(Georgia Institute of Technology, 2003-01)
Dodds, Peter Sheridan; Weitz, Joshua S.
We study growth limited by packing for irregular objects in two dimensions. We generate packings by seeding objects randomly in time and space and allowing each object to grow until it collides with another
object. The objects we consider allow us to investigate the separate effects of anisotropy and nonunit aspect ratio. By means of a connection to the decay of pore-space volume, we measure power law exponents for the object size distribution. We carry out a scaling analysis, showing that it provides an upper bound for the size
distribution exponent. We find that while the details of the growth mechanism are irrelevant, the exponent is strongly shape dependent. Potential applications lie in ecological and biological environments where sessile organisms compete for limited space as they grow.
(Georgia Institute of Technology, 2002-05-06)
Dodds, Peter Sheridan; Weitz, Joshua S.
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 d52, 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 d54.