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.

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We study the ground state properties of classical Coulomb charges interacting with a 1/r potential moving on a plane but confined either by a circular hard wall boundary or by a harmonic potential. The charge density in the continuum limit is determined analytically and is non-uniform. Because of the non-uniform density there are both disclinations and dislocations present and their distribution across the system is calculated and shown to be in agreement with numerical studies of the ground state (or at least low-energy states) of N charges, where values of N up to 5000 have been studied. A consequence of these defects is that although the charges locally form into a triangular lattice structure, the lattice lines acquire a marked curvature. A study is made of conformal crystals to illuminate the origin of this curvature. The scaling of various terms which contribute to the overall energy of the system of charges viz, the continuum electrostatic energy, correlation energy, surface energy (and so on) as a function of the number of particles N is determined. "Magic number" clusters are those at special values of N whose energies take them below the energy estimated from the scaling forms and are identified with charge arrangements of high symmetry.

Buckling of a linear chain of hard spheres in a harmonic confining potential: Numerical and analytical results for low and high compression.

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.