Coarsening in potential and nonpotential models of oblique stripe patterns

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.