Off-lattice noise reduced diffusion-limited aggregation in three dimensions.
Using off-lattice noise reduction, it is possible to estimate the asymptotic properties of diffusion-limited aggregation clusters grown in three dimensions with greater accuracy than would otherwise be possible. The fractal dimension of these aggregates is found to be 2.50+/-0.01 , in agreement with earlier studies, and the asymptotic value of the relative penetration depth is xi/ R(dep) =0.122+/-0.002 . The multipole powers of the growth measure also exhibit universal asymptotes. The fixed point noise reduction is estimated to be epsilon(f) approximately 0.0035 , meaning that large clusters can be identified with a low noise regime. The slowest correction to scaling exponents are measured for a number of properties of the clusters, and the exponent for the relative penetration depth and quadrupole moment are found to be significantly different from each other. The relative penetration depth exhibits the slowest correction to scaling of all quantities, which is consistent with a theoretical result derived in two dimensions. We also note fast corrections to scaling, whose limited relevance is consistent with the requirement that clusters grow far enough in radius to support sufficient scales of ramification.
Bowler
Neill E
NE
Met Office, Fitzroy Road, Exeter, EX1 3PB, United Kingdom. Neill.Bowler@metoffice.gov.uk
Ball
Robin C
RC