  We numerically investigate the transport of a suspended overdamped Brownian
particle which is driven through a two-dimensional rectangular array of
circular obstacles with finite radius. Two limiting cases are considered in
detail, namely, when the constant drive is parallel to the principal or the
diagonal array axes. This corresponds to studying the Brownian transport in
periodic channels with reflecting walls of different topologies. The mobility
and diffusivity of the transported particles in such channels are determined as
functions of the drive and the array geometric parameters. Prominent transport
features, like negative differential mobilities, excess diffusion peaks, and
unconventional asymptotic behaviors, are explained in terms of two distinct
lengths, the size of single obstacles (trapping length) and the lattice
constant of the array (local correlation length). Local correlation effects are
further analyzed by continuously rotating the drive between the two limiting
orientations.
