeq$ 500 nm$^2$). Moreover, particle trajectories reveal a
position-independent damping coefficient that is unexpected given the large
viscosity contrast between phases. These observations are attributed to the
remarkably diffuse nature of the water/water interface and the adsorption and
entanglement of polymer chains in the semidilute solutions. This work offers
some first insights on the adsorption dynamics/kinetics of microparticles at
water/water interfaces in bio-colloidal systems. | 1711.10024v2 |
2018-09-19 | Magnetic non-contact friction from domain wall dynamics actuated by oscillatory mechanical motion | Magnetic friction is a form of non-contact friction arising from the
dissipation of energy in a magnet due to spin reorientation in a magnetic
field. In this paper we study magnetic friction in the context of
micromagnetics, using our recent implementation of smooth spring-driven motion
[Phys. Rev. E. 97, 053301 (2018)] to simulate ring-down measurements in two
setups where domain wall dynamics is induced by mechanical motion. These
include a single thin film with a domain wall in an external field and a setup
mimicking a magnetic cantilever tip and substrate, in which the two magnets
interact through dipolar interactions. We investigate how various micromagnetic
parameters influence the domain wall dynamics actuated by the oscillatory
spring-driven mechanical motion and the resulting damping coefficient. Our
simulations show that the magnitude of magnetic friction can be comparable to
other forms of non-contact friction. For oscillation frequencies lower than
those inducing excitations of the internal structure of the domain walls, the
damping coefficient is found to be independent of frequency. Hence, our results
obtained in the frequency range from 8 to 112 MHz are expected to be relevant
also for typical experimental setups operating in the 100 kHz range. | 1809.07130v2 |
2019-09-29 | Tunable parametric amplification of a graphene nanomechanical resonator in the nonlinear regime | Parametric amplification is widely used in nanoelectro-mechanical systems to
enhance the transduced mechanical signals. Although parametric amplification
has been studied in different mechanical resonator systems, the nonlinear
dynamics involved receives less attention. Taking advantage of the excellent
electrical and mechanical properties of graphene, we demonstrate electrical
tunable parametric amplification using a doubly clamped graphene nanomechanical
resonator. By applying external microwave pumping with twice the resonant
frequency, we investigate parametric amplification in the nonlinear regime. We
experimentally show that the extracted coefficient of the nonlinear Duffing
force {\alpha} and the nonlinear damping coefficient {\eta} vary as a function
of external pumping power, indicating the influence of higher-order
nonlinearity beyond the Duffing (~x^3) and van der Pol (~x^2 dx/dt) types in
our device. Even when the higher-order nonlinearity is involved, parametric
amplification still can be achieved in the nonlinear regime. The parametric
gain increases and shows a tendency of saturation with increasing external
pumping power. Further, the parametric gain can be electrically tuned by the
gate voltage with a maximum gain of 10.2 dB achieved at the gate voltage of 19
V. Our results will benefit studies on nonlinear dynamics, especially nonlinear
damping in graphene nanomechanical resonators that has been debated in the
community over past decade. | 1909.13219v2 |
2019-11-21 | Cosmic ray transport in starburst galaxies | Starburst galaxies are efficient $\gamma$-ray producers, because their high
supernova rates generate copious cosmic ray (CR) protons, and their high gas
densities act as thick targets off which these protons can produce neutral
pions and thence $\gamma$-rays. In this paper we present a first-principles
calculation of the mechanisms by which CRs propagate through such environments,
combining astrochemical models with analysis of turbulence in weakly ionised
plasma. We show that CRs cannot scatter off the strong large-scale turbulence
found in starbursts, because efficient ion-neutral damping prevents such
turbulence from cascading down to the scales of CR gyroradii. Instead, CRs
stream along field lines at a rate determined by the competition between
streaming instability and ion-neutral damping, leading to transport via a
process of field line random walk. This results in an effective diffusion
coefficient that is nearly energy-independent up to CR energies of $\sim 1$
TeV. We apply our computed diffusion coefficient to a simple model of CR escape
and loss, and show that the resulting $\gamma$-ray spectra are in good
agreement with the observed spectra of the starbursts NGC 253, M82, and Arp
220. In particular, our model reproduces these galaxies' relatively hard GeV
$\gamma$-ray spectra and softer TeV spectra without the need for any
fine-tuning of advective escape times or the shape of the CR injection
spectrum. | 1911.09774v2 |
2020-12-01 | Solvable Theory of a Strange Metal at the Breakdown of a Heavy Fermi Liquid | We introduce an effective theory for quantum critical points (QCPs) in heavy
fermion systems, involving a change in carrier density without symmetry
breaking. Our new theory captures a strongly coupled metallic QCP, leading to
robust marginal Fermi liquid transport phenomenology, and associated linear in
temperature ($T$) "strange metal" resistivity, all within a controlled large
$N$ limit. In the parameter regime of strong damping of emergent bosonic
excitations, the QCP also displays a near-universal "Planckian" transport
lifetime, $\tau_{\mathrm{tr}}\sim\hbar/(k_BT)$. This is contrasted with the
conventional so-called "slave boson" theory of the Kondo breakdown, where the
large $N$ limit describes a weak coupling fixed point and non-trivial transport
behavior may only be obtained through uncontrolled $1/N$ corrections. We also
compute the weak-field Hall coefficient within the effective model as the
system is tuned across the transition. We further find that between the two
plateaus, reflecting the different carrier densities in the two Fermi liquid
phases, the Hall coefficient can develop a peak in the critical crossover
regime, like in recent experimental findings, in the parameter regime of weak
boson damping. | 2012.00763v2 |
2021-11-30 | Transient Stability of Low-Inertia Power Systems with Inverter-Based Generation | This study examines the transient stability of low-inertia power systems with
inverter-based generation (IBG) and proposes a sufficient stability criterion.
In low-inertia grids, transient interactions are induced between the
electromagnetic dynamics of the IBG and the electromechanical dynamics of the
synchronous generator (SG) under a fault. For this, a hybrid IBG-SG system is
established and a delta-power-frequency model is developed. Based on this
model, new mechanisms of transient instability different from those of
conventional power systems from the energy perspective are discovered. First,
two loss-of-synchronization (LOS) types are identified based on the relative
power imbalance owing to the mismatch between the inertia of the IBG and SG
under a fault. Second, the relative angle and frequency will jump at the moment
of a fault, thus affecting the system energy. Third, the cosine damping
coefficient induces a positive energy dissipation, thereby contributing to the
system stability. A unified criterion for identifying the two LOS types is
proposed using the energy function method. This criterion is proved to be a
sufficient stability condition for addressing the effects of the jumps and
cosine damping coefficient on the system stability. The new mechanisms and
effectiveness of the criterion are verified based on simulation results. | 2111.15380v3 |
2023-10-12 | An improved dynamical Poisson equation solver for self-gravity | Since self-gravity is crucial in the structure formation of the universe,
many hydrodynamics simulations with the effect of self-gravity have been
conducted. The multigrid method is widely used as a solver for the Poisson
equation of the self-gravity; however, the parallelization efficiency of the
multigrid method becomes worse when we use a massively parallel computer, and
it becomes inefficient with more than $10^4$ cores, even for highly tuned
codes. To perform large-scale parallel simulations ($> 10^4$ cores), developing
a new gravity solver with good parallelization efficiency is beneficial. In
this article, we develop a new self-gravity solver using the telegraph equation
with a damping coefficient, $\kappa$. Parallelization is much easier than the
case of the elliptic Poisson equation since the telegraph equation is a
hyperbolic partial differential equation. We analyze convergence tests of our
telegraph equations solver and determine that the best non-dimensional damping
coefficient of the telegraph equations is $\tilde{\kappa} \simeq 2.5$. We also
show that our method can maintain high parallelization efficiency even for
massively parallel computations due to the hyperbolic nature of the telegraphic
equation by weak-scaling tests. If the time step of the calculation is
determined by heating/cooling or chemical reactions, rather than the CFL
condition, our method may provide the method for calculating self-gravity
faster than other previously known methods such as the fast Fourier transform
and multigrid iteration solvers because gravitational phase velocity determined
by the CFL condition using these timescales is much larger than the fluid
velocity plus sound speed. | 2310.08030v1 |
2002-01-31 | Electron impact excitation of helium-like oxygen up to n = 4 levels including radiation damping | The primary X-ray diagnostic lines in He-like ions are mainly excited by
electron impact from the ground level to the n = 2 levels, but at high
temperatures n > 2 levels are also excited. In order to describe the atomic
processes more completely collision strengths are computed for OVII including
for the first time all of the following: (i) relativistic fine structure, (ii)
levels up to the n = 4, and (iii) radiation damping of autoionizing resonances.
The calculations are carried out using the Breit-Pauli R-matrix (BPRM) method
with a 31-level eigenfunction expansion. Resonance structures in collision
strengths are delineated in detail up to the n = 4 thresholds. For highly
charged He-like ions radiation damping of autoionizing resonances is known to
be significant. We investigate this effect in detail and find that while
resonances are discernibly damped radiatively as the series limit n --> infty
is approached from below, the overall effect on effective cross sections and
rate coefficients is found to be very small. Collision strengths for the
principal lines important in X-ray plasma diagnostics, w,x,y and z,
corresponding to the 4 transitions to the ground level 1s^2 (^1S_0) <-- 1s2p
(^1P^o_1), 1s2p (^3P^o_2), 1s2p (^3P^o_1), 1s2s (^3S_1), are explicitly shown.
It is found that the effective collision strength of the forbidden z-line is up
to a factor of 4 higher at T < 10^6 K than previous values. This is likely to
be of considerable importance in the diagnostics of photoionized astrophysical
plasmas. Significant differences are also found with previous works for several
other transitions. This work is carried out as part of the Iron Project-RmaX
Network. | 0201535v1 |
2015-10-10 | Boundary layers and incompressible Navier-Stokes-Fourier limit of the Boltzmann Equation in Bounded Domain (I) | We establish the incompressible Navier-Stokes-Fourier limit for solutions to
the Boltzmann equation with a general cut-off collision kernel in a bounded
domain. Appropriately scaled families of DiPerna-Lions-(Mischler) renormalized
solutions with Maxwell reflection boundary conditions are shown to have
fluctuations that converge as the Knudsen number goes to zero. Every limit
point is a weak solution to the Navier-Stokes-Fourier system with different
types of boundary conditions depending on the ratio between the accommodation
coefficient and the Knudsen number. The main new result of the paper is that
this convergence is strong in the case of Dirichlet boundary condition. Indeed,
we prove that the acoustic waves are damped immediately, namely they are damped
in a boundary layer in time. This damping is due to the presence of viscous and
kinetic boundary layers in space. As a consequence, we also justify the first
correction to the infinitesimal Maxwellian that one obtains from the
Chapman-Enskog expansion with Navier-Stokes scaling.
This extends the work of Golse and Saint-Raymond \cite{Go-Sai04, Go-Sai05}
and Levermore and Masmoudi \cite{LM} to the case of a bounded domain. The case
of a bounded domain was considered by Masmoudi and Saint-Raymond \cite{M-S} for
linear Stokes-Fourier limit and Saint-Raymond \cite{SRM} for Navier-Stokes
limit for hard potential kernels. Both \cite{M-S} and \cite{SRM} didn't study
the damping of the acoustic waves. This paper extends the result of \cite{M-S}
and \cite{SRM} to the nonlinear case and includes soft potential kernels. More
importantly, for the Dirichlet boundary condition, this work strengthens the
convergence so as to make the boundary layer visible. This answers an open
problem proposed by Ukai \cite{Ukai}. | 1510.02977v1 |
2017-12-05 | Harnessing Electrical Power from Vortex-Induced Vibration of a Circular Cylinder | The generation of electrical power from Vortex-Induced Vibration (VIV) of a
cylinder is investigated numerically. The cylinder is free to oscillate in the
direction transverse to the incoming flow. The cylinder is attached to a magnet
that can move along the axis of a coil made from conducting wire. The magnet
and the coil together constitute a basic electrical generator. When the
cylinder undergoes VIV, the motion of the magnet creates a voltage across the
coil, which is connected to a resistive load. By Lenz's law, induced current in
the coil applies a retarding force to the magnet. Effectively, the electrical
generator applies a damping force on the cylinder with a spatially varying
damping coefficient. For the initial investigation reported here, the Reynolds
number is restricted to Re < 200, so that the flow is laminar and
two-dimensional (2D). The incompressible 2D Navier-Stokes equations are solved
using an extensively validated spectral-element based solver. The effects of
the electromagnetic (EM) damping constant xi_m, coil dimensions (radius a,
length L), and mass ratio on the electrical power extracted are quantified. It
is found that there is an optimal value of xi_m (xi_opt) at which maximum
electrical power is generated. As the radius or length of the coil is
increased, the value of xi_opt is observed to increase. Although the maximum
average power remains the same, a larger coil radius or length results in a
more robust system in the sense that a relatively large amount of power can be
extracted when xi_m is far from xi_opt, unlike the constant damping ratio case.
The average power output is also a function of Reynolds number, primarily
through the increased maximum oscillation amplitude that occurs with increased
Reynolds number at least within the laminar range, although the general
qualitative findings seem likely to carry across to high Reynolds number VIV. | 1712.01588v1 |
2020-02-14 | Testing Physical Models for Cosmic Ray Transport Coefficients on Galactic Scales: Self-Confinement and Extrinsic Turbulence at GeV Energies | The microphysics of ~GeV cosmic ray (CR) transport on galactic scales remain
deeply uncertain, with almost all studies adopting simple prescriptions (e.g.
constant-diffusivity). We explore different physically-motivated, anisotropic,
dynamical CR transport scalings in high-resolution cosmological FIRE
simulations of dwarf and ~$L_{\ast}$ galaxies where scattering rates vary with
local plasma properties motivated by extrinsic turbulence (ET) or
self-confinement (SC) scenarios, with varying assumptions about e.g. turbulent
power spectra on un-resolved scales, Alfven-wave damping, etc. We
self-consistently predict observables including $\gamma$-rays ($L_{\gamma}$),
grammage, residence times, and CR energy densities to constrain the models. We
demonstrate many non-linear dynamical effects (not captured in simpler models)
tend to enhance confinement. For example, in multi-phase media, even allowing
arbitrary fast transport in neutral gas does not substantially reduce CR
residence times (or $L_{\gamma}$), as transport is rate-limited by the ionized
WIM and 'inner CGM' gaseous halo ($10^{4}-10^{6}$ K gas within 10-30 kpc), and
$L_{\gamma}$ can be dominated by trapping in small 'patches.' Most physical ET
models contribute negligible scattering of ~1-10 GeV CRs, but it is crucial to
account for anisotropy and damping (especially of fast modes) or else
scattering rates would violate observations. We show that the most
widely-assumed scalings for SC models produce excessive confinement by factors
>100 in the WIM and inner CGM, where turbulent and Landau damping dominate.
This suggests either a breakdown of quasi-linear theory used to derive the CR
transport parameters in SC, or that other novel damping mechanisms dominate in
intermediate-density ionized gas. | 2002.06211v2 |
2023-12-25 | IMEX-RK methods for Landau-Lifshitz equation with arbitrary damping | Magnetization dynamics in ferromagnetic materials is modeled by the
Landau-Lifshitz (LL) equation, a nonlinear system of partial differential
equations. Among the numerical approaches, semi-implicit schemes are widely
used in the micromagnetics simulation, due to a nice compromise between
accuracy and efficiency. At each time step, only a linear system needs to be
solved and a projection is then applied to preserve the length of
magnetization. However, this linear system contains variable coefficients and a
non-symmetric structure, and thus an efficient linear solver is highly desired.
If the damping parameter becomes large, it has been realized that efficient
solvers are only available to a linear system with constant, symmetric, and
positive definite (SPD) structure. In this work, based on the implicit-explicit
Runge-Kutta (IMEX-RK) time discretization, we introduce an artificial damping
term, which is treated implicitly. The remaining terms are treated explicitly.
This strategy leads to a semi-implicit scheme with the following properties:
(1) only a few linear system with constant and SPD structure needs to be solved
at each time step; (2) it works for the LL equation with arbitrary damping
parameter; (3) high-order accuracy can be obtained with high-order IMEX-RK time
discretization. Numerically, second-order and third-order IMEX-RK methods are
designed in both the 1-D and 3-D domains. A comparison with the backward
differentiation formula scheme is undertaken, in terms of accuracy and
efficiency. The robustness of both numerical methods is tested on the first
benchmark problem from National Institute of Standards and Technology. The
linearized stability estimate and optimal rate convergence analysis are
provided for an alternate IMEX-RK2 numerical scheme as well. | 2312.15654v1 |
2020-07-21 | Random walk of a massive quasiparticle in the phonon gas of an ultralow temperature superfluid | We consider a 3D homogeneous superfluid at low temperature $T$ with 2 types
of excitations, gapless phonons with a linear dispersion relation at low
wavenumber, and gapped quasiparticles with a quadratic dispersion relation
around extrema. We calculate the scattering amplitude of a phonon on a
quasiparticle to leading order in $T$ for all subsonic quasiparticle
velocities, with a $S$-matrix formalism between exact asymptotic states dressed
by virtual phonons. We then characterize the erratic motion of the
quasiparticle in the superfluid due to its unceasing collisions with thermal
phonons through mean force $F(k)$, longitudinal and transverse $k$-dependent
momentum diffusion coefficients, and spatial diffusion coefficient. At the
minimum location $k_0$ of the dispersion relation, where the velocity vanishes,
$F(k)$ varies linearly with velocity with an isotropic friction coefficient; if
$k_0=0$, the momentum diffusion is also isotropic and $F(k_0)=0$; if $k_0>0$,
it is not, and $F(k_0)$ is nonzero but subleading with respect to friction by
one order in $T$. The velocity time correlation function, whose integral is the
spatial diffusion coefficient, decays with the mean velocity damping rate if
$k_0=0$; if $k_0>0$, it has a second exponential component, with an amplitude
and a damping rate lower by a factor $\propto T$ (it is the velocity direction
thermalization rate). We also characterize force and momentum diffusion close
to the stability domain sonic edge. Our general expressions are expected to be
exact to leading order in $T$. We illustrate them in the BCS approximation, for
a fermionic quasiparticle (an unpaired fermion) in a superfluid of spin 1/2
fermions, realisable with cold atoms in flat bottom traps. We also refute the
statement of Lerch, Bartosch and Kopietz (2008), that there would be no
fermionic quasiparticle in such a superfluid. | 2007.10678v2 |
1998-09-15 | Solid friction at high sliding velocities: an explicit 3D dynamical SPH approach | We present realistic 3D numerical simulations of elastic bodies sliding on
top of each other in a regime of velocities ranging from meters to tens of
meters per second using the so-called Smoothed Particle Hydrodynamics (SPH)
method. Our investigations are restricted to regimes of pressure and roughness
where only elastic deformations occur between asperities at the contact surface
between the slider block and the substrate. In this regime, solid friction is
due to the generation of vibrational radiations which are subsequently damped
out. We study periodic commensurate and incommensurate asperities and various
types of disordered surfaces. We report the evidence of a transition from zero
(or non-measurable $\mu < 0.001$) friction to a finite friction as the normal
pressure increases above about $10^6~Pa$. For larger normal pressures (up to
$10^9~Pa$), we find a remarkably universal value for the friction coefficient
$\mu \approx 0.06$, which is independent of the internal dissipation strength
over three order of magnitudes, and independent of the detailled nature of the
slider block-substrate interactions. We find that disorder may either decrease
or increase $\mu$ due to the competition between two effects: disorder detunes
the coherent vibrations of the asperties that occur in the periodic case,
leading to weaker acoustic radiation and thus weaker damping. On the other
hand, large disorder leads to stronger vibration amplitudes at local asperities
and thus stronger damping. Our simulations have confirmed the existence of
jumps over steps or asperities of the slider blocks occurring at the largest
velocities studied ($10~m/s$). These jumps lead to chaotic motions similar to
the bouncing-ball problem. We find a velocity strengthening with a doubling of
the friction coefficient as the velocity increases from $1~m/s$ to $10~m/s$. | 9809213v1 |
2011-11-25 | Application of a damped Locally Optimized Combination of Images method to the spectral characterization of faint companions using an Integral Field Spectrograph | High-contrast imaging instruments are now being equipped with integral field
spectrographs (IFS) to facilitate the detection and characterization of faint
substellar companions. Algorithms currently envisioned to handle IFS data, such
as the Locally Optimized Combination of Images (LOCI) algorithm, rely upon
aggressive point-spread-function (PSF) subtraction, which is ideal for
initially identifying companions but results in significantly biased photometry
and spectroscopy due to unwanted mixing with residual starlight. This
spectro-photometric issue is further complicated by the fact that algorithmic
color response is a function of the companion's spectrum, making it difficult
to calibrate the effects of the reduction without using iterations involving a
series of injected synthetic companions. In this paper, we introduce a new PSF
calibration method, which we call "damped LOCI", that seeks to alleviate these
concerns. By modifying the cost function that determines the weighting
coefficients used to construct PSF reference images, and also forcing those
coefficients to be positive, it is possible to extract companion spectra with a
precision that is set by calibration of the instrument response and
transmission of the atmosphere, and not by post-processing. We demonstrate the
utility of this approach using on-sky data obtained with the Project 1640 IFS
at Palomar. Damped-LOCI does not require any iterations on the underlying
spectral type of the companion, nor does it rely upon priors involving the
chromatic and statistical properties of speckles. It is a general technique
that can readily be applied to other current and planned instruments that
employ IFS's. | 1111.6102v1 |
2024-03-04 | Exploring Standing and Reflected Slow-mode Waves in Flaring Coronal Loops: A Parametric Study Using 2.5D MHD Modeling | Recent observations of reflected propagating and standing slow-mode waves in
hot flaring coronal loops have spurred our investigation into their underlying
excitation and damping mechanisms. To understand these processes, we conduct
2.5D magnetohydrodynamic (MHD) simulations using an arcade active region model
that includes a hot and dense loop. Our simulations allow for in-depth
parametric investigations complementing and expanding our previous 3D MHD
modeling results. We excite these waves in two distinct models as motivated by
observations from the SDO/AIA. Model 1 incorporates classical compressive
viscosity coefficient, while Model 2 adopts a 10-times enhanced viscosity
coefficient. We find that: (1) Our 2.5D MHD simulations reinforce previous
conclusions derived from 1D and 3D MHD models that significantly enhanced
viscosity is crucial for the rapid excitation of standing slow waves with
damping times consistent with observations by Wang et al. (2015). (2) We
uncover that nonlinearity in Model 1 delays the conversion of a reflected
propagating wave into a standing wave. In contrast, Model 2 exhibits a much
weak influence of nonlinearity. (3) Our results reveal that the transverse
temperature structure holds more influence on wave behavior than the density
structure. In Model 1, increased loop temperature contrast significantly
enhances wave trapping within the structure, mitigating the impact of
temperature-dependent viscous damping. Conversely, in Model 2, the impact of
temperature structure on wave behavior weakens in comparison to the effect of
viscosity. (4) Model 1 displays evident nonlinear coupling to the fast and kink
magnetoacoustic waves and pronounced wave leakage into the corona. However,
analyzing three observed wave events by SDO/AIA aligns with Model 2
predictions, providing further support for the substantial viscosity increase. | 2403.02464v1 |
2021-02-09 | Binet's factorial series and extensions to Laplace transforms | We investigate a generalization of Binet's factorial series in the parameter
$\alpha$ \[ \mu\left( z\right) =\sum_{m=1}^{\infty}\frac{b_{m}\left(
\alpha\right) }{\prod_{k=0}^{m-1}(z+\alpha+k)}% \] due to Gilbert, for the
Binet function \[ \mu\left( z\right) =\log\Gamma\left( z\right) -\left(
z-\frac{1} {2}\right) \log z+z-\frac{1}{2}\log\left( 2\pi\right) \] After a
review of the Binet function $\mu\left( z\right) $ and Gilbert's investigations
of $\mu\left( z\right) $, several properties of the Binet polynomials
$b_{m}\left( \alpha\right) $ are presented. We compare Gilbert's generalized
factorial series with Stirling's asymptotic expansion and demonstrate by a
numerical example that, with a same number of terms evaluated, the Gilbert
generalized factorial series with an optimized value of $\alpha$ can beat the
best possible accuracy of Stirling's expansion. Finally, we extend Binet's
method to factorial series of Laplace transforms. | 2102.04891v7 |
2002-06-26 | General Formula for the Thermoelectric Transport Phenomena based on the Fermi Liquid Theory: Thermopower, Nernst Coefficient, and Thermal Conductivity | On the basis of the linear response transport theory, the general expressions
for the thermoelectric transport coefficients, such as thermoelectric power
(S), Nernst coefficient (\nu), and thermal conductivity (\kappa), are derived
by using the Fermi liquid theory. The obtained expression is exact as for the
most singular term in terms of 1/\gamma_k^* (\gamma_k^* being the quasiparticle
damping rate). We utilize the Ward identities for the heat current which is
derived by the local energy conservation law. Based on the derived expressions,
we can calculate various thermoelectric transport coefficients within the
framework of the Baym-Kadanoff type conserving approximation. Thus, the present
expressions are very useful for studying the strongly correlated electrons such
as high-Tc superconductors, organic metals, and heavy Fermion systems, where
the current vertex corrections are expected to play important roles. By using
the derived expression, we calculate the thermal conductivity \kappa in a
free-dispersion model up to the second-order with respect to U. We find that it
is slightly enhanced due to the vertex correction for the heat current,
although the vertex correction for electron current makes the conductivity
(\sigma) of this system diverge, reflecting the absence of the Umklapp process. | 0206501v3 |
2012-12-05 | Stationary two-dimensional turbulence statistics using a Markovian forcing scheme | In this study we investigate the statistics of two-dimensional stationary
turbulence using a Markovian forcing scheme, which correlates the forcing
process in the current time step to the previous time step according to a
defined memory coefficient. In addition to the Markovian forcing mechanism, the
hyperviscous dissipation mechanism for small scales and the Ekman friction type
of linear damping mechanism for the large scales are included in the model. We
examine the effects of various dissipation and forcing parameters on the
turbulence statistics in both wave space and physical space. Our analysis
includes the effects of the effective forcing scale, the bandwidth of the
forcing, the memory correlation coefficient, and the forcing amplitude, along
with the large scale friction and small scale dissipation coefficients. Scaling
exponents of structure functions and energy spectra are calculated, and the
role of the parameters associated with the Markovian forcing is discussed. We
found that the scaling exponents are approximately invariant and show a
universal behavior for the various forms of forcing schemes used. We found,
however, that the final states strongly depend on the large scale friction
mechanism considered. When the large scale friction mechanism is included in
the model with a high friction coefficient, we demonstrate that the behavior is
no longer universal. Our analysis also shows that the second-order vorticity
structure function has an asymptotic scaling exponent for larger dissipation.
Additionally, we confirmed that vorticity behaves as a passive scalar when the
dissipation mechanism becomes less effective. Finally, although turbulence is
not believed to have a separation of time scales in the dynamics of the
velocity field, we conjectured that a separation of time scales exists in the
dynamics of the energy spectrum. | 1212.0916v1 |
2023-06-12 | Dynamics of the $O(4)$ critical point in QCD: critical pions and diffusion in Model G | We present a detailed study of the finite momentum dynamics of the $O(4)$
critical point of QCD, which lies in the dynamic universality class of Model G.
The critical scaling of the model is analyzed in multiple dynamical channels.
For instance, the finite momentum analysis allows us to precisely extract the
pion dispersion curve below the critical point. The pion velocity is in
striking agreement with the predictions relation and static universality. The
pion damping rate and velocity are both consistent with the dynamical critical
exponent $\zeta = 3/2$ of Model G. Similarly, although the critical amplitude
for the diffusion coefficient of the conserved $O(4)$ charges is small, it is
clearly visible both in the restored phase and with finite explicit symmetry
breaking, and its dynamical scaling is again consistent with $\zeta=3/2$. We
determine a new set of universal dynamical critical amplitude ratios relating
the diffusion coefficient to a suitably defined order parameter relaxation
time. We also show that in a finite volume simulation, the chiral condensate
diffuses on the coset manifold in a manner consistent with dynamical scaling,
and with a diffusion coefficient that is determined by the transport
coefficients of hydrodynamic pions. Finally, the amplitude ratios (together
with other non-universal amplitudes also reported here) compile all relevant
information for further studies of Model G both in and out of equilibrium. | 2306.06887v2 |
2024-03-12 | Cosmic Ray Feedback on Bi-stable ISM Turbulence | Despite being energetically important, the effect of cosmic rays on the
dynamics of the interstellar medium (ISM) is assumed to be negligible because
the cosmic ray energy diffusion coefficient parallel to the magnetic field is
relatively large. Using numerical simulations, we explore how variation of the
cosmic ray diffusion coefficient as a function of gas temperature could impact
the dynamics of the ISM. We create a two-zone model of cosmic ray transport,
reflecting the strong damping of the small scale magnetic field fluctuations,
which scatter the cosmic rays, in a gas with low ionization. The variable
diffusion coefficient allows more cold gas to form. However, setting the
diffusion coefficient at a critical value in the warm phase allows the cosmic
rays to adjust the kinetic energy cascade. Specifically, we show the slope of
the cascade changes for motion perpendicular to the mean magnetic field,
whereas kinetic energy parallel to the magnetic field is reduced equally across
inertial scales. We show that cosmic ray energization (or reacceleration) comes
at the expense of total radiated energy generated during the formation of a
cold cloud. We also show that our two-zone model of cosmic ray transport is
capable of matching estimates of the grammage for some paths through the
simulation, but full comparison of the grammage requires simulating turbulence
in a larger volume. | 2403.07976v1 |
2023-10-11 | High-speed photonic crystal modulator with non-volatile memory via structurally-engineered strain concentration in a piezo-MEMS platform | Numerous applications in quantum and classical optics require scalable,
high-speed modulators that cover visible-NIR wavelengths with low footprint,
drive voltage (V) and power dissipation. A critical figure of merit for
electro-optic (EO) modulators is the transmission change per voltage, dT/dV.
Conventional approaches in wave-guided modulators seek to maximize dT/dV by the
selection of a high EO coefficient or a longer light-material interaction, but
are ultimately limited by nonlinear material properties and material losses,
respectively. Optical and RF resonances can improve dT/dV, but introduce added
challenges in terms of speed and spectral tuning, especially for high-Q
photonic cavity resonances. Here, we introduce a cavity-based EO modulator to
solve both trade-offs in a piezo-strained photonic crystal cavity. Our approach
concentrates the displacement of a piezo-electric actuator of length L and a
given piezoelectric coefficient into the PhCC, resulting in dT/dV proportional
to L under fixed material loss. Secondly, we employ a material deformation that
is programmable under a "read-write" protocol with a continuous, repeatable
tuning range of 5 GHz and a maximum non-volatile excursion of 8 GHz. In
telecom-band demonstrations, we measure a fundamental mode linewidth = 5.4 GHz,
with voltage response 177 MHz/V corresponding to 40 GHz for voltage spanning
-120 to 120 V, 3dB-modulation bandwidth of 3.2 MHz broadband DC-AC, and 142 MHz
for resonant operation near 2.8 GHz operation, optical extinction down to
min(log(T)) = -25 dB via Michelson-type interference, and an energy consumption
down to 0.17 nW/GHz. The strain-enhancement methods presented here are
applicable to study and control other strain-sensitive systems. | 2310.07798v2 |
2000-05-29 | Entropy Production in a Persistent Random Walk | We consider a one-dimensional persisent random walk viewed as a deterministic
process with a form of time reversal symmetry. Particle reservoirs placed at
both ends of the system induce a density current which drives the system out of
equilibrium. The phase space distribution is singular in the stationary state
and has a cumulative form expressed in terms of generalized Takagi functions.
The entropy production rate is computed using the coarse-graining formalism of
Gaspard, Gilbert and Dorfman. In the continuum limit, we show that the value of
the entropy production rate is independent of the coarse-graining and agrees
with the phenomenological entropy production rate of irreversible
thermodynamics. | 0005063v1 |
2012-12-13 | A convergent finite element approximation for the quasi-static Maxwell--Landau--Lifshitz--Gilbert equations | We propose a $\theta$-linear scheme for the numerical solution of the
quasi-static Maxwell-Landau-Lifshitz-Gilbert (MLLG) equations. Despite the
strong nonlinearity of the Landau-Lifshitz-Gilbert equation, the proposed
method results in a linear system at each time step. We prove that as the time
and space steps tend to zero (with no further conditions when
$\theta\in(1/2,1]$), the finite element solutions converge weakly to a weak
solution of the MLLG equations. Numerical results are presented to show the
applicability of the method. | 1212.3369v1 |
2013-09-28 | Global Well-Posedness of the Landau-Lifshitz-Gilbert equation for initial data in Morrey space | We establish the global well-posedness of the Landau-Lifshitz-Gilbert
equation in $\mathbb R^n$ for any initial data ${\bf m}_0\in H^1_*(\mathbb
R^n,\mathbb S^2)$ whose gradient belongs to the Morrey space $M^{2,2}(\mathbb
R^n)$ with small norm $\displaystyle\|\nabla {\bf m}_0\|_{M^{2,2}(\mathbb
R^n)}$. The method is based on priori estimates of a dissipative Schr\"odinger
equation of Ginzburg-Landau types obtained from the Landau-Lifshitz-Gilbert
equation by the moving frame technique. | 1309.7426v1 |
2016-10-26 | Iterated Gilbert Mosaics and Poisson Tropical Plane Curves | We propose an iterated version of the Gilbert model, which results in a
sequence of random mosaics of the plane. We prove that under appropriate
scaling, this sequence of mosaics converges to that obtained by a classical
Poisson line process with explicit cylindrical measure. Our model arises from
considerations on tropical plane curves, which are zeros of random tropical
polynomials in two variables. In particular, the iterated Gilbert model
convergence allows one to derive a scaling limit for Poisson tropical plane
curves. Our work raises a number of open questions at the intersection of
stochastic and tropical geometry. | 1610.08533v1 |
2017-05-29 | Strong solvability of regularized stochastic Landau-Lifshitz-Gilbert equation | We examine a stochastic Landau-Lifshitz-Gilbert equation based on an exchange
energy functional containing second-order derivatives of the unknown field.
Such regularizations are featured in advanced micromagnetic models recently
introduced in connection with nanoscale topological solitons. We show that, in
contrast to the classical stochastic Landau-Lifshitz-Gilbert equation based on
the Dirichlet energy alone, the regularized equation is solvable in the
stochastically strong sense. As a consequence it preserves the topology of the
initial data, almost surely. | 1705.10184v1 |
2021-04-03 | Improving the Gilbert-Varshamov Bound by Graph Spectral Method | We improve Gilbert-Varshamov bound by graph spectral method. Gilbert graph
$G_{q,n,d}$ is a graph with all vectors in $\mathbb{F}_q^n$ as vertices where
two vertices are adjacent if their Hamming distance is less than $d$. In this
paper, we calculate the eigenvalues and eigenvectors of $G_{q,n,d}$ using the
properties of Cayley graph. The improved bound is associated with the minimum
eigenvalue of the graph. Finally we give an algorithm to calculate the bound
and linear codes which satisfy the bound. | 2104.01403v3 |
2000-05-10 | Hydrodynamical Survey of First Overtone Cepheids | A hydrodynamical survey of the pulsational properties of first overtone
Galactic Cepheids is presented. The goal of this study is to reproduce their
observed light- and radial velocity curves. The comparison between the models
and the observations is made in a quantitative manner on the level of the
Fourier coefficients. Purely radiative models fail to reproduce the observed
features, but convective models give good agreement.
It is found that the sharp features in the Fourier coefficients are indeed
caused by the P1/P4 = 2 resonance, despite the very large damping of the 4th
overtone. For the adopted mass-luminosity relation the resonance center lies
near a period of 4.2d +/- 0.2 as indicated by the observed radial velocity
data, rather than near 3.2d as the light-curves suggest. | 0005230v2 |
2007-02-09 | Bulk viscosity in kaon condensed matter | We investigate the effect of $K^-$ condensed matter on bulk viscosity and
r-mode instability in neutron stars. The bulk viscosity coefficient due to the
non-leptonic process $n \rightleftharpoons p + K^-$ is studied here. In this
connection, equations of state are constructed within the framework of
relativistic field theoretical models where nucleon-nucleon and kaon-nucleon
interactions are mediated by the exchange of scalar and vector mesons. We find
that the bulk viscosity coefficient due to the non-leptonic weak process in the
condensate is suppressed by several orders of magnitude. Consequently, kaon
bulk viscosity may not damp the r-mode instability in neutron stars. | 0702259v2 |
2005-07-28 | Theory of transverse spin dynamics in a polarized Fermi liquid and an itinerant ferromagnet | The linear equations for transverse spin dynamics in a weakly polarized
degenerate Fermi liquid with arbitrary relationship between temperature and
polarization are derived from Landau-Silin phenomenological kinetic equation
with general form of two-particle collision integral. Unlike the previous
treatment where Fermi velocity and density of states have been taken as
constants independent of polarization here we made derivation free from this
assumption. The obtained equations are applicable for description of spin
dynamics in paramagnetic Fermi liquid with finite polarization as well in an
itinerant ferromagnet. In both cases transverse spin wave frequency is found to
be proportional to the square of the wave vector with complex constant of
proportionality (diffusion coefficient) such that the damping has a finite
value at T=0. The polarization dependence of the diffusion coefficient is found
to be different for a polarized Fermi liquid and for an itinerant ferromagnet.
These conclusions are confirmed by derivation of transverse spin wave
dispersion law in frame of field theoretical methods from the integral equation
for the vortex function. It is shown that similar derivation taking into
consideration the divergency of static transverse susceptibility also leads to
the same attenuating spin wave spectrum. | 0507675v1 |
1993-12-02 | Standard Model CP-violation and Baryon asymmetry | Simply based on CP arguments, we argue against a Standard Model explanation
of the baryon asymmetry of the universe in the presence of a first order phase
transition. A CP-asymmetry is found in the reflection coefficients of quarks
hitting the phase boundary created during the electroweak transition. The
problem is analyzed both in an academic zero temperature case and in the
realistic finite temperature one. The building blocks are similar in both
cases: Kobayashi-Maskawa CP-violation, CP-even phases in the reflection
coefficients of quarks, and physical transitions due to fermion self-energies.
In both cases an effect is present at order $\alpha_W^2$ in rate. A standard
GIM behaviour is found as intuitively expected. In the finite temperature case,
a crucial role is played by the damping rate of quasi-particles in a hot
plasma, which is a relevant scale together with $M_W$ and the temperature. The
effect is many orders of magnitude below what observation requires, and
indicates that non standard physics is indeed needed in the cosmological
scenario. | 9312215v1 |
1996-04-17 | Variation of transport coefficients for average fission dynamics with temperature and shape | We study slow collective motion at finite thermal excitations on the basis of
linear response theory applied to the locally harmonic approximation. The
transport coefficients for average motion, friction \gamma, inertia M and the
local stiffness C are computed along a fission path of Th-224 within a
quasi-static picture. The inverse relaxation time \beta=\gamma/M and the
effective damping rate \eta=\gamma/(2\sqrt{M|C|}) are found to increase with
temperature, but do not change much with the collective variable. The values
found for \eta and \beta as well as their behavior with temperature are in
accord with experimental findings. | 9604024v3 |
2001-03-05 | Nuclear fission: The "onset of dissipation" from a microscopic point of view | Semi-analytical expressions are suggested for the temperature dependence of
those combinations of transport coefficients which govern the fission process.
This is based on experience with numerical calculations within the linear
response approach and the locally harmonic approximation. A reduced version of
the latter is seen to comply with Kramers' simplified picture of fission. It is
argued that for variable inertia his formula has to be generalized, as already
required by the need that for overdamped motion the inertia must not appear at
all. This situation may already occur above T=2 MeV, where the rate is
determined by the Smoluchowski equation. Consequently, comparison with
experimental results do not give information on the effective damping rate, as
often claimed, but on a special combination of local stiffnesses and the
friction coefficient calculated at the barrier. | 0103013v3 |
2008-12-08 | Partial integrability of the anharmonic oscillator | We consider the anharmonic oscillator with an arbitrary-degree anharmonicity,
a damping term and a forcing term, all coefficients being time-dependent: u" +
g_1(x) u' + g_2(x) u + g_3(x) u^n + g_4(x) = 0, n real. Its physical
applications range from the atomic Thomas-Fermi model to Emden gas dynamics
equilibria, the Duffing oscillator and numerous dynamical systems. The present
work is an overview which includes and generalizes all previously known results
of partial integrability of this oscillator. We give the most general two
conditions on the coefficients under which a first integral of a particular
type exists. A natural interpretation is given for the two conditions. We
compare these two conditions with those provided by the Painleve' analysis. | 0812.1451v1 |
2010-11-29 | Viscous lock-exchange in rectangular channels | In a viscous lock-exchange gravity current, which describes the reciprocal
exchange of two fluids of different densities in a horizontal channel, the
front between two Newtonian fluids spreads as the square root of time. The
resulting diffusion coefficient reflects the competition between the buoyancy
driving effect and the viscous damping, and depends on the geometry of the
channel. This lock-exchange diffusion coefficient has already been computed for
a porous medium, a 2D Stokes flow between two parallel horizontal boundaries
separated by a vertical height, H, and, recently, for a cylindrical tube. In
the present paper, we calculate it, analytically, for a rectangular channel
(horizontal thickness b, vertical height, H) of any aspect ratio (H/b) and
compare our results with experiments in horizontal rectangular channels for a
wide range of aspect ratios (1/10-10). We also discuss the 2D Stokes-Darcy
model for flows in Hele-Shaw cells and show that it leads to a rather good
approximation, when an appropriate Brinkman correction is used. | 1011.6262v1 |
2011-02-15 | Decay of energy and suppression of Fermi acceleration in a dissipative driven stadium-like billiard | The behavior of the average energy for an ensemble of non-interacting
particles is studied using scaling arguments in a dissipative time-dependent
stadium-like billiard. The dynamics of the system is described by a four
dimensional nonlinear mapping. The dissipation is introduced via inelastic
collisions between the particles and the moving boundary. For different
combinations of initial velocities and damping coefficients, the long time
dynamics of the particles leads them to reach different states of final energy
and to visit different attractors, which change as the dissipation is varied.
The decay of the average energy of the particles, which is observed for a large
range of restitution coefficients and different initial velocities, is
described using scaling arguments. Since this system exhibits unlimited energy
growth in the absence of dissipation, our results for the dissipative case give
support to the principle that Fermi acceleration seem not to be a structurally
stable phenomenon. | 1102.3139v4 |
2012-05-31 | Spin diffusion of lattice fermions in one dimension | We study long-time spin diffusion of harmonically trapped lattice fermions in
one dimension. Combining thermodynamic Bethe ansatz approach and local density
approximation, we calculate spin current and spin diffusion coefficient driven
by the population imbalance. We find spin current is driven by susceptibility
effects rather than typical diffusion where magnetization would transport from
regions of high magnetization to low. As expected, spin transport is zero
through insulating regions and are only present in the metallic regions. In the
weak coupling limit, the local spin diffusion coefficient shows maxima at all
the insulating regions. Further, we estimate damping rate of diffusion modes in
the weak coupling limit within the lower metallic portion of the cloud. The
predicted spin current pattern can be probed via currently available
experimental techniques. | 1205.7019v2 |
2012-11-15 | A localized orthogonal decomposition method for semi-linear elliptic problems | In this paper we propose and analyze a new Multiscale Method for solving
semi-linear elliptic problems with heterogeneous and highly variable
coefficient functions. For this purpose we construct a generalized finite
element basis that spans a low dimensional multiscale space. The basis is
assembled by performing localized linear fine-scale computations in small
patches that have a diameter of order H |log H| where H is the coarse mesh
size. Without any assumptions on the type of the oscillations in the
coefficients, we give a rigorous proof for a linear convergence of the H1-error
with respect to the coarse mesh size. To solve the arising equations, we
propose an algorithm that is based on a damped Newton scheme in the multiscale
space. | 1211.3551v2 |
2014-11-27 | Transport coefficients in superfluid neutron stars | We study the shear and bulk viscosity coefficients as well as the thermal
conductivity as arising from the collisions among phonons in superfluid neutron
stars. We use effective field theory techniques to extract the allowed phonon
collisional processes, written as a function of the equation of state and the
gap of the system. The shear viscosity due to phonon scattering is compared to
calculations of that coming from electron collisions. We also comment on the
possible consequences for r-mode damping in superfluid neutron stars. Moreover,
we find that phonon collisions give the leading contribution to the bulk
viscosities in the core of the neutron stars. We finally obtain a
temperature-independent thermal conductivity from phonon collisions and compare
it with the electron-muon thermal conductivity in superfluid neutron stars. | 1411.7622v1 |
2015-02-19 | Nonequilibrium inhomogeneous steady state distribution in disordered, mean-field rotator systems | We present a novel method to compute the phase space distribution in the
nonequilibrium stationary state of a wide class of mean-field systems involving
rotators subject to quenched disordered external drive and dissipation. The
method involves a series expansion of the stationary distribution in inverse of
the damping coefficient; the expansion coefficients satisfy recursion relations
whose solution requires computing a sparse matrix, making numerical evaluation
simple and efficient. We illustrate our method for the paradigmatic Kuramoto
model of spontaneous collective synchronization and for its two mode
generalization, in presence of noise and inertia, and demonstrate an excellent
agreement between simulations and theory for the phase space distribution. | 1502.05559v2 |
2016-06-17 | Unveiling the scattering behavior of small spheres | A classical way for exploring the scattering behavior of a small sphere is to
approximate Mie coefficients with a Taylor series expansion. This ansatz
delivered a plethora of insightful results, mostly for small spheres supporting
localized plasmonic resonances. However, many scattering aspects are still
uncharted, especially with regards to magnetic resonances. Here, an alternative
system ansatz is proposed based on the Pad\'e approximants for the Mie
coefficients. The result reveal the existence of a self-regulating radiative
damping mechanism for the first magnetic resonance and new general resonating
aspects for the higher order multipoles. Hence, a systematic way of exploring
the scattering behavior is introduced, sharpening our understanding about the
sphere's scattering behavior and its emergent functionalities. | 1606.05523v4 |
2016-08-08 | Simulations of Energetic Particles Interacting with Nonlinear Anisotropic Dynamical Turbulence | We investigate test-particle diffusion in dynamical turbulence based on a
numerical approach presented before. For the turbulence we employ the nonlinear
anisotropic dynamical turbulence model which takes into account wave
propagation effects as well as damping effects. We compute numerically
diffusion coefficients of energetic particles along and across the mean
magnetic field. We focus on turbulence and particle parameters which should be
relevant for the solar system and compare our findings with different
interplanetary observations. We vary different parameters such as the
dissipation range spectral index, the ratio of the turbulence bendover scales,
and the magnetic field strength in order to explore the relevance of the
different parameters. We show that the bendover scales as well as the magnetic
field ratio have a strong influence on diffusion coefficients whereas the
influence of the dissipation range spectral index is weak. The best agreement
with solar wind observations can be found for equal bendover scales and a
magnetic field ratio of $\delta$B/B0 = 0.75. | 1609.05226v1 |
2017-02-06 | General Scattering Characteristics of Resonant Core-Shell Spheres | This article presents and discusses the general features and aspects
regarding the electromagnetic scattering by a small core-shell plasmonic
sphere. First, the thickness effects on the plasmonic resonances are presented
in the electrostatic (Rayleigh) limit, utilizing the MacLaurin expansion of the
Mie coefficients of hollow scatterers. Several aspects regarding the core
effects are given, illustrating the enabling mechanisms and peculiarities of
its resonant scattering response on it electrostatic limit. The electrodynamic
aspects of the scattering process are revealed through the newly introduced
Pad\'e expansion of the Mie coefficients. Additionally we expose how the core
material affects the dynamic mechanisms, such as the dynamic depolarization and
radiative damping. The described method can be expanded for other type of
resonances and canonical shapes, while the general characteristics presented
here are expected to stimulate further studies regarding the functionalities of
the core-shell scatterers. | 1702.01620v2 |
2017-07-10 | Model Identification and Controller Parameter Optimization for an Autopilot Design for Autonomous Underwater Vehicles | Nowadays an accurate modeling of the system to be controlled is essential for
reliable autopilot. This paper presents a non-linear model of the autonomous
underwater vehicle 'CWolf'. Matrices and the corresponding coefficients
generate a parameterized representation for added mass, Coriolis and
centripetal forces, damping, gravity and buoyancy, using the equations of
motion, for all six degrees of freedom. The determination of actuator behaviour
by surge tests allows the conversion of propeller revolutions to the respective
forces and moments. Based on geometric approximations, the coefficients of the
model can be specified by optimization algorithms in 'open loop' sea trials.
The realistic model is the basis for the subsequent design of the autopilot.
The reference variables used in the four decoupled adaptive PID controllers for
surge, heading, pitch and heave are provided a 'Line of Sight' - guidance
system. A constraint criteria optimization determines the required controller
parameters. The verification by 'closed loop' sea trials ensures the results. | 1707.02767v1 |
2017-08-06 | Dynamics and locomotion of flexible foils in a frictional environment | Over the past few decades, oscillating flexible foils have been used to study
the physics of organismal propulsion in different fluid environments. Here we
extend this work to a study of flexible foils in a frictional environment. When
the foil is oscillated by heaving at one end but not allowed to locomote
freely, the dynamics change from periodic to non-periodic and chaotic as the
heaving amplitude is increased or the bending rigidity is decreased. For
friction coefficients lying in a certain range, the transition passes through a
sequence of $N$-periodic and asymmetric states before reaching chaotic
dynamics. Resonant peaks are damped and shifted by friction and large heaving
amplitudes, leading to bistable states.
When the foil is allowed to locomote freely, the horizontal motion smoothes
the resonant behaviors. For moderate frictional coefficients, steady but slow
locomotion is obtained. For large transverse friction and small tangential
friction corresponding to wheeled snake robots, faster locomotion is obtained.
Traveling wave motions arise spontaneously, and and move with horizontal speed
that scales as transverse friction to the 1/4 power and input power that scales
as transverse friction to the 5/12 power. These scalings are consistent with a
boundary layer form of the solutions near the foil's leading edge. | 1708.01827v1 |
2017-09-19 | On well-posedness of Ericksen-Leslie's hyperbolic incompressible liquid crystal model | We study the Ericksen-Leslie's hyperbolic incompressible liquid crystal
model. Under some constraints on the Leslie coefficients which ensure the basic
energy law is dissipative, we prove the local-in-time existence and uniqueness
of the classical solution to the system with finite initial energy.
Furthermore, with an additional assumption on the coefficients which provides a
damping effect, and the smallness of the initial energy, the unique global
classical solution can be established. | 1709.06370v3 |
2017-09-19 | Higher-order Fermi-liquid corrections for an Anderson impurity away from half-filling | We study the higher-order Fermi-liquid relations of Kondo systems for
arbitrary impurity-electron fillings, extending the many-body quantum
theoretical approach of Yamada-Yosida. It includes partly a microscopic
clarification of the related achievements based on Nozi\`{e}res'
phenomenological description: Filippone, Moca, von Delft, and Mora [Phys.\
Rev.\ B {\bf 95}, 165404 (2017)]. In our formulation, the Fermi-liquid
parameters such as the quasi-particle energy, damping, and transport
coefficients are related to each other through the total vertex
$\Gamma_{\sigma\sigma';\sigma'\sigma} (\omega, \omega'; \omega', \omega)$,
which may be regarded as a generalized Landau quasi-particle interaction. We
obtain exactly this function up to linear order with respect to the frequencies
$\omega$ and $\omega'$ using the anti-symmetry and analytic properties. The
coefficients acquire additional contributions of three-body fluctuations away
from half-filling through the non-linear susceptibilities. We also apply the
formulation to non-equilibrium transport through a quantum dot, and clarify how
the zero-bias peak evolves in a magnetic field. | 1709.06385v2 |
2019-02-06 | Solar energetic particle propagation in wave turbulence and the possibility of wave generation | A complete theory for the complex interaction between solar energetic
particles and the turbulent interplanetary magnetic field remains elusive. In
this work we aim to contribute towards such a theory by modelling the
propagation of solar energetic particle electrons in plasma wave turbulence. We
specify a background turbulence spectrum, as constrained through observations,
calculate the transport coefficients from first principles, and simulate the
propagation of these electrons in the inner heliosphere. We have also, for the
first time, included dynamical effects into the perpendicular diffusion
coefficient. We show that such a "physics-first" approach can lead to
reasonable results, when compared qualitatively to observations. In addition,
we include the effect of wave growth/damping due to streaming electrons and
show that these particles can significantly alter the turbulence levels close
to the Sun for the largest events. | 1902.02038v1 |
2019-02-20 | Influence of Physical Properties of Hockey Stick Blade on Shots | Parameters of a shot of an ice hockey player are mostly determined by the
capabilities of the player and the physical properties of the stick used. To
reach better performance, every hockey player uses also a hockey tape for an
adjustment of the stick blade, that changes both the damping properties as well
as the friction coefficient of the blade surface. To show the unexpected extent
to which these physical properties of the blade affect the shot, we compared
two types of blade cover: traditional tape (rolled onto the blade) and a blade
sticker that adheres to both sides of the hockey stick blade. We analysed
high-speed recordings of two types of shots by 13 players, ranging from
amateurs and junior players to NHL superstars. The two covers differ greatly in
friction coefficient and stiffness, which results in significantly (more than
$99\%$ confidence) greater speed, rotation and energy when using the stiffer
and rougher sticker. | 1903.02635v2 |
2020-07-30 | A diffusive origin for the cosmic-ray spectral hardening reveals signatures of a nearbysource in the leptons and protons data | In this work we aim at reproducing, simultaneously, the spectral feature at
$\sim 10 \, \mathrm{TeV}$ in the cosmic-ray proton spectrum, recently reported
by the DAMPE Collaboration, together with the spectral break at $\sim 1 \,
\mathrm{TeV}$ measured by H.E.S.S. in the lepton spectrum. Those features are
interpreted as signatures of one nearby hidden cosmic-ray accelerator. We show
that this interpretation is consistent with the dipole-anisotropy data as long
as the rigidity scaling of the diffusion coefficient features a hardening at
$\sim 200 \, \mathrm{GV}$, as suggested by the light-nuclei data measured with
high accuracy by the AMS-02 Collaboration. Such rigidity-dependent diffusion
coefficient is applied consistently to the large-scale diffuse cosmic-ray sea
as well as to the particles injected by the nearby source. | 2007.15321v2 |
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