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Trevor Reid's abstract "Twist in a Torus: Minimization of Nematic Conﬁgurations with Discontinuous Director Fields in Toroidal Coordinates" Long Title
The ring disclination is a topological defect that may be suitable for light polarization inside of a nematic liquid crystal. Due to its stability and chirality, the ring disclination could also allow for theoretical applications to quantum and classical ﬁeld theories as a model for fundamental particles. In order to model this defect within a nematic liquid crystal, we simulate a director ﬁeld outside of a torus boundary. Equations are derived for the energy density of this conﬁguration. Toroidal coordinates are implemented as a mesh on which the conﬁguration is deﬁned so that calculations remain stable for small tori. Deterministic iterative methods are developed for calculating the minimum energy of the system. Proof of the vector Laplacian as the correct minimization operator for generalized orthogonal coordinates is demonstrated using diﬀerential forms and Lagrange multipliers. The vector Laplacian is derived in toroidal coordinates and implemented in a hybrid regime with minimization of regions far from the torus surface occurring in Cartesian coordinates. This is implemented with mixed results. The minimized energy scales linearly with torus size as expected by dimensional analysis, but challenges remain for energy minimization at small sizes of torus. Possible solutions for extending the domain are discussed.
Nima Laal's abstract "Nano Grav"
Gravitational waves (GWs), predicted by the general theory of relativity and many other competing spacetime theories, are the perturbations in space and time caused by accelerating massive objects such as super massive black holes. These waves are the movement of the fabric of space and time causing any physical entity to oscillate with them. Influenced by the polarization of GWs, the pattern of oscillation of entities impacted by such waves yields valuable information about the type of theory and the astrophysical sources they are allowed to be generated under. Since there are many competing theories that predict emission of a certain type of GWs, detection of such waves and studying their polarization content allows for probing various spacetime theories. My passion as a researcher is to detect these elusive waves and further study their polarization with the goal of testing the established spacetime theories.