  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.
