Okushima T, Niiyama T, Ikeda K S, Shimizu Y
Department of Physics, Ritsumeikan University, Noji-higashi 1-1-1, Kusatsu 525-8577, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Sep;80(3 Pt 2):036112. doi: 10.1103/PhysRevE.80.036112. Epub 2009 Sep 17.
The aim of this paper is twofold: one is to give a detailed description of an alternative graph-based analysis method, which we call saddle connectivity graph, for analyzing the global topography and the dynamical properties of many-dimensional potential-energy landscapes and the other is to give examples of applications of this method in the analysis of the kinetics of realistic systems. A Dijkstra-type shortest path algorithm is proposed to extract dynamically dominant transition pathways by kinetically defining transition costs. The applicability of this approach is first confirmed by an illustrative example of a low-dimensional random potential. We then show that a coarse-graining procedure tailored for saddle connectivity graphs can be used to obtain the kinetic properties of 13- and 38-atom Lennard-Jones clusters. The coarse-graining method not only reduces the complexity of the graphs, but also, with iterative use, reveals a self-similar hierarchical structure in these clusters. We also propose that the self-similarity is common to many-atom Lennard-Jones clusters.
一是详细描述一种基于图的分析方法，我们称之为鞍点连通性图，用于分析多维势能面的全局地形和动力学性质；二是给出该方法在实际系统动力学分析中的应用实例。提出了一种迪杰斯特拉型最短路径算法，通过动力学定义转移成本来提取动力学上占主导地位的转移路径。首先通过一个低维随机势的示例验证了该方法的适用性。然后我们表明，为鞍点连通性图量身定制的粗粒化程序可用于获得13原子和38原子的 Lennard-Jones 簇的动力学性质。粗粒化方法不仅降低了图的复杂性，而且通过迭代使用，揭示了这些簇中的自相似层次结构。我们还提出，自相似性在多原子 Lennard-Jones 簇中是普遍存在的。
