  We numerically investigate collective ordering and disordering effects for
vortices in type-II superconductors interacting with square and triangular
substrate arrays under a dc drive that is slowly rotated with respect to the
fixed substrate. A series of directional locking transitions occur when the
particle motion locks to symmetry directions of the substrate, producing a
series of steps in the velocity-force curves. The locking transitions coincide
with structural transitions between triangular, square, smectic, or disordered
particle arrangements, which can be identified using the structure factor. We
show that the widths of the locking steps pass through local minima and maxima
as a function of the ratio of the number of particles to the number of
substrate minima. Unlike a static system, where matching effects occur for
simple integer commensuration ratios, our system exhibits dynamical
commensuration effects where an integer number of particle chains flow between
one-dimensional lines of substrate minima. As the system enters and exits the
locking steps, order-disorder transitions in the structure of the moving
particle assembly occur. We identify two distinct symmetry locking regimes as a
function of substrate strength which produce different locking step
characteristics. For weak substrates, all the particles are in motion and a
portion of the particles flow through the substrate minima, leading to
structural transitions at certain driving angles. For strong substrates, some
particles are permanently pinned while the remaining particles flow around
them. At the crossover between these two regimes of substrate strength, the
locking steps are destroyed due to the onset of chaotic plastic flow which
produces pronounced changes in the transport characteristics. Similar effects
occur for colloidal particles driven over square and triangular substrate
arrays.
