LAPLACIAN FRACTAL GROWTH IN MEDIA WITH QUENCHED DISORDER

We study the combined effect of a Laplacian field and quenched disorde r in the generation of fractal structures in the quenched dielectric b reakdown model. The growth dynamics is shown to evolve from the avalan ches of invasion percolation (IF) to the smooth growth of Laplacian fr actals, i.e., diffusion limited aggregation and the dielectric breakdo wn model (DBM). The fractal dimension is strongly reduced with respect to both the DBM and IF, due to the combined effect of memory and fiel d screening. This implies a specific relation between the fractal dime nsion of the breakdown structures and the microscopic properties of di sordered materials.