Phys. Rev. E 77, 066203 (2008) [5 pages]Dimensions, maximal growth sites, and optimization in the dielectric breakdown modelReceived 10 December 2007; revised 4 April 2008; published 5 June 2008 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 αmin) as a function of the growth exponent η of the DBM model. We do not find evidence for a phase transition from fractal to nonfractal growth for a finite η value. Simultaneously, we observe that the limit of nonfractal growth (D→1) is consistent with αmin→1∕2. Finally, using an optimization principle, we give a recipe on how to estimate the effective value of η from temporal growth data of fractal aggregates. © 2008 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.77.066203
DOI:
10.1103/PhysRevE.77.066203
PACS:
05.45.Df, 61.43.Hv, 05.70.Fh
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