Abstract
Diffusion-controlled cluster formation has been simulated in two-, three-, and four- dimensional space. The radii of gyration () of the resulting clusters have a power-law dependence on the number of particles in the cluster . The corresponding Hausdorff dimensionality () is related to the Euclidean dimensionality by the relationship for and 4. For the two-dimensional case we find that has a value about 2% smaller (0.847 ± 0.01). However, a value of (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 () over the range .
- Received 21 June 1982
DOI:https://doi.org/10.1103/PhysRevA.27.604
©1983 American Physical Society