  A variety of soft and hard condensed matter systems are known to form stripe
patterns. Here we use numerical simulations to analyze how such stripe states
depin and slide when interacting with a random substrate and with driving in
different directions with respect to the orientation of the stripes. Depending
on the strength and density of the substrate disorder, we find that there can
be pronounced anisotropy in the transport produced by different dynamical flow
phases. We also find a disorder-induced "peak effect" similar to that observed
for superconducting vortex systems, which is marked by a transition from
elastic depinning to a state where the stripe structure fragments or partially
disorders at depinning. Under the sudden application of a driving force, we
observe pronounced metastability effects similar to those found near the
order-disorder transition associated with the peak effect regime for
three-dimensional superconducting vortices. The characteristic transient time
required for the system to reach a steady state diverges in the region where
the flow changes from elastic to disordered. We also find that anisotropy of
the flow persists in the presence of thermal disorder when thermally-induced
particle hopping along the stripes dominates. The thermal effects can wash out
the effects of the quenched disorder, leading to a thermally-induced stripe
state. We map out the dynamical phase diagram for this system, and discuss how
our results could be explored in electron liquid crystal systems, type-1.5
superconductors, and pattern-forming colloidal assemblies.
