Fractals, Diffusion and Relaxation in Disordered Complex by Yuri P. Kalmykov, William T. Coffey, Stuart A. Rice

By Yuri P. Kalmykov, William T. Coffey, Stuart A. Rice

Fractals, Diffusion, and leisure in Disordered advanced structures is a distinct guest-edited, two-part quantity of Advances in Chemical Physics that keeps to record contemporary advances with major, updated chapters via across the world well-known researchers

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Dc-Conductivity Problems The dielectric spectroscopy study of conductive samples is very complicated because of the need to take into account the effect of dc-conductivity. The dcconductivity s0 contributes, in the frequency domain, to the imaginary part of the complex dielectric permittivity in the form of additional function s0 =ðe0 oÞ. The presence of dc-conductivity makes it difficult to analyze relaxation processes especially when the contribution of the conductivity is much greater than the amplitude of the process.

And it is available through an intuitive visual interface. Key features of the program include:  Advanced data visualization and preprocessing tools for displaying complex dielectric permittivity data and selecting appropriate frequency and temperature intervals for modeling  A library of standard relaxation fit functions  Simultaneous fit of both real and imaginary components of the complex dielectric permittivity data  Linear and nonlinear fitting methods, from least-squares and logarithmic to fitting procedures based on the entropy norm  Global fit procedure on all selected temperature ranges for continuous parameter estimation  Hilbert transform for computing dc-conductivity  Parameter visualization tool for displaying fitting parameter functions via temperature and subsequent analysis of the graphs The methodology described above, utilized in the presented program [132], reduces the problem of dielectric data analysis to choosing the appropriate model functions and an estimation of their model parameters.

In an important modification of regular TDR systems, a nonuniform sampling technique (parallel or series) has been developed [86,112]. In the series realization, consecutive segments of the reflected signal on an increasing time scale are registered and linked into a combined time scale. The combined response is then transformed using a running Laplace transform to produce the broad frequency spectra [112]. In the parallel realization a multi-window sampling time scale is created [86]. The implemented time scale is the piecewise approximation of the logarithmic scale.

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