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Four-thirds power law for knots and links

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  • Gregory Buck

    (Saint Anselm College)

Abstract

Physical knot theory has recently been applied to polymer dynamics, and specifically to gel electrophoresis of DNA1,2. Knot energies3,4,5,6 measure the complexity of a knot conformation; minimum energy conformations are considered canonical or ‘ideal’ conformations. The rope length of a knot is one such measure of energy6, and an approximately linear relationship between rope length and the average crossing number for minimum rope-length conformations of simple knots has been reported7. Here I show that a linear relationship cannot hold in general: the rope length required to tie an N-crossing knot or link varies at least between ˜N3/4 and ˜N.

Suggested Citation

  • Gregory Buck, 1998. "Four-thirds power law for knots and links," Nature, Nature, vol. 392(6673), pages 238-239, March.
    • Handle: RePEc:nat:nature:v:392:y:1998:i:6673:d:10.1038_32561
    DOI: 10.1038/32561
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    Cited by:

    1. Buck, Gregory, 2015. "The role of curvature in entanglement," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 435(C), pages 22-27.

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