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

  • N. I. Lebovka F.D. Ovcharenko Biocolloidal Chemistry Institute, Nat. Acad. of Sci. of Ukraine
  • L. A. Bulavin Taras Shevchenko National University of Kyiv, Faculty of Physics
  • I. A. Melnyk Taras Shevchenko National University of Kyiv, Faculty of Physics
  • K. F. Repnin Taras Shevchenko National University of Kyiv, Faculty of Physics
  • V. I. Kovalchuk Taras Shevchenko National University of Kyiv, Faculty of Physics
Keywords: aggregation, anisotropy, correlated percolation, elongated systems, electrical conductivity

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 × 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.

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Published
2019-01-15
How to Cite
Lebovka, N., Bulavin, L., Melnyk, I., Repnin, K., & Kovalchuk, V. (2019). Impact of Aggregation on the Percolation Anisotropy on a Square Lattice in an Elongated Geometry. Ukrainian Journal of Physics, 60(9), 910. https://doi.org/10.15407/ujpe60.09.0910
Section
Solid matter

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