Two approaches to quantification of force networks in particulate systems

TL;DR

This paper demonstrates that key features of force networks in particulate systems can be effectively analyzed using incomplete force data, simplifying experimental measurements while preserving understanding of network evolution.

Contribution

It introduces a method to analyze force network evolution using incomplete data, reducing the need for detailed interparticle force measurements.

Findings

Force network features can be captured with total force data.

Algebraic topology tools effectively compare network evolution.

Incomplete data suffices for understanding dominant network features.

Abstract

The interactions between particles in particulate systems are organized in `force networks', mesoscale features that bridge between the particle scale and the scale of the system as a whole. While such networks are known to be crucial in determining the system wide response, extracting their properties, particularly from experimental systems, is difficult due to the need to measure the interparticle forces. In this work, we show by analysis of the data extracted from simulations that such detailed information about interparticle forces may not be necessary, as long as the focus is on extracting the most dominant features of these networks. The main finding is that a reasonable understanding of the time evolution of force networks can be obtained from incomplete information such as total force on the particles. To compare the evolution of the networks based on the completely known particle interactions and the networks based on incomplete information (total force each grain) we use tools of algebraic topology. In particular we will compare simple measures defined on persistence diagrams that provide useful summaries of the force network features.