Variational Methods on Elastic Curves

<p>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.</p>

Name thesis:degree_name

Master of Science in Mathematics (M.S.)

Level thesis:degree_level

Thesis (open access)

Discipline thesis:degree_discipline

Department of Mathematical Sciences

Year dc:date.available

2013

Author dc:creator

• Rocker, Daniel D.

Contributors dc:contributor

• Yi Lin
• Chunshan Zhao

• ETD
• elastic curves
• negative gradient
• numerical integration
• minimize bending energy
• Mathematics

Repository record dc:identifier

https://digitalcommons.georgiasouthern.edu/etd/46

OAI identifier oai:identifier

oai:digitalcommons.georgiasouthern.edu:etd-1046