Networks of forces in pinned, frictionless jammed systems

Square, triangular, honeycomb and random lattices of fixed pins are shown to systematically modify the force network in a jammed solid of bidisperse, frictionless discs.  Point J remains isostatic, yet the number of contacts is reduced, which lowers the elastic moduli.  Weak contacts become more common, both supporting “buckler” particles and involving “enabler” pins. Further, pins fatten the tail of the normalized force distribution from a gaussian to a power law relationship.  Heatmaps of the geometrical and dynamical network reveal a rich local structure.  Finally, we examine the stress state via persistent homology – how structure in the contact network changes with increasing contact force filtration. We report the zeroth and first Betti numbers as a function of the threshold force. These quantify the connectedness and circuit rank of the filtered contact network as it varies with pin density and arrangement.