Jamming and percolation for deposition of k^{2}-mers on square lattices: A Monte Carlo simulation study.
Identifieur interne : 000512 ( Main/Exploration ); précédent : 000511; suivant : 000513Jamming and percolation for deposition of k^{2}-mers on square lattices: A Monte Carlo simulation study.
Auteurs : A J Ramirez-Pastor [Argentine] ; P M Centres [Argentine] ; E E Vogel [Chili] ; J F Valdés [Chili]Source :
- Physical review. E [ 2470-0053 ] ; 2019.
Abstract
Percolation and jamming of k×k square tiles (k^{2}-mers) deposited on square lattices have been studied by numerical simulations complemented with finite-size scaling theory and exact enumeration of configurations for small systems. The k^{2}-mers were irreversibly deposited into square lattices of sizes L×L with L/k ranging between 128 and 448 (64 and 224) for jamming (percolation) calculations. Jamming coverage θ_{j,k} was determined for a wide range of k values (2≤k≤100 with many intermediate k values to allow a fine scaling analysis). θ_{j,k} exhibits a decreasing behavior with increasing k, being θ_{j,k=∞}=0.5623(3) the limit value for large k^{2}-mer sizes. In addition, a finite-size scaling analysis of the jamming transition was carried out, and the corresponding spatial correlation length critical exponent ν_{j} was measured, being ν_{j}≈1. On the other hand, the obtained results for the percolation threshold θ_{c,k} showed that θ_{c,k} is an increasing function of k in the range 1≤k≤3. For k≥4, all jammed configurations are nonpercolating states and, consequently, the percolation phase transition disappears. An explanation for this phenomenon is offered in terms of the rapid increase with k of the number of surrounding occupied sites needed to reach percolation, which gets larger than the sufficient number of occupied sites to define jamming. In the case of k=2 and 3, the percolation thresholds are θ_{c,k=2}(∞)=0.60355(8) and θ_{c,k=3}=0.63110(9). Our results significantly improve the previously reported values of θ_{c,k=2}^{Naka}=0.601(7) and θ_{c,k=3}^{Naka}=0.621(6) [Nakamura, Phys. Rev. A 36, 2384 (1987)0556-279110.1103/PhysRevA.36.2384]. In parallel, a comparison with previous results for jamming on these systems is also done. Finally, a complete analysis of critical exponents and universality has been done, showing that the percolation phase transition involved in the system has the same universality class as the ordinary random percolation, regardless of the size k considered.
DOI: 10.1103/PhysRevE.99.042131
PubMed: 31108638
Affiliations:
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Argentina.</nlm:affiliation><country xml:lang="fr">Argentine</country><wicri:regionArea>Departamento de Física, Instituto de Física Aplicada, Universidad Nacional de San Luis-CONICET, Ejército de Los Andes 950, D5700HHW, San Luis</wicri:regionArea><wicri:noRegion>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, Ejército de Los Andes 950, D5700HHW, 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, Ejército de Los Andes 950, D5700HHW, San Luis</wicri:regionArea><wicri:noRegion>San Luis</wicri:noRegion></affiliation></author><author><name sortKey="Vogel, E E" sort="Vogel, E E" uniqKey="Vogel E" first="E E" last="Vogel">E E Vogel</name><affiliation wicri:level="1"><nlm:affiliation>Departamento de Física, Universidad de La Frontera, Casilla 54-D, Temuco, Chile.</nlm:affiliation><country xml:lang="fr">Chili</country><wicri:regionArea>Departamento de Física, Universidad de La Frontera, Casilla 54-D, Temuco</wicri:regionArea><wicri:noRegion>Temuco</wicri:noRegion></affiliation></author><author><name sortKey="Valdes, J F" sort="Valdes, J F" uniqKey="Valdes J" first="J F" last="Valdés">J F Valdés</name><affiliation wicri:level="1"><nlm:affiliation>Departamento de Física, Universidad de La Frontera, Casilla 54-D, Temuco, Chile.</nlm:affiliation><country xml:lang="fr">Chili</country><wicri:regionArea>Departamento de Física, Universidad de La Frontera, Casilla 54-D, Temuco</wicri:regionArea><wicri:noRegion>Temuco</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">Percolation and jamming of k×k square tiles (k^{2}-mers) deposited on square lattices have been studied by numerical simulations complemented with finite-size scaling theory and exact enumeration of configurations for small systems. The k^{2}-mers were irreversibly deposited into square lattices of sizes L×L with L/k ranging between 128 and 448 (64 and 224) for jamming (percolation) calculations. Jamming coverage θ_{j,k} was determined for a wide range of k values (2≤k≤100 with many intermediate k values to allow a fine scaling analysis). θ_{j,k} exhibits a decreasing behavior with increasing k, being θ_{j,k=∞}=0.5623(3) the limit value for large k^{2}-mer sizes. In addition, a finite-size scaling analysis of the jamming transition was carried out, and the corresponding spatial correlation length critical exponent ν_{j} was measured, being ν_{j}≈1. On the other hand, the obtained results for the percolation threshold θ_{c,k} showed that θ_{c,k} is an increasing function of k in the range 1≤k≤3. For k≥4, all jammed configurations are nonpercolating states and, consequently, the percolation phase transition disappears. An explanation for this phenomenon is offered in terms of the rapid increase with k of the number of surrounding occupied sites needed to reach percolation, which gets larger than the sufficient number of occupied sites to define jamming. In the case of k=2 and 3, the percolation thresholds are θ_{c,k=2}(∞)=0.60355(8) and θ_{c,k=3}=0.63110(9). Our results significantly improve the previously reported values of θ_{c,k=2}^{Naka}=0.601(7) and θ_{c,k=3}^{Naka}=0.621(6) [Nakamura, Phys. Rev. A 36, 2384 (1987)0556-279110.1103/PhysRevA.36.2384]. In parallel, a comparison with previous results for jamming on these systems is also done. Finally, a complete analysis of critical exponents and universality has been done, showing that the percolation phase transition involved in the system has the same universality class as the ordinary random percolation, regardless of the size k considered.</div></front></TEI><affiliations><list><country><li>Argentine</li><li>Chili</li></country></list><tree><country name="Argentine"><noRegion><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></noRegion><name sortKey="Centres, P M" sort="Centres, P M" uniqKey="Centres P" first="P M" last="Centres">P M Centres</name></country><country name="Chili"><noRegion><name sortKey="Vogel, E E" sort="Vogel, E E" uniqKey="Vogel E" first="E E" last="Vogel">E E Vogel</name></noRegion><name sortKey="Valdes, J F" sort="Valdes, J F" uniqKey="Valdes J" first="J F" last="Valdés">J F Valdés</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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