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

TL;DR

This paper investigates cooperative phenomena like clustering, arching, and anomalous collision probabilities in dry granular media, revealing how density instabilities and correlations affect collision distributions and challenge traditional assumptions.

Contribution

It demonstrates the impact of density instabilities on collision statistics and highlights the limitations of molecular chaos in granular flow analysis.

Findings

Collision frequency distribution shows power-law decay in cooperative regimes.

Molecular chaos assumption is valid only in homogeneous cooling states.

Correlations significantly influence large-scale behavior in granular flows.

Abstract

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.