Static percolation

A. Static Percolation in Porous Materials, Fractal Concept, and Porosity Determination... 

The set of structural parameters obtained by fitting and by using relationship (79) allows us to reconstruct the cluster size distribution function w(s,sm) and to treat the dynamic percolation in ionic microemulsions in terms of the classical static percolation model. 

One way to determine the characteristics of these trajectories is by solving a transport equation with different probabilities of hopping of the charge carrier and the corresponding diffusion parameters of the host droplet. Another way, which we shall use here, is based on a visualization of the equivalent static cluster structure. This approach allows us to interpret the dynamic percolation process in terms of the static percolation. 

In the static percolation model the trajectory of the charge carrier passes through both a real and visual percolation cluster. While the real cluster in the dynamic percolation is invisible, the charge carrier trajectory can be drawn. In order to visualize the real cluster in the case of dynamic percolation let us assume that the site of trajectory intersections belongs to the equivalent static... 

Note that the dynamic fractal dimension obtained on the basis of the temporal scaling law should not necessarily have a value equal to that of the static percolation. We shall show here that in order to establish a relationship between the static and dynamic fractal dimensions, we must go beyond relationships (83) and (84) for the scaling exponents. 

In order to establish the relationship between the static and dynamic fractal dimensions, the initial conditions of the classical static percolation model must be considered for the solution of differential equation (89) which can be written as 0 = Qs = 1 for D = Ds. Here the notation s corresponds to the static percolation model, and the condition s = 1 is fulfilled for an isotropic cubic hyperlattice. The solution of (89) with the above-mentioned initial conditions may be written as... 

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