We study the optimal packing of hard spheres in an infinitely long cylinder [1-4]. Our simulations have yielded dozens of periodic, mechanically stable, structures as the ratio of the cylinder (D) to sphere (d) diameter is varied. Up to D/d=2.715 the densest structures are composed entirely of spheres which are in contact with the cylinder. The density reaches a maximum at discrete values of D/d when a maximum number of contacts are established. These maximal contact packings are of the classic "phyllotactic" type, familiar in biology. However, between these points we observe another type of packing, termed line-slip.
An analytic understanding of these rigid structures follows by recourse to a yet simpler problem: the packing of disks on a cylinder. We show that maximal contact packings correspond to the perfect wrapping of a honeycomb arrangement of disks around a cylindrical tube. While line-slip packings are inhomogeneous deformations of the honeycomb lattice modified to wrap around the cylinder (and have fewer contacts per sphere).
Beyond D/d=2.715 the structures are more complex, since they incorporate internal spheres, but an analysis in terms of contacts or constraints is still illuminating. We review some relevant experiments with hard spheres and small bubbles. We also discuss on-going and future areas of work related to this project.
ABOUT THE SPEAKER
Dr. Adil Mughal completed his undergraduate studies in theoretical physics at the University of Manchester, U.K. in 2002. Continuing his studies at the University of Manchester, Dr. Mughal pursued a PhD under the supervision of Professor Mike Moore.
Since 2010, Dr. Mughal has held the position of Lecturer in Mathematical Modeling at Aberystwyth University, U.K. as well as postdoctoral positions in Germany and Italy. His current research is focused on packing problem and the tole of topology & geometry in soft condensed matter physics.