SCALING PROPERTIES OF A PERCOLATION MODEL WITH LONG-RANGE CORRELATIONS

We present the results of Monte Carlo simulations of a percolation mod el with long-range correlations in two and three dimensions. The corre lations are generated by a fractional Brownian motion. The nature of t he percolation transition in this model is discussed. The percolation thresholds and the critical exponents of the model are calculated. The exponents are found to be mostly nonuniversal and dependent on a para meter that characterizes the nature of the correlations. Some possible applications of the model are discussed in detail, including flow in field-scale porous media (with megascopic disorder) with a given perme ability distribution, and estimating their effective permeability, and transport and dispersion in geological formations and explaining the anomalous and nonuniversal behavior of the dispersivity that has been observed in many field-scale experiments, in terms of the nonuniversal properties of our model.