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2021-08-21 | Heterogeneous multiscale methods for the Landau-Lifshitz equation | In this paper, we present a finite difference heterogeneous multiscale method
for the Landau-Lifshitz equation with a highly oscillatory diffusion
coefficient. The approach combines a higher order discretization and artificial
damping in the so-called micro problem to obtain an efficient implementation.
The influence of different parameters on the resulting approximation error is
discussed. Numerical examples for both periodic as well as more general
coefficients are given to demonstrate the functionality of the approach. | 2108.09463v1 |
2022-04-22 | Coefficient of restitution of a linear dashpot on a rigid surface | The linear dashpot model is applied to a single ball bouncing on a rigid
surface. It is shown that when gravity is included the coefficient of
restitution depends on impact velocity, in contrast to previous work that
ignored the effects of gravity. This velocity dependence is most pronounced at
low impact velocities and high damping. Previous work has considered the ball
to be in contact with the floor when the compression is nonzero, while other
analysis terminates the collision earlier, to prevent an attractive force. We
compare these models and propose a hybrid between the two. The hybrid model is
successful in reproducing experimental results for a cart bouncing repeatedly
on a spring. | 2204.10917v1 |
2023-05-05 | When does an active bath behave as an equilibrium one? | Active baths are characterized by a non-Gaussian velocity distribution and a
quadratic dependence with active velocity $v_0$ of the kinetic temperature and
diffusion coefficient. While these results hold in over-damped active systems,
inertial effects lead to normal velocity distributions, with kinetic
temperature and diffusion coefficient increasing as $\sim v_0^\alpha$ with
$1<\alpha<2$. Remarkably, the late-time diffusivity and mobility decrease with
mass. Moreover, we show that the equilibrium Einstein relation is
asymptotically recovered with inertia. In summary, the inertial mass restores
an equilibrium-like behavior. | 2305.03830v1 |
2023-08-09 | Quantitative analysis of secondary Bjerkenes forces in various liquids | Numerically calculating the interaction forces between two free bubbles under
the action of a background of random acoustic radiation, we highlight the
contributions of radiative coefficient and absorption damping coefficient to
the size of these forces.It is quantitatively demonstrated, for different radii
of the oscillating bubbles, that the scattering absorption forces and the
scattering scattering forces are close in magnitude.For superfluid helium, the
forces change direction, oscillatingly, and the ratio of the forces is much
less than one. | 2308.13530v1 |
2010-11-29 | Long-time dynamics of Kirchhoff wave models with strong nonlinear damping | We study well-posedness and long-time dynamics of a class of quasilinear wave
equations with a strong damping. We accept the Kirchhoff hypotheses and assume
that the stiffness and damping coefficients are $C^1$ functions of the
$L_2$-norm of the gradient of the displacement. We first prove the existence
and uniqueness of weak solutions and study their properties for a rather wide
class of nonlinearities which covers the case of possible degeneration (or even
negativity) of the stiffness coefficient and the case of a supercritical source
term. Our main results deal with global attractors. In the case of strictly
positive stiffness factors we prove that in the natural energy space endowed
with a partially strong topology there exists a global attractor whose fractal
dimension is finite. In the non-supercritical case the partially strong
topology becomes strong and a finite dimensional attractor exists in the strong
topology of the energy space. Moreover, in this case we also establish the
existence of a fractal exponential attractor and give conditions that guarantee
the existence of a finite number of determining functionals. Our arguments
involve a recently developed method based on "compensated" compactness and
quasi-stability estimates. | 1011.6271v3 |
2013-09-13 | Analytical and experimental stability investigation of a hardware-in-the-loop satellite docking simulator | The European Proximity Operation Simulator (EPOS) of the DLR-German Aerospace
Center is a robotics-based simulator that aims at validating and verifying a
satellite docking phase. The generic concept features a robotics tracking
system working in closed loop with a force/torque feedback signal. Inherent
delays in the tracking system combined with typical high stiffness at contact
challenge the stability of the closed-loop system. The proposed concept of
operations is hybrid: the feedback signal is a superposition of a measured
value and of a virtual value that can be tuned in order to guarantee a desired
behavior. This paper is concerned with an analytical study of the system's
closed-loop stability, and with an experimental validation of the hybrid
concept of operations in one dimension (1D). The robotics simulator is modeled
as a second-order loop-delay system and closed-form expressions for the
critical delay and associated frequency are derived as a function of the
satellites' mass and the contact dynamics stiffness and damping parameters. A
numerical illustration sheds light on the impact of the parameters on the
stability regions. A first-order Pade approximation provides additional means
of stability investigation. Experiments were performed and tests results are
described for varying values of the mass and the damping coefficients. The
empirical determination of instability is based on the coefficient of
restitution and on the observed energy. There is a very good agreement between
the critical damping values predicted by the analysis and observed during the
tests... | 1309.3512v1 |
2014-06-13 | Magnetic-Field Amplification in the Thin X-ray Rims of SN1006 | Several young supernova remnants (SNRs), including SN1006, emit synchrotron
X-rays in narrow filaments, hereafter thin rims, along their periphery. The
widths of these rims imply 50 to 100 $\mu$G fields in the region immediately
behind the shock, far larger than expected for the interstellar medium
compressed by unmodified shocks, assuming electron radiative losses limit rim
widths. However, magnetic-field damping could also produce thin rims. Here we
review the literature on rim width calculations, summarizing the case for
magnetic-field amplification. We extend these calculations to include an
arbitrary power-law dependence of the diffusion coefficient on energy, $D
\propto E^{\mu}$. Loss-limited rim widths should shrink with increasing photon
energy, while magnetic-damping models predict widths almost independent of
photon energy. We use these results to analyze Chandra observations of SN 1006,
in particular the southwest limb. We parameterize the full widths at half
maximum (FWHM) in terms of energy as FWHM $\propto E^{m_E}_{\gamma}$. Filament
widths in SN1006 decrease with energy; $m_E \sim -0.3$ to $-0.8$, implying
magnetic field amplification by factors of 10 to 50, above the factor of 4
expected in strong unmodified shocks. For SN 1006, the rapid shrinkage rules
out magnetic damping models. It also favors short mean free paths (small
diffusion coefficients) and strong dependence of $D$ on energy ($\mu \ge 1$). | 1406.3630v2 |
2015-04-17 | Effective Action for Cosmological Scalar Fields at Finite Temperature | Scalar fields appear in many theories beyond the Standard Model of particle
physics. In the early universe, they are exposed to extreme conditions,
including high temperature and rapid cosmic expansion. Understanding their
behavior in this environment is crucial to understand the implications for
cosmology. We calculate the finite temperature effective action for the field
expectation value in two particularly important cases, for damped oscillations
near the ground state and for scalar fields with a flat potential. We find that
the behavior in both cases can in good approximation be described by a complex
valued effective potential that yields Markovian equations of motion. Near the
potential minimum, we recover the solution to the well-known Langevin equation.
For large field values we find a very different behavior, and our result for
the damping coefficient differs from the expressions frequently used in the
literature. We illustrate our results in a simple scalar model, for which we
give analytic approximations for the effective potential and damping
coefficient. We also provide various expressions for loop integrals at finite
temperature that are useful for future calculations in other models. | 1504.04444v2 |
2017-05-19 | Analytical Prediction of Reflection Coefficients for Wave Absorbing Layers in Flow Simulations of Regular Free-Surface Waves | Undesired wave reflections, which occur at domain boundaries in flow
simulations with free-surface waves, can be minimized by applying source terms
in the vicinity of the boundary to damp the waves. Examples of such approaches
are absorbing layers, damping zones, forcing zones, relaxation zones and sponge
layers. A problem with these approaches is that the effectivity of the wave
damping depends on the parameters in the source term functions, which are
case-dependent and must be adjusted to the wave. The present paper presents a
theory which analytically predicts the reflection coefficients and which can be
used to optimally select the source term parameters before running the
simulation. The theory is given in a general form so that it is applicable to
many existing implementations. It is validated against results from
finite-volume-based flow simulations of regular free-surface waves and found to
be of satisfactory accuracy for practical purposes. | 1705.06940v2 |
2018-07-26 | Aspherical deformations of the Choptuik spacetime | We perform dynamical and nonlinear numerical simulations to study critical
phenomena in the gravitational collapse of massless scalar fields in the
absence of spherical symmetry. We evolve axisymmetric sets of initial data and
examine the effects of deviation from spherical symmetry. For small deviations
we find values for the critical exponent and echoing period of the discretely
self-similar critical solution that agree well with established values;
moreover we find that such small deformations behave like damped oscillations
whose damping coefficient and oscillation frequencies are consistent with those
predicted in the linear perturbation calculations of Martin-Garcia and
Gundlach. However, we also find that the critical exponent and echoing period
appear to decrease with increasing departure from sphericity, and that, for
sufficiently large departures from spherical symmetry, the deviations become
unstable and grow, confirming earlier results by Choptuik et.al.. We find some
evidence that these growing modes lead to a bifurcation, similar to those
reported by Choptuik et.al., with two centers of collapse forming on the
symmetry axis above and below the origin. These findings suggest that nonlinear
perturbations of the critical solution lead to changes in the effective values
of the critical exponent, echoing period and damping coefficient, and may even
change the sign of the latter, so that perturbations that are stable in the
linear regime can become unstable in the nonlinear regime. | 1807.10342v2 |
2019-03-07 | Non-linear diffusion of cosmic rays escaping from supernova remnants - II. Hot ionized media | We study the problem of the escape and transport of Cosmic-Rays (CR) from a
source embedded in a fully ionised, hot phase of the interstellar medium (HIM).
In particular, we model the CR escape and their propagation in the source
vicinity taking into account excitation of Alfv\'enic turbulence by CR
streaming and mechanisms damping the self-excited turbulence itself. Our
estimates of escape radii and times result in large values (100 pc,
$2\times10^5$ yr) for particle energies $\lesssim20$ GeV and smaller values for
particles with increasing energies (35 pc and 14 kyr at 1 TeV). These escape
times and radii, when used as initial conditions for the CR propagation outside
the source, result in relevant suppression of the diffusion coefficient (by a
factor 5-10) on time-scales comparable with their (energy dependent) escape
time-scale. The damping mechanisms are fast enough that even on shorter time
scales the Alfv\'enic turbulence is efficiently damped, and the ratio between
random and ordered component of the magnetic field is $\delta B/B_0\ll 1$,
justifying the use of quasi-linear theory. In spite of the suppressed diffusion
coefficient, and then the increased residence time in the vicinity (<200 pc) of
their source, the grammage accumulated by CRs after their escape is found to be
negligible (at all energies) as compared to the one accumulated while diffusing
in the whole Galaxy, due to the low density of the HIM. | 1903.03193v1 |
1997-09-04 | Cosmic-Ray Momentum Diffusion In Magnetosonic Versus Alfvenic Turbulent Field | Energetic particle transport in a finite amplitude magnetosonic and Alfvenic
turbulence is considered using Monte Carlo particle simulations, which involve
an integration of particle equation of motion. We show that in a low-Betha
plasma cosmic ray can be the most important damping process for magnetosonic
waves. Assuming such conditions we derive the momentum diffusion coefficient
for relativistic particles in the presence of anisotropic finite-amplitude
turbulent wave field, for flat and Kolmogorov-type turbulence spectra. We
confirm the possibility of larger values of a momentum diffusion coefficient
occuring due to transit-time damping resonance interaction in the presence of
isotropic fast-mode waves in comparison to the Alfven waves of the same
amplitude. | 9709039v2 |
2003-05-01 | Scalar perturbation spectra from warm inflation | We present a numerical integration of the cosmological scalar perturbation
equations in warm inflation. The initial conditions are provided by a
discussion of the thermal fluctuations of an inflaton field and thermal
radiation using a combination of thermal field theory and thermodynamics. The
perturbation equations include the effects of a damping coefficient $\Gamma$
and a thermodynamic potential $V$. We give an analytic expression for the
spectral index of scalar fluctuations in terms of a new slow-roll parameter
constructed from $\Gamma$. A series of toy models, inspired by spontaneous
symmetry breaking and a known form of the damping coefficient, lead to a
spectrum with $n_s>1$ on large scales and $n_s<1$ on small scales. | 0305015v3 |
2000-09-21 | Landau-Khalatnikov two-fluid hydrodynamics of a trapped Bose gas | Starting from the quantum kinetic equation for the non-condensate atoms and
the generalized Gross-Pitaevskii equation for the condensate, we derive the
two-fluid hydrodynamic equations of a trapped Bose gas at finite temperatures.
We follow the standard Chapman-Enskog procedure, starting from a solution of
the kinetic equation corresponding to the complete local equilibrium between
the condensate and the non-condensate components. Our hydrodynamic equations
are shown to reduce to a form identical to the well-known Landau-Khalatnikov
two-fluid equations, with hydrodynamic damping due to the deviation from local
equilibrium. The deviation from local equilibrium within the thermal cloud
gives rise to dissipation associated with shear viscosity and thermal
conduction. In addition, we show that effects due to the deviation from the
diffusive local equilibrium between the condensate and the non-condensate
(recently considered by Zaremba, Nikuni and Griffin) can be described by four
frequency-dependent second viscosity transport coefficients. We also derive
explicit formulas for all the transport coefficients. These results are used to
introduce two new characteristic relaxation times associated with hydrodynamic
damping. These relaxation times give the rate at which local equilibrium is
reached and hence determine whether one is in the two-fluid hydrodynamic
region. | 0009333v1 |
1999-05-28 | Existence threshold for the ac-driven damped nonlinear Schrödinger solitons | It has been known for some time that solitons of the externally driven,
damped nonlinear Schr\"odinger equation can only exist if the driver's
strength, $h$, exceeds approximately $(2/ \pi) \gamma$, where $\gamma$ is the
dissipation coefficient. Although this perturbative result was expected to be
correct only to the leading order in $\gamma$, recent studies have demonstrated
that the formula $h_{thr}= (2 /\pi) \gamma$ gives a remarkably accurate
description of the soliton's existence threshold prompting suggestions that it
is, in fact, exact. In this note we evaluate the next order in the expansion of
$h_{thr}(\gamma)$ showing that the actual reason for this phenomenon is simply
that the next-order coefficient is anomalously small: $h_{thr}=(2/ \pi) \gamma
+ 0.002 \gamma^3$. Our approach is based on a singular perturbation expansion
of the soliton near the turning point; it allows to evaluate $h_{thr}(\gamma)$
to all orders in $\gamma$ and can be easily reformulated for other perturbed
soliton equations. | 9906001v1 |
2009-11-11 | Ginzburg-Landau equation for dynamical four-wave mixing in gain nonlinear media with relaxation | We consider the dynamical degenerate four-wave mixing (FWM) model in a cubic
nonlinear medium including both the time relaxation of the induced nonlinearity
and the nonlocal coupling. The initial ten-dimensional FWM system can be
rewritten as a three-variable intrinsic system (namely the intensity pattern,
the amplitude of the nonlinearity and the total net gain) which is very close
to the pumped Maxwell-Bloch system. In the case of a purely nonlocal response
the initial system reduces to a real damped sine-Gordon (SG) equation. We
obtain a new solution of this equation in the form of a sech function with a
time-dependent coefficient. By applying the reductive perturbation method to
this damped SG equation, we obtain exactly the cubic complex Ginzburg Landau
equation (CGL3), but with a time dependence in the loss/gain coefficient. The
CGL3 describes the properties of the spatially localized interference pattern
formed by the FWM. | 0911.2129v1 |
2010-02-05 | Damped-driven KdV and effective equation for long-time behaviour of its solutions | For the damped-driven KdV equation $$ \dot
u-\nu{u_{xx}}+u_{xxx}-6uu_x=\sqrt\nu \eta(t,x), x\in S^1, \int u dx\equiv
\int\eta dx\equiv0, $$ with $0<\nu\le1$ and smooth in $x$ white in $t$ random
force $\eta$, we study the limiting long-time behaviour of the KdV integrals of
motions $(I_1,I_2,...)$, evaluated along a solution $u^\nu(t,x)$, as $\nu\to0$.
We prove that %if $u=u^\nu(t,x)$ is a solution of the equation above, for
$0\le\tau:= \nu t \lesssim1$ the vector $
I^\nu(\tau)=(I_1(u^\nu(\tau,\cdot)),I_2(u^\nu(\tau,\cdot)),...), $ converges in
distribution to a limiting process $I^0(\tau)=(I^0_1,I^0_2,...)$. The $j$-th
component $I_j^0$ equals $\12(v_j(\tau)^2+v_{-j}(\tau)^2)$, where
$v(\tau)=(v_1(\tau), v_{-1}(\tau),v_2(\tau),...)$ is the vector of Fourier
coefficients of a solution of an {\it effective equation} for the
dam-ped-driven KdV. This new equation is a quasilinear stochastic heat equation
with a non-local nonlinearity, written in the Fourier coefficients. It is well
posed. | 1002.1294v1 |
2011-07-13 | q-damped Oscillator and degenerate roots of constant coefficients q-difference ODE | The classical model of q-damped oscillator is introduced and solved in terms
of Jackson q-exponential function for three different cases, under-damped,
over-damped and the critical one. It is shown that in all three cases solution
is oscillating in time but is unbounded and non-periodic. By q-periodic
function modulation, the self-similar micro-structure of the solution for small
time intervals is derived. In the critical case with degenerate roots, the
second linearly independent solution is obtained as a limiting case of two
infinitesimally close roots. It appears as standard derivative of q-exponential
and is rewritten in terms of the q-logarithmic function. We extend our result
by constructing n linearly independent set of solutions to a generic constant
coefficient q-difference equation degree N with n degenerate roots. | 1107.2518v1 |
2011-12-21 | A numerical method for computing radially symmetric solutions of a dissipative nonlinear modified Klein-Gordon equation | In this paper we develop a finite-difference scheme to approximate radially
symmetric solutions of the initial-value problem with smooth initial conditions
in an open sphere around the origin, where the internal and external damping
coefficients are constant, and the nonlinear term follows a power law. We prove
that our scheme is consistent of second order when the nonlinearity is
identically equal to zero, and provide a necessary condition for it to be
stable order n. Part of our study will be devoted to compare the physical
effects of the damping coefficients. | 1112.4921v1 |
2013-08-20 | Group classification and exact solutions of variable-coefficient generalized Burgers equations with linear damping | Admissible point transformations between Burgers equations with linear
damping and time-dependent coefficients are described and used in order to
exhaustively classify Lie symmetries of these equations. Optimal systems of
one- and two-dimensional subalgebras of the Lie invariance algebras obtained
are constructed. The corresponding Lie reductions to ODEs and to algebraic
equations are carried out. Exact solutions to particular equations are found.
Some generalized Burgers equations are linearized to the heat equation by
composing equivalence transformations with the Hopf-Cole transformation. | 1308.4265v2 |
2015-05-21 | Control and stabilization of degenerate wave equations | We study a wave equation in one space dimension with a general diffusion
coefficient which degenerates on part of the boundary. Degeneracy is measured
by a real parameter $\mu_a>0$. We establish observability inequalities for
weakly (when $\mu_a \in [0,1[$) as well as strongly (when $\mu_a \in [1,2[$)
degenerate equations. We also prove a negative result when the diffusion
coefficient degenerates too violently (i.e. when $\mu_a>2$) and the blow-up of
the observability time when $\mu_a$ converges to $2$ from below. Thus, using
the HUM method we deduce the exact controllability of the corresponding
degenerate control problem when $\mu_a \in [0,2[$. We conclude the paper by
studying the boundary stabilization of the degenerate linearly damped wave
equation and show that a suitable boundary feedback stabilizes the system
exponentially. We extend this stability analysis to the degenerate nonlinearly
boundary damped wave equation, for an arbitrarily growing nonlinear feedback
close to the origin. This analysis proves that the degeneracy does not affect
the optimal energy decay rates at large time. We apply the optimal-weight
convexity method of \cite{alaamo2005, alajde2010} together with the results of
the previous section, to perform this stability analysis. | 1505.05720v1 |
2020-04-14 | Stability results of an elastic/viscoelastic transmission problem of locally coupled waves with non smooth coefficients | We investigate the stabilization of a locally coupled wave equations with
only one internal viscoelastic damping of Kelvin-Voigt type. The main novelty
in this paper is that both the damping and the coupling coefficients are non
smooth. First, using a general criteria of Arendt-Batty, combined with an
uniqueness result, we prove that our system is strongly stable. Next, using a
spectrum approach, we prove the non-exponential (uniform) stability of the
system. Finally, using a frequency domain approach, combined with a piecewise
multiplier technique and the construction of a new multiplier satisfying some
ordinary differential equations, we show that the energy of smooth solutions of
the system decays polynomially of type t^{-1}. | 2004.06758v1 |
2020-12-23 | The fate of nonlinear perturbations near the QCD critical point | The impact of the QCD critical point on the propagation of nonlinear waves
has been studied. The effects have been investigated within the scope of
second-order causal dissipative hydrodynamics by incorporating the critical
point into the equation of state, and the scaling behaviour of transport
coefficients and of thermodynamic response functions. Near the critical point,
the nonlinear waves are found to be significantly damped which may result in
the disappearance of the Mach cone effects of the away side jet. Such damping
may lead to enhancement in the fluctuations of elliptic and higher flow
coefficients. Therefore, the disappearance of Mach cone effects and the
enhancement of fluctuations in flow harmonics in the event-by-event analysis
may be considered as signals of the critical endpoint. | 2012.12668v3 |
2021-01-29 | Quarter and Full Car Models Optimisation of Passive and Active Suspension System Using Genetic Algorithm | This study evaluates a suspension design of a passenger car to obtain maximum
rider's comfort when the vehicle is subjected to different road profile or road
surface condition. The challenge will be on finding a balance between the
rider's comfort and vehicle handling to optimize design parameters. The study
uses a simple passive suspension system and an active suspension model
integrated with a pneumatic actuator controlled by proportional integral
derivative (PID) controller in both quarter car and full car models having a
different degree of freedoms (DOF) and increasing degrees of complexities. The
quarter car considered as a 2-DOF model, while the full car model is a 7-DOF
model. The design process set to optimise the spring stiffnesses, damping
coefficients and actuator PID controller gains. For optimisation, the research
featured genetic algorithm optimisation technique to obtain a balanced response
of the vehicle as evaluated from the displacement, velocity and acceleration of
sprung and unsprung masses along with different human comfort and vehicle
performance criteria. The results revealed that the active suspension system
with optimised spring stiffness, damping coefficients and PID gains
demonstrated the superior riding comfort and road holding compared to a passive
suspension system. | 2101.12629v1 |
2021-03-06 | Deep learning stochastic processes with QCD phase transition | It is non-trivial to recognize phase transitions and track dynamics inside a
stochastic process because of its intrinsic stochasticity. In this paper, we
employ the deep learning method to classify the phase orders and predict the
damping coefficient of fluctuating systems under Langevin's description. As a
concrete set-up, we demonstrate this paradigm for the scalar condensation in
QCD matter near the critical point, in which the order parameter of chiral
phase transition can be characterized in a $1+1$-dimensional Langevin equation
for $\sigma$ field. In a supervised learning manner, the Convolutional Neural
Networks(CNNs) accurately classify the first-order phase transition and
crossover based on $\sigma$ field configurations with fluctuations. Noise in
the stochastic process does not significantly hinder the performance of the
well-trained neural network for phase order recognition. For mixed dynamics
with diverse dynamical parameters, we further devise and train the machine to
predict the damping coefficients $\eta$ in a broad range. The results show that
it is robust to extract the dynamics from the bumpy field configurations. | 2103.04090v1 |
2022-05-23 | Global existence, uniqueness and $L^{\infty}$-bound of weak solutions of fractional time-space Keller-Segel system | This paper studies the properties of weak solutions to a class of space-time
fractional parabolic-elliptic Keller-Segel equations with logistic source terms
in $\mathbb{R}^{n}$, $n\geq 2$. The global existence and $L^{\infty}$-bound of
weak solutions are established. We mainly divide the damping coefficient into
two cases: (i) $b>1-\frac{\alpha}{n}$, for any initial value and birth rate;
(ii) $0<b\leq 1-\frac{\alpha}{n}$, for small initial value and small birth
rate. The existence result is obtained by verifying the existence of a solution
to the constructed regularization equation and incorporate the generalized
compactness criterion of time fractional partial differential equation. At the
same time, we get the $L^{\infty}$-bound of weak solutions by establishing the
fractional differential inequality and using the Moser iterative method.
Furthermore, we prove the uniqueness of weak solutions by using the
hyper-contractive estimates when the damping coefficient is strong. Finally, we
also propose a blow-up criterion for weak solutions, that is, if a weak
solution blows up in finite time, then for all $h>q$, the $L^{h}$-norms of the
weak solution blow up at the same time. | 2205.11041v1 |
2023-03-30 | Superfluid $^3$He-B Surface States in a Confined Geometry Probed by a Microelectromechanical Oscillator | A microelectromechanical oscillator with a 0.73 $\mu$m gap structure is
employed to probe the surface Andreev bound states in superfluid $^3$He-B. The
surface specularity of the oscillator is increased by preplating it with 1.6
monolayers of $^4$He. In the linear regime, the temperature dependence of the
damping coefficient is measured at various pressures, and the normalized energy
gap is extracted. The damping coefficient increases after preplating at lower
pressures, which is attributed to the decreased energy minigap of the surface
bound states. The device is also driven into the nonlinear regime, where the
temperature independent critical velocity at each pressure is measured. The
critical velocity is observed to increase after preplating at all pressures,
which might be related to the increased average energy gap. The observed
behavior warrants a microscopic theory beyond a single parameter
characterization of the surface. | 2303.17073v1 |
2023-06-10 | Discrepant Approaches to Modeling Stellar Tides, and the Blurring of Pseudosynchronization | We examine the reasons for discrepancies between two alternative approaches
to modeling small-amplitude tides in binary systems. The 'direct solution' (DS)
approach solves the governing differential equations and boundary conditions
directly, while the 'modal decomposition' (MD) approach relies on a normal-mode
expansion. Applied to a model for the primary star in the heartbeat system
KOI-54, the two approaches predict quite different behavior of the secular
tidal torque. The MD approach exhibits the pseudosynchronization phenomenon,
where the torque due to the equilibrium tide changes sign at a single,
well-defined and theoretically predicted stellar rotation rate. The DS approach
instead shows 'blurred' pseudosynchronization, where positive and negative
torques intermingle over a range of rotation rates.
We trace a major source of these differences to an incorrect damping
coefficient in the profile functions describing the frequency dependence of the
MD expansion coefficients. With this error corrected some differences between
the approaches remain; however, both are in agreement that
pseudosynchronization is blurred in the KOI-54 system. Our findings generalize
to any type of star for which the tidal damping depends explicitly or
implicitly on the forcing frequency. | 2306.06429v1 |
2023-08-25 | The time dimensional reduction method to determine the initial conditions without the knowledge of damping coefficients | This paper aims to reconstruct the initial condition of a hyperbolic equation
with an unknown damping coefficient. Our approach involves approximating the
hyperbolic equation's solution by its truncated Fourier expansion in the time
domain and using a polynomial-exponential basis. This truncation process
facilitates the elimination of the time variable, consequently, yielding a
system of quasi-linear elliptic equations. To globally solve the system without
needing an accurate initial guess, we employ the Carleman contraction
principle. We provide several numerical examples to illustrate the efficacy of
our method. The method not only delivers precise solutions but also showcases
remarkable computational efficiency. | 2308.13152v1 |
2024-02-05 | Symmetries and conservation laws of a fifth-order KdV equation with time-dependent coefficients and linear damping | A fifth-order KdV equation with time dependent coefficients and linear
damping has been studied. Symmetry groups have several different applications
in the context of nonlinear differential equations. For instance, they can be
used to determine conservation laws. We obtain the symmetries of the model
applying Lie's classical method. The choice of some arbitrary functions of the
equation by the equivalence transformation enhances the study of Lie symmetries
of the equation. We have determined the subclasses of the equation which are
nonlinearly self-adjoint. This allow us to obtain conservation laws by using a
theorem proved by Ibragimov which is based on the concept of adjoint equation
for nonlinear differential equations. | 2402.03265v1 |
2022-10-11 | Finite-time singularity formations for the Landau-Lifshitz-Gilbert equation in dimension two | We construct finite time blow-up solutions to the Landau-Lifshitz-Gilbert
equation (LLG) from ${\mathbb R}^2$ into $S^2$ \begin{equation*} \begin{cases}
u_t= a(\Delta u+|\nabla u|^2u) -b u\wedge \Delta u &\ \mbox{ in }\ {\mathbb
R}^2\times(0,T), u(\cdot,0) = u_0\in S^2 &\ \mbox{ in }\ {\mathbb R}^2,
\end{cases} \end{equation*} where $a^2+b^2=1,~a > 0,~ b\in {\mathbb R}$. Given
any prescribed $N$ points in $\mathbb{R}^2$ and small $T>0$, we prove that
there exists regular initial data such that the solution blows up precisely at
these points at finite time $t=T$, taking around each point the profile of
sharply scaled degree 1 harmonic map with the type II blow-up speed
\begin{equation*} \| \nabla u\|_{L^\infty } \sim \frac{|\ln(T-t)|^2}{ T-t } \
\mbox{ as } \ t\to T. \end{equation*} The proof is based on the {\em parabolic
inner-outer gluing method}, developed in \cite{17HMF} for Harmonic Map Flow
(HMF). However, a direct consequence of the presence of dispersion is the {\em
lack of maximum principle} for suitable quantities, which makes the analysis
more delicate even at the linearized level. To overcome this difficulty, we
make use of two key technical ingredients: first, for the inner problem we
employ the tool of {\em distorted Fourier transform}, as developed by Krieger,
Miao, Schlag and Tataru \cite{Krieger09Duke,KMS20WM}. Second, the linear theory
for the outer problem is achieved by means of the sub-Gaussian estimate for the
fundamental solution of parabolic system in non-divergence form with
coefficients of Dini mean oscillation in space ($\mathsf{DMO_x}$), which was
proved by Dong, Kim and Lee \cite{dong22-non-divergence} recently. | 2210.05800v1 |
2023-03-07 | Multilevel Monte Carlo methods for stochastic convection-diffusion eigenvalue problems | We develop new multilevel Monte Carlo (MLMC) methods to estimate the
expectation of the smallest eigenvalue of a stochastic convection-diffusion
operator with random coefficients. The MLMC method is based on a sequence of
finite element (FE) discretizations of the eigenvalue problem on a hierarchy of
increasingly finer meshes. For the discretized, algebraic eigenproblems we use
both the Rayleigh quotient (RQ) iteration and implicitly restarted Arnoldi
(IRA), providing an analysis of the cost in each case. By studying the variance
on each level and adapting classical FE error bounds to the stochastic setting,
we are able to bound the total error of our MLMC estimator and provide a
complexity analysis. As expected, the complexity bound for our MLMC estimator
is superior to plain Monte Carlo. To improve the efficiency of the MLMC
further, we exploit the hierarchy of meshes and use coarser approximations as
starting values for the eigensolvers on finer ones. To improve the stability of
the MLMC method for convection-dominated problems, we employ two additional
strategies. First, we consider the streamline upwind Petrov--Galerkin
formulation of the discrete eigenvalue problem, which allows us to start the
MLMC method on coarser meshes than is possible with standard FEs. Second, we
apply a homotopy method to add stability to the eigensolver for each sample.
Finally, we present a multilevel quasi-Monte Carlo method that replaces Monte
Carlo with a quasi-Monte Carlo (QMC) rule on each level. Due to the faster
convergence of QMC, this improves the overall complexity. We provide detailed
numerical results comparing our different strategies to demonstrate the
practical feasibility of the MLMC method in different use cases. The results
support our complexity analysis and further demonstrate the superiority over
plain Monte Carlo in all cases. | 2303.03673v2 |
2008-12-31 | Weak Solutions of the Stochastic Landau-Lifshitz-Gilbert Equation | The Landau-Lifshitz-Gilbert equation perturbed by a multiplicative
space-dependent noise is considered for a ferromagnet filling a bounded
three-dimensional domain. We show the existence of weak martingale solutions
taking values in a sphere $\mathbb S^2$. The regularity of weak solutions is
also discussed. Some of the regularity results are new even for the
deterministic Landau-Lifshitz-Gilbert equation. | 0901.0039v1 |
2023-09-08 | Branching points in the planar Gilbert--Steiner problem have degree 3 | Gilbert--Steiner problem is a generalization of the Steiner tree problem on a
specific optimal mass transportation.
We show that every branching point in a solution of the planar
Gilbert--Steiner problem has degree 3. | 2309.04202v2 |
2000-03-27 | Electron-Ion Recombination Rate Coefficients and Photoionization Cross Sections for Astrophysically Abundant Elements IV. Relativistic calculations for C IV and C V for UV and X-ray modeling | The first complete set of unified cross sections and rate coefficients are
calculated for photoionization and recombination of He- and Li-like ions using
the relativistic Breit-Pauli R-matrix method. We present total, unified (e +
ion) recombination rate coefficients for (e + C VI ---> C V) and (e + C V
\longrightarrow C IV) including fine structure. Level-specific recombination
rate coefficients up to the n = 10 levels are also obtained for the first time;
these differ considerably from the approximate rates currently available.
Applications to recombination-cascade coefficients in X-ray spectral models of
K-alpha emission from the important He-like ions is pointed out. The overall
uncertainty in the total recombination rates should not exceed 10-20%.
Ionization fractions for Carbon are recomputed in the coronal approximation
using the new rates.
The present (e + ion) recombination rate coefficients are compared with
several sets of available data, including previous LS coupling results, and
`experimentally derived' rate coefficients. The role of relativistic fine
structure, resolution of resonances, radiation damping, and interference
effects is discussed. Two general features of recombination rates are noted:
(i) the non-resonant (radiative recombination) peak as E,T ---> 0, and the (ii)
the high-T resonant (di-electronic recombination) peak. | 0003411v2 |
2018-07-19 | Magnetization nutation induced by surface effects in nanomagnets | We investigate the magnetization dynamics of ferromagnetic nanoparticles in
the atomistic approach taking account of surface anisotropy and the spin
misalignment it causes. We demonstrate that such inhomogeneous spin
configurations induce nutation in the dynamics of the particle's magnetization.
More precisely, in addition to the ordinary precessional motion with frequency
$f_{p}\sim10\,{\rm GHz}$, we find that the dynamics of the net magnetic moment
exhibits two more resonance peaks with frequencies $f_{c}$ and $f_{n}$ which
are higher than the frequency $f_{p} : f_{c}=4\times f_{p}\sim40\,{\rm GHz}$ is
related with the oscillations of the particle's magnetic moment between the
minima of the effective potential induced by weak surface anisotropy. On the
other hand, the much higher frequency $f_{n}\sim1\,{\rm THz}$ is attributed to
the magnetization fluctuations at the atomic level driven by exchange
interaction. We have compared our results on nutation induced by surface
effects with those rendered by the macroscopic approach based on the
Landau-Lifshitz-Gilbert equation augmented by an inertial term (proportional to
the second-order time derivative of the macroscopic moment) with a
phenomenological coefficient. The good agreement between the two models have
allowed us to estimate the latter coefficient in terms of the atomistic
parameters such as the surface anisotropy constant. We have thus proposed a new
origin for the magnetization nutations as being induced by surface effects and
have interpreted the corresponding resonance peaks and their frequencies. | 1807.07392v1 |
2021-07-02 | Scaling of Turbulent Viscosity and Resistivity: Extracting a Scale-dependent Turbulent Magnetic Prandtl Number | Turbulent viscosity $\nu_t$ and resistivity $\eta_t$ are perhaps the simplest
models for turbulent transport of angular momentum and magnetic fields,
respectively. The associated turbulent magnetic Prandtl number $Pr_t\equiv
\nu_t/\eta_t$ has been well recognized to determine the final magnetic
configuration of accretion disks. Here, we present an approach to determining
these ''effective transport'' coefficients acting at different length-scales
using coarse-graining and recent results on decoupled kinetic and magnetic
energy cascades [Bian & Aluie 2019]. By analyzing the kinetic and magnetic
energy cascades from a suite of high-resolution simulations, we show that our
definitions of $\nu_t$, $\eta_t$, and $Pr_t$ have power-law scalings in the
''decoupled range.'' We observe that $Pr_t\approx1 \text{~to~}2$ at the
smallest inertial-inductive scales, increasing to $\approx 5$ at the largest
scales. However, based on physical considerations, our analysis suggests that
$Pr_t$ has to become scale-independent and of order unity in the decoupled
range at sufficiently high Reynolds numbers (or grid-resolution), and that the
power-law scaling exponents of velocity and magnetic spectra become equal. In
addition to implications to astrophysical systems, the scale-dependent
turbulent transport coefficients offer a guide for large eddy simulation
modeling. | 2107.00861v1 |
2023-01-23 | Correction of high-order phase variation effects in dynamic field monitoring | Purpose: Field monitoring measures field perturbations, which can be
accounted for during image reconstructions. In certain field monitoring
environments, significant phase deviations can arise far from isocenter due to
the finite extent of the gradient and/or main magnet. This can degrade the
accuracy of field dynamics when field probes are placed near or outside the
diameter spherical volume of the gradient coils and/or main magnet, leading to
corrupted image quality. The objective of this work was to develop a correction
algorithm that reduces errors from highly nonlinear phase variations at distant
field probes in field dynamic fits. Methods: The algorithm is split into three
components. Component one fits phase coefficients one spatial order at a time,
while the second implements a weighted least squares solution based on probe
distance. After initial fitting, component three calculates phase residuals and
removes the phase for distant probes before re-fitting. Two healthy volunteers
were scanned on a head-only 7T MRI using diffusion-weighted single-shot spiral
and EPI sequences and field monitoring was performed. Images were reconstructed
with and without phase coefficient correction and compared qualitatively.
Results: The algorithm was able to correct corrupted field dynamics, resulting
in image quality improvements. Significant artefact reduction was observed when
correcting higher order fits, especially for diffusion weighted images.
Stepwise fitting provided the most correction benefit, which was marginally
improved when adding weighted least squares and phase residual corrections.
Conclusion: The proposed algorithm can mitigate effects of phase errors in
field monitoring, providing improved reliability of field dynamic
characterization. | 2301.09726v1 |
2003-03-17 | Quantum phase space function formulation of reactive flux theory | On the basis of a coherent state representation of quantum noise operator and
an ensemble averaging procedure a scheme for quantum Brownian motion has been
proposed recently [Banerjee {\it et al}, Phys. Rev. E {\bf65}, 021109 (2002);
{\bf66}, 051105 (2002)]. We extend this approach to formulate reactive flux
theory in terms of quantum phase space distribution functions and to derive a
time dependent quantum transmission coefficient - a quantum analogue of
classical Kramers'-Grote-Hynes coefficient in the spirit of Kohen and Tannor's
classical formulation. The theory is valid for arbitrary noise correlation and
temperature. The specific forms of this coefficient in the Markovian as well as
in the non-Markovian limits have been worked out in detail for intermediate to
strong damping regime with an analysis of quantum effects. While the classical
transmission coefficient is independent of temperature, its quantum counterpart
has significant temperature dependence particularly in the low temperature
regime. | 0303319v1 |
2017-01-30 | Regularized solutions for some backward nonlinear parabolic equations with statistical data | In this paper, we study the backward problem of determining initial condition
for some class of nonlinear parabolic equations in multidimensional domain
where data are given under random noise. This problem is ill-posed, i.e., the
solution does not depend continuously on the data. To regularize the instable
solution, we develop some new methods to construct some new regularized
solution. We also investigate the convergence rate between the regularized
solution and the solution of our equations. In particular, we establish results
for several equations with constant coefficients and time dependent
coefficients. The equations with constant coefficients include heat equation,
extended Fisher-Kolmogorov equation, Swift-Hohenberg equation and many others.
The equations with time dependent coefficients include Fisher type Logistic
equations, Huxley equation, Fitzhugh-Nagumo equation. The methods developed in
this paper can also be applied to get approximate solutions to several other
equations including 1-D Kuramoto-Sivashinsky equation, 1-D modified
Swift-Hohenberg equation, strongly damped wave equation and 1-D Burger's
equation with randomly perturbed operator. | 1701.08459v2 |
2019-04-18 | Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems | Many studies on biological and soft matter systems report the joint presence
of a linear mean-squared displacement and a non-Gaussian probability density
exhibiting, for instance, exponential or stretched-Gaussian tails. This
phenomenon is ascribed to the heterogeneity of the medium and is captured by
random parameter models such as "superstatistics" or "diffusing diffusivity".
Independently, scientists working in the area of time series analysis and
statistics have studied a class of discrete-time processes with similar
properties, namely, random coefficient autoregressive models. In this work we
try to reconcile these two approaches and thus provide a bridge between
physical stochastic processes and autoregressive models. We start from the
basic Langevin equation of motion with time-varying damping or diffusion
coefficients and establish the link to random coefficient autoregressive
processes. By exploring that link we gain access to efficient statistical
methods which can help to identify data exhibiting Brownian yet non-Gaussian
diffusion. | 1904.08737v2 |
2023-05-10 | Poles of hydrodynamic spectral functions and Einstein-Helfand formulas for transport coefficients | The local-equilibrium approach to transport processes is related to the
approach based on time-dependent correlation functions and their associated
spectral functions characterizing the equilibrium fluctuations of particle,
momentum and other densities. On the one hand, the transport coefficients are
calculated with the Einstein-Helfand formulas derived in the local-equilibrium
approach. On the other hand, the poles of the spectral functions at complex
frequencies give the damping rates of the hydrodynamic modes. Since these rates
also depend on the transport coefficients, their values can be compared to the
predictions of the local-equilibrium approach. This comparison is
systematically carried out for the hard-sphere fluid by computing numerically
the transport coefficients, the spectral functions, and their poles as a
function of the wave number in the hydrodynamic limit. The study shows the
consistency between the two approaches for the determination of the transport
properties. | 2305.06287v1 |
2023-06-08 | Temperature anomalies of oscillating diffusion in ac-driven periodic systems | We analyse the impact of temperature on the diffusion coefficient of an
inertial Brownian particle moving in a symmetric periodic potential and driven
by a symmetric time-periodic force. Recent studies have revealed the low
friction regime in which the diffusion coefficient shows giant damped
quasi-periodic oscillations as a function of the amplitude of the time-periodic
force [I. G. Marchenko et al., Chaos 32, 113106 (2022)]. We find out that when
temperature grows the diffusion coefficient increases at its minima, however,
it decreases at the maxima within a finite temperature window. This curious
behavior is explained in terms of the deterministic dynamics perturbed by
thermal fluctuations and mean residence time of the particle in the locked and
running trajectories. We demonstrate that temperature dependence of the
diffusion coefficient can be accurately reconstructed from the stationary
probability to occupy the running trajectories. | 2306.04977v1 |
2024-03-22 | Investigating the Relationship between Simulation Parameters and Flow Variables in Simulating Atmospheric Gravity Waves in Wind Energy Applications | Wind farms, particularly offshore clusters, are becoming larger than ever
before. Besides influencing wind farms and local meteorology downstream, large
wind farms can trigger atmospheric gravity waves in the inversion layer and the
free atmosphere aloft. Wind farm-induced gravity waves can cause adverse
pressure gradients upstream of the wind farm, that contribute to the global
blockage effect, and favorable pressure gradients above and downstream of the
wind farm that enhance wake recovery.
Numerical modeling is a powerful means of studying wind farm-induced
atmospheric gravity waves, but it comes with the challenge of handling spurious
reflections of these waves from domain boundaries. Approaches like radiation
boundary conditions and forcing zones are used to avoid the reflections.
However, the simulation setup heavily relies on ad-hoc processes. For instance,
the widely used Rayleigh damping method requires ad-hoc tuning to acquire a
setup only applicable to a particular case. To surmount this hurdle, we conduct
a systematic LES study for flow over a 2D hill and through wind farm canopies
that explores the dependence of domain size and damping layer setup on
parameters driving linearly stratified atmospheric flows.
Mainly the internal waves in the free atmosphere reflect from the boundaries,
therefore by simulation linearly stratified conditions we focus on internal
waves only. The Froude number drives most of the internal wave properties, such
as wavelengths, amplitude, and direction. Therefore, the domain sizing and
Rayleigh damping layer setup mainly depends on the Froude number. We
anticipated the effective wavelengths to be the correct length scale to size
the domain and damping layer thickness. Also, the damping coefficient is scaled
with Brunt-V\"ais\"al\"a frequency. | 2403.18863v1 |
2000-02-23 | Two-frequency forced Faraday waves: Weakly damped modes and pattern selection | Recent experiments (Kudrolli, Pier and Gollub, 1998) on two-frequency
parametrically excited surface waves exhibit an intriguing "superlattice" wave
pattern near a codimension-two bifurcation point where both subharmonic and
harmonic waves onset simultaneously, but with different spatial wavenumbers.
The superlattice pattern is synchronous with the forcing, spatially periodic on
a large hexagonal lattice, and exhibits small-scale triangular structure.
Similar patterns have been shown to exist as primary solution branches of a
generic 12-dimensional $D_6\dot{+}T^2$-equivariant bifurcation problem, and may
be stable if the nonlinear coefficients of the bifurcation problem satisfy
certain inequalities (Silber and Proctor, 1998). Here we use the spatial and
temporal symmetries of the problem to argue that weakly damped harmonic waves
may be critical to understanding the stabilization of this pattern in the
Faraday system. We illustrate this mechanism by considering the equations
developed by Zhang and Vinals (1997, J. Fluid Mech. 336) for small amplitude,
weakly damped surface waves on a semi-infinite fluid layer. We compute the
relevant nonlinear coefficients in the bifurcation equations describing the
onset of patterns for excitation frequency ratios of 2/3 and 6/7. For the 2/3
case, we show that there is a fundamental difference in the pattern selection
problems for subharmonic and harmonic instabilities near the codimension-two
point. Also, we find that the 6/7 case is significantly different from the 2/3
case due to the presence of additional weakly damped harmonic modes. These
additional harmonic modes can result in a stabilization of the superpatterns. | 0002041v2 |
2007-12-28 | Role of antikaon condensation in r-mode instability | We investigate the effect of antikaon condensed matter on bulk viscosity in
rotating neutron stars. We use relativistic field theoretical models to
construct the equation of state of neutron stars with the condensate, where the
phase transition from nucleonic to $K^-$ condensed phase is assumed to be of
first order. We calculate the coefficient of bulk viscosity due to the
non-leptonic weak interaction n --> p + K^-. The influence of antikaon bulk
viscosity on the gravitational radiation reaction driven instability in the
r-modes is investigated. We compare our results with the previously studied
non-leptonic weak interaction $n + p --> p + \Lambda$ involving hyperons on the
damping of the r-mode oscillations.
We find that the bulk viscosity coefficient due to the non-leptonic weak
process involving the condensate is suppressed by several orders of magnitude
in comparison with the non-superfluid hyperon bulk viscosity coefficient.
Consequently, the antikaon bulk viscosity may not be able to damp the r-mode
instability, while hyperon bulk viscosity can effectively suppress r-mode
oscillations at low temperatures. Hence neutron stars containing $K^-$
condensate in their core could be possible sources of gravitational waves. | 0712.4347v1 |
2020-03-30 | DAMPE proton spectrum indicates a slow-diffusion zone in the nearby ISM | The hardening and softening features in the DAMPE proton spectrum are very
likely to be originated from a nearby supernova remnant (SNR). The proton
spectrum from the nearby SNR is required to be very hard below $\approx10$ TeV.
To reproduce this feature, we illustrate that anomalously slow-diffusion zone
for cosmic rays (CRs) must be existed in the local interstellar medium (ISM)
after also taking the dipole anisotropy of CRs into account. Assuming that the
diffusion coefficient is homogeneous in the nearby ISM, we show that the
diffusion coefficient is constrained to the magnitude of $10^{26}$ cm$^2$
s$^{-1}$ when normalized to 1 GeV, which is about 100 times smaller than the
average value in the Galaxy. We further discuss the spatial distribution of the
slow diffusion and find two distinct possibilities. In one case, the SNR is
several hundred of parsecs away from the solar system, meanwhile both the SNR
and the solar system are required to be included in a large slow-diffusion
zone. The homogeneous diffusion belongs to this case. In the other case, the
SNR is very close with a distance of $\sim50$ pc and the slow-diffusion zone is
only limited around the SNR. The required diffusion coefficient is further
smaller in the latter case. This work provides a new way of studying the CR
diffusion in the local ISM. | 2003.13635v1 |
2021-08-20 | Cosmic-Ray Transport in Simulations of Star-forming Galactic Disks | Cosmic ray transport on galactic scales depends on the detailed properties of
the magnetized, multiphase interstellar medium (ISM). In this work, we
post-process a high-resolution TIGRESS magnetohydrodynamic simulation modeling
a local galactic disk patch with a two-moment fluid algorithm for cosmic ray
transport. We consider a variety of prescriptions for the cosmic rays, from a
simple purely diffusive formalism with constant scattering coefficient, to a
physically-motivated model in which the scattering coefficient is set by
critical balance between streaming-driven Alfv\'en wave excitation and damping
mediated by local gas properties. We separately focus on cosmic rays with
kinetic energies of $\sim 1$ GeV (high-energy) and $\sim 30$~MeV (low-energy),
respectively important for ISM dynamics and chemistry. We find that
simultaneously accounting for advection, streaming, and diffusion of cosmic
rays is crucial for properly modeling their transport. Advection dominates in
the high-velocity, low-density, hot phase, while diffusion and streaming are
more important in higher density, cooler phases. Our physically-motivated model
shows that there is no single diffusivity for cosmic-ray transport: the
scattering coefficient varies by four or more orders of magnitude, maximal at
density $n_\mathrm{H} \sim 0.01\, \mathrm{cm}^{-3}$. Ion-neutral damping of
Alfv\'en waves results in strong diffusion and nearly uniform cosmic ray
pressure within most of the mass of the ISM. However, cosmic rays are trapped
near the disk midplane by the higher scattering rate in the surrounding
lower-density, higher-ionization gas. The transport of high-energy cosmic rays
differs from that of low-energy cosmic rays, with less effective diffusion and
greater energy losses for the latter. | 2108.09356v1 |
2021-08-29 | Sound induced by a simple impact oscillator | Acoustic radiation due to vibration and impact of a spring-mass-damper
oscillator whose motion is constrained by a barrier is analyzed at a field
point in a free field. Impact between the mass and the barrier is modeled using
a coefficient of restitution model. Non-linear behavior of the oscillator is
observed due to motion constraint. Steady state response is studied using a
bifurcation diagram. For small amplitudes of oscillation, the pressure
perturbation by a vibrating mass in a compressible fluid is modeled as an
acoustic dipole with its center at the equilibrium position of the mass and its
axis aligned with the motion of the oscillator. The boundary condition for the
acoustic domain is an acoustic free-field condition. It is observed that the
unsteady acoustic pressure resulting from the impact force is a few orders of
magnitude greater relative to the pressure field resulting from vibration alone
before or after impact. We also analyzed the influence of coefficient of
restitution, damping ratio, the ration of base excitation frequency to the
natural frequency, and the ratio of the distance of the barrier to the base
excitation amplitude on the acoustic radiation. Damping ratio and coefficient
of restituion are shown to be the most significant paramters that affect the
acoustic radiation from the vibro-impact oscillator. | 2108.12804v1 |
2022-04-30 | A spectral element solution of the 2D linearized potential flow radiation problem | We present a scalable 2D Galerkin spectral element method solution to the
linearized potential flow radiation problem for wave induced forcing of a
floating offshore structure. The pseudo-impulsive formulation of the problem is
solved in the time-domain using a Gaussian displacement signal tailored to the
discrete resolution. The added mass and damping coefficients are then obtained
via Fourier transformation. The spectral element method is used to discretize
the spatial fluid domain, whereas the classical explicit 4-stage 4th order
Runge-Kutta scheme is employed for the temporal integration. Spectral
convergence of the proposed model is established for both affine and
curvilinear elements, and the computational effort is shown to scale with
$\mathcal{O}(N^p)$, with $N$ begin the total number of grid points and $p
\approx 1$. Temporal stability properties, caused by the spatial resolution,
are considered to ensure a stable model. The solver is used to compute the
hydrodynamic coefficients for several floating bodies and compare against known
public benchmark results. The results are showing excellent agreement,
ultimately validating the solver and emphasizing the geometrical flexibility
and high accuracy and efficiency of the proposed solver strategy. Lastly, an
extensive investigation of non-resolved energy from the pseudo-impulse is
carried out to characterise the induced spurious oscillations of the free
surface quantities leading to a verification of a proposal on how to
efficiently and accurately calculate added mass and damping coefficients in
pseudo-impulsive solvers. | 2205.00184v1 |
2007-02-23 | Organization of the Modulopt collection of optimization problems in the Libopt environment -- Version 1.0 | This note describes how the optimization problems of the Modulopt collection
are organized within the Libopt environment. It is aimed at being a guide for
using and enriching this collection in this environment. | 0702695v1 |
2005-10-17 | Comment on "Operator Quantum Error Correction" | The attempt to equate operator quantum error correction (quant-ph/0504189v1)
with the quantum computer condition (quant-ph/0507141) in version two of
quant-ph/0504189 is shown to be invalid. | 0510116v1 |
2007-09-17 | H-Decompositions | We show that for all graphs H of size n, the complete graph $K_{2n+1}$ has an
$H$-decomposition. | 0709.2525v5 |
2008-10-06 | Unsolvability of the isomorphism problem for [free abelian]-by-free groups | The isomorphism problem for [free abelian]-by-free groups is unsolvable. | 0810.0935v2 |
2011-11-27 | Comment on "Capturing correlations in chaotic diffusion by approximation methods" | This is a comment on [G. Knight and R. Klages, Phys. Rev. E 84, 041135
(2011); also available at arXiv:1107.5293v2 [math-ph]]. | 1111.6271v1 |
2014-01-11 | Hashimoto transform for stochastic Landau-Lifshitz-Gilbert equation | We show that Hashimoto transformation is applicable to the one dimensional
stochastic Landau-Lifshitz-Gilbert (LLG) equation and transforms it to the
stochastic generalized heat equation with nonlocal (in space) interaction. | 1401.2520v1 |
2017-01-04 | Non-linear Cyclic Codes that Attain the Gilbert-Varshamov Bound | We prove that there exist non-linear binary cyclic codes that attain the
Gilbert-Varshamov bound. | 1701.01043v1 |
2019-01-28 | Conformal deformations preserving the Finslerian $R$-Einstein criterion | Given a Finslerian metric $F$ on a $C^4$-manifold, conformal deformations of
$F$ preserving the $R$-Einstein criterion are presented. In particular, locally
conformal invariance between two Finslerian $R$-Einstein metrics is
characterized. | 1902.00069v1 |
2022-04-07 | How to design a network architecture using availability | The best way to design a network is to take into account Availability values
and Capacity Planning. You already saw Availability expressed with numbers such
as 99.99%. The purpose of this document is to introduce the way to compute
Availability values using Reliability Block Diagrams. | 2204.03311v1 |
2022-01-06 | Parameter-free quantum hydrodynamic theory for plasmonics: Electron density-dependent damping rate and diffusion coefficient | Plasmonics is a rapid growing field, which has enabled both fundamental
science and inventions of various quantum optoelectronic devices. An accurate
and efficient method to calculate the optical response of metallic structures
with feature size in the nanoscale plays an important role. Quantum
hydrodynamic theory (QHT) provides an efficient description of the
free-electron gas, where quantum effects of nonlocality and spill-out are taken
into account. In this work, we introduce a general QHT that includes diffusion
to account for the broadening, which is a key problem in practical applications
of surface plasmon. We will introduce a density-dependent diffusion coefficient
to give very accurate linewidth. It is a self-consistent method, in which both
the ground and excited states are solved by using the same energy functional,
with the kinetic energy described by the Thomas-Fermi and von Weizs\"{a}cker
(vW) formalisms. In addition, our QHT method is stable by introduction of an
electron density-dependent damping rate. For sodium nanosphere of various
sizes, the plasmon energy and broadening by our QHT method are in excellent
agreement with those by density functional theory and Kreibig formula. By
applying our QHT method to sodium jellium nanorods, we clearly show that our
method enables a parameter-free simulation, i.e. without resorting to any
empirical parameter, such as size-dependent damping rate and diffusing
coefficient. It is found that there exists a perfect linear relation between
the resonance wavelength and aspect radio. The width decreases with increasing
aspect ratio and height. The calculations show that our QHT method provides an
explicit and unified way to account for size-dependent frequency shifts and
broadening of arbitrarily shaped geometries. It is reliable and robust with
great predicability, and hence provides a general and efficient platform to
study plasmonics. | 2201.03426v3 |
2010-02-22 | Transport and magnetization dynamics in a superconductor/single-molecule magnet/superconductor junction | We study dc-transport and magnetization dynamics in a junction of arbitrary
transparency consisting of two spin-singlet superconducting leads connected via
a single classical spin precessing at the frequency $\Omega$. The presence of
the spin in the junction provides different transmission amplitudes for spin-up
and spin-down quasiparticles as well as a time-dependent spin-flip transmission
term. For a phase biased junction, we show that a steady-state superconducting
charge current flows through the junction and that an out-of-equilibrium
circularly polarized spin current, of frequency $\Omega$, is emitted in the
leads. Detailed understanding of the charge and spin currents is obtained in
the entire parameter range. In the adiabatic regime, $\hbar \Omega \ll 2\Delta$
where $\Delta$ is the superconducting gap, and for high transparencies of the
junction, a strong suppression of the current takes place around $\vp \approx
0$ due to an abrupt change in the occupation of the Andreev bound-states. At
higher values of the phase and/or precession frequency, extended
(quasi-particle like) states compete with the bound-states in order to carry
the current. Well below the superconducting transition, these results are shown
to be weakly affected by the back-action of the spin current on the dynamics of
the precessing spin. Indeed, we show that the Gilbert damping due to the
quasi-particle spin current is strongly suppressed at low-temperatures, which
goes along with a shift of the precession frequency due to the condensate. The
results obtained may be of interest for on-going experiments in the field of
molecular spintronics. | 1002.3929v4 |
2013-06-18 | Baryons do trace dark matter 380,000 years after the big bang: Search for compensated isocurvature perturbations with WMAP 9-year data | Primordial isocurvature fluctuations between photons and either neutrinos or
non-relativistic species such as baryons or dark matter are known to be
sub-dominant to adiabatic fluctuations. Perturbations in the relative densities
of baryons and dark matter (known as compensated isocurvature perturbations, or
CIPs), however, are surprisingly poorly constrained. CIPs leave no imprint in
the cosmic microwave background (CMB) on observable scales, at least at linear
order in their amplitude and zeroth order in the amplitude of adiabatic
perturbations. It is thus not yet empirically known if baryons trace dark
matter at the surface of last scattering. If CIPs exist, they would spatially
modulate the Silk damping scale and acoustic horizon, causing distinct
fluctuations in the CMB temperature/polarization power spectra across the sky:
this effect is first order in both the CIP and adiabatic mode amplitudes. Here,
temperature data from the Wilkinson Microwave Anisotropy Probe (WMAP) are used
to conduct the first CMB-based observational search for CIPs, using
off-diagonal correlations and the CMB trispectrum. Reconstruction noise from
weak lensing and point sources is shown to be negligible for this data set. No
evidence for CIPs is observed, and a 95%-confidence upper limit of $1.1\times
10^{-2}$ is imposed to the amplitude of a scale-invariant CIP power spectrum.
This limit agrees with CIP sensitivity forecasts for WMAP, and is competitive
with smaller scale constraints from measurements of the baryon fraction in
galaxy clusters. It is shown that the root-mean-squared CIP amplitude on 5-100
degree scales is smaller than 0.07-0.17 (depending on the scale) at the
95%-confidence level. Temperature data from the Planck satellite will provide
an even more sensitive probe for the existence of CIPs, as will the upcoming
ACTPol and SPTPol experiments on smaller angular scales. | 1306.4319v1 |
2015-05-29 | Microscopic Theory for Coupled Atomistic Magnetization and Lattice Dynamics | A coupled atomistic spin and lattice dynamics approach is developed which
merges the dynamics of these two degrees of freedom into a single set of
coupled equations of motion. The underlying microscopic model comprises local
exchange interactions between the electron spin and magnetic moment and the
local couplings between the electronic charge and lattice displacements. An
effective action for the spin and lattice variables is constructed in which the
interactions among the spin and lattice components are determined by the
underlying electronic structure. In this way, expressions are obtained for the
electronically mediated couplings between the spin and lattice degrees of
freedom, besides the well known inter-atomic force constants and spin-spin
interactions. These former susceptibilities provide an atomistic ab initio
description for the coupled spin and lattice dynamics. It is important to
notice that this theory is strictly bilinear in the spin and lattice variables
and provides a minimal model for the coupled dynamics of these subsystems and
that the two subsystems are treated on the same footing. Questions concerning
time-reversal and inversion symmetry are rigorously addressed and it is shown
how these aspects are absorbed in the tensor structure of the interaction
fields. By means of these results regarding the spin-lattice coupling, simple
explanations of ionic dimerization in double anti-ferromagnetic materials, as
well as, charge density waves induced by a non-uniform spin structure are
given. In the final parts, a set of coupled equations of motion for the
combined spin and lattice dynamics are constructed, which subsequently can be
reduced to a form which is analogous to the Landau-Lifshitz-Gilbert equations
for spin dynamics and damped driven mechanical oscillator for the ... | 1505.08005v3 |
2016-04-28 | Dynamics of skyrmionic states in confined helimagnetic nanostructures | In confined helimagnetic nanostructures, skyrmionic states in the form of
incomplete and isolated skyrmion states can emerge as the ground state in
absence of both external magnetic field and magnetocrystalline anisotropy. In
this work, we study the dynamic properties (resonance frequencies and
corresponding eigenmodes) of skyrmionic states in thin film FeGe disk samples.
We employ two different methods in finite-element based micromagnetic
simulation: eigenvalue and ringdown method. The eigenvalue method allows us to
identify all resonance frequencies and corresponding eigenmodes that can exist
in the simulated system. However, using a particular experimentally feasible
excitation can excite only a limited set of eigenmodes. Because of that, we
perform ringdown simulations that resemble the experimental setup using both
in-plane and out-of-plane excitations. In addition, we report the nonlinear
dependence of resonance frequencies on the external magnetic bias field and
disk sample diameter and discuss the possible reversal mode of skyrmionic
states. We compare the power spectral densities of incomplete skyrmion and
isolated skyrmion states and observe several key differences that can
contribute to the experimental identification of the state present in the
sample. We measure the FeGe Gilbert damping, and using its value we determine
what eigenmodes can be expected to be observed in experiments. Finally, we show
that neglecting the demagnetisation energy contribution or ignoring the
magnetisation variation in the out-of-film direction - although not changing
the eigenmode's magnetisation dynamics significantly - changes their resonance
frequencies substantially. Apart from contributing to the understanding of
skyrmionic states physics, this systematic work can be used as a guide for the
experimental identification of skyrmionic states in confined helimagnetic
nanostructures. | 1604.08347v2 |
2017-04-13 | Low energy magnon dynamics and magneto-optics of the skyrmionic Mott insulator Cu$_2$OSeO$_3$ | In this work, we present a comprehensive study of the low energy optical
magnetic response of the skyrmionic Mott insulator Cu$_2$OSeO$_3$ via high
resolution time-domain THz spectroscopy. In zero field, a new magnetic
excitation not predicted by spin-wave theory with frequency $f$ = 2.03 THz is
observed and shown, with accompanying time-of-flight neutron scattering
experiments, to be a zone folded magnon from the $\mathrm{R}$ to
$\mathrm{\Gamma}$ points of the Brillouin zone. Highly sensitive polarimetry
experiments performed in weak magnetic fields, $\mu_0$H $<$ 200 mT, observe
Faraday and Kerr rotations which are proportional to the sample magnetization,
allowing for optical detection of the skyrmion phase and construction of a
magnetic phase diagram. From these measurements, we extract a critical exponent
of $\beta$ = 0.35 $\pm$ 0.04, in good agreement with the expected value for the
3D Heisenberg universality class of $\beta$ = 0.367. In large magnetic fields,
$\mu_0$H $>$ 5 T, we observe the magnetically active uniform mode of the
ferrimagnetic field polarized phase whose dynamics as a function of field and
temperature are studied. In addition to extracting a $g_\text{eff}$ = 2.08
$\pm$ 0.03, we observe the uniform mode to decay through a non-Gilbert damping
mechanism and to possesses a finite spontaneous decay rate, $\Gamma_0$
$\approx$ 25 GHz, in the zero temperature limit. Our observations are
attributed to Dzyaloshinkii-Moriya interactions, which have been proposed to be
exceptionally strong in Cu$_2$OSeO$_3$ and are expected to impact the low
energy magnetic response of such chiral magnets. | 1704.04228v1 |
2017-08-25 | Role of dimensional crossover on spin-orbit torque efficiency in magnetic insulator thin films | Magnetic insulators (MIs) attract tremendous interest for spintronic
applications due to low Gilbert damping and absence of Ohmic loss. Magnetic
order of MIs can be manipulated and even switched by spin-orbit torques (SOTs)
generated through spin Hall effect and Rashba-Edelstein effect in heavy
metal/MI bilayers. SOTs on MIs are more intriguing than magnetic metals since
SOTs cannot be transferred to MIs through direct injection of electron spins.
Understanding of SOTs on MIs remains elusive, especially how SOTs scale with
the film thickness. Here, we observe the critical role of dimensionality on the
SOT efficiency by systematically studying the MI layer thickness dependent SOT
efficiency in tungsten/thulium iron garnet (W/TmIG) bilayers. We first show
that the TmIG thin film evolves from two-dimensional to three-dimensional
magnetic phase transitions as the thickness increases, due to the suppression
of long-wavelength thermal fluctuation. Then, we report the significant
enhancement of the measured SOT efficiency as the thickness increases. We
attribute this effect to the increase of the magnetic moment density in concert
with the suppression of thermal fluctuations. At last, we demonstrate the
current-induced SOT switching in the W/TmIG bilayers with a TmIG thickness up
to 15 nm. The switching current density is comparable with those of heavy
metal/ferromagnetic metal cases. Our findings shed light on the understanding
of SOTs in MIs, which is important for the future development of ultrathin
MI-based low-power spintronics. | 1708.07584v2 |
2018-07-04 | Phase Boundary Exchange Coupling in the Mixed Magnetic Phase Regime of a Pd-doped FeRh Epilayer | Spin-wave resonance measurements were performed in the mixed magnetic phase
regime of a Pd-doped FeRh epilayer that appears as the first-order
ferromagnetic-antiferromagnetic phase transition takes place. It is seen that
the measured value of the exchange stiffness is suppressed throughout the
measurement range when compared to the expected value of the fully
ferromagnetic regime, extracted via the independent means of a measurement of
the Curie point, for only slight changes in the ferromagnetic volume fraction.
This behavior is attributed to the influence of the antiferromagnetic phase:
inspired by previous experiments that show ferromagnetism to be most persistent
at the surfaces and interfaces of FeRh thin films, we modelled the
antiferromagnetic phase as forming a thin layer in the middle of the epilayer
through which the two ferromagnetic layers are coupled up to a certain critical
thickness. The development of this exchange stiffness is then consistent with
that expected from the development of an exchange coupling across the magnetic
phase boundary, as a consequence of a thickness dependent phase transition
taking place in the antiferromagnetic regions and is supported by complimentary
computer simulations of atomistic spin-dynamics. The development of the Gilbert
damping parameter extracted from the ferromagnetic resonance investigations is
consistent with this picture. | 1807.01615v6 |
2018-07-26 | EPIC 246851721 b: A Tropical Jupiter Transiting a Rapidly Rotating Star in a Well-Aligned Orbit | We report the discovery of EPIC 246851721 b, a "tropical" Jupiter in a
6.18-day orbit around the bright ($V=11.439$) star EPIC 246851721 (TYC
1283-739-1). We present a detailed analysis of the system using $K2$ and
ground-based photometry, radial velocities, Doppler tomography and adaptive
optics imaging. From our global models, we infer that the host star is a
rapidly rotating ($v \sin i = 74.92 $ km s$^{-1}$) F dwarf with
$T_\mathrm{eff}$ = 6202 K, $R_\star = 1.586 \ R_\odot$ and $M_\star= 1.317 \
M_\odot$. EPIC 246851721 b has a radius of $1.051 \pm 0.044 R_J$, and a mass of
3.0$^{+1.1}_{-1.2} M_J$ . Doppler tomography reveals an aligned spin-orbit
geometry, with a projected obliquity of $-1.47^{\circ\ +0.87}_{\ -0.86}$,
making EPIC 246851721 the fourth hottest star to host a Jovian planet with $P >
5$ days and a known obliquity. Using quasi-periodic signatures in its light
curve that appear to be spot modulations, we estimate the star's rotation
period, and thereby infer the true obliquity of the system to be $3.7^{\circ\
+3.7}_{\ -1.8}$. We argue that this near-zero obliquity is likely to be
primordial rather than a result of tidal damping. The host star also has a
bound stellar companion, a $0.4 \ M_\odot$ M dwarf at a projected separation of
2100 AU, but the companion is likely incapable of emplacing EPIC 246851721 b in
its current orbit via high eccentricity Kozai-Lidov migration. | 1807.10298v2 |
2018-09-10 | Magnetic properties and field-driven dynamics of chiral domain walls in epitaxial Pt/Co/Au$_x$Pt$_{1-x}$ trilayers | Chiral domain walls in ultrathin perpendicularly magnetised layers have a
N\'{e}el structure stabilised by a Dzyaloshinskii-Moriya interaction (DMI) that
is generated at the interface between the ferromagnet and a heavy metal.
Different heavy metals are required above and below a ferromagnetic film in
order to generate the structural inversion asymmetry needed to ensure that the
DMI arising at the two interfaces does not cancel. Here we report on the
magnetic properties of epitaxial Pt/Co/Au$_x$Pt$_{1-x}$ trilayers grown by
sputtering onto sapphire substrates with 0.6 nm thick Co. As $x$ rises from 0
to 1 a structural inversion asymmetry is generated. We characterise the
epilayer structure with x-ray diffraction and cross-sectional transmission
electron microscopy, revealing (111) stacking. The saturation magnetization
falls as the proximity magnetisation in Pt is reduced, whilst the perpendicular
magnetic anisotropy $K_\mathrm{u}$ rises. The micromagnetic DMI strength $D$
was determined using the bubble expansion technique and also rises from a
negligible value when $x=0$ to $\sim 1$ mJ/m$^2$ for $x = 1$. The depinning
field at which field-driven domain wall motion crosses from the creep to the
depinning regime rises from $\sim 40$ to $\sim 70$ mT, attributed to greater
spatial fluctuations of the domain wall energy with increasing Au
concentration. Meanwhile, the increase in DMI causes the Walker field to rise
from $\sim 10$ to $\sim 280$ mT, meaning that only in the $x = 1$ sample is the
steady flow regime accessible. The full dependence of domain wall velocity on
driving field bears little resemblance to the prediction of a simple
one-dimensional model, but can be described very well using micromagnetic
simulations with a realistic model of disorder. These reveal a rise in Gilbert
damping as $x$ increases. | 1809.03217v2 |
2019-09-06 | Macrospin analysis of RF excitations within fully perpendicular magnetic tunnel junctions with second order easy-axis magnetic anisotropy contribution | The conditions of field and voltage for inducing steady state excitations in
fully perpendicular magnetic tunnel junctions (pMTJs), adapted for memory
applications, were numerically investigated by the resolution of the
Landau-Lifshitz-Gilbert equation in the macrospin approach. Both damping-like
and the field-like spin transfer torque terms were taken into account in the
simulations, as well as the contribution of the second order uniaxial
anisotropy term (K2), which has been recently revealed in MgO-based pMTJs. An
in-plane applied magnetic field balances the out of plane symmetry of the pMTJ
and allows the signal detection. Using this model, we assessed the states of
the free layer magnetization as a function of strength of K2 and polar theta_H
angle of the applied field (varied from 90 to 60 deg.). There are two stable
states, with the magnetization in-plane or out of plane of the layer, and two
dynamic states with self-sustained oscillations, called in-plane precession
state (IPP) or out of plane precession state (OPP). The IPP mode, with
oscillation frequencies up to 7 GHz, appears only for positive voltages if
theta_H = 90 deg. However, it shows a more complex distribution when the field
is slightly tilted out of plane. The OPP mode is excited only if K2 is
considered and reaches a maximum oscillation frequency of 15 GHz. Large areas
of dynamic states with high frequencies are obtained for strong values of the
field-like torque and K2, when applying a slightly tilted external field toward
the out of plane direction. The non-zero temperature does not modify the phase
diagrams, but reduces drastically the power spectral density peak amplitudes. | 1909.02926v1 |
2021-04-21 | Atomic Layer Deposition of Yttrium Iron Garnet Thin Films for 3D Magnetic Structures | A wide variety of new phenomena such as novel magnetization configurations
have been predicted to occur in three dimensional magnetic nanostructures.
However, the fabrication of such structures is often challenging due to the
specific shapes required, such as magnetic tubes and spirals. Furthermore, the
materials currently used to assemble these structures are predominantly
magnetic metals that do not allow to study the magnetic response of the system
separately from the electronic one. In the field of spintronics, the
prototypical material used for such experiments is the ferrimagnetic insulator
yttrium iron garnet (Y$_3$Fe$_5$O$_{12}$, YIG). YIG is one of the best
materials especially for magnonic studies due to its low Gilbert damping. Here,
we report the first successful fabrication of YIG thin films via atomic layer
deposition. To that end we utilize a supercycle approach based on the
combination of sub-nanometer thin layers of the binary systems Fe$_2$O$_3$ and
Y$_2$O$_3$ in the correct atomic ratio on Y$_3$Al$_5$O$_{12}$ substrates with a
subsequent annealing step. Our process is robust against typical growth-related
deviations, ensuring a good reproducibility. The ALD-YIG thin films exhibit a
good crystalline quality as well as magnetic properties comparable to other
deposition techniques. One of the outstanding characteristics of atomic layer
deposition is its ability to conformally coat arbitrarily-shaped substrates.
ALD hence is the ideal deposition technique to grant an extensive freedom in
choosing the shape of the magnetic system. The atomic layer deposition of YIG
enables the fabrication of novel three dimensional magnetic nanostructures,
which in turn can be utilized for experimentally investigating the phenomena
predicted in those structures. | 2104.10293v2 |
2022-11-03 | Skyrmion Jellyfish in Driven Chiral Magnets | Chiral magnets can host topological particles known as skyrmions, which carry
an exactly quantised topological charge $Q=-1$. In the presence of an
oscillating magnetic field ${\bf B}_1(t)$, a single skyrmion embedded in a
ferromagnetic background will start to move with constant velocity ${\bf
v}_{\text{trans}}$. The mechanism behind this motion is similar to the one used
by a jellyfish when it swims through water. We show that the skyrmion's motion
is a universal phenomenon, arising in any magnetic system with translational
modes. By projecting the equation of motion onto the skyrmion's translational
modes and going to quadratic order in ${\bf B}_1(t)$, we obtain an analytical
expression for ${\bf v}_{\text{trans}}$ as a function of the system's linear
response. The linear response and consequently ${\bf v}_{\text{trans}}$ are
influenced by the skyrmion's internal modes and scattering states, as well as
by the ferromagnetic background's Kittel mode. The direction and speed of ${\bf
v}_{\text{trans}}$ can be controlled by changing the polarisation, frequency
and phase of the driving field ${\bf B}_1(t)$. For systems with small Gilbert
damping parameter $\alpha$, we identify two distinct physical mechanisms used
by the skyrmion to move. At low driving frequencies, the skyrmion's motion is
driven by friction, and $v_{\text{trans}}\sim\alpha$, whereas at higher
frequencies above the ferromagnetic gap, the skyrmion moves by magnon emission,
and $v_{\text{trans}}$ becomes independent of $\alpha$. | 2211.01714v5 |
2023-04-05 | Threshold current of field-free perpendicular magnetization switching using anomalous spin-orbit torque | Spin-orbit torque (SOT) is a candidate technique in next generation magnetic
random-access memory (MRAM). Recently, experiments show that some material with
low-symmetric crystalline or magnetic structures can generate anomalous SOT
that has an out-of-plane component, which is crucial in switching perpendicular
magnetization of adjacent ferromagnetic (FM) layer in the field-free condition.
In this work, we analytically derive the threshold current of field-free
perpendicular magnetization switching using the anomalous SOT. And we
numerically calculate the track of the magnetic moment in a FM free layer when
an applied current is smaller and greater than the threshold current. After
that, we study the applied current dependence of the switching time and the
switching energy consumption, which shows the minimum energy consumption
decreases as out-of-plane torque proportion increases. Then we study the
dependences of the threshold current on anisotropy strength, out-of-plane
torque proportion, FM free layer thickness and Gilbert damping constant, and
the threshold current shows negative correlation with the out-of-plane torque
proportion and positive correlation with the other three parameters. Finally,
we demonstrate that when the applied current is smaller than the threshold
current, although it cannot switch the magnetization of FM free layer, it can
still equivalently add an effective exchange bias field H_{bias} on the FM free
layer. The H_{bias} is proportional to the applied current J_{SOT}, which
facilitates the determination of the anomalous SOT efficiency. This work helps
us to design new spintronic devices that favor field-free switching
perpendicular magnetization using the anomalous SOT, and provides a way to
adjust the exchange bias field, which is helpful in controlling FM layer
magnetization depinning. | 2304.02248v2 |
1997-07-15 | Linear Response, Dynamical Friction and the Fluctuation-Dissipation Theorem in Stellar Dynamics | We apply linear response theory to a general, inhomogeneous, stationary
stellar system, with particular emphasis on dissipative processes analogous to
Landau damping. Assuming only that the response is causal, we show that the
irreversible work done by an external perturber is described by the
anti-Hermitian part of a linear response operator, and damping of collective
modes is described by the anti-Hermitian part of a related polarization
operator. We derive an exact formal expression for the response operator, which
is the classical analog of a well-known result in quantum statistical physics.
When the self-gravity of the response can be ignored, and the ensemble-averaged
gravitational potential is integrable, the expressions for the mode energy,
damping rate, and polarization operator reduce to well-known formulae derived
from perturbation theory in action-angle variables. In this approximation,
dissipation occurs only via resonant interaction with stellar orbits or
collective modes. For stellar systems in thermal equilibrium, the
anti-Hermitian part of the response operator is directly related to the
correlation function of the fluctuations. Thus dissipative properties of the
system are completely determined by the spectrum of density fluctuations---the
fluctuation-dissipation theorem. In particular, we express the coefficient of
dynamical friction for an orbiting test particle in terms of the fluctuation
spectrum; this reduces to the known Chandrasekhar formula in the restrictive
case of an infinite homogeneous system with a Maxwellian velocity distribution. | 9707161v1 |
2003-06-10 | Oscillations of Bose-Einstein condensates with vortex lattices. II. Finite temperatures | We derive the finite temperature oscillation modes of a harmonically confined
Bose-Einstein condensed gas undergoing rigid body rotation supported by a
vortex lattice in the condensate. The hydrodynamic modes separate into two
classes corresponding to in-phase (center-of-mass) and counter-phase (relative)
oscillations of the thermal cloud and the condensate. The in- and counter-phase
oscillations are independent of each other in the case where the thermal cloud
is inviscid for all modes studied, except the radial pulsations which couple
them because the pressure perturbations of the condensate and the thermal cloud
are governed by different adiabatic indices. If the thermal cloud is viscous,
the two classes of oscillations are coupled, i.e. each type of motion involves
simultaneously mass and entropy currents. The counter-phase oscillations are
damped by the mutual friction between the condensate and the thermal cloud
mediated by the vortex lattice. The damping is large for the values of the
drag-to-lift ratio of the order of unity and becomes increasingly ineffective
in either limit of small or large friction. An experimental measurement of a
subset of these oscillation modes and their damping rates can provide
information on the values of the phenomenological mutual friction coefficients,
and hence the quasiparticle-vortex scattering processes in dilute atomic Bose
gases. | 0306245v2 |
2005-01-28 | Summation of divergent series and Borel summability for strongly dissipative equations with periodic or quasi-periodic forcing terms | We consider a class of second order ordinary differential equations
describing one-dimensional systems with a quasi-periodic analytic forcing term
and in the presence of damping. As a physical application one can think of a
resistor-inductor-varactor circuit with a periodic (or quasi-periodic) forcing
function, even if the range of applicability of the theory is much wider. In
the limit of large damping we look for quasi-periodic solutions which have the
same frequency vector of the forcing term, and we study their analyticity
properties in the inverse of the damping coefficient. We find that already the
case of periodic forcing terms is non-trivial, as the solution is not analytic
in a neighbourhood of the origin: it turns out to be Borel-summable. In the
case of quasi-periodic forcing terms we need Renormalization Group techniques
in order to control the small divisors arising in the perturbation series. We
show the existence of a summation criterion of the series in this case also,
but, however, this can not be interpreted as Borel summability. | 0501500v1 |
2009-09-30 | Dynamic polarization of graphene by moving external charges: random phase approximation | We evaluate the stopping and image forces on a charged particle moving
parallel to a doped sheet of graphene by using the dielectric response
formalism for graphene's $\pi$-electron bands in the random phase approximation
(RPA). The forces are presented as functions of the particle speed and the
particle distance for a broad range of charge-carrier densities in graphene. A
detailed comparison with the results from a kinetic equation model reveal the
importance of inter-band single-particle excitations in the RPA model for high
particle speeds. We also consider the effects of a finite gap between graphene
and a supporting substrate, as well as the effects of a finite damping rate
that is included through the use of Mermin's procedure. The damping rate is
estimated from a tentative comparison of the Mermin loss function with a HREELS
experiment. In the limit of low particle speeds, several analytical results are
obtained for the friction coefficient that show an intricate relationship
between the charge-carrier density, the damping rate, and the particle
distance, which may be relevant to surface processes and electrochemistry
involving graphene. | 0909.5598v3 |
2010-03-12 | Improving the model of emission from spinning dust: effects of grain wobbling and transient spin-up | Observations continue to support the interpretation of the anomalous
microwave foreground as electric dipole radiation from spinning dust grains as
proposed by Draine and Lazarian (1998ab). In this paper we present a refinement
of the original model by improving the treatment of a number of physical
effects. First, we consider a disk-like grain rotating with angular velocity at
an arbitrary angle with respect to the grain symmetry axis and derive the
rotational damping and excitation coefficients arising from infrared emission,
plasma-grain interactions and electric dipole emission. The angular velocity
distribution and the electric dipole emission spectrum for grains is calculated
using the Langevin equation, for cases both with and without fast internal
relaxation. Our results show that, the peak emissivity of spinning dust,
compared to earlier studies, increases by a factor of ~2 for the Warm Neutral
Medium (WNM), the Warm Ionized Medium (WIM), the Cold Neutral Medium (CNM) and
the Photodissociation Region (PDR), and by a factor ~4 for Reflection Nebulae
(RN). The frequency at the emission peak also increases by factors ~1.4 to ~2
for these media. The increased emission and peak frequency result from the
non-sphericity of grain shape and from the anisotropy in damping and excitation
along directions parallel and perpendicular to the grain symmetry axis. Second,
we provide a detailed numerical study including transient spin-up of grains by
single-ion collisions. The impulses broaden the emission spectrum and increase
the peak emissivity for the CNM, WNM and WIM. In addition, we present an
improved treatment of rotational excitation and damping by infrared emission. | 1003.2638v2 |
2013-05-15 | Beam energy dependence of the viscous damping of anisotropic flow | The flow harmonics $v_{2,3}$ for charged hadrons, are studied for a broad
range of centrality selections and beam collision energies in Au+Au
($\sqrt{s_{NN}}= 7.7 - 200$ GeV) and Pb+Pb ($\sqrt{s_{NN}}= 2.76$ TeV)
collisions. They validate the characteristic signature expected for the system
size dependence of viscous damping at each collision energy studied. The
extracted viscous coefficients, that encode the magnitude of the ratio of shear
viscosity to entropy density $\eta/s$, are observed to decrease to an apparent
minimum as the collision energy is increased from $\sqrt{s_{NN}}= 7.7$ to
approximately 62.4 GeV; thereafter, they show a slow increase with
$\sqrt{s_{NN}}$ up to 2.76 TeV. This pattern of viscous damping provides the
first experimental constraint for $\eta/s$ in the temperature-baryon chemical
potential ($T, \mu_B$) plane, and could be an initial indication for decay
trajectories which lie close to the critical end point in the phase diagram for
nuclear matter. | 1305.3341v3 |
2014-07-15 | C$ν$B damping of primordial gravitational waves and the fine-tuning of the C$γ$B temperature anisotropy | Damping of primordial gravitational waves due to the anisotropic stress
contribution owing to the cosmological neutrino background (C$\nu$B) is
investigated in the context of a radiation-to-matter dominated Universe.
Besides its inherent effects on the gravitational wave propagation, the
inclusion of the C$\nu$B anisotropic stress into the dynamical equations also
affects the tensor mode contribution to the anisotropy of the cosmological
microwave background (C$\gamma$B) temperature. Given that the fluctuations of
the C$\nu$B temperature in the (ultra)relativistic regime are driven by a
multipole expansion, the mutual effects on the gravitational waves and on the
C$\gamma$B are obtained through a unified prescription for a
radiation-to-matter dominated scenario. The results are confronted with some
preliminary results for the radiation dominated scenario. Both scenarios are
supported by a simplified analytical framework, in terms of a scale independent
dynamical variable, $k \eta$, that relates cosmological scales, $k$, and the
conformal time, $\eta$. The background relativistic (hot dark) matter
essentially works as an effective dispersive medium for the gravitational waves
such that the damping effect is intensified for the Universe evolving to the
matter dominated era. Changes on the temperature variance owing to the
inclusion of neutrino collision terms into the dynamical equations result into
spectral features that ratify that the multipole expansion coefficients
$C_{l}^{T}$'s die out for $l \sim 100$. | 1407.4058v1 |
2014-12-08 | Variable frequency characterization of interaction at nanoscale in linear dynamic AFM: an FFM primer | Using electrostatic coupling between an AFM tip and a metallic surface as a
test interaction, we here present the measurement of the force between the tip
and the surface, together with the measurement of the interaction stiffness and
the associated dissipation. These three quantities constitute a full
characterization of the interaction at nanoscale. They are measured
independently, simultaneously and quantitatively at the same place. This is
made possible thanks to a force feedback method that ensures the DC immobility
of the tip and to the simultaneous application of a sub-nanometer oscillation
to the tip. In this established linear regime, stiffness and damping are
directly obtained from amplitude and phase change measurements. The needed
information for this linear transformation is solely the lever properties in
the experimental context. Knowledge of k, its stiffness, its damping
coefficient and Q0, its first resonance frequency is shown to be sufficient in
the frequency range we are here exploring. Finally, we demonstrate that this
method is not restricted to the lever resonance frequency. To the contrary,
this interaction characterization whose resolution is limited by the Brownian
motion, can be used at any frequencies with essentially the same performances.
We believe that simultaneous and independent measurements of force, stiffness
and damping, out of lever resonance, at nanoscale, and within the context of
linear response define a new AFM paradigm that we call Force Feedback
Microscopy (FFM). This article details the use of FFM using a well known and
easy to implement electrostatic interaction between a regular AFM tip and a
metallic surface in air. | 1412.2640v1 |
2016-06-29 | On the global existence and blowup of smooth solutions to the multi-dimensional compressible Euler equations with time-depending damping | In this paper, we are concerned with the global existence and blowup of
smooth solutions to the multi-dimensional compressible Euler equations with
time-depending damping \begin{equation*}
\partial_t\rho+\operatorname{div}(\rho u)=0, \quad
\partial_t(\rho u)+\operatorname{div}\left(\rho u\otimes
u+p\,I_d\right)=-\alpha(t)\rho u, \quad
\rho(0,x)=\bar \rho+\varepsilon\rho_0(x),\quad u(0,x)=\varepsilon u_0(x),
\end{equation*} where $x=(x_1, \cdots, x_d)\in\Bbb R^d$ $(d=2,3)$, the
frictional coefficient is $\alpha(t)=\frac{\mu}{(1+t)^\lambda}$ with
$\lambda\ge0$ and $\mu>0$, $\bar\rho>0$ is a constant, $\rho_0,u_0 \in
C_0^\infty(\Bbb R^d)$, $(\rho_0,u_0)\not\equiv 0$, $\rho(0,x)>0$, and
$\varepsilon>0$ is sufficiently small. One can totally divide the range of
$\lambda\ge0$ and $\mu>0$ into the following four cases:
Case 1: $0\le\lambda<1$, $\mu>0$ for $d=2,3$;
Case 2: $\lambda=1$, $\mu>3-d$ for $d=2,3$;
Case 3: $\lambda=1$, $\mu\le 3-d$ for $d=2$;
Case 4: $\lambda>1$, $\mu>0$ for $d=2,3$.
\noindent We show that there exists a global $C^{\infty}-$smooth solution
$(\rho, u)$ in Case 1, and Case 2 with $\operatorname{curl} u_0\equiv 0$, while
in Case 3 and Case 4, in general, the solution $(\rho, u)$ blows up in finite
time. Therefore, $\lambda=1$ and $\mu=3-d$ appear to be the critical power and
critical value, respectively, for the global existence of small amplitude
smooth solution $(\rho, u)$ in $d-$dimensional compressible Euler equations
with time-depending damping. | 1606.08935v1 |
2017-12-22 | Low-momentum dynamic structure factor of a strongly interacting Fermi gas at finite temperature: A two-fluid hydrodynamic description | We provide a description of the dynamic structure factor of a homogeneous
unitary Fermi gas at low momentum and low frequency, based on the dissipative
two-fluid hydrodynamic theory. The viscous relaxation time is estimated and is
used to determine the regime where the hydrodynamic theory is applicable and to
understand the nature of sound waves in the density response near the
superfluid phase transition. By collecting the best knowledge on the shear
viscosity and thermal conductivity known so far, we calculate the various
diffusion coefficients and obtain the damping width of the (first and second)
sounds. We find that the damping width of the first sound is greatly enhanced
across the superfluid transition and very close to the transition the second
sound might be resolved in the density response for the transferred momentum up
to the half of Fermi momentum. Our work is motivated by the recent measurement
of the local dynamic structure factor at low momentum at Swinburne University
of Technology and the on-going experiment on sound attenuation of a homogeneous
unitary Fermi gas at Massachusetts Institute of Technology. We discuss how the
measurement of the velocity and damping width of the sound modes in
low-momentum dynamic structure factor may lead to an improved determination of
the universal superfluid density, shear viscosity and thermal conductivity of a
unitary Fermi gas. | 1712.08320v1 |
2018-10-17 | Resonance-broadened transit time damping of particles in MHD turbulence | As a fundamental astrophysical process, the scattering of particles by
turbulent magnetic fields has its physical foundation laid by the
magnetohydrodynamic (MHD) turbulence theory. In the framework of the modern
theory of MHD turbulence, we derive a generalized broadened resonance function
by taking into account both the magnetic fluctuations and nonlinear
decorrelation of turbulent magnetic fields arising in MHD turbulence, and we
specify the energy range of particles for the dominance of different broadening
mechanisms. The broadened resonance allows for scattering of particles beyond
the energy threshold of the linear resonance. By analytically determining the
pitch-angle diffusion coefficients for transit time damping (TTD) with slow and
fast modes, we demonstrate that the turbulence anisotropy of slow modes
suppresses their scattering efficiency. Furthermore, we quantify the dependence
of the relative importance between slow and fast modes in TTD scattering on (i)
particle energy, (ii) plasma $\beta$ (the ratio of gas pressure to magnetic
pressure), and (iii) damping of MHD turbulence, and we also provide the
parameter space for the dominance of slow modes. To exemplify its applications,
we find that among typical partially ionized interstellar phases, in the warm
neutral medium slow and fast modes have comparable efficiencies in TTD
scattering of cosmic rays. For low-energy particles, e.g., sub-Alfv\'{e}nic
charged grains, we show that slow modes always dominate TTD scattering. | 1810.07726v1 |
2019-05-17 | Statics and Dynamics of Polymeric Droplets on Chemically Homogeneous and Heterogeneous Substrates | We present a molecular dynamics study of the motion of cylindrical polymer
droplets on striped surfaces. We first consider the equilibrium properties of
droplets on different surfaces, we show that for small stripes the
Cassie-Baxter equation gives a good approximation of the equilibrium contact
angle. As the stripe width becomes non-negligible compared to the dimension of
the droplets, the droplet has to deform significantly to minimize its free
energy, this results in a smaller value of the contact angle than the continuum
model predicts. We then evaluate the slip length, and thus the damping
coefficient as a function of the stripe width. For very small stripes, the
heterogeneous surface behaves as an effective surface, with the same damping as
an homogeneous surface with the same contact angle. However, as the stripe
width increases, damping at the surface increases until reaching a plateau.
Afterwards, we study the dynamics of droplets under a bulk force. We show that
if the stripes are large enough the droplets are pinned until a critical
acceleration. The critical acceleration increases linearly with stripe width.
For large enough accelerations, the average velocity increases linearly with
the acceleration, we show that it can then be predicted by a model depending
only the size of droplet, viscosity and slip length. We show that the velocity
of the droplet varies sinusoidally as a function of its position on the
substrate. On the other hand, for accelerations just above the depinning
acceleration we observe a characteristic stick-slip motion, with successive
pinnings and depinnings. | 1905.07214v1 |
2020-05-22 | Quasinormal modes, shadow and greybody factors of 5D electrically charged Bardeen black holes | We study quasinormal modes (QNMs) in 5D electrically charged Bardeen black
holes spacetime by considering the scalar and electromagnetic field
perturbations. The black holes spacetime is an exact solution of Einstein
gravity coupled to nonlinear electrodynamics in five dimensions, which has
nonsingular behavior. To calculate QNMs, we use the WKB approximation method up
to sixth order. Due to the presence of electric charge $q_e > 0$, both the
scalar and electromagnetic field perturbations decay more slowly when compared
to the Schwarzschild-Tangherlini black holes. We discover that the scalar field
perturbations oscillate more rapidly when compared to the electromagnetic field
perturbations. In terms of damping, the scalar field perturbations damp more
quickly. Graphically we show that the transmission (reflection) coefficients
decrease (increase) with an increase in the magnitude of the electric charge
$q_e$. The emission of gravitational waves allows spacetime to undergo damped
oscillations due to the nonzero value of the imaginary part, which is always
negative. The imaginary part of the QNMs frequencies is continuously decreasing
with an increase in the magnitude of the electric charge $q_e$ for a given mode
($l,n$). A connection between the QNMs frequencies and the black hole shadow,
as well as the geometric cross-section in the eikonal limit, is also described. | 2005.11080v2 |
2020-09-25 | Direct computation of nonlinear mapping via normal form for reduced-order models of finite element nonlinear structures | The direct computation of the third-order normal form for a geometrically
nonlinear structure discretised with the finite element (FE) method, is
detailed. The procedure allows to define a nonlinear mapping in order to derive
accurate reduced-order models (ROM) relying on invariant manifold theory. The
proposed reduction strategy is direct and simulation free, in the sense that it
allows to pass from physical coordinates (FE nodes) to normal coordinates,
describing the dynamics in an invariant-based span of the phase space. The
number of master modes for the ROM is not a priori limited since a complete
change of coordinate is proposed. The underlying theory ensures the quality of
the predictions thanks to the invariance property of the reduced subspace,
together with their curvatures in phase space that accounts for the nonresonant
nonlinear couplings. The method is applied to a beam discretised with 3D
elements and shows its ability in recovering internal resonance at high energy.
Then a fan blade model is investigated and the correct prediction given by the
ROMs are assessed and discussed. A method is proposed to approximate an
aggregate value for the damping, that takes into account the damping
coefficients of all the slave modes, and also using the Rayleigh damping model
as input. Frequency-response curves for the beam and the blades are then
exhibited, showing the accuracy of the proposed method. | 2009.12145v1 |
2020-10-08 | A blow-up result for the wave equation with localized initial data: the scale-invariant damping and mass term with combined nonlinearities | We are interested in this article in studying the damped wave equation with
localized initial data, in the \textit{scale-invariant case} with mass term and
two combined nonlinearities. More precisely, we consider the following
equation: $$ (E) {1cm} u_{tt}-\Delta
u+\frac{\mu}{1+t}u_t+\frac{\nu^2}{(1+t)^2}u=|u_t|^p+|u|^q, \quad \mbox{in}\
\mathbb{R}^N\times[0,\infty), $$ with small initial data. Under some
assumptions on the mass and damping coefficients, $\nu$ and $\mu>0$,
respectively, we show that blow-up region and the lifespan bound of the
solution of $(E)$ remain the same as the ones obtained in \cite{Our2} in the
case of a mass-free wave equation, it i.e. $(E)$ with $\nu=0$.
Furthermore, using in part the computations done for $(E)$, we enhance the
result in \cite{Palmieri} on the Glassey conjecture for the solution of $(E)$
with omitting the nonlinear term $|u|^q$. Indeed, the blow-up region is
extended from $p \in (1, p_G(N+\sigma)]$, where $\sigma$ is given by (1.12)
below, to $p \in (1, p_G(N+\mu)]$ yielding, hence, a better estimate of the
lifespan when $(\mu-1)^2-4\nu^2<1$. Otherwise, the two results coincide.
Finally, we may conclude that the mass term {\it has no influence} on the
dynamics of $(E)$ (resp. $(E)$ without the nonlinear term $|u|^q$), and the
conjecture we made in \cite{Our2} on the threshold between the blow-up and the
global existence regions obtained holds true here. | 2010.05455v1 |
2021-07-31 | Damped inertial dynamics with vanishing Tikhonov regularization: strong asymptotic convergence towards the minimum norm solution | In a Hilbert space, we provide a fast dynamic approach to the hierarchical
minimization problem which consists in finding the minimum norm solution of a
convex minimization problem. For this, we study the convergence properties of
the trajectories generated by a damped inertial dynamic with Tikhonov
regularization. When the time goes to infinity, the Tikhonov regularization
parameter is supposed to tend towards zero, not too fast, which is a key
property to make the trajectories strongly converge towards the minimizer of
$f$ of minimum norm. According to the structure of the heavy ball method for
strongly convex functions, the viscous damping coefficient is proportional to
the square root of the Tikhonov regularization parameter. Therefore, it also
converges to zero, which will ensure rapid convergence of values. Precisely,
under a proper tuning of these parameters, based on Lyapunov's analysis, we
show that the trajectories strongly converge towards the minimizer of minimum
norm, and we provide the convergence rate of the values. We show a trade off
between the property of fast convergence of values, and the property of strong
convergence towards the minimum norm solution. This study improves several
previous works where this type of results was obtained under restrictive
hypotheses. | 2108.00203v1 |
2021-08-11 | Numerical investigation of the formation and stability of homogeneous pairs of soft particles in inertial microfluidics | We investigate the formation and stability of a pair of identical soft
capsules in channel flow under mild inertia. We employ a combination of the
lattice Boltzmann, finite element and immersed boundary methods to simulate the
elastic particles in flow. Validation tests show excellent agreement with
numerical results obtained by other research groups. Our results reveal new
trajectory types that have not been observed for pairs of rigid particles.
While particle softness increases the likelihood of a stable pair forming, the
pair stability is determined by the lateral position of the particles. A key
finding is that stabilisation of the axial distance occurs after lateral
migration of the particles. During the later phase of pair formation, particles
undergo damped oscillations that are independent of initial conditions. These
damped oscillations are driven by a strong hydrodynamic coupling of the
particle dynamics, particle inertia and viscous dissipation. While the
frequency and damping coefficient of the oscillations depend on particle
softness, the pair formation time is largely determined by the initial particle
positions: the time to form a stable pair grows exponentially with the initial
axial distance. Our results demonstrate that particle softness has a strong
impact on the behaviour of particle pairs. The findings could have significant
ramifications for microfluidic applications where a constant and reliable axial
distance between particles is required, such as flow cytometry. | 2108.05277v1 |
2021-11-13 | Attenuation of surface modes in granular media | In this work, an unconsolidated granular medium, made of silica microbeads,
is experimentally tested in a laboratory setting. The objective is to
investigate the attenuation mechanisms of vertically polarized seismic waves
traveling at the surface of unconsolidated substrates that are characterized by
power-law rigidity profiles. Both geometric spreading and material damping due
to skeletal dissipation are considered. An electromagnetic shaker is employed
to excite the granular medium between 300 and 550 Hz, generating linear modes
that are localized near the surface. A densely sampled section is recorded at
the surface using a laser vibrometer. The explicit solution of the geometric
attenuation law of Rayleigh-like waves in layered media is employed to
calculate the geometric spreading function of the vertically polarized surface
modes within the granular material. In accordance with recent studies, the
dynamics of these small-amplitude multi-modal linear waves can be analysed by
considering the granular medium as perfectly continuous and elastic. By
performing a non-linear regression analysis on particle displacements,
extracted from experimental velocity data, we determine the frequency-dependent
attenuation coefficients, which account for the material damping.
The findings of this work show that laboratory-scale physical models can be
used to study the geometric spreading of vertically polarized seismic waves
induced by the soil inhomogeneity and characterize the material damping of the
medium. | 2111.07199v1 |
2021-11-15 | The Interplay of Regularizing Factors in the Model of Upper Hybrid Oscillations of Cold Plasma | A one-dimensional nonlinear model of the so-called upper hybrid oscillations
in a magnetoactive plasma is investigated taking into account electron-ion
collisions. It is known that both the presence of an external magnetic field of
strength $ B_0 $ and a sufficiently large collisional factor $ \nu $ help
suppress the formation of a finite-dimensional singularity in a solution
(breaking of oscillations). Nevertheless, the suppression mechanism is
different: an external magnetic field increases the oscillation frequency, and
collisions tend to stabilize the medium and suppress oscillations. In terms of
the initial data and the coefficients $ B_0 $ and $ \nu $, we establish a
criterion for maintaining the global smoothness of the solution. Namely, for
fixed $ B_0 $ and $ \nu \ge 0 $ one can precisely divide the initial data into
two classes: one leads to stabilization to the equilibrium and the other leads
to the destruction of the solution in a finite time. Next, we examine the
nature of the stabilization. We show that for small $ B_0 $ an increase in the
intensity factor first leads to a change in the oscillatory behavior of the
solution to monotonic damping, which is then again replaced by oscillatory
damping. At large values of $ B_0 $, the solution is characterized by
oscillatory damping regardless of the value of the intensity factor $ \nu $. | 2111.07826v3 |
2021-11-20 | Excitation and Damping of Slow Magnetosonic Waves in Flaring Hot Coronal Loops: Effects of Compressive Viscosity | Slow magnetosonic waves associated with flares were observed in coronal loops
by SOHO/SUMER, SDO/AIA in various EUV bandpasses, and other instruments. The
excitation and damping of slow magnetosonic waves provides information on the
magnetic, temperature, and density structure of the loops. Recently, it was
found using 1.5D models that the thermal conduction is suppressed and
compressive viscosity is enhanced in hot (T>6 MK) flaring coronal loops. We
model the excitation and dissipation of slow magnetosonic waves in hot coronal
loops with realistic magnetic geometry, enhanced density, and temperature
(compared to background corona) guided by EUV observations using 3D MHD
visco-resistive model. The effects of compressive viscosity tensor component
along the magnetic field are included with classical and enhanced viscosity
coefficient values for the first time in 3D MHD coronal loop model. The waves
are excited by a velocity pulse at the footpoint of the loop at coronal lower
boundary. The modeling results demonstrate the excitation of the slow
magnetosonic waves and nonlinear coupling to other wave modes, such as the kink
and fast magnetosonic. We find significant leakage of the waves from the hot
coronal loops with small effect of viscous dissipation in cooler (6MK) loops,
and more significant effects of viscous dissipation in hotter (10.5MK) coronal
loops. Our results demonstrate that nonlinear 3D MHD models are required to
fully account for various wave couplings, damping, standing wave formation, and
viscous dissipation in hot flaring coronal loops. Our viscous 3D MHD code
provides a new tool for improved coronal seismology. | 2111.10696v1 |
2022-10-17 | Interpretations of the cosmic ray secondary-to-primary ratios measured by DAMPE | Precise measurements of the boron-to-carbon and boron-to-oxygen ratios by
DAMPE show clear hardenings around $100$ GeV/n, which provide important
implications on the production, propagation, and interaction of Galactic cosmic
rays. In this work we investigate a number of models proposed in literature in
light of the DAMPE findings. These models can roughly be classified into two
classes, driven by propagation effects or by source ones. Among these models
discussed, we find that the re-acceleration of cosmic rays, during their
propagation, by random magnetohydrodynamic waves may not reproduce sufficient
hardenings of B/C and B/O, and an additional spectral break of the diffusion
coefficient is required. The other models can properly explain the hardenings
of the ratios. However, depending on simplifications assumed, the models differ
in their quality in reproducing the data in a wide energy range. The models
with significant re-acceleration effect will under-predict low-energy
antiprotons but over-predict low-energy positrons, and the models with
secondary production at sources over-predict high-energy antiprotons. For all
models high-energy positron excess exists. | 2210.09205v3 |
2022-12-28 | Scattering of the UHECR at small pitch angle by damped plasma waves | In spite a lot of theoretical and experimental effort that has been achieved
in ultra-high energy cosmic ray (UHECR) scattering research in last few
decades, some questions remain unanswered, or partially answered. Two of them,
that will be in the focus of this paper are: possible source of UHECRs and the
acceleration mechanism of cosmic rays beyond PeV energies. Small pitch-angle
scattering of UHECRs and possible confinement has been investigated using
quasilinear theory in order to analytically calculate pitch-angle Fokker-Planck
coefficient. CR particles resonantly interact with oblique low frequency damped
waves. We show that the resonance function is broadened due to damping effects
and this result is compared with the nonlinear broadening. Unlike the case of
purely parallel (or antiparallel) propagating waves in slab turbulence, the
presence of the compressive magnetic field component of oblique fast-mode waves
allows the cosmic ray particles to resonantly interact with these waves through
the n = 0 resonance, together with gyroresonance, which strongly influence the
Hillas limit. The derived results can be used to compute the parallel mean free
path for all forms of the turbulence spectrum; it has been applied on the
transport and propagation of CRs close to ultra-high energies in the Galaxy. An
accurate understanding of particle acceleration in astrophysical sources could
help to interpret eventual transition from Galactic to extragalactic origin of
cosmic rays, if any, and the shape of the UHECR spectrum at the highest
energies. | 2212.13755v1 |
2001-03-19 | Fluctuations in the Cosmic Microwave Background I: Form Factors and their Calculation in Synchronous Gauge | It is shown that the fluctuation in the temperature of the cosmic microwave
background in any direction may be evaluated as an integral involving scalar
and dipole form factors, which incorporate all relevant information about
acoustic oscillations before the time of last scattering. A companion paper
gives asymptotic expressions for the multipole coefficient $C_\ell$ in terms of
these form factors. Explicit expressions are given here for the form factors in
a simplified hydrodynamic model for the evolution of perturbations. | 0103279v2 |
2005-08-05 | Damping of vortex waves in a superfluid | The damping of vortex cyclotron modes is investigated within a generalized
quantum theory of vortex waves. Similarly to the case of Kelvin modes, the
friction coefficient turns out to be essentially unchanged under such
oscillations, but it is shown to be affected by appreciable memory corrections.
On the other hand, the nonequilibrium energetics of the vortex, which is
investigated within the framework of linear response theory, shows that its
memory corrections are negligible. The vortex response is found to be of the
Debye type, with a relaxation frequency whose dependence on temperature and
impurity concentration reflects the complexity of the heat bath and its
interaction with the vortex. | 0508167v1 |
2005-09-02 | Inhomogeneous soliton ratchets under two ac forces | We extend our previous work on soliton ratchet devices [L. Morales-Molina et
al., Eur. Phys. J. B 37, 79 (2004)] to consider the joint effect of two ac
forces including non-harmonic drivings, as proposed for particle ratchets by
Savele'v et al. [Europhys. Lett. 67}, 179 (2004); Phys. Rev. E {\bf 70} 066109
(2004)]. Current reversals due to the interplay between the phases, frequencies
and amplitudes of the harmonics are obtained. An analysis of the effect of the
damping coefficient on the dynamics is presented. We show that solitons give
rise to non-trivial differences in the phenomenology reported for particle
systems that arise from their extended character. A comparison with soliton
ratchets in homogeneous systems with biharmonic forces is also presented. This
ratchet device may be an ideal candidate for Josephson junction ratchets with
intrinsic large damping. | 0509051v1 |
2007-01-16 | Influence of Lorentz violation on Dirac quasinormal modes in the Schwarzschild black hole spacetime | Using the third-order WKB approximation and monodromy methods, we investigate
the influence of Lorentz violating coefficient $b$ (associated with a special
axial-vector $b_{\mu}$ field) on Dirac quasinormal modes in the Schwarzschild
black hole spacetime. At fundamental overtone, the real part decreases linearly
as the parameter $b$ increases. But the variation of the imaginary part with
$b$ becomes more complex. For the larger multiple moment $k$, the magnitude of
imaginary part increases with the increase of $b$, which means that presence of
Lorentz violation makes Dirac field damps more rapidly. At high overtones, it
is found that the real part of high-damped quasinormal frequency does not tend
to zero, which is quite a different from the symptotic Dirac quasinormal modes
without Lorentz violation. | 0701089v1 |
1994-01-21 | Transport Properties of Quark and Gluon Plasmas | The kinetic properties of relativistic quark-gluon and electron-photon
plasmas are described in the weak coupling limit. The troublesome Rutherford
divergence at small scattering angles is screened by Debye screening for the
longitudinal or electric part of the interactions. The transverse or magnetic
part of the interactions is effectively screened by Landau damping of the
virtual photons and gluons transferred in the QED and QCD interactions
respectively. Including screening a number of transport coefficients for QCD
and QED plasmas can be calculated to leading order in the interaction strength,
including rates of momentum and thermal relaxation, electrical conductivity,
viscosities, flavor and spin diffusion of both high temperature and degenerate
plasmas. Damping of quarks and gluons as well as color diffusion in quark-gluon
plasmas is, however, shown not to be sufficiently screened and the rates
depends on an infrared cut-off of order the ``magnetic mass", $m_{\rm mag}\sim
g^2 T$. | 9401300v1 |
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