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Published on: March 27, 2017
Densest local sphere-packing diversity: general concepts and application to two dimensions
Adam B Hopkins1, Frank H Stillinger, Salvatore Torquato
1Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.
Summary
Researchers found the densest packings for circular disks, determining the minimum radius Rmin(N) for N disks. This provides a realizability condition for sphere packing pair-correlation functions and an upper bound on maximal density.
Area of Science:
- Computational Physics
- Materials Science
- Geometry
Background:
- Understanding sphere packing is crucial in various scientific fields.
- Determining densest packings provides insights into material properties and physical limits.
Purpose of the Study:
- To find the densest local packings of N identical nonoverlapping circular disks.
- To establish a realizability condition for pair-correlation functions and an upper bound on maximal density for sphere packings.
Main Methods:
- Utilized nonlinear programming combined with stochastic search in configuration space.
- Focused on the two-dimensional circular disk problem for selected N up to 348.
Main Results:
- Identified putative densest packings and corresponding Rmin(N) values.
- Derived a realizability condition for pair-correlation functions and an upper bound on maximal density.
- Observed significant variability in symmetries and contact networks of dense packings, differing from the triangular lattice.
Conclusions:
- The study provides a method to determine optimal sphere packing configurations.
- The findings have implications for packaging, nucleation theory, and surface physics.
- Densest packings exhibit complex structures, deviating from simple lattice models.
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