Mathematical Sciences: Phase Boundary Problems in Pure Material and Alloys

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This research concerns the modeling and analysis of various free- boundary problems related to phase transition. In particular, the general approach of phase field model is applied to several basic problems: alloys, triple points, and crystal growth. The goal is to gain insight into the freezing and melting processes in alloys, and the mechanisms of crystal growth. The results of this research will contribute to the objectives of the advanced materials processing program.