Universality in Dynamic Coarsening of a Fractal Cluster

TL;DR

This paper develops a theoretical framework for understanding the self-similar coarsening dynamics of fractal clusters formed by diffusion-controlled growth, providing explicit scaling exponents across dimensions.

Contribution

It introduces an exact mathematical model and a mean field theory that incorporate shadowing effects and conservation laws for fractal coarsening.

Findings

Coarsening dynamics are self-similar across dimensions.

Explicit dynamic scaling exponents are derived for any Euclidean dimension.

The model accounts for shadowing effects during growth.

Abstract

Dynamics of coarsening of a statistically homogeneous fractal cluster, created by a morphological instability of diffusion-controlled growth, is investigated theoretically. An exact mathematical setting of the problem is presented that obeys a global conservation law. A statistical mean field theory is developed that accounts for shadowing during the growth instability and assumes that the total mass and fractal dimension of the cluster remain constant. The coarsening dynamics are shown to be self-similar, and the dynamic scaling exponents are calculated for any Euclidean dimension.