Ropelength of tight polygonal knots

Details Ropelength of tight polygonal knots Ropelength of tight polygonal knots

2004-09-21

arxiv.org/abs/physics/0409108v1

Physics

Computational Physics

27 pages, to appear in "Physical and Numerical Models in Knot Theory and their Application to the Life Sciences"

Scientific paper

A physical interpretation of the rope simulated by the SONO algorithm is presented. Properties of the tight polygonal knots delivered by the algorithm are analyzed. An algorithm for bounding the ropelength of a smooth inscribed knot is shown. Two ways of calculating the ropelength of tight polygonal knots are compared. An analytical calculation performed for a model knot shows that an appropriately weighted average should provide a good estimation of the minimum ropelength for relatively small numbers of edges.

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