ISSN:
1572-9613
Keywords:
Nonlinear Composites
;
duality
;
effective properties
;
percolation
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
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 scaling 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1023251701546
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