Bethe格点上随机电阻网络电导率Stinchcombe解的各向异性推广
Anisotropic generalization of Stinchcombe's solution for conductivity of random resistor network on a Bethe lattice
摘要：
我们的研究是基于Stinchcombe [1974 \emph{J. Phys. C} \textbf{7} 179]的工作，并致力于计算放置在各向异性Bethe晶格上的随机电阻网络的平均电导率。Bethe格的结构被假定为表示规则格的法线方向。我们计算的各向异性电导率的Bethe晶格的逆配位数的幂的扩展。保留的扩展项提供了在逾渗阈值以上的电阻器浓度下的电导率的精确近似。我们把我们的分析结果与Bernasconi [1974]中\emph{Phys. Rev. B} \textbf{9} 4575的结果作了比较。
英文摘要：
Our study is based on the work of Stinchcombe [1974 \emph{J. Phys. C} \textbf{7} 179] and is devoted to the calculations of average conductivity of random resistor networks placed on an anisotropic Bethe lattice. The structure of the Bethe lattice is assumed to represent the normal directions of the regular lattice. We calculate the anisotropic conductivity as an expansion in powers of inverse coordination number of the Bethe lattice. The expansion terms retained deliver an accurate approximation of the conductivity at resistor concentrations above the percolation threshold. We make a comparison of our analytical results with those of Bernasconi [1974 \emph{Phys. Rev. B} \textbf{9} 4575] for the regular lattice.
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