Berlin 2012 – scientific programme

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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 Ras^1,3, Rolf Schilling¹, and Martin Weigel^1,2 — 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 ϕ_d(X). It could be 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 [1].

[1] T. Ras, R. Schilling and M. Weigel, Phys. Rev. Lett. 107, 215503 (2011)