Term of Award
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (open access)
Department of Mathematical Sciences
Committee Member 1
Committee Member 2
Committee Member 3
In this thesis we investigate elastic curves. These are curves with minimal bending energy as measured by the total squared curvature functional. We show that these can be computed by evolving curves in the direction of the negative gradient in certain Hilbert space settings. By discretizing the curves and using numerical integration, we compute approximate minimizers and display using computer graphics. We propose a conjecture based on the rotation number of a curve that predicts the critical point curves that minimize bending energy.
Rocker, Daniel D., "Variational Methods on Elastic Curves" (2013). Electronic Theses and Dissertations. 46.