title: Packing-limited growth.
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.
authors.affiliation: Columbia Earth Institute, Columbia University, New York, New York 10027, USA. dodds@ldeo.columbia.edu
authors.forename: Peter Sheridan
authors.initials: PS
authors.lastname: Dodds
authors.forename: Joshua S
authors.initials: JS
authors.lastname: Weitz