Quantization of energy and writhe in self-repelling knots


Autoria(s): Hoidn P.; Kusner R.B.; Stasiak A.
Data(s)

2002

Resumo

Probably the most natural energy functional to be considered for knotted strings is that given by electrostatic repulsion. In the absence of counter-charges, a charged, knotted string evolving along the energy gradient of electrostatic repulsion would progressively tighten its knotted domain into a point on a perfectly circular string. However, in the presence of charge screening self-repelling knotted strings can be stabilized. It is known that energy functionals in which repulsive forces between repelling charges grow inversely proportionally to the third or higher power of their relative distance stabilize self-repelling knots. Especially interesting is the case of the third power since the repulsive energy becomes scale invariant and does not change upon Mobius transformations (reflections in spheres) of knotted trajectories. We observe here that knots minimizing their repulsive Mobius energy show quantization of the energy and writhe (measure of chirality) within several tested families of knots.

Identificador

http://serval.unil.ch/?id=serval:BIB_447497EF5428

isbn:1367-2630

isiid:000174624000001

doi:10.1088/1367-2630/4/1/320

Idioma(s)

en

Fonte

New Journal of Physics, vol. 4, pp. 20.1-20.11

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Tipo

info:eu-repo/semantics/article

article