Ordering kinetics of stripe patterns

Abstract

We study domain coarsening of two dimensional stripe patterns by numerically solving the Swift-Hohenberg model of Rayleigh-Benard convection. Near the bifurcation threshold, the evolution of disordered configurations is dominated by grain boundary motion through a background of largely immobile curved stripes. A numerical study of the distribution of local stripe curvatures, of the structure factor of the order parameter, and a finite size scaling analysis of the grain boundary perimeter, suggest that the linear scale of the structure grows as a power law of time with a craracteristic exponent z=3. We interpret theoretically the exponent z=3 from the law of grain boundary motion.