Evolving a Kirchhoff elastic rod without self-intersections

Chun-Chi Lin; Hartmut R. Schwetlick

doi:10.1007/s10910-008-9383-6

Evolving a Kirchhoff elastic rod without self-intersections

Chun-Chi Lin, Hartmut R. Schwetlick

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	748-768
Number of pages	21
Journal	Journal of Mathematical Chemistry
Volume	45
Issue number	3
DOIs	https://doi.org/10.1007/s10910-008-9383-6
Publication status	Published - 2009 Mar 1

Keywords

Fourth-order parabolic equations
Geometric flows
Kirchhoff elastic rods
Writhe

ASJC Scopus subject areas

Chemistry(all)
Applied Mathematics

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