Shell structures with "magic numbers" of spheres in a swirled dish.

Area of Science:

• Physics
• Materials Science
• Computational Science

Background:

• Granular media typically exhibit fluid or solid behavior based on density and external forces.
• Understanding phase transitions in confined granular systems is crucial for various applications.

Purpose of the Study:

• To investigate the self-assembly and structural properties of a low number of spheres in a dynamic, confined environment.
• To identify critical particle numbers leading to stable, ordered structures versus disordered states.

Main Methods:

• Utilized molecular dynamic simulations to model the behavior of N spheres (N ≤ 54) within a swirled dish.
• Analyzed particle arrangements, focusing on the formation of rings and shell structures.
• Quantified switching dynamics between rings and characterized structural classifications.

Main Results:

• Observed the emergence of solid-like shell structures with stable rings at specific particle numbers (N = 7, 8, 12, 14, 19, 21, 30, 37, 40).
• Identified intermittent particle switching between rings, with switching time scaling exponentially with a control parameter, or fluid-like disorder at other N values.
• Classified stable shell structures based on geometric arrangements: one-centered hexagonal, one-centered quasicircular, three-centered, and four-centered.

Conclusions:

• Solidification in this low-N granular system is highly dependent on discrete particle counts, deviating from typical granular media behavior.
• The study reveals distinct phase transitions and ordered structures governed by geometry and particle number.
• These findings contribute to the understanding of self-organization in confined granular systems.