A Master equation for force distributions in polydisperse frictional particles

TL;DR

This paper introduces a Master equation to describe force distributions in polydisperse frictional particles, revealing how microscopic friction and size distribution influence force correlations and distribution tails.

Contribution

It develops a novel Master equation framework for force distributions in polydisperse frictional particles based on simulation data.

Findings

Friction narrows the tails of force distribution distributions.

Wider size distributions lead to broader force distribution tails.

Microscopic friction reduces correlations of overlaps.

Abstract

An incremental evolution equation, i.e. a Master equation in statistical mechanics, is introduced for force distributions in polydisperse frictional particle packings. As basic ingredients of the Master equation, the conditional probability distributions of particle overlaps are determined by molecular dynamics simulations. Interestingly, tails of the distributions become much narrower in the case of frictional particles than frictionless particles, implying that correlations of overlaps are strongly reduced by microscopic friction. Comparing different size distributions, we find that the tails are wider for the wider distribution.