### 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 language | English (US) |
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Pages (from-to) | 593-644 |

Number of pages | 52 |

Journal | Journal of Statistical Physics |

Volume | 48 |

Issue number | 3-4 |

DOIs | |

State | Published - Aug 1 1987 |

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### Keywords

- Chemical turbulence
- cellular automaton
- dynamical systems

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Statistical Physics*,

*48*(3-4), 593-644. https://doi.org/10.1007/BF01019690