Jin Weiwei, Lu Peng, Liu Lufeng, Li Shuixiang
Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Apr;91(4):042203. doi: 10.1103/PhysRevE.91.042203. Epub 2015 Apr 27.
The disordered packings of tetrahedra often show no obvious macroscopic orientational or positional order for a wide range of packing densities, and it has been found that the local order in particle clusters is the main order form of tetrahedron packings. Therefore, a cluster analysis is carried out to investigate the local structures and properties of tetrahedron packings in this work. We obtain a cluster distribution of differently sized clusters, and peaks are observed at two special clusters, i.e., dimer and wagon wheel. We then calculate the amounts of dimers and wagon wheels, which are observed to have linear or approximate linear correlations with packing density. Following our previous work, the amount of particles participating in dimers is used as an order metric to evaluate the order degree of the hierarchical packing structure of tetrahedra, and an order map is consequently depicted. Furthermore, a constraint analysis is performed to determine the isostatic or hyperstatic region in the order map. We employ a Monte Carlo algorithm to test jamming and then suggest a new maximally random jammed packing of hard tetrahedra from the order map with a packing density of 0.6337.
在很宽的堆积密度范围内，四面体的无序堆积通常没有明显的宏观取向或位置有序性，并且已经发现粒子团簇中的局部有序是四面体堆积的主要有序形式。因此，在这项工作中进行了聚类分析以研究四面体堆积的局部结构和性质。我们获得了不同大小团簇的聚类分布，并且在两个特殊团簇处观察到峰值，即二聚体和车轮状结构。然后我们计算二聚体和车轮状结构的数量，观察到它们与堆积密度具有线性或近似线性的相关性。根据我们之前的工作，将参与二聚体的粒子数量用作序参量来评估四面体分层堆积结构的有序程度，并据此描绘了一个序图。此外，进行了约束分析以确定序图中的等静区或超静区。我们采用蒙特卡罗算法来测试堵塞情况，然后从序图中提出一种新的硬四面体最大随机堵塞堆积，其堆积密度为0.6337。
