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CPP: Fachverband Chemische Physik und Polymerphysik
CPP 34: Colloids and Complex Liquids II
CPP 34.2: Talk
Thursday, March 29, 2012, 15:30–15:45, C 130
Regular packings on periodic lattices — •Tadeus Ras1,3, Rolf Schilling1, and Martin Weigel1,2 — 1Institut für Physik, Johannes Gutenberg-Universität Mainz, Germany — 2Applied Mathematics Research Centre, Coventry University, England — 3Present address: Fachbereich Physik, Universität Konstanz, Germany
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 ϕd(X). It could be proved to be continuous with an infinite number of singular points Xνmin, Xνmax 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 ϕd(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 [1].
[1] T. Ras, R. Schilling and M. Weigel, Phys. Rev. Lett. 107, 215503 (2011)