Lubachevsky–Stillinger algorithm: Difference between revisions

Revision as of 04:54, 2 April 2011

Revision as of 03:05, 4 April 2011

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a numerical procedure that simulates or imitates

a physical process of compressing an assembly

of hard particles. TheAs the LSA may need thousands of arithmetic operations even for a few particles,

and so it is usually carried on a digital computer.

A real physical process of compression typically

(but not always) involves a contracting container

boundary, such as a piston pressing against the particles,. and theThe LSA is able to simulate just

such a scenario, like in ???.

However,

in a more frequently used setting theand LSA compressesin the

example reported in paper ???,

where the LSA was firstly

introduced,

the LSA compresses

the virtual particles by "swelling" or expanding them

in a fixed, final (but not necessarily bounded if a periodic

boundary condition is adopted as is done in ???)

virtual volume.

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

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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

(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.

But as long as the shape is spherical,

the LSA is able to handle particle ensembles
in tens to hundreds of thousands

on atoday's (2011) standard personal computer of todaycomputers.

of particles

How useful is the LSA in dimensions higher than 3

on a standard personal computer of today.

is unknown.

== References ==