| Issue |
Europhys. Lett.
Volume 54, Number 2, April 2001
|
|
|---|---|---|
| Page(s) | 187 - 193 | |
| Section | Condensed matter: structural, mechanical and thermal properties | |
| DOI | https://doi.org/10.1209/epl/i2001-00294-2 | |
| Published online | 01 December 2003 | |
Fractal growth from local instabilities
1
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
Received:
2
August
2000
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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