Localized hexagonal patterns- morphological and size aspects -

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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.

Original languageEnglish
Pages (from-to)29-47
Number of pages19
JournalProgress of Theoretical Physics
Volume121
Issue number1
DOIs
StatePublished - Jan 2009

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