Random packing of regular polygons and star polygons on a flat two-dimensional surface

Area of Science:

• Physics
• Materials Science
• Computational Modeling

Background:

• Understanding how irregular shapes pack on surfaces is crucial for materials science and physics.
• Previous studies have focused primarily on spherical or simple polygonal packing.

Purpose of the Study:

• To numerically investigate the random sequential adsorption of unoriented regular and star polygons on a 2D surface.
• To determine the saturated random packing ratio and analyze packing kinetics.
• To measure density autocorrelation and available surface functions for different shapes.

Main Methods:

• Utilized the random sequential adsorption (RSA) algorithm for numerical simulations.
• Analyzed simulation data to calculate packing ratios, density autocorrelation functions, and surface availability.
• Compared packing behaviors of regular polygons and star polygons.

Main Results:

• Star polygons generally yield lower packing ratios compared to regular polygons.
• As the number of vertices increases, both polygons and star polygons approach the packing behavior of disks.
• Packing density and kinetics were quantified, revealing shape-dependent trends.

Conclusions:

• The packing efficiency of polygons and star polygons is influenced by their geometric complexity.
• The study confirms that complex shapes, given sufficient vertices, exhibit packing properties similar to disks.
• Findings contribute to the understanding of disordered packing phenomena in materials science.