Equilibrium shapes of flat knots |
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Authors: | Metzler Ralf Hanke Andreas Dommersnes Paul G Kantor Yacov Kardar Mehran |
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Affiliation: | Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. |
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Abstract: | We study the equilibrium shapes of prime and composite knots confined to two dimensions. Using scaling arguments we show that, due to self-avoiding effects, the topological details of prime knots are localized 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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