Packing-limited growth of irregular objects

TL;DR

This paper investigates how irregularly shaped objects grow within a confined space until they collide, revealing that shape influences size distribution exponents, with implications for ecological and biological systems.

Contribution

It introduces a growth model for irregular objects considering anisotropy and aspect ratio, linking shape to size distribution exponents through scaling analysis.

Findings

Size distribution exponents depend strongly on object shape.

Growth mechanism details are irrelevant to the exponent.

Scaling analysis provides an upper bound for the size distribution exponent.

Abstract

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 non-unit 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.