Lubachevsky–Stillinger algorithm: Difference between revisions

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'''Lubachevsky-Stillinger (compression) algorithm''' (LS algorithm, LSA, or LS protocol) is

or LS protocol) is

a numerical procedure that simulates or imitates

a physical process of compressing an assembly

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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 <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) </ref>

such a scenario ???.

<ref> Crystalline-Amorphous Interface Packings for Disks and Spheres, F. H. Stillinger and B. D. Lubachevsky, J. Stat. Phys. 73, 497-514 (1993)</ref> .

However,

the LSA was firstly

introduced ???<ref> B. D. Lubachevsky and F. H. Stillinger, Geometric properties of random disk pack- ings, J. Statistical Physics 60 (1990), 561-583 </ref> in the setting with periodic

boundary conditions

where

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is that it was designed to practically work only

for spherical particles, though the spheres may be

of different sizes ??? ???. Any deviation from the spherical

<ref> Computer Generation of Dense Polydisperse Sphere Packings, | A.R. Kansal, S. Torquato, and F.H. Stillinger, J. Chem. Phys. 117, 8212-8218 (2002)</ref>.

(or circular in two dimensions) shape, even a simplest one, when spheres are replaced with ellipsoids (or ellipses in two dimensions) ??? ???, causes thus modified LSA to slow down dramatically.

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) ??? ???, causes thus modified LSA to slow down dramatically.

<ref> Unusually Dense Crystal Packings of Ellipsoids, A. Donev, F.H. Stillinger, P.M. Chaikin, and S. Torquato, Phys. Rev. Letters 92, 255506 (2004)</ref>

, causes thus modified LSA to slow down dramatically

<ref> pack-any-shape.com </ref> .

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

How useful the LSA is in dimensions higher than 3

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

is unknown.

Howin usefulusing the LSA is in dimensions higher than 3.

== References ==