TY - JOUR

T1 - Series expansion for a weakly nonlinear conductivity of random composites

AU - Levy, Ohad

AU - Bergman, David J.

N1 - Funding Information:
This researchw as supportedi n part by a grant from the US-Israel al Science Foundation.

PY - 1992/12/15

Y1 - 1992/12/15

N2 - We discuss the nonlinear behavior of a simple cubic two-component random resistor network (RRN), in which the local current and voltage are related by I = gV+b|V|2V and b|V|2≪g. The macroscopic nonlinear conductivity bc is expanded as a power series in the relative difference between the ohmic conductivities of the components. The expansion is carried up to the third order. Graphs are used to aid in implementing the calculation. In the continuum case only the first term of the expansion can be calculated explicitly without detailed knowledge of the microgeometry.

AB - We discuss the nonlinear behavior of a simple cubic two-component random resistor network (RRN), in which the local current and voltage are related by I = gV+b|V|2V and b|V|2≪g. The macroscopic nonlinear conductivity bc is expanded as a power series in the relative difference between the ohmic conductivities of the components. The expansion is carried up to the third order. Graphs are used to aid in implementing the calculation. In the continuum case only the first term of the expansion can be calculated explicitly without detailed knowledge of the microgeometry.

UR - http://www.scopus.com/inward/record.url?scp=0642360108&partnerID=8YFLogxK

U2 - 10.1016/0378-4371(92)90571-7

DO - 10.1016/0378-4371(92)90571-7

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AN - SCOPUS:0642360108

SN - 0378-4371

VL - 191

SP - 475

EP - 478

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

IS - 1-4

ER -