Scaling structure of the growth-probability distribution in diffusion-limited aggregation processes

Y. Hayakawa, S. Sato, M. Matsushita

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    84 Citations (Scopus)


    In nonequilibrium growth such as diffusion-limited aggregation (DLA), the growth-site probability distribution characterizes these growth processes. By solving the Laplace equation numerically, we calculate the growth probability Pg(x) at the perimeter site x of clusters for the DLA and its generalized version called the model, and obtain the generalized dimension D(q) and the f spectrum proposed by Halsey et al. [Phys. Rev. A 33, 1141 (1986)]. It is found that D(q) depends strongly on q and that the f spectrum is continuous. Our results suggest that these growth processes cannot be described by a simple scaling theory with a few scaling exponents. This is in clear contrast to the Botet-Jullien model [Phys. Rev. Lett. 55, 1943 (1985)] which yields equilibrium patterns whose D(q) is constant. It is also found that the information dimension D(1) which represents the properties of the unscreened surface is in good agreement with our recent theory.

    Original languageEnglish
    Pages (from-to)1963-1966
    Number of pages4
    JournalPhysical Review A
    Issue number4
    Publication statusPublished - 1987 Jan 1

    ASJC Scopus subject areas

    • Atomic and Molecular Physics, and Optics


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