Lubachevsky–Stillinger algorithm: Difference between revisions

Revision as of 12:23, 12 May 2011

Revision as of 02:43, 13 May 2011

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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]].

==Phenomenology (what is being simulated)==

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>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 </ref>

<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 pack- ings, J. Statistical Physics 60 (1990), 561-583 </ref>

<ref> 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 </ref>

where the virtual particles were "swelling" or expanding

in a fixed, finite virtual volume

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for spherical particles, though the spheres may be

of 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)</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)

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<ref>M. Skoge, A. Donev, F.H. Stillinger, and S. Torquato, Packing Hyperspheres in High-Dimensional Euclidean Spaces, Phys. Rev. E 74, 041127 (2006)</ref>

in using the LSA in dimensions higher than 3.

==Implementation (how the calculations are performed)==

The state of particle jamming is achieved via simulating

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the same task of simulating [[granular flow]],

like, for example, the algorithm of D.C. Rapaport

<ref> D.C. Rapaport,

The Event Scheduling Problem in Molecular Dynamic Simulation,

Journal of Computational Physics

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simulations

as an "inelastic collapse"

<ref> S. McNamara, and W.R. Young, Inelastic collapse in two dimensions, Physical

Review E 50: pp. R28-R31, 1994

</ref>

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Thesis, Univ. Western Ontario, Canada, 2004.

http://imaging.robarts.ca/~jdrozd/thesisjd.pdf

</ref>

== History ==

The LSA was a by-product of an attempt to find

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B.D. Lubachevsky, Simulating Billiards: Serially and in Parallel, Int.J. in Computer Simulation, Vol. 2 (1992), pp. 373-411.

</ref>

== References ==

<!--- See http://en.wikipedia.org/wiki/Wikipedia:Footnotes on how to create references using <ref></ref> tags which will then appear here automatically -->

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* [http://cherrypit.princeton.edu/Packing/C++/ Source C++ codes of a version of the LSA in arbitrary dimensions]

* [http://people.physics.anu.edu.au/~tas110/Pubblicazioni/ReggioC_10a.pdf Volume fluctuation distribution in granular packs studied using the LSA]

* [http://www.pack-any-shape.com/ LSA generalized for particles of arbitrary shape]

* [http://onlinelibrary.wiley.com/doi/10.1002/pamm.200610180/pdf LSA used for production of representative volumes of microscale failures in packed granular materials]

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