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Full-Text Articles in Physics
The Fixed-Scale Transformation Approach To Fractal Growth, A Erzan, L Pietronero, A Vespignani
The Fixed-Scale Transformation Approach To Fractal Growth, A Erzan, L Pietronero, A Vespignani
Alessandro Vespignani
Irreversible fractal-growth models like diffusion-limited aggregation (DLA) and the dielectric breakdown model (DBM) have confronted us with theoretical problems of a new type for which standard concepts like field theory and renormalization group do not seem to be suitable. The fixed-scale transformation (FST) is a theoretical scheme of a novel type that can deal with such problems in a reasonably systematic way. The main idea is to focus on the irreversible dynamics at a given scale and to compute accurately the nearest-neighbor correlations at this scale by suitable lattice path integrals. The next basic step is to identify the scale-invariant …
Monte Carlo Fixed Scale Transformation For Nonlocal Fractal Growth Models, M Piccioni, R Cafiero, A Vespignani
Monte Carlo Fixed Scale Transformation For Nonlocal Fractal Growth Models, M Piccioni, R Cafiero, A Vespignani
Alessandro Vespignani
The fixed scale transformation (FST) is a theoretical framework developed for the evaluation of scaling dimensions in a vast class of complex systems showing fractal geometric correlations. For models with long range interactions, such as Laplacian growth models, the identification by analytical methods of the transformation's basic elements is a very difficult task. Here we present a Monte Carlo renormalization approach which allows the direct numerical evaluation of the FST transfer matrix, overcoming the usual problems of analytical and numerical treatments. The scheme is explicitly applied to the diffusion limited aggregation case where a scale invariant regime is identified and …