Equilibrium shapes of flat knots.
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.
Metzler
Ralf
R
Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
Hanke
Andreas
A
Dommersnes
Paul G
PG
Kantor
Yacov
Y
Kardar
Mehran
M
D004247:DNA / Q000737:chemistry; D007700:Kinetics; D008956:Models, Chemical; D008968:Molecular Conformation; D009690:Nucleic Acid Conformation; D011108:Polymers / Q000737:chemistry*
D011108:Polymers; D004247:DNA