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Dynamic renormalization group analysis of propagation of elastic waves in two-dimensional heterogeneous media

Sepehrinia, R ; Sharif University of Technology | 2008

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  1. Type of Document: Article
  2. DOI: 10.1103/PhysRevB.77.014203
  3. Publisher: 2008
  4. Abstract:
  5. We study localization of elastic waves in two-dimensional heterogeneous solids with randomly distributed Lamé coefficients, as well as those with long-range correlations with a power-law correlation function. The Matin-Siggia-Rose method is used, and the one-loop renormalization group (RG) equations for the coupling constants are derived in the limit of long wavelengths. The various phases of the coupling constants space, which depend on the value ρ, the exponent that characterizes the power-law correlation function, are determined and described. Qualitatively different behaviors emerge for ρ<1 and ρ>1. The Gaussian fixed point (FP) is stable (unstable) for ρ<1 (ρ>1). For ρ<1, there is a region of the coupling constants space in which the RG flows are toward the Gaussian FP, implying that the disorder is irrelevant and the waves are delocalized. In the rest of the disorder space, the elastic waves are localized. We compare the results with those obtained previously for acoustic wave propagation in the same type of heterogeneous media and describe the similarities and differences between the two phenomena. © 2008 The American Physical Society
  6. Keywords:
  7. Two-dimensional heterogeneous media ; Propagation of elastic waves ; Matin-Siggia-Rose
  8. Source: Physical Review B - Condensed Matter and Materials Physics ; Volume 77, Issue 1 , 2008 ; 10980121 (ISSN)
  9. URL: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.77.014203