Lubachevsky-Stillinger (compression) algorithm (LS algorithm, LSA,
or LS protocol) is
a numerical procedure that simulates or imitates
a physical process of compressing an assembly
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.
A real 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 just
such a scenario ???.
However,
the LSA was firstly
introduced ??? in the setting with periodic
boundary conditions
where
the virtual particles are compressed
by "swelling" or expanding
in a fixed, final
virtual volume without hard boundary.
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
within "cages" formed by their immobile, jammed neighbors
and the boundary, if any.
A substantial limitation of the original LS protocol
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 today's (2011) standard personal computers.
How useful the LSA is in dimensions higher than 3
is unknown.
