Abstract
A model of cluster formation in the percolation system is proposed. On its basis a system of differential equations for finite clusters and a differential equation for and infinite cluster are obtained. The solutions of these equations for several limiting cases are investigated. A method of approximate closure of the equation for an infinite cluster using a system of equations for a number of finite clusters is developed, and an expression for the percolation probability in the entire range of change of the part of the conducting bonds in the system is obtained by means of this method.
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Grinchuk, P.S. System of Differential Equations for the Lattice Problems of the Percolation Theory. Journal of Engineering Physics and Thermophysics 74, 596–612 (2001). https://doi.org/10.1023/A:1016795908533
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DOI: https://doi.org/10.1023/A:1016795908533