Liquid crystals are a type of soft matter that is intermediate between crystalline solids and
isotropic fluids. The study of liquid crystals has made tremendous progress over the past four …

Reservoir simulation is used to demonstrate the dynamic physical processes of rocks and
fluid properties with high-order nonlinear equations. Currently, different types of simulation …

In this paper, a new finite-element solution to the potential formulation of the geophysical
electromagnetic (EM) problem that explicitly implements the Coulomb gauge, and that …

We consider the one-constant Landau-de Gennes model for nematic liquid crystals. The
order parameter is a traceless tensor field QQ, which is constrained to be uniaxial: Q= s (n ⊗ …

We analyze two types of block preconditioners for a class of saddle point problems arising
from the modeling of liquid crystal directors using finite elements. Spectral properties of the …

We consider the generalized Ericksen model of liquid crystals, which is an energy with 8
independent “elastic” constants that depends on two order parameters n (director) and s …

This paper outlines an energy-minimization finite-element approach to the modeling of
equilibrium configurations for nematic liquid crystals in the presence of internal and external …

We present a robust discretization of the Ericksen model of liquid crystals with variable
degree of orientation coupled with colloidal effects and electric fields. The total energy …

This chapter is about the modeling of nematic liquid crystals (LCs) and their numerical
simulation. We begin with an overview of the basic physics of LCs and discuss some of their …

This paper compares the performance of penalty and Lagrange multiplier approaches for
the necessary unit-length constraint in the computation of liquid crystal equilibrium …