The Mathematics and Physics of Disordered Media

Random processes and random systems: An introduction.- On the wedding of certain dynamical processes in disordered complex materials to the theory of stable (Lévy) distribution functions.- Fractal stochastic processes: Clusters and intermittancies.- Percolation and fractal properties of thin gold films.- Percolation and capillary fluid displacement.- Recent progress and current puzzles in percolation.- Markov fields, correlated percolation, and the Ising model.- Directionality effects in percolation.- Percolation and related systems in equilibrium statistical mechanics.- Branched polymers, polymer gels and percolation theory.- Critical probabilities in percolation models.- Critical exponents and thresholds for percolation and conduction.- Models of disordered media: Some new results, including some new connections between composite-media, fluid-state, and random-flight theories.- Variational bounds on the diffusive and hydrodynamic permeabilities of randomly perforated sheets.- Diffusions and random walks in random media.- Waves in disordered media.- Microscopic origins of stochastic crack growth.