Wang-Landau algorithm for entropic sampling of arch-based microstates in the volume ensemble of static granular packings

TL;DR

This paper applies the Wang-Landau algorithm to efficiently sample and compute the entropy of static granular packings modeled by stable arches, enabling analysis of larger systems and more complex models.

Contribution

It introduces a novel application of the Wang-Landau algorithm to granular systems modeled by arches, detailing how to define microstates and moves for accurate sampling.

Findings

Successful implementation of the algorithm for large systems

Agreement with previous exact calculations at moderate sizes

Potential to analyze more complex granular models

Abstract

We implement the Wang-Landau algorithm to sample with equal probabilities the static configurations of a model granular system. The "non-interacting rigid arch model" used is based on the description of static configurations by means of splitting the assembly of grains into sets of stable arches. This technique allows us to build the entropy as a function of the volume of the packing for large systems. We make a special note of the details that have to be considered when defining the microstates and proposing the moves for the correct sampling in these unusual models. We compare our results with previous exact calculations of the model made at moderate system sizes. The technique opens a new opportunity to calculate the entropy of more complex granular models.