Series expansion for the macroscopic conductivity of a random resistor network

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Abstract

The macroscopic conductivity sigma e of a simple cubic, two-component, random resistor network is systematically expanded as a power series in the relative difference between the two basic conductances. Graphs are developed to aid in implementing the calculation. A single-bond T-matrix-type rearrangement of the series leads to various types of single-bond approximations, and to an improved graph expansion for sigma e. The improved expansion is worked out up to seventh order, and used to discuss the singular properties of sigma e.

Original languageEnglish
Article number014
Pages (from-to)3365-3382
Number of pages18
JournalJournal of Physics C: Solid State Physics
Volume14
Issue number23
DOIs
StatePublished - 1981

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