Content deleted Content added
Rahul Narain (talk | contribs) mNo edit summary |
|||
Line 1:
'''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]].[[File:1000 triangles packed in rectangle.png|thumb|Using a variant of Lubachevsky-Stillinger algorithm, 1000 congruent isosceles triangles are randomly packed by compression in a rectangle with periodic (wrap-around) boundary. The rectangle which is the period of pattern repetition in both directions is shown. Packing density is 0.8776]]
==Phenomenology
A 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 such a scenario.<ref>F. H. Stillinger and B. D. Lubachevsky, Crystalline-Amorphous Interface Packings for Disks and Spheres, J. Stat. Phys. 73, 497-514 (1993)</ref> However, the LSA was originally introduced in the setting without a hard boundary<ref>B. D. Lubachevsky and F. H. Stillinger, Geometric properties of random disk packings, J. Statistical Physics 60 (1990), 561-583 http://www.princeton.edu/~fhs/geodisk/geodisk.pdf</ref><ref>B.D. Lubachevsky, How to Simulate Billiards and Similar Systems, Journal of Computational Physics Volume 94 Issue 2, May 1991 http://arxiv.org/PS_cache/cond-mat/pdf/0503/0503627v2.pdf</ref> where the virtual particles were "swelling" or expanding
in a fixed, finite virtual volume with [[periodic boundary conditions]]. The absolute sizes of the particles were increasing but particle-to-particle relative sizes remained constant. In general, the LSA can handle an external compression and an internal particle expansion, both occurring simultaneously and possibly, but not necessarily, combined with a hard boundary. In addition, the boundary can be mobile.
Line 18:
in using the LSA in dimensions higher than 3.
==Implementation
The state of particle jamming is achieved via simulating a [[granular flow]]. The flow is rendered as a [[discrete event simulation]], the events being particle-particle or particle-boundary collisions. Ideally, the calculations should have been
performed with the infinite precision. Then the jamming would have occurred [[ad infinitum]]. In practice, the precision is finite as is the available resolution of representing the real numbers in the [[computer memory]], for example, a [[double-precision]] resolution. The real calculations are stopped when inter-collision runs of the non-rattler particles become
| |||