Numerical study of domain coarsening in anisotropic stripe patterns

TL;DR

This study investigates the coarsening dynamics of anisotropic stripe patterns in smectic polycrystals using an anisotropic Swift-Hohenberg model, revealing different growth regimes and defect behaviors depending on quench depth.

Contribution

It provides a numerical analysis of domain coarsening in anisotropic stripe patterns, highlighting the effects of anisotropic pinning and defect mobility.

Findings

Average domain size grows as t^{1/2} near onset.

Dislocation density decays as t^{-1/3}.

Chevron boundaries are pinned while dislocation arrays remain mobile.

Abstract

We study the coarsening of two-dimensional smectic polycrystals characterized by grains of oblique stripes with only two possible orientations. For this purpose, an anisotropic Swift-Hohenberg equation is solved. For quenches close enough to the onset of stripe formation, the average domain size increases with time as $t^{1/2}$. Further from onset, anisotropic pinning forces similar to Peierls stresses in solid crystals slow down defects, and growth becomes anisotropic. In a wide range of quench depths, dislocation arrays remain mobile and dislocation density roughly decays as $t^{-1/3}$, while chevron boundaries are totally pinned. We discuss some agreements and disagreements found with recent experimental results on the coarsening of anisotropic electroconvection patterns.