Eur. Phys. J. B 80, 59-63 (2011)
https://doi.org/10.1140/epjb/e2011-20016-3

Extended acoustic waves in diluted random systems

Instituto de Física, Universidade Federal de Alagoas, Campus A. C. Simes, BR 104 km 14, Tabuleiro dos Martins, 57072-970 Maceió, AL, Brazil

Corresponding author: ^a fidelis@if.ufal.br

Received: 9 January 2011
Revised: 4 February 2011
Published online: 9 March 2011

Abstract

In this paper we study the propagation of acoustic waves in an one-dimensional diluted random media which is composed of two interpenetrating chains with pure and random elasticity. We considered a discrete one-dimensional version of the wave equation where the elasticity distribution appears as an effective spring constant. By using a matrix recursive reformulation we compute the localization length within the band of allowed frequencies. In addition, we apply a second-order finite difference method for both time and spatial variables, and study the nature of the waves that propagate in the chain. We numerically demonstrate that the diluted random elasticity distribution promotes extended acoustic modes at high-frequencies.