Ensemble Theory for Force Networks in Hyperstatic Granular Matter

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dc.creatorSnoeijer, Jacco H.
dc.creatorVlugt, Thijs J. H.
dc.creatorEllenbroek, Wouter G.
dc.creatorvan Hecke, Martin
dc.creatorvan Leeuwen, J. M. J.
dc.date2004-07-01
dc.date2004-09-13
dc.date.accessioned2026-07-07T02:58:58Z
dc.date.available2026-07-07T02:58:58Z
dc.descriptionAn ensemble approach for force networks in static granular packings is developed. The framework is based on the separation of packing and force scales, together with an a-priori flat measure in the force phase space under the constraints that the contact forces are repulsive and balance on every particle. In this paper we will give a general formulation of this force network ensemble, and derive the general expression for the force distribution $P(f)$. For small regular packings these probability densities are obtained in closed form, while for larger packings we present a systematic numerical analysis. Since technically the problem can be written as a non-invertible matrix problem (where the matrix is determined by the contact geometry), we study what happens if we perturb the packing matrix or replace it by a random matrix. The resulting $P(f)$'s differ significantly from those of normal packings, which touches upon the deep question of how network statistics is related to the underlying network structure. Overall, the ensemble formulation opens up a new perspective on force networks that is analytically accessible, and which may find applications beyond granular matter.
dc.description17 pages, 17 figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0407027
dc.identifierhttp://arxiv.org/abs/cond-mat/0407027
dc.identifierPhys. Rev. E 70, 061306 (2004)
dc.identifierdoi:10.1103/PhysRevE.70.061306
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/24327
dc.subjectDisordered Systems and Neural Networks
dc.subjectSoft Condensed Matter
dc.subjectStatistical Mechanics
dc.titleEnsemble Theory for Force Networks in Hyperstatic Granular Matter
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