Differential Equations Seminar: Scott Dusek
Monday, April 29, 2019 · 11 AM - Noon
Title: The Effect of Varying Parameters on Equilibrium Configurations of Trefoil Knot with Contact Potential
Abstract: The classical formulation of the elastic rod does not prevent self-penetration of the rod, yet realistically two distinct points on the rod cannot occupy the same point in space and as a result limits the plausibility of the model. In this thesis, we consider a discretization of the continuous elastic rod and minimize a discrete energy potential that includes a term that reflects the elastic potential and a term that prevents self-penetration using an electrostatic repulsion term. Using a trefoil knot as an initial configuration, the total discrete energy is numerically minimized. We examine the effect of varying parameters on the energy.