Exact Relations between Elastic and Electrical Response of d-Dimensional Percolating Networks with Angle-Bending Forces

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Abstract

Arguments are presented to demonstrate that exact equality relations exist between the critical exponents which characterize the macroscopic conductivity σe, and the macroscopic elastic stiffness moduli Ce of percolating systems of any dimensionality. Using the notation σ e, ∝ Δpt, Ce ∝ Δp T for the critical behavior of a randomly diluted system slightly above the percolation threshold pc, (Δp ≡ p-p c > 0) and σe, ∝ |Δp|-s, Ce ∝|Δp|-s for the critical behavior of a random mixture of normal and perfectly conducting or normal and perfectly rigid constituents slightly below that threshold, (Δp ≡ p-pe < 0) we show that T = t+2v and S = s, where v is the percolation correlation length critical exponent ξ ∝ |Δp|-v (Δp >< 0).

Original languageEnglish
Pages (from-to)171-199
Number of pages29
JournalJournal of Statistical Physics
Volume111
Issue number1-2
DOIs
StatePublished - Apr 2003

Keywords

  • Composite media
  • Critical exponents
  • Elastic percolation
  • Exact results

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