Persistence of force networks in compressed granular media.

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.