Arching in tapped deposits of hard disks

TL;DR

This study uses simulations to analyze arch formation in tapped hard disk beds, revealing an order-disorder transition and complex relationships between arches and packing density.

Contribution

It provides a detailed analysis of arch properties and their relation to tapping amplitude in a 2D system, highlighting differences from 3D behaviors.

Findings

Order-disorder transition at specific tapping amplitudes

Arches exhibit regular shapes in the ordered regime

Number of arches does not always correlate with packing fraction

Abstract

We simulate the tapping of a bed of hard disks in a rectangular box by using a pseudo dynamic algorithm. In these simulations, arches are unambiguously defined and we can analyze their properties as a function of the tapping amplitud. We find that an order--disorder transition occurs within a narrow range of tapping amplitudes as it has been seen by others. Arches are always present in the system althought they exhibit regular shapes in the ordered regime. Interestingly, an increase in the number of arches does not always correspond to a reduction in the packing fraction. This is in contrast with what is found in three-dimensional systems.