  We numerically examine the dynamic phases and pattern formation of
two-dimensional monodisperse repulsive disks driven over random quenched
disorder. We show that there is a series of distinct dynamic regimes as a
function of increasing drive, including a clogged or pile-up phase near
depinning, a homogeneous disordered flow state, and a dynamically phase
separated regime consisting of high density crystalline regions surrounded by a
low density of disordered disks. At the highest drives the disks arrange into
one-dimensional moving lanes. The phase separated regime has parallels with
phase separation observed in active matter systems, and arises in the disk
system due to the combination of nonequilibrium fluctuations and density
dependent mobility. We discuss how this system exhibits pronounced differences
from previous studies of driven particles moving over random substrates where
the particles, such as superconducting vortices or electron crystals, have
longer range repulsive interactions, and where dynamical phase separation and
strong one-dimensional moving chain effects are not observed. The system we
consider could be realized experimentally using sterically interacting colloids
driven over random pinning arrays or quasi-two-dimensional granular matter
flowing over rough landscapes.
