Lubachevsky–Stillinger algorithm: Difference between revisions

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==Phenomenology==

A physical process of compression often involves a contracting hard boundary of the container, such as a piston pressing against the particles. The LSA is able to simulate such a scenario.<ref>F. H. Stillinger and B. D. Lubachevsky, Crystalline-Amorphous Interface Packings for Disks and Spheres, J. Stat. Phys. 73, 497-514 (1993)</ref> However, the LSA was originally introduced in the setting without a hard boundary<ref>B. D. Lubachevsky and F. H. Stillinger, Geometric properties of random disk packings, J. Statistical Physics 60 (1990), 561-583 http://www.princeton.edu/~fhs/geodisk/geodisk.pdf</ref><ref>B.D. Lubachevsky, How to Simulate Billiards and Similar Systems, Journal of Computational Physics Volume 94 Issue 2, May 1991 httphttps://arxiv.org/PS_cache/cond-mat/pdf/0503/0503627v2.pdf</ref> where the virtual particles were "swelling" or expanding

in a fixed, finite virtual volume with [[periodic boundary conditions]]. The absolute sizes of the particles were increasing but particle-to-particle relative sizes remained constant. In general, the LSA can handle an external compression and an internal particle expansion, both occurring simultaneously and possibly, but not necessarily, combined with a hard boundary. In addition, the boundary can be mobile.

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short range particle-particle force interaction. External [[force fields]], such as [[gravitation]], can be also introduced, as long as the inter-collision motion of each particle can be represented by a simple one-step calculation.

Using LSA for spherical particles of different sizes and/or for jamming in a non-commeasureable size container proved to be a useful technique for generating and studying micro-structures formed under conditions of a [[crystallographic defect]]<ref>F. H. Stillinger and B. D. Lubachevsky. Patterns of Broken Symmetry in the Impurity-Perturbed Rigid Disk Crystal, J. Stat. Phys. 78, 1011-1026 (1995)</ref> or a [[geometrical frustration]]<ref>Boris D. Lubachevsky and Frank H. Stillinger, Epitaxial frustration in deposited packings of rigid disks and spheres. Physical Review E 70:44, 41604 (2004) httphttps://arxiv.org/PS_cache/cond-mat/pdf/0405/0405650v5.pdf</ref><ref>Boris D. Lubachevsky, Ron L. Graham, and Frank H. Stillinger, Spontaneous Patterns in Disk Packings. Visual Mathematics, 1995. http://vismath5.tripod.com/lub/</ref> It should be added that the original LS protocol was designed primarily for spheres of same or different sizes.<ref>A.R. Kansal, S. Torquato, and F.H. Stillinger, Computer Generation of Dense Polydisperse Sphere Packings, J. Chem. Phys. 117, 8212-8218 (2002) http://cat.inist.fr/?aModele=afficheN&cpsidt=13990882</ref>

Any deviation from the spherical (or circular in two dimensions) shape, even a simplest one, when spheres are replaced with ellipsoids (or ellipses in two dimensions),<ref>A. Donev, F.H. Stillinger, P.M. Chaikin, and S. Torquato, Unusually Dense Crystal Packings of Ellipsoids, Physical Review Letters 92, 255506 (2004)</ref> causes thus modified LSA to slow down substantially.