9703483 Fife Solid and liquid materials can exist in different ``states'', whether the concept of state is that of the usual liquid/solid phase, or some other condition like a variant of a crystal, etc. The processes which cause and accompany changes of state, while usually known in broad terms, often also have mysterious aspects. The understanding of these processes is a basic thrust of present day materials science. In the face of little known basic physics, mathematical models are continually being proposed in the hopes of shedding insight. The present proposal focusses attention on certain classes of continuum models for the spatio-temporal variation of phase transformations. In typical cases, this variation consists of motion of an interface between two phases or between more general types of states. Different models do not always predict the same thing, an example being the detailed nature of the motion of the interface in anisotropic media. One aim in the proposed work will be to better elucidate the differing assumptions of important classes of models, and to tie these different assumptions more clearly with their predictions. Special attention, in comparing these models, will be paid to nonlocal ones. Finally, a mysterious specific type of phase transformation for solid binary alloys known as discontinuous precipitation or cellular precipitation will be further modeled and analyzed. The development of new high performance materials is vital to economic and other national interests. Among the many properties of materials which are relevant to their performance is the possibility of progressive phase change and the development of interfaces between alternate solid phases or crystalline variants. There is need for a great deal more basic understanding of the processes by which such interfaces are formed and move. This research will contribute to this understanding by the development, comparison, and analysis of mathematical models of these phen omena based on physical laws.
