Comparison of methods for estimating continuous distributions of relaxation times

The nonparametric estimation of the distribution of relaxation times approach is not as frequently used in the analysis of dispersed response of dielectric or conductive materials as are other immittance data analysis methods based on parametric curve fitting techniques. Nevertheless, such distributions can yield important information about the physical processes present in measured material. In this letter, we apply two quite different numerical inversion methods to estimate the distribution of relaxation times for glassy \lila\ dielectric frequency-response data at 225 \kelvin. Both methods yield unique distributions that agree very closely with the actual exact one accurately calculated from the corrected bulk-dispersion Kohlrausch model established independently by means of parametric data fit using the corrected modulus formalism method. The obtained distributions are also greatly superior to those estimated using approximate functions equations given in the literature.Comment: 4 pages and 4 figure

How can one probe Podolsky Electrodynamics?

We investigate the possibility of detecting the Podolsky generalized electrodynamics constant $a$. First we analyze an ion interferometry apparatus proposed by B. Neyenhuis, et al (Phys. Rev. Lett. 99, (2007) 200401) who looked for deviations from Coulomb's inverse-square law in the context of Proca model. Our results show that this experiment has not enough precision for measurements of $a$. In order to set up bounds for $a$ we investigate the influence of Podolsky's electrostatic potential on the ground state of the Hydrogen atom. The value of the ground state energy of the Hydrogen atom requires Podolsky's constant to be smaller than 5.6 fm, or in energy scales larger than 35.51 MeV.Comment: 12 pages, 2 figure

Extracting spectral density function of a binary composite without a-priori assumption

The spectral representation separates the contributions of geometrical arrangement (topology) and intrinsic constituent properties in a composite. The aim of paper is to present a numerical algorithm based on the Monte Carlo integration and contrainted-least-squares methods to resolve the spectral density function for a given system. The numerical method is verified by comparing the results with those of Maxwell-Garnett effective permittivity expression. Later, it is applied to a well-studied rock-and-brine system to instruct its utility. The presented method yields significant microstructural information in improving our understanding how microstructure influences the macroscopic behaviour of composites without any intricate mathematics.Comment: 4 pages, 5 figures and 1 tabl

On micro-structural effects in dielectric mixtures

The paper presents numerical simulations performed on dielectric properties of two-dimensional binary composites on eleven regular space filling tessellations. First, significant contributions of different parameters, which play an important role in the electrical properties of the composite, are introduced both for designing and analyzing material mixtures. Later, influence of structural differences and intrinsic electrical properties of constituents on the composite's over all electrical properties are investigated. The structural differences are resolved by the spectral density representation approach. The numerical technique, without any {\em a-priori} assumptions, for extracting the spectral density function is also presented.Comment: 24 pages, 8 figure and 7 tables. It is submitted to IEEE Transactions on Dielectrics and Electrical Insulatio