Equilibrium shapes of flat knots

Details Equilibrium shapes of flat knots Equilibrium shapes of flat knots

2001-10-12

arxiv.org/abs/cond-mat/0110266v1

Phys. Rev. Lett. 88, 188101 (2002)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figures

Scientific paper

10.1103/PhysRevLett.88.188101

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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