TY - JOUR

T1 - Strongly nonlinear composite dielectrics

T2 - A perturbation method for finding the potential field and bulk effective properties

AU - Blumenfeld, Raphael

AU - Bergman, David J.

PY - 1991

Y1 - 1991

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0012516654&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.44.7378

DO - 10.1103/PhysRevB.44.7378

M3 - מאמר

AN - SCOPUS:0012516654

VL - 44

SP - 7378

EP - 7386

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 1098-0121

IS - 14

ER -