Structure of force networks in tapped particulate systems of disks and pentagons. II. Persistence analysis.
Structure of force networks in tapped particulate systems of disks and pentagons. II. Persistence analysis.
复制标题
圆盘和五边形的攻丝颗粒系统中力网络的结构。
作者：
L. Kondic;M. Kramár;L. Pugnaloni;C. M. Carlevaro;K. Mischaikow
在配套论文[Pugnaloni et al., Phys。[Rev. E 93, 062902 (2016)10.1103/PhysRevE.93.062902]，我们使用基于力概率密度函数（pdf）和Betti数（量化与力链和环相关的组件数量）的经典度量来描述圆盘和五角大楼的分接系统中的力网络。在目前的工作中，我们专注于持久性分析的使用，这使我们能够更详细地描述这些网络。这种方法不仅允许我们描述，而且还可以量化在系统的不同实现中，在考虑域的不同部分中，或在不同系统中力网络之间的差异。我们表明，持久性分析清楚地区分了使用其他方法很难或不可能区分的系统。一个重要的发现是，当考虑环路时，圆盘和五边形之间的力网络差异最为明显：即使其他度量（组件的特性、贝蒂数、力pdf或应力张量）不能清楚地区分或完全区分所研究的系统，描述环路特性的量也可能显著不同。
In the companion paper [Pugnaloni et al., Phys. Rev. E 93, 062902 (2016)10.1103/PhysRevE.93.062902], we use classical measures based on force probability density functions (PDFs), as well as Betti numbers (quantifying the number of components, related to force chains, and loops), to describe the force networks in tapped systems of disks and pentagons. In the present work, we focus on the use of persistence analysis, which allows us to describe these networks in much more detail. This approach allows us not only to describe but also to quantify the differences between the force networks in different realizations of a system, in different parts of the considered domain, or in different systems. We show that persistence analysis clearly distinguishes the systems that are very difficult or impossible to differentiate using other means. One important finding is that the differences in force networks between disks and pentagons are most apparent when loops are considered: the quantities describing properties of the loops may differ significantly even if other measures (properties of components, Betti numbers, force PDFs, or the stress tensor) do not distinguish clearly or at all the investigated systems.