The statistical mechanics and dynamics of disordered systems will be investigated using analytical and numerical methods. Three major areas will be studied: 1) Self-avoiding walks in random environments, 2) The superfluid transition for Helium in porous media and 3) Random resistor and elastic networks. These topics will be investigated by a variety of modern methods of statistical mechanics; including field theory and the renormalization group, Lifshitz type arguments, and numerical simulation. This research is directly relevant to understanding current experiments in the areas of superfluids in porous glasses and polymers in gels. A second fundamental objective of this work is to advance the development of theoretical tools for the study of disordered systems.
