Percolation of linear k-mers on a square lattice: from isotropic through partially ordered to completely aligned states.
Identifieur interne : 000A21 ( Ncbi/Merge ); précédent : 000A20; suivant : 000A22Percolation of linear k-mers on a square lattice: from isotropic through partially ordered to completely aligned states.
Auteurs : Yuri Yu Tarasevich [Russie] ; Nikolai I. Lebovka ; Valeri V. LaptevSource :
- Physical review. E, Statistical, nonlinear, and soft matter physics [ 1550-2376 ] ; 2012.
Abstract
Numerical simulations by means of Monte Carlo method and finite-size scaling analysis have been performed to study the percolation behavior of linear k-mers (also denoted in publications as rigid rods, needles, sticks) on two-dimensional square lattices L × L with periodic boundary conditions. Percolation phenomena are investigated for anisotropic relaxation random sequential adsorption of linear k-mers. Especially, effect of anisotropic placement of the objects on the percolation threshold has been investigated. A detailed study of the behavior of percolation probability R(L)(p) that a lattice of size L percolates at concentration p in dependence on k, anisotropy, and lattice size L has been performed. A nonmonotonic size dependence for the percolation threshold has been confirmed in the isotropic case. We propose a fitting formula for percolation threshold, p(c) = a/k(α)+blog(10)k+c, where a, b, c, and α are the fitting parameters depending on anisotropy. We predict that for large k-mers (k >/≈ 1.2 × 10(4)) isotropically placed at the lattice, percolation cannot occur, even at jamming concentration.
DOI: 10.1103/PhysRevE.86.061116
PubMed: 23367902
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Lebovka</name></author><author><name sortKey="Laptev, Valeri V" sort="Laptev, Valeri V" uniqKey="Laptev V" first="Valeri V" last="Laptev">Valeri V. Laptev</name></author></analytic><series><title level="j">Physical review. E, Statistical, nonlinear, and soft matter physics</title><idno type="eISSN">1550-2376</idno><imprint><date when="2012" type="published">2012</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Numerical simulations by means of Monte Carlo method and finite-size scaling analysis have been performed to study the percolation behavior of linear k-mers (also denoted in publications as rigid rods, needles, sticks) on two-dimensional square lattices L × L with periodic boundary conditions. Percolation phenomena are investigated for anisotropic relaxation random sequential adsorption of linear k-mers. Especially, effect of anisotropic placement of the objects on the percolation threshold has been investigated. A detailed study of the behavior of percolation probability R(L)(p) that a lattice of size L percolates at concentration p in dependence on k, anisotropy, and lattice size L has been performed. A nonmonotonic size dependence for the percolation threshold has been confirmed in the isotropic case. We propose a fitting formula for percolation threshold, p(c) = a/k(α)+blog(10)k+c, where a, b, c, and α are the fitting parameters depending on anisotropy. We predict that for large k-mers (k >/≈ 1.2 × 10(4)) isotropically placed at the lattice, percolation cannot occur, even at jamming concentration.</div></front></TEI><pubmed><MedlineCitation Status="PubMed-not-MEDLINE" Owner="NLM"><PMID Version="1">23367902</PMID><DateCompleted><Year>2013</Year><Month>07</Month><Day>23</Day></DateCompleted><DateRevised><Year>2013</Year><Month>02</Month><Day>01</Day></DateRevised><Article PubModel="Print-Electronic"><Journal><ISSN IssnType="Electronic">1550-2376</ISSN><JournalIssue CitedMedium="Internet"><Volume>86</Volume><Issue>6 Pt 1</Issue><PubDate><Year>2012</Year><Month>Dec</Month></PubDate></JournalIssue><Title>Physical review. E, Statistical, nonlinear, and soft matter physics</Title><ISOAbbreviation>Phys Rev E Stat Nonlin Soft Matter Phys</ISOAbbreviation></Journal><ArticleTitle>Percolation of linear k-mers on a square lattice: from isotropic through partially ordered to completely aligned states.</ArticleTitle><Pagination><MedlinePgn>061116</MedlinePgn></Pagination><Abstract><AbstractText>Numerical simulations by means of Monte Carlo method and finite-size scaling analysis have been performed to study the percolation behavior of linear k-mers (also denoted in publications as rigid rods, needles, sticks) on two-dimensional square lattices L × L with periodic boundary conditions. Percolation phenomena are investigated for anisotropic relaxation random sequential adsorption of linear k-mers. Especially, effect of anisotropic placement of the objects on the percolation threshold has been investigated. A detailed study of the behavior of percolation probability R(L)(p) that a lattice of size L percolates at concentration p in dependence on k, anisotropy, and lattice size L has been performed. A nonmonotonic size dependence for the percolation threshold has been confirmed in the isotropic case. We propose a fitting formula for percolation threshold, p(c) = a/k(α)+blog(10)k+c, where a, b, c, and α are the fitting parameters depending on anisotropy. We predict that for large k-mers (k >/≈ 1.2 × 10(4)) isotropically placed at the lattice, percolation cannot occur, even at jamming concentration.</AbstractText></Abstract><AuthorList CompleteYN="Y"><Author ValidYN="Y"><LastName>Tarasevich</LastName><ForeName>Yuri Yu</ForeName><Initials>YY</Initials><AffiliationInfo><Affiliation>Astrakhan State University, 20a Tatishchev Street, 414056 Astrakhan, Russia.</Affiliation></AffiliationInfo></Author><Author ValidYN="Y"><LastName>Lebovka</LastName><ForeName>Nikolai I</ForeName><Initials>NI</Initials></Author><Author ValidYN="Y"><LastName>Laptev</LastName><ForeName>Valeri V</ForeName><Initials>VV</Initials></Author></AuthorList><Language>eng</Language><PublicationTypeList><PublicationType UI="D016428">Journal Article</PublicationType></PublicationTypeList><ArticleDate DateType="Electronic"><Year>2012</Year><Month>12</Month><Day>12</Day></ArticleDate></Article><MedlineJournalInfo><Country>United States</Country><MedlineTA>Phys Rev E Stat Nonlin Soft Matter Phys</MedlineTA><NlmUniqueID>101136452</NlmUniqueID><ISSNLinking>1539-3755</ISSNLinking></MedlineJournalInfo></MedlineCitation><PubmedData><History><PubMedPubDate PubStatus="received"><Year>2012</Year><Month>08</Month><Day>17</Day></PubMedPubDate><PubMedPubDate PubStatus="entrez"><Year>2013</Year><Month>2</Month><Day>2</Day><Hour>6</Hour><Minute>0</Minute></PubMedPubDate><PubMedPubDate PubStatus="pubmed"><Year>2013</Year><Month>2</Month><Day>2</Day><Hour>6</Hour><Minute>0</Minute></PubMedPubDate><PubMedPubDate PubStatus="medline"><Year>2013</Year><Month>2</Month><Day>2</Day><Hour>6</Hour><Minute>1</Minute></PubMedPubDate></History><PublicationStatus>ppublish</PublicationStatus><ArticleIdList><ArticleId IdType="pubmed">23367902</ArticleId><ArticleId IdType="doi">10.1103/PhysRevE.86.061116</ArticleId></ArticleIdList></PubmedData></pubmed><affiliations><list><country><li>Russie</li></country></list><tree><noCountry><name sortKey="Laptev, Valeri V" sort="Laptev, Valeri V" uniqKey="Laptev V" first="Valeri V" last="Laptev">Valeri V. Laptev</name><name sortKey="Lebovka, Nikolai I" sort="Lebovka, Nikolai I" uniqKey="Lebovka N" first="Nikolai I" last="Lebovka">Nikolai I. Lebovka</name></noCountry><country name="Russie"><noRegion><name sortKey="Tarasevich, Yuri Yu" sort="Tarasevich, Yuri Yu" uniqKey="Tarasevich Y" first="Yuri Yu" last="Tarasevich">Yuri Yu Tarasevich</name></noRegion></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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