On theories of transport in disordered media

Abstract

Various approaches to the theory of electrical conduction in disordered media are examined to make a better assessment of the possibility of improving the simple effective approximation. A cluster calculation is reported for the bond percolation model in three dimensions and the results are compared with the effective medium theory and Monte Carlo calculations. A comparison is made between the bond percolation model and the generally accepted equivalent model for a continuum. A breakdown is found in this assumed equivalence, which stems from correlations present in the continuum model but absent in lattices. The cumulant theory is studied in the lattice context. Although it gives good results for the simple cubic lattice when compared with Monte Carlo calculations, the reasons offered in the continuum model study do not apply here. The effect of cluster shape on site percolation calculations is studied.