纽结扩散的普遍性
Universality in the diffusion of knots
摘要：
通过流体动力学相互作用下的布朗动力学，我们计算了具有给定结$K$的环状聚合物和具有相同分子量的线性聚合物在溶液中的扩散常数之间的普适比值.发现该比率相对于单体数$N$是恒定的，因此对于各种聚合物模型，在某些$N$的估计值在$N$的宽范围内实际上应该是有效的。有趣的是，该比率由打结曲线$K$的理想构象的平均交叉数（$N_{AC}$）确定，即理想结的平均交叉数。因此，理想纽结的$N_{AC}$应该是纽结动力学的基础。
英文摘要：
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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