Weitz Group @ Georgia Tech Theoretical Ecology and Quantitative Biology

Packing-limited growth

TitlePacking-limited growth
Publication TypeJournal Article
Year of Publication2002
AuthorsDodds PS, Weitz JS
JournalPhysical Review E
Date PublishedMAY

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.