O. Levy et Dj. Bergman, WEAKLY NONLINEAR CONDUCTIVITY OF RANDOM COMPOSITES - A SERIES EXPANSION APPROACH, Journal of statistical physics, 82(5-6), 1996, pp. 1327-1344
We present a series expansion calculation of the bulk effective coeffi
cient of weakly nonlinear behavior in some continuum composite conduct
ors and in simple cubic random resistor networks. The expansion is in
powers of the relative difference between the linear Ohmic conductivit
ies of the components. It is carried up to third order for an independ
ent random bond network and a diagrammatic scheme is used to aid in im
plementing the calculation. For continuum composites, only the first t
erm of the expansion can be calculated explicitly without detailed inf
ormation about the microgeometry. Such information is difficult to acq
uire and even more difficult to exploit.