Impact of defects on percolation in random sequential adsorption of linear k-mers on square lattices.
Identifieur interne : 001753 ( Main/Exploration ); précédent : 001752; suivant : 001754Impact of defects on percolation in random sequential adsorption of linear k-mers on square lattices.
Auteurs : Yuri Yu Tarasevich [Russie] ; Valeri V. Laptev [Russie] ; Nikolai V. Vygornitskii [Ukraine] ; Nikolai I. Lebovka [Ukraine]Source :
- Physical review. E, Statistical, nonlinear, and soft matter physics [ 1550-2376 ] ; 2015.
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Abstract
The effect of defects on the percolation of linear k-mers (particles occupying k adjacent sites) on a square lattice is studied by means of Monte Carlo simulation. The k-mers are deposited using a random sequential adsorption mechanism. Two models L(d) and K(d) are analyzed. In the L(d) model it is assumed that the initial square lattice is nonideal and some fraction of sites d is occupied by nonconducting point defects (impurities). In the K(d) model the initial square lattice is perfect. However, it is assumed that some fraction of the sites in the k-mers d consists of defects, i.e., is nonconducting. The length of the k-mers k varies from 2 to 256. Periodic boundary conditions are applied to the square lattice. The dependences of the percolation threshold concentration of the conducting sites p(c) vs the concentration of defects d are analyzed for different values of k. Above some critical concentration of defects d(m), percolation is blocked in both models, even at the jamming concentration of k-mers. For long k-mers, the values of d(m) are well fitted by the functions d(m)∝k(m)(-α)-k(-α) (α=1.28±0.01 and k(m)=5900±500) and d(m)∝log(10)(k(m)/k) (k(m)=4700±1000) for the L(d) and K(d) models, respectively. Thus, our estimation indicates that the percolation of k-mers on a square lattice is impossible even for a lattice without any defects if k⪆6×10(3).
DOI: 10.1103/PhysRevE.91.012109
PubMed: 25679572
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E, Statistical, nonlinear, and soft matter physics</title><idno type="eISSN">1550-2376</idno><imprint><date when="2015" type="published">2015</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Adsorption</term><term>Models, Theoretical</term><term>Monte Carlo Method</term></keywords><keywords scheme="KwdFr" xml:lang="fr"><term>Adsorption</term><term>Modèles théoriques</term><term>Méthode de Monte-Carlo</term></keywords><keywords scheme="MESH" xml:lang="en"><term>Adsorption</term><term>Models, Theoretical</term><term>Monte Carlo Method</term></keywords><keywords scheme="MESH" xml:lang="fr"><term>Adsorption</term><term>Modèles théoriques</term><term>Méthode de Monte-Carlo</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">The effect of defects on the percolation of linear k-mers (particles occupying k adjacent sites) on a square lattice is studied by means of Monte Carlo simulation. The k-mers are deposited using a random sequential adsorption mechanism. Two models L(d) and K(d) are analyzed. In the L(d) model it is assumed that the initial square lattice is nonideal and some fraction of sites d is occupied by nonconducting point defects (impurities). In the K(d) model the initial square lattice is perfect. However, it is assumed that some fraction of the sites in the k-mers d consists of defects, i.e., is nonconducting. The length of the k-mers k varies from 2 to 256. Periodic boundary conditions are applied to the square lattice. The dependences of the percolation threshold concentration of the conducting sites p(c) vs the concentration of defects d are analyzed for different values of k. Above some critical concentration of defects d(m), percolation is blocked in both models, even at the jamming concentration of k-mers. For long k-mers, the values of d(m) are well fitted by the functions d(m)∝k(m)(-α)-k(-α) (α=1.28±0.01 and k(m)=5900±500) and d(m)∝log(10)(k(m)/k) (k(m)=4700±1000) for the L(d) and K(d) models, respectively. Thus, our estimation indicates that the percolation of k-mers on a square lattice is impossible even for a lattice without any defects if k⪆6×10(3).</div></front></TEI><affiliations><list><country><li>Russie</li><li>Ukraine</li></country></list><tree><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><name sortKey="Laptev, Valeri V" sort="Laptev, Valeri V" uniqKey="Laptev V" first="Valeri V" last="Laptev">Valeri V. Laptev</name></country><country name="Ukraine"><noRegion><name sortKey="Vygornitskii, Nikolai V" sort="Vygornitskii, Nikolai V" uniqKey="Vygornitskii N" first="Nikolai V" last="Vygornitskii">Nikolai V. Vygornitskii</name></noRegion><name sortKey="Lebovka, Nikolai I" sort="Lebovka, Nikolai I" uniqKey="Lebovka N" first="Nikolai I" last="Lebovka">Nikolai I. Lebovka</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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