Math Colloquium: Finite Element Scheme For Ericksen Model w/ Colloidal Effects and External Fields

Monday, February 6, 2017

3:00 PM-4:00 PM

Shawn Walker, PhD, Louisiana State University

Abstract: We present a finite element method (FEM) for computing equilibrium configurations of liquid crystals with variable degree of orientation. The model consists of a Frank-like energy with an additional "s" parameter that allows for line defects with finite energy, but leads to a degenerate elliptic equation for the director field. Our FEM uses a special discrete form of the energy that does not require regularization, and allows us to obtain a stable (gradient flow) scheme for computing minimizers of the energy. We apply our method to investigate the behavior of collidal inclusions in the Ericksen model, as well as the effect of external fields (e.g. to model the so-called "Freedricksz Transition"). Simulations in 2-D and 3-D are presented to illustrate the method.

Contact Information

Ron Perline
rperline@math.drexel.edu