Shahbazi F, Bahraminasab Alireza, Allaei S Mehdi Vaez, Sahimi Muhammad, Tabar M Reza Rahimi
Department of Physics, Isfahan University of Technology, Isfahan 84156, Iran.
Phys Rev Lett. 2005 Apr 29;94(16):165505. doi: 10.1103/PhysRevLett.94.165505. Epub 2005 Apr 28.
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 nondecaying 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 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.
我们使用马丁 - 西格亚 - 罗斯方法，研究弹性常数具有广泛分布的强非均匀介质中声波的传播。考虑了高斯白分布的弹性常数，以及具有非衰减幂律相关函数的长程相关性的弹性常数。这项研究部分是受最近一项发现的推动，即大长度尺度下岩石的弹性模量可能由长程幂律相关函数表征。根据无序情况，重整化群（RG）流在任何维度都会呈现向局域化状态的转变。我们分别使用转移矩阵方法和直接数值模拟对一维和二维系统进行了数值检验RG结果。
