Structure of the active zone in diffusion-limited aggregation, cluster-cluster aggregation, and the screened-growth model

The structure of the active zone has been explored for several nonequilibrium-growth models (the Witten-Sander model for diffusion-limited aggregation, the screened-growth model, and the cluster-cluster aggregation model). In all of these models the structure of the active zone (spatial distribution of growth probability) can be characterized by fractal dimensionality (or dimensionalities) which is not related in any obvious way to the fractal dimensionality of the nonequilibrium structure itself. In the case of diffusion-limited aggregation the active zone has a fractal dimensionality close to 1.0 in accord with the theoretical results of Grassberger. The distribution of growth probabilities was also investigated for some of these models. Our results indicate that this distribution is a power law with a cutoff at high growth probabilities.