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On the energy spectrum of magnetic knots and links

Date: 
Thursday 6th December 2012 - 10:00 to 10:20
Venue: 
INI Seminar Room 1
Session Title: 
Knots in mathematics: Tight Knots, etc.
Session Chair: 
Rob Kusner
Abstract: 
The groundstate energy spectrum of the first 250 zero-framed prime knots and links is studied by using an exact analytical expression derived by the constrained relaxation of standard magnetic flux tubes in ideal magneto-hydrodynamics (Maggioni & Ricca, 2009) and data obtained by the RIDGERUNNER tightening algorithm (Ashton et al., 2011). The magnetic energy is normalized with respect to the reference energy of the tight torus and is plotted against increasing values of ropelength. A remarkable generic behavior characterizes the spectrum of both knots and links. A comparative study of the bending energy reveals that curvature information provides a rather good indicator of magnetic energy levels.

(2009) Maggioni F and Ricca RL. On the groundstate energy of tight knots. Proc. R. Soc. A 465, 2761–2783. (2011) Ashton T, Cantarella J, Piatek M and Rawdon E. Knot tightening by constrained gradient descent. Experim. Math. 20, 57-90.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons