Localization properties of acoustic waves in the random-dimer media (original) (raw)

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 mediumwhich corresponds to the RD model-the localization-delocalization transition occurs at a resonance frequency ω c. The divergence of ξ near ω c is studied, and the critical exponents that characterize the power-law behavior of ξ near ω c are estimated for the regimes ω > ω c and ω < ω c. 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.