Structure of force networks in tapped particulate systems of disks and pentagons (Part 2): Persistence analysis

TL;DR

This paper applies persistence analysis to detailedly characterize and differentiate force networks in tapped particulate systems of disks and pentagons, revealing distinctions especially in loop structures that other measures miss.

Contribution

It introduces persistence analysis as a novel, detailed method to quantify and compare force networks in granular systems, surpassing traditional measures.

Findings

Persistence analysis distinguishes force networks more effectively than classical measures.

Differences between disk and pentagon systems are most evident in loop properties.

Persistence analysis reveals subtle structural differences in force networks.

Abstract

In the companion paper~\cite{paper1}, 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, that allows to describe these networks in much more detail. This approach allows 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, or force PDFs) do not distinguish clearly the investigated systems.