Abstract
Kinetic fractal aggregation in a particle bath where a fractionf of the sites are initially occupied is studied withd=2 computer simulations. Independent particles diffusing to a fixed cluster produce an aggregate with fractal dimensionD≅ 1.7 up to a correlation lengthξ(f). At larger lengthsD→2.ξ(f) → ∞ asf → 0. When the particles remain fixed but the cluster undergoes a rigid random walkD appears constant at larger scales but varies withf. D → 1.95 at largef andD → 1.7 asf → 0. In both cases, the aggregate sizeN(t) grows with timet γ(f) . Aggregation on a surface by independently diffusing particles produces shapes reminiscent of electrochemical dendritic growth. The dependence of growth rate and geometry is studied as a function of particle concentration and sticking probability.
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References
S. R. Forrest and T. A. Witten,J. Phys. A 12:L109 (1979).
B. B. Mandelbrot,The Fractal Geometry of Nature (Freeman, New York, 1982).
T. A. Witten and L. M. Sander,Phys. Rev. Lett. 47:1400 (1981);Phys. Rev. B 27:5686 (1983).
P. Meakin,Phys. Rev. A 27:604 (1983).
R. F. Voss,Bull. Am. Phys. Soc. 28:487 (1983);Phys. Rev. B 30:334 (1984).
M. Muthukumar,Phys. Rev. Lett. 50:839 (1983).
R. Ball, M. Nauenberg, and T. Witten, NSF ITP preprint.
M. Nauenberg,Phys. Rev. B 28:449 (1983).
M. Nauenberg, R. Richter, and L. M. Sander,Phys. Rev. B 28:449 (1983).
H. Gould, F. Family, and H. E. Stanley,Phys. Rev. Lett. 50:686 (1983).
D. Stauffer,Phys. Rep. 54:1 (1979).
R. F. Voss, R. B. Laibowitz, and E. I. AlesandriniPhys. Rev. Lett. 49:1441 (1982).
J. M. Deutch and P. Meakin,J. Chem. Phys. 78:2093 (1983).
J. O'M. Bockris and G. A. Razumney,Fundamental Aspects of Electrocrystallization (Plenum Press, New York, 1967).
M. Tomkiewicz and R. F. Voss, to be published.
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Voss, R.F. Multiparticle fractal aggregation. J Stat Phys 36, 861–872 (1984). https://doi.org/10.1007/BF01012945
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DOI: https://doi.org/10.1007/BF01012945