Coarsening of "clouds" and dynamic scaling in a far-from-equilibrium model system

A two-dimensional lattice gas of two species, driven in opposite directions by an external force, undergoes a jamming transition if the filling fraction is sufficiently high. Using Monte Carlo simulations, we investigate the growth of these jams ("clouds"), as the system approaches a non-equilibrium steady state from a disordered initial state. We monitor the dynamic structure factor $S(k_x,k_y;t)$ and find that the $k_x=0$ component exhibits dynamic scaling, of the form $S(0,k_y;t)=t^\beta \tilde{S}(k_yt^\alpha)$. Over a significant range of times, we observe excellent data collapse with $\alpha=1/2$ and $\beta=1$. The effects of varying filling fraction and driving force are discussed.