Diffusion-controlled cluster formation in two, three, and four dimensions

Diffusion-controlled cluster formation has been simulated in two-, three-, and four- dimensional space. The radii of gyration (R₆) of the resulting clusters have a power-law dependence on the number of particles in the cluster (N) R₆=N^. The corresponding Hausdorff dimensionality (D=1) is related to the Euclidean dimensionality d by the relationship D56d for d=3 and 4. For the two-dimensional case we find that Dd has a value about 2% smaller (0. 847 0. 01). However, a value of 56 (0. 833) is only just outside the 95% confidence limits and cannot be completely ruled out. In the two-dimensional simulations is insensitive to lattice details and in both two- and three-dimensional simulations is insensitive to the sticking coefficient (S) over the range 1. 00. 1.