Cates of the University of Edinburgh and his collaborators proposed a theoretical approach incorporating the notion that grains tend to settle into a pattern of "nested arches," an assortment of bridges oriented in all directions.
Herrmann of the Institute for Computer Applications at the University of Stuttgart in Germany and his collaborators have developed a two-dimensional, Tetris-like model in which rectangular particles with different orientations drift downward and settle into place, filling a cylinder.
When they are cooled to temperatures near absolute zero and held in electromagnetic traps, the ions settle into distinctive patterns -- from a few ions strung out like beads in a necklace to thousands of ions arranged as the surfaces of concentric shells.
They stay as far apart as possible and settle into patterns in which they are evenly spaced.
For very large numbers of ions, theoretical predictions suggest the shell structure should wash out and the ions settle into a type of cubic lattice.