Eur. Phys. J. E 6, 123-128 (2001)

Tight open knots

P. Pieranski¹, S. Przybyl¹ and A. Stasiak<sup>2

1</sup>  Poznan University of Technology, Nieszawska 13, 60 965 Poznan, Poland
²  Laboratory of Ultrastructural Analysis, University of Lausanne, Lausanne, Switzerland

Piotr.Pieranski@put.poznan.pl

(Received 7 March 2001 and Received in final form 17 August 2001)

Abstract
The tightest open conformations of a few prime knots (3₁, 4₁, 5₁, 5₂, and 6₃) found with the use of the SONO algorithm are presented and discussed. The conformations are obtained from the tightest closed conformations of the knots by cutting and opening them at different locations. The length of the rope engaged in each of the open conformations is calculated. The curvature and torsion profiles of the unique tightest conformations of the 3₁ and 4₁ open knots are presented and discussed. In particular, symmetry properties of the knots reflected within their curvature and torsion profiles are analysed. Connections with the physics of polymers are discussed.

PACS
87.10.Ac - Subcellular structure and processes: Theory and modeling; computer simulation.
02.10.Kn - Knot theory.


© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2001