Dimensions, maximal growth sites, and optimization in the dielectric breakdown model.
We study the growth of fractal clusters in the dielectric breakdown model (DBM) by means of iterated conformal mappings. In particular we investigate the fractal dimension and the maximal growth site (measured by the Hoelder exponent alpha_{min} ) as a function of the growth exponent eta of the DBM model. We do not find evidence for a phase transition from fractal to nonfractal growth for a finite eta value. Simultaneously, we observe that the limit of nonfractal growth (D-->1) is consistent with alpha_{min}-->12 . Finally, using an optimization principle, we give a recipe on how to estimate the effective value of eta from temporal growth data of fractal aggregates.
Mathiesen
Joachim
J
Physics of Geological Processes, University of Oslo, P.O. 1048 Oslo, Norway. joachim.mathiesen@fys.uio.no
Jensen
Mogens H
MH
Bakke
Jan Oystein Haavig
JO