What is the length of a knot in a polymer?
arXiv:cond-mat/0405253 · doi:10.1088/0305-4470/38/1/L03
Abstract
We give statistical definitions of the length, l, of a loose prime knot tied into a long, fluctuating ring macromolecule. Monte Carlo results for the equilibrium, good solvent regime show that < l > ~ N^t, where N is the ring length and t ~ 0.75 is independent of the knot topology. In the collapsed regime below the theta temperature, length determinations based on the entropic competition of different knots within the same ring show delocalization (t~1).
9 pages, 5 Postscript figures