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Paper IPM / P / 8855  


Abstract:  
Propagation of acoustic waves in the onedimensional (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 shortrange correlation in the medium 
which corresponds to the RD model  the
localizationdelocalization transition occurs at a resonance
frequency w_{c}. The divergence of ξ near w_{c} is
studied, and the critical exponents that characterize the
powerlaw behavior of ξ near w_{c} are estimated for the
regimes w > w_{c} and w < w_{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.
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