Configuration spaces of hard spheres
Configuration spaces of hard spheres
复制标题
硬球的构型空间
DOI：
10.1103/physreve.104.055304
复制
发表时间：
2021
影响因子：
2.4
通讯作者：
Mason, J. K.
中科院分区：
文献类型：
--
作者：
Eriçok, O. B.;Ganesan, K.;Mason, J. K.
硬球系统通常用于模拟简单流体。三维环面模各种对称群中硬球的位形空间比较简单，可以提供有关相变性质的有价值的信息。具体地说，作为填充分数的函数的配置空间中的拓扑变化已被证明与一级相变的发生有关。1至12个球的临界配置使用莫尔斯理论的方法进行采样，它们可以在一个在线的，交互式的数据库。对双球系统的位形空间构造了显式三角剖分，并研究了它们的拓扑和几何性质。临界配置被发现与几何变化的配置空间，连接以前遥远的地区，并减少配置空间直径测量的通勤时间和扩散距离。固-液相变的填充分数周围的这种临界配置的数量与球体的数量呈指数增加，这表明在热力学极限中的一阶相变的开始与配置空间直径的不连续性相关。
Hard sphere systems are often used to model simple fluids. The configuration spaces of hard spheres in a three-dimensional torus modulo various symmetry groups are comparatively simple and could provide valuable information about the nature of phase transitions. Specifically, the topological changes in the configuration space as a function of packing fraction have been conjectured to be related to the onset of first-order phase transitions. The critical configurations for 1 to 12 spheres are sampled using a Morse-theoretic approach, and they are available in an online, interactive database. Explicit triangulations are constructed for the configuration spaces of the two sphere system, and their topological and geometric properties are studied. The critical configurations are found to be associated with geometric changes to the configuration space that connect previously distant regions and reduce the configuration space diameter as measured by the commute time and diffusion distances. The number of such critical configurations around the packing fraction of the solid-liquid phase transition increases exponentially with the number of spheres, suggesting that the onset of the first-order phase transition in the thermodynamic limit is associated with a discontinuity in the configuration space diameter.