31 citations · 78 across the 10 of their papers we have counts for
12 papers
Optimal Control of the Landau-de Gennes Model of Nematic Liquid Crystals
Thomas M. Surowiec, Shawn W. Walker
We present an analysis and numerical study of an optimal control problem for the Landau-de Gennes (LdG) model of nematic liquid crystals (LCs), which is a crucial component in mode…
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…
A Finite Element Method for a Phase Field Model of Nematic Liquid Crystal Droplets
Amanda E. Diegel, Shawn W. Walker
We develop a novel finite element method for a phase field model of nematic liquid crystal droplets. The continuous model considers a free energy comprised of three components: the…
The Ericksen Model of Liquid Crystals with Colloidal and Electric Effects
Ricardo H. Nochetto, Shawn W. Walker, Wujun Zhang
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…
Analysis of the finite element method for the Laplace--Beltrami equation on surfaces with regions of high curvature using graded meshes
Johnny Guzman, Alexandre Madureira, Marcus Sarkis +1
We derive error estimates for the piecewise linear finite element approximation of the Laplace--Beltrami operator on a bounded, orientable, , surface without boundary on gener…
A finite element method for nematic liquid crystals with variable degree of orientation
Ricardo H. Nochetto, Shawn W. Walker, Wujun Zhang
We consider the simplest one-constant model, put forward by J. Ericksen, for nematic liquid crystals with variable degree of orientation. The equilibrium state is described by a di…
Optimal Control Of Surface Shape
Harbir Antil, Shawn W. Walker
Controlling the shapes of surfaces provides a novel way to direct self-assembly of colloidal particles on those surfaces and may be useful for material design. This motivates the i…
A Diffuse Interface Model for Electrowetting with Moving Contact Lines
Ricardo H. Nochetto, Abner J. Salgado, Shawn W. Walker
We introduce a diffuse interface model for the phenomenon of electrowetting on dielectric and present an analysis of the arising system of equations. Moreover, we study discretizat…