Topological data analysis of the stress state of granular packings.

We apply topological data analysis to describe the multi-scale structure of the stress state of granular systems. Our approach differs from prior efforts by analyzing the interactions over all geometric length scales, instead of just at physical contact. We demonstrate this analysis on data from packings of photoelastic grains and molecular dynamics simulations of packings of bidisperse spheres in 2 and 3 dimensions. We observe nontrivial persistence in higher-dimension homology groups. We hypothesize these higher-dimensional features represent mechanically significant structures which cannot be identified in more conventional 'force chain'-inspired topological analyses.