Percolation of aligned rigid rods on two-dimensional triangular lattices.
Identifieur interne : 000434 ( Main/Exploration ); précédent : 000433; suivant : 000435Percolation of aligned rigid rods on two-dimensional triangular lattices.
Auteurs : P. Longone [Argentine] ; P M Centres [Argentine] ; A J Ramirez-Pastor [Argentine]Source :
- Physical review. E [ 2470-0053 ] ; 2019.
Abstract
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+sqrt[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.
DOI: 10.1103/PhysRevE.100.052104
PubMed: 31870027
Affiliations:
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Longone</name><affiliation wicri:level="1"><nlm:affiliation>Departamento de Física, Instituto de Física Aplicada, Universidad Nacional de San Luis-CONICET, Chacabuco 917, D5700BWS San Luis, Argentina.</nlm:affiliation><country xml:lang="fr">Argentine</country><wicri:regionArea>Departamento de Física, Instituto de Física Aplicada, Universidad Nacional de San Luis-CONICET, Chacabuco 917, D5700BWS San Luis</wicri:regionArea><wicri:noRegion>D5700BWS San Luis</wicri:noRegion></affiliation></author><author><name sortKey="Centres, P M" sort="Centres, P M" uniqKey="Centres P" first="P M" last="Centres">P M Centres</name><affiliation wicri:level="1"><nlm:affiliation>Departamento de Física, Instituto de Física Aplicada, Universidad Nacional de San Luis-CONICET, Chacabuco 917, D5700BWS San Luis, Argentina.</nlm:affiliation><country xml:lang="fr">Argentine</country><wicri:regionArea>Departamento de Física, Instituto de Física Aplicada, Universidad Nacional de San Luis-CONICET, Chacabuco 917, D5700BWS San Luis</wicri:regionArea><wicri:noRegion>D5700BWS San Luis</wicri:noRegion></affiliation></author><author><name sortKey="Ramirez Pastor, A J" sort="Ramirez Pastor, A J" uniqKey="Ramirez Pastor A" first="A J" last="Ramirez-Pastor">A J Ramirez-Pastor</name><affiliation wicri:level="1"><nlm:affiliation>Departamento de Física, Instituto de Física Aplicada, Universidad Nacional de San Luis-CONICET, Chacabuco 917, D5700BWS San Luis, Argentina.</nlm:affiliation><country xml:lang="fr">Argentine</country><wicri:regionArea>Departamento de Física, Instituto de Física Aplicada, Universidad Nacional de San Luis-CONICET, Chacabuco 917, D5700BWS San Luis</wicri:regionArea><wicri:noRegion>D5700BWS San Luis</wicri:noRegion></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PubMed</idno><date when="2019">2019</date><idno type="RBID">pubmed:31870027</idno><idno type="pmid">31870027</idno><idno type="doi">10.1103/PhysRevE.100.052104</idno><idno type="wicri:Area/PubMed/Corpus">000320</idno><idno type="wicri:explorRef" wicri:stream="PubMed" wicri:step="Corpus" wicri:corpus="PubMed">000320</idno><idno type="wicri:Area/PubMed/Curation">000320</idno><idno type="wicri:explorRef" wicri:stream="PubMed" wicri:step="Curation">000320</idno><idno type="wicri:Area/PubMed/Checkpoint">000431</idno><idno type="wicri:explorRef" wicri:stream="Checkpoint" wicri:step="PubMed">000431</idno><idno type="wicri:Area/Ncbi/Merge">002445</idno><idno type="wicri:Area/Ncbi/Curation">002445</idno><idno type="wicri:Area/Ncbi/Checkpoint">002445</idno><idno type="wicri:Area/Main/Merge">000437</idno><idno type="wicri:Area/Main/Curation">000434</idno><idno type="wicri:Area/Main/Exploration">000434</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">Percolation of aligned rigid rods on two-dimensional triangular lattices.</title><author><name sortKey="Longone, P" sort="Longone, P" uniqKey="Longone P" first="P" last="Longone">P. Longone</name><affiliation wicri:level="1"><nlm:affiliation>Departamento de Física, Instituto de Física Aplicada, Universidad Nacional de San Luis-CONICET, Chacabuco 917, D5700BWS San Luis, Argentina.</nlm:affiliation><country xml:lang="fr">Argentine</country><wicri:regionArea>Departamento de Física, Instituto de Física Aplicada, Universidad Nacional de San Luis-CONICET, Chacabuco 917, D5700BWS San Luis</wicri:regionArea><wicri:noRegion>D5700BWS San Luis</wicri:noRegion></affiliation></author><author><name sortKey="Centres, P M" sort="Centres, P M" uniqKey="Centres P" first="P M" last="Centres">P M Centres</name><affiliation wicri:level="1"><nlm:affiliation>Departamento de Física, Instituto de Física Aplicada, Universidad Nacional de San Luis-CONICET, Chacabuco 917, D5700BWS San Luis, Argentina.</nlm:affiliation><country xml:lang="fr">Argentine</country><wicri:regionArea>Departamento de Física, Instituto de Física Aplicada, Universidad Nacional de San Luis-CONICET, Chacabuco 917, D5700BWS San Luis</wicri:regionArea><wicri:noRegion>D5700BWS San Luis</wicri:noRegion></affiliation></author><author><name sortKey="Ramirez Pastor, A J" sort="Ramirez Pastor, A J" uniqKey="Ramirez Pastor A" first="A J" last="Ramirez-Pastor">A J Ramirez-Pastor</name><affiliation wicri:level="1"><nlm:affiliation>Departamento de Física, Instituto de Física Aplicada, Universidad Nacional de San Luis-CONICET, Chacabuco 917, D5700BWS San Luis, Argentina.</nlm:affiliation><country xml:lang="fr">Argentine</country><wicri:regionArea>Departamento de Física, Instituto de Física Aplicada, Universidad Nacional de San Luis-CONICET, Chacabuco 917, D5700BWS San Luis</wicri:regionArea><wicri:noRegion>D5700BWS San Luis</wicri:noRegion></affiliation></author></analytic><series><title level="j">Physical review. E</title><idno type="eISSN">2470-0053</idno><imprint><date when="2019" type="published">2019</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">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+sqrt[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.</div></front></TEI><affiliations><list><country><li>Argentine</li></country></list><tree><country name="Argentine"><noRegion><name sortKey="Longone, P" sort="Longone, P" uniqKey="Longone P" first="P" last="Longone">P. Longone</name></noRegion><name sortKey="Centres, P M" sort="Centres, P M" uniqKey="Centres P" first="P M" last="Centres">P M Centres</name><name sortKey="Ramirez Pastor, A J" sort="Ramirez Pastor, A J" uniqKey="Ramirez Pastor A" first="A J" last="Ramirez-Pastor">A J Ramirez-Pastor</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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