Three-dimensional granular deposits characterized by persistent homology

In this work, we analyze the performance of different topological metrics to characterize the three-dimensional structure of a granular sample. In particular, we investigate the problem of granular tapping as it has been shown that different tapping intensities may drive the system to configurations that, sharing the same global packing fraction, are slightly different; hence supposing a challenge in terms of differentiation using only geometrical features. Provided that persistent homology was shown to be a convenient tool to distinguish among two-dimensional deposits in the same scenario, we further extend this machinery to evaluate its performance in 3D cases. We find that, generically, two-dimensional topological features are more appropriate to distinguishing among different states than one-dimensional ones.