  We examine the ordering, pinning, and dynamics of two-dimensional pattern
forming systems interacting with a periodic one-dimensional substrate. In the
absence of the substrate, particles with competing long-range repulsion and
short-range attraction form anisotropic crystal, stripe, and bubble states.
When the system is tuned across the stripe transition in the presence of a
substrate, we find that there is a peak effect in the critical depinning force
when the stripes align and become commensurate with the substrate. Under an
applied drive, the anisotropic crystal and stripe states can exhibit soliton
depinning and plastic flow. When the stripes depin plastically, they
dynamically reorder into a moving stripe state that is perpendicular to the
substrate trough direction. We also find that when the substrate spacing is
smaller than the widths of the bubbles or stripes, the system forms pinned
stripe states that are perpendicular to the substrate trough direction. The
system exhibits multiple reentrant pinning effects as a function of increasing
attraction, with the anisotropic crystal and large bubble states experiencing
weak pinning but the stripe and smaller bubble states showing stronger pinning.
We map out the different dynamic phases as a function of filling, the strength
of the attractive interaction term, the substrate strength, and the drive, and
demonstrate that the different phases produce identifiable features in the
transport curves and particle orderings.
