eprintid: 1177
rev_number: 9
eprint_status: archive
userid: 6
dir: disk0/00/00/11/77
datestamp: 2012-02-24 13:19:35
lastmod: 2012-02-27 15:00:59
status_changed: 2012-02-24 13:19:35
type: article
metadata_visibility: show
creators_name: Cafiero, Raffaele
creators_name: Caldarelli, Guido
creators_name: Gabrielli, Andrea
creators_id: 
creators_id: guido.caldarelli@imtlucca.it
creators_id: 
title: Surface effects in invasion percolation
ispublished: pub
subjects: QC
divisions: EIC
full_text_status: none
keywords: PACS: 05.40.+j, 68.70.+w

abstract: Boundary effects for invasion percolation are introduced and discussed here. The presence of boundaries determines a set of critical exponents characteristic of the boundary. In this paper we present numerical simulations showing a remarkably different fractal dimension for the region of the percolating cluster near the boundary. In fact, near the surface we find a value of $D^{sur}=1.65\pm 0.02$,(for IP with trapping $D_{tr}^{sur}=1.59\pm 0.03$), compared with the bulk value of $D_{sur}=1.88\pm 0.02$ ($D_{tr}^{sur}=1.85\pm 0.02$). 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 $x_c=0.5$, which coincides with the bulk critical threshold. The exponent $\tau^{sur}$  of the boundary
avalanche distribution for IP without trapping is $\tau^{sur}=1.56\pm 0.05$; 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: 1997-08
date_type: published
publication: Physical Review E
volume: 56
number: 2
publisher: American Physical Society
pagerange: R1291-R1294
id_number: 10.1103/PhysRevE.56.R1291
refereed: TRUE
issn: 1539-3755
official_url: http://dx.doi.org/10.1103/PhysRevE.56.R1291
citation:   Cafiero, Raffaele and Caldarelli, Guido and Gabrielli, Andrea  Surface effects in invasion percolation.  Physical Review E, 56 (2).  R1291-R1294.  ISSN 1539-3755      (1997)