Linear and nonlinear, scalar and vector transport processes in heterogeneous media: Fractals, percolation, and scaling laws

Abstract

We discuss recent developments in the application of fractal concepts and percolation theory to transport processes in heterogeneous media. The phenomena that we discuss include several types of nonlinear transport processes in disordered systems, which are relevant to the flow of non-Newtonian fluids in porous media, to electrical current in composites and doped polycrystalline semiconductors, to fracture and breakdown in disordered materials and natural rock, to elastic and viscoelastic properties of solids, polymers and gels, to flow in geological formations, and to several other problems. We emphasize the universal aspects of such phenomena, i.e., those that are independent of the microscopic or small-scale features of the systems in which they occur.