Geometric frustration in granular packings

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We propose an easily set-up and analyzed experiment to characterize the statistical properties of a frustrated physical system and to analyze the influence of relevant parameters on these properties, both qualitatively and quantitatively. This is achieved by an optical investigation of monodisperse spheres in a thin container.Packing problems of solid particles play an important role in many situations, nevertheless they are in general not well understood. The Kepler conjecture on the densest packing of identical spheres, for example, is known since centuries but was proven only in recent years. A problem that is often encountered in practical situations is that of dense disordered (random) packings. This problem still retained a number of open questions, even for the simple case of monodisperse spheres. If geometrical restrictions are added, packing problems become more complicated in general.We show that dense packings of spheres in a flat container exhibit complex geometrical properties because of frustration.. These can be analyzed and described only on a statistical level. The characteristics of the emerging distorted crystalline packinge are not only interesting in view of the particular system investigated here, but they bear relevance for geometric frustration in other physical systems, too, for example for antiferromagnetic spin systems on a triangular lattice. The experiment proposed here is excellently suitable for a characterization of frustrated geometries.In our experiment we will analyze fundamental properties of the packings of monodisperse spheres in flat containers with statistical methods, and derive models for their general description. The two main goals of the proposal are a better understanding of disordered packings of granular matter, and second the derivation of general statements about the properties of frustrated systems, on the basis of a systematic variation of the experimental geometry. In particular, we will explore the broken symmetry in tilted cells. With respect to the analogy noted above, the straight cell corresponds to the ground state of the antiferromagnet, while the tilted cell lifts degeneracy of the two cell planes and plays the same role as an external magnetic field for the spin system.