Sideband instabilities and defects of quasipatterns

B. Echebarria, H. Riecke

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

Quasipatterns have been found in dissipative systems ranging from Faraday waves in vertically vibrated fluid layers to nonlinear optics. We describe the dynamics of octagonal, decagonal and dodecagonal quasipatterns by means of coupled Ginzburg-Landau equations and study their stability to sideband perturbations analytically using long-wave equations as well as by direct numerical simulation. Of particular interest is the influence of the phason modes, which are associated with the quasiperiodicity, on the stability of the patterns. In the dodecagonal case, in contrast to the octagonal and the decagonal case, the phase modes and the phason modes decouple and there are parameter regimes in which the quasipattern first becomes unstable with respect to phason modes rather than phase modes. We also discuss the different types of defects that can arise in each kind of quasipattern as well as their dynamics and interactions. Particularly interesting is the decagonal quasipattern, which allows two different types of defects. Their mutual interaction can be extremely weak even at small distances.

Original languageEnglish (US)
Pages (from-to)45-68
Number of pages24
JournalPhysica D: Nonlinear Phenomena
Volume158
Issue number1-4
DOIs
StatePublished - Oct 15 2001

Keywords

  • Defects
  • Ginzburg-Landau equations
  • Phase equation
  • Quasipatterns
  • Sideband instabilities

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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