Abstract
The heterogeneous force networks in static granular media are distinguished from othernetwork structures in that they must satisfy constraints of mechanical equilibrium on everyvertex/grain. Here we study the statistics of ensembles of hyperstatic frictionless forcenetworks, which are composed of more forces than can be determined uniquely from forcebalance. Hyperstatic force networks possess degrees of freedom that rearrange one balancednetwork into another. We calculate the equation of state and demonstrate that the numberof rearrangements governs the macroscopic statistical properties of the ensemble, inparticular the macroscopic fluctuations of stress, which scale with distance to the isostaticpoint. We then show that a maximum entropy postulate allows one to quantitativelycapture many features of the microscopic statistics. All predictions are testedagainst highly accurate Monte Carlo numerical simulations employing umbrellasampling.
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