Comment on ``Connection between the Burgers equation with an elastic forcing term and a stochastic process''

In the above mentioned paper by E. Moreau and O. Vall\'{e}e [Phys. Rev. {\bf E 73}, 016112, (2006)], the one-dimensional Burgers equation with an elastic (attractive) forcing term has been claimed to be connected with the Ornstein-Uhlenbeck process. We point out that this connection is valid only in case of the repulsive forcing.Comment: Phys. Rev. E Commen

The Brownian gyrator: a minimal heat engine on the nano-scale

A Brownian particle moving in the vicinity of a generic potential minimum under the influence of dissipation and thermal noise from two different heat baths is shown to act as a minimal heat engine, generating a systematic torque onto the physical object at the origin of the potential and an opposite torque onto the medium generating the dissipation.Comment: Phys. Rev. Lett., in pres

Nonequilibrium Steady State Driven by a Nonlinear Drift Force

We investigate the properties of the nonequilibrium steady state for the stochastic system driven by a nonlinear drift force and influenced by noises which are not identically and independently distributed. The nonequilibrium steady state (NESS) current results from a residual part of the drift force which is not cancelled by the diffusive action of noises. From our previous study for the linear drift force the NESS current was found to circulate on the equiprobability surface with the maximum at a stable fixed point of the drift force. For the nonlinear drift force, we use the perturbation theory with respect to the cubic and quartic coefficients of the drift force. We find an interesting potential landscape picture where the probability maximum shifts from the fixed point of the drift force and, furthermore, the NESS current has a nontrivial circulation which flows off the equiprobability surface and has various centers not located at the probability maximum. The theoretical result is well confirmed by the computer simulation.Comment: 10 pages, 4 figure

Jamming at zero temperature, zero friction, and finite applied shear stress

Via molecular dynamics simulations, we unveil the hysteretic nature of the jamming transition of soft repulsive frictionless spheres, as it occurs varying the volume fraction or the shear stress. In a given range of control parameters the system may be found both in a flowing and in an jammed state, depending on the preparation protocol. The hysteresis is due to an underlying energy landscape with many minima, as explained by a simple model, and disappears in the presence of strong viscous forces and in the small $\sigma$ limit. In this limit, structural quantities are continuous at the transition, while the asymptotic values of two time quantities such as the self-intermediate scattering function are discontinuous, giving to the jamming transition a mixed first-order second-order character close to that found at the glass transition of thermal systems

Steering the potential barriers: entropic to energetic

We propose a new mechanism to alter the nature of the potential barriers when a biased Brownian particle under goes a constrained motion in narrow, periodic channel. By changing the angle of the external bias, the nature of the potential barriers changes from purely entropic to energetic which in turn effects the diffusion process in the system. At an optimum angle of the bias, the nonlinear mobility exhibits a striking bell-shaped behavior. Moreover, the enhancement of the scaled effective diffusion coefficient can be efficiently controlled by the angle of the bias. This mechanism enables the proper design of channel structures for transport of molecules and small particles. The approximative analytical predictions have been verified by precise Brownian dynamic simulations.Comment: (6 pages, 7 figures) Submitted to PR

Exact corrections for finite-time drift and diffusion coefficients

Real data are constrained to finite sampling rates, which calls for a suitable mathematical description of the corrections to the finite-time estimations of the dynamic equations. Often in the literature, lower order discrete time approximations of the modeling diffusion processes are considered. On the other hand, there is a lack of simple estimating procedures based on higher order approximations. For standard diffusion models, that include additive and multiplicative noise components, we obtain the exact corrections to the empirical finite-time drift and diffusion coefficients, based on It\^o-Taylor expansions. These results allow to reconstruct the real hidden coefficients from the empirical estimates. We also derive higher-order finite-time expressions for the third and fourth conditional moments, that furnish extra theoretical checks for that class of diffusive models. The theoretical predictions are compared with the numerical outcomes of some representative artificial time-series.Comment: 18 pages, 5 figure

Influence of magnetic viscosity on domain wall dynamics under spin-polarized currents

We present a theoretical study of the influence of magnetic viscosity on current-driven domain wall dynamics. In particular we examine how domain wall depinning transitions, driven by thermal activation, are influenced by the adiabatic and nonadiabatic spin-torques. We find the Arrhenius law that describes the transition rate for activation over a single energy barrier remains applicable under currents but with a current-dependent barrier height. We show that the effective energy barrier is dominated by a linear current dependence under usual experimental conditions, with a variation that depends only on the nonadiabatic spin torque coefficient beta.Comment: 8 pages, 4 figure

Geometric and projection effects in Kramers-Moyal analysis

Kramers-Moyal coefficients provide a simple and easily visualized method with which to analyze stochastic time series, particularly nonlinear ones. One mechanism that can affect the estimation of the coefficients is geometric projection effects. For some biologically-inspired examples, these effects are predicted and explored with a non-stochastic projection operator method, and compared with direct numerical simulation of the systems' Langevin equations. General features and characteristics are identified, and the utility of the Kramers-Moyal method discussed. Projections of a system are in general non-Markovian, but here the Kramers-Moyal method remains useful, and in any case the primary examples considered are found to be close to Markovian.Comment: Submitted to Phys. Rev.

Effective temperature in nonequilibrium steady states of Langevin systems with a tilted periodic potential

We theoretically study Langevin systems with a tilted periodic potential. It has been known that the ratio $\Theta$ of the diffusion constant to the differential mobility is not equal to the temperature of the environment (multiplied by the Boltzmann constant), except in the linear response regime, where the fluctuation dissipation theorem holds. In order to elucidate the physical meaning of $\Theta$ far from equilibrium, we analyze a modulated system with a slowly varying potential. We derive a large scale description of the probability density for the modulated system by use of a perturbation method. The expressions we obtain show that $\Theta$ plays the role of the temperature in the large scale description of the system and that $\Theta$ can be determined directly in experiments, without measurements of the diffusion constant and the differential mobility

Relaxation of a Colloidal Particle into a Nonequilibrium Steady State

We study the relaxation of a single colloidal sphere which is periodically driven between two nonequilibrium steady states. Experimentally, this is achieved by driving the particle along a toroidal trap imposed by scanned optical tweezers. We find that the relaxation time after which the probability distributions have been relaxed is identical to that obtained by a steady state measurement. In quantitative agreement with theoretical calculations the relaxation time strongly increases when driving the system further away from thermal equilibrium