Grain-boundary motion in layered phases - art. no. 061704

We study the motion of a grain boundary that separates two sets of mutually perpendicular rolls in Rayleigh-Benard convection above onset. The problem is treated either analytically from the corresponding amplitude equations, or numerically by solving the Swift-Hohenberg equation. We find that if th e rolls are curved by a slow transversal modulation, a net translation of t he boundary follows. We show analytically that although this motion is a no nlinear effect, it occurs in a time scale much shorter than that of the lin ear relaxation of the curved rolls. The total distance traveled by the boun dary scales as epsilon (-1/2), where epsilon is the reduced Rayleigh number . We obtain analytical expressions for the relaxation rate of the modulatio n and for the time-dependent traveling velocity of the boundary, and especi ally their dependence on wave number. The results agree well with direct nu merical solutions of the Swift-Hohenberg equation. We finally discuss the i mplications of our results on the coarsening rate of an ensemble of differe ntly oriented domains in which grain-boundary motion through curved rolls i s the dominant coarsening mechanism.