Shape of a Wave Front in a Heterogenous Medium

S. Mehdi Vaez Allaei and Muhammad Sahimi
Phys. Rev. Lett. 96, 075507 – Published 23 February 2006

Abstract

Wave propagation in a heterogeneous medium, characterized by a distribution of local elastic moduli, is studied. Both acoustic and elastic waves are considered, as are spatially random and power-law correlated distributions of the elastic moduli with nondecaying correlations. Three models—a continuum scalar model, and two discrete models—are utilized. Numerical simulations indicate the existence, at all times, of the relation, α=H, where α is the roughness exponent of the wave front in the medium, and H is the Hurst exponent that characterizes the spatial correlations in the distribution of the local elastic moduli. Hence, a direct relation between the static morphology of an inhomogeneous correlated medium and its dynamical properties is established. In contrast, for a wave front in random media, α=0 (logarithmic growth) at short times, followed by a crossover to the classical value, α=1/2, at long times.

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  • Received 24 July 2005

DOI:https://doi.org/10.1103/PhysRevLett.96.075507

©2006 American Physical Society

Authors & Affiliations

S. Mehdi Vaez Allaei1 and Muhammad Sahimi2,*

  • 1Institute for Advanced Studies in Basic Sciences, Gava Zang, Zanjan 45195-1159, Iran
  • 2Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, California 90089-1211, USA

  • *Electronic address: moe@iran.usc.edu

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Issue

Vol. 96, Iss. 7 — 24 February 2006

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