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

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

D. A. Adams, B. Schmittmann, and R. K. P. Zia

Phys. Rev. E 75, 041123 – Published 30 April 2007

Abstract

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 nonequilibrium 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 $S (0, k_{y}; t) = t^{β} \tilde{S} (k_{y} t^{α})$ . Over a significant range of times, we observe excellent data collapse with $α = 1 ∕ 2$ and $β = 1$ . The effects of varying filling fraction and driving force are discussed.