Granular Response to Impact: Topology of the Force Networks

TL;DR

This paper uses topological methods to analyze the evolution of force networks in granular matter during impact, revealing correlations with intruder dynamics and identifying key structural features.

Contribution

It introduces the application of persistent homology to quantify and relate the structure and evolution of force networks to intruder dynamics in granular impact.

Findings

Topological measures correlate with intruder acceleration.

Identified key features of force networks relevant to dynamics.

Defined upper bounds on the time scale of network evolution.

Abstract

Impact of an intruder on granular matter leads to formation of mesoscopic force networks seen particularly clearly in the recent experiments carried out with photoelastic particles, e.g., Clark et al., Phys. Rev. Lett., 114 144502 (2015). These force networks are characterized by complex structure and evolve on fast time scales. While it is known that total photoelastic activity in the granular system is correlated with the acceleration of the intruder, it is not known how the structure of the force network evolves during impact, and if there is a dominant features in the networks that can be used to describe intruder's dynamics. Here, we use topological tools, in particular persistent homology, to describe these features. Persistent homology allows quantification of both structure and time evolution of the resulting force networks. We find that there is a clear correlation of the intruder's dynamics and some of the topological measures implemented. This finding allows us to discuss which properties of the force networks are most important when attempting to describe intruder's dynamics. Regarding temporal evolution of the networks, we are able to define the upper bound on the relevant time scale on which the networks evolve.