Abstract
We present a self-consistent picture of diffusion limited aggregation (DLA) growth based on the assumption that the probability density for the next particle to be attached within the distance to the center of the cluster is expressible in the scale-invariant form . It follows from this assumption that there is no multiscaling issue in DLA and there is only a single fractal dimension for all length scales. We check our assumption self-consistently by calculating the particle-density distribution with a measured function on an ensemble with 1000 clusters of particles each. We also show that a nontrivial multiscaling function can be obtained only when small clusters () are used to calculate . Hence, multiscaling is a finite-size effect and is not intrinsic to DLA.
- Received 11 September 2011
DOI:https://doi.org/10.1103/PhysRevLett.108.015501
© 2012 American Physical Society