Applied Math Seminar-Assessing Quality of Numerical Solutions to Phase Separation Problems

Date and Time: Friday, Oct. 14th, 3:30-4:30 pm
Place: Rome 771
Title: Assessing Quality of Numerical Solutions to Phase Separation Problems
Speaker: Michael Barg (Niagara University)

Abstract: We begin with a brief overview of some widely studied phase separation problems in non-inhibitory systems.  One often approaches such problems by seeking a solution to a constrained energy minimization problem, where the free energy is an integral over a compact surface.  Both analytical and numerical approaches have yielded interesting results, but our focus is primarily on computing numerical solutions.  Using a finite element method, we seek to understand how closely the shape of a numerical solution is to a geodesic disk.  Additionally, we seek to understand differences in solutions to the problem when a linear constraint is used and when a nonlinear constraint is applied.  Using a “geodesic protocol” and statistical analysis, we present recent results in this vein.  Time permitting, we will discuss some ongoing and future work in which extensions of our numerical model and solution quality procedures are implemented for higher genus surfaces and energies that include an inhibitory term.