Eur. Phys. J. B 79, 253-256 (2011)
https://doi.org/10.1140/epjb/e2010-10840-2

Extended acoustic waves in a one-dimensional aperiodic system

Instituto de Física, Universidade Federal de Alagoas, 57072-970 Maceió, AL, Brazil

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

Received: 3 November 2010
Revised: 23 November 2010
Published online: 14 January 2011

Abstract

We numerically study the propagation of acoustic waves in a one-dimensional system with an aperiodic pseudo-random elasticity distribution. The elasticity distribution was generated by using a sinusoidal function whose phase varies as a power-law, , where n labels the positions along the media. By considering a discrete one-dimensional version of the wave equation and 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 the time and spatial variables and study the nature of the waves that propagate in the chain. Our numerical data indicates the presence of extended acoustic waves with non-zero frequency for sufficient degree of aperiodicity.