Lubachevsky-Stillinger (compression) algorithm (LS algorithm, LSA, or LS protocol) is
a numerical procedure that simulates or imitates
a physical process of compressing an assembly
of hard particles. As the LSA may need thousands of arithmetic operations even for a few particles,
it is usually carried out on a digital computer.
A real 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 just
such a scenario [1]
[2] .
However,
the LSA was firstly
introduced [3]
[4]
in the setting with periodic
boundary conditions
where
the virtual particles are compressed
by "swelling" or expanding
in a fixed, final
virtual volume without hard boundary.
The absolute sizes of the particles are increasing but particle-to-particle relative sizes remain constant.
As a result, in a final, compressed, or "jammed" state,
some particles, the so-called "rattlers," turn out not to be jammed. Rattlers are mobile
within "cages" formed by their immobile, jammed neighbors
and the boundary, if any.
A substantial limitation of the original LS protocol
is that it was designed to practically work only
for spherical particles, though the spheres may be
of different sizes
[5].
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)
[6]
, causes thus modified LSA to slow down dramatically
[7] .
But as long as the shape is spherical,
the LSA is able to handle particle ensembles
in tens to hundreds of thousands
on today's (2011) standard personal computers.
Only a very limited experience was reported
[8]
in using the LSA in dimensions higher than 3.
References
- ^ Boris D. Lubachevsky and Frank H. Stillinger, Epitaxial frustration in deposited packings of rigid disks and spheres. Physical Review E 70:44, 41604 (2004) http://arxiv.org/PS_cache/cond-mat/pdf/0405/0405650v5.pdf
- ^ Crystalline-Amorphous Interface Packings for Disks and Spheres, F. H. Stillinger and B. D. Lubachevsky, J. Stat. Phys. 73, 497-514 (1993)
- ^ B. D. Lubachevsky and F. H. Stillinger, Geometric properties of random disk pack- ings, J. Statistical Physics 60 (1990), 561-583
- ^ B.D. Lubachevsky, How to Simulate Billiards and Similar Systems, Journal of Computational Physics Volume 94 Issue 2, May 1991 http://arxiv.org/PS_cache/cond-mat/pdf/0503/0503627v2.pdf
- ^ Computer Generation of Dense Polydisperse Sphere Packings, | A.R. Kansal, S. Torquato, and F.H. Stillinger, J. Chem. Phys. 117, 8212-8218 (2002)
- ^ Unusually Dense Crystal Packings of Ellipsoids, A. Donev, F.H. Stillinger, P.M. Chaikin, and S. Torquato, Phys. Rev. Letters 92, 255506 (2004)
- ^ http://www.pack-any-shape.com
- ^ Packing Hyperspheres in High-Dimensional Euclidean Spaces," M. Skoge, A. Donev, F.H. Stillinger, and S. Torquato, Phys. Rev. E 74, 041127 (2006)