Scaling properties of a percolation model with long-range correlations

We present the results of Monte Carlo simulations of a percolation model with long-range correlations in two and three dimensions. The correlations are generated by a fractional Brownian motion. The nature of the 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 parameter 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 permeability 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.