Tuesdays, 3:30–4:30 PM | Room: Lockett 136
Welcome to the Informal Analysis Seminar! We are a seminar run by graduate students with an emphasis on providing a space for graduate students to give analysis talks. Everyone is encouraged to participate.
Speaker:Han Nguyen
Title: Modelling and simulation of the cholesteric Landau-de Gennes model
Abstract:This paper discusses modelling and numerical issues in the simulation of the Landau-de Gennes (LdG) model of nematic liquid crystals (LCs) with cholesteric effects. We propose a fully implicit, (weighted) L2 gradient flow for computing energy minimizers of the LdG model, and note a timestep restriction for the flow to be energy decreasing. Furthermore, we give a mesh size restriction, for finite-element discretizations, that is critical to avoid spurious numerical artifacts in discrete minimizers, particularly when simulating cholesteric LCs that exhibit ‘twist.’ Furthermore, we perform a computational exploration of the model and present several numerical simulations in three dimensions, on both slab geometries and spherical shells, with our finite-element method. The simulations are consistent with experiments, illustrate the richness of the cholesteric model, and demonstrate the importance of the mesh size restriction.
Name: Stephen Shipman
Email: shipman@math.lsu.edu