Dynamics of complex interfaces

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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 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.

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