Abstract
We show that aggregation processes naturally evolve into self-organized critical states. The associated critical exponents provide a new characterization of fractal growth. We consider diffusion-limited aggregation (DLA) and compare our description with that based on the f(α) spectrum. We find that a critical value α c of a exists, above which the spectrum fails to characterize the growth, and below which only a spiky part of the aggregate is described. For DLA, α c = 1.
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References
P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987).
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See, e.g., Time-Dependent Effects in Disordered Materials, eds. R. Pynn and T. Riste (Plenum, New York, 1987).
See, e.g., T. E. Harris, The Theory of Branching Processes (Springer, Berlin, 1963), p. 32.
T. C. Halsey, P. Meakin, and I. Procaccia, Phys. Rev. Lett. 56, 854 (1986), and references therein.
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© 1988 Kluwer Academic Publishers
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Alstrøm, P., Trunfio, P., Stanley, H.E. (1988). Self-Organized Criticality: The Origin of Fractal Growth. In: Stanley, H.E., Ostrowsky, N. (eds) Random Fluctuations and Pattern Growth: Experiments and Models. NATO ASI Series, vol 157. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2653-0_49
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DOI: https://doi.org/10.1007/978-94-009-2653-0_49
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-0073-1
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