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

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.

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

Detecting charge noise with a Josephson junction: A problem of thermal escape in presence of non-Gaussian fluctuations

Motivated by several experimental activities to detect charge noise produced by a mesoscopic conductor with a Josephson junction as on-chip detector, the switching rate out of its zero-voltage state is studied. This process is related to the fundamental problem of thermal escape in presence of non-Gaussian fluctuations. In the relevant case of weak higher than second order cumulants, an effective Fokker-Planck equation is derived, which is then used to obtain an explicit expression for the escape rate. Specific results for the rate asymmetry due to the third moment of current noise allow to analyse experimental data and to optimize detection circuits.Comment: 4 pages, 1 figure; minor typos corrected, some revisions in the tex

Analysis of stochastic time series in the presence of strong measurement noise

A new approach for the analysis of Langevin-type stochastic processes in the presence of strong measurement noise is presented. For the case of Gaussian distributed, exponentially correlated, measurement noise it is possible to extract the strength and the correlation time of the noise as well as polynomial approximations of the drift and diffusion functions from the underlying Langevin equation.Comment: 12 pages, 10 figures; corrected typos and reference

Separation of suspended particles by arrays of obstacles in microfluidic devices

The stochastic transport of suspended particles through a periodic pattern of obstacles in microfluidic devices is investigated by means of the Fokker-Planck equation. Asymmetric arrays of obstacles have been shown to induce the continuous separation of DNA molecules of different length. The analysis presented here of the asymptotic distribution of particles in a unit cell of these systems shows that separation is only possible in the presence of a driving force with a non-vanishing normal component at the surface of the solid obstacles. In addition, vector separation, in which different species move, in average, in different directions within the device, is driven by differences on the force acting on the various particles and not by differences in the diffusion coefficient. Monte-Carlo simulations performed for different particles and force fields agree with the numerical solutions of the Fokker-Planck equation in the periodic system

Drift without flux: Brownian walker with a space dependent diffusion coefficient

Space dependent diffusion of micrometer sized particles has been directly observed using digital video microscopy. The particles were trapped between two nearly parallel walls making their confinement position dependent. Consequently, not only did we measure a diffusion coefficient which depended on the particles' position, but also report and explain a new effect: a drift of the particles' individual positions in the direction of the diffusion coefficient gradient, in the absence of any external force or concentration gradient.Comment: 4 pages, 4 ps figures, include