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 languageEnglish
Pages (from-to)2727-2743
Number of pages17
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume19
Issue number8
DOIs
StatePublished - Aug 2009

Bibliographical note

Funding Information:
The simulation software DIMX developed at the laboratory INLN in France has been used for numerical simulations. D. Escaff thanks the support of FONDECYT (Project No. 3070013). O. Descalzi wishes to acknowledge the support of FONDECYT (Project No. 1070098). It is the pleasure of the authors to thank Prof. H. R. Brand for the stimulating discussions and hospitality during our staying at the University of Bayreuth, Germany. The authors acknowledge support from FAI (Project No. ICIV-003-08) and ACT15 (Anillo en Ciencia y Tecnología).

Keywords

  • Hexagons
  • Localized structures
  • Pattern formation

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