  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.
