Steffen Martens

TL;DR: Transport of point-size Brownian particles under the influence of a constant and uniform force field through a planar three-dimensional channel with smoothly varying, axis-symmetric periodic side walls is investigated and it is demonstrated that the leading-order term is equivalent to the Fick-Jacobs approximation.

TL;DR: A generalized Fick-Jacobs approach is developed leading to an effective one-dimensional description involving the potential of mean force in the transport of Brownian particles through a corrugated channel caused by a force field containing curl-free and divergence-free parts.

TL;DR: In this paper, a generalized Fick-Jacobs approach was developed for the transport of Brownian particles through a corrugated channel caused by a force field containing curl-free (scalar potential) and divergence free (vector potential) parts.

TL;DR: In this paper, the authors numerically investigated the transport of a suspended overdamped Brownian particle which is driven through a two-dimensional rectangular array of circular obstacles with finite radius, and the mobility and diffusivity of the transported particles in such channels were determined as functions of the drive and array geometric parameters.

TL;DR: It is demonstrated that this estimate is more accurate for extremely corrugated geometries compared with the common applied method using a spatially-dependent diffusion coefficient D(x, f) which substitutes the constant diffusion coefficient in the common Fick-Jacobs equation.