2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/224403We 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.8 pages, 14 figuresSoft Condensed Mattertext