SYSTEM OF DIFFERENTIAL EQUATIONS FOR 
THE LATTICE PROBLEMS OF THE PERCOLATION THEORY
P. S. Grinchuk

UDC 539.217.1

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.

Academic Scientific Complex "A. V. Luikov Heat and Mass 
Transfer Institute," National Academy of Sciences of Belarus, Minsk, 
Belarus; email: gps@hmti.ac.by. Translated from Inzhenerno-Fizicheskii 
Zhurnal, Vol. 74, No. 3, pp. 44-55, May-June, 2001. 
Original article submitted November 1, 2000.

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