AN SBV RELAXATION OF THE CROSS-NEWELL ENERGY FOR MODELING STRIPE PATTERNS AND THEIR DEFECTS

Research output: Contribution to journalArticlepeer-review

Abstract

We investigate stripe patterns formation far from threshold using a combination of topological, analytic, and numerical methods. We first give a definition of the mathematical structure of 'multi-valued' phase functions that are needed for describing layered structures or stripe patterns containing defects. This definition yields insight into the appropriate 'gauge symmetries' of patterns, and leads to the formulation of variational problems, in the class of special functions with bounded variation, to model patterns with defects. We then discuss approaches to discretize and numerically solve these variational problems. These energy minimizing solutions support defects having the same character as seen in experiments.

Original languageEnglish (US)
Pages (from-to)2719-2746
Number of pages28
JournalDiscrete and Continuous Dynamical Systems - Series S
Volume15
Issue number9
DOIs
StatePublished - Sep 2022

Keywords

  • measured foliations
  • Pattern formation
  • phase reduction
  • relaxation
  • special functions of bounded variation
  • split-Bregman method

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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