Part of the study is a theoretical program to investigate the spatial structure and complex dynamics in non-equilibrium systems near the threshold of an instability at finite wavenumber. Considerable progress has been made for stationary instabilities, exemplified by convection in pure fluids. Experiments on convection in binary fluid mixtures provide the impetus for theoretical work on the rich behavior near the threshold of a dynamic instability. The methods to be used are perturbational schemes leading to "amplitude" and "phase" equations; numerical solution of the full fluid equations to answer specific questions; and the numerical simulation of simpler model equations constructed to capture the important physics near the instabilities. Although fluid systems provide convenient systems for a careful comparison between theory and experiment, the results should have wide applicability in diverse fields. The other part of the work will study bulk and interfacial Helium, both to understand the microscopic behavior of these simple but challenging model quantum systems, and to investigate them as laboratories for novel physics in new parameter regimes, where quantum effects dominate thermal, and collisional relaxation effects are often small. Monte-Carlo methods provide an important tool for investigating the microscopic physics, but must be tied in with analytic phenomenology to yield any real understanding. Interfacial Helium provides an interesting two- dimensional thermodynamic system, and has remarkable and experimentally vital transport behavior that remains poorly understood.
