Lubachevsky–Stillinger algorithm: Difference between revisions

Revision as of 17:48, 25 April 2011

Revision as of 01:30, 26 April 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,

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an external compression and

an internal particle expansion,

both occurring simultaneously and possibly,

but not necessarily,

combined with a present or

absent hard boundary.

hard boundary, and the boundary can be mobile.

In a final, compressed, or "jammed" state,

some particles, the so-called "rattlers," are not jammed, they are able to move

within "cages" formed by their immobile, jammed neighbors

and the boundary, if any.

In its pre-"jammed" mode when the particle density is

low and they are mobile, the compression and expansion can be stopped, if so desired, and then the LSA, in effect, would be

simulating

dynamic [[granular flow]].

External forces, such as gravitation, can be easily

introduced, as long as the intercollisioninter-collision motion

of each particle can be represented

by a simple one-step calculation.

A substantial limitation of the original LS protocol

is that it was designed to practically work only

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<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>

in using the LSA in dimensions higher than 3.

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

== Comments on the algorithm ==

The state of particle jamming is achieved via simulating

[[granular flow]].

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smaller than an explicitly or implicitly

specified small threshold.

The LSA is efficient in the sense that

the event are processed essentially in an

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, the LSA is distinguished by a simpler data structure

and data handling.

For any particle at any stage of calculations

the LSA maintains the record of only two events:

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to be the old one,

whereas the next new event is being scheduled,

with its new time-stamp, new state, and new partner.

The LSA successfully achieves the jamming state

As the calculations of the LSA progress,

when collision rates of different particles

remainthe comparablecollision (andrates thoseof ratesparticles may and usually do

increase in simulated time without an uppera bound).

TheStill the LSA successfully achieves the jamming state

as long as those rates remains comparable among most

particles (except the rattlers, those experience

low collision rates).

However, a possibility exists

that aon smallapproach fractionto ofa thecertain particlesimulated ensembletime,

ina thesmall limitfraction evenof a singlethe particle ensemble,

even a single particle,

would exhibit an ever increasing collision rate

not only in the absolute termterms, but also

as compared with the rates of collisions

in the rest of the ensemble.

Then the simulation might not be able

to advance beyond a point inthis simulated time,

andeventhough atthe thatprocess point theof jamming would not be

close

to its completeness.

The same failure of being "stuck in time" failure

can also occur when using LSA

just for simulating a granular flow,

without the particle compression