Viewing Rearrangements of Granular Material as a Network

Granular systems are common in nature and everyday life, but their behavior can be hard to predict, especially when they suddenly fail, as in an avalanche. To study this problem, we use a simple two-dimensional model of 19 particles inside a box. The particles can form stable jammed states or failure states where they are free to move. We analyze transition networks created with the Hydra String Method to see how these states are connected. After removing rattler particles, we classify each endpoint as jammed, unstable, or failure using Hessian eigenvalues. We then measure how close each jammed state is to failure using shortest path length (the number of transitions), and weighted shortest path length (sum of energy barriers along the path). Many jammed states are only a few transitions away from failure, but paths with the same number of hops can require different amounts of energy. We also find that larger particle movements from a minimum to a saddle usually have larger average energy barriers. These results show that network structure, energy barriers, and particle motion each give useful information about how close the system is to failure.