# Twist in a Torus: Minimization of Nematic Configurations with Discontinuous Director Fields in Toroidal Coordinates

# Twist in a Torus: Minimization of Nematic Configurations with Discontinuous Director Fields in Toroidal Coordinates

In recent years, applied topological research has become increasingly common in experimental physics, largely due to advantages over symmetry in studying microscopic condensed matter properties. Topological defects have been studied using a variety of methods and materials, notably in topological insulators and in super-fluid Helium-3. However, liquid crystals have been one of the more cost eective and widely adopted strategies for studying topological defects, especically in their nematic phase. This project aims to study a defect known as a ring disclination that may have applications to high energy physics and nematic liquid crystal study. The defect is modeled as a constant nematic field that represents the orientation of liquid crystals with a torus shaped hole. Inside the hole, the field smoothly rotates by π radians. In a vector field, this produces a discontinuity, so a bi-directional director field is utilized to represent the orientation of the liquid crystals. Using this model, the energy can be calculated for different sizes of torus, and energy minimization techniques are applied to the twist to find the minimum required energy to produce and maintain such a defect in a molecular field. This may allow us to model and predict behavior in certain fundamental particles.

Biography: Trevor Reid is a senior in Physics, studying under the direction of Prof. Pavel Kornilovich.