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Abstract
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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 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 . The divergence of near is
studied, and the critical exponents that characterize the power-law behavior of near are estimated for the
regimes and . 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
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