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.
N1 - Publisher Copyright:
© 2018 Elsevier B.V.
PY - 2019/3/11
Y1 - 2019/3/11
N2 - 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 - 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.
KW - Connectivity degree
KW - Fractal networks
KW - Percolation threshold
KW - Ramification
UR - http://www.scopus.com/inward/record.url?scp=85058658787&partnerID=8YFLogxK
U2 - 10.1016/j.physleta.2018.12.018
DO - 10.1016/j.physleta.2018.12.018
M3 - Artículo
SN - 0375-9601
VL - 383
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
IS - 10
ER -