Computational Mathematics Colloquium | Scott MacLachlan, Finite-Element Modeling of Liquid Crystal Equilibria

please email compmath@uwaterloo.ca for the zoom link

Speaker

Scott MacLachlan | University of Toronto

Title

Finite-Element Modeling of Liquid Crystal Equilibria

Abstract

Numerical simulation tools for fluid and solid mechanics are often based on the discretisation of coupled systems of partial differential equations, which can easily be identified in terms of physical conservation laws.  In contrast, equilibrium configurations of many liquid crystal phases are more naturally described by the first-order optimality conditions of constrained free-energy functionals.  In this talk, I will present a variational finite-element approach for computing liquid crystal equilibria, and demonstrate its use for both nematic (rod-like) and smectic (soap-like) liquid crystals.  As the main scientific and engineering interest in liquid crystals comes from their ability to exhibit multiple distinct stable equilibrium states,
I will discuss the combination of this framework with a nonlinear deflation technique that allows discovery of the energy landscapes for
these problems.