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• W2023913449 abstract "Diffusion-controlled cluster formation has been simulated on lattices of dimensionality 2-6. For the case of a sticking probability of 1.0 at nearest-neighbor sites, we find that the radius of gyration (${R}_{g}$) of the cluster is related to the number of particles ($N$) by ${R}_{g}ensuremath{sim}{N}^{ensuremath{beta}}$ (for large $N$). The exponent $ensuremath{beta}$ is given by $frac{ensuremath{beta}ensuremath{sim}6}{5d}$, where $d$ is the classical (Euclidean) dimensionality of the lattice. These results indicate that the Hausdorff (fractal) dimensionality ($D$) is related to the Euclidean dimensionality ($d$) by $Densuremath{approx}frac{5d}{6}$ ($d=2ensuremath{-}6$). Similar results can be obtained from the density-density correlation function in two-dimensional simulations. Nonlattice simulations have also been carried out in two- and three-dimensional space. The radius-of-gyration exponents ($ensuremath{beta}$) obtained from these simulations are essentially equal to those obtained in the lattice model simulations. We have also investigated the effects of sticking probabilities ($S$) less than 1.0 on diffusion-limited cluster formation on two- and three-dimensional lattices. While smaller sticking probabilities do lead to the formation of denser clusters, the radius-of-gyration exponents are insensitive to sticking coefficients over the range $0.1ensuremath{le}Sensuremath{le}1.0$." @default.
• W2023913449 created "2016-06-24" @default.
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• W2023913449 date "1983-03-01" @default.
• W2023913449 modified "2023-10-11" @default.
• W2023913449 title "Diffusion-controlled cluster formation in 2—6-dimensional space" @default.
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• W2023913449 doi "https://doi.org/10.1103/physreva.27.1495" @default.
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