Strongly nonlinear composite dielectrics: A perturbation method for finding the potential field and bulk effective properties

Raphael Blumenfeld, David J. Bergman

Research output: Contribution to journalArticlepeer-review

Abstract

A class of strongly nonlinear composite dielectrics is studied. We develop a general method to reduce the scalar-potential-field problem to the solution of a set of linear Poisson-type equations in rescaled coordinates. The method is applicable for a large variety of nonlinear materials. For a power-law relation between the displacement and the electric fields, it is used to solve explicitly for the value of the bulk effective dielectric constant e to second order in the fluctuations of its local value. A simlar procedure for the vector potential, whose curl is the displacement field, yields a quantity analogous to the inverse dielectric constant in linear dielectrics. The bulk effective dielectric constant is given by a set of linear integral expressions in the rescaled coordinates and exact bounds for it are derived.

Original languageEnglish
Pages (from-to)7378-7386
Number of pages9
JournalPhysical Review B-Condensed Matter
Volume44
Issue number14
DOIs
StatePublished - 1991

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