  We examine directional locking effects in an assembly of disks driven through
a square array of obstacles as the angle of drive rotates from zero to ninety
degrees. For increasing disk densities, the system exhibits a series of
different dynamic patterns along certain locking directions, including
one-dimensional or multiple row chain phases and density modulated phases. For
non-locking driving directions, the disks form disordered patterns or clusters.
When the obstacles are small or far apart, a large number of locking phases
appear; however, as the number of disks increases, the number of possible
locking phases drops due to the increasing frequency of collisions between the
disks and obstacles. For dense arrays or large obstacles, we find an increased
clogging effect in which immobile and moving disks coexist.
