Laplacian Fractal Growth in Media with Quenched Disorder

Details Laplacian Fractal Growth in Media with Quenched Disorder Laplacian Fractal Growth in Media with Quenched Disorder

1997-02-19

arxiv.org/abs/cond-mat/9702174v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

11 pages Latex (revtex), 3 postscript figures included. Submitted to PRL

Scientific paper

10.1103/PhysRevLett.79.1503

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.

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