Abstract
The irreversible accretion of diffusing particles onto a large cluster results in a tenuous aggregate characterized by a fractal dimension smaller than that of space. The rate of aggregation onto the fastest-growing sites in such a process must not increase indefinitely as the cluster grows. This fact sets a lower limit on the fractal dimension, viz., the dimension of space minus 1. For aggregation of ballistically moving particles, this bound implies that the aggregate must be compact: The fractal dimension must equal that of space. In general, if the aggregating particles follow trajectories of fractal dimension , the bound implies .
- Received 2 January 1984
DOI:https://doi.org/10.1103/PhysRevA.29.2966
©1984 American Physical Society