Abstract
The Fixed Scale Transformation (FST)1 is a new theoretical method that appears particularly suitable for irreversible growth models like Diffusion Limited Aggregation (DLA)2 and the Dielectric Breakdown Model (DBM).3 The FST exploits an additional invariance property than the Renormalization Group. The idea is that the structure is invariant both with respect to scale transformation and with respect to the dynamical evolution at the same scale. The FST is related to the second type of invariance and it appears more convenient for problems of irreversible growth. It is defined with respect to the dynamical growth process at the same scale and then the corresponding fixed point is used at all scales, so that the FST approach should be combined with a scale invariance analysis of the growth process.4 Originally the FST method has been applied to DLA and DBM in two dimensions.1 It has also been applied to the percolating cluster and to invasion percolation obtaining results for the fractal dimension that are within one percent from the exact results.5
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References
L. Pietronero, A. Erzan and C. Evertsz, Phys. Rev. Lett. 61, 861 (1988); for a detailed description see Physica A 151, 207 (1988).
T. A. Witten and L. M. Sander, Phys. Rev. Lett. 47, 1400 (1981).
L. Niemeyer, L. Pietronero and H. J. Wiesmann, Phys. Rev. Lett. 52, 1033 (1984).
R. De Angelis, M. Marsili, L. Pietronero and A. Vespignani, preprint.
L. Pietronero, W. R. Schneider and A. Stella, Phys. Rev. Lett., submitted.
A. Vespignani and L. Pietronero, Physica A, submitted.
S. Tolman and P. Meakin, Physica A 158, 801 (1989).
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© 1990 Kluwer Academic Publishers
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Vespignani, A., Pietronero, L. (1990). Fixed Scale Transformation Approach to Fractal Growth in Three Dimensions. In: Stanley, H.E., Ostrowsky, N. (eds) Correlations and Connectivity. NATO ASI Series, vol 188. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2157-3_32
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DOI: https://doi.org/10.1007/978-94-009-2157-3_32
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