Clustering Instabilities, Arching, and Anomalous Interaction Probabilities as Examples for Cooperative Phenomena in Dry Granular Media

Details Clustering Instabilities, Arching, and Anomalous Interaction Probabilities as Examples for Cooperative Phenomena in Dry Granular Media Clustering Instabilities, Arching, and Anomalous Interaction Probabilities as Examples for Cooperative Phenomena in Dry Granular Media

1998-10-09

arxiv.org/abs/cond-mat/9810116v1

T.A.S.K. Quarterly, Scientific Bulletin of Academic Computer Centre of the Technical University of Gdansk 2(3), 417-443, July

Physics

Condensed Matter

Statistical Mechanics

27 pages 14 figs (2 color)

Scientific paper

In a freely cooling granular material fluctuations in density and temperature cause position dependent energy loss. Due to strong local dissipation, pressure and energy drop rapidly and material moves from `hot' to `cold' regions, leading to even stronger dissipation and thus causing the density instability. The assumption of `molecular chaos' is valid only in the homogeneous cooling regime. As soon as the density instability occurs, the impact parameter is not longer uniformly distributed. The pair-correlation and the structure functions show that the molecular chaos assumption --- together with reasonable excluded volume modeling --- is important for short distances and irrelevant on large length scales. In this study, the probability distribution of the collision frequency is examined for pipe flow and for freely cooling granular materials as well. Uncorrelated events lead to a Poisson distribution for the collision frequencies. In contrast, the fingerprint of the cooperative phenomena discussed here is a power-law decay of the probability for many collisions per unit time. Keywords: discrete element method, event driven simulations, clustering instability, arching, shock waves, power-law distribution, cooperative phenomena.

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