Logarithmic relaxation due to minimization of interactions in the Burridge-Knopoff model

B. A. H. Huisman and A. Fasolino
Phys. Rev. E 74, 026110 – Published 10 August 2006

Abstract

The time evolution of macroscopic quantities describing the relaxation of complex systems often contains a domain with logarithmic time dependence. This logarithmic behavior at the macroscopic level is often associated with strongly interacting elements at the microscopic level, whose interactions depend significantly on their history. In this paper we show that stress relaxation in the Burridge-Knopoff (BK) model of multicontact friction behaves logarithmically, when the model is in, or close to, the solitary state where the elements move independently. For this regime we present an automaton that allows us to follow the decay of stress relaxation over the entire range where it behaves logarithmically in time. We show that our model can be mapped onto a system of noninteracting elements subject to a uniform distribution of forces, for which logarithmic stress relaxation is derived analytically.

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  • Received 13 January 2006

DOI:https://doi.org/10.1103/PhysRevE.74.026110

©2006 American Physical Society

Authors & Affiliations

B. A. H. Huisman1 and A. Fasolino1,2

  • 1Van ’t Hoff Institute for Molecular Sciences, University of Amsterdam, Nieuwe Achtergracht 166, 1018 WV Amsterdam, The Netherlands
  • 2Theory of Condensed Matter, Institute for Molecules and Materials, Radboud University Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands

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Vol. 74, Iss. 2 — August 2006

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