A Preconditioned Nullspace Method for Liquid Crystal Director Modeling

Local Stability and a Renormalized Newton Method for Equilibrium Liquid Crystal Director Modeling

We consider the nonlinear systems of equations that result from discretizations of a prototype variational model for the equilibrium director field characterizing the orientational properties of a liquid crystal material. In the presence of pointwise unit-vector constraints and coupled electric fields, the numerical solution of such equations by Lagrange-Newton methods leads to problems with a ...

A Renormalized Newton Method for Liquid Crystal Director Modeling

We consider the nonlinear systems of equations that result from discretizations of a prototype variational model for the equilibrium director field characterizing the orientational properties of a liquid crystal material. In the presence of pointwise unit-vector constraints and coupled electric fields, the numerical solution of such equations by Lagrange-Newton methods leads to linear systems w...

Fast Q-tensor method for modeling the dynamics of defects in a liquid crystal director field.

A fast Q-tensor method, which can model the defect dynamics in a liquid crystal director field, is presented. Conceptually based on the Oseen-Frank approach, we have added temperature energy density terms in addition to the strain energy terms, and an improved normalization method for fast calculations. The method is more compact and allows a larger time step than previous methods. The method i...

Fast Q-Tensor Method for Modeling Liquid Crystal Director Configurations with Defects

Director Structures in a Chiral Nematic Slab: Threshold Field and Pitch Variations

Abstract The liquid crystal director distribution is determined for a confined chiral nematic slab. The molecular director distribution of the field-controlled chiral nematic slab is directly calculated. The director profiles for the tilt and the twist angles, under different applied fields, are calculated in the slab with weak boundary conditions. Then, the dependence of the threshold field on...