CONDUCTANCE FLUCTUATIONS IN WEAKLY INHOMOGENEOUS FINITE-SIZE RANDOM-MEDIA

Weakly inhomogeneous, finite-size, two-phase, continuous materials are studied. The two phases are randomly assigned either of two conductivities, 1 or 2, in such a way that the total concentration of 1 becomes p. The conductance of the resulting material has a standard deviation denoted Dc. An approximate expression for the two-dimensional random checkerboard, Dc [2p(1-p) 2/(1-p)(1-)][1/(N-1)], where =(1-2)/1 and N is the linear dimension, is derived on theoretical grounds and found to apply through numerical calculations on resistor networks. The problem of discretization involved in this procedure is discussed. © 1990 The American Physical Society.