A topological method to characterize tapped granular media from the position of the particles

TL;DR

This paper introduces a topological approach using the first Betti number to differentiate granular packings based on particle positions, effectively distinguishing states with identical packing fractions but different tapping histories through simulations and experiments.

Contribution

It presents a novel topological method to characterize granular media solely from particle positions, without contact or force information, distinguishing states with similar densities.

Findings

Successfully differentiates granular states with same packing fraction

Validates method with both simulations and experiments

Uses topological features to analyze granular structures

Abstract

We use the first Betti number of a complex to characterize the morphological structure of granular samples in mechanical equilibrium. We analyze two-dimensional granular packings after a tapping process by means of both simulations and experiments. States with equal packing fraction obtained with different tapping intensities are distinguished after the introduction of a filtration parameter which determines the particles (nodes in the network) that are joined by an edge. We first use numerical simulations to characterize the effect of the precision in the particles localization by artificially adding different levels of noise in this magnitude. The outcomes obtained for the simulations are then compared with the experimental results allowing a clear distinction of experimental packings that have the same density. This is accomplished by just using the position of the particles and no other information about the possible contacts, or magnitude of forces.