Shawn W. Walker
YOU?
Author Swipe
View article: Modelling and simulation of the cholesteric Landau-de Gennes model
Modelling and simulation of the cholesteric Landau-de Gennes model Open
This paper discusses modelling and numerical issues in the simulation of the Landau-de Gennes (LdG) model of nematic liquid crystals (LCs) with cholesteric effects. We propose a fully implicit, (weighted) gradient flow for computing en…
View article: Optimal Control of the Landau-de Gennes Model of Nematic Liquid Crystals
Optimal Control of the Landau-de Gennes Model of Nematic Liquid Crystals Open
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 modern technology. They exhibit long range orientational order …
View article: THE TOXIC TURN? CONCEPTUAL AND METHODOLOGICAL ADVANCES ON PROBLEMATIC CONTENTS ON SOCIAL MEDIA
THE TOXIC TURN? CONCEPTUAL AND METHODOLOGICAL ADVANCES ON PROBLEMATIC CONTENTS ON SOCIAL MEDIA Open
The ‘toxic turn’ in social media platforms continues unabated. Hate speech, mis- and disinformation, misogynistic and racist speech, images, memes and videos are all far too common on social media platforms and more broadly on the internet…
View article: Toroidal nuclei of columnar lyotropic chromonic liquid crystals coexisting with isotropic phase
Toroidal nuclei of columnar lyotropic chromonic liquid crystals coexisting with isotropic phase Open
Nuclei of ordered materials emerging from the isotropic state usually show a shape topologically equivalent to a sphere; the well-known examples are crystals and nematic liquid crystal droplets. In this work, we explore experimentally and …
View article: Accelerated Gradient Descent Methods for the Uniaxially Constrained Landau-de Gennes Model
Accelerated Gradient Descent Methods for the Uniaxially Constrained Landau-de Gennes Model Open
This paper illustrates the efficacy of using accelerated gradient descent schemes for minimizing a uniaxially constrained Landau-de Gennes model for nematic liquid crystals. Three (alternating direction) minimization schemes are applied to…
View article: Optimal control of volume-preserving mean curvature flow
Optimal control of volume-preserving mean curvature flow Open
We develop a framework and numerical method for controlling the full space-time tube of a geometrically driven flow. We consider an optimal control problem for the mean curvature flow of a curve or surface with a volume constraint, where t…
View article: Fine structure of viral dsDNA encapsidation
Fine structure of viral dsDNA encapsidation Open
Unraveling the mechanisms of packing of DNA inside viral capsids is of fundamental importance to understanding the spread of viruses. It could also help develop new applications to targeted drug delivery devices for a large range of therap…
View article: The $\mathbf{Q}$-tensor Model with Uniaxial Constraint
The $\mathbf{Q}$-tensor Model with Uniaxial Constraint Open
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 many applications. Next, we delve into the modeling argumen…
View article: The Hellan--Herrmann--Johnson Method with Curved Elements
The Hellan--Herrmann--Johnson Method with Curved Elements Open
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 convergence on domains with piecewise $C^{k+1}$ boundary for $k \g…
View article: A Finite Element Method for a Phase Field Model of Nematic Liquid Crystal Droplets
A Finite Element Method for a Phase Field Model of Nematic Liquid Crystal Droplets Open
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 Ericksen's energy for liquid crystals, the Cahn-Hilliard en…
View article: On The Correct Thermo-dynamic Potential for Electro-static Dielectric Energy
On The Correct Thermo-dynamic Potential for Electro-static Dielectric Energy Open
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). This paper explains how to derive the correct thermo-dynamic …
View article: A Finite Element Method for a Phase Field Model of Nematic Liquid Crystal Droplets
A Finite Element Method for a Phase Field Model of Nematic Liquid Crystal Droplets Open
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 Ericksen's energy for liquid crystals, the Cahn-Hilliard e…
View article: A Finite Element Method for Nematic Liquid Crystals with Variable Degree of Orientation
A Finite Element Method for Nematic Liquid Crystals with Variable Degree of Orientation Open
We consider the simplest one-constant model, put forward by J. Ericksen, for\nnematic liquid crystals with variable degree of orientation. The equilibrium\nstate is described by a director field $\\mathbf{n}$ and its degree of\norientation…
View article: A mixed formulation of the Stefan problem with surface tension
A mixed formulation of the Stefan problem with surface tension Open
A dual formulation and finite element method is proposed and analyzed for simulating the Stefan problem with surface tension. The method uses a mixed form of the heat equation in the solid and liquid (bulk) domains, and imposes a weak form…
View article: The Shapes of Things
The Shapes of Things Open
Many things around us have properties that depend on their shape-for example, the drag characteristics of a rigid body in a flow. This self-contained overview of differential geometry explains how to differentiate a function (in the calcul…
View article: Droplet Footprint Control
Droplet Footprint Control Open
Controlling droplet shape via surface tension has numerous technological applications, such as droplet lenses and lab-on-a-chip. This motivates a partial differential equation-constrained shape optimization approach for controlling the sha…