Fronts between hexagons and squares in a generalized Swift-Hohemberg equation

Abstract

Pinning effects in domain walls separating different orientations in patterns in nonequilibrium systems are studied. Usually, theoretical studies consider perfect structures, but in experiments, point defects, grain boundaries, etc., always appear. The aim of this paper is to perform an analysis of the stability of fronts between hexagons and squares in a generalized Swift-Hohenberg model equation. We focus the analysis on pinned fronts between domains with different symmetries by using amplitude equations and by considering the small-scale structure in the pattern. The conditions for pinning effects and stable fronts are determined. This study is completed with direct simulations of the generalized Swift-Hohenberg equation. The results agree qualitatively with recent observations in convection and in ferrofluid instabilities.