9311444 Cross This proposal is concerned with the theoretical understanding of pattern forming systems far from thermodynamic equilibrium. The PI is well known for his work here and has just finished coauthoring a long "Reviews of Modern Physics" article on the subject. The techniques used by the PI are multifold - varying from linear and non-linear stability analyses of spatially homogeneous states - to including the effects of defects and boundaries on the pattern evolution - to the numerical investigation of model systems. Specifically, the PI proposes to consider instabilities and paterns in fluid and chemical systems - such as stripe phases, convective phases and stationary periodic chemical patterns. Further, the PI proposes to study the less well-characterized field of patterns in materials systems - such as deformation bands and dislocation patterns in strained crystals. %%% Many fluid systems exhibit patterns when they are kept under conditions away from equilibrium. For example, a fluid between hot (bottom) and cold (top) plates exhibits convective patterns. Similarly, solid materials under applied stress (eg shearing) can develop deformation bands. Such non-equilibrium conditions occur all the time in everyday life (eg the formation of clouds) - and form by far the majority of cases in the processing of materials (milling, rolling, sintering etc). Their study is important in the understanding of material and liquid behavior. This proposal undertakes a theoretical study of these phenomena. The PI is one of the leading lights in this field and the work is at the cutting- edge of what is known and understood. ***
