Packing-Limited Growth

Details Packing-Limited Growth Packing-Limited Growth

2002-03-12

arxiv.org/abs/cond-mat/0203252v2

Physics

Condensed Matter

Soft Condensed Matter

6 pages, 5 figures, 4 tables, revtex4 to appear in Phys. Rev. E, May 2002

Scientific paper

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.

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