Im. Khalatnikov et Ay. Kamenshchik, A diagram technique for perturbation theory calculations of the effective conductivity of two-dimensional systems, J EXP TH PH, 91(6), 2000, pp. 1261-1267
The perturbation theory for calculating the effective conductivity of the p
lane consisting of pieces of different conductivities is constructed, and a
convenient diagram technique is elaborated for this perturbation theory. I
t is shown that for the chessboard, perturbative calculations give results
that are in agreement with the well-known formula sigma (eff) = root sigma
(1)sigma (2). The components of the effective conductivity tensor for the a
nisotropic three-color chessboard are calculated. It is shown that the isot
ropic (symmetric) part of the effective conductivity calculated up to the s
ixth order of perturbation theory satisfies the Bruggeman effective medium
equation for symmetric three-color structures with equally partitioned comp
onents. We also consider an isotropic three-color chessboard with nonequal
weights of colors. In this case, the perturbation theory in the fourth orde
r contradicts the results following from the Bruggeman equation for nonequa
l weights. (C) 2000 MAIK "Nauka/Interperiodica".