Fractal growth from local instabilities

Cafiero, Raffaele and Caldarelli, Guido Fractal growth from local instabilities. EPL (Europhysics Letters), 54 (2). pp. 187-193. ISSN 0295-5075 (2001)

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Abstract

We study, both with numerical simulations and theoretical methods, a cellular automata model for surface growth in the presence of a local instability, driven by an external flux of particles. The growing tip is selected with probability proportional to the local curvature. A probability p of developing overhangs through lateral growth is also introduced. For small external fluxes, we find a fractal regime of growth. The value of p determines the fractal dimension of the aggregate. Furthermore, for each value of p a crossover between two different fractal dimensions is observed. The roughness exponent χ of the aggregates, instead, does not depend on p (χ simeq 0.5). A Fixed Scale Transformation (FST) approach is applied to compute theoretically the fractal dimension for one of the branches of the structure.

Item Type: Article 10.1209/epl/i2001-00294-2 PACS: 68.35.Ja Surface and interface dynamics and vibrations; 61.43.Hv Fractals; macroscopic aggregates (including diffusion-limited aggregates) Q Science > QC PhysicsQ Science > QD Chemistry Economics and Institutional Change Ms T. Iannizzi 22 Feb 2012 10:36 20 Nov 2013 14:15 http://eprints.imtlucca.it/id/eprint/1144