Lubachevsky–Stillinger algorithm: Difference between revisions

Revision as of 20:20, 5 May 2011

Revision as of 02:35, 6 May 2011

Line 33:

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.

TheThese rattlersfree-to-move particles are not an artifact, designed, or

or pre-designed, or target feature of the LSA,

ofbut the LSA, butrather a real phenomenon,.

The simulation revealed this phenomenon,

that the simulation, somewhat unexpectedly, reveals.

Frank Stillinger coined the term from the observation

infor the restauthors of the ensembleLSA.

that if one physically shakes a compressed bunch of hard

particles,Frank someH. ofStillinger them,coined the term "rattlers, will be rattling."

for the free-to-move particles,

because

that if one physically shakes a compressed bunch of hard

particles (except, the rattlers, thosewill be experiencerattling.

In the pre-"jammed" mode

when the density of the particlesconfiguration is

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

simulating

dynamica [[granular flow]].

Various dynamics of the instantaneous collisions

can be simulated such as: with or without a full restitution,

Line 55 ⟶ 59:

into account.

It is also easy and sometimes proves useful to

"fluidize" a "jammed" configuration,

by decreasing the sizes of all or some of the particles.

Another possible extension of the LSA is replacing

the hard collision [[force]] [[potential]]

(zero outside the particle, infinity at or inside) with

a piece-wise constant [[force]] [[potential]]. Thus modifiedThe LSA

thus modified would approximate

a molecular dynamic simulation with continuous

short range particle-particle force interaction.

Line 147 ⟶ 151:

increase without a bound.

Still the LSA successfully achieves the jamming state

as long as those rates remain comparable among mostall

the

particles (except the rattlers, those experience

particles, except for the rattlers.

low collision rates).

(Rattlers experience consistently

However, a possibility exists

low collision rates, and that is one way to detect

that along the approach to a certain simulated time,

them during calculations.)

a small fraction of the particle ensemble,

However,

even a single particle,

it is possible for a few particles,

would exhibit an ever increasing collision rate

even just for a single particle,

not only in the absolute terms, but also

to experience a very high collision

as compared with the rates of collisions

rate

in the rest of the ensemble.

that along the approach to a certain simulated time,.

Then the simulation might not be able

The rate will be not only increasing without

a bound but will be also outstandingly higher

than the rates of collisions in the rest of the particle ensemble.

If this happens,

Thenthen the simulation might not be able

to advance beyond this simulated time,

even thoughif the process of jamming wouldwill not be complete.

close

to its completeness on the approach to such a time.

The "stuck in time" failure

Line 168 ⟶ 175:

just for simulating a granular flow,

without the particle compression

or expansion. This failure mode,

butThis thatfailure existsmode was recognized in the area of granular flow

not necessarily attributed only to the LSA,

simulations at large,

but that exists in the area of granular flow

simulations at large,

has been recognized by some practitioners

as an "inelastic collapse"

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

Line 182 ⟶ 187:

at collisions is low (and hence

the collisions are inelastic).

The failure is not specific to just the LSA algorithm.

Techniques to avoid the failure have

been proposed.

== History ==

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

a fair measure of [[speedup]] in [[parallel simulations]]. The

[[Time Warp]] parallel simulation algorithm

by David Jefferson was advanced as a method

Line 211 ⟶ 217:

on a [[multiprocessor]], when executing the same

parallel [[Time Warp]] algorithm.

An objection raised by Boris D. Lubachevsky was that

such a speedup assessment might be faulty because

executing a [[parallel algorithm]] for a task on a [[uniprocessor]]

Line 221 ⟶ 227:

and hence to have a more fair assessment of the

[[parallel speedup]].

Later on, a parallel simulation algorithm,

different from the [[Time Warp]],

was also proposed, that, when run on a [[uniprocessor]],

reduces to the LSA.