Exact result for the effective conductivity of a continuum percolation model

Percolation model for a selective response of the resistance of composite semiconducting np systems with respect to reducing gases

It is shown that a two-component percolation model on a simple cubic lattice can explain an experimentally observed behavior [Savage et al., Sens. Actuators B 79, 17 (2001); Sens. Actuators B 72, 239 (2001).], namely, that a network built up by a mixture of sintered nanocrystalline semiconducting n and p grains can exhibit selective behavior, i.e., respond with a resistance increase when exposed to a reducing gas A and with a resistance decrease in response to another reducing gas B. To this end, a simple model is developed, where the n and p grains are simulated by overlapping spheres, based on realistic assumptions about the gas reactions on the grain surfaces. The resistance is calculated by random walk simulations with nn, pp, and np bonds between the grains, and the results are found in very good agreement with the experiments. Contrary to former assumptions, the np bonds are crucial to obtain this accordance.

Double-threshold percolation behavior of effective kinetic coefficients

We investigate thresholds of percolation in two-phase macroscopically inhomogeneous media. It is shown that, unlike standard percolation behavior there are systems in which effective kinetic coefficients of two-phase macroscopically inhomogeneous media have two percolation thresholds. As examples, thermoelectric and galvanomagnetic phenomena in such media are considered.

Comment on "Walker diffusion method for calculation of transport properties of composite materials"

In a recent paper [C. DeW. Van Siclen, Phys. Rev. E 59, 2804 (1999)], a random-walk algorithm was proposed as the best method to calculate transport properties of composite materials. It was claimed that the method is applicable both to discrete and continuum systems. The limitations of the proposed algorithm are analyzed. We show that the algorithm does not capture the peculiarities of continuum systems (e.g., "necks" or "choke points") and we argue that it is the stochastic analog of the finite-difference method.