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2010-06-25 | Molecular Dynamics at Low Time Resolution | The internal dynamics of macro-molecular systems is characterized by widely
separated time scales, ranging from fraction of ps to ns. In ordinary molecular
dynamics simulations, the elementary time step dt used to integrate the
equation of motion needs to be chosen much smaller of the shortest time scale,
in order not to cut-off important physical effects. We show that, in systems
obeying the over-damped Langevin Eq., the fast molecular dynamics which occurs
at time scales smaller than dt can be analytically integrated out and gives
raise to a time-dependent correction to the diffusion coefficient, which we
rigorously compute. The resulting effective Langevin equation describes by
construction the same long-time dynamics, but has a lower time resolution
power, hence it can be integrated using larger time steps dt. We illustrate and
validate this method by studying the diffusion of a point-particle in a
one-dimensional toy-model and the denaturation of a protein. | 1006.5045v1 |
2010-07-15 | Universal Quantum Viscosity in a Unitary Fermi Gas | A Fermi gas of atoms with resonant interactions is predicted to obey
universal hydrodynamics, where the shear viscosity and other transport
coefficients are universal functions of the density and temperature. At low
temperatures, the viscosity has a universal quantum scale $\hbar n$ where $n$
is the density, while at high temperatures the natural scale is $p_T^3/\hbar^2$
where $p_T$ is the thermal momentum. We employ breathing mode damping to
measure the shear viscosity at low temperature. At high temperature $T$, we
employ anisotropic expansion of the cloud to find the viscosity, which exhibits
precise $T^{3/2}$ scaling. In both experiments, universal hydrodynamic
equations including friction and heating are used to extract the viscosity. We
estimate the ratio of the shear viscosity to the entropy density and compare to
that of a perfect fluid. | 1007.2625v2 |
2010-07-26 | Phase-Field Reaction-Pathway Kinetics of Martensitic Transformations in a Model Fe3Ni Alloy | A three-dimensional phase-field approach to martensitic transformations that
uses reaction pathways in place of a Landau potential is introduced and applied
to a model of Fe3Ni. Pathway branching involves an unbounded set of variants
through duplication and rotations by the rotation point groups of the austenite
and martensite phases. Path properties, including potential energy and elastic
tensors, are calibrated by molecular statics. Acoustic waves are dealt with via
a splitting technique between elastic and dissipative behaviors in a
large-deformation framework. The sole free parameter of the model is the
damping coefficient associated to transformations, tuned by comparisons with
molecular dynamics simulations. Good quantitative agreement is then obtained
between both methods. | 1007.4515v1 |
2010-08-07 | Fermi acceleration and suppression of Fermi acceleration in a time-dependent Lorentz Gas | We study some dynamical properties of a Lorentz gas. We have considered both
the static and time dependent boundary. For the static case we have shown that
the system has a chaotic component characterized with a positive Lyapunov
Exponent. For the time-dependent perturbation we describe the model using a
four-dimensional nonlinear map. The behaviour of the average velocity is
considered in two situations (i) non-dissipative and (ii) dissipative. Our
results show that the unlimited energy growth is observed for the
non-dissipative case. However, when dissipation, via damping coefficients, is
introduced the senary changes and the unlimited engergy growth is suppressed.
The behaviour of the average velocity is described using scaling approach. | 1008.1344v2 |
2010-11-01 | Terahertz surface plasmons in optically pumped graphene structures | We analyze the surface plasmons (SPs) propagating along the optically pumped
single-graphene layer (SGL) and multiple-graphene layer (MGL) structures. It is
shown that at sufficiently strong optical pumping when the real part of dynamic
conductivity of SGL and MGL structures becomes negative in the terahertz (THz)
range of frequencies due to the interband population inversion, the damping of
the THz SPs can give way to their amplification. This effect can be used in
graphene-based THz lasers and other devices. Due to relatively small SP group
velocity, the absolute value of their absorption coefficient (SP gain) can be
large, substantially exceeding that of the optically pumped structures with the
dielectric waveguide. The comparison of the SGL and MGL structures shows that
to maximize the SP gain the number of GL layers should be properly choosen. | 1011.0238v1 |
2010-11-01 | In-flight dissipation as a mechanism to suppress Fermi acceleration | Some dynamical properties of time-dependent driven elliptical-shaped billiard
are studied. It was shown that for the conservative time-dependent dynamics the
model exhibits the Fermi acceleration [Phys. Rev. Lett. 100, 014103 (2008)]. On
the other hand, it was observed that damping coefficients upon collisions
suppress such phenomenon [Phys. Rev. Lett. 104, 224101 (2010)]. Here, we
consider a dissipative model under the presence of in-flight dissipation due to
a drag force which is assumed to be proportional to the square of the
particle's velocity. Our results reinforce that dissipation leads to a phase
transition from unlimited to limited energy growth. The behaviour of the
average velocity is described using scaling arguments. | 1011.0419v1 |
2010-12-29 | Dependence of boundary lubrication on the misfit angle between the sliding surfaces | Using molecular dynamics based on Langevin equations with a coordinate- and
velocity-dependent damping coefficient, we study the frictional properties of a
thin layer of "soft" lubricant (where the interaction within the lubricant is
weaker than the lubricant-substrate interaction) confined between two solids.
At low driving velocities the system demonstrates stick-slip motion. The
lubricant may or may not be melted during sliding, thus exhibiting either the
"liquid sliding" (LS) or the "layer over layer sliding" (LoLS) regimes. The
LoLS regime mainly operates at low sliding velocities. We investigate the
dependence of friction properties on the misfit angle between the sliding
surfaces and calculate the distribution of static frictional thresholds for a
contact of polycrystalline surfaces. | 1012.5922v1 |
2010-12-31 | Structural optimization of the Ziegler's pendulum: singularities and exact optimal solutions | Structural optimization of non-conservative systems with respect to stability
criteria is a research area with important applications in fluid-structure
interactions, friction-induced instabilities, and civil engineering. In
contrast to optimization of conservative systems where rigorously proven
optimal solutions in buckling problems have been found, for non-conservative
optimization problems only numerically optimized designs were reported. The
proof of optimality in the non-conservative optimization problems is a
mathematical challenge related to multiple eigenvalues, singularities on the
stability domain, and non-convexity of the merit functional. We present a study
of the optimal mass distribution in a classical Ziegler's pendulum where local
and global extrema can be found explicitly. In particular, for the undamped
case, the two maxima of the critical flutter load correspond to a vanishing
mass either in a joint or at the free end of the pendulum; in the minimum, the
ratio of the masses is equal to the ratio of the stiffness coefficients. The
role of the singularities on the stability boundary in the optimization is
highlighted and extension to the damped case as well as to the case of higher
degrees of freedom is discussed. | 1101.0246v1 |
2011-01-24 | Boundary crisis and suppression of Fermi acceleration in a dissipative two dimensional non-integrable time-dependent billiard | Some dynamical properties for a dissipative time-dependent oval-shaped
billiard are studied. The system is described in terms of a four-dimensional
nonlinear mapping. Dissipation is introduced via inelastic collisions of the
particle with the boundary, thus implying that the particle has a fractional
loss of energy upon collision. The dissipation causes profound modifications in
the dynamics of the particle as well as in the phase space of the non
dissipative system. In particular, inelastic collisions can be assumed as an
efficient mechanism to suppress Fermi acceleration of the particle. The
dissipation also creates attractors in the system, including chaotic. We show
that a slightly modification of the intensity of the damping coefficient yields
a drastic and sudden destruction of the chaotic attractor, thus leading the
system to experience a boundary crisis. We have characterized such a boundary
crisis via a collision of the chaotic attractor with its own basin of
attraction and confirmed that inelastic collisions do indeed suppress Fermi
acceleration in two-dimensional time dependent billiards. | 1101.4593v1 |
2011-04-14 | Phenomenological modeling of long range noncontact friction in micro- and nanoresonators | Motivated by the results of an experiment using atomic force microscopy
performed by Gotsmann and Fuchs [Phys. Rev. Lett. {\bf 86}, 2597 (2001)], where
a strong energy loss due to the tip-sample interaction was measured, we
investigate the potential implications of this energy loss channel to the
quality factor of suspended micro- and nanoresonators. Because the observed
tip-sample dissipation remains without a satisfactory theoretical explanation,
two phenomenological models are proposed to generalize the experimental
observations. A minimal phenomenological model simply extends for larger
separations the range of validity of the power law found experimentally for the
damping coefficient. A more elaborate phenomenological model assumes that the
noncontact friction is a consequence of the Casimir force acting between the
closely spaced surfaces. Both models provide quantitative results for the
noncontact friction between any two objects which are then used to estimate the
energy loss for suspended bar micro- and nanoresonators. Its is concluded that
the energy loss due to the unknown mechanism has the potential to seriously
restrict the quality factor of both micro- and nanoresonators. | 1104.2832v2 |
2011-05-03 | Nonequilibrium chiral fluid dynamics including dissipation and noise | We present a consistent theoretical approach for the study of nonequilibrium
effects in chiral fluid dynamics within the framework of the linear sigma model
with constituent quarks. Treating the quarks as an equilibrated heat bath we
use the influence functional formalism to obtain a Langevin equation for the
sigma field. This allows us to calculate the explicit form of the damping
coefficient and the noise correlators. For a selfconsistent derivation of both
the dynamics of the sigma field and the quark fluid we have to employ the 2PI
(two-particle irreducible) effective action formalism. The energy dissipation
from the field to the fluid is treated in the exact formalism of the 2PI
effective action where a conserved energy-momentum tensor can be constructed.
We derive its form and comment on approximations generating additional terms in
the energy-momentum balance of the entire system. | 1105.0622v1 |
2011-05-05 | Long-range three-body atom-diatom potential for doublet Li${}_3$ | An accurate long-range {\em ab initio} potential energy surface has been
calculated for the ground state ${}^2A'$ lithium trimer in the frozen diatom
approximation using all electron RCCSD(T). The {\em ab initio} energies are
corrected for basis set superposition error and extrapolated to the complete
basis limit. Molecular van der Waals dispersion coefficients and three-body
dispersion damping terms for the atom-diatomic dissociation limit are presented
from a linear least squares fit and shown to be an essentially exact
representation of the {\em ab initio} surface at large range. | 1105.1090v2 |
2011-05-12 | Searching for Perfect Fluids: Quantum Viscosity in a Universal Fermi Gas | We measure the shear viscosity in a two-component Fermi gas of atoms, tuned
to a broad s-wave collisional (Feshbach) resonance. At resonance, the atoms
strongly interact and exhibit universal behavior, where the equilibrium
thermodynamic properties and the transport coefficients are universal functions
of the density $n$ and temperature $T$. We present a new calibration of the
temperature as a function of global energy, which is directly measured from the
cloud profiles. Using the calibration, the trap-averaged shear viscosity in
units of $\hbar\,n$ is determined as a function of the reduced temperature at
the trap center, from nearly the ground state to the unitary two-body regime.
Low temperature data is obtained from the damping rate of the radial breathing
mode, while high temperature data is obtained from hydrodynamic expansion
measurements. We also show that the best fit to the high temperature expansion
data is obtained for a vanishing bulk viscosity. The measured trap-averaged
entropy per particle and shear viscosity are used to estimate the ratio of the
shear viscosity to the entropy density, which is compared that conjectured for
a perfect fluid. | 1105.2496v1 |
2011-05-21 | Stochastic population oscillations in spatial predator-prey models | It is well-established that including spatial structure and stochastic noise
in models for predator-prey interactions invalidates the classical
deterministic Lotka-Volterra picture of neutral population cycles. In contrast,
stochastic models yield long-lived, but ultimately decaying erratic population
oscillations, which can be understood through a resonant amplification
mechanism for density fluctuations. In Monte Carlo simulations of spatial
stochastic predator-prey systems, one observes striking complex spatio-temporal
structures. These spreading activity fronts induce persistent correlations
between predators and prey. In the presence of local particle density
restrictions (finite prey carrying capacity), there exists an extinction
threshold for the predator population. The accompanying continuous
non-equilibrium phase transition is governed by the directed-percolation
universality class. We employ field-theoretic methods based on the Doi-Peliti
representation of the master equation for stochastic particle interaction
models to (i) map the ensuing action in the vicinity of the absorbing state
phase transition to Reggeon field theory, and (ii) to quantitatively address
fluctuation-induced renormalizations of the population oscillation frequency,
damping, and diffusion coefficients in the species coexistence phase. | 1105.4242v1 |
2011-06-17 | Sequential vibrational resonance in multistable systems | The phenomenon of sequential vibrational resonance existed in a multistable
system that is excited by both high- and low-frequency signals is reported. By
the method of direct separation of motions, the theoretical investigation on
vibrational resonance is conducted in both cases of underdamped and overdamped,
and the analytical predictions are in good agreement with the numerical
simulations. In view of the theoretical results, the zero-order Bessel function
related to the high-frequency signal is included in the renormalized resonant
frequency, and which leads to the appearance of the sequential vibrational
resonance. In the case of underdamped system with small damping coefficient,
the resonance occurs in a series of discrete parameter regions. The sequential
vibrational resonance is different from the traditional multiple vibrational
resonance, because its appearance is much more regular. The results in this
work may be helpful in the field of signal processing electronics, especially
for dealing with the very-low-frequency signal. | 1106.3431v1 |
2011-10-27 | Existence of global strong solutions for the shallow-water equations with large initial data | This work is devoted to the study of a viscous shallow-water system with
friction and capillarity term. We prove in this paper the existence of global
strong solutions for this system with some choice of large initial data when
$N\geq 2$ in critical spaces for the scaling of the equations. More precisely,
we introduce as in \cite{Hprepa} a new unknown,\textit{a effective velocity}
$v=u+\mu\n\ln h$ ($u$ is the classical velocity and $h$ the depth variation of
the fluid) with $\mu$ the viscosity coefficient which simplifies the system and
allow us to cancel out the coupling between the velocity $u$ and the depth
variation $h$. We obtain then the existence of global strong solution if
$m_{0}=h_{0}v_{0}$ is small in $B^{\N-1}_{2,1}$ and $(h_{0}-1)$ large in
$B^{\N}_{2,1}$. In particular it implies that the classical momentum
$m_{0}^{'}=h_{0} u_{0}$ can be large in $B^{\N-1}_{2,1}$, but small when we
project $m_{0}^{'}$ on the divergence field. These solutions are in some sense
\textit{purely compressible}. We would like to point out that the friction term
term has a fundamental role in our work inasmuch as coupling with the pressure
term it creates a damping effect on the effective velocity. | 1110.6100v1 |
2011-10-28 | Nonlinear instability of solutions in parabolic and hyperbolic diffusion | We consider semilinear evolution equations of the form $a(t)\partial_{tt}u +
b(t) \partial_t u + Lu = f(x,u)$ and $b(t) \partial_t u + Lu = f(x,u),$ with
possibly unbounded $a(t)$ and possibly sign-changing damping coefficient
$b(t)$, and determine precise conditions for which linear instability of the
steady state solutions implies nonlinear instability. More specifically, we
prove that linear instability with an eigenfunction of fixed sign gives rise to
nonlinear instability by either exponential growth or finite-time blow-up. We
then discuss a few examples to which our main theorem is immediately
applicable, including evolution equations with supercritical and exponential
nonlinearities. | 1110.6240v3 |
2011-11-09 | Numerical stability of the Z4c formulation of general relativity | We study numerical stability of different approaches to the discretization of
a conformal decomposition of the Z4 formulation of general relativity. We
demonstrate that in the linear, constant coefficient regime a novel
discretization for tensors is formally numerically stable with a method of
lines time-integrator. We then perform a full set of apples with apples tests
on the non-linear system, and thus present numerical evidence that both the new
and standard discretizations are, in some sense, numerically stable in the
non-linear regime. The results of the Z4c numerical tests are compared with
those of BSSNOK evolutions. We typically do not employ the Z4c constraint
damping scheme and find that in the robust stability and gauge wave tests the
Z4c evolutions result in lower constraint violation at the same resolution as
the BSSNOK evolutions. In the gauge wave tests we find that the Z4c evolutions
maintain the desired convergence factor over many more light-crossing times
than the BSSNOK tests. The difference in the remaining tests is marginal. | 1111.2177v1 |
2012-01-30 | Non-contact Friction and Relaxational Dynamics of Surface Defects | Motion of cantilever near sample surfaces exhibits additional friction even
before two bodies come into mechanical contact. Called non-contact friction
(NCF), this friction is of great practical importance to the ultrasensitive
force detection measurements. Observed large NCF of a micron-scale cantilever
found anomalously large damping that exceeds theoretical predictions by 8-11
orders of magnitude. This finding points to contribution beyond fluctuating
electromagnetic fields within van der Waals approach. Recent experiments
reported by Saitoh et al. (Phys. Rev. Lett. 105, 236103 (2010)) also found
nontrivial distance dependence of NCF. Motivated by these observations, we
propose a mechanism based on the coupling of cantilever to the relaxation
dynamics of surface defects. We assume that the surface defects couple to the
cantilever tip via spin-spin coupling and their spin relaxation dynamics gives
rise to the backaction terms and modifies both the friction coefficient and the
spring constant. We explain the magnitude, as well as the distance dependence
of the friction due to these backaction terms. Reasonable agreement is found
with the experiments. | 1201.6378v1 |
2012-02-09 | Casimir-Polder interaction of fullerene molecules with surfaces | We calculate the thermal Casimir--Polder potential of C60 and C70 fullerene
molecules near gold and silicon nitride surfaces, motivated by their relevance
for molecular matter wave interference experiments. We obtain the coefficients
governing the asymptotic power laws of the interaction in the thermal, retarded
and nonretarded distance regimes and evaluate the full potential numerically.
The interaction is found to be dominated by electronic transitions, and hence
independent of the internal temperature of the molecules. The contributions
from phonon transitions, which are affected by the molecular temperature, give
rise to only a small correction. Moreover, we find that the sizeable molecular
line widths of thermal fullerenes may modify the nonretarded interaction,
depending on the model used. Detailed measurements of the nonretarded potential
of fullerene thus allow one to distinguish between different theories of
incorporating damping. | 1202.1982v1 |
2012-04-30 | New integrability case for the Riccati equation | A new integrability condition of the Riccati equation
$dy/dx=a(x)+b(x)y+c(x)y^{2}$ is presented. By introducing an auxiliary equation
depending on a generating function $f(x)$, the general solution of the Riccati
equation can be obtained if the coefficients $a(x)$, $b(x)$, $c(x)$, and the
function $f(x)$ satisfy a particular constraint. The validity and reliability
of the method are tested by obtaining the general solutions of some Riccati
type differential equations. Some applications of the integrability conditions
for the case of the damped harmonic oscillator with time dependent frequency,
and for solitonic wave, are briefly discussed. | 1204.6546v1 |
2012-06-23 | Superlattice formed by quantum-dot sheets: density of states and IR absorption | Low-energy continuous states of electron in heterosrtucture with periodically
placed quantum-dot sheets are studied theoretically. The Green's function of
electron is governed by the Dyson equation with the self-energy function which
is determined the boundary conditions at quantum-dot sheets with weak damping
in low-energy region. The parameters of superlattice formed by quantum-dot
sheets are determined using of the short-range model of quantum dot. The
density of states and spectral dependencies of the anisotropic absorption
coefficient under mid-IR transitions from doped quantum dots into miniband
states of superlattice strongly depend on dot concentration and on period of
sheets. These dependencies can be used for characterization of the multi-layer
structure and they determine parameters of different optoelectronic devices
exploiting vertical transport of carriers through quantum-dot sheets. | 1206.5418v1 |
2012-07-27 | Spin transition rates in nanowire superlattices: Rashba spin-orbit coupling effects | We investigate the influence of Rashba spin-orbit coupling in a parabolic
nanowire modulated by longitudinal periodic potential. The modulation potential
can be obtained from realistically grown supperlattices (SLs). Our study shows
that the Rashba spin-orbit interaction induces the level crossing point in the
parabolic nanowire SLs. We estimate large anticrossing width (approximately 117
$\mu eV$) between singlet-triplet states. We study the phonon and
electromagnetic field mediated spin transition rates in the parabolic nanowire
SLs. We report that the phonon mediated spin transition rate is several order
of magnitude larger than the electromagnetic field mediated spin transition
rate. Based on the Feynman disentangling technique, we find the exact spin
transition probability. For the case wave vector $k=0$, we report that the
transition probability can be tuned in the form of resonance at fixed time
interval. For the general case ($k\neq 0$), we solve the Riccati equation and
find that the arbitrary values of $k$ induces the damping in the transition
probability. At large value of Rashba spin-orbit coupling coefficients for
($k\neq 0$), spin transition probability freezes. | 1207.6580v2 |
2012-09-24 | Non-stationary Magnetic Microstructures in Stellar Thin Accretion Discs | We examine the morphology of magnetic structures in thin plasma accretion
discs, generalizing a stationary ideal MHD model to the time-dependent
visco-resistive case. Our analysis deals with small scale perturbations to a
central dipole-like magnetic field, which give rise -- as in the ideal case --
to the periodic modulation of magnetic flux surfaces along the radial
direction, corresponding to the formation of a toroidal current channels
sequence. These microstructures suffer an exponential damping in time because
of the non-zero resistivity coefficient, allowing us to define a configuration
lifetime which mainly depends on the midplane temperature and on the length
scale of the structure itself. By means of this lifetime we show that the
microstructures can exist within the inner region of stellar discs in a precise
range of temperatures, and that their duration is consistent with local
transient processes (minutes to hours). | 1209.5227v2 |
2013-03-22 | Scattering Rates For Leptogenesis: Damping of Lepton Flavour Coherence and Production of Singlet Neutrinos | Using the Closed-Time-Path approach, we perform a systematic leading order
calculation of the relaxation rate of flavour correlations of left-handed
Standard Model leptons. This quantity is of pivotal relevance for flavoured
Leptogenesis in the Early Universe, and we find it to be 5.19*10^-3 T at T=10^7
GeV and 4.83*10^-3 T at T=10^13 GeV. These values apply to the Standard Model
with a Higgs-boson mass of 125 GeV. The dependence of the numerical coefficient
on the temperature T is due to the renormalisation group running. The leading
linear and logarithmic dependencies of the flavour relaxation rate on the gauge
and top-quark couplings are extracted, such that the results presented in this
work can readily be applied to extensions of the Standard Model. We also derive
the production rate of light (compared to the temperature) sterile right-handed
neutrinos, a calculation that relies on the same methods. We confirm most
details of earlier results, but find a substantially larger contribution from
the t-channel exchange of fermions. | 1303.5498v1 |
2013-06-18 | Spinor dynamics in an antiferromagnetic spin-1 thermal Bose gas | We present experimental observations of coherent spin-population oscillations
in a cold thermal, Bose gas of spin-1 sodium-23 atoms. The population
oscillations in a multi-spatial-mode thermal gas have the same behavior as
those observed in a single-spatial-mode antiferromagnetic spinor Bose Einstein
condensate. We demonstrate this by showing that the two situations are
described by the same dynamical equations, with a factor of two change in the
spin-dependent interaction coefficient, which results from the change to
particles with distinguishable momentum states in the thermal gas. We compare
this theory to the measured spin population evolution after times up to a few
hundreds of ms, finding quantitative agreement with the amplitude and period.
We also measure the damping time of the oscillations as a function of magnetic
field. | 1306.4255v1 |
2013-06-19 | Soliton dynamics in an extended nonlinear Schrodinger equation with a spatial counterpart of the stimulated Raman scattering | Dynamics of solitons is considered in the framework of the extended nonlinear
Schrodinger equation (NLSE), which is derived from a system of Zakharov's type
for the interaction between high- and low-frequency (HF and LF) waves, in which
the LF field is subject to diffusive damping. The model may apply to the
propagation of HF waves in plasmas. The resulting NLSE includes a
pseudo-stimulated-Raman-scattering (PSRS) term, i.e., a spatial-domain
counterpart of the SRS term which is well known as an ingredient of the
temporal-domain NLSE in optics. Also included is inhomogeneity of the spatial
second-order diffraction (SOD). It is shown that the wavenumber downshift of
solitons, caused by the PSRS, may be compensated by an upshift provided by the
SOD whose coefficient is a linear function of the coordinate. An analytical
solution for solitons is obtained in an approximate form. Analytical and
numerical results agree well, including the predicted balance between the PSRS
and the linearly inhomogeneous SOD. | 1306.4550v1 |
2013-09-18 | On an auto-controlled global existence scheme of the incompressible Navier Stokes equation | We propose a global scheme for the incompressible Navier Stokes equation,
where at each time step a damping potential term is introduced via a time
dilation transformation of the equation itself. This leads a global upper
bounds of the value function and its spatial derivatives. The regularity is
limited only by the regularity of the viscosity coefficient function and by the
regularity and polynomial decay of the data. On an analytical level the scheme
proposed is an alternative to schemes with external control functions. | 1309.4824v11 |
2013-10-21 | Cosmic ray propagation in galactic turbulence | We revisit propagation of galactic cosmic rays (CRs) in light of recent
advances in CR diffusion theory in realistic interstellar turbulence. We use a
tested model of turbulence in which it has been shown that fast modes dominate
scattering of CRs. As a result, propagation becomes inhomogeneous and
environment dependent. By adopting the formalism of the nonlinear theory
developed by Yan & Lazarian, we calculate the diffusion of CRs
self-consistently from first principles. We assume a two- phase model for the
Galaxy to account for different damping mechanisms of the fast modes, and we
find that the energy dependence of the diffusion coefficient is mainly affected
by medium properties. We show that it gives a correct framework to interpret
some of the recent CR puzzles. | 1310.5732v2 |
2013-10-23 | Spectroscopic investigation of local mechanical impedance of living cells | The mechanical properties of PC12 living cells have been studied at the
nanoscale with a Force Feedback Microscope using two experimental approaches.
Firstly, the local mechanical impedance of the cell membrane has been mapped
simultaneously to the cell morphology at constant force. As the force of the
interaction is gradually increased, we observed the appearance of the
sub-membrane cytoskeleton. We shall compare the results obtained with this
method with the measurement of other existing techniques. Secondly, a
spectroscopic investigation has been performed varying the indentation of the
tip in the cell membrane and consequently the force applied on it. In contrast
with conventional dynamic atomic force microscopy techniques, here the small
oscillation amplitude of the tip is not necessarily imposed at the cantilever
first eigenmode. This allows the user to arbitrarily choose the excitation
frequency in developing spectroscopic AFM techniques. The mechanical response
of the PC12 cell membrane is found to be frequency dependent in the 1 kHz - 10
kHz range. The damping coefficient is reproducibly observed to decrease when
the excitation frequency is increased. | 1310.6201v1 |
2013-11-21 | Note on the super inflation in loop quantum cosmology | Phenomenological effect of the super-inflation in loop quantum cosmology
(LQC) is discussed. We investigate the case that the Universe is filled with
the interacting field between massive scalar field and radiation. Considering
the damping coefficient $\Gamma$ as a constant, the changes of the scale factor
during super-inflation with four different initial conditions are discussed,
and we find that the changes of the scale factor depends on the initial values
of energy density of the scalar field and radiation at the bounce point. But no
matter which initial condition is chosen, the radiation always dominated at the
late time. Moreover, we investigate whether the super-inflation can provide
enough e-folding number. For the super-inflation starts from the quantum bounce
point, the initial value of Hubble parameter $H(t_i)\sim0$, then it is possible
to solve the flatness problem and horizon problem. As an example, following the
method of \cite{Amoros-prd} to calculate particle horizon on the condition that
the radiation dominated at bounce point, and we find that the Universe has had
enough time to be homogeneous and isotopic. | 1311.5325v1 |
2013-12-10 | Delaying the waterfall transition in warm hybrid inflation | We analyze the dynamics and observational predictions of supersymmetric
hybrid inflation in the warm regime, where dissipative effects are mediated by
the waterfall fields and their subsequent decay into light degrees of freedom.
This produces a quasi-thermal radiation bath with a slowly-varying temperature
during inflation and further damps the inflaton's motion, thus prolonging
inflation. As in the standard supercooled scenario, inflation ends when the
waterfall fields become tachyonic and can no longer sustain a nearly constant
vacuum energy, but the interaction with the radiation bath makes the waterfall
fields effectively heavier and delays the phase transition to the
supersymmetric minimum. In this work, we analyze for the first time the effects
of finite temperature corrections and SUSY mass splittings on the quantum
effective potential and the resulting dissipation coefficient. We show, in
particular, that dissipation can significantly delay the onset of the tachyonic
instability to yield 50-60 e-folds of inflation and an observationally
consistent primordial spectrum, which is not possible in the standard
supercooled regime when inflation is driven by radiative corrections. | 1312.2961v1 |
2013-12-11 | Modelling of the optical properties of silver with use of six fitting parameters | We propose a realistic model of the optical properties of silver, in which
inter-band transition with a threshold energy of ~ 4 eV is described
phenomenologically by an ensemble of oscillators with same damping constant and
a certain distribution of resonant frequencies in the interband transition
threshold to infinity. The contribution of the conduction electrons in the
dielectric function is determined by the Drude formula. The proposed model
actually contains the features of both the Drude-Lorentz model (Raki\'c et al.
1998) and Tauc-Lorentz model (Jian-Hong Qiu et al. 2005). However, unlike these
works proposed model contains only six fitting parameters, with the square root
of the mean square deviation of the absorption coefficient and refractive index
of silver from the experimental values in the range of 0.6 nm - 6.0 nm being of
the order of 0.05. | 1312.3100v1 |
2014-02-17 | Spatio-temporal dynamics of an active, polar, viscoelastic ring | Constitutive equations for a one-dimensional, active, polar, viscoelastic
liquid are derived by treating the strain field as a slow hydrodynamic
variable. Taking into account the couplings between strain and polarity allowed
by symmetry, the hydrodynamics of an active, polar, viscoelastic body include
an evolution equation for the polarity field that generalizes the damped
Kuramoto-Sivashinsky equation. Beyond thresholds of the active coupling
coefficients between the polarity and the stress or the strain rate,
bifurcations of the homogeneous state lead first to stationary waves, then to
propagating waves of the strain, stress and polarity fields. I argue that these
results are relevant to living matter, and may explain rotating actomyosin
rings in cells and mechanical waves in epithelial cell monolayers. | 1402.3987v1 |
2014-05-14 | An exactly solvable $\mathcal{PT}$-symmetric dimer from a Hamiltonian system of nonlinear oscillators with gain and loss | We show that a pair of coupled nonlinear oscillators, of which one oscillator
has positive and the other one negative damping of equal rate, can form a
Hamiltonian system. Small-amplitude oscillations in this system are governed by
a $\mathcal{PT}$-symmetric nonlinear Schr\"odinger dimer with linear and cubic
coupling. The dimer also represents a Hamiltonian system and is found to be
exactly solvable in elementary functions. We show that the nonlinearity softens
the $\mathcal{PT}$-symmetry breaking transition in the nonlinearly-coupled
dimer: stable periodic and quasiperiodic states with large enough amplitudes
persist for an arbitrarily large value of the gain-loss coefficient. | 1405.3588v2 |
2014-07-02 | Basins of attraction in forced systems with time-varying dissipation | We consider dissipative periodically forced systems and investigate cases in
which having information as to how the system behaves for constant dissipation
may be used when dissipation varies in time before settling at a constant final
value. First, we consider situations where one is interested in the basins of
attraction for damping coefficients varying linearly between two given values
over many different time intervals: we outline a method to reduce the
computation time required to estimate numerically the relative areas of the
basins and discuss its range of applicability. Second, we observe that
sometimes very slight changes in the time interval may produce abrupt large
variations in the relative areas of the basins of attraction of the surviving
attractors: we show how comparing the contracted phase space at a time after
the final value of dissipation has been reached with the basins of attraction
corresponding to that value of constant dissipation can explain the presence of
such variations. Both procedures are illustrated by application to a pendulum
with periodically oscillating support. | 1407.0556v1 |
2014-09-24 | Scaling laws for the bifurcation-escape rate in a nanomechanical resonator | We report on experimental and theoretical studies of the fluctuation-induced
escape time from a metastable state of a nanomechanical Duffing resonator in
cryogenic environment. By tuning in situ the non-linear coefficient $\gamma$ we
could explore a wide range of the parameter space around the bifurcation point,
where the metastable state becomes unstable. We measured in a relaxation
process the distribution of the escape times. We have been able to verify its
exponential distribution and extract the escape rate $\Gamma$. We investigated
the scaling of $\Gamma$ with respect to the distance to the bifurcation point
and $\gamma$, finding an unprecedented quantitative agreement with the
theoretical description of the stochastic problem. Simple power scaling laws
turn out to hold in a large region of the parameter's space, as anticipated by
recent theoretical predictions. These unique findings, implemented in a model
dynamical system, are relevant to all systems experiencing under-damped
saddle-node bifurcation. | 1409.6971v3 |
2014-09-30 | Numerical Simulation of Two Dimentional sine-Gordon Solitons Using the Modified Cubic B-Spline Differential Quadrature Method | In this article, a numerical simulation of two dimensional nonlinear
sine-Gordon equation with Neumann boundary condition is obtained by using a
composite scheme referred to as a modified cubic B spline differential
quadrature method. The modified cubic B-spline serves as a basis function in
the differential quadrature method to compute the weighting coefficients. Thus,
the sine-Gordon equation is converted into a system of second order ordinary
differential equations (ODEs). We solve the resulting system of ODEs by an
optimal five stage and fourth-order strong stability preserving Runge Kutta
scheme. Both damped and undamped cases are considered for the numerical
simulation with Josephson current density function with value minus one. The
computed results are found to be in good agreement with the exact solutions and
other numerical results available in literature. | 1410.0058v1 |
2014-11-12 | Semi-active Suspension Control using Modern Methodology: Comprehensive Comparison Study | Semi-active suspensions have drawn particular attention due to their superior
performance over the other types of suspensions. One of their advantages is
that their damping coefficient can be controlled without the need for any
external source of power. In this study, three control approaches are
implemented on a quarter-car model using MATLAB/Simulink. The investigated
control methodologies are Acceleration Driven Damper, Power Driven Damper, and
H_infinity Robust Control. The three controllers are known as comfort-oriented
approaches. H_infinity Robust Control is an advanced method that guarantees
transient performance and rejects external disturbances. It is shown that
H_infinity with the proposed modification, has the best performance although
its relatively high cost of computation could be potentially considered as a
drawback. | 1411.3305v1 |
2015-03-19 | Quasinormal modes of test fields around regular black holes | We study scalar, electromagnetic and gravitational test fields in the
Hayward, Bardeen and Ay\'on-Beato-Garc\'ia regular black hole spacetimes and
demonstrate that the test fields are stable in all these spacetimes. Using the
sixth order WKB approximation of the linear "axial" perturbative scheme, we
determine dependence of the quasinormal mode (QNM) frequencies on the
characteristic parameters of the test fields and the spacetime charge
parameters of the regular black holes. We give also the greybody factors,
namely the transmission and reflection coefficients of scattered scalar,
electromagnetic and gravitational waves. We show that damping of the QNMs in
regular black hole spacetimes is suppressed in comparison to the case of
Schwarzschild black holes, and increasing charge parameter of the regular black
holes increases reflection and decreases transmission factor of incident waves
for each of the test fields. | 1503.05737v2 |
2015-04-03 | Role of attractive forces in determining the equilibrium structure and dynamics of simple liquids | Molecular Dynamics simulations of a Lennard-Jones system with different range
of attraction show that the attractive forces modify the radial distribution of
the particles. For condensed liquids only, the forces within the the first
coordination shell (FCS) are important, but for gases and moderate condensed
fluids, even the attractive forces outside the FCS play a role. The changes in
the distribution caused by neglecting the attractive forces, lead to a too high
pressure. The weak long-range attractions damp the dynamics and the diffusion
of the particles in gas-, super critical fluid- and in liquid states. The
values of self-diffusion coefficients (SDC) agree qualitatively with a modified
Cohen-Turnbull model. The SDC-s along the critical isotherm show no anomaly at
the critical point in agreement with experimental data. | 1504.00809v1 |
2015-06-08 | Another derivation of generalized Langevin equations | The formal derivation of Langevin equations (and, equivalently Fokker-Planck
equations) with projection operator techniques of Mori, Zwanzig, Kawasaki and
others apparently not has widely found its way into textbooks. It has been
reproduced dozens of times on the fly with many references to the literature
and without adding much substantially new. Here we follow the tradition, but
strive to produce a self-contained text. Furthermore, we address questions that
naturally arise in the derivation. Among other things the meaning of the
divergence of the Poisson brackets is explained, and the role of nonlinear
damping coefficients is clarified. The derivation relies on classical
mechanics, and encompasses everything one can construct from point particles
and potentials: solids, liquids, liquid crystals, conductors, polymers, systems
with spin-like degrees of freedom ... Einstein relations and Onsager
reciprocity relations come for free. | 1506.02650v2 |
2015-06-09 | Sensitivity analysis for shape optimization of a focusing acoustic lens in lithotripsy | We are interested in shape sensitivity analysis for an optimization problem
arising in medical applications of high intensity focused ultrasound. The goal
is to find the optimal shape of a focusing acoustic lens so that the desired
acoustic pressure at a kidney stone is achieved. Coupling of the silicone
acoustic lens and nonlinearly acoustic fluid region is modeled by the
Westervelt equation with nonlinear strong damping and piecewise constant
coefficients. We follow the variational approach to calculating the shape
derivative of the cost functional which does not require computing the shape
derivative of the state variable; however assumptions of certain spatial
regularity of the primal and the adjoint state are needed to obtain the
derivative, in particular for its strong form according to the
Delfour-Hadamard-Zol\' esio Structure Theorem. | 1506.02781v1 |
2015-06-26 | Dimer with gain and loss: Integrability and $\mathcal{PT}$-symmetry restoration | A $\mathcal{PT}$-symmetric nonlinear Schr\"odinger dimer is a two-site
discrete nonlinear Schr\"odinger equation with one site losing and the other
one gaining energy at the same rate. In this paper, two four-parameter families
of cubic $\mathcal{PT}$-symmetric dimers are constructed as gain-loss
extensions of their conservative, Hamiltonian, counterparts. We prove that all
these damped-driven equations define completely integrable Hamiltonian systems.
The second aim of our study is to identify nonlinearities that give rise to the
spontaneous $\mathcal{PT}$-symmetry restoration. When the symmetry of the
underlying linear dimer is broken and an unstable small perturbation starts to
grow, the nonlinear coupling of the required type diverts progressively large
amounts of energy from the gaining to the losing site. As a result, the
exponential growth is saturated and all trajectories remain trapped in a finite
part of the phase space regardless of the value of the gain-loss coefficient. | 1506.08229v2 |
2015-07-09 | Background field method in the gradient flow | In perturbative consideration of the Yang--Mills gradient flow, it is useful
to introduce a gauge non-covariant term ("gauge-fixing term") to the flow
equation that gives rise to a Gaussian damping factor also for gauge degrees of
freedom. In the present paper, we consider a modified form of the gauge-fixing
term that manifestly preserves covariance under the background gauge
transformation. It is shown that our gauge-fixing term does not affect
gauge-invariant quantities as the conventional gauge-fixing term. The
formulation thus allows a background gauge covariant perturbative expansion of
the flow equation that provides, in particular, a very efficient computational
method of expansion coefficients in the small flow time expansion. The
formulation can be generalized to systems containing fermions. | 1507.02360v3 |
2015-07-16 | Fast Convergence of an Inertial Gradient-like System with Vanishing Viscosity | In a real Hilbert space $\mathcal H$, we study the fast convergence
properties as $t \to + \infty$ of the trajectories of the second-order
evolution equation $$ \ddot{x}(t) + \frac{\alpha}{t} \dot{x}(t) + \nabla \Phi
(x(t)) = 0, $$ where $\nabla \Phi$ is the gradient of a convex continuously
differentiable function $\Phi : \mathcal H \rightarrow \mathbb R$, and $\alpha$
is a positive parameter. In this inertial system, the viscous damping
coefficient $\frac{\alpha}{t}$ vanishes asymptotically in a moderate way. For
$\alpha > 3$, we show that any trajectory converges weakly to a minimizer of
$\Phi$, just assuming that the set of minimizers is nonempty. The strong
convergence is established in various practical situations. These results
complement the $\mathcal O(t^{-2})$ rate of convergence for the values obtained
by Su, Boyd and Cand\`es. Time discretization of this system, and some of its
variants, provides new fast converging algorithms, expanding the field of rapid
methods for structured convex minimization introduced by Nesterov, and further
developed by Beck and Teboulle. This study also complements recent advances due
to Chambolle and Dossal. | 1507.04782v1 |
2015-07-29 | Gravitational, shear and matter waves in Kantowski-Sachs cosmologies | A general treatment of vorticity-free, perfect fluid perturbations of
Kantowski-Sachs models with a positive cosmological constant are considered
within the framework of the 1+1+2 covariant decomposition of spacetime. The
dynamics is encompassed in six evolution equations for six harmonic
coefficients, describing gravito-magnetic, kinematic and matter perturbations,
while a set of algebraic expressions determine the rest of the variables. The
six equations further decouple into a set of four equations sourced by the
perfect fluid, representing forced oscillations and two uncoupled damped
oscillator equations.
The two gravitational degrees of freedom are represented by pairs of
gravito-magnetic perturbations. In contrast with the Friedmann case one of them
is coupled to the matter density perturbations, becoming decoupled only in the
geometrical optics limit. In this approximation, the even and odd tensorial
perturbations of the Weyl tensor evolve as gravitational waves on the
anisotropic Kantowski-Sachs background, while the modes describing the shear
and the matter density gradient are out of phase dephased by $\pi /2$ and share
the same speed of sound. | 1507.08300v2 |
2015-08-14 | Reactive collisions of polar molecules in quasi-two-dimensional traps | We investigate collisions of polar molecules in quasi-2D traps in the
presence of an external electric field perpendicular to the collision plane. We
use the quantum-defect model characterized by two dimensionless parameters: $y$
and $s$. The first of them is related to the probability of the reaction at
short distances, whereas the latter one defines the wave function phase at
short distances. For $y$ close to unity we obtain universal collision rates
determined by the quantum reflection process from the long-range part of the
interaction potential that depends only on the van der Waals coefficient,
dipole-dipole interaction and the trap frequency. For small short-range
reaction probabilities collision rates are highly nonuniversal and trap induced
shape resonances are visible. For high dipole moments we observe the damping of
reactive collisions, which can stabilize the ultracold gas of polar molecules.
The calculations were performed with help of multichannel wave funcion
propagation by imposing short-range boundary condition derived from the
quantum-defect model. | 1508.03443v1 |
2015-11-06 | Curvature and torsion effects in the spin-current driven domain wall motion | The domain wall motion along a helix-shaped nanowire is studied for the case
of spin-current driving via Bazaliy-Zhang-Li mechanism. The analysis is based
on collective variable approach. Two new effects are ascertained: (i) the
curvature results in appearance of the Walker limit for a uniaxial wire, (ii)
the torsion results in effective shift of the nonadiabatic spin torque
parameter $\beta$. The latter effect changes considerably the domain wall
velocity and can result in negative domain wall mobility. This effect can be
also used for an experimental determination of the nonadiabatic parameter
$\beta$ and damping coefficient $\alpha$. | 1511.02193v1 |
2015-11-15 | Fluid friction and wall viscosity of the 1D blood flow model | We study the behavior of the pulse waves of water into a flexible tube for
application to blood flow simulations. In pulse waves both fluid friction and
wall viscosity are damping factors, and difficult to evaluate separately. In
this paper, the coefficients of fluid friction and wall viscosity are estimated
by fitting a nonlinear 1D flow model to experimental data. In the experimental
setup, a distensible tube is connected to a piston pump at one end and closed
at another end. The pressure and wall displacements are measured
simultaneously. A good agreement between model predictions and experiments was
achieved. For amplitude decrease, the effect of wall viscosity on the pulse
wave has been shown as important as that of fluid viscosity. | 1511.04729v1 |
2016-01-10 | Classic Calculations of Static Properties of the Nucleons reexamined | Classic calculations of the magnetic moments mu_p and mu_n of the nucleons
using the traditional exponential kernel show instability with respect to
variations of the Borel mass as well as arbitrariness with respect to the
choice of the onset of perturbative QCD. The use of a polynomial kernel, the
coefficients of which are determined by the masses of the nucleon resonances
stabilizes the calculation and provides much better damping of the unknown
contribution of the nucleon continuum. The method is also applied to the
evaluation of the coupling gA of proton to the axial current and to the strong
part of the neutron-proton mass difference Delta M_np. All these quantities
depend sensitively on the value of the 4-quark condensate < 0 | qqqq | 0 > and
the value < 0 | qqqq | 0 > ~ 1.5< 0 | qq | 0 >^2 reproduces the experimental
results. | 1601.02247v2 |
2016-01-28 | Dynamic system classifier | Stochastic differential equations describe well many physical, biological and
sociological systems, despite the simplification often made in their
derivation. Here the usage of simple stochastic differential equations to
characterize and classify complex dynamical systems is proposed within a
Bayesian framework. To this end, we develop a dynamic system classifier (DSC).
The DSC first abstracts training data of a system in terms of time dependent
coefficients of the descriptive stochastic differential equation. Thereby the
DSC identifies unique correlation structures within the training data. For
definiteness we restrict the presentation of DSC to oscillation processes with
a time dependent frequency {\omega}(t) and damping factor {\gamma}(t). Although
real systems might be more complex, this simple oscillator captures many
characteristic features. The {\omega} and {\gamma} timelines represent the
abstract system characterization and permit the construction of efficient
signal classifiers. Numerical experiments show that such classifiers perform
well even in the low signal-to-noise regime. | 1601.07901v2 |
2016-05-11 | Electromagnetic properties of a double layer graphene system with electron-hole pairing | We study electromagnetic properties of a double layer graphene system in
which electrons from one layer are coupled with holes from the other layer. The
gauge invariant linear response functions are obtained. The frequency
dependences of the transmission, reflection and absorption coefficients are
computed. We predict a peak in the reflection and absorption at the frequency
equals to the gap in the quasiparticle spectrum. It is shown that the
electron-hole pairing results in an essential modification of the spectrum of
surface TM plasmons. We find that the optical TM mode splits into a low
frequency undamped branch and a high frequency damped branch. At zero
temperature the lower branch disappears. It is established that the pairing
does not influence the acoustic TM mode. It is also shown that the pairing
opens the frequency window in the subgap range for the surface TE wave. | 1605.03307v1 |
2016-08-02 | Nonperturbative quasi-classical theory of the nonlinear electrodynamic response of graphene | An electromagnetic response of a single graphene layer to a uniform,
arbitrarily strong electric field $E(t)$ is calculated by solving the kinetic
Boltzmann equation within the relaxation-time approximation. The theory is
valid at low (microwave, terahertz, infrared) frequencies satisfying the
condition $\hbar\omega\lesssim 2E_F$, where $E_F$ is the Fermi energy. We
investigate the saturable absorption and higher harmonics generation effects,
as well as the transmission, reflection and absorption of radiation incident on
the graphene layer, as a function of the frequency and power of the incident
radiation and of the ratio of the radiative to scattering damping rates. We
show that the optical bistability effect, predicted in Phys. Rev. B 90, 125425
(2014) on the basis of a perturbative approach, disappears when the problem is
solved exactly. We show that, under the action of a high-power radiation
($\gtrsim 100$ kW/cm$^2$) both the reflection and absorption coefficients
strongly decrease and the layer becomes transparent. | 1608.00877v2 |
2016-09-23 | Underdamped scaled Brownian motion: (non-)existence of the overdamped limit in anomalous diffusion | It is quite generally assumed that the overdamped Langevin equation provides
a quantitative description of the dynamics of a classical Brownian particle in
the long time limit. We establish and investigate a paradigm anomalous
diffusion process governed by an underdamped Langevin equation with an explicit
time dependence of the system temperature and thus the diffusion and damping
coefficients. We show that for this underdamped scaled Brownian motion (UDSBM)
the overdamped limit fails to describe the long time behaviour of the system
and may practically even not exist at all for a certain range of the parameter
values. Thus persistent inertial effects play a non-negligible role even at
significantly long times. From this study a general questions on the
applicability of the overdamped limit to describe the long time motion of an
anomalously diffusing particle arises, with profound consequences for the
relevance of overdamped anomalous diffusion models. We elucidate our results in
view of analytical and simulations results for the anomalous diffusion of
particles in free cooling granular gases. | 1609.07250v1 |
2016-11-25 | Random and quasi-coherent aspects in particle motion and their effects on transport and turbulence evolution | The quasi-coherent effects in two-dimensional incompressible turbulence are
analyzed starting from the test particle trajectories. They can acquire
coherent aspects when the stochastic potential has slow time variation and the
motion is not strongly perturbed. The trajectories are, in these conditions,
random sequences of large jumps and trapping or eddying events. Trapping
determines quasi-coherent trajectory structures, which have a micro-confinement
effect that is reflected in the transport coefficients. They determine
non-Gaussian statistics and flows associated to an average velocity. Trajectory
structures also influence the test modes on turbulent plasmas. Nonlinear
damping and generation of zonal flow modes is found in drift turbulence in
uniform magnetic field. The coupling of test particle and test mode studies
permitted to evaluate the self-consistent evolution of the drift turbulence in
an iterated approach. The results show an important nonlinear effect of ion
diffusion, which can prevent the transition to the nonlinear regime at small
drive of the instability. At larger drive, quasi-coherent trajectory structures
appear and they have complex effects on turbulence. | 1611.08521v1 |
2017-01-07 | A quantitative description of Nernst effect in high-temperature superconductors | A quantitative vortex-fluid model for flux-flow resistivity $\rho$ and Nernst
signal $e_N$ in high-temperature superconductors (HTSC) is proposed. Two kinds
of vortices, magnetic and thermal, are considered, and the damping viscosity
$\eta$ is modeled by extending the Bardeen-Stephen model to include the
contributions of flux pinning at low temperature and in weak magnetic fields,
and vortex-vortex collisions in strong magnetic fields. Remarkably accurate
descriptions for both Nernst signal of six samples and flux flow resistivity
are achieved over a wide range of temperature $T$ and magnetic field $B$. A
discrepancy of three orders of magnitude between data and Anderson's model of
Nernst signal is pointed out and revised using experimental values of $\eta$
from magnetoresistance. Furthermore, a two-step procedure is developed to
reliably extract, from the Nernst signal, a set of physical parameters
characterizing the vortex dynamics, which yields predictions of local
superfluid density $n_s$, the Kosterlitz coefficient $b$ of thermal vortices,
and upper critical field and temperature. Application of the model and
systematic measurement of relevant physical quantities from Nernst signal in
other HTSC samples are discussed. | 1701.01832v1 |
2017-01-23 | Understanding stability diagram of perpendicular magnetic tunnel junctions | Perpendicular magnetic tunnel junctions (MTJ) with a bottom pinned reference
layer and a composite free layer (FL) are investigated. Different thicknesses
of the FL were tested to obtain an optimal balance between tunneling
magnetoresistance (TMR) ratio and perpendicular magnetic anisotropy. After
annealing at 400 $^\circ$C, the TMR ratio for 1.5 nm thick CoFeB sublayer
reached 180 % at room temperature and 280 % at 20 K with an MgO tunnel barrier
thickness corresponding to the resistance area product RA = 10
Ohm$\mathrm{\mu}$m$^2$. The voltage vs. magnetic field stability diagrams
measured in pillar-shaped MTJs with 130 nm diameter indicate the competition
between spin transfer torque (STT), voltage controlled magnetic anisotropy
(VCMA) and temperature effects in the switching process. An extended stability
phase diagram model that takes into account all three parameters and the
effective damping measured independently using broadband ferromagnetic
resonance technique enabled the determination of both STT and VCMA coefficients
that are responsible for the FL magnetization switching. | 1701.06411v1 |
2017-01-27 | Evaluating the Friction of Rotary Joints in Molecular Machines | A computationally-efficient method for evaluating friction in molecular
rotary bearings is presented. This method estimates drag from fluctuations in
molecular dynamics simulations via the fluctuation-dissipation theorem. This is
effective even for simulation times short compared to a bearing's energy
damping time and for rotation speeds comparable to or below typical thermal
values. We apply this method to two molecular rotary bearings of similar size
at 300K: previously studied nested (9,9)/(14,14) double-walled carbon nanotubes
and a hypothetical rotary joint consisting of single acetylenic bonds in a
rigid diamondoid housing. The acetylenic joint has a rotational frictional drag
coefficient of $2 \times 10^{-35}\,\mbox{kg m${}^2$/s}$. The friction for the
nested nanotubes is 120 times larger, comparable to values reported by previous
studies. This fluctuation-based method could evaluate dissipation in a variety
of molecular systems with similarly rigid and symmetric bearings. | 1701.08202v2 |
2017-04-01 | Homogenization for a Class of Generalized Langevin Equations with an Application to Thermophoresis | We study a class of systems whose dynamics are described by generalized
Langevin equations with state-dependent coefficients. We find that in the
limit, in which all the characteristic time scales vanish at the same rate, the
position variable of the system converges to a homogenized process, described
by an equation containing additional drift terms induced by the noise. The
convergence results are obtained using the main result in
\cite{hottovy2015smoluchowski}, whose version is proven here under a weaker
spectral assumption on the damping matrix. We apply our results to study
thermophoresis of a Brownian particle in a non-equilibrium heat bath. | 1704.00134v2 |
2017-04-03 | Parametrization of the Tkatchenko-Scheffler dispersion correction scheme for popular exchange-correlation density functionals: effect on the description of liquid water | We present a list of optimized damping range parameters $s_R$ to be used with
the Tkatchenko-Scheffler van der Waals dispersion-correction scheme [Phys. Rev.
Lett. 102, 073005 (2009)]. The optimal $s_R$ are obtained for seven popular
generalized-gradient approximation exchange-correlation density functionals:
PBE, RPBE, revPBE, PBEsol, BLYP, AM05 and PW91. The optimization is carried out
in the standard way by minimizing the mean absolute error of the S22 test set,
where the reference interaction energies are taken from coupled-cluster
calculations. With the optimized range parameters, we assess the impact of van
der Waals corrections on the ability of these functionals to accurately
describe structural and thermodynamic properties of liquid water: radial
distribution functions, self-diffusion coefficients and standard molar
entropies. | 1704.00761v2 |
2017-04-13 | Stochastic Gradient Descent as Approximate Bayesian Inference | Stochastic Gradient Descent with a constant learning rate (constant SGD)
simulates a Markov chain with a stationary distribution. With this perspective,
we derive several new results. (1) We show that constant SGD can be used as an
approximate Bayesian posterior inference algorithm. Specifically, we show how
to adjust the tuning parameters of constant SGD to best match the stationary
distribution to a posterior, minimizing the Kullback-Leibler divergence between
these two distributions. (2) We demonstrate that constant SGD gives rise to a
new variational EM algorithm that optimizes hyperparameters in complex
probabilistic models. (3) We also propose SGD with momentum for sampling and
show how to adjust the damping coefficient accordingly. (4) We analyze MCMC
algorithms. For Langevin Dynamics and Stochastic Gradient Fisher Scoring, we
quantify the approximation errors due to finite learning rates. Finally (5), we
use the stochastic process perspective to give a short proof of why Polyak
averaging is optimal. Based on this idea, we propose a scalable approximate
MCMC algorithm, the Averaged Stochastic Gradient Sampler. | 1704.04289v2 |
2017-05-19 | Phenomenology of light- and strange-quark simultaneous production at high energies | This letter presents an extension of EPL116(2017)62001 to light- and
strange-quark nonequilibrium chemical phase-space occupancy factors
($\gamma_{q,s}$). The resulting damped trigonometric functionalities relating
$\gamma_{q,s}$ to the nucleon-nucleon center-of-mass energies $(\sqrt{s_{NN}})$
looks very similar except different coefficients. The phenomenology of the
resulting $\gamma_{q,s}(\sqrt{s_{NN}})$ describes a rapid decrease at
$\sqrt{s_{NN}}\lesssim7~$GeV followed by a faster increase up to $\sim20~$GeV.
Then, both $\gamma_{q,s}$ become nonsensitive to $\sqrt{s_{NN}}$. Although
these differ from $\gamma_{s}(\sqrt{s_{NN}})$ obtained at
$\gamma_q(\sqrt{s_{NN}})=1$, various particle ratios including
$\mathrm{K}^+/\pi^+$, $\mathrm{K}^-/\pi^-$, $\mathrm{\Lambda}/\pi^-$,
$\bar{\mathrm{\Lambda}}/\pi^-$, $\mathrm{\Xi}^+/\pi^+$, and
$\mathrm{\Omega}/\pi^-$, can well be reproduced, as well. We conclude that
$\gamma_{q,s}(\sqrt{s_{NN}})$ should be instead determined from fits of various
particle yields and ratios but not merely from fits to the particle ratio
$\mathrm{K}^+/\pi^+$. | 1705.06961v1 |
2017-11-08 | An Extended Kalman Filter Enhanced Hilbert-Huang Transform in Oscillation Detection | Hilbert-Huang transform (HHT) has drawn great attention in power system
analysis due to its capability to deal with dynamic signal and provide
instantaneous characteristics such as frequency, damping, and amplitudes.
However, its shortcomings, including mode mixing and end effects, are as
significant as its advantages. A preliminary result of an extended Kalman
filter (EKF) method to enhance HHT and hopefully to overcome these
disadvantages is presented in this paper. The proposal first removes dynamic DC
components in signals using empirical mode decomposition. Then an EKF model is
applied to extract instant coefficients. Numerical results using simulated and
real-world low-frequency oscillation data suggest the proposal can help to
overcome the mode mixing and end effects with a properly chosen number of
modes. | 1711.04644v1 |
2017-11-15 | Probing Split-Ring Resonator Permeabilities with Loop-Gap Resonators | A method is proposed to experimentally determine the effective complex
permeability of split-ring resonator (SRR) arrays used in the design of
metamaterials at microwave frequencies. We analyze the microwave response of a
loop-gap resonator (LGR) whose bore has been partially loaded with one or more
SRRs. Our analysis reveals that the resonance frequency, magnetic plasma
frequency, and damping constant of the effective permeability of the SRR array
can be extracted from fits to the reflection coefficient (S11) of an
inductively-coupled LGR. We propose LGR designs that would allow both a
one-dimensional array of SRRs and small three-dimensional arrays of SRRs to be
characterized. Finally, we demonstrate the method using a toroidal LGR loaded
with a single extended SRR of length z. | 1711.05819v1 |
2017-12-01 | Some Optimizations on Detecting Gravitational Wave Using Convolutional Neural Network | This work investigates the problem of detecting gravitational wave (GW)
events based on simulated damped sinusoid signals contaminated with white
Gaussian noise. It is treated as a classification problem with one class for
the interesting events. The proposed scheme consists of the following two
successive steps: decomposing the data using a wavelet packet, representing the
GW signal and noise using the derived decomposition coefficients; and
determining the existence of any GW event using a convolutional neural network
(CNN) with a logistic regression output layer. The characteristics of this work
is its comprehensive investigations on CNN structure, detection window width,
data resolution, wavelet packet decomposition and detection window overlap
scheme. Extensive simulation experiments show excellent performances for
reliable detection of signals with a range of GW model parameters and
signal-to-noise ratios. While we use a simple waveform model in this study, we
expect the method to be particularly valuable when the potential GW shapes are
too complex to be characterized with a template bank. | 1712.00356v2 |
2018-02-12 | Dynamics of a magnetic skyrmionium driven by spin waves | The magnetic skyrmionium is a skyrmion-like structure but carries a zero net
skyrmion number, which can be used as a building block for non-volatile
information processing devices. Here, we study the dynamics of a magnetic
skyrmionium driven by propagating spin waves. It is found that the skyrmionium
can be effectively driven into motion by spin waves showing tiny skyrmion Hall
effect, of which the mobility is much better than that of the skyrmion at the
same condition. We also show that the skyrmionium mobility depends on the
nanotrack width and damping coefficient, and can be controlled by an external
out-of-plane magnetic field. Besides, we demonstrate the skyrmionium motion
driven by spin waves is inertial. Our results indicate that the skyrmionium is
a promising building block for building spin-wave spintronic devices. | 1802.03868v2 |
2018-02-16 | Articulatory information and Multiview Features for Large Vocabulary Continuous Speech Recognition | This paper explores the use of multi-view features and their discriminative
transforms in a convolutional deep neural network (CNN) architecture for a
continuous large vocabulary speech recognition task. Mel-filterbank energies
and perceptually motivated forced damped oscillator coefficient (DOC) features
are used after feature-space maximum-likelihood linear regression (fMLLR)
transforms, which are combined and fed as a multi-view feature to a single CNN
acoustic model. Use of multi-view feature representation demonstrated
significant reduction in word error rates (WERs) compared to the use of
individual features by themselves. In addition, when articulatory information
was used as an additional input to a fused deep neural network (DNN) and CNN
acoustic model, it was found to demonstrate further reduction in WER for the
Switchboard subset and the CallHome subset (containing partly non-native
accented speech) of the NIST 2000 conversational telephone speech test set,
reducing the error rate by 12% relative to the baseline in both cases. This
work shows that multi-view features in association with articulatory
information can improve speech recognition robustness to spontaneous and
non-native speech. | 1802.05853v1 |
2018-02-26 | A magnetic resonance in high-frequency viscosity of two-dimensional electrons | Two-dimensional (2D) electrons in high-quality nanostructures at low
temperatures can form a viscous fluid. We develop a theory of high-frequency
magnetotransport in such fluid. The time dispersion of viscosity should be
taken into account at the frequencies about and above the rate of
electron-electron collisions. We show that the shear viscosity coefficients as
functions of magnetic field and frequency have the only resonance at the
frequency equal to the doubled cyclotron frequency. We demonstrate that such
resonance manifests itself in the plasmon damping. Apparently, the predicted
resonance is also responsible for the peaks and features in photoresistance and
photovoltage, recently observed on the best-quality GaAs quantum wells. The
last fact should considered as an important evidence of forming a viscous
electron fluid in such structures. | 1802.09179v3 |
2018-03-14 | Langevin equation in systems with also negative temperatures | We discuss how to derive a Langevin equation (LE) in non standard systems,
i.e. when the kinetic part of the Hamiltonian is not the usual quadratic
function. This generalization allows to consider also cases with negative
absolute temperature. We first give some phenomenological arguments suggesting
the shape of the viscous drift, replacing the usual linear viscous damping, and
its relation with the diffusion coefficient modulating the white noise term. As
a second step, we implement a procedure to reconstruct the drift and the
diffusion term of the LE from the time-series of the momentum of a heavy
particle embedded in a large Hamiltonian system. The results of our
reconstruction are in good agreement with the phenomenological arguments.
Applying the method to systems with negative temperature, we can observe that
also in this case there is a suitable Langevin equation, obtained with a
precise protocol, able to reproduce in a proper way the statistical features of
the slow variables. In other words, even in this context, systems with negative
temperature do not show any pathology. | 1803.05317v2 |
2018-04-07 | Chemotaxis effect vs logistic damping on boundedness in the 2-D minimal Keller-Segel model | In this paper, we study chemotaxis effect vs logistic dampening on
boundedness for the two-dimensional minimal Keller-Segel model with logistic
source in a 2-D smooth and bounded domain. It is well-known that this model
allows only for global and uniform-in-time bounded solutions for any
chemotactic strength and logistic dampening. Here, we carefully employ a simple
and new method to regain its boundedness and, with particular attention to how
boundedness depends qualitatively on the coefficient of chemotactic strength
and logistic dampening rate. Up to a scaling constant depending only on initial
data and the domain, we provide explicit upper bounds for the the solution
components of the corresponding initial-boundary value problem. This
qualitative boundedness results seems to be the first result in the regard. | 1804.02501v1 |
2018-05-07 | Lewis-Riesenfeld quantization and SU(1,1) coherent states for 2D damped harmonic oscillator | In this paper we study a two-dimensional [2D] rotationally symmetric harmonic
oscillator with time-dependent frictional force. At the classical level, we
solve the equations of motion for a particular case of the time-dependent
coefficient of friction. At the quantum level, we use the Lewis-Riesenfeld
procedure of invariants to construct exact solutions for the corresponding
time-dependent Schr\"{o}dinger equations. The eigenfunctions obtained are in
terms of the generalized Laguerre polynomials. By mean of the solutions we
verify a generalization version of the Heisenberg's uncertainty relation and
derive the generators of the $su(1,1)$ Lie algebra. Based on these generators,
we construct the coherent states $\grave{\textrm{a}}$ la Barut-Girardello and
$\grave{\textrm{a}}$ la Perelomov and respectively study their properties. | 1805.02484v2 |
2018-05-16 | Numerical analysis of the weakly nonlinear Boussinesq system with a freely moving body on the bottom | In this study, the numerical analysis of a specific fluid-solid interaction
problem is detailed. The weakly nonlinear Boussinesq system is considered with
the addition of a solid object lying on the flat bottom, allowed to move
horizontally under the pressure forces created by the waves. We present an
accurate finite difference scheme for this physical model, finely tuned to
preserve important features of the original coupled system: nonlinear effects
for the waves, energy dissipation due to the frictional movement of the solid.
The moving bottom case is compared with a system where the same object is fixed
to the bottom in order to observe the qualitative and quantitative differences
in wave transformation. In particular a loss of wave amplitude is observed. The
influence of the friction on the whole system is also measured, indicating
differences for small and large coefficients of friction. Overall, hydrodynamic
damping effects reminiscent to the dead-water phenomenon can be established. | 1805.07216v1 |
2018-05-21 | Squeezed in three dimensions, moving in two: Hydrodynamic theory of 3D incompressible easy-plane polar active fluids | We study the hydrodynamic behavior of three dimensional (3D) incompressible
collections of self-propelled entities in contact with a momentum sink in a
state with non-zero average velocity, hereafter called 3D easy-plane
incompressible polar active fluids. We show that the hydrodynamic model for
this system belongs to the same universality class as that of an equilibrium
system, namely a special 3D anisotropic magnet. The latter can be further
mapped onto yet another equilibrium system, a DNA-lipid mixture in the sliding
columnar phase. Through these connections we find a divergent renormalization
of the damping coefficients in 3D easy-plane incompressible polar active
fluids, and obtain their equal-time velocity correlation functions. | 1805.07930v1 |
2018-06-12 | Complex magnetism and non-Fermi liquid state in the vicinity of the quantum critical point in the CeCo$_{1-x}$Fe$_x$Ge$_3$ series | We report extensive studies on the CeCo$_{1-x}$Fe$_{x}$Ge$_3$ alloys, which
show quantum critical point (QCP) due to damping the antiferromagnetic order in
CeCoGe$_3$ down to 0 K by doping with the paramagnetic CeFeGe$_3$ compound. The
presence of QCP is confirmed by detecting the non-Fermi liquid behavior (NFL)
using a wide range of the experimental methods: magnetic susceptibility,
specific heat, electrical resistivity, magnetoresistance, and thermoelectric
power. In the case of the thermoelectric power we find a clear enhancement of
the Seebeck coefficient for $x$ around 0.6, i.e. in the neighborhood of QCP.
Finally, the different complementary studies enabled construction of the
complex magnetic phase diagram for the CeCo$_{1-x}$Fe$_{x}$Ge$_3$ system,
including the energy scale imposed by the crystal electric field splitting of
the Ce ground state. | 1806.04656v1 |
2018-08-21 | Position Sensor-less and Adaptive Speed Design for Controlling Brush-less DC Motor Drives | This paper proposes a method for direct torque control of Brushless DC (BLDC)
motors. Evaluating the trapezium of back-EMF is needed, and is done via a
sliding mode observer employing just one measurement of stator current. The
effect of the proposed estimation algorithm is reducing the impact of switching
noise and consequently eliminating the required filter. Furthermore, to
overcome the uncertainties related to BLDC motors, Recursive Least Square (RLS)
is regarded as a real-time estimator of inertia and viscous damping
coefficients of the BLDC motor. By substituting the estimated load torque in
mechanical dynamic equations, the rotor speed can be calculated. Also, to
increase the robustness and decrease the rise time of the system, Modified
Model Reference Adaptive System (MMRAS) is applied in order to design a new
speed controller. Simulation results confirm the validity of this recommended
method. | 1808.06768v1 |
2018-09-28 | Unifying averaged dynamics of the Fokker-Planck equation for Paul traps | Collective dynamics of a collisional plasma in a Paul trap is governed by the
Fokker-Planck equation, which is usually assumed to lead to a unique asymptotic
time-periodic solution irrespective of the initial plasma distribution. This
uniqueness is, however, hard to prove in general due to analytical
difficulties. For the case of small damping and diffusion coefficients, we
apply averaging theory to a special solution to this problem, and show that the
averaged dynamics can be represented by a remarkably simple 2D phase portrait,
which is independent of the applied rf field amplitude. In particular, in the
2D phase portrait, we have two regions of initial conditions. From one region,
all solutions are unbounded. From the other region, all solutions go to a
stable fixed point, which represents a unique time-periodic solution of the
plasma distribution function, and the boundary between these two is a parabola. | 1809.10952v2 |
2018-10-29 | Three Mechanisms of Weight Decay Regularization | Weight decay is one of the standard tricks in the neural network toolbox, but
the reasons for its regularization effect are poorly understood, and recent
results have cast doubt on the traditional interpretation in terms of $L_2$
regularization. Literal weight decay has been shown to outperform $L_2$
regularization for optimizers for which they differ. We empirically investigate
weight decay for three optimization algorithms (SGD, Adam, and K-FAC) and a
variety of network architectures. We identify three distinct mechanisms by
which weight decay exerts a regularization effect, depending on the particular
optimization algorithm and architecture: (1) increasing the effective learning
rate, (2) approximately regularizing the input-output Jacobian norm, and (3)
reducing the effective damping coefficient for second-order optimization. Our
results provide insight into how to improve the regularization of neural
networks. | 1810.12281v1 |
2018-11-05 | Logarithmic estimates for continuity equations | The aim of this short note is twofold. First, we give a sketch of the proof
of a recent result proved by the authors in the paper [Colombo, Crippa, and
Spirito, Calc. Var. Partial Differential Equations 2015] concerning existence
and uniqueness of renormalized solutions of continuity equations with unbounded
damping coefficient. Second, we show how the ideas in [Colombo, Crippa, and
Spirito, Calc. Var. Partial Differential Equations 2015] can be used to provide
an alternative proof of the result in [Clop, Jiang, Mateu, and Orobitg, Calc.
Var. Partial Differential Equations 2016], [Desjardins, Comm. Partial Diff. Eq.
1996], and [Mucha, J. Differential Equations 2010] where the usual requirement
of boundedness of the divergence of the vector field has been relaxed to
various settings of exponentially integrable functions. | 1811.02463v1 |
2018-12-20 | Edge modes and Fabry-Perot Plasmonic Resonances in anomalous-Hall Thin Films | We study plasmon propagation on a metallic two-dimensional surface partially
coated with a thin film of anomalous-Hall material. The resulting three
regions, separated by two sharp interfaces, are characterised by different Hall
conductivities but identical normal conductivities. A single bound mode is
found, which can localise to either interface and has an asymmetric potential
profile across the region. For propagating modes, we calculate the reflection
and transmission coefficients through the magnetic region. We find Airy
transmission patterns with sharp maxima and minima as a function of the plasmon
incidence angle. The system therefore behaves as a high-quality filter. | 1812.08798v2 |
2019-01-01 | Gravitational Waves in the Presence of Viscosity | We analyze gravitational waves propagating in an isotropic cosmic fluid
endowed with a bulk viscosity $\zeta$ and a shear viscosity $\eta$, assuming
these coefficients to vary with fluid density $\rho$ as $\rho^\lambda$, with
$\lambda=1/2$ favored by experimental evidence. We give the general governing
equation for the gravitational waves, and focus thereafter on two examples. The
first concerns waves in the very late universe, close to the Big Rip, where the
fate of the comic fluid is dependent highly on the values of the parameters.
Our second example considers the very early universe, the lepton era; the
motivation for this choice being that the microscopical bulk viscosity as
calculated from statistical mechanics is then at maximum. We find that the
gravitational waves on such an underlying medium are damped, having a decay
constant equal to the inverse of the conformal Hubble parameter. Our results
turn out to be in good agreement with other viscosity-based approaches. | 1901.00767v3 |
2019-01-20 | Fate of spin polarization in a relativistic fluid: An entropy-current analysis | We derive relativistic hydrodynamic equations with a dynamical spin degree of
freedom on the basis of an entropy-current analysis. The first and second laws
of local thermodynamics constrain possible structures of the constitutive
relations including a spin current and the antisymmetric part of the
(canonical) energy-momentum tensor. Solving the obtained hydrodynamic equations
within the linear-mode analysis, we find spin-diffusion modes, indicating that
spin density is damped out after a characteristic time scale controlled by
transport coefficients introduced in the antisymmetric part of the
energy-momentum tensor in the entropy-current analysis. This is a consequence
of mutual convertibility between spin and orbital angular momentum. | 1901.06615v2 |
2019-01-24 | A priori error estimates for the finite element approximation of Westervelt's quasilinear acoustic wave equation | We study the spatial discretization of Westervelt's quasilinear strongly
damped wave equation by piecewise linear finite elements. Our approach employs
the Banach fixed-point theorem combined with a priori analysis of a linear wave
model with variable coefficients. Degeneracy of the semi-discrete Westervelt
equation is avoided by relying on the inverse estimates for finite element
functions and the stability and approximation properties of the interpolation
operator. In this way, we obtain optimal convergence rates in $L^2$-based
spatial norms for sufficiently small data and mesh size and an appropriate
choice of initial approximations. Numerical experiments in a setting of a 1D
channel as well as for a focused-ultrasound problem illustrate our theoretical
findings. | 1901.08510v3 |
2019-02-26 | Coulomb drag of excitons in Bose-Fermi mixtures | We develop a microscopic theory of the Coulomb drag effect in a hybrid system
consisting of spatially separated two-dimensional quantum gases of degenerate
electrons and dipolar excitons. We consider both the normal-phase and
condensate regimes of the exciton subsystem and investigate the cross-mobility
of the system being the kinetic coefficient, which couples the static electric
field applied to the electron layer with the particle density current (flux) in
the exciton subsystem. We study the temperature dependence of the
cross-mobility and its dependence on the interlayer separation. We show that
exciton-exciton interaction plays a dramatic role. If the exciton gas is in the
normal phase, then the screening of interlayer interaction by the exciton
subsystem results in an exponential damping of the cross-mobility with the
decrease of temperature, while at low temperatures, the interactions result in
a robust bosonic transport due to the emergence of the Bogoliubov
quasiparticles. | 1902.09721v1 |
2019-04-23 | Generalized Moment Correction for Long-Ranged Electrostatics | Describing long-ranged electrostatics using short-ranged pair potentials is
appealing since the computational complexity scales linearly with the number of
particles. The foundation of this approach is to mimic the long-ranged medium
response by cancelling electric multipoles within a small cutoff sphere. We
propose a rigorous and formally exact new method that cancels up to infinitely
many multipole moments and is free of operational damping parameters often
required in existing theories. Using molecular dynamics simulations of water
with and without added salt, we discuss radial distribution functions,
Kirkwood-Buff integrals, dielectrics, diffusion coefficients, and angular
correlations in relation to existing electrostatic models. We find that the
proposed method is an efficient and accurate alternative for handling
long-ranged electrostatics as compared to Ewald summation schemes. The
methodology and proposed parameterization is applicable also for dipole-dipole
interactions. | 1904.10335v2 |
2019-06-02 | Analytical prediction of logarithmic Rayleigh scattering in amorphous solids from tensorial heterogeneous elasticity with power-law disorder | The damping or attenuation coefficient of sound waves in solids due to
impurities scales with the wavevector to the fourth power, also known as
Rayleigh scattering. In amorphous solids, Rayleigh scattering may be enhanced
by a logarithmic factor although computer simulations offer conflicting
conclusions regarding this enhancement and its microscopic origin. We present a
tensorial replica field-theoretic derivation based on heterogeneous or
fluctuating elasticity (HE), which shows that long-range (power-law) spatial
correlations of the elastic constants, is the origin of the logarithmic
enhancement to Rayleigh scattering of phonons in amorphous solids. We also
consider the case of zero spatial fluctuations in the elastic constants, and of
power-law decaying fluctuations in the internal stresses. Also in this case the
logarithmic enhancement to the Rayleigh scattering law can be derived from the
proposed tensorial HE framework. | 1906.00372v3 |
2019-05-31 | Deterministic and stochastic damage detection via dynamic response analysis | The paper proposes a method of damage detection in elastic materials, which
is based on analyzing the time-dependent (dynamic) response of the material
excited by an acoustic signal. A case study is presented consisting of
experimental measurements and their mathematical analysis. The decisive
parameters (wave speed and damping coefficient) of a mathematical model of the
acoustic wave are calibrated by comparing the measurement data with the
numerically evaluated exact solution predicted by the mathematical model. The
calibration is done both deterministically by minimizing the square error over
time and stochastically by a Bayesian approach, implemented through the
Metropolis-Hastings algorithm. The resulting posterior distribution of the
parameters can be used to construct a Bayesian test for damage. | 1906.00797v2 |
2019-07-21 | Supersolutions for parabolic equations with unbounded diffusion and its applications to some classes of parabolic and hyperbolic equations | This paper is concerned with supersolutions to parabolic equations of the
form \begin{equation} \partial_t U (x,t)-D(x)\Delta U(x,t)=0, \quad (x,t)\in
\mathbb{R}^N \times (0,\infty), \end{equation} where $D\in C(\mathbb{R}^N)$ is
positive. Under the behavior of the diffusion coefficient $D$ with polynomial
order at spatial infinity, a family of supersolutions with slowly decaying
property at spatial infinity is provided. As a first application, weighted
$L^2$ type decay estimates for the initial-boundary value problem of the
corresponding parabolic equation are proved. The second application is the
study of the exterior problem of wave equations with space-dependent damping
terms. By using supersolutions provided above, energy estimates with polynomial
weight and diffusion phenomena are shown. | 1907.08992v1 |
2019-08-11 | A computational study of transient shear banding in soft jammed solids | We have designed 3D numerical simulations of a soft spheres model, with size
polidispersity and in athermal conditions, to study the transient shear banding
that occurs during yielding of jammed soft solids. We analyze the effects of
different types of drag coefficients used in the simulations and compare the
results obtained using Lees-Edwards periodic boundary conditions with the case
in which the same model solid is confined between two walls. The specific
damping mechanism and the different boundary conditions indeed modify the load
curves and the velocity profiles in the transient regime. Nevertheless, we find
that the presence of a stress-overshoot and of a related transient banding
phenomenon for large enough samples are a robust feature for overdamped
systems, where their presence do not depend on the specific drag used and on
the different boundary conditions. | 1908.03943v1 |
2019-09-10 | Diffusion and memory effect in a stochastic processes and the correspondence to an information propagation in a social system | A generalized Langevin equation is suggested to describe a system with
memory($u(t,t') = \frac{1}{\Gamma (\nu )}(t - t')^\nu $) as well as with
positive and negative damping. The equation can be transformed into the
Fokker-Planck equation by using the Kramers-Moyal expansion. The solution of
Fokker-Planck equation shows that velocity obeys a Gaussian distribution. The
distribution curve will flatten as the memory parameter increases, which
indicates that memory can enhance the randomness of the system. There are also
some other memory effects behind this distribution, which can be characterized
by calculating the transport coefficients, mean square displacement and
correlation between the noise and space. These discussions can be paralleled to
a social system to understand the propagation of social ideology caused by
memory. | 1909.04220v1 |
2019-10-10 | Mesoscopic theory for systems with competing interactions near a confining wall | Mesoscopic theory for self-assembling systems near a planar confining surface
is developed. Euler- Lagrange (EL) equations and the boundary conditions (BC)
for the local volume fraction and the correlation function are derived from the
DFT expression for the grand thermodynamic potential. Various levels of
approximation can be considered for the obtained equations. The lowest-order
nontrivial approximation (GM) resembles the Landau-Brazovskii type theory for a
semiinfinite system. Unlike in the original phenomenological theory, however,
all coefficients in our equations and BC are expressed in terms of the
interaction potential and the thermodynamic state. Analytical solutions of the
linearized equations in GM are presented and discussed on a general level and
for a particular example of the double-Yukawa potential. We show exponentially
damped oscillations of the volume fraction and the correlation function in the
direction perpendicular to the confining surface. The correlations show
oscillatory decay in directions parallel to this surface too, with the decay
length increasing significantly when the system boundary is approached. The
framework of our theory allows for a systematic improvement of the accuracy of
the results. | 1910.04474v2 |
2019-11-11 | Orbit-like trajectory of the vortex core in a magnetic nanodot | In physics, conserved quantities are key to understanding and describing
physical phenomena. These conserved quantities are related to Noether's theorem
and the Lagrangian description both in classical mechanics and in field theory.
In this article we have found the equation of the vortex core trajectory in
terms of two conserved physical quantities, namely the energy, $E$, and a
vector perpendicular to the orbit plane, $\vec{A} = -\vec{L} + \vec{G} \,
|\vec{r}_c|^2/2$ where $\vec{G}$, $\vec{L}$ and $\vec{r}_c$ are the topological
gyrovector, the angular momentum and the position of the vortex core,
respectively. We find that in the absence of a dissipative term, for small
deviations of the vortex core, the trajectory is bounded between two concentric
circles. On the contrary, under the action of a dissipative term proportional
to the damping coefficient, $\vec{A}$ is no longer conservative and the vortex
core moves either towards the center or out of the cylinder, depending on the
circularity of the magnetic vortex and the intensity of the magnetic field
applied in the plane of the cylinder. | 1911.04555v2 |
2019-12-04 | A high-order discontinuous Galerkin method for nonlinear sound waves | We propose a high-order discontinuous Galerkin scheme for nonlinear acoustic
waves on polytopic meshes. To model sound propagation with and without losses,
we use Westervelt's nonlinear wave equation with and without strong damping.
Challenges in the numerical analysis lie in handling the nonlinearity in the
model, which involves the derivatives in time of the acoustic velocity
potential, and in preventing the equation from degenerating. We rely in our
approach on the Banach fixed-point theorem combined with a stability and
convergence analysis of a linear wave equation with a variable coefficient in
front of the second time derivative. By doing so, we derive an a priori error
estimate for Westervelt's equation in a suitable energy norm for the polynomial
degree $p \geq 2$. Numerical experiments carried out in two-dimensional
settings illustrate the theoretical convergence results. In addition, we
demonstrate efficiency of the method in a three-dimensional domain with varying
medium parameters, where we use the discontinuous Galerkin approach in a hybrid
way. | 1912.02281v1 |
2019-12-05 | The blow up of solutions to semilinear wave equations on asymptotically Euclidean manifolds | In this paper, we investigate the problem of blow up and sharp upper bound
estimates of the lifespan for the solutions to the semilinear wave equations,
posed on asymptotically Euclidean manifolds. Here the metric is assumed to be
exponential perturbation of the spherical symmetric, long range asymptotically
Euclidean metric. One of the main ingredients in our proof is the construction
of (unbounded) positive entire solutions for
$\Delta_{g}\phi_\lambda=\lambda^{2}\phi_\lambda$, with certain estimates which
are uniform for small parameter $\lambda\in (0,\lambda_0)$. In addition, our
argument works equally well for semilinear damped wave equations, when the
coefficient of the dissipation term is integrable (without sign condition) and
space-independent. | 1912.02540v1 |
2019-12-08 | Dynamical Primal-Dual Accelerated Method with Applications to Network Optimization | This paper develops a continuous-time primal-dual accelerated method with an
increasing damping coefficient for a class of convex optimization problems with
affine equality constraints. This paper analyzes critical values for parameters
in the proposed method and prove that the rate of convergence in terms of the
duality gap function is $O(\tfrac{1}{t^2})$ by choosing suitable parameters. As
far as we know, this is the first continuous-time primal-dual accelerated
method that can obtain the optimal rate. Then this work applies the proposed
method to two network optimization problems, a distributed optimization problem
with consensus constraints and a distributed extended monotropic optimization
problem, and obtains two variant distributed algorithms. Finally, numerical
simulations are given to demonstrate the efficacy of the proposed method. | 1912.03690v2 |
2020-01-08 | Assessing different approaches to ab initio calculations of spin wave stiffness | Ab initio calculations of the spin wave stiffness constant $D$ for elemental
Fe and Ni performed by different groups in the past have led to values with a
considerable spread of 50-100 %. We present results for the stiffness constant
$D$ of Fe, Ni, and permalloy Fe$_{0.19}$Ni$_{0.81}$ obtained by three different
approaches: (i) by finding the quadratic term coefficient of the power
expansion of the spin wave energy dispersion, (ii) by a damped real-space
summation of weighted exchange coupling constants, and (iii) by integrating the
appropriate expression in reciprocal space. All approaches are implemented by
means of the same Korringa-Kohn-Rostoker (KKR) Green function formalism. We
demonstrate that if properly converged, all procedures yield comparable values,
with uncertainties of 5-10 % remaining. By a careful analysis of the influence
of various technical parameters we estimate the margin of errors for the
stiffness constants evaluated by different approaches and suggest procedures to
minimize the risk of getting incorrect results. | 2001.02558v2 |
2020-02-12 | Exact Solution for the Heat Conductance in Harmonic Chains | We present an exact solution for the heat conductance along a harmonic chain
connecting two reservoirs at different temperatures. In this model, the end
points correspond to Brownian particles with different damping coefficients.
Such analytical expression for the heat conductance covers its behavior from
mesoscopic to very long one-dimensional quantum chains, and validates the
ballistic nature of the heat transport in the latter example. This implies the
absence of the Fourier law for classical and quantum harmonic chains. We also
provide a thorough analysis of the normal modes of system which helps us to
satisfactorily interpret these results. | 2002.05195v2 |
2020-04-17 | On Enhanced Dissipation for the Boussinesq Equations | In this article we consider the stability and damping problem for the 2D
Boussinesq equations with partial dissipation near a two parameter family of
stationary solutions which includes Couette flow and hydrostatic balance.
In the first part we show that for the linearized problem in an infinite
periodic channel the evolution is asymptotically stable if any diffusion
coefficient is non-zero. In particular, this imposes weaker conditions than for
example vertical diffusion. Furthermore, we study the interaction of shear
flow, hydrostatic balance and partial dissipation.
In a second part we adapt the methods used by Bedrossian, Vicol and Wang in
the Navier-Stokes problem and combine them with cancellation properties of the
Boussinesq equations to establish small data stability and enhanced dissipation
results for the nonlinear Boussinesq problem with full dissipation. | 2004.08125v1 |
2020-05-05 | Heavy quark diffusion in an overoccupied gluon plasma | We extract the heavy-quark diffusion coefficient \kappa and the resulting
momentum broadening <p^2> in a far-from-equilibrium non-Abelian plasma. We find
several features in the time dependence of the momentum broadening: a short
initial rapid growth of <p^2>, followed by linear growth with time due to
Langevin-type dynamics and damped oscillations around this growth at the
plasmon frequency. We show that these novel oscillations are not easily
explained using perturbative techniques but result from an excess of gluons at
low momenta. These oscillation are therefore a gauge invariant confirmation of
the infrared enhancement we had previously observed in gauge-fixed correlation
functions. We argue that the kinetic theory description of such systems becomes
less reliable in the presence of this IR enhancement. | 2005.02418v2 |
2020-09-02 | Frustrated bearings | In a bearing state, touching spheres (disks in two dimensions) roll on each
other without slip. Here we frustrate a system of touching spheres by imposing
two different bearing states on opposite sides and search for the
configurations of lowest energy dissipation. If the dissipation between
contacts of spheres is viscous (with random damping constants), the angular
momentum continuously changes from one bearing state to the other. For Coulomb
friction (with random friction coefficients) in two dimensions, a sharp line
separates the two bearing states and we show that this line corresponds to the
minimum cut. Astonishingly however, in three dimensions, intermediate bearing
domains, that are not synchronized with either side, are energetically more
favorable than the minimum-cut surface. Instead of a sharp cut, the steady
state displays a fragmented structure. This novel type of state of minimum
dissipation is characterized by a spanning network of slipless contacts that
reaches every sphere. Such a situation becomes possible because in three
dimensions bearing states have four degrees of freedom. | 2009.01295v1 |
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