### Abstract

Complex interfacial dynamics is studied in an oscillatory medium described by a deterministic coupled-map lattice. This dynamical system supports only stable periodic attractors. The interfaces that separate the stable homogeneous phases exhibit different types of behavior ranging from simple planar fronts with low periodicity to highly irregular fronts with complex spatiotemporal transients. A dynamical analysis of the system is carried out for a small interface length L, in which the probabilities of occurrence of given periodic orbits, the velocities of the corresponding interfaces, and Lyapunov exponents are calculated. The importance of transient dynamics for large L is demonstrated. In the large-L regime the interfacial evolution and structure are characterized in statistical terms and the simulation results are compared with phenomenological stochastic models such as the Edwards-Wilkinson and Kardar-Parisi-Zhang equations. In some parameter regions, the deterministic, transient interfacial dynamics of the coupled-map model is described well by such models if finite-size effects are taken into account. Nucleation and growth dynamics are also investigated. The system provides a framework in which to study complex interfacial structures.

Original language | English |
---|---|

Pages (from-to) | 2009-2022 |

Number of pages | 14 |

Journal | Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 49 |

Issue number | 3 |

Publication status | Published - Mar 1994 |

### Keywords

- GROWING INTERFACES
- TURBULENCE
- SYSTEMS

### Cite this

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*49*(3), 2009-2022.

**DYNAMICS OF COMPLEX INTERFACES.** / KAPRAL, R ; LIVI, R ; OPPO, G L ; POLITI, A .

Research output: Contribution to journal › Article

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 49, no. 3, pp. 2009-2022.

}

TY - JOUR

T1 - DYNAMICS OF COMPLEX INTERFACES

AU - KAPRAL, R

AU - LIVI, R

AU - OPPO, G L

AU - POLITI, A

PY - 1994/3

Y1 - 1994/3

N2 - Complex interfacial dynamics is studied in an oscillatory medium described by a deterministic coupled-map lattice. This dynamical system supports only stable periodic attractors. The interfaces that separate the stable homogeneous phases exhibit different types of behavior ranging from simple planar fronts with low periodicity to highly irregular fronts with complex spatiotemporal transients. A dynamical analysis of the system is carried out for a small interface length L, in which the probabilities of occurrence of given periodic orbits, the velocities of the corresponding interfaces, and Lyapunov exponents are calculated. The importance of transient dynamics for large L is demonstrated. In the large-L regime the interfacial evolution and structure are characterized in statistical terms and the simulation results are compared with phenomenological stochastic models such as the Edwards-Wilkinson and Kardar-Parisi-Zhang equations. In some parameter regions, the deterministic, transient interfacial dynamics of the coupled-map model is described well by such models if finite-size effects are taken into account. Nucleation and growth dynamics are also investigated. The system provides a framework in which to study complex interfacial structures.

AB - Complex interfacial dynamics is studied in an oscillatory medium described by a deterministic coupled-map lattice. This dynamical system supports only stable periodic attractors. The interfaces that separate the stable homogeneous phases exhibit different types of behavior ranging from simple planar fronts with low periodicity to highly irregular fronts with complex spatiotemporal transients. A dynamical analysis of the system is carried out for a small interface length L, in which the probabilities of occurrence of given periodic orbits, the velocities of the corresponding interfaces, and Lyapunov exponents are calculated. The importance of transient dynamics for large L is demonstrated. In the large-L regime the interfacial evolution and structure are characterized in statistical terms and the simulation results are compared with phenomenological stochastic models such as the Edwards-Wilkinson and Kardar-Parisi-Zhang equations. In some parameter regions, the deterministic, transient interfacial dynamics of the coupled-map model is described well by such models if finite-size effects are taken into account. Nucleation and growth dynamics are also investigated. The system provides a framework in which to study complex interfacial structures.

KW - GROWING INTERFACES

KW - TURBULENCE

KW - SYSTEMS

M3 - Article

VL - 49

SP - 2009

EP - 2022

JO - Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 3

ER -