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Keywords = Davidson–Cole model

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18 pages, 426 KB  
Article
A New Look at the Capacitor Theory
by Manuel Duarte Ortigueira, Valeriy Martynyuk, Volodymyr Kosenkov and Arnaldo Guimarães Batista
Fractal Fract. 2023, 7(1), 86; https://doi.org/10.3390/fractalfract7010086 - 12 Jan 2023
Cited by 28 | Viewed by 5172
Abstract
The mathematical description of the charging process of time-varying capacitors is reviewed and a new formulation is proposed. For it, suitable fractional derivatives are described. The case of fractional capacitors that follow the Curie–von Schweidler law is considered. Through suitable substitutions, a similar [...] Read more.
The mathematical description of the charging process of time-varying capacitors is reviewed and a new formulation is proposed. For it, suitable fractional derivatives are described. The case of fractional capacitors that follow the Curie–von Schweidler law is considered. Through suitable substitutions, a similar scheme for fractional inductors is obtained. Formulae for voltage/current input/output are presented. Backward coherence with classic results is established and generalised to the variable order case. The concept of a tempered fractor is introduced and related to the Davidson–Cole model. Full article
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14 pages, 5296 KB  
Article
Hopping Conductivity and Dielectric Relaxations in Ag/PAN Nanocomposites
by M.A. Kudryashov, A.A. Logunov, L.A. Mochalov, Yu.P. Kudryashova, M.M. Trubyanov, A.V. Barykin and I.V. Vorotyntsev
Polymers 2021, 13(19), 3251; https://doi.org/10.3390/polym13193251 - 24 Sep 2021
Cited by 10 | Viewed by 3208
Abstract
The dependence of the conductivity and electric modulus of silver/polyacrylonitrile nanocomposites on the frequency of an alternating electric field has been studied at different temperatures and starting mixture AgNO3 contents. The frequency dependences on the conductivity of the nanocomposites in the range [...] Read more.
The dependence of the conductivity and electric modulus of silver/polyacrylonitrile nanocomposites on the frequency of an alternating electric field has been studied at different temperatures and starting mixture AgNO3 contents. The frequency dependences on the conductivity of the nanocomposites in the range of 103–106 Hz are in good agreement with the power law f0.8. The observed relaxation maxima in the relation of the imaginary part of the electric modulus on the frequency can be explained by interfacial polarization. It was shown that the frequency dispersions of conductivity and electric modulus were well described by the Dyre and Cole-Davidson models, respectively. Using these models, we have estimated the relaxation times and the activation energies of these structures. A mechanism of charge transport responsible for the conductivity of nanocomposites is proposed. An assumption is made regarding the presence of Ag42+ and Ag82+ silver clusters in the polymer. Full article
(This article belongs to the Topic Multiple Application for Novel and Advanced Materials)
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15 pages, 4851 KB  
Article
Realization of Cole–Davidson Function-Based Impedance Models: Application on Plant Tissues
by Stavroula Kapoulea, Costas Psychalinos and Ahmed S. Elwakil
Fractal Fract. 2020, 4(4), 54; https://doi.org/10.3390/fractalfract4040054 - 30 Nov 2020
Cited by 14 | Viewed by 4807
Abstract
The Cole–Davidson function is an efficient tool for describing the tissue behavior, but the conventional methods of approximation are not applicable due the form of this function. In order to overcome this problem, a novel scheme for approximating the Cole–Davidson function, based on [...] Read more.
The Cole–Davidson function is an efficient tool for describing the tissue behavior, but the conventional methods of approximation are not applicable due the form of this function. In order to overcome this problem, a novel scheme for approximating the Cole–Davidson function, based on the utilization of a curve fitting procedure offered by the MATLAB software, is introduced in this work. The derived rational transfer function is implemented using the conventional Cauer and Foster RC networks. As an application example, the impedance model of the membrane of mesophyll cells is realized, with simulation results verifying the validity of the introduced procedure. Full article
(This article belongs to the Special Issue Fractional-Order Circuits and Systems)
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10 pages, 275 KB  
Article
Dielectric Properties of Binary Solvent Mixtures of Dimethyl Sulfoxide with Water
by Li-Jun Yang, Xiao-Qing Yang, Ka-Ma Huang, Guo-Zhu Jia and Hui Shang
Int. J. Mol. Sci. 2009, 10(3), 1261-1270; https://doi.org/10.3390/ijms10031261 - 17 Mar 2009
Cited by 73 | Viewed by 16699
Abstract
In this paper, the dielectric properties of water-dimethylsulfoxide (DMSO) mixtures with different mole ratios have been investigated in the range of 1 GHz to 40 GHz at 298 K by using a molecular dynamics (MD) simulation. Only one dielectric loss peak was observed [...] Read more.
In this paper, the dielectric properties of water-dimethylsulfoxide (DMSO) mixtures with different mole ratios have been investigated in the range of 1 GHz to 40 GHz at 298 K by using a molecular dynamics (MD) simulation. Only one dielectric loss peak was observed in the frequency range and the relaxation in these mixtures can be described by a single relaxation time of the Davidson-Cole. It was observed that within experimental error the dielectric relaxation can be described by the Debye-like model (β ≈ 1, S.M. Puranik, et al. J. Chem. Soc. Faraday Trans.1992, 88, 433 - 435). In general, the results are very consistent with the experimental measurements. Full article
(This article belongs to the Section Physical Chemistry, Theoretical and Computational Chemistry)
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