Effective Medium Approximation in Voronoi Network Systems

The validity of the effective medium approximation in the two-dimensional Voronoi network is investigated. Two different Voronoi network models are introduced as the electric models of the polycrystalline materials. One is a random resistor model in which the Voronoi polygon and the boundary between the polygons are regarded as an insulator and a resistor, respectively. The other is a random capacitor model in which the Voronoi polygon and the boundary are regarded as a pure conductor and a capacitor, respectively. It is found that the accuracy of the effective medium approximation for the Voronoi network models is sufficient to estimate the average resistance or capacitance of the network.