Grain boundary motion in layered phases

Abstract

We study the motion of a grain boundary that separates two sets of mutually perpendicular rolls in Rayleigh-Bénard 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 the rolls are curved by a slow transversal modulation, a net translation of the boundary follows. We show analytically that although this motion is a nonlinear effect, it occurs in a time scale much shorter than that of the linear relaxation of the curved rolls. The total distance traveled by the boundary scales as ${\epsilon }^{-1/2}$, where $\epsilon$ is the reduced Rayleigh number. We obtain analytical expressions for the relaxation rate of the modulation and for the time dependent traveling velocity of the boundary, and especially their dependence on wavenumber. The results agree well with direct numerical solutions of the Swift-Hohenberg equation. We finally discuss the implications of our results on the coarsening rate of an ensemble of differently oriented domains in which grain boundary motion through curved rolls is the dominant coarsening mechanism.

16 pages, 5 figures

Cited by in corpus (7)

• Grain boundary pinning and glassy dynamics in stripe phases
• Ordering kinetics of stripe patterns
• Nucleation of stable cylinders from a metastable lamellar phase in a diblock copolymer melt
• Defect Structures in the Growth Kinetics of the Swift-Hohenberg Model
• Grain boundary dynamics in stripe phases of non potential systems
• Shear induced grain boundary motion for lamellar phases in the weakly nonlinear regime
• A Model for Striped Growth