Granular response to impact: Topology of the force networks.

The impact of an intruder on granular matter leads to the formation of mesoscopic force networks, which were seen particularly clearly in the recent experiments carried out with photoelastic particles [Clark et al., Phys. Rev. Lett. 114, 144502 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.144502]. 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 are dominant features in the networks that can be used to describe the 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 the intruder's dynamics. In particular, we find that the presence of loops in the force network, quantified by persistent homology, is strongly correlated to the deceleration of the intruder. In some cases, particularly for the impact on soft particles, the measures derived from the persistence analysis describe the deceleration of the intruder even better than the total photoelastic activity. We are also able to define an upper bound on the relevant time scale over which the force networks evolve.