### 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) |
---|---|

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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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Statistical Physics*,

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

}

*Journal of Statistical Physics*, vol. 48, no. 3-4, pp. 593-644. https://doi.org/10.1007/BF01019690

**A cell dynamical system model of chemical turbulence.** / Oono, Y.; Yeung, C.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A cell dynamical system model of chemical turbulence

AU - Oono, Y.

AU - Yeung, C.

PY - 1987/8/1

Y1 - 1987/8/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0012953714&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0012953714&partnerID=8YFLogxK

U2 - 10.1007/BF01019690

DO - 10.1007/BF01019690

M3 - Article

AN - SCOPUS:0012953714

VL - 48

SP - 593

EP - 644

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 3-4

ER -