Stochastically perturbed flows: Delayed and interrupted evolution

We present analytical expressions for the time-dependent and stationary probability distributions corresponding to a stochastically perturbed one-dimensional flow with critical points, in two physically relevant situations: delayed evolution, in which the flow alternates with a quiescent state in which the variate remains frozen at its current value for random intervals of time; and interrupted evolution, in which the variate is also re-set in the quiescent state to a random value drawn from a fixed distribution. In the former case, the effect of the delay upon the first passage time statistics is analyzed. In the latter case, the conditions under which an extended stationary distribution can exist as a consequence of the competition between an attractor in the flow and the random re-setting are examined. We elucidate the role of the normalization condition in eliminating the singularities arising from the unstable critical points of the flow, and present a number of representative examples. A simple formula is obtained for the stationary distribution and interpreted physically. A similar interpretation is also given for the known formula for the stationary distribution in a full-fledged dichotomous flow.Comment: 27 pages; no figures. Submitted to Stochastics and Dynamic

Jarzynski equality for the Jepsen gas

We illustrate the Jarzynski equality on the exactly solvable model of a one-dimensional ideal gas in uniform expansion or compression. The analytical results for the probability density $P(W)$ of the work $W$ performed by the gas are compared with the results of molecular dynamics simulations for a two-dimensional dilute gas of hard spheres.Comment: 7 pages, 4 figures, submitted to Europhys. Let

Stochastic Stokes' drift of a flexible dumbbell

We consider the stochastic Stokes drift of a flexible dumbbell. The dumbbell consists of two isotropic Brownian particles connected by a linear spring with zero natural length, and is advected by a sinusoidal wave. We find an asymptotic approximation for the Stokes drift in the limit of a weak wave, and find good agreement with the results of a Monte Carlo simulation. We show that it is possible to use this effect to sort particles by their flexibility even when all the particles have the same diffusivity.Comment: 12 pages, 1 figur

Critical Behaviour of Non-Equilibrium Phase Transitions to Magnetically Ordered States

We describe non-equilibrium phase transitions in arrays of dynamical systems with cubic nonlinearity driven by multiplicative Gaussian white noise. Depending on the sign of the spatial coupling we observe transitions to ferromagnetic or antiferromagnetic ordered states. We discuss the phase diagram, the order of the transitions, and the critical behaviour. For global coupling we show analytically that the critical exponent of the magnetization exhibits a transition from the value 1/2 to a non-universal behaviour depending on the ratio of noise strength to the magnitude of the spatial coupling.Comment: 4 pages, 5 figure

Efficiency at maximum power: An analytically solvable model for stochastic heat engines

We study a class of cyclic Brownian heat engines in the framework of finite-time thermodynamics. For infinitely long cycle times, the engine works at the Carnot efficiency limit producing, however, zero power. For the efficiency at maximum power, we find a universal expression, different from the endoreversible Curzon-Ahlborn efficiency. Our results are illustrated with a simple one-dimensional engine working in and with a time-dependent harmonic potential.Comment: 6 pages, 3 figure

Reconstructing Colonization Dynamics of the Human Parasite Schistosoma mansoni following Anthropogenic Environmental Changes in Northwest Senegal

© 2015 Van den Broeck et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. The attached file is the published version of the article