text: Columnar structures arise naturally in the context of dense hard sphere packings inside a cylinder. Mughal et al. studied such packings using simulated annealing up to the diameter ratio of  for cylinder diameter  to sphere diameter . This includes some structures with internal spheres that are not in contact with the cylinder wall.
  They calculated the packing fraction for all these structures as a function of the diameter ratio. At the peaks of this curve lie the uniform structures. In-between these discrete diameter ratios are the line slips at a lower packing density. Their packing fraction is significantly smaller than that of an unconfined lattice packing such as fcc, bcc, or hcp due to the free volume left by the cylindrical confinement.
  The rich variety of such ordered structures can also be obtained by sequential depositioning the spheres into the cylinder. Chan reproduced all dense sphere packings up to  using an algorithm, in which the spheres are placed sequentially dropped inside the cylinder.
  Mughal et al. also discovered that such structures can be related to disk packings on a surface of a cylinder. The contact network of both packings are identical. For both packing types, it was found that different uniform structures are connected with each other by line slips.
  Fu et al. extended this work to higher diameter ratios  using linear programming and discovered 17 new dense structures with internal spheres that are not in contact with the cylinder wall.
  A similar variety of dense crystalline structures have also been discovered for columnar packings of spheroids through Monte Carlo simulations. Such packings include achiral structures with specific spheroid orientations and chiral helical structures with rotating spheroid orientations.