No Access

PERCOLATION PROPERTIES AND UNIVERSALITY CLASS OF A MULTIFRACTAL RANDOM TILING

International Center for Complex Systems and Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Campus Universitário 59078 970, Natal, RN, Brazil

Search for more papers by this author

G. CORSO

International Center for Complex Systems and Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Campus Universitário 59078 970, Natal, RN, Brazil

Departamento de Biofísica, Centro de Biociências, Universidade Federal do Rio Grande do Norte, Campus Universitário 59072 970, Natal, RN, Brazil

Search for more papers by this author

L. S. LUCENA

International Center for Complex Systems and Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Campus Universitário 59078 970, Natal, RN, Brazil

Search for more papers by this author

, and

J. E. FREITAS

International Center for Complex Systems and Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Campus Universitário 59078 970, Natal, RN, Brazil

Search for more papers by this author

https://doi.org/10.1142/S0129183105007121Cited by:2 (Source: Crossref)

Abstract

We study percolation as a critical phenomenon on a random multifractal support. The scaling exponent β related to the mass of the infinite cluster and the fractal dimension of the percolating cluster d_f are quantities that have the same value as the ones from the standard two-dimensional regular lattice percolation. The scaling exponent ν related to the correlation length is sensitive to the local anisotropy and assumes a value different from standard percolation. We compare our results with those obtained from the percolation on a deterministic multifractal support. The analysis of ν indicates that the deterministic multifractal is more anisotropic than the random multifractal. We also analyze connections with correlated percolation problems and discuss some possible applications.

Keywords:

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

G. Corsoet al., Phys. Rev. E 69, 066135 (2004), cond-mat/0212530. Web of Science, Google Scholar
L. S. Lucenaet al., Brazilian J. Phys. 33, 637 (2003). Web of Science, ADS, Google Scholar
J. E. Freitas, G. Corso and L. S. Lucena, cond-mat/0310779 (2003) . Google Scholar
M. G. Pereiraet al., Chaos, Solitons and Fractals 23, 1105 (2005), cond-mat/0402372. Web of Science, ADS, Google Scholar
P. Meakin , Fractals, Scaling and Growth Far from Equilibrium ( Cambridge University Press , Cambridge, UK , 1998 ) . Google Scholar
J. Muller, Ann. Geophys. Atmospheres Hydrospheres and Space Sciences 11, 525 (1993). Google Scholar
P. N. Khueet al., J. Phys. Condensed Matter 14, 2347 (2002). Web of Science, ADS, Google Scholar
R. H. Riedi, Multifractals and wavelets: a potential tool in geophysics, Proc. 68th SEG Meeting, New Orleans, Louisiana, USA (1998) . Google Scholar
P. Hubert, Hydrological Sci. J. 46, 897 (2001). Web of Science, Google Scholar
F. Herrmann, A scaling medium representation, a discussion on well-logs, fractals and waves, PhD. thesis, Delft University of Technology (1997) . Google Scholar
S. Sachs, S. Lovejoy and D. Schertzer, Fractals 10, 253 (2002). Link, Web of Science, Google Scholar
J. E. de Freitas, L. S. Lucena and S. Roux, Physica A 266, 81 (1999). Web of Science, ADS, Google Scholar
M. E. J. Newman and R. M. Ziff, Phys. Rev. Lett. 85, 4104 (2000). Web of Science, ADS, Google Scholar
J. E. de Freitas and L. S. Lucena, Int. J. Mod. Phys. C 11, 1581 (2000). Link, Web of Science, ADS, Google Scholar
J. E. de Freitas, L. S. Lucena and S. Roux, Phys. Rev. E 64, 051405 (2001). Web of Science, Google Scholar
D. Stauffer and A. Aharony , Introduction to Percolation Theory ( Taylor & Francis , London , 1994 ) . Google Scholar
A. Coniglio, H. E. Stanley and W. Klein, Phys. Rev. Lett. 42, 518 (1979). Web of Science, ADS, Google Scholar
D. He, N. N. Ekere and L. Cai, Phys. Rev. E 65, 061304 (2002). Web of Science, Google Scholar
H. A. Makseet al., Phys. Rev. E 54, 3129 (1996). Web of Science, ADS, Google Scholar
A. Hansen and J. Schmittbuhl, Phys. Rev. Lett. 90, 045504 (2003). Web of Science, Google Scholar
S. Rouxet al., J. Stat. Phys. 52, 237 (1988). Web of Science, ADS, Google Scholar
L. S. Lucenaet al., Phys. Rev. Lett. 72, 230 (1994). Web of Science, ADS, Google Scholar
Z. J. Tanet al., Phys. Rev. E 65, 057201 (2002). Web of Science, Google Scholar
H. A. Makse, S. Havlin and H. E. Stanley, Nature 377, 608 (1966). Web of Science, ADS, Google Scholar
H. Makseet al., Phys. Rev. E 58, 7054 (1998). Web of Science, ADS, Google Scholar