THE SCALING LAW FOR THE DISCRETE KINETIC GROWTH PERCOLATION MODEL

Subject Areas : International Journal of Mathematical Modelling & Computations

K. Yamamoto ¹ , Y. Yamada ² , S. Miyazima ³

1 - Setsunan University 17-8 Ikeda-Nakamachi, Neyagawa Osaka 572-8508 Japan Faculty of Engineering
2 - Chubu University 1200 Matsumoto, Kasugai Aichi 487-8501 Japan Department of Natural Science
3 - Chubu University 1200 Matsumoto, Kasugai Aichi 487-8501 Japan Department of Natural Science

Received: 2016-04-13 Accepted : 2016-04-13 Published : 2011-09-23

Keywords: Percolation problem, Scaling law, Kinetic growth model, Leath algorithm,

Abstract :

The Scaling Law for the Discrete Kinetic Growth Percolation Model The critical exponent of the total number of finite clusters α is calculated directly without using scaling hypothesis both below and above the percolation threshold pcbased on a kinetic growth percolation model in two and three dimensions. Simultaneously, we can calculate other critical exponents β and γ, and show that the scaling law α + 2β +γ = 2 has been held in the simulation result above the percolation threshold pc.