Shape and size effects in localized hexagonal patterns

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Abstract

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 SwiftHohenberg 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.
Original languageAmerican English
Pages (from-to)2727-2743
Number of pages17
JournalInternational Journal of Bifurcation and Chaos
Volume19
Issue number8
DOIs
StatePublished - 1 Jan 2009

Keywords

  • Hexagons
  • Localized structures
  • Pattern formation

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