Abstract

A classical geometry, widely observed in systems far from equilibrium, is the formation of hexagonal patterns. Using a prototype Swift-Hohenberg equation for the order parameter we study the localization mechanism for hexagons surrounded by a uniform phase. Numerical simulations show that the existence range for localized structures depends on the size and morphology of the structure. We propose a scale expansion in order to estimate the stress at the interfaces between the hexagons and the uniform phase. This scaling approach supplies a good physical description of the mechanisms involved in the localization of the hexagonal pattern.