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