Percolation for a model of statistically inhomogeneous random media

We study clustering and percolation phenomena for a model of statistically inhomogeneous two-phase random media, including functionally graded materia ls. This model consists of inhomogeneous fully penetrable (Poisson distribu ted) disks and can be constructed for any specified variation of volume fra ction. We quantify the transition zone in the model, defined by the frontie r of the cluster of disks which are connected to the disk-covered portion o f the model, by defining the coastline function and correlation functions f or the coastline. We find that the behavior of these functions becomes larg ely independent of the specific choice of grade in volume fraction as the s eparation of length scales becomes large. We also show that the correlation function behaves in a manner similar to that of fractal Brownian motion. F inally, we study fractal characteristics of the frontier itself and compare to similar properties for two-dimensional percolation on a lattice. In par ticular, we show that the average location of the frontier appears to be re lated to the percolation threshold for homogeneous fully penetrable disks. (C) 1999 American Institute of Physics. [S0021-9606(99)51037-4].