Fractal-to-Compact Transition and Velocity Selection in Aggregation from Lattice Gas

Velocity selection has been studied for aggregate growth from a lattice gas, which interpolates between the diffusion-limited aggregation (DLA) and the Eden model. At a low gas density n g , the aggregate is fractal and similar to the DLA up to a length ξ, beyond which it becomes compact and uniform. The growth rate V is expected to follow as V ∼ξ -1 ∼ n g 1/( d - D f ) , where D f =1.71, being the fractal dimension of the DLA. The above theoretical hypothesis is confirmed by Monte Carlo simulations.