Interface Problems and Phase Field Computations
Previous work has shown that a broad spectrum of interface models (see Figure) can be attained as distinguished asymptotic limits of the phase field equations. The possibility of computing these diverse models by varying a single set of parameters has also been demonstrated. Current computations focus on the following objectives:
1. Carrying out the computations for dendritic growth and in order to compare with microgravity experiments performed on the Space Shuttle and test some of the basic ideas of pattern formation. This work is in collaboration with Y. B.Altundas.
2. Examining the large time behavior of the interface for the several dimensional parameter space that defines the models shown in the Figure.
3. Utilizing the computations above as an experimental laboratory that lends insight into scaling relationships. This will then make the connection with the renormalization group approach.
4. Using phase field methods to study key problems in alloys such as the pattern in which solute is frozen into the solid. The mathematically challenging aspect of this issue is that the solute diffusivity vanishes in the solid, thereby resulting in a degenerate differential equation (parabolic to ordinary differential equation).
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