Pulling Knotted Polymers

"Complex knots in Single DNA Molecules,"

X.R. Bao, H.J. Lee, and S.R. Quake, PRL91, 265506 (2003)

In control experiments ... (knots) are present about 10% of the time, ...

O. Farago, Y. Kantor and M. Kardar, Europhys. Lett. 60, 53 (2002)

Scaling theory predicts that for an unknotted polymer of length N

Comparison of simulation results for sizes N=225 (diamonds), 335 (triangles), 500 (squares), 750 (circles), with (solid) and without (open) a knot in the polymer:

The presence of the knot introduces a new length scale into the problem

Can we use the lack of scaling to deduce a knot size?

Interestingly, the correction to scaling exponent of 0.56 in d=3 is consistent with t=0.4 0.1.

However, a recent study by

B. Marcone, E. Orlandini, A.L. Stella, and F. Zonta (cond-mat/040523) claims t=0.75 0.14.