Evolving a Kirchhoff elastic rod without self-intersections

Chun-Chi Lin, Hartmut R. Schwetlick

Research output: Contribution to journalArticle

Abstract

In this paper we study the problem on how to find an equilibrium state of a Kirchhoff elastic rod by evolving it in a certain way, called a geometric flow. The elastic energy of rods would decrease during the geometric flow. We show that rods remain smooth during the geometric flow as long as they stay embedded, e.g., self-penetrations do no occur. Furthermore, rods would approach an equilibrium configuration asymptotically if self-penetrations are avoided during the flow.

Original languageEnglish
Pages (from-to)748-768
Number of pages21
JournalJournal of Mathematical Chemistry
Volume45
Issue number3
DOIs
Publication statusPublished - 2009 Mar 1

Fingerprint

Geometric Flows
Elastic Rods
Self-intersection
Penetration
Equilibrium State
Decrease
Configuration
Energy

Keywords

  • Fourth-order parabolic equations
  • Geometric flows
  • Kirchhoff elastic rods
  • Writhe

ASJC Scopus subject areas

  • Chemistry(all)
  • Applied Mathematics

Cite this

Evolving a Kirchhoff elastic rod without self-intersections. / Lin, Chun-Chi; Schwetlick, Hartmut R.

In: Journal of Mathematical Chemistry, Vol. 45, No. 3, 01.03.2009, p. 748-768.

Research output: Contribution to journalArticle

Lin, Chun-Chi ; Schwetlick, Hartmut R. / Evolving a Kirchhoff elastic rod without self-intersections. In: Journal of Mathematical Chemistry. 2009 ; Vol. 45, No. 3. pp. 748-768.
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