The Landau-Lifshitz/Looyenga dielectric mixture expression and its self-similar fractal nature

Enis Tuncer

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arXiv · cond-mat/0503750

The Landau-Lifshitz/Looyenga dielectric mixture expression and its self-similar fractal nature

Enis Tuncer

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Abstract

In this paper, dielectric permittivity of dielectric mixtures is discussed in view of the spectral density representation method. A distinct representation is derived for predicting the dielectric properties [Tuncer E 2005 J. Phys. Condens. Matter 17 L125]. In order to illustrate the strength of the representation and confirm the proposed hypothesis, Landau-Lifshitz/Looyenga expression is selected, and the structural information of the mixture is extracted. Both a recently developed numerical method to solve inverse integral transforms and the proposed empirical scaled permittivity expression are employed to estimate the spectral density function of the Landau-Lifshitz/Looyenga expression. In the simulations the concentration q of the inclusions phase are varied. The estimated spectral functions for the mixtures with different inclusion concentration compositions show similar spectral density functions, composed of couple of bell-shaped distributions, with coinciding peak locations. We think therefore that the coincidence is an absolute illustration of a self-similar fractal nature of mixture topology (structure) for the considered Landau-Lifshitz/Looyenga expression. Consequently, the spectra are not altered significantly with increased filler concentration level--exhibit a self-similar spectral density functions for different concentration levels. We conclude that the Landau-Lifshitz/Looyenga expression is therefore suitable for complex composite systems that have hierarchical order in their structure, which confirms the finding in the literature.

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Enis Tuncer. 2005-03-31. The Landau-Lifshitz/Looyenga dielectric mixture expression and its self-similar fractal nature. https://arxiv.org/abs/cond-mat/0503750

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