Laplacian Fractal Growth in Media with Quenched Disorder

TL;DR

This paper investigates how the interplay of Laplacian fields and quenched disorder influences fractal growth, revealing a transition from avalanche-like to smooth structures and a reduction in fractal dimension.

Contribution

It introduces a combined numerical and theoretical analysis of the quenched dielectric breakdown model, highlighting the impact of disorder and field effects on fractal growth dynamics.

Findings

Fractal dimension is significantly reduced by quenched disorder.

Growth transitions from avalanche-like to smooth Laplacian fractals.

A relation between fractal dimension and material disorder properties is established.

Abstract

We analyze the combined effect of a Laplacian field and quenched disorder for the generation of fractal structures with a study, both numerical and theoretical, of the quenched dielectric breakdown model (QDBM). The growth dynamics is shown to evolve from the avalanches of invasion percolation (IP) to the smooth growth of Laplacian fractals, i. e. diffusion limited aggregation (DLA) and the dielectric breakdown model (DBM). The fractal dimension is strongly reduced with respect to both DBM and IP, due to the combined effect of memory and field screening. This implies a specific relation between the fractal dimension of the breakdown structures (dielectric or mechanical) and the microscopic properties of disordered materials.