Visual Exploration of the Phase Field Model.

Gail Mackin in colaboration with Rukmini Sriranganathan

Background

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.

Project Objective

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.

Implimentation

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.

Team work

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.