The equilibrium shapes of prime and composite knots were studied. It was showed that the topological details of prime knots were localized on a small portion of the larger ring polymer due to self-avoiding effects. The original knot configuration could assume a hierarchy of contracted shape, the dominating one given by one small loop, within this region. For the flat trefoil knot, this hierarchy was studied in detail and corroborated by Monte Carlo simulations.
Ralf Metzler, et. al., (2002) Equilibrium shapes of flat knots.Physical Review Letters88:181881011. DOI: http://doi.org/10.1103/PhysRevLett.88.188101
Physical Review Letters