We present numerical simulations of AC conductance for a random resistorcapacitor network. The conductance obeys a probability density function p(g)∝g−α(0<α<1). We use a highly efficient propagation algorithm to calculate the effective conductance of a long strip of a lattice. At low frequencies, we find that for the concentration p of conducting bonds less than the percolation threshold pc, the imaginary part of conductance is proportional to frequency Im(geff)≃ω and the real part of conductance shows an anomalous frequency dependence Re(geff)≃ω2−α. The results of simulations in such a continuum system are in agreement with the predictions of the effective medium and the Maxwell-Garnett approximation. We also calculate the non-universal DC conductivity exponents in continuum percolation; the result are consistent with earlier theoretical predictions and numerical calculations.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)