Competing long-range bonds and site dilution in the one-dimensional bond-percolation problem
Autor(a) principal: | |
---|---|
Data de Publicação: | 2003 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Brazilian Journal of Physics |
Texto Completo: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332003000300032 |
Resumo: | The long-range bond-percolation problem, on a linear chain (d = 1), in the presence of diluted sites (with an occupancy probability p s for an active site) is studied by means of a Monte Carlo simulation. The occupancy probability for a bond between two active sites i and j, separated by a distance r ij is given by p ij = <img width=32 height=32 id="_x0000_i1026" src="../../img/revistas/bjp/v33n3/a32img01.gif" align=absbottom>, where p represents the usual occupancy probability between nearest-neighbor sites. This model allows one to analyse the competition between long-range bonds (which enhance percolation) and diluted sites (which weaken percolation). By varying the parameter a (a > 0), one may find a crossover between a nonextensive regime and an extensive regime; in particular, the cases a = 0 and a ® ¥ represent, respectively, two well-known limits, namely, the mean-field (infinite-range bonds) and first-neighbor-bond limits. The percolation order parameter, P¥, was investigated numerically for different values of a and p s. Two characteristic values of a were found, which depend on the site-occupancy probability p s, namely, a1(p s) and a2(p s) (a2(p s) > a1(p s) > 0). The parameter P¥ equals unit, "p > 0, for 0 < a < a1(p s) and vanishes, "p < 1, for a > a2(p s). In the interval a1(p s) < a < a2(p s), the parameter P¥ displays a familiar behavior, i.e., 0 for p < p c(a) and finite otherwise. It is shown that both a1(p s) and a2(p s) decrease with the inclusion of diluted sites. For a fixed p s, it is shown that a convenient variable, p* º p*(p, a, N), may be defined in such a way that plots of P¥ versus p* collapse for different sizes and values of a in the nonextensive regime. |
id |
SBF-2_2d5dd792afc1bdfed8f02007a025ebc3 |
---|---|
oai_identifier_str |
oai:scielo:S0103-97332003000300032 |
network_acronym_str |
SBF-2 |
network_name_str |
Brazilian Journal of Physics |
repository_id_str |
|
spelling |
Competing long-range bonds and site dilution in the one-dimensional bond-percolation problemThe long-range bond-percolation problem, on a linear chain (d = 1), in the presence of diluted sites (with an occupancy probability p s for an active site) is studied by means of a Monte Carlo simulation. The occupancy probability for a bond between two active sites i and j, separated by a distance r ij is given by p ij = <img width=32 height=32 id="_x0000_i1026" src="../../img/revistas/bjp/v33n3/a32img01.gif" align=absbottom>, where p represents the usual occupancy probability between nearest-neighbor sites. This model allows one to analyse the competition between long-range bonds (which enhance percolation) and diluted sites (which weaken percolation). By varying the parameter a (a > 0), one may find a crossover between a nonextensive regime and an extensive regime; in particular, the cases a = 0 and a ® ¥ represent, respectively, two well-known limits, namely, the mean-field (infinite-range bonds) and first-neighbor-bond limits. The percolation order parameter, P¥, was investigated numerically for different values of a and p s. Two characteristic values of a were found, which depend on the site-occupancy probability p s, namely, a1(p s) and a2(p s) (a2(p s) > a1(p s) > 0). The parameter P¥ equals unit, "p > 0, for 0 < a < a1(p s) and vanishes, "p < 1, for a > a2(p s). In the interval a1(p s) < a < a2(p s), the parameter P¥ displays a familiar behavior, i.e., 0 for p < p c(a) and finite otherwise. It is shown that both a1(p s) and a2(p s) decrease with the inclusion of diluted sites. For a fixed p s, it is shown that a convenient variable, p* º p*(p, a, N), may be defined in such a way that plots of P¥ versus p* collapse for different sizes and values of a in the nonextensive regime.Sociedade Brasileira de Física2003-09-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332003000300032Brazilian Journal of Physics v.33 n.3 2003reponame:Brazilian Journal of Physicsinstname:Sociedade Brasileira de Física (SBF)instacron:SBF10.1590/S0103-97332003000300032info:eu-repo/semantics/openAccessFulco,U. L.Silva,L. R. daNobre,F. D.Lucena,L. S.eng2003-11-11T00:00:00Zoai:scielo:S0103-97332003000300032Revistahttp://www.sbfisica.org.br/v1/home/index.php/pt/ONGhttps://old.scielo.br/oai/scielo-oai.phpsbfisica@sbfisica.org.br||sbfisica@sbfisica.org.br1678-44480103-9733opendoar:2003-11-11T00:00Brazilian Journal of Physics - Sociedade Brasileira de Física (SBF)false |
dc.title.none.fl_str_mv |
Competing long-range bonds and site dilution in the one-dimensional bond-percolation problem |
title |
Competing long-range bonds and site dilution in the one-dimensional bond-percolation problem |
spellingShingle |
Competing long-range bonds and site dilution in the one-dimensional bond-percolation problem Fulco,U. L. |
title_short |
Competing long-range bonds and site dilution in the one-dimensional bond-percolation problem |
title_full |
Competing long-range bonds and site dilution in the one-dimensional bond-percolation problem |
title_fullStr |
Competing long-range bonds and site dilution in the one-dimensional bond-percolation problem |
title_full_unstemmed |
Competing long-range bonds and site dilution in the one-dimensional bond-percolation problem |
title_sort |
Competing long-range bonds and site dilution in the one-dimensional bond-percolation problem |
author |
Fulco,U. L. |
author_facet |
Fulco,U. L. Silva,L. R. da Nobre,F. D. Lucena,L. S. |
author_role |
author |
author2 |
Silva,L. R. da Nobre,F. D. Lucena,L. S. |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Fulco,U. L. Silva,L. R. da Nobre,F. D. Lucena,L. S. |
description |
The long-range bond-percolation problem, on a linear chain (d = 1), in the presence of diluted sites (with an occupancy probability p s for an active site) is studied by means of a Monte Carlo simulation. The occupancy probability for a bond between two active sites i and j, separated by a distance r ij is given by p ij = <img width=32 height=32 id="_x0000_i1026" src="../../img/revistas/bjp/v33n3/a32img01.gif" align=absbottom>, where p represents the usual occupancy probability between nearest-neighbor sites. This model allows one to analyse the competition between long-range bonds (which enhance percolation) and diluted sites (which weaken percolation). By varying the parameter a (a > 0), one may find a crossover between a nonextensive regime and an extensive regime; in particular, the cases a = 0 and a ® ¥ represent, respectively, two well-known limits, namely, the mean-field (infinite-range bonds) and first-neighbor-bond limits. The percolation order parameter, P¥, was investigated numerically for different values of a and p s. Two characteristic values of a were found, which depend on the site-occupancy probability p s, namely, a1(p s) and a2(p s) (a2(p s) > a1(p s) > 0). The parameter P¥ equals unit, "p > 0, for 0 < a < a1(p s) and vanishes, "p < 1, for a > a2(p s). In the interval a1(p s) < a < a2(p s), the parameter P¥ displays a familiar behavior, i.e., 0 for p < p c(a) and finite otherwise. It is shown that both a1(p s) and a2(p s) decrease with the inclusion of diluted sites. For a fixed p s, it is shown that a convenient variable, p* º p*(p, a, N), may be defined in such a way that plots of P¥ versus p* collapse for different sizes and values of a in the nonextensive regime. |
publishDate |
2003 |
dc.date.none.fl_str_mv |
2003-09-01 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332003000300032 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332003000300032 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/S0103-97332003000300032 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
text/html |
dc.publisher.none.fl_str_mv |
Sociedade Brasileira de Física |
publisher.none.fl_str_mv |
Sociedade Brasileira de Física |
dc.source.none.fl_str_mv |
Brazilian Journal of Physics v.33 n.3 2003 reponame:Brazilian Journal of Physics instname:Sociedade Brasileira de Física (SBF) instacron:SBF |
instname_str |
Sociedade Brasileira de Física (SBF) |
instacron_str |
SBF |
institution |
SBF |
reponame_str |
Brazilian Journal of Physics |
collection |
Brazilian Journal of Physics |
repository.name.fl_str_mv |
Brazilian Journal of Physics - Sociedade Brasileira de Física (SBF) |
repository.mail.fl_str_mv |
sbfisica@sbfisica.org.br||sbfisica@sbfisica.org.br |
_version_ |
1754734860438601728 |