Regensburg 2002 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 23: Brownsche Bewegung

DY 23.2: Vortrag

Dienstag, 12. März 2002, 12:00–12:15, H3

Phase transition in the Fractal Spectrum of Diffusion Limited Aggregation — •Anders Levermann¹, Joachim Mathiesen², Mogens H. Jensen² und Itamar Procaccia¹ — ¹Weizmann Institute of Science, Rehovot, Israel — ²Niels Bohr Institute, Copenhagen, Denmark

We study the nature of the phase transition in the multifractal formalism of the harmonic measure of Diffusion Limited Aggregates (DLA). Contrary to previous work that relied on random walk simulations or ad-hoc models to estimate the low probability events of deep fjord penetration, we employ the method of iterated conformal maps to obtain an accurate computation of the probability of the rarest events. We resolve probabilities as small as 10⁻³⁵. We show that the generalized dimensions D_q are infinite for q<q^*, where q^*= −0.2± 0.05. In the language of f(α) this means that α_max is finite. We present a converged f(α) curve. We consider the geometric structure of the regions that support the lowest parts of the harmonic measure, and thus offer an explanation for the phase transition, rationalizing the value of q^* and f(α_max). We thus offer a satisfactory physical picture of the scaling properties of this multifractal measure. [1] Phys. Rev. Lett. 87, (2001), p. 164101 [2] cond-mat/0110203