Coarsening in potential and nonpotential models of oblique stripe patterns

TL;DR

This paper investigates the coarsening dynamics of oblique stripe patterns in anisotropic Swift-Hohenberg models, revealing different growth regimes, dislocation behaviors, and drawing parallels with Model A in external fields, with experimental comparisons.

Contribution

It provides a detailed numerical analysis of coarsening in potential and nonpotential models, highlighting anisotropic growth laws and dislocation dynamics, which were not previously characterized.

Findings

Near onset, isotropic coarsening with length scale ~ t^{1/2}.

Far from onset, different growth exponents along x and y directions (~ 1/3 and 1/2).

Nonpotential effects can arrest or accelerate coarsening, affecting domain growth.

Abstract

We study the coarsening of two-dimensional oblique stripe patterns by numerically solving potential and nonpotential anisotropic Swift-Hohenberg equations. Close to onset, all models exhibit isotropic coarsening with a single characteristic length scale growing in time as $t^{1/2}$. Further from onset, the characteristic lengths along the preferred directions $\hat{x}$ and $\hat{y}$ grow with different exponents, close to 1/3 and 1/2, respectively. In this regime, one-dimensional dynamical scaling relations hold. We draw an analogy between this problem and Model A in a stationary, modulated external field. For deep quenches, nonpotential effects produce a complicated dislocation dynamics that can lead to either arrested or faster-than-power-law growth, depending on the model considered. In the arrested case, small isolated domains shrink down to a finite size and fail to disappear. A comparison with available experimental results of electroconvection in nematics is presented.