Minimum spanning tree analysis of force networks in granular media

Force networks, formed by particles interacting with repulsive contact forces, are a salient feature of dense granular media, and play an important role in determining mechanical properties of granular media. We use a graph-theoretic approach based on the minimum spanning tree (MST) algorithm to analyze force networks in a dense granular bed under vibration and to provide structural information in a statistical sense. Using particle information from a molecular dynamics simulation, we show that the MST approach is able to capture the important structural information. We also developed a multi-pass MST algorithm, which is able to recover all the contacts within the force network and thus is able to recover the force distribution and force correlation. The results indicate that effect of wall friction transmits through the medium over several tens of particle diameters and affects the dynamical behavior of the system through local short-range interactions as indicated by the spatial force correlation. Therefore, the MST provides a possible route to constructing a continuum model with structural information supplied from this algorithm.