Percolation of aligned rigid rods on two-dimensional triangular lattices

Autores
Longone, Pablo Jesus; Centres, Paulo Marcelo; Ramirez Pastor, Antonio Jose
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The percolation behavior of aligned rigid rods of length k ( k -mers) on two-dimensional triangular lattices has been studied by numerical simulations and finite-size scaling analysis. The k -mers, containing k identical units (each one occupying a lattice site), were irreversibly deposited along one of the directions of the lattice. The connectivity analysis was carried out by following the probability R L , k ( p ) that a lattice composed of L × L sites percolates at a concentration p of sites occupied by particles of size k . The results, obtained for k ranging from 2 to 80, showed that the percolation threshold p c ( k ) exhibits a increasing function when it is plotted as a function of the k -mer size. The dependence of p c ( k ) was determined, being p c ( k ) = A + B / ( C + √ k ) , where A = p c ( k → ∞ ) = 0.582 ( 9 ) is the value of the percolation threshold by infinitely long k -mers, B = − 0.47 ( 0.21 ) , and C = 5.79 ( 2.18 ) . This behavior is completely different from that observed for square lattices, where the percolation threshold decreases with k . In addition, the effect of the anisotropy on the properties of the percolating phase was investigated. The results revealed that, while for finite systems the anisotropy of the deposited layer favors the percolation along the parallel direction to the alignment axis, in the thermodynamic limit, the value of the percolation threshold is the same in both parallel and transversal directions. Finally, an exhaustive study of critical exponents and universality was carried out, showing that the phase transition occurring in the system belongs to the standard random percolation universality class regardless of the value of k considered.
Fil: Longone, Pablo Jesus. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich". Universidad Nacional de San Luis. Facultad de Ciencias Físico Matemáticas y Naturales. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich"; Argentina
Fil: Centres, Paulo Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich". Universidad Nacional de San Luis. Facultad de Ciencias Físico Matemáticas y Naturales. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich"; Argentina
Fil: Ramirez Pastor, Antonio Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich". Universidad Nacional de San Luis. Facultad de Ciencias Físico Matemáticas y Naturales. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich"; Argentina
Materia
PERCOLATION
NEMATIC
JAMMING
PHASE TRANSITION
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/118779
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/118779
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Percolation of aligned rigid rods on two-dimensional triangular latticesLongone, Pablo JesusCentres, Paulo MarceloRamirez Pastor, Antonio JosePERCOLATIONNEMATICJAMMINGPHASE TRANSITIONhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1The percolation behavior of aligned rigid rods of length k ( k -mers) on two-dimensional triangular lattices has been studied by numerical simulations and finite-size scaling analysis. The k -mers, containing k identical units (each one occupying a lattice site), were irreversibly deposited along one of the directions of the lattice. The connectivity analysis was carried out by following the probability R L , k ( p ) that a lattice composed of L × L sites percolates at a concentration p of sites occupied by particles of size k . The results, obtained for k ranging from 2 to 80, showed that the percolation threshold p c ( k ) exhibits a increasing function when it is plotted as a function of the k -mer size. The dependence of p c ( k ) was determined, being p c ( k ) = A + B / ( C + √ k ) , where A = p c ( k → ∞ ) = 0.582 ( 9 ) is the value of the percolation threshold by infinitely long k -mers, B = − 0.47 ( 0.21 ) , and C = 5.79 ( 2.18 ) . This behavior is completely different from that observed for square lattices, where the percolation threshold decreases with k . In addition, the effect of the anisotropy on the properties of the percolating phase was investigated. The results revealed that, while for finite systems the anisotropy of the deposited layer favors the percolation along the parallel direction to the alignment axis, in the thermodynamic limit, the value of the percolation threshold is the same in both parallel and transversal directions. Finally, an exhaustive study of critical exponents and universality was carried out, showing that the phase transition occurring in the system belongs to the standard random percolation universality class regardless of the value of k considered.Fil: Longone, Pablo Jesus. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich". Universidad Nacional de San Luis. Facultad de Ciencias Físico Matemáticas y Naturales. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich"; ArgentinaFil: Centres, Paulo Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich". Universidad Nacional de San Luis. Facultad de Ciencias Físico Matemáticas y Naturales. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich"; ArgentinaFil: Ramirez Pastor, Antonio Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich". Universidad Nacional de San Luis. Facultad de Ciencias Físico Matemáticas y Naturales. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich"; ArgentinaAmerican Physical Society2019-11-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/118779Longone, Pablo Jesus; Centres, Paulo Marcelo; Ramirez Pastor, Antonio Jose; Percolation of aligned rigid rods on two-dimensional triangular lattices; American Physical Society; Physical Review. E; 100; 5; 4-11-2019; 1-11; 0521042470-00452470-0053CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pre/abstract/10.1103/PhysRevE.100.052104info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.100.052104info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:33:37Zoai:ri.conicet.gov.ar:11336/118779instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:33:37.649CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Percolation of aligned rigid rods on two-dimensional triangular lattices
title Percolation of aligned rigid rods on two-dimensional triangular lattices
spellingShingle Percolation of aligned rigid rods on two-dimensional triangular lattices
Longone, Pablo Jesus
PERCOLATION
NEMATIC
JAMMING
PHASE TRANSITION
title_short Percolation of aligned rigid rods on two-dimensional triangular lattices
title_full Percolation of aligned rigid rods on two-dimensional triangular lattices
title_fullStr Percolation of aligned rigid rods on two-dimensional triangular lattices
title_full_unstemmed Percolation of aligned rigid rods on two-dimensional triangular lattices
title_sort Percolation of aligned rigid rods on two-dimensional triangular lattices
dc.creator.none.fl_str_mv Longone, Pablo Jesus
Centres, Paulo Marcelo
Ramirez Pastor, Antonio Jose
author Longone, Pablo Jesus
author_facet Longone, Pablo Jesus
Centres, Paulo Marcelo
Ramirez Pastor, Antonio Jose
author_role author
author2 Centres, Paulo Marcelo
Ramirez Pastor, Antonio Jose
author2_role author
author
dc.subject.none.fl_str_mv PERCOLATION
NEMATIC
JAMMING
PHASE TRANSITION
topic PERCOLATION
NEMATIC
JAMMING
PHASE TRANSITION
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The percolation behavior of aligned rigid rods of length k ( k -mers) on two-dimensional triangular lattices has been studied by numerical simulations and finite-size scaling analysis. The k -mers, containing k identical units (each one occupying a lattice site), were irreversibly deposited along one of the directions of the lattice. The connectivity analysis was carried out by following the probability R L , k ( p ) that a lattice composed of L × L sites percolates at a concentration p of sites occupied by particles of size k . The results, obtained for k ranging from 2 to 80, showed that the percolation threshold p c ( k ) exhibits a increasing function when it is plotted as a function of the k -mer size. The dependence of p c ( k ) was determined, being p c ( k ) = A + B / ( C + √ k ) , where A = p c ( k → ∞ ) = 0.582 ( 9 ) is the value of the percolation threshold by infinitely long k -mers, B = − 0.47 ( 0.21 ) , and C = 5.79 ( 2.18 ) . This behavior is completely different from that observed for square lattices, where the percolation threshold decreases with k . In addition, the effect of the anisotropy on the properties of the percolating phase was investigated. The results revealed that, while for finite systems the anisotropy of the deposited layer favors the percolation along the parallel direction to the alignment axis, in the thermodynamic limit, the value of the percolation threshold is the same in both parallel and transversal directions. Finally, an exhaustive study of critical exponents and universality was carried out, showing that the phase transition occurring in the system belongs to the standard random percolation universality class regardless of the value of k considered.
Fil: Longone, Pablo Jesus. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich". Universidad Nacional de San Luis. Facultad de Ciencias Físico Matemáticas y Naturales. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich"; Argentina
Fil: Centres, Paulo Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich". Universidad Nacional de San Luis. Facultad de Ciencias Físico Matemáticas y Naturales. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich"; Argentina
Fil: Ramirez Pastor, Antonio Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich". Universidad Nacional de San Luis. Facultad de Ciencias Físico Matemáticas y Naturales. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich"; Argentina
description The percolation behavior of aligned rigid rods of length k ( k -mers) on two-dimensional triangular lattices has been studied by numerical simulations and finite-size scaling analysis. The k -mers, containing k identical units (each one occupying a lattice site), were irreversibly deposited along one of the directions of the lattice. The connectivity analysis was carried out by following the probability R L , k ( p ) that a lattice composed of L × L sites percolates at a concentration p of sites occupied by particles of size k . The results, obtained for k ranging from 2 to 80, showed that the percolation threshold p c ( k ) exhibits a increasing function when it is plotted as a function of the k -mer size. The dependence of p c ( k ) was determined, being p c ( k ) = A + B / ( C + √ k ) , where A = p c ( k → ∞ ) = 0.582 ( 9 ) is the value of the percolation threshold by infinitely long k -mers, B = − 0.47 ( 0.21 ) , and C = 5.79 ( 2.18 ) . This behavior is completely different from that observed for square lattices, where the percolation threshold decreases with k . In addition, the effect of the anisotropy on the properties of the percolating phase was investigated. The results revealed that, while for finite systems the anisotropy of the deposited layer favors the percolation along the parallel direction to the alignment axis, in the thermodynamic limit, the value of the percolation threshold is the same in both parallel and transversal directions. Finally, an exhaustive study of critical exponents and universality was carried out, showing that the phase transition occurring in the system belongs to the standard random percolation universality class regardless of the value of k considered.
publishDate 2019
dc.date.none.fl_str_mv 2019-11-04
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/118779
Longone, Pablo Jesus; Centres, Paulo Marcelo; Ramirez Pastor, Antonio Jose; Percolation of aligned rigid rods on two-dimensional triangular lattices; American Physical Society; Physical Review. E; 100; 5; 4-11-2019; 1-11; 052104
2470-0045
2470-0053
CONICET Digital
CONICET
url http://hdl.handle.net/11336/118779
identifier_str_mv Longone, Pablo Jesus; Centres, Paulo Marcelo; Ramirez Pastor, Antonio Jose; Percolation of aligned rigid rods on two-dimensional triangular lattices; American Physical Society; Physical Review. E; 100; 5; 4-11-2019; 1-11; 052104
2470-0045
2470-0053
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pre/abstract/10.1103/PhysRevE.100.052104
info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.100.052104
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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