Causality bound on the density of aggregates
- 1 May 1984
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 29 (5), 2966-2967
- https://doi.org/10.1103/physreva.29.2966
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 .
Keywords
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