Term of Award
Spring 2013
Degree Name
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (open access)
Copyright Statement / License for Reuse
This work is licensed under a Creative Commons Attribution 4.0 License.
Department
Department of Mathematical Sciences
Committee Chair
Scott Kersey
Committee Member 1
Yi Lin
Committee Member 2
Chunshan Zhao
Committee Member 3
Chunshan Zhao
Abstract
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.
Recommended Citation
Rocker, Daniel D., "Variational Methods on Elastic Curves" (2013). Electronic Theses and Dissertations. 46.
https://digitalcommons.georgiasouthern.edu/etd/46
Research Data and Supplementary Material
No
