Packing-Limited Growth

TL;DR

This paper investigates the statistical properties of packing-limited growth of spheres in multiple dimensions, revealing universal behaviors and developing a scaling theory that links fractal structure to pore space decay.

Contribution

It introduces a theoretical framework and simulations for understanding sphere packing growth, identifying universal radius distributions and a scaling relation in multiple dimensions.

Findings

Sphere radius distributions follow a universal power-law exponent.

Scaling theory accurately predicts the exponent bounds and matches numerical results in 4D.

The model links fractal structure to pore space decay in 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.