Unbiased diffusion in tubes with corrugated walls.

This study is devoted to unbiased motion of a point Brownian particle in a tube with corrugated walls made of conical sections of a varying length. Effective one-dimensional description in terms of the generalized Fick-Jacobs equation is used to derive a formula which gives the effective diffusion coefficient of the particle as a function of the geometric parameters of the tube. Comparison with the results of Brownian dynamics simulations allows us to establish the domain of applicability of both the one-dimensional description and the formula for the effective diffusion coefficient.