A Quasicrystallic Domain Wall in Nonlinear Dissipative Patterns

Boris A. Malomed, Horacio G. Rotstein

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We propose an indirect approach to the generation of a two-dimensional quasiperiodic (QP) pattern in convection and similar nonlinear dissipative systems where a direct generation of stable uniform QP planforms is not possible. An eightfold QP pattern can be created as a broad transient layer between two domains filled by square cells (SC) oriented under an angle of 45 degrees relative to each other. A simplest particular type of transient layer is considered in detail. The structure of the pattern is described in terms of a system of coupled real Ginzburg-Landau (GL) equations, which are solved by means of combined numerical and analytical methods. It is found that the transient "quasicrystallic" pattern exists exactly in a parametric region in which the uniform SC pattern is stable. In fact, the transient layer consists of two different sublayers, with a narrow additional one between them. The width of one sublayer (which locally looks like the eightfold QP pattern) is large, while the other sublayer (that seems like a pattern having a quasiperiodicity only in one spatial direction) has a width ∼ 1. Similarly, a broad stripe of a twelvefold QP pattern can be generated as a transient region between two domains of hexagonal cells oriented at an angle of 30 degrees.

Original languageEnglish (US)
Pages (from-to)164-168
Number of pages5
JournalPhysica Scripta
Issue number2-3
StatePublished - 2000
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics
  • Mathematical Physics
  • Condensed Matter Physics


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