title: Integral formula for the effective diffusion coefficient in two-dimensional channels.
abstract: The effective one-dimensional description of diffusion in two-dimensional channels of varying cross section is revisited. The effective diffusion coefficient D(x), extending Fick-Jacobs equation, depending on the longitudinal coordinate x, is derived here without use of scaling of the transverse coordinates. The result of the presented method is an integral formula for D(x), calculating its value at x as an integral of contributions from the neighboring positions x^{'} depending on h(x^{'}), a function shaping the channel. Unlike the standard formulas based on the scaling, the new proposed formula also describes D(x) correctly near the cusps, or in wider channels.
authors: Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 84511, Bratislava, Slovakia.
authors: Pavol
authors: P
authors: Kalinay