title: Phyllotactic description of hard sphere packing in cylindrical channels.
abstract: We develop a simple analytical theory that relates dense sphere packings in a cylinder to corresponding disk packings on its surface. It applies for ratios R=D/d (where d and D are the diameters of the hard spheres and the bounding cylinder, respectively) up to R=1+1/sin(π/5). Within this range the densest packings are such that all spheres are in contact with the cylindrical boundary. The detailed results elucidate extensive numerical simulations by ourselves and others by identifying the nature of various competing phases.
authors.affiliation: Institute of Mathematics and Physics, Aberystwyth University, Penglais, Aberystwyth, Ceredigion, Wales, SY23 3BZ, United Kingdom.
authors.forename: A
authors.initials: A
authors.lastname: Mughal
authors.forename: H K
authors.initials: HK
authors.lastname: Chan
authors.forename: D
authors.initials: D
authors.lastname: Weaire