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Published on: December 4, 2021
Optimal packings of superballs.
Y Jiao1, F H Stillinger, S Torquato
1Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA.
Summary
Researchers developed analytical constructions for the densest superball packings, offering insights into hard-particle packing and materials science. These findings advance understanding of nonspherical particle systems and their phase behavior.
Area of Science:
- Condensed matter physics
- Materials science
- Statistical mechanics
Background:
- Dense hard-particle packings are crucial for understanding low-temperature matter phases, heterogeneous materials, and granular media.
- While spherical particles have been extensively studied, research into nonspherical shapes like ellipsoids is more recent.
- Superballs offer a versatile family of convex and concave particles with tunable shapes, providing a rich platform for packing studies.
Purpose of the Study:
- To provide analytical constructions for the densest known superball packings across all convex and concave cases.
- To investigate the relationship between superball symmetries and their optimal packing arrangements.
- To explore the packing density as a function of superball shape parameter 'p' and identify nonanalytic behaviors.
Main Methods:
- Analytical construction of Bravais lattice packings for superballs.
- Analysis of global symmetries of superballs and their consistency with lattice structures.
- Calculation and characterization of maximal packing densities for various superball shapes.
Main Results:
- Analytical constructions for the densest known superball packings (convex and concave) are presented.
- Candidate optimal packings for convex superballs (p>=0.5) are identified, based on Bravais lattices with 12 neighbors.
- Nonanalytic behaviors in maximal packing density are observed at p=1 (sphere), pc*=1.1509..., and po*=0.7924..., indicating transitions between different packing structures.
Conclusions:
- The developed superball packings provide a foundation for quantifying equilibrium phase behavior in these systems.
- The study deepens the understanding of statistical thermodynamics in nonspherical-particle systems.
- Superball packing characteristics reveal richer complexity compared to 2D superdisks and differ significantly from ellipsoid packings.
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