Percolation and conductivity: A computer study. I

摘要: In this paper we present a large number of computer solutions various types resistor networks. Some these are analogous to physical problems such as impurity conduction in lightly compensated semiconductors and variable-range hopping amorphous semiconductors. A significant extension the standard relaxation techniques was required implement solutions. The results calculations compared percolation-model predictions based on concepts developed first series. simple criterion is found for applicability critical-percolation-path analysis type used formulate an accurate prediction impurity-conduction case. Arguments percolation models also given show that ${T}^{\ensuremath{-}\frac{1}{4}}$ ${T}^{\ensuremath{-}\frac{1}{3}}$ dependence ${log}_{10}\ensuremath{\sigma}$ often predicted three-dimensional two-dimensional indeed expected be observed, resistivity networks shown consistent with arguments. Accurate empirical formulas deduced from use them analyze some recent data films $a$-Ge. Employing preceding paper, several experimental studies, our have examined utility critical-volume-fraction rule Sher Zallen solving mixture problems. We find application appropriate only rather limited circumstances, general knowledge topological properties must employed finding threshold.