Final report for Grant DE-FG02-84ER45131

This Final Report surveys the work done on understanding the properties and behavior of driven interfaces. It is presented under two topics: (1) interfaces driven in pure and perturbed Hele-Shaw cells; (2) gels, colloids, and polymer solutions as complex media for interface growth and motion. This work has contributed to the international effort to learn about nonlinear and pattern forming systems. The data have been influential as theoretical and computational groups have attempted to understand the dynamics and nonlinear processing steps and the structure-property relations of complex materials. The Hele-Shaw cell was especially productive during this period of intense interest in ''simple'' nonlinear pattern formation, providing the simplest and best understood pattern forming system which could then be complicated with changes of boundary condition or changes of fluid property to test in a controlled way the effect on pattern formation of added physical/mathematical complexity