Dimensions, Maximal Growth Sites and Optimization in the Dielectric Breakdown Model

Details Dimensions, Maximal Growth Sites and Optimization in the Dielectric Breakdown Model Dimensions, Maximal Growth Sites and Optimization in the Dielectric Breakdown Model

2007-12-11

arxiv.org/abs/0712.1739v2

Physics

Condensed Matter

Statistical Mechanics

5 pages, 7 figures; v2: extra figures and new data added

Scientific paper

10.1103/PhysRevE.77.066203

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 non-fractal growth for a finite $\eta$-value. Simultaneously, we observe that the limit of non-fractal growth ($D\to 1$) is consistent with $\alpha_{min} \to 1/2$. 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.

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