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Dense granular flow at the critical state: maximum entropy and topological disorder

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Abstract

After extensive quasi-static shearing, dense dry granular flows attain a steady-state condition of porosity and deviatoric stress, even as particles are continually rearranged. The paper considers two-dimensional flow and derives the probability distributions of two topological measures of particle arrangement—coordination number and void valence—that maximize topological entropy. By only considering topological dispersion, the method closely predicts the distribution of void valences, as measured in discrete element (DEM) simulations. Distributions of coordination number are also derived by considering packings that are geometrically and kinetically consistent with the particle sizes and friction coefficient. A cross-entropy principle results in a distribution of coordination numbers that closely fits DEM simulations.

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Acknowledgments

This work is dedicated to the memory of Prof. Colin B. Brown (1929–2013), who made significant contributions to the understanding of granular entropy.

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  1. Donald P. Shiley School of Engineering, University of Portland, Portland, OR , 97203, USA

    Matthew R. Kuhn

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  1. Matthew R. Kuhn
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Correspondence to Matthew R. Kuhn.

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Kuhn, M.R. Dense granular flow at the critical state: maximum entropy and topological disorder. Granular Matter 16, 499–508 (2014). https://doi.org/10.1007/s10035-014-0496-2

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