20 citations · 21 across the 3 of their papers we have counts for
5 papers
Numerical method for the equilibrium configurations of a Maier-Saupe bulk potential in a Q-tensor model of an anisotropic nematic liquid crystal
Cody D. Schimming, Jorge Viñals, Shawn W. Walker
We present a numerical method, based on a tensor order parameter description of a nematic phase, that allows fully anisotropic elasticity. Our method thus extends the Landau-de Gen…
The -tensor Model with Uniaxial Constraint
Juan Pablo Borthagaray, Shawn W. Walker
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…
A structure-preserving FEM for the uniaxially constrained -tensor model of nematic liquid crystals
Juan Pablo Borthagaray, Ricardo H. Nochetto, Shawn W. Walker
We consider the one-constant Landau - de Gennes model for nematic liquid crystals. The order parameter is a traceless tensor field , which is constrained to be uniaxial…
The Hellan-Herrmann-Johnson method with curved elements
Douglas N. Arnold, Shawn W. Walker
We study the finite element approximation of the Kirchhoff plate equation on domains with curved boundaries using the Hellan-Herrmann-Johnson (HHJ) method. We prove optimal converg…
On The Correct Thermo-dynamic Potential for Electro-static Dielectric Energy
Shawn W. Walker
Various types of equilibrium processes involve electric fields. In some cases, the electrical energy appears to be negative (e.g. if the voltage is fixed by an external source). Th…