Propagation and localization of acoustic and elastic waves in heterogeneous materials: renormalization group analysis and numerical simulations

Extensive computer simulations have been carried out to study propagation of acoustic waves in a two-dimensional disordered fractured porous medium, as a prelude to studying elastic wave propagation in such media. The fracture network is represented by randomly distributed channels of finite width and length, the contrast in the properties of the porous matrix and the fractures is taken into account, and the propagation of the waves is studied over broad ranges of the fracture number density ρ and width b. The most significant result of the study is that, at short distances from the wave source, the waves' amplitude, as well as their energy, decays exponentially with the distance from the source, which is similar to the classical problem of electron localization in disordered solids, whereas the amplitude decays as a stretched exponential function of the distance x that corresponds to sublocalization, exp(-x(α)) with α < 1. Moreover, the exponent α depends on both ρ and b. This is analogous to electron localization in percolation systems at the percolation threshold. Similar results are obtained for the decay of the waves' amplitude with the porosity of the fracture network. Moreover, the amplitude decays faster with distance from the source x in a fractured porous medium than in one without fractures. The mean speed of wave propagation decreases linearly with the fractures' number density.

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Probability of overall collapse for concrete gravity dam based on renormalization group theory of unequal probability unit

Gu¹,

Deng²,

Tang³

et al. 2013

Hydraulic Engineering II

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Propagation and localization of acoustic and elastic waves in heterogeneous materials: renormalization group analysis and numerical simulations

Cited by 4 publications

References 43 publications

Approaching complexity by stochastic methods: From biological systems to turbulence

Approaching complexity by stochastic methods: From biological systems to turbulence

Wave propagation in disordered fractured porous media

Probability of overall collapse for concrete gravity dam based on renormalization group theory of unequal probability unit

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