The ant in the labyrinth: Diffusion in random networks near the percolation threshold

J. P. Straley

Research output: Contribution to journalArticlepeer-review

72 Scopus citations

Abstract

The parameters which describe the mean-squared displacement (R 2(t)) of a random walker on a random network have a characteristic singular dependence on epsilon =(p-pc)/pc near the percolation threshold. The critical exponents, which characterise the singularities of the diffusion constant, moment of inertia of finite clusters, and time constants for development of the long-time behaviour, are related by a scaling theory. They may also be related to the exponent theories for the percolation and percolation conduction problems. An equivalent resistor network can be described which is equivalent to the time Laplace transform of the diffusion problem. These problems will be given explicit treatment for the Cayley tree.

Original languageEnglish
Article number009
Pages (from-to)2991-3002
Number of pages12
JournalJournal of Physics C: Solid State Physics
Volume13
Issue number16
DOIs
StatePublished - 1980

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Engineering (all)
  • Physics and Astronomy (all)

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