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Full-Text Articles in Physics
Parallel Diffusion-Limited Aggregation, H Kaufman, A Vespignani, B B. Mandelbrot, L Woog
Parallel Diffusion-Limited Aggregation, H Kaufman, A Vespignani, B B. Mandelbrot, L Woog
Alessandro Vespignani
We present methods for simulating very large diffusion-limited aggregation (DLA) clusters using parallel processing (PDLA). With our techniques, we have been able to simulate clusters of up to 130 million particles. The time required for generating a 100 million particle PDLA is approximately 13 h. The fractal behavior of these ''parallel'' clusters changes from a multiparticle aggregation dynamics to the usual DLA dynamics. The transition is described by simple scaling assumptions that define a characteristic cluster size separating the two dynamical regimes. We also use DLA clusters as seeds for parallel processing. In this case, the transient regime disappears and …
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 …
Persistence Of Screening And Self-Criticality In The Scale-Invariant Dynamics Of Diffusion-Limited Aggregation, R Cafiero, L Pietronero, A Vespignani
Persistence Of Screening And Self-Criticality In The Scale-Invariant Dynamics Of Diffusion-Limited Aggregation, R Cafiero, L Pietronero, A Vespignani
Alessandro Vespignani
The origin of fractal properties in diffusion limited aggregation is related to the persistence of screening in the scale invariant growth regime. This effect is described by the effective noise reduction parameter S spontaneously generated by the scale invariant dynamics. The renormalization of this parameter under scale transformation shows the following: (i) The fixed point is attractive, implying the self-critical nature of the process. (ii) The fixed point value S* is of the order of unity, showing that the small scale growth rules are already close to the scale invariant ones and that screening effects persist in the asymptotic regime.