**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).

**A Related Paper is *Computations
of dendrites in 3-D and comparison with microgravity experiments (with Y.B.
Altundas)

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publications.