Characterizing the effect of boundary conditions on striped phases

David Morrissey, Arnd Scheel

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

We study the influence of boundary conditions on stationary, periodic patterns in one-dimensional systems. We show how a conceptual understanding of the structure of equilibria in large domains can be based on the characterization of boundary layers through displacement-strain curves. Most prominently, we distinguish wavenumber-selecting and phase-selecting boundary conditions and show how they impact the set of equilibria as the domain size tends to infinity. We illustrate the abstract concepts in the phase-diffusion and the Ginzburg-Landau approximations. We also show how to compute displacement-strain curves in more general systems such as the Swift-Hohenberg equation using continuation methods.

Original languageEnglish (US)
Pages (from-to)1387-1417
Number of pages31
JournalSIAM Journal on Applied Dynamical Systems
Volume14
Issue number3
DOIs
StatePublished - 2015

Keywords

  • Boundary layers
  • Ginzburg-Landau equation
  • Heteroclinic orbits
  • Swift-Hohenberg equation
  • Turing patterns

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