# Dense granular flow at the critical state: maximum entropy and topological disorder

## TL;DR

This paper models dense granular flows at the critical state using maximum entropy principles to predict topological distributions, aligning well with simulation data.

## Contribution

It introduces a maximum entropy framework for predicting topological measures in dense granular flows, incorporating both topological and geometric considerations.

## Key findings

- Predicted void valence distribution matches DEM simulations.
- Coordination number distribution aligns with observed data.
- Topological entropy maximization effectively models steady-state granular arrangements.

## Abstract

After extensive quasi-static shearing, dense dry granular flows attain a steady-state condition of porosity and deviatoric stress, even as particles are continually rearranged. The paper considers two-dimensional flow and derives the probability distributions of two topological measures of particle arrangement---coordination number and void valence---that maximize topological entropy. By only considering topological dispersion, the method closely predicts the distribution of void valences, as measured in discrete element (DEM) simulations. Distributions of coordination number are also derived by considering packings that are geometrically and kinetically consistent with the particle sizes and friction coefficient. A cross-entropy principle results in a distribution of coordination numbers that closely fits DEM simulations.