Deslocalização de ondas acústicas em sistemas unidimensionais não periódicos

Abstract

In this master degree thesis we numerically study the propagation of acoustic waves in one-dimensional non-periodic medium. We focus on two kinds of medium: (1) a media with scale-free long-range correlated elasticity distribution and (2) medium with an aperiodic pseudo-random elasticity distribution. In the first case, the random elasticity distribution is assumed to have a power spectrum S (k) ~ 1 / kª. By using a transfer matrix method we solve the discrete version of the scalar wave equation and comput the location length. In addition, we apply a second-order infinite-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 high degree of correlations. In contrast with local correlation, we numerically demonstrated that scale-free correlations promote a stable phase of free acoustic waves in the thermodynamic limit. In the another case, elasticity distribution was generated by using a sinusoidal function whose phase varies as a power law, φ α nv, where n labels the positions along the media. By considering again a discrete one-dimensional version of the wave equation and a matrix recursive reformulation we compute the location length within the band of allowed frequencies. Our numerical data indicates the presence of extended acoustic waves with non-zero frequency for a sufficient degree of aperiodicity.