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The analysis shows that the effective medium approximation is valid even when periodicity is comparable to wavelength.

The effective medium approximation is used to relate explicitly the conductance of a macroscopic model stochastic network to the structural characteristics of its constituent microscopic elements.

A Bruggeman effective medium approximation is used to calculate the effective dielectric function of the rough layer that is assumed to consist of 50% TiO2 and 50% voids of refractive index unity [43].

A model based on the effective medium approximation is presented which describes surface diffusivity on an energetically heterogeneous surface as a function of overall surface coverage and a heterogeneity parameter.

The Bruggeman effective medium approximation is used to obtain the refractive index of the porous layer (neff) from the refractive index of the aluminum oxide[25] and that of air (nair = 1) taking into account the corresponding volume fractions: 1 - P n Alumina 2 - n eff 2 n Alumina 2 + 2 n eff 2 + P 1 - n eff 2 1 + 2 n ef f 2 = 0. (1).

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Bruggeman effective medium approximation was used to describe the optical functions of intermediate layers.

The limits of validity and the discrepancies due to the optically thin medium approximation are also investigated.

To predict the variation of refractive index n versus x, the Bruggeman effective medium approximation was used based on the approach described in [25].

Bruggeman effective medium approximation was used to estimate the effective optical parameters of PSi [37, 38]: f P ε Si − ε PSi ε Si + 2 ε PSi + ( 1 − f P ) 1 − ε PSi 1 + 2 ε PSi = 0 (6).

The results of the two analytical methods agree very well with the numerical results for high Peclet numbers; however, the predictions of the semi-infinite medium approximation are inaccurate at low Peclet numbers and for positive nozzle exit angles.

For two- and three-dimensional networks, an effective-medium approximation is developed to predict the effective reaction rate, the effective diffusivity (under reactive conditions), the distribution of the concentrations of the reactants in the porespace, and the effectiveness factor.

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