title: Regular packings on periodic lattices.
abstract: We investigate the problem of packing identical hard objects on regular lattices in d dimensions. Restricting configuration space to parallel alignment of the objects, we study the densest packing at a given aspect ratio X. For rectangles and ellipses on the square lattice as well as for biaxial ellipsoids on a simple cubic lattice, we calculate the maximum packing fraction φ(d)(X). It is proved to be continuous with an infinite number of singular points X(ν)(min), X(ν)(max), ν = 0, ±1, ±2,…. In two dimensions, all maxima have the same height, whereas there is a unique global maximum for the case of ellipsoids. The form of φ(d)(X) is discussed in the context of geometrical frustration effects, transitions in the contact numbers, and number-theoretical properties. Implications and generalizations for more general packing problems are outlined.
authors.affiliation: Institut für Physik, Johannes Gutenberg-Universität Mainz, Germany.
authors.forename: Tadeus
authors.initials: T
authors.lastname: Ras
authors.forename: Rolf
authors.initials: R
authors.lastname: Schilling
authors.forename: Martin
authors.initials: M
authors.lastname: Weigel