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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
52/2003

On the geometric flows of Kirchhoff elastic rods

Chun-Chi Lin and Hartmut Schwetlick

Abstract

Rod theory has been applied to the modelling of DNA and bacterial fibers in their mechanics aspects. In this paper, we relate a geometric functional of curves to the simplest Kirchhoff elastic energy of rods so that the generalized elastic curves are the centerlines of elastic rods in equilibrium. Then, under a mild assumption, we derive the long time existence of the length preserving evolution of the elastic rods.

Received:
29.06.03
Published:
29.06.03
MSC Codes:
35K55, 53C44, 74B20, 74L15
Keywords:
geometric flows, fourth order, kirchhoff elastic rods

Related publications

inJournal
2005 Repository Open Access
Chun-Chi Lin and Hartmut R. Schwetlick

On the geometric flow of Kirchhoff elastic rods

In: SIAM journal on applied mathematics, 65 (2005) 2, pp. 720-736