eprintid: 1170
rev_number: 7
eprint_status: archive
userid: 6
dir: disk0/00/00/11/70
datestamp: 2012-02-24 12:07:20
lastmod: 2013-11-20 13:28:33
status_changed: 2012-02-24 12:07:20
type: article
metadata_visibility: show
creators_name: Gabrielli, Andrea
creators_name: Cafiero, Raffaele
creators_name: Caldarelli, Guido
creators_id: 
creators_id: 
creators_id: guido.caldarelli@imtlucca.it
title: Theory of boundary effects in invasion percolation
ispublished: pub
subjects: QC
divisions: EIC
full_text_status: none
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
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. 
date: 1999-05
date_type: published
publication: Journal of Physics A: Mathematical and General
volume: 31
number: 37
publisher: IOPscience
pagerange: 7429-7446
id_number: 10.1088/0305-4470/31/37/006
refereed: TRUE
issn: 0305-4470
official_url: http://dx.doi.org/10.1088/0305-4470/31/37/006
related_url_url: http://arxiv.org/abs/cond-mat/9807372
citation:   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)