Laplacian growth phenomena with the third boundary condition: Crossover from dense structure to diffusion-limited aggregation fractal

Transition in the fractal properties from diffusion-limited aggregation to Laplacian growth via their generalization.

We study the fractal and multifractal properties (i.e., the generalized dimensions of the harmonic measure) of a two-parameter family of growth patterns that result from a growth model that interpolates between diffusion-limited aggregation (DLA) and Laplacian growth patterns in two dimensions. The two parameters are beta that determines the size of particles accreted to the interface, and C th...

Laplacian growth and diffusion limited aggregation: different universality classes.

It had been conjectured that diffusion limited aggregates and Laplacian growth patterns (with small surface tension) are in the same universality class. Using iterated conformal maps we construct a one-parameter family of fractal growth patterns with a continuously varying fractal dimension. This family can be used to bound the dimension of Laplacian growth patterns from below. The bound value ...

Crossover from nonequilibrium fractal growth to equilibrium compact growth.

Radial viscous fingers and diffusion-limited aggregation: Fractal dimension and growth sites.

We show that fractal viscous fingers can be formed in a Hele-Shaw cell with radial symmetry, thereby permitting their study —for the first time —without the complicating effects of boundary conditions such as those present in the conventional linear cell. We find —for a wide range of shear-thinning fluids, flow rates, and plate separations —that radial viscous fingers have a fractal dimension d...

Fractal Aggregation Growth and the Surrounding Diffusion Field

Silver metal trees grow and form a forest at the edge of a Cu plate in the AgNO3 water solution in a two dimensional(d = 2) cell. The local structure of the forest is similar to that of the diffusion-limited aggregation (DLA), but the whole pattern approaches a uniform structure. Its growth dynamics is characterized by the fractal dimension Df of DLA. Time-dependence of the tip height is found ...