Eur. Phys. J. B 71, 281-288 (2009)
https://doi.org/10.1140/epjb/e2009-00301-6

On the geometry of stiff knots

¹ Laboratoire de Spectrométrie Physique, CNRS Univ. J. Fourier, BP87, Grenoble 1, 38402 Saint Martin d'Hères, France
² Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP, UK

Corresponding author: ^a olivier.pierre-louis@ujf-grenoble.fr

Received: 12 February 2009
Revised: 17 June 2009
Published online: 11 September 2009

Abstract

We analyse the geometry of a thin knotted string with bending rigidity. Two types of geometric properties are investigated. First, following the approach of von der Mosel [H. von der Mosel, Asymptotic Anal. 18, 49 (1998)], we derive upper bounds for the multiplicity of crossings and braids. Then, using a general inequality for the length of 3D curves derived by Chakerian [G.D. Chakerian, Proc. of the American Math. Soc. 15, 886 (1964)], we analyze the size and confinement of a knot