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A colloidal viewpoint on the sausage catastrophe and the finite sphere packing problem

Author

Listed:
  • Susana Marín-Aguilar

    (Utrecht University)

  • Fabrizio Camerin

    (Utrecht University
    Hiroshima University)

  • Stijn Ham

    (University of Twente)

  • Andréa Feasson

    (University of Twente)

  • Hanumantha Rao Vutukuri

    (University of Twente)

  • Marjolein Dijkstra

    (Utrecht University
    Hiroshima University)

Abstract

It is commonly believed that the most efficient way to pack a finite number of equal-sized spheres is by arranging them tightly in a cluster. However, mathematicians have conjectured that a linear arrangement may actually result in the densest packing. Here, our combined experimental and simulation study provides a physical realization of the finite sphere packing problem by studying arrangements of colloids in a flaccid lipid vesicle. We map out a state diagram displaying linear, planar, and cluster conformations of spheres, as well as bistable states which alternate between cluster-plate and plate-linear conformations due to membrane fluctuations. Finally, by systematically analyzing truncated polyhedral packings, we identify clusters of 56 ≤ N ≤ 70 number of spheres, excluding N = 57 and 63, that pack more efficiently than linear arrangements.

Suggested Citation

  • Susana Marín-Aguilar & Fabrizio Camerin & Stijn Ham & Andréa Feasson & Hanumantha Rao Vutukuri & Marjolein Dijkstra, 2023. "A colloidal viewpoint on the sausage catastrophe and the finite sphere packing problem," Nature Communications, Nature, vol. 14(1), pages 1-10, December.
    • Handle: RePEc:nat:natcom:v:14:y:2023:i:1:d:10.1038_s41467-023-43722-0
    DOI: 10.1038/s41467-023-43722-0
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