Mean-field conductivity in a certain class of networks

M. V. Chubynsky, Michael Thorpe

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

We consider resistor networks, which are lattices with bonds represented by conductors and some of the bonds removed. It is known that effective medium theories predict that the effective conductivity of such networks is a linear function of the number of bonds present above the percolation threshold, but exact results for completely random networks deviate from linearity. We show that if instead we take a randomly chosen tree spanning the lattice and then start adding bonds to it at random, the conductivity changes linearly with the number of added bonds and coincides with the effective medium result for a given bond concentration. We also make comparisons with some related models.

Original languageEnglish (US)
Article number056105
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume71
Issue number5
DOIs
StatePublished - May 2005

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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