Diffusion of a ring polymer in good solution via the Brownian dynamics

Diffusion constants D_{R} and D_{L} of ring and linear polymers of the same molecular weight in a good solvent, respectively, have been evaluated through the Brownian dynamics with hydrodynamic interaction. The ratio $C=D_{R}/D_{L}$, which should be universal in the context of the renormalization group, has been estimated as $C= 1.11 \pm 0.01$ for the large-N limit. It should be consistent with that of synthetic polymers, while it is smaller than that of DNAs such as $C \approx 1.3$. Furthermore, the probability of the ring polymer being a nontrivial knot is found to be very small, while bond crossings may occur at almost all time steps in the present simulation that realizes the good solvent conditions.