Fluctuations and distributions in random aggregates

We have measured the distribution of mass $P_s$(r) within a distance r measured from occupied sites in the screened-growth model ($d_f$=1.25, 1.5, and 1.75, where $d_f$ is the fractal dimension), off-lattice diffusion-limited cluster-cluster aggregates ($d_f$=1.43), and off-lattice diffusion-limited aggregation (DLA) clusters. Here $P_s$(r) is the probability that a circle of radius r centered on an occupied site will contain S occupied sites or particles. For the screened-growth and cluster-cluster aggregation models, the distributions $P_s$(r) can be described in terms of the scaling &). The dependence of the moments 〈$S^n$〉/〈S${〉}^n$ on the distance r has also been measured. For the screened-growth and cluster-cluster aggregation models these quantities are essentially independent of r for n≥1. For DLA the simple scaling form for $P_s$(r) does not describe the mass distribution and (1/n)ln(〈$S^n$〉/〈S${〉}^n$), with n=2–10, has a linear dependence on ln(r) with negative slopes which are different for different values of n for small values of r. Since 〈$S^n$〉/〈S${〉}^n$ has a lower bound of 1, this cannot be the true asymptotic behavior for off-lattice DLA. It suggests that DLA has a more complex structure than either the screened-growth model or cluster-cluster aggregation.