Energy relaxation in discrete nonlinear lattices

A. Bikaki; N. K. Voulgarakis; S. Aubry; G. P. Tsironis

doi:10.1103/PhysRevE.59.1234

Energy relaxation in discrete nonlinear lattices

A. Bikaki, N. K. Voulgarakis, S. Aubry, and G. P. Tsironis

Phys. Rev. E 59, 1234 – Published 1 January 1999

Abstract

We numerically investigate energy relaxation in discrete nonlinear lattices in one and two spatial dimensions. We find that energy relaxation follows a stretched exponential law, and we study its dependence on the initial temperature. We attribute this behavior to hierarchies of discrete breathers that relax with different time constants, leading to a hierarchy of relaxation time scales in the system. Using heuristic arguments, we derive a nonlinear diffusion equation for the local energy density of the oscillators that results in similar relaxation dynamics.

Received 17 July 1998

DOI:https://doi.org/10.1103/PhysRevE.59.1234

Authors & Affiliations

A. Bikaki and N. K. Voulgarakis

Department of Physics, University of Crete, P. O. Box 2208, 71003 Heraklion, Crete, Greece

S. Aubry^* and G. P. Tsironis^†

Center for Nonlinear Studies, MS-B258, Los Alamos National Laboratory, Los Alamos, New Mexico 87545

^*Permanent address: Laboratoire Léon Brillouin, CEA-CNRS, CE Saclay, 91191 Gif-sur-Yvette Cedex, France.
^†Permanent address: Department of Physics, University of Crete and Foundation for Research and Technology–Hellas, P. O. Box 2208, 71003 Heraklion, Crete, Greece.

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Vol. 59, Iss. 1 — January 1999

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