Driven lattice gas with nearest-neighbor exclusion: shear-like drive
  We present Monte Carlo simulations of the lattice gas with nearest-neighbor exclusion and Kawasaki (hopping) dynamics, under the influence of a nonuniform drive, on the square lattice. The drive, which favors motion along the +$x$ and inhibits motion in the opposite direction, varies linearly with $y$, mimicking the velocity profile of laminar flow between parallel plates with distinct velocities. We study two drive configurations and associated boundary conditions: (1) a linear drive profile, with rigid walls at the layers with zero and maximum bias, and (2) a symmetric (piecewise linear) profile with periodic boundaries. The transition to a sublattice-ordered phase occurs at a density of about 0.298, lower than in equilibrium ($\rho_c \simeq 0.37$), but somewhat higher than in the uniformly driven case at maximal bias ($\rho_c \simeq 0.272$). For smaller global densities ($\rho \leq 0.33$), particles tend to accumulate in the low-drive region. Above this density we observe a surprising reversal in the density profile, with particles migrating to the high-drive region and forming structures similar to force chains in granular systems. 
Fabricio Q. Potiguar and Ronald Dickman