Criteria for dynamical clustering in permanently excited granular gases: Comparison and estimation with machine learning

When dense granular gases in microgravity are continuously excited mechanically, spatial inhomogeneities of the particle distribution can emerge. With a sufficiently large overall packing fraction, a significant share of particles tend to concentrate in strongly overpopulated regions, the so-called clusters. This phenomenon, dynamical clustering, is caused by a complex interaction between energy influx and dissipation. The number density of particles, the geometry of the container, and the excitation strength influence cluster formation. Quantification of the clustering thresholds is not trivial. We perform Discrete Element Method (DEM) simulations for ensembles of frictional spheres in a cuboid container to generate synthetic data and apply the Kolmogorov–Smirnov test and a caging criterion to the local packing fraction profiles. Both tests yield similar thresholds in some cases but significantly diverge in others. We identify major drawbacks in these approaches and discuss more advanced statistical criteria based on dynamical properties of the ensemble.A machine learning approach that predicts dynamic clustering from known system parameters is proposed and tested. It avoids the necessity of complex numerical simulations.