Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2005-04-25
Physics
Condensed Matter
Statistical Mechanics
5 pages, 4 figures, to appear in Phys. Rev. Lett
Scientific paper
10.1103/PhysRevLett.94.165505
Using the Martin-Siggia-Rose method, we study propagation of acoustic waves in strongly heterogeneous media which are characterized by a broad distribution of the elastic constants. Gaussian-white distributed elastic constants, as well as those with long-range correlations with non-decaying power-law correlation functions, are considered. The study is motivated in part by a recent discovery that the elastic moduli of rock at large length scales may be characterized by long-range power-law correlation functions. Depending on the disorder, the renormalization group (RG) flows exhibit a transition to localized regime in {\it any} dimension. We have numerically checked the RG results using the transfer-matrix method and direct numerical simulations for one- and two-dimensional systems, respectively.
Bahraminasab Alireza
Rahimi Tabar Reza M.
Sahimi Muhammad
Shahbazi Farhad
Vaez Allaei Mehdi S.
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