Computational study of the percolation phenomena in inhomogeneous two- and three-dimensional systems

In this paper, the results of computer investigation of the percolation processes in inhomogeneous lattices are discussed. The inhomogeneity 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 analysed. It is demonstrated that all these parameters essentially depend on the linear size and relative area. of the obstacles.