Volume 54, Number 2, April 2001
|Page(s)||187 - 193|
|Section||Condensed matter: structural, mechanical and thermal properties|
|Published online||01 December 2003|
Fractal growth from local instabilities
PMMH Ecole Supérieure de Physique et de Chimie
Industrielles (ESPCI) 10, rue Vauquelin - 75231
Paris Cedex 05, France
2 Sezione INFM di Roma1 and Dipartimento di Fisica, Università “La Sapienza” P.le A. Moro 2, 00185 Roma, Italy
Accepted: 6 February 2001
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 (). A Fixed Scale Transformation (FST) approach is applied to compute theoretically the fractal dimension for one of the branches of the structure.
PACS: 61.43.Hv – Fractals; macroscopic aggregates (including diffusion-limited aggregates) / 68.35.Ja – Surface and interface dynamics and vibrations
© EDP Sciences, 2001
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