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arXiv · 0807.0304

Universality in the diffusion of knots

Naoko Kanaeda·Tetsuo Deguchi
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Abstract

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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Naoko Kanaeda, Tetsuo Deguchi. 2009-03-25. Universality in the diffusion of knots. https://doi.org/10.1103/physreve.79.021806

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