Directed percolation, the fixed scale transformation and the renormalization group (Q2771419)
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scientific article; zbMATH DE number 1705480
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Directed percolation, the fixed scale transformation and the renormalization group |
scientific article; zbMATH DE number 1705480 |
Statements
21 November 2002
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diffusion-limited aggregation
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fractal growth problem
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fractal dimension
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self-similar correlations
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random Cantor set
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self-organized criticality
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Directed percolation, the fixed scale transformation and the renormalization group (English)
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The paper gives a detailed description of a method -- the fixed scale transformation (FSC) -- which was elaborated and applied in the papers by \textit{L. Pietronero, A. Erzan} and \textit{C. Evertsz} [Physica A 151, 207-245 (1988; Zbl 0681.58047)] and \textit{A. Erzan, L. Pietronero} and \textit{A. Vespignani} [Rev. Mod. Phys. 67, 545-604 (1995)]. This novel method is designed to deal with such irreversible fractal-growth phenomena as diffusion-limited aggregation, dielectric breakdown, chemical instabilities. As an application of the FSC, the author determines the fractal dimension of the directed percolation cluster. Further development of the FSC on the base of the renormalization group approach is also performed in the paper.NEWLINENEWLINEFor the entire collection see [Zbl 0959.00018].
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