Gabrielli, Andrea and Cafiero, Raffaele and Caldarelli, Guido
*Theory of boundary effects in invasion percolation.*
Journal of Physics A: Mathematical and General, 31 (37).
pp. 7429-7446.
ISSN 0305-4470
(1999)

## Abstract

We study the boundary effects in invasion percolation (IP) with and without trapping. We find that the presence of boundaries introduces a new set of surface critical exponents, as in the case of standard percolation. Numerical simulations show a fractal dimension, for the region of the percolating cluster near the boundary, remarkably different from the bulk one. In fact, on the surface we find a value of (for IP with trapping ), compared with the bulk value of . We find a logarithmic crossover from surface to bulk fractal properties, as one would expect from the finite-size theory of critical systems. The distribution of the quenched variables on the growing interface near the boundary self-organizes into an asymptotic shape characterized by a discontinuity at a value , which coincides with the bulk critical threshold. The exponent of the boundary avalanche distribution for IP without trapping is ; this value is very near to the bulk one. Then we conclude that only the geometrical properties (fractal dimension) of the model are affected by the presence of a boundary, while other statistical and dynamical properties are unchanged. Furthermore, we are able to present a theoretical computation of the relevant critical exponents near the boundary. This analysis combines two recently introduced theoretical tools, the fixed scale transformation and the run time statistics, which are particularly suited for the study of irreversible self-organized growth models with quenched disorder. Our theoretical results are in rather good agreement with numerical data.

Item Type: | Article |
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Identification Number: | 10.1088/0305-4470/31/37/006 |

Uncontrolled Keywords: | PACS: 64.60.A- Specific approaches applied to studies of phase transitions; 64.60.F- Equilibrium properties near critical points, critical exponents; 05.45.Df Fractals |

Subjects: | Q Science > QC Physics |

Research Area: | Economics and Institutional Change |

Depositing User: | Ms T. Iannizzi |

Date Deposited: | 24 Feb 2012 12:07 |

Last Modified: | 20 Nov 2013 13:28 |

URI: | http://eprints.imtlucca.it/id/eprint/1170 |

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