Breakdown of Scale Invariance in the Phase Ordering of Fractal Clusters

TL;DR

This paper demonstrates that coarsening of fractal clusters is not scale-invariant, with power-law behaviors observed in certain measures, and introduces a sharp-interface model to describe the full dynamics of the process.

Contribution

It reveals the breakdown of scale invariance in fractal cluster coarsening and presents a comprehensive sharp-interface model for diffusion-controlled growth and fragmentation.

Findings

Coarsening of fractal clusters is not scale-invariant.

Power laws govern the evolution of length scale and interfacial area.

The initial lower cutoff length scale influences the dynamics.

Abstract

Our numerical simulations with the Cahn-Hilliard equation show that coarsening of fractal clusters (FCs) is not a scale-invariant process. On the other hand, a typical coarsening length scale and interfacial area of the FC exhibit power laws in time, while the mass fractal dimension remains invariant. The initial value of the lower cutoff is a relevant length scale. A sharp-interface model is formulated that can follow the whole dynamics of a diffusion controlled growth, coarsening, fragmentation and approach to equilibrium in a system with conserved order parameter.