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Equilibrium shapes of flat knots

Ralf Metzler·Andreas Hanke·Paul G. Dommersnes·Yacov Kantor·Mehran Kardar
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Abstract

We study the equilibrium shapes of prime and composite knots confined to two dimensions. Using rigorous scaling arguments we show that, due to self-avoiding effects, the topological details of prime knots are localised on a small portion of the larger ring polymer. Within this region, the original knot configuration can assume a hierarchy of contracted shapes, the dominating one given by just one small loop. This hierarchy is investigated in detail for the flat trefoil knot, and corroborated by Monte Carlo simulations.

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Ralf Metzler, Andreas Hanke, Paul G. Dommersnes, Yacov Kantor, Mehran Kardar. 2001-10-12. Equilibrium shapes of flat knots. https://doi.org/10.1103/physrevlett.88.188101

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