Dense packings of spheres in cylinders: Simulations

Abstract

We study the optimal packing of hard spheres in an infinitely long cylinder, using simulated annealing, and compare our results with the analogous problem of packing disks on the unrolled surface of a cylinder. The densest structures are described and tabulated in detail up to D/d = 2.873 (ratio of cylinder and sphere diameters). This extends previous computations into the range of structures which include internal spheres that are not in contact with the cylinder.

An experimental study of columnar crystals using monodisperse microbubbles

“…In contrast, far less is known about packing within a bounded space, despite the fact that such problems are ubiquitous throughout science, nature and even daily life. D d is a computationally demanding task and as such multilayer arrangements remain largely unexplored [3]. In this paper we show that micron-sized spherical bubbles can spontaneously self-assemble into crystalline arrangements inside capillary tubes, which closely resemble multilayer columnar crystals.…”

“…al. [3] As λ increases the situation is more complicated due to the formation of two-structures with internal spheres. An accurate determination of the exact onset of this transition is not possible from these tomographic experiments due to the inability to continuously measure the structural changes with increasing λ.…”

“…However, we see that structures without internal spheres form up to λ = 2.5 while the next successfully imaged structure, at λ = 2.9, shows the emergence of such spheres. This range of λ values includes λ = 2.73, the value associated A c c e p t e d M a n u s c r i p t with the first occurrence of internal spheres in simulation [3].…”

“…The resulting foam packings are then compared to the hard-sphere simulations of Pickett and Mughal [2,3,4].…”

Screw symmetry in columnar crystals

“…An example of this is the densest packing arrangement of equal sized hard spheres of diameter d, in an unbounded cylinder, of diameter D. Recently we have conducted numerical simulations [1,2] (based on simulated annealing) which have so far identified 40 distinct spiral structures in the range 1 ≤ D/d ≤ 2.873. Our simulations greatly extend the list of packings discovered by the earlier work of Pickett et.…”