论文标题
关于协调几何空间的拓扑
On the topology of the space of coordination geometries
论文作者
论文摘要
协调的几何形状描述了中央粒子的邻居如何布置在其周围。可以认为这种几何形状位于抽象的拓扑空间中。这个空间的模型可以为理解晶体，液体和眼镜中的物理转化提供数学基础。通过这种动机，目前的工作提出了三维协调几何形状空间的度量模型。该模型是通过局部定向顺序参数的概括来构想的，并且似乎与几何直觉一致。它似乎暗示了与五个主要类别的协调几何形状的分类学，每个类别具有不同的特征。引入了定量典型性的定量概念，并发现其与定向顺序的相互作用可以证明有关点对称性的统计规律性。通过对本文建模空间的拓扑拓扑的断言，可以在分子动力学模拟中使用顺序参数解决的结构范围大大增加。
Coordination geometries describe how the neighbours of a central particle are arranged around it. Such geometries can be thought to lie in an abstract topological space; a model of this space could provide a mathematical basis for understanding physical transformations in crystals, liquids, and glasses. With this motivation, the present work proposes a metric model of the space of three-dimensional coordination geometries. This model is conceived through the generalisation of a local orientational order parameter and seems to be consistent with geometric intuition. It appears to suggest a taxonomy of coordination geometries with five main classes, each with a distinct character. A quantitative notion of orientational typicality is introduced and its interplay with orientational order is found to evidence a statistical regularity with respect to point symmetry. By the assertion of axioms on the topology of the space herein modelled, the range of structures that are possible to resolve with the order parameter in molecular dynamics simulations is greatly increased.
