Degree
Doctor of Philosophy (PhD)
Department
Mathematics
Document Type
Dissertation
Abstract
This thesis gives an analysis of modeling and numerical issues in the Landau-de Gennes (LdG) model of nematic liquid crystals (LCs) with cholesteric effects. We derive various time-step restrictions for a (weighted) $L^2$ gradient flow scheme to be energy decreasing. Furthermore, we prove a mesh size restriction, for finite element discretizations, that is critical to avoid spurious numerical artifacts in discrete minimizers that is not well-known in the LC literature, particularly when simulating cholesteric LCs that exhibit ``twist''. Furthermore, we perform a computational exploration of the model and present several numerical simulations in 3-D, on both slab geometries and spherical shells, using a fully-implicit gradient flow scheme applied to a finite element discretization of the model. The simulations are consistent with experiments, illustrate the richness of the cholesteric model, and demonstrate the importance of the mesh size restriction.
Date
4-1-2024
Recommended Citation
Hicks, Andrew L., "Modeling and Numerical Analysis of the Cholesteric Landau-de Gennes Model" (2024). LSU Doctoral Dissertations. 6390.
https://repository.lsu.edu/gradschool_dissertations/6390
Committee Chair
Walker, Shawn
DOI
10.31390/gradschool_dissertations.6390
Included in
Atomic, Molecular and Optical Physics Commons, Numerical Analysis and Computation Commons