  We study the motion of an active Brownian particle (ABP) using overdamped
Langevin dynamics on a two-dimensional substrate with periodic array of
obstacles and in a quasi-one-dimensional corrugated channel comprised of
periodically arrayed obstacles. The periodic arrangement of the obstacles
enhances the persistent motion of the ABP in comparison to its motion in the
free space. Persistent motion increases with the activity of the ABP. We note
that the periodic arrangement induces directionality in ABP motion at late
time, and it increases with the size of the obstacles. We also note that the
ABP exhibits a super-diffusive dynamics in the corrugated channel. The
transport property is independent of the shape of the channel; rather it
depends on the packing fraction of the obstacles in the system. However, the
ABP shows the usual diffusive dynamics in the quasi-one-dimensional channel
with flat boundary.
