TL;DR
This paper investigates the screw symmetry in optimal sphere packings within infinite cylinders, providing a detailed quantitative description of the screw operation across various diameter ratios.
Contribution
It introduces a comprehensive analysis of screw symmetry in sphere packings inside cylinders, expanding understanding of their structural organization.
Findings
Optimal packings exhibit screw symmetry with a consistent twist angle.
Quantitative description of screw operation for diameter ratios 1 to 2.715.
Discussion of the helicity of these structures.
Abstract
We show that the optimal packing of hard spheres in an infinitely long cylinder yields structures characterised by a screw symmetry. Each packing can be assembled by stacking a basic unit cell ad infinitum along the length of the cylinder with each subsequent unit cell rotated by the same twist angle with respect to the previous one. In this paper we quantitatively describe the nature of this screw operation for all such packings in the range 1 <= D/d <= 2.715 and also briefly discuss their helicity.
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