Visual Exploration of the Phase Field Model.
Gail Mackin in colaboration with Rukmini Sriranganathan
The phase field equations
tau * phi_t = epsilon^2 * Laplacian ( phi ) + G( phi ) + 2 * u
u_t + l/2 * phi_t = K * Laplacian ( u )
model the solidification of a pure material in 2-D space. Here u(t,x)
is the absolute temperature, phi(t,x) is an order parameter, or phase
field, tau, l and K are constants. G( phi) is the derivative of a double well
potential function, thus there exists an interval ( phi_1, phi_2 ) in which
the problem is chaotic in nature. This model is closely related to the
area of study for my disertation in Mathematics.
I intend to use a fortran program written by Dr. Matthias Heinkenschloss
which solves the above equations to illustrate the behavior of liquid-solid
phase transitions in the plane. A variety of initial and boundary conditions
will be implemented and compared. A short presentation aimed at fellow
graduate students will be made to illistrate solution behavior.
Dr. Heinkenschloss' program stores the data for t, x}, u and phi in
ascii format. I will need to modify his program so that data may be used
directly from the output files. I then intend to use Spyglass Dicer and/or
Wave to investigate the solutions. Animations of the various solutions will
demonstrate the growth of phase boundaries. I will also use any other
software packages that I consider appropriate in my investigation.
Rukmini and I intend to colaborate on this project, though I will design
the outline for the presentation and write most of the programs. Rukmini
has agree to help as much as her schedule allows.