Morphological transition between diffusion-limited and ballistic aggregation growth patterns

In this work, the transition between diffusion-limited (DLA) and ballistic aggregation (BA) models was reconsidered using a model in which biased random walks simulate the particle trajectories. The bias is controlled by a parameter lambda, which assumes the value lambda = 0 (1) for the ballistic (diffusion-limited) aggregation model. Patterns growing from a single seed were considered. In order to simulate large clusters, an efficient algorithm was developed. For lambda not equal 0, the patterns are fractal on small length scales, but homogeneous on large ones. We evaluated the mean density of particles p in the region defined by a circle of radius r centered at the initial seed. As a function of r, r reaches the asymptotic value p(0) (lambda) following a power law p = p(0) + Ar-gamma with a universal exponent gamma = 0.46(2), independent of lambda. The asymptotic value has the behavior p(0) similar to vertical bar 1-lambda vertical bar(beta), where beta = 0.26(1). The characteristic crossover length that determines the transition from DLA- to BA- like scaling regimes is given by xi similar to vertical bar 1-lambda vertical bar(-v), where v=0.61(1), while the cluster mass at the crossover follows a power law M xi similar to vertical bar 1- lambda vertical bar(-a), where alpha=0.97(2). We deduce the scaling relations beta=v gamma and beta=2v-alpha between these exponents.