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Frustrated packing in a granular system under geometrical confinement

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Abstract

Optimal packings of uniform spheres are solved problems in two and three dimensions. The main difference between them is that the two-dimensional ground state can be easily achieved by simple dynamical processes while in three dimensions, this is impossible due to the difference in the local and global optimal packings. In this paper we show experimentally and numerically that in 2 + ε dimensions, realized by a container which is in one dimension slightly wider than the spheres, the particles organize themselves in a triangular lattice, while touching either the front or rear side of the container. If these positions are denoted by up and down the packing problem can be mapped to a 1/2 spin system. At first it looks frustrated with spin-glass like configurations, but the system has a well defined ground state built up from isosceles triangles. When the system is agitated, it evolves very slowly towards the potential energy minimum through metastable states. We show that the dynamics is local and is driven by the optimization of the volumes of 7-particle configurations and by the vertical interaction between touching spheres.

Graphical abstract: Frustrated packing in a granular system under geometrical confinement

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Publication details

The article was received on 21 Sep 2017, accepted on 26 Nov 2017 and first published on 27 Nov 2017


Article type: Paper
DOI: 10.1039/C7SM01900A
Citation: Soft Matter, 2018, Advance Article
  • Open access: Creative Commons BY-NC license
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    Frustrated packing in a granular system under geometrical confinement

    S. Lévay, D. Fischer, R. Stannarius, B. Szabó, T. Börzsönyi and J. Török, Soft Matter, 2018, Advance Article , DOI: 10.1039/C7SM01900A

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