Open Conference Systems, StatPhys 27 Main Conference

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Force network ensemble on a single grain: a Monte Carlo study reproducing experimental and simulation results
Manuel Antonio Cardenas-Barrantes, Jose Daniel Muñoz, William Fernando Oquendo

##manager.scheduler.building##: Edificio Santa Maria
##manager.scheduler.room##: Auditorio San Agustin
Date: 2019-07-10 12:00 PM – 03:45 PM
Last modified: 2019-06-14

Abstract


The force network ensemble of a granular medium accounts for all force configurations at mechanical equilibrium consistent with some external stress, and defines a temperature like-parameter, the angoricity, which under isotropic compression is a scalar variable. Although usually studied on sets of many grains, previous works have shown that spatial correlations can be neglected in many cases, opening the door to studies on a single grain, like the granulocentric nodel. In a recent study [Granular Matter 20 (2018), 1] we develop a Monte Carlo method to sample the force ensemble on a single grain at constant angoricity and coordination number on two and three-dimensional mono-disperse granular systems, with or without static friction. The results show that, despite the steric exclusions and the constrictions of Coulomb’s limit and repulsive normal forces, the pressure per grain always show a k-gamma distribution, with the angoricity 1/&alpha as scale parameter and the number of free force variables as shape parameter k, in close analogy to previous results for tje statistics of volumes inside the packing. Moreover, the average pressure per grain fulfills in all cases an equipartition theorem <p>=k/&alpha (in close parallelism with an ideal gas). These results are in excellent agreement with previous experiments on acrylic beads poured into a cylindrical container, with previous Monte Carlo samplings on frictionless disk sets and with our own molecular dynamics simulations on frictional monodisperse spheres under isotropic compression with both rolling and sliding friction. These findings introduces a novel procedure to measure angoricity and suggest an easy way of roundly estimating the force entropy just by counting the number of degrees of freedom in the force network. They constitute, therefore, a further step in the understanding of the force network ensemble for granular media.