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Localization properties of acoustic waves in the random-dimer media

Esmailpour, A ; Sharif University of Technology | 2008

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  1. Type of Document: Article
  2. DOI: 10.1103/PhysRevB.78.134206
  3. Publisher: 2008
  4. Abstract:
  5. Propagation of acoustic waves in the one-dimensional (1D) random-dimer (RD) medium is studied by three distinct methods. First, using the transfer-matrix method, we calculate numerically the localization length ξ of acoustic waves in a binary chain (one in which the elastic constants take on one of two values). We show that when there exists short-range correlation in the medium-which corresponds to the RD model-the localization-delocalization transition occurs at a resonance frequency ωc. The divergence of ξ near ωc is studied, and the critical exponents that characterize the power-law behavior of ξ near ωc are estimated for the regimes ω> ωc and ω< ωc. Second, an exact analytical analysis is carried out for the delocalization properties of the waves in the RD media. In particular, we predict the resonance frequency at which the waves can propagate in the entire chain. Finally, we develop a dynamical method, based on the direct numerical simulation of the governing equation for propagation of the waves, and study the nature of the waves that propagate in the chain. It is shown that only the resonance frequency can propagate through the 1D media. The results obtained with all the three methods are in agreement with each other. © 2008 The American Physical Society
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  8. Source: Physical Review B - Condensed Matter and Materials Physics ; Volume 78, Issue 13 , 2008 ; 10980121 (ISSN)
  9. URL: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.78.134206