TY - JOUR

T1 - Effects of ramification and connectivity degree on site percolation threshold on regular lattices and fractal networks

AU - Balankin, Alexander S.

AU - Martínez-Cruz, M. A.

AU - Álvarez-Jasso, M. D.

AU - Patiño-Ortiz, M.

AU - Patiño-Ortiz, J.

PY - 2019/3/11

Y1 - 2019/3/11

N2 - © 2018 Elsevier B.V. This Letter is focused on the impact of network topology on the site percolation. Specifically, we study how the site percolation threshold depends on the network dimensions (topological d and fractal D), degree of connectivity (quantified by the mean coordination number Z ∞ ), and arrangement of bonds (characterized by the connectivity index Q also called the ramification exponent). Using the Fisher's containment principle, we established exact inequalities between percolation thresholds on fractal networks contained in the square lattice. The values of site percolation thresholds on some fractal lattices were found by numerical simulations. Our findings suggest that the most relevant parameters to describe properly the values of site percolation thresholds on fractal networks contained in square lattice (Sierpiński carpets and Cantor tartans) and based on the square lattice (weighted planar stochastic fractal and Cantor lattices) are the mean coordination number and ramification exponent, but not the fractal dimension. Accordingly, we propose an empirical formula providing a good approximation for the site percolation thresholds on these networks. We also put forward an empirical formula for the site percolation thresholds on d-dimensional simple hypercubic lattices.

AB - © 2018 Elsevier B.V. This Letter is focused on the impact of network topology on the site percolation. Specifically, we study how the site percolation threshold depends on the network dimensions (topological d and fractal D), degree of connectivity (quantified by the mean coordination number Z ∞ ), and arrangement of bonds (characterized by the connectivity index Q also called the ramification exponent). Using the Fisher's containment principle, we established exact inequalities between percolation thresholds on fractal networks contained in the square lattice. The values of site percolation thresholds on some fractal lattices were found by numerical simulations. Our findings suggest that the most relevant parameters to describe properly the values of site percolation thresholds on fractal networks contained in square lattice (Sierpiński carpets and Cantor tartans) and based on the square lattice (weighted planar stochastic fractal and Cantor lattices) are the mean coordination number and ramification exponent, but not the fractal dimension. Accordingly, we propose an empirical formula providing a good approximation for the site percolation thresholds on these networks. We also put forward an empirical formula for the site percolation thresholds on d-dimensional simple hypercubic lattices.

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U2 - 10.1016/j.physleta.2018.12.018

DO - 10.1016/j.physleta.2018.12.018

M3 - Article

SP - 957

EP - 966

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

ER -