Competition between Diffusion and Fragmentation: An Important Evolutionary Process of Nature

TL;DR

This paper models the competition between diffusion and fragmentation in natural systems, deriving an exact solution for the size distribution of fragments that matches experimental data from ice crystals and protein structures.

Contribution

It introduces a novel rate equation and provides an exact analytical solution for the universal distribution of fragment sizes in natural systems.

Findings

The stationary size distribution follows a universal Bessel distribution.

The model accurately fits experimental data from ice crystal sizes.

The approach applies to diverse natural systems with fragmentation processes.

Abstract

We investigate systems of nature where the common physical processes diffusion and fragmentation compete. We derive a rate equation for the size distribution of fragments. The equation leads to a third order differential equation which we solve exactly in terms of Bessel functions. The stationary state is a universal Bessel distribution described by one parameter, which fits perfectly experimental data from two very different system of nature, namely, the distribution of ice crystal sizes from the Greenland ice sheet and the length distribution of alpha-helices in proteins.