Journal of Statistical Physics

, Volume 60, Issue 5–6, pp 561–583 | Cite as

Geometric properties of random disk packings

  • Boris D. Lubachevsky
  • Frank H. Stillinger


Random packings ofN⩽2000 rigid disks in the plane, subject to periodic boundary conditions on a square primitive cell, have been generated by a concurrent construction which treats all disks on an equal footing, as opposed to previously investigated sequential constructions. The particles start with random positions and velocities, and as they move about they grow uniformly in size, from points to jammed disks. The collection of packings displays several striking geometric features. These include (for largeN) typically polycrystalline textures with irregular grain boundaries and linear shear fractures. The packings occasionally contain monovacancies and trapped but unjammed “rattler” disks. The latter appear to be confined to the grain boundaries. The linear shear fractures preserve bond orientational order, but disrupt translational order, within the crystalline grains. A new efficient event-driven simulation algorithm is employed to generate the histories of colliding and jamming disks. On a computer which can process one million floating-point instructions per second the algorithm processes more than one million pairwise collisions per hour.

Key words

Rigid disks rigid spheres random packings rattlers grain boundaries vacancies hexatic phases 


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Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • Boris D. Lubachevsky
    • 1
  • Frank H. Stillinger
    • 1
  1. 1.AT&T Bell LaboratoriesMurray Hill

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