A cell dynamical system model of chemical turbulence

Y. Oono, C. Yeung

Research output: Contribution to journalArticle

Abstract

A cellular-automaton-like caricature of chemical turbulence on an infinite one-dimensional lattice is studied. The model exhibits apparently "turbulent" space-time patterns. To make this statement precise, the following problems or points are discussed: (1) The infinite-system-size limit of such cell-dynamical systems and its observability is defined. (2) It is proved that the invariant state in the large-system-size limit of the "turbulent" phase exhibits spatial patterns governed by a Gibbs random field. (3) Potential characteristics of "turbulent" space-time patterns are critically surveyed and a working definition of (weak) turbulence is proposed. (4) It is proved that the invariant state of the 'turbulent" phase is actually (weak) turbulent. Furthermore, we conjecture that the turbulent phase of our model is an example of a K system that is not Bernoulli.

Original languageEnglish (US)
Pages (from-to)593-644
Number of pages52
JournalJournal of Statistical Physics
Volume48
Issue number3-4
DOIs
StatePublished - Aug 1 1987

Keywords

  • Chemical turbulence
  • cellular automaton
  • dynamical systems

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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