Packing-Limited Growth
Soft Condensed Matter
2007-05-23 v2
Abstract
We consider growing spheres seeded by random injection in time and space. Growth stops when two spheres meet leading eventually to a jammed state. We study the statistics of growth limited by packing theoretically in d dimensions and via simulation in d=2, 3, and 4. We show how a broad class of such models exhibit distributions of sphere radii with a universal exponent. We construct a scaling theory that relates the fractal structure of these models to the decay of their pore space, a theory that we confirm via numerical simulations. The scaling theory also predicts an upper bound for the universal exponent and is in exact agreement with numerical results for d=4.
Cite
@article{arxiv.cond-mat/0203252,
title = {Packing-Limited Growth},
author = {Peter Sheridan Dodds and Joshua S. Weitz},
journal= {arXiv preprint arXiv:cond-mat/0203252},
year = {2007}
}
Comments
6 pages, 5 figures, 4 tables, revtex4 to appear in Phys. Rev. E, May 2002