Nonscaling calculation of the effective diffusion coefficient in periodic channels.

An algorithm calculating the effective diffusion coefficient D(x) in 2D and 3D channels with periodically varying cross section along the longitudinal coordinate x is presented. Unlike other methods, it is not based on scaling of the transverse coordinates, or the smallness of the width of the channel. The result is expressed as an integral of specific contributions to D(x) coming from the positions neighboring to x. The method avoids the hierarchy of derivatives of the channel shaping function h(x), so it is also suitable for the channels with cusps or jumps of their width. The method describes correctly D(x) in wide channels, giving the expected behavior in the limit of infinite width (no confinement).