Boundary conditions in random sequential adsorption

TL;DR

This paper investigates how different boundary conditions affect the density of random disk packings generated by sequential adsorption, highlighting the advantages of periodic boundaries and correction methods for open and wall boundaries.

Contribution

It introduces a comparative analysis of boundary conditions on packing density and proposes correction techniques to improve results for open and wall boundaries.

Findings

Periodic boundary conditions minimize finite size effects.

Open and wall boundaries can be corrected for better packing density.

Effective packing size and correction terms improve density estimates.

Abstract

The influence of different boundary conditions on the density of random packings of disks is studied. Packings are generated using the random sequential adsorption algorithm with three different types of boundary conditions: periodic, open, and wall. It is found that the finite size effects are smallest for periodic boundary conditions, as expected. On the other hand, in the case of open and wall boundaries it is possible to introduce an effective packing size and a constant correction term to significantly improve the packing densities.