Standard and inverse site percolation of straight rigid rods on triangular lattices: Isotropic and perfectly oriented deposition and removal

Autores
Ramírez, Lucía Soledad; Pasinetti, Pedro Marcelo; Lebrecht, W.; Ramirez Pastor, Antonio Jose
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Numerical simulations and finite-size scaling analysis have been carried out to study standard and inverse percolation of straight rigid rods on triangular lattices. In the case of standard percolation, the lattice is initially empty. Then, linear k-mers (particles occupying k consecutive sites along one of the lattice directions) are randomly and sequentially deposited on the lattice. In the case of inverse percolation, the process starts with an initial configuration where all lattice sites are occupied by single monomers (each monomer occupies one lattice site) and, consequently, the opposite sides of the lattice are connected by nearest-neighbor occupied sites. Then the system is diluted by randomly removing sets of k consecutive monomers (linear k-mers) from the lattice. Two schemes are used for the depositing/removing process: an isotropic scheme, where the deposition (removal) of the linear objects occurs with the same probability in any lattice direction, and an anisotropic (perfectly oriented) scheme, where one lattice direction is privileged for depositing (removing) the particles. The study is conducted by following the behavior of four critical concentrations with size k: (i) [(ii)] standard isotropic[oriented] percolation threshold θc,k[ϑc,k], which represents the minimum concentration of occupied sites at which an infinite cluster of occupied nearest-neighbor sites extends from one side of the system to the other. θc,k[ϑc,k] is reached by isotropic[oriented] deposition of straight rigid k-mers on an initially empty lattice; and (iii) [(iv)] inverse isotropic[oriented] percolation threshold θc,ki[ϑc,ki], which corresponds to the maximum concentration of occupied sites for which connectivity disappears. θc,ki[ϑc,ki] is reached after removing isotropic [completely aligned] straight rigid k-mers from an initially fully occupied lattice. θc,k, ϑc,k, θc,ki, and ϑc,ki are determined for a wide range of k (2≤k≤512). The obtained results indicate that (1)θc,k[θc,ki] exhibits a nonmonotonous dependence on the size k. It decreases[increases] for small particle sizes, goes through a minimum[maximum] at around k=11, and finally increases and asymptotically converges towards a definite value for large segments θc,k→∞=0.500(2) [θc,k→∞i=0.500(1)]; (2)ϑc,k[ϑc,ki] depicts a monotonous behavior in terms of k. It rapidly increases[decreases] for small particle sizes and asymptotically converges towards a definite value for infinitely long k-mers ϑc,k→∞=0.5334(6) [ϑc,k→∞i=0.4666(6)]; (3) for both isotropic and perfectly oriented models, the curves of standard and inverse percolation thresholds are symmetric to each other with respect to the line θ(ϑ)=0.5. Thus a complementary property is found θc,k+θc,ki=1 (and ϑc,k+ϑc,ki=1) which has not been observed in other regular lattices. This condition is analytically validated by using exact enumeration of configurations for small systems, and (4) in all cases, the critical concentration curves divide the θ space in a percolating region and a nonpercolating region. These phases extend to infinity in the space of the parameter k so that the model presents percolation transition for the whole range of k.
Fil: Ramírez, Lucía Soledad. 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: Pasinetti, Pedro 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: Lebrecht, W.. Universidad de La Frontera; Chile
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
Percolación
Jamming
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:11336/183164

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spelling Standard and inverse site percolation of straight rigid rods on triangular lattices: Isotropic and perfectly oriented deposition and removalRamírez, Lucía SoledadPasinetti, Pedro MarceloLebrecht, W.Ramirez Pastor, Antonio JosePercolaciónJamminghttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1Numerical simulations and finite-size scaling analysis have been carried out to study standard and inverse percolation of straight rigid rods on triangular lattices. In the case of standard percolation, the lattice is initially empty. Then, linear k-mers (particles occupying k consecutive sites along one of the lattice directions) are randomly and sequentially deposited on the lattice. In the case of inverse percolation, the process starts with an initial configuration where all lattice sites are occupied by single monomers (each monomer occupies one lattice site) and, consequently, the opposite sides of the lattice are connected by nearest-neighbor occupied sites. Then the system is diluted by randomly removing sets of k consecutive monomers (linear k-mers) from the lattice. Two schemes are used for the depositing/removing process: an isotropic scheme, where the deposition (removal) of the linear objects occurs with the same probability in any lattice direction, and an anisotropic (perfectly oriented) scheme, where one lattice direction is privileged for depositing (removing) the particles. The study is conducted by following the behavior of four critical concentrations with size k: (i) [(ii)] standard isotropic[oriented] percolation threshold θc,k[ϑc,k], which represents the minimum concentration of occupied sites at which an infinite cluster of occupied nearest-neighbor sites extends from one side of the system to the other. θc,k[ϑc,k] is reached by isotropic[oriented] deposition of straight rigid k-mers on an initially empty lattice; and (iii) [(iv)] inverse isotropic[oriented] percolation threshold θc,ki[ϑc,ki], which corresponds to the maximum concentration of occupied sites for which connectivity disappears. θc,ki[ϑc,ki] is reached after removing isotropic [completely aligned] straight rigid k-mers from an initially fully occupied lattice. θc,k, ϑc,k, θc,ki, and ϑc,ki are determined for a wide range of k (2≤k≤512). The obtained results indicate that (1)θc,k[θc,ki] exhibits a nonmonotonous dependence on the size k. It decreases[increases] for small particle sizes, goes through a minimum[maximum] at around k=11, and finally increases and asymptotically converges towards a definite value for large segments θc,k→∞=0.500(2) [θc,k→∞i=0.500(1)]; (2)ϑc,k[ϑc,ki] depicts a monotonous behavior in terms of k. It rapidly increases[decreases] for small particle sizes and asymptotically converges towards a definite value for infinitely long k-mers ϑc,k→∞=0.5334(6) [ϑc,k→∞i=0.4666(6)]; (3) for both isotropic and perfectly oriented models, the curves of standard and inverse percolation thresholds are symmetric to each other with respect to the line θ(ϑ)=0.5. Thus a complementary property is found θc,k+θc,ki=1 (and ϑc,k+ϑc,ki=1) which has not been observed in other regular lattices. This condition is analytically validated by using exact enumeration of configurations for small systems, and (4) in all cases, the critical concentration curves divide the θ space in a percolating region and a nonpercolating region. These phases extend to infinity in the space of the parameter k so that the model presents percolation transition for the whole range of k.Fil: Ramírez, Lucía Soledad. 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: Pasinetti, Pedro 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: Lebrecht, W.. Universidad de La Frontera; ChileFil: 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 Society2021-07info: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/11336/183164Ramírez, Lucía Soledad; Pasinetti, Pedro Marcelo; Lebrecht, W.; Ramirez Pastor, Antonio Jose; Standard and inverse site percolation of straight rigid rods on triangular lattices: Isotropic and perfectly oriented deposition and removal; American Physical Society; Physical Review E; 104; 1; 7-2021; 1-122470-00452470-0053CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.aps.org/doi/10.1103/PhysRevE.104.014101info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.104.014101info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:40:49Zoai:ri.conicet.gov.ar:11336/183164instacron: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 09:40:49.733CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Standard and inverse site percolation of straight rigid rods on triangular lattices: Isotropic and perfectly oriented deposition and removal
title Standard and inverse site percolation of straight rigid rods on triangular lattices: Isotropic and perfectly oriented deposition and removal
spellingShingle Standard and inverse site percolation of straight rigid rods on triangular lattices: Isotropic and perfectly oriented deposition and removal
Ramírez, Lucía Soledad
Percolación
Jamming
title_short Standard and inverse site percolation of straight rigid rods on triangular lattices: Isotropic and perfectly oriented deposition and removal
title_full Standard and inverse site percolation of straight rigid rods on triangular lattices: Isotropic and perfectly oriented deposition and removal
title_fullStr Standard and inverse site percolation of straight rigid rods on triangular lattices: Isotropic and perfectly oriented deposition and removal
title_full_unstemmed Standard and inverse site percolation of straight rigid rods on triangular lattices: Isotropic and perfectly oriented deposition and removal
title_sort Standard and inverse site percolation of straight rigid rods on triangular lattices: Isotropic and perfectly oriented deposition and removal
dc.creator.none.fl_str_mv Ramírez, Lucía Soledad
Pasinetti, Pedro Marcelo
Lebrecht, W.
Ramirez Pastor, Antonio Jose
author Ramírez, Lucía Soledad
author_facet Ramírez, Lucía Soledad
Pasinetti, Pedro Marcelo
Lebrecht, W.
Ramirez Pastor, Antonio Jose
author_role author
author2 Pasinetti, Pedro Marcelo
Lebrecht, W.
Ramirez Pastor, Antonio Jose
author2_role author
author
author
dc.subject.none.fl_str_mv Percolación
Jamming
topic Percolación
Jamming
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Numerical simulations and finite-size scaling analysis have been carried out to study standard and inverse percolation of straight rigid rods on triangular lattices. In the case of standard percolation, the lattice is initially empty. Then, linear k-mers (particles occupying k consecutive sites along one of the lattice directions) are randomly and sequentially deposited on the lattice. In the case of inverse percolation, the process starts with an initial configuration where all lattice sites are occupied by single monomers (each monomer occupies one lattice site) and, consequently, the opposite sides of the lattice are connected by nearest-neighbor occupied sites. Then the system is diluted by randomly removing sets of k consecutive monomers (linear k-mers) from the lattice. Two schemes are used for the depositing/removing process: an isotropic scheme, where the deposition (removal) of the linear objects occurs with the same probability in any lattice direction, and an anisotropic (perfectly oriented) scheme, where one lattice direction is privileged for depositing (removing) the particles. The study is conducted by following the behavior of four critical concentrations with size k: (i) [(ii)] standard isotropic[oriented] percolation threshold θc,k[ϑc,k], which represents the minimum concentration of occupied sites at which an infinite cluster of occupied nearest-neighbor sites extends from one side of the system to the other. θc,k[ϑc,k] is reached by isotropic[oriented] deposition of straight rigid k-mers on an initially empty lattice; and (iii) [(iv)] inverse isotropic[oriented] percolation threshold θc,ki[ϑc,ki], which corresponds to the maximum concentration of occupied sites for which connectivity disappears. θc,ki[ϑc,ki] is reached after removing isotropic [completely aligned] straight rigid k-mers from an initially fully occupied lattice. θc,k, ϑc,k, θc,ki, and ϑc,ki are determined for a wide range of k (2≤k≤512). The obtained results indicate that (1)θc,k[θc,ki] exhibits a nonmonotonous dependence on the size k. It decreases[increases] for small particle sizes, goes through a minimum[maximum] at around k=11, and finally increases and asymptotically converges towards a definite value for large segments θc,k→∞=0.500(2) [θc,k→∞i=0.500(1)]; (2)ϑc,k[ϑc,ki] depicts a monotonous behavior in terms of k. It rapidly increases[decreases] for small particle sizes and asymptotically converges towards a definite value for infinitely long k-mers ϑc,k→∞=0.5334(6) [ϑc,k→∞i=0.4666(6)]; (3) for both isotropic and perfectly oriented models, the curves of standard and inverse percolation thresholds are symmetric to each other with respect to the line θ(ϑ)=0.5. Thus a complementary property is found θc,k+θc,ki=1 (and ϑc,k+ϑc,ki=1) which has not been observed in other regular lattices. This condition is analytically validated by using exact enumeration of configurations for small systems, and (4) in all cases, the critical concentration curves divide the θ space in a percolating region and a nonpercolating region. These phases extend to infinity in the space of the parameter k so that the model presents percolation transition for the whole range of k.
Fil: Ramírez, Lucía Soledad. 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: Pasinetti, Pedro 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: Lebrecht, W.. Universidad de La Frontera; Chile
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 Numerical simulations and finite-size scaling analysis have been carried out to study standard and inverse percolation of straight rigid rods on triangular lattices. In the case of standard percolation, the lattice is initially empty. Then, linear k-mers (particles occupying k consecutive sites along one of the lattice directions) are randomly and sequentially deposited on the lattice. In the case of inverse percolation, the process starts with an initial configuration where all lattice sites are occupied by single monomers (each monomer occupies one lattice site) and, consequently, the opposite sides of the lattice are connected by nearest-neighbor occupied sites. Then the system is diluted by randomly removing sets of k consecutive monomers (linear k-mers) from the lattice. Two schemes are used for the depositing/removing process: an isotropic scheme, where the deposition (removal) of the linear objects occurs with the same probability in any lattice direction, and an anisotropic (perfectly oriented) scheme, where one lattice direction is privileged for depositing (removing) the particles. The study is conducted by following the behavior of four critical concentrations with size k: (i) [(ii)] standard isotropic[oriented] percolation threshold θc,k[ϑc,k], which represents the minimum concentration of occupied sites at which an infinite cluster of occupied nearest-neighbor sites extends from one side of the system to the other. θc,k[ϑc,k] is reached by isotropic[oriented] deposition of straight rigid k-mers on an initially empty lattice; and (iii) [(iv)] inverse isotropic[oriented] percolation threshold θc,ki[ϑc,ki], which corresponds to the maximum concentration of occupied sites for which connectivity disappears. θc,ki[ϑc,ki] is reached after removing isotropic [completely aligned] straight rigid k-mers from an initially fully occupied lattice. θc,k, ϑc,k, θc,ki, and ϑc,ki are determined for a wide range of k (2≤k≤512). The obtained results indicate that (1)θc,k[θc,ki] exhibits a nonmonotonous dependence on the size k. It decreases[increases] for small particle sizes, goes through a minimum[maximum] at around k=11, and finally increases and asymptotically converges towards a definite value for large segments θc,k→∞=0.500(2) [θc,k→∞i=0.500(1)]; (2)ϑc,k[ϑc,ki] depicts a monotonous behavior in terms of k. It rapidly increases[decreases] for small particle sizes and asymptotically converges towards a definite value for infinitely long k-mers ϑc,k→∞=0.5334(6) [ϑc,k→∞i=0.4666(6)]; (3) for both isotropic and perfectly oriented models, the curves of standard and inverse percolation thresholds are symmetric to each other with respect to the line θ(ϑ)=0.5. Thus a complementary property is found θc,k+θc,ki=1 (and ϑc,k+ϑc,ki=1) which has not been observed in other regular lattices. This condition is analytically validated by using exact enumeration of configurations for small systems, and (4) in all cases, the critical concentration curves divide the θ space in a percolating region and a nonpercolating region. These phases extend to infinity in the space of the parameter k so that the model presents percolation transition for the whole range of k.
publishDate 2021
dc.date.none.fl_str_mv 2021-07
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/11336/183164
Ramírez, Lucía Soledad; Pasinetti, Pedro Marcelo; Lebrecht, W.; Ramirez Pastor, Antonio Jose; Standard and inverse site percolation of straight rigid rods on triangular lattices: Isotropic and perfectly oriented deposition and removal; American Physical Society; Physical Review E; 104; 1; 7-2021; 1-12
2470-0045
2470-0053
CONICET Digital
CONICET
url http://hdl.handle.net/11336/183164
identifier_str_mv Ramírez, Lucía Soledad; Pasinetti, Pedro Marcelo; Lebrecht, W.; Ramirez Pastor, Antonio Jose; Standard and inverse site percolation of straight rigid rods on triangular lattices: Isotropic and perfectly oriented deposition and removal; American Physical Society; Physical Review E; 104; 1; 7-2021; 1-12
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://link.aps.org/doi/10.1103/PhysRevE.104.014101
info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.104.014101
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)
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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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