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Ukr. J. Phys. 2015, Vol. 60, N 9, p.910-916
doi:10.15407/ujpe60.09.0910    Paper

Lebovka N.I.1, Bulavin L.A.2, Melnyk I.A.2, Repnin K.F.2, Kovalchuk V.I.2

1 F.D. Ovcharenko Biocolloidal Chemistry Institute, Nat. Acad. of Sci. of Ukraine
(42, Academician Vernadsky Blvd., Kyiv 03142, Ukraine; e-mail: lebovka@gmail.com)
2 Taras Shevchenko National University of Kyiv, Faculty of Physics
(2, Academician Glushkov Prosp., Kyiv 03022, Ukraine)

Impact of Aggregation on the Percolation Anisotropy on a Square Lattice in an Elongated Geometry

Section: Solid matter
Original Author's Text: English

Abstract: The Monte Carlo simulation is applied to study the impact of the aggregation on the percolation anisotropy on a square lattice in the elongated Lx X Ly geometry. An interactive cluster-growth model, in which the probability of occupying a site on a lattice fz is dependent on the number of occupied neighboring sites z is used. The value of fz is 1/r at z = 0 and is equal to 1 in other cases. The degree of the aggregation parameter r ≥ 1 controls the morphology of aggregates. The transition from r = 1 to r →∞ corresponds to the transition from the ordinary random percolation to the percolation of compact Eden clusters. The effects of the lattice aspect ratio a = Lx/Ly (Lx > Ly ) on the finite-size scaling and the electrical conductivity are studied. The data evidence that the percolation threshold pc goes through the minimum, and the finite-size effects are enhanced with increase in r. The dependence of the electrical conductivity on the measuring direction (x or y) at different values of r and a is discussed.

Key words: aggregation, anisotropy, correlated percolation, elongated systems, electrical conductivity.