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Abstract: The heterogeneous force networks in static granular media - formed fromcontact forces between grains and spanning from boundary to boundary in thepacking - are distinguished from other network structures in that they mustsatisfy constraints of mechanical equilibrium on every vertex-grain. Here westudy the statistics of ensembles of hyperstatic frictionless force networks,which are composed of more forces than can be determined uniquely from forcebalance. Hyperstatic force networks possess degrees of freedom that rearrangeone balanced network into another. We construct these rearrangements, countthem, identify their elementary building blocks, and show that in twodimensions they are related via duality to so-called floppy modes, which playan important role in many other aspects of granular physics. We demonstratethat the number of rearrangements governs the macroscopic statisticalproperties of the ensemble, in particular the macroscopic fluctuations ofstress, which scale with distance to the isostatic point. We then show that amaximum entropy postulate allows one to quantitatively capture many features ofthe microscopic statistics. Boundaries are shown to influence the statisticsstrongly: the probability distribution of large forces can have a qualitativelydifferent form on the boundary and in the bulk. Finally, we consider the roleof spatial correlations and dimension. All predictions are tested againsthighly accurate numerical simulations of the ensemble, performed using umbrellasampling.



Autor: Brian P. Tighe, Thijs J.H. Vlugt

Fuente: https://arxiv.org/







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