Geometrical cluster ensemble analysis of random sphere packings

Area of Science:

• Physics
• Materials Science
• Computational Science

Background:

• Understanding random sphere packings is crucial in materials science and physics.
• Existing models often struggle to accurately represent both loose and dense packing scenarios.
• Hard-sphere models provide a fundamental basis for studying packing phenomena.

Purpose of the Study:

• To introduce a novel geometric analysis for random sphere packings.
• To investigate the volume fractions and radial distribution functions of hard-sphere clusters.
• To model and understand both random loose packing (RLP) and random close packing (RCP) using ensemble averaging.

Main Methods:

• Ensemble averaging of hard-sphere clusters generated via local rules.
• Inclusion of a nonoverlap constraint for hard spheres.
• Varying cluster generation rules to model different packing densities.

Main Results:

• The cluster ensemble analysis shows strong agreement with computer simulations and experimental data.
• A lower bound for the volume fraction of random loose packing was identified, closely matching the freezing volume fraction.
• Random close packing exhibited an unexpected split peak in the distribution of local configuration volume fractions.

Conclusions:

• The geometric analysis provides a robust framework for studying random sphere packings.
• Collective and global effects play a significant role in the properties of random sphere packings.
• The findings offer new insights into the distinct characteristics of loose versus dense sphere packing.