A variational theory for point defects in patterns

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Abstract

We derive a rigorous scaling law for minimizers in a natural version of the regularized Cross-Newell model for pattern formation far from threshold. These energy-minimizing solutions support defects having the same character as what is seen in experimental studies of the corresponding physical systems and in numerical simulations of the microscopic equations that describe these systems.

Original languageEnglish (US)
Pages (from-to)267-300
Number of pages34
JournalJournal of Nonlinear Science
Volume19
Issue number3
DOIs
StatePublished - Jun 1 2009

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Keywords

  • Calculus of variations
  • Defects
  • Patterns

ASJC Scopus subject areas

  • Modeling and Simulation
  • Engineering(all)
  • Applied Mathematics

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