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| 11 KNOT ENERGIES | |||||||||||||
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| SOFTWARE | |||||||||||||
| DIRECTOR | |||||||||||||
| John M. Sullivan | |||||||||||||
| Custom Software, Evolver, Geomview | |||||||||||||
| PRODUCER | HARDWARE | ||||||||||||
| Silicon Graphics | |||||||||||||
| John M. Sullivan | |||||||||||||
| SUMMARY | |||||||||||||
| FURTHER INFORMATION | |||||||||||||
| Minimizing an energy for knots (motivated by spreading electric charge along the knot) should lead to canonical configurations for each knot or link type. We show experiments with one such energy, whose Möbius invariance is demonstrated with a tour through the conformal group. Minimizing the energy simplifies a complicated unknot to the round circle, and finds symmetric configurations for other simple links including the trefoil knot and the Borromean rings. Surprisingly, minimization breaks the symmetry of some other torus knots. | |||||||||||||
| www.math.uiuc.edu/~jms | |||||||||||||
| CONTACT | |||||||||||||
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John M. Sullivan
Univ. of Illinois, Dept. of Mathematics 250 Altgeld Hall 1409 W Green St Urbana, IL 61801 USA Tel: +1.217.239.4194
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