Universality in the diffusion of knots

Details Universality in the diffusion of knots Universality in the diffusion of knots

2008-07-02

arxiv.org/abs/0807.0304v2

Phys. Rev. E 79, 021806 (2009) [5 pages]

Physics

Condensed Matter

Soft Condensed Matter

8 pages, 14 figures

Scientific paper

10.1103/PhysRevE.79.021806

We have evaluated a universal ratio between diffusion constants of the ring polymer with a given knot $K$ and a linear polymer with the same molecular weight in solution through the Brownian dynamics under hydrodynamic interaction. The ratio is found to be constant with respect to the number of monomers, $N$, and hence the estimate at some $N$ should be valid practically over a wide range of $N$ for various polymer models. Interestingly, the ratio is determined by the average crossing number ($N_{AC}$) of an ideal conformation of knotted curve $K$, i.e. that of the ideal knot. The $N_{AC}$ of ideal knots should therefore be fundamental in the dynamics of knots.

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