Examination of saturation coverage of polygons using random sequential adsorption algorithm

TL;DR

This study investigates the saturation coverage of various regular polygons using a random sequential adsorption algorithm, employing the separating axis theorem to determine overlaps and estimating the packing limit when the process slows down.

Contribution

It provides new estimates of saturated polygon packings for multiple regular shapes using RSA and overlap detection with the separating axis theorem.

Findings

Results align with previous extrapolation studies.

Saturation is identified when RSA addition becomes slow.

Applicable to multiple regular polygon shapes.

Abstract

The goal of random sequential adsorption (RSA), a time-dependent packing method, is to create a regular or asymmetric covering of an empty space that can fit in the allocated space without overlapping. The density of coverage tends to reach a limit in the infinite-time limit. We attempt to estimate saturated packing of oriented 2-D polygons, including squares(4-sides), regular pentagons (5-sides), regular hexagons (6-sides), regular heptagons (7-sides), regular octagons (8-sides), regular nonagons (9-sides), regular decagons (10-sides), and regular dodecagons (12-sides), in this study. We obtained results that are consistent with previous, extrapolation-based studies1. We utilised the "separating axis theorem" to determine if there is overlap between arriving polygons and those that have previously been placed. Saturation as a lower limit is considered to have been reached when RSA addition becomes excessively slow, according to us.