Abstract
Viscous fingering in porous media is considered as the diffusion-limited aggregation (DLA) on the percolating cluster. The crossover between percolation and DLA is studied by using a three-parameter position-space renormalization-group approach. The global flow diagram in the two-parameter space is obtained. It is found that there are two nontrivial fixed points, the percolation point and the DLA point. Above the percolation threshold, the system crosses eventually over to the DLA fractal on the perfect lattice. The fractal nature and the multifractal structure of the growth probability distribution are derived from the position-space renormalization-group method. The multifractal structure at the percolation threshold is compared with that at the perfect lattice.
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