Transparency effects in cluster-cluster aggregation with linear trajectories

Two hierarchical models of cluster-cluster aggregation whose aggregates follow random linear trajectories with (model I) or without (model II) random impact parameter are investigated numerically. The difference of the fractal dimension D of the clusters as a function of space dimension d is attributed to transparency effects which are less important in model II. A simple argument is given which suggests that, in contrast with model I, model II should not have an upper critical dimension.