We numerically study the propagation of acoustic waves in a one-dimensional medium with a scale-free long-range correlated elasticity distribution. The random elasticity distribution is assumed to have a power spectrum S(k) ∼ 1/k α . By using a transfer-matrix method we solve the discrete version of the scalar wave equation and compute the localization length. In addition, we apply a second-order finite-difference method for both the time and spatial variables and study the nature of the waves that propagate in the chain. Our numerical data indicate the presence of extended acoustic waves for a high degree of correlations. In contrast with local correlations, we numerically demonstrate that scale-free correlations promote a stable phase of free acoustic waves in the thermodynamic limit.

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In this paper we study the propagation of acoustic waves in a one-dimensional medium with a short range correlated elasticity distribution. In order to generate local correlations we consider a disordered binary distribution in which the effective elastic constants can take on only two values, η(A) and η(B). We add an additional constraint that the η(A) values appear only in finite segments of length n. This is a generalization of the well-known random-dimer model. By using an analytical procedure we demonstrate that the system displays n - 1 resonances with frequencies ω(r). Furthermore, we apply a numerical transfer matrix formalism and a second-order finite-difference method to study in detail the waves that propagate in the chain. Our results indicate that all the modes with ω ≠ ω(r) decay and the medium transmits only the frequencies ω(r).

In this paper we study the propagation of acoustic waves in a one-dimensional system with nonstationary chaotic elasticity distribution. The elasticity distribution is assumed to have a power spectrum S(f) ~ 1/f(2B-3)/(B-1) for B ≥ 1.5. By using a transfer-matrix method we solve the discrete version of the scalar wave equation and compute the Lyapunov exponent. In addition, we apply a second-order finite-difference method for both the time and spatial variables and study the nature of the waves that propagate in the chain. Our numerical data indicate the presence of weak localized acoustic waves for high degree of correlations (B > 2).