9314938 Goldenfeld This proposal concerns the study of non-equilibrium phenomena, primarily in polymeric systems. The PIs have had much prior success in studying the approach to equilibrium following phase transitions; growth of complex spatial patterns; and the use of Renormalization Group methods to access the long time behavior of systems far from equilibrium. They have also developed a cellular- automata-type numerical scheme, the "Cell Dynamical Systems" approach, to study mesoscale phenomena. They propose to study 1) spinodal decomposition in binary alloy systems; 2) descriptions of vibrating powder systems; 3) chiral symmetry breaking in Langmuir monolayers; 4) Renormalization Group methods to study the long-time behavior of spatially extended non-linear systems; 5) theory of vulcanization; 6) Large Deviation approaches to nonequilibrium systems (both the fundamentals of the method and some concrete applications). %%% The PIs work in the area of understanding the behavior of nonequilibrium systems; particularly of complex systems such as polymers, rubbers, alloys etc. Here, they propose to study what happens to mesoscale structures of alloys when they are quenched; how best to descibe the state of a powder when it is vibrated; mathematical methods to understand the time dependent behavior of systems which have been moved out of equilibrium (and how they thence may establish spatial patterns as they evolve) and, lastly, a new (at least to many physicists) theoretical method for describing the thermodynamics of both equilibrium and nonequilibrium systems which relies on the mathematical laws governing large numbers. These two PI's are held in the highest esteem by their community and their work is rated at the very front of this field. They do a nice combination of fundamental work and "real-world" problems - for example they have helped experimentalists with the understanding of their experiments. ***
