Densest packing in wide cylinders at varying heights

Determine the densest packing of hard spheres in cylinders as a function of cylinder height when the cylinder diameter is much larger than the sphere diameter, in order to establish how tight the optimized-cylinder-orientation lower bound is in this regime.

Background

The paper develops an analytically exact lower bound by masking FCC and HCP close-packed solids with a finite cylinder and then optimizes the cylinder orientation through the OCO procedure. The authors expect this lower bound to become close to optimal for large cylinders, but their quantitative assessment is limited because benchmark data for the densest packings of wide cylinders at different heights are unavailable.

The unresolved issue concerns cylinders with large diameter-to-sphere ratios, specifically the regime in which 2R/σ is much greater than 1. Establishing the optimal packing fraction as a function of H/σ in this regime would permit a direct comparison with the OCO lower bound and determine whether the predicted packings are asymptotically optimal.