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A phase diagram for jammed matter

Author

Listed:
  • Chaoming Song

    (City College of New York, New York, New York 10031, USA)

  • Ping Wang

    (City College of New York, New York, New York 10031, USA)

  • Hernán A. Makse

    (City College of New York, New York, New York 10031, USA
    Universidade Federal do Ceará, 60451-970 Fortaleza, Ceará, Brazil)

Abstract

Jammed matter: Mathematics of the spheres The search for the most efficient way of filling a container with balls is one of the oldest of mathematical puzzles. Aside from its intrinsic interest, the problem has practical relevance in systems as varied as granular processing, fruit packing, colloid behaviour and in living cells. Experiments have shown that the loosest way to pack spheres (random loose packing) gives a density of about 55% and that the most compact (random close packing, or RCP) gives a maximum density of about 64%. These values appear robust, but there is as yet no physical interpretation for them. Now Chaoming Song et al. show analytically that, indeed, spheres cannot pack in three dimensions above the 63.4% limit found by experiment. The limit arises from a statistical picture of the jammed states in which the RCP can be defined as the ground state of the ensemble of jammed matter. These results ultimately lead to a phase diagram for jammed matter that provides a unifying view of the sphere-packing problem.

Suggested Citation

  • Chaoming Song & Ping Wang & Hernán A. Makse, 2008. "A phase diagram for jammed matter," Nature, Nature, vol. 453(7195), pages 629-632, May.
    • Handle: RePEc:nat:nature:v:453:y:2008:i:7195:d:10.1038_nature06981
    DOI: 10.1038/nature06981
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    Citations

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    Cited by:

    1. Jin, Yuliang & Makse, Hernán A., 2010. "A first-order phase transition defines the random close packing of hard spheres," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(23), pages 5362-5379.
    2. Bailera, Manuel & Pascual, Sara & Lisbona, Pilar & Romeo, Luis M., 2021. "Modelling calcium looping at industrial scale for energy storage in concentrating solar power plants," Energy, Elsevier, vol. 225(C).
    3. Yoshio Kono & Koji Ohara & Nozomi M. Kondo & Hiroki Yamada & Satoshi Hiroi & Fumiya Noritake & Kiyofumi Nitta & Oki Sekizawa & Yuji Higo & Yoshinori Tange & Hirokatsu Yumoto & Takahisa Koyama & Hirosh, 2022. "Experimental evidence of tetrahedral symmetry breaking in SiO2 glass under pressure," Nature Communications, Nature, vol. 13(1), pages 1-8, December.
    4. Kyeyune-Nyombi, Eru & Morone, Flaviano & Liu, Wenwei & Li, Shuiqing & Gilchrist, M. Lane & Makse, Hernán A., 2018. "High-resolution of particle contacts via fluorophore exclusion in deep-imaging of jammed colloidal packings," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1387-1395.
    5. Agapie Stefan C. & Whitlock Paula A., 2010. "Random packing of hyperspheres and Marsaglia's parking lot test," Monte Carlo Methods and Applications, De Gruyter, vol. 16(3-4), pages 197-209, January.
    6. Stéphan T. Grilli & Mike Shelby & Olivier Kimmoun & Guillaume Dupont & Dmitry Nicolsky & Gangfeng Ma & James T. Kirby & Fengyan Shi, 2017. "Modeling coastal tsunami hazard from submarine mass failures: effect of slide rheology, experimental validation, and case studies off the US East Coast," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 86(1), pages 353-391, March.
    7. Tejada, Ignacio G., 2011. "A new statistical mechanics approach to dense granular media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(14), pages 2664-2677.

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