Knot probabilities in equilateral random polygons
Knot probabilities in equilateral random polygons
复制标题
等边随机多边形中的结概率
DOI：
10.1088/1751-8121/ac1fc2
复制
发表时间：
2021
期刊：
影响因子：
--
通讯作者：
S. Whittington
中科院分区：
文献类型：
--
作者：
A. Xiong;A. J. Taylor;Mark R. Dennis;S. Whittington
我们考虑欧几里得三维空间中等边随机多边形的打结概率，该模型以随机聚合物为例。从随机多边形的广泛蒙特卡罗数据集的结果表明，一个通用的缩放公式的打结概率与边的数量。这个缩放公式涉及一个指数函数，与结类型无关，幂律因子取决于结的素数组成部分的数量。解结以零分量的复合结的形式出现，以一个小的负幂律进行缩放，与之前的研究表明的纯粹指数缩放形成对比。该方法结合了先前研究的几个改进：我们的随机多边形数据集是使用快速，无偏算法生成的，并且使用基于Alexander多项式的优化结不变量集来检测打结。
We consider the probability of knotting in equilateral random polygons in Euclidean three-dimensional space, which model, for instance, random polymers. Results from an extensive Monte Carlo dataset of random polygons indicate a universal scaling formula for the knotting probability with the number of edges. This scaling formula involves an exponential function, independent of knot type, with a power law factor that depends on the number of prime components of the knot. The unknot, appearing as a composite knot with zero components, scales with a small negative power law, contrasting with previous studies that indicated a purely exponential scaling. The methodology incorporates several improvements over previous investigations: our random polygon data set is generated using a fast, unbiased algorithm, and knotting is detected using an optimised set of knot invariants based on the Alexander polynomial.
影响因子：
2.4
作者：
Katritch, V;Olson, WK;Stasiak, A
通讯作者：
Stasiak, A