Effective diffusivity

We study two-dimensional Brownian motion in an ordered periodic system of linear reflecting barriers using the sampling method and conformal transformations. We calculate the effective diffusivity for the Brownian particle. When the periods are fixed but the length of the barrier goes to zero, the effective diffusivity in the direction perpendicular to the barriers differs from the standard one by a term of order [epsilon squared] where [epsilon] is the length of a barrier