When one attempts to modulate and control the characteristics of composite materials, limit of the modulation may be dictated by the mathematical threshold of the percolation transition. We report our computer simulation, in which percolation behavior can strongly be controlled by introducing size differences in the insulator particles rather than the conductor particles. This modulation effectively lowers the transition point to 0.52, from about 0.59 achieved with the conventional 2D site percolation model. Although a similar effect has already been reported for off-lattice systems and experiments, this is the first observation and analysis made in a basic 2D lattice model. Also, we show that this effect of threshold reduction is also related to the shape difference of the insulator particles. Such an observation in a basic model is believed to be fundamental to exploiting this phenomenon in real applications.

Electric conductance of percolation clusters is calculated by means of the random circuit approximation, under a binary distribution in the size of the conducting particles. Although we have already investigated the same size distribution model in terms of the percolation threshold, the electric transport conductance of this model is never reported before. The size distribution of conducting particles induces a clear difference in the ensemble of random circuit. However, the observed critical behavior and critical exponents are closely matched to those reported for monodisperse cases.

Particles made by coating an insulating core with a thin layer (shell) of conducting materials, called core-shell particles, are recently proposed to realize materials with particular nano-scale structures. Such structures work as a ''porous media'' of electric current, and its modified characteristics may be useful to improve some materials, for example the transparent conducting films.In this report, the basic feasibility of this idea is tested in the framework of the percolation model and the random register network model. The observed critical behavior and critical exponents of conductivity are also discussed, for the first time for 2D situations with core-shell particles.

Particles made by coating an insulating core with a thin layer (shell) of conducting materials, called core-shell particles, were recently proposed to realize materials with particular nano-scale structures. Such structures work as a ''porous medium'' of electric current, and their modified characteristics may be useful to improve some materials, such as transparent conducting films. We have already reported 2D simulation of such a conducting film with core-shell particles.In this report, the basic feasibility of this idea is tested within the framework of the percolation model and the random register network model. The observed critical behavior and critical exponents of conductivity are also discussed, for the first time for 3D situations with core-shell particles.

Electric conductance of percolation clusters is calculated by means of random circuit approximation under a binary distribution in the size of the conducting particles. Although we have already investigated a similar size distribution model in 2D, a 3D version of this model has not been reported before. The size distribution of conducting particles induces a clear difference in the ensemble of a random circuit. Consequently, a significant change in the critical point and conductance compared to the monodisperse cases is observed.