Physical Review E, volume 86, issue 6, publication number 061116

Percolation of lineark-mers on a square lattice: From isotropic through partially ordered to completely aligned states

Tarasevich Yuri I. ¹

Lebovka Nikolai ²

Laptev Valeri V. ³

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Astrakhan State University, 20a Tatishchev Street, 414056 Astrakhan, Russia |

Institute of Biocolloidal Chemistry named after F.D. Ovcharenko, NAS of Ukraine, 42, Boulevard Vernadskogo, 03142 Kiev, Ukraine |

Astrakhan State Technical University, 16 Tatishchev Street, 414025 Astrakhan, Russia and Astrakhan State University, 20a Tatishchev Street, 414056 Astrakhan, Russia

Astrakhan State Technical University

Astrakhan State University

Publication type: Journal Article

Publication date: 2012-12-12

American Physical Society (APS)

Journal: Physical Review E

Quartile SCImago

Quartile WOS

Impact factor: 2.4

ISSN: 24700045, 24700053, 15393755, 15502376, 1063651X, 10953787

DOI: 10.1103/PhysRevE.86.061116

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General Medicine

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 the literature as rigid rods, needles, sticks) on two-dimensional square lattices $L \times L$ 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. Moreover, the behavior of percolation probability $R_L(p)$ that a lattice of size $L$ percolates at concentration $p$ has been studied in details in dependence on $k$, anisotropy and lattice size $L$. A nonmonotonic size dependence for the percolation threshold has been confirmed in isotropic case. We propose a fitting formula for percolation threshold $p_c = a/k^{\alpha}+b\log_{10} k+ c$, where $a$, $b$, $c$, $\alpha$ are the fitting parameters varying with anisotropy. We predict that for large $k$-mers ($k\gtrapprox 1.2\times10^4$) isotropic placed at the lattice, percolation cannot occur even at jamming concentration.

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	5 10 15 20 25 30 35
Physical Review E	Physical Review E, 32, 52.46% Physical Review E 32 publications, 52.46%
Journal of Statistical Mechanics: Theory and Experiment	Journal of Statistical Mechanics: Theory and Experiment, 12, 19.67% Journal of Statistical Mechanics: Theory and Experiment 12 publications, 19.67%
Physica A: Statistical Mechanics and its Applications	Physica A: Statistical Mechanics and its Applications, 7, 11.48% Physica A: Statistical Mechanics and its Applications 7 publications, 11.48%
Journal of Physics: Conference Series	Journal of Physics: Conference Series, 2, 3.28% Journal of Physics: Conference Series 2 publications, 3.28%
Physical Review Research	Physical Review Research, 2, 3.28% Physical Review Research 2 publications, 3.28%
Journal of Applied Physics	Journal of Applied Physics, 1, 1.64% Journal of Applied Physics 1 publication, 1.64%
European Physical Journal B	European Physical Journal B, 1, 1.64% European Physical Journal B 1 publication, 1.64%
Journal of Molecular Modeling	Journal of Molecular Modeling, 1, 1.64% Journal of Molecular Modeling 1 publication, 1.64%
Advances in Colloid and Interface Science	Advances in Colloid and Interface Science, 1, 1.64% Advances in Colloid and Interface Science 1 publication, 1.64%
Macromolecular Theory and Simulations	Macromolecular Theory and Simulations, 1, 1.64% Macromolecular Theory and Simulations 1 publication, 1.64%
Physical Review Letters	Physical Review Letters, 1, 1.64% Physical Review Letters 1 publication, 1.64%
	5 10 15 20 25 30 35

Citations by publishers

	5 10 15 20 25 30 35
American Physical Society (APS)	American Physical Society (APS), 35, 57.38% American Physical Society (APS) 35 publications, 57.38%
IOP Publishing	IOP Publishing, 14, 22.95% IOP Publishing 14 publications, 22.95%
Elsevier	Elsevier, 8, 13.11% Elsevier 8 publications, 13.11%
Springer Nature	Springer Nature, 2, 3.28% Springer Nature 2 publications, 3.28%
American Institute of Physics (AIP)	American Institute of Physics (AIP), 1, 1.64% American Institute of Physics (AIP) 1 publication, 1.64%
Wiley	Wiley, 1, 1.64% Wiley 1 publication, 1.64%
	5 10 15 20 25 30 35

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Tarasevich Y. I., Lebovka N., Laptev V. V. Percolation of lineark-mers on a square lattice: From isotropic through partially ordered to completely aligned states // Physical Review E. 2012. Vol. 86. No. 6. 061116

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TY - JOUR

DO - 10.1103/PhysRevE.86.061116

UR - https://doi.org/10.1103%2FPhysRevE.86.061116

TI - Percolation of lineark-mers on a square lattice: From isotropic through partially ordered to completely aligned states

T2 - Physical Review E

AU - Tarasevich, Yuri I.

AU - Lebovka, Nikolai

AU - Laptev, Valeri V.

PY - 2012

DA - 2012/12/12 00:00:00

PB - American Physical Society (APS)

IS - 6

VL - 86

SN - 2470-0045

SN - 2470-0053

SN - 1539-3755

SN - 1550-2376

SN - 1063-651X

SN - 1095-3787

ER -

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@article{2012_Tarasevich,

author = {Yuri I. Tarasevich and Nikolai Lebovka and Valeri V. Laptev},

title = {Percolation of lineark-mers on a square lattice: From isotropic through partially ordered to completely aligned states},

journal = {Physical Review E},

year = {2012},

volume = {86},

publisher = {American Physical Society (APS)},

month = {dec},

url = {https://doi.org/10.1103%2FPhysRevE.86.061116},

number = {6},

doi = {10.1103/PhysRevE.86.061116}

}

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Publisher

American Physical Society (APS)

Journal

Physical Review E

Quartile SCImago

Quartile WOS

Impact factor

2.4

ISSN

24700045 (Print)
24700053 (Electronic)
15393755 (Print)
15502376 (Electronic)
1063651X (Print)
10953787 (Electronic)

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Mathematical modeling and information technologies in science and education

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