TY - JOUR

T1 - Scaling structure of the growth-probability distribution in diffusion-limited aggregation processes

AU - Hayakawa, Y.

AU - Sato, S.

AU - Matsushita, M.

PY - 1987/1/1

Y1 - 1987/1/1

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevA.36.1963

DO - 10.1103/PhysRevA.36.1963

M3 - Article

AN - SCOPUS:0000067645

VL - 36

SP - 1963

EP - 1966

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 4

ER -