Duality relations for non-Ohmic composites, with applications to behavior near percolation

Ohad Levy, Robert Kohn

Research output: Contribution to journalArticle

Abstract

Keller, Dykhne, and others have exploited duality to derive exact results for the effective behavior of two-dimensional Ohmic composites. This paper addresses similar issues in the non-Ohmic context. We focus primarily on three different types of nonlinearity: (a) the weakly nonlinear regime; (b) power-law behavior; and (c) dielectric breakdown. We first make the consequences of duality explicit in each setting. Then we draw conclusions concerning the critical exponents and sealing functions of "dual pairs" of random non-Ohmic composites near a percolation threshold. These results generalize, unify, and simplify relations previously derived for nonlinear resistor networks. We also discuss some self-dual nonlinear composites. Our treatment is elementary and self-contained; however, we also link it with the more abstract mathematical discussions of duality by Jikov and Kozlov.

Original languageEnglish (US)
Pages (from-to)159-189
Number of pages31
JournalJournal of Statistical Physics
Volume90
Issue number1-2
StatePublished - Jan 1998

Fingerprint

Duality
Composite
composite materials
Percolation Threshold
sealing
Exact Results
resistors
Critical Exponents
Breakdown
Simplify
Power Law
breakdown
nonlinearity
exponents
Nonlinearity
Generalise
thresholds
Context

Keywords

  • Duality
  • Effective properties
  • Nonlinear Composites
  • Percolation

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

Duality relations for non-Ohmic composites, with applications to behavior near percolation. / Levy, Ohad; Kohn, Robert.

In: Journal of Statistical Physics, Vol. 90, No. 1-2, 01.1998, p. 159-189.

Research output: Contribution to journalArticle

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