Double-crossover phenomena in Laplacian growth: Effects of sticking probability and finite viscosity ratio

A combined effect of sticking probability and finite viscosity ratio is studied on the pattern formation in Laplacian growth. A renormalization-group theory is developed to study the crossover phenomena between the diffusion-limited aggregation (DLA) and nonfractal structure. A two-stage crossover phenomenon is analyzed by using a three-parameter position-space renormalization-group method. A global flow diagram in three-parameter space is obtained. It is found that there are three nontrivial fixed points, the first Eden point, the DLA point and the second Eden point. The second Eden point corresponding to the dense structure is stable in all directions, while the first Eden point and the DLA point are saddle points. When the sticking probability P is small and the viscosity ratio is finite, the aggregate must cross over from the dense structure, through the DLA fractal, finally to the dense aggregate.