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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
1/2001

Global injectivity and topological constraints for spatial nonlinearly elastic rods

Friedemann Schuricht

Abstract

In this paper we study the local and global injectivity of spatial deformations of shearable nonlinearly elastic rods. We adopt an analytical condition introduced by Ciarlet & Necas in nonlinear elasticity to ensure global injectivity in that case. In particular we verify the existence of an energy minimizing equilibrium state without self-penetration which may be also restricted by a rigid obstacle. Furthermore we consider the special situation where the ends of the rod are glued together. In that case we can still impose topological restrictions as, e.g., that the shape of the rod belongs to a given knot type. Again we show the existence of a globally injective energy minimizer which now in addition respects the topological constraints. Note that the investigation of super-coiled DNA molecules is an important application of the presented results.

Received:
Jan 26, 2001
Published:
Jan 26, 2001

Related publications

inJournal
2002 Repository Open Access
Friedemann Schuricht

Global injectivity and topological constraints for spatial nonlinearly elastic rods

In: Journal of nonlinear science, 12 (2002) 5, pp. 423-444