Shape and size effects in localized hexagonal patterns

We study the process of localization of a hexagonal pattern in a uniform background, specifically, the role played by the shape and size of the domain where the hexagonal pattern is confined. We base our analysis on a numerical study of a Swift–Hohenberg type equation (which exhibits coexistence between hexagons and a uniform state), and in a scale expansion to estimate the stress undergoing by the interface (the curve that separates the hexagonal phase from the uniform one). Our scaling approach supplies us a good physical picture of what we observe numerically.