9805036 Levine This is a renewal grant which puts forward an ambitious plan for making substantial progress on interface structure and motion in spatially-extended non-equilibrium systems. The primary focus is on the disordered interfacial structure (sometimes with fractal scaling) seen in diffusion-limited growth, unstable viscous fingering and related processes. Interfaces which arise in non-equilibrium chemical reactions and interfaces that arise in simple models of of biological evolution will also be studied. One recurrent theme is that in all of these cases, one has both deterministic effects and stochastic ones; the stochastic effects typically enter as multiplicative noise acting on a set of reaction- diffusion equations describing the "mean" structure. These studies will use both computational techniques and analytical methods; formulations will be investigated in terms of stochastic partial differential equations, or alternatively in terms of coupled correlation functions. The goals include a better understanding of the origin of scaling, a more quantitative approach to the calculation of the overall probability distribution of the growth patterns and a deeper appreciation of exactly which changes at the microscopic level can drastically alter macroscopic structure. If successful, our efforts will provide a firmer basis for applications of interface dynamics to systems ranging from enhanced oil recovery and alloy solidification to diffusion-controlled chemical reactions and microbiological evolution. The lessons learned here will also have a significant impact on the understanding of non- equilibrium spatially-extended dynamical processes, one of the frontiers of modern physics. %%% This theoretical grant will support research on interface structure and motion in spatially-extended non-equilibrium systems. The analysis will include both deterministic and random effects. Results will provide a foundation for applications of interface dynamics to enhanced oil recovery, alloy solidification, diffusion-controlled chemical reactions and microbiological evolution. ***
