The tail of the contact force distribution in static granular materials

TL;DR

This study uses numerical methods to analyze the distribution of contact forces in static granular materials, revealing a decay faster than exponential in both 2D and 3D systems.

Contribution

It introduces an ensemble-based numerical approach with umbrella sampling to accurately determine the force distribution tail in granular packings.

Findings

Force distribution decays faster than exponential.

Decay exponent approximately 2.0 in 2D.

Decay exponent approximately 1.7 in 3D.

Abstract

We numerically study the distribution P(f) of contact forces in frictionless bead packs, by averaging over the ensemble of all possible force network configurations. We resort to umbrella sampling to resolve the asymptotic decay of P(f) for large f, and determine P(f) down to values of order 10^{-45} for ordered and disordered systems in two and three dimensions. Our findings unambiguously show that, in the ensemble approach, the force distributions decay much faster than exponentially: P(f) ~ exp(-f^{\alpha}), with alpha \approx 2.0 for 2D systems, and alpha \approx 1.7 for 3D systems.