LINEAR AND NONLINEAR, SCALAR AND VECTOR TRANSPORT PROCESSES IN HETEROGENEOUS MEDIA - FRACTALS, PERCOLATION, AND SCALING LAWS

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 trans port processes in disordered systems, which are relevant to the Row of non-Newtonian fluids in porous media, to electrical current in compos ites and doped polycrystalline semiconductors, to fracture and breakdo wn in disordered materials and natural rock, to elastic and viscoelast ic properties of solids, polymers and gels, to flow in geological form ations, and to several other problems. We emphasize the universal aspe cts of such phenomena, i.e., those that are independent of the microsc opic or small-scale features of the systems in which they occur.