Controllability of Granular Packings

Granular packings are disordered, athermal systems common in our everyday lives. Following perturbation, their evolution depends on their mesoscale stress-distributing structure, or force-chain network. Yet, it remains unclear precisely how force-chain networks change under applied stress. Here, we tackle this gap in knowledge using network control theory (NCT). NCT is a branch of systems engineering and statistical physics developed to understand and control the activity of networked systems in technology, robotics, and many other contexts. NCT is a promising approach to study force-chain networks both conceptually and mathematically, because it considers the network of connectivity between units, modeling the nature of the system’s dynamics as being constrained by that connectivity. We use NCT to estimate the control energy needed for a packing to transition between contact states. Our preliminary results indicate that control energy increases with system size and jamming, providing physical intuition for characterizing force-chain architecture evolution. More broadly, our findings can inform design principles by determining how changing the physical features of a granular packing impacts the system's force-chain network architecture and stress behavior.