拓扑聚合物的回转半径、收缩因子和细分
Radius of Gyration, Contraction Factors, and Subdivisions of Topological Polymers
摘要：
研究了拓扑聚合物的拓扑约束无规行走模型。在这个模型中，聚合物形成一个任意的图形，其边缘是从一个适当的多变量高斯，考虑到图形类型所施加的约束。我们恢复的结果，期望的回转半径可以准确地给出的基尔霍夫指数的图。然后，我们考虑预期的回转半径的拓扑聚合物，其边缘被细分为$n$片。我们证明了一个细分的聚合物的收缩因子接近一个极限的细分的数目的增加，并计算的限制，正是在度Kirchhoff指数的原始图。该极限对应于统计力学中的热力学极限，并且是拓扑聚合物物理学中的基础。此外，这些渐近收缩因子被证明符合分子动力学模拟。
英文摘要：
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.
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