Arch-based configurations in the volume ensemble of static granular systems

TL;DR

This paper introduces an arch-based ensemble approach to count static configurations in granular systems, deriving exact state densities and validating results with simulations and analytical solutions.

Contribution

It presents a novel arch-based method for counting stable configurations, enabling new analytical and simulation studies of granular packings.

Findings

Exact density of states for a 2D non-interacting arch model

Arch size distribution matches simulation results

Validation against analytical solution for frictionless disks

Abstract

We propose an alternative approach to count the microscopic static configurations of granular packs under gravity by considering arches. This strategy simplifies the problem of filtering out configurations that are not mechanically stable, opening the way for a range of granular models to be studied via ensemble theory. Following this arch-based approach, we have obtained the exact density of states for a two-dimensional non-interacting rigid arch model of granular assemblies. The calculated arch size distribution and volume fluctuations show qualitative agreement with realistic simulations of tapped granular beds. We have also validated our calculations by comparing with the analytic solution for the limiting case of a quasi-one-dimensional column of frictionless disks.