Research: Simulational and Computational Approach to Condensed Matter Physics Materials Growth and Deposition Many of the most significant technological advances today are directly related to synthesis and processing of materials, particularly for applications in the electronic and emerging optoelectronic industries. With the development of atomic dimension growth and characterization instruments and techniques, modern materials synthesis and processing has become an enormously complex field. Because of the increase in the resolution and control in materials processing it is now impractical to search the experimental parameter space by empirical methods. It is obvious that our ability to control the structure and the properties of materials will require a fundamental level understanding of the intricate physics of materials growth. The main impediment to advances in this direction is that the growth and deposition techniques used in materials processing involve kinetic far from equilibrium processes which are not well understood. Even a qualitative understanding of such processes is difficult because despite its obvious importance in many areas of science and technology -- from materials science to biology -- no standard theoretical approach to nonequilibrium phenomena has yet emerged. In the past few years, however, our research group has made considerable advances in understanding nonequilibrium surface and interface growth phenomena through the development of new concepts and techniques in theoretical, simulational and experimental studies. In particular, the importance and the role of nonlinear dynamical processes, scaling and fractals in growth phenomena has been recognized and novel techniques were introduced that can be applied to similar processes. As part of a Materials Theory research grant funded by the National Science Foundation (NSF grant DMR-9214308) my research group will develop and apply new computational and simulational modeling techniques to problems in the growth and deposition of materials. In particular, we intend to concentrate on the following specific projects: (1) Order-Disorder Transition in Epitaxial Growth, (2) Strain Relaxation in Thin Film Growth, (3) Theoretical Models of Thin Film Growth, (4) Microscopic Modeling of Chemical Vapor Deposition, and (5) Modeling Porous Silicon. Although the above projects are focused on specific materials, we expect that our models will be applicable to a broad range of related materials and processes. Once their utility in the proposed projects has been established, we fully expect that the extension and the application of our models and techniques to related phenomena will be straightforward. Far From Equilibrium Phenomena The key to the solution of many scientific and technological "Grand Challenge" problems today is a first principle understanding of the dynamics of interacting many-body systems far from equilibrium. The reason is that many of the technological challenges facing different industries today involve nonequilibrium dynamical processes. For example, understanding how surfaces are formed and how smooth or rough surfaces can be manufactured will be crucial in solving major technological problems in such diverse industries as semiconductors, optoelectronics, petroleum, paint, chemicals, biotechnology and computers. Therefore any progress in the direction of a fundamental understanding of far from equilibrium phenomena would be a major step towards solving a number of important scientific and technological problems. Unfortunately, in contrast to equilibrium statistical mechanics, no standard theoretical framework exists for describing far from equilibrium phenomena. In recent years, scientific computation has become the leading technique for studying nonequilibrium processes and important advances have been made in this direction. It has now become possible to study the dynamics of such systems at sufficiently large enough time and length scales to make a direct comparison with experiments possible. As part of a research program funded by the Office of Naval Research my research group will apply computational approaches including coarse-grained parallel computers to investigate a number of projects involving interacting many-body systems far from equilibrium. The general areas of proposed research are: (1) Dynamics of Growing Surfaces and Interfaces, (2) Cluster Growth Phenomena, and (3) Self-Organized Criticality. We plan to carry out large-scale numerical solutions of nonlinear models and continuum equations (nonlinear PDEs) for surface and interface growth, and self-organized criticality. We are also studying detailed models that will be studied using Monte Carlo, Molecular Dynamics and hybrid Monte Carlo/Molecular Dynamics techniques in order to understand the role of surface diffusion in surface growth, growth competition and universality in aggregation processes, and the dynamics of unstable interfaces in cluster growth. We will also develop Lattice Gas models to study the dynamics of two-fluid flow in porous media and past rough surfaces, problems which are closely related to turbulence and interfacial dynamics. We expect that our computational techniques and modeling approaches will be useful in the study of many related problems in the study of many-body systems far from equilibrium.