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Soft Matter and Biological Physics

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

Tight open knots

P. Pieranski1, S. Przybyl1 and A. Stasiak2

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


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

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.

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