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Fixed scale transformation applied to cluster-cluster aggregation in two and three dimensions

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  • Sidoretti, S.
  • Vespignani, A.

Abstract

Recently it has been introduced a new theoretical framework named fixed scale transformation (FST), which appears particularly suitable to study the growth of fractal structures. This method allows the first analytical study of the process of cluster-cluster aggregation (CCA). The FST approach can in fact be generalized in a natural and relatively simple way to the case of CCA. Here we present detailed results for teh analytical calculation of the fractal dimension of the aggregates. For CCA in two dimensions the computed value is D = 1.39 and in three dimensions is D = 1.9, to be compared with the simulation results that are respectively D = 1.45 and D = 1.9. Furthermore the approximation scheme of the FST can be implemented in a systematic way to estimate quantitatively higher order corrections and to study variation of the original model. This application is of particular relevance because CCA has eluded all the standard theoretical approach and in particular it cannot even be formulated from the point of view of renormalization group methods.

Suggested Citation

  • Sidoretti, S. & Vespignani, A., 1992. "Fixed scale transformation applied to cluster-cluster aggregation in two and three dimensions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 185(1), pages 202-210.
    • Handle: RePEc:eee:phsmap:v:185:y:1992:i:1:p:202-210
    DOI: 10.1016/0378-4371(92)90457-2
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    1. Kinsey, Jean, 1985. "Farm Family Financial Stress: Impact on Consumers," Working Papers 257281, University of Minnesota, The Food Industry Center.
    2. Pietronero, L. & Erzan, A. & Evertsz, C., 1988. "Theory of Laplacian fractals: Diffusion limited aggregation and dielectric breakdown model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 151(2), pages 207-245.
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