When considering the hydrodynamics of Brownian particles, one is confronted to a difficult closure problem. One possibility to close the hierarchy of hydrodynamic equations is to consider a strong friction limit. This leads to the Smoluchowski equation that reduces to the ordinary diffusion...

Non-Markovian effects on the Brownian movement of a free particle in the presence as well as in the absence of inertial force are investigated under the framework of generalized Fokker–Planck equations (Rayleigh and Smoluchowski equations). More specifically, it is predicted that non-Markovian...

Movements of molecular motors on cytoskeletal filaments are described by directed walks on a line. Detachment from this line is allowed to occur with a small probability. Motion in the surrounding fluid is described by symmetric random walks. Effects of detachment and reattachment are calculated...

By analytical methods we study the large time properties of the solution of a simple one-dimensional model of stochastic Stokes’ drift. Semi-explicit formulae allow us to characterize the behaviour of the solutions and compute global quantities such as the asymptotic speed of the center of...

In the last decade there has been an increasing interest in generating useful work on the nano-scale to promote transport of particles. The essential theoretical formalism, rooted in non-equilibrium statistical physics, has been successfully applied to the description of physical principles...