论文标题
回旋的半径，收缩因子和拓扑聚合物的细分
Radius of Gyration, Contraction Factors, and Subdivisions of Topological Polymers
论文作者
论文摘要
我们考虑拓扑聚合物的拓扑限制随机步行模型。在此模型中，聚合物形成一个任意图，其边缘是从适当的多元高斯选择的，它考虑了图形类型施加的约束。我们恢复了可以按照图的Kirchhoff索引准确给出预期回旋半径的结果。然后，我们考虑拓扑聚合物的回旋半径的预期半径，该聚合物的边缘被细分为$ n $。我们证明，分细的聚合物的收缩因子接近限制，因为细分数量增加，并根据原始图的kirchhoff索引准确地计算了极限。该极限对应于统计力学的热力学极限，并且在拓扑聚合物的物理学中是基础。此外，这些渐近收缩因子被证明与分子动力学模拟非常吻合。
We consider the topologically constrained random walk model for topological polymers. In this model, the polymer forms an arbitrary graph whose edges are selected from an appropriate multivariate Gaussian which takes into account the constraints imposed by the graph type. We recover the result that the expected radius of gyration can be given exactly in terms of the Kirchhoff index of the graph. We then consider the expected radius of gyration of a topological polymer whose edges are subdivided into $n$ pieces. We prove that the contraction factor of a subdivided polymer approaches a limit as the number of subdivisions increases, and compute the limit exactly in terms of the degree-Kirchhoff index of the original graph. This limit corresponds to the thermodynamic limit in statistical mechanics and is fundamental in the physics of topological polymers. Furthermore, these asymptotic contraction factors are shown to fit well with molecular dynamics simulations.
