DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:**Jeff Snider, George Mason University

**Title: ***
Thermodynamic equilibrium phase diagram calculation
*

**Abstract:**
Traditional software packages (such as Thermocalc) for thermodynamic equilibrium phase diagram calculation rely on Newton-like methods for solving nonlinear system of equations to compute phase equilibria, which requires a good initial guess for convergence and often calls for a special handling when it comes to formulations involving miscibility gaps and sublatticesĀ. We developed a new methodology that avoids some of these pitfalls by making efficient use of the state-of-the-art constrained optimization algorithms that tackle the original Gibbs energy minimization problem. We formulate a general mathematical problem of finding global equilibria in muticomponent multiphase systems with an arbitrary number of sublattices and miscibility gaps, and test the new approach on a system known to be computationally challenging for other approaches. Further, we propose a new unified AMPL set-based description for representing the thermodynamic data that optimizes the data storage as well as computational complexity and makes it possible to subject a task of calculating phase diagram for an arbitrary thermodynamic system to numerous general purpose optimization strategies. The comparison of the results using several traditional and new optimization techniques suggests that a re-evaluation of some of the previously computed diagrams might be necessary, where a sub-optimal equilibrium might have been mistakenly identified as a global one.

**Time:** Friday, May 3, 2013, 11:30-12:30 p.m.

**Place:** Planetary Hall (formerly S & T I), Room 242

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491