Kramar M, Goullet A, Kondic L, Mischaikow K
Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854-8019, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Apr;87(4):042207. doi: 10.1103/PhysRevE.87.042207. Epub 2013 Apr 22.
We utilize the tools of persistent homology to analyze features of force networks in dense granular matter, modeled as a collection of circular, inelastic frictional particles. The proposed approach describes these networks in a precise and tractable manner, allowing us to identify features that are difficult or impossible to characterize by other means. In contrast to other techniques that consider each force threshold level separately, persistent homology allows us to consider all threshold levels at once to describe the force network in a complete and insightful manner. We consider continuously compressed system of particles characterized by varied polydispersity and friction in two spatial dimensions. We find significant differences between the force networks in these systems, suggesting that their mechanical response may differ considerably as well.
我们利用持久同调工具来分析致密颗粒物质中力网络的特征，该物质被建模为圆形、非弹性摩擦颗粒的集合。所提出的方法以精确且易于处理的方式描述这些网络，使我们能够识别出用其他方法难以或无法表征的特征。与其他分别考虑每个力阈值水平的技术不同，持久同调使我们能够一次性考虑所有阈值水平，以完整且有洞察力的方式描述力网络。我们考虑在两个空间维度上具有不同多分散性和摩擦力的连续压缩颗粒系统。我们发现这些系统中的力网络存在显著差异，这表明它们的力学响应可能也会有很大不同。
