Computer investigation of the percolation processes in two- and three-dimensional systems with heterogeneous internal structure

The results of computer investigation of the percolation processes in two- and three-dimensional heterogeneous lattices are presented. The heterogeneous condition is simulated by a random distribution of obstacles differing in size and number. The influence of obstacles on the parameters (critical concentration, average number of sites in finite clusters, percolation probability, critical exponents, and fractal and spectral dimensions of a percolation cluster) characterizing the percolation in the system is analyzed. It is demonstrated that all these parameters essentially depend on features of the heterogeneous internal structure (linear size and relative area of the obstacles) of the system.