### Abstract

The thermodynamic formalism for dynamical systems is applied to a class of mappings of laminar-turbulent temporal intermittency. The corresponding statistical system is shown to be a lattice gas with many-body interactions of clustering type. This one-dimensional system bears a close analogy with the Fisher-Felderhof droplet model of condensation. The abnormal dynamic fluctuations give rise to a phase transition. The critical behaviors, which depend solely on the characteristic exponent z of the original map, are studied analytically, and a number of unexpected results are obtained. In the pressure-temperature plane, the intermittant state is located on a critical line that separates the chaotic (turbulent) state from the periodic (laminar) state. The transition from one phase to the other may be of first order if z<2. On the other hand, for 2z, the sporadic state introduced by Gaspard and Wang [Proc. Natl. Acad. Sci. U.S.A. 85, 4591 (1988)] is existent and corresponds to a codimension-two point on the critical curve.

Original language | English (US) |
---|---|

Pages (from-to) | 6647-6661 |

Number of pages | 15 |

Journal | Physical Review A |

Volume | 40 |

Issue number | 11 |

DOIs | |

State | Published - 1989 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A*,

*40*(11), 6647-6661. https://doi.org/10.1103/PhysRevA.40.6647

**Statistical physics of temporal intermittency.** / Wang, Xiao-Jing.

Research output: Contribution to journal › Article

*Physical Review A*, vol. 40, no. 11, pp. 6647-6661. https://doi.org/10.1103/PhysRevA.40.6647

}

TY - JOUR

T1 - Statistical physics of temporal intermittency

AU - Wang, Xiao-Jing

PY - 1989

Y1 - 1989

N2 - The thermodynamic formalism for dynamical systems is applied to a class of mappings of laminar-turbulent temporal intermittency. The corresponding statistical system is shown to be a lattice gas with many-body interactions of clustering type. This one-dimensional system bears a close analogy with the Fisher-Felderhof droplet model of condensation. The abnormal dynamic fluctuations give rise to a phase transition. The critical behaviors, which depend solely on the characteristic exponent z of the original map, are studied analytically, and a number of unexpected results are obtained. In the pressure-temperature plane, the intermittant state is located on a critical line that separates the chaotic (turbulent) state from the periodic (laminar) state. The transition from one phase to the other may be of first order if z<2. On the other hand, for 2z, the sporadic state introduced by Gaspard and Wang [Proc. Natl. Acad. Sci. U.S.A. 85, 4591 (1988)] is existent and corresponds to a codimension-two point on the critical curve.

AB - The thermodynamic formalism for dynamical systems is applied to a class of mappings of laminar-turbulent temporal intermittency. The corresponding statistical system is shown to be a lattice gas with many-body interactions of clustering type. This one-dimensional system bears a close analogy with the Fisher-Felderhof droplet model of condensation. The abnormal dynamic fluctuations give rise to a phase transition. The critical behaviors, which depend solely on the characteristic exponent z of the original map, are studied analytically, and a number of unexpected results are obtained. In the pressure-temperature plane, the intermittant state is located on a critical line that separates the chaotic (turbulent) state from the periodic (laminar) state. The transition from one phase to the other may be of first order if z<2. On the other hand, for 2z, the sporadic state introduced by Gaspard and Wang [Proc. Natl. Acad. Sci. U.S.A. 85, 4591 (1988)] is existent and corresponds to a codimension-two point on the critical curve.

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U2 - 10.1103/PhysRevA.40.6647

DO - 10.1103/PhysRevA.40.6647

M3 - Article

VL - 40

SP - 6647

EP - 6661

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 11

ER -