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References in periodicals archive ?
There are several mixing rules commonly used in the literature; 1) molar refraction and absorption, 2) volume-weighted linear average of the refractive indices, 3) Maxwell-Garnett rule, 4) dynamic effective approximation, and 5) Bruggeman rule (Abo Riziq et al.
(2005) found similar agreement when applying the shell-and-core and the Maxwell-Garnett rules to urban-industrial climatologies.
On the other hand, Maxwell-Garnett based analysis of (1) and (4) indicates that even far from ENZ conditions a superconductor-dielectric metamaterial must have larger [DELTA] and higher [T.sub.c] compared to the original undiluted superconducting host.
Similar to the random superconductor-dielectric mixture considered above, the diagonal dielectric permittivity components of the layered superconductor-dielectric metamaterial maybe calculated using Maxwell-Garnett approximation.
However, apart from the core-shell model, the classical mixing formulas such as the Mean-field approach by Maxwell-Garnett [12], the Litchenker's Logarithmic mixture formula [13,14], the Bruggeman mixing formula [15], the analytical approaches using the diagrammatic expansions [16] and Fourier series [17] have also the potential to be used for the metal powder composites in a way similar to the dielectric mixtures for which these formulas were originally proposed.
These estimated material properties are then compared with the standard Maxwell-Garnett law [12], the Logarithmic law of mixing [13, 14], and the Clausius-Mossotti relationship [32] for various volume fractions and permittivity values in order to validate the proposed approach.
Firstly, the proposed unit cell approach is validated for some standard mixed dielectric samples by comparing the results of the proposed unit cell approach assuming a TEM mode propagation with those obtained by the conventional mixing formulas such as the Maxwell-Garnett, Logarithmic laws etc.
Various EMTs have been published,[3,4] including a recent technical review.[10] Two theoretical formulations were used in the current study, a self-consistent theory similar to that of Webman[4] and a modification of the Maxwell-Garnett theory.[3]
Equation 5 and the more familiar Maxwell-Garnett formulation become numerically equivalent when either the composite constituents have permittivities that are not too different, that is, [Epsilon.sub.1]/ [Epsilon.sub.2][is less than or equal to]5 for a two-component mixture, or in the limit of small volume fraction, that is, [f.sub.1][Is less than or equal to] 0.15 in a two-component mixture.
Those results are similar to those that applied the Maxwell-Garnett model in the optimum design of mm-wave windows.[13]
G., "Active Maxwell-Garnett composite with the unit refractive index," Physica B: Condensed Matter, Vol.
[20.] Ruppin, R., "Evaluation of extended Maxwell-Garnett theories," Optics Communications, Vol.