Local contact numbers in two dimensional packings of frictional disks

TL;DR

This study investigates the local contact structure of two-dimensional frictional disk packings, revealing power-law scaling of contact fractions with pressure and how these fractions depend on friction, supported by a simple predictive model.

Contribution

It provides the first systematic analysis of contact number distributions in frictional packings across varying pressure and friction coefficients, introducing a model for their zero-pressure values.

Findings

Contact fractions scale as power laws with pressure for all friction coefficients.

Zero-pressure contact fractions vary systematically with friction coefficient.

A simple model effectively captures the variation of contact fractions with friction.

Abstract

We analyze the local structure of two dimensional packings of frictional disks numerically. We focus on the fractions x_i of particles that are in contact with i neighbors, and systematically vary the confining pressure p and friction coefficient \mu. We find that for all \mu, the fractions x_i exhibit powerlaw scaling with p, which allows us to obtain an accurate estimate for x_i at zero pressure. We uncover how these zero pressure fractions x_i vary with \mu, and introduce a simple model that captures most of this variation. We also probe the correlations between the contact numbers of neighboring particles.