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Journal ArticleDOI

Composition law for the Cole-Cole relaxation and ensuing evolution equations

23 May 2019-Physics Letters A (North-Holland)-Vol. 383, Iss: 15, pp 1716-1721
TL;DR: In this article, the authors investigate the composition law required to be satisfied by the Cole-Cole relaxation and find its explicit form given by an integro-differential relation playing the role of the time evolution equation.
About: This article is published in Physics Letters A.The article was published on 2019-05-23 and is currently open access. It has received 8 citations till now. The article focuses on the topics: Relaxation (physics) & Cole–Cole equation.
Citations
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Journal ArticleDOI
TL;DR: The Mittag-Leffler function is universally acclaimed as the Queen function of fractional calculus as mentioned in this paper, and the Prabhakar function is a generalization of this function.
Abstract: The Mittag-Leffler function is universally acclaimed as the Queen function of fractional calculus. The aim of this work is to survey the key results and applications emerging from the three-parameter generalization of this function, known as the Prabhakar function. Specifically, after reviewing key historical events that led to the discovery and modern development of this peculiar function, we discuss how the latter allows one to introduce an enhanced scheme for fractional calculus. Then, we summarize the progress in the application of this new general framework to physics and renewal processes. We also provide a collection of results on the numerical evaluation of the Prabhakar function.

66 citations

Journal ArticleDOI
Yurun Feng1, Xue Guo1, Hongyu Gong1, Yujun Zhang1, Xiao Lin1 
TL;DR: In this paper, the Fe/C/SiCN composite ceramics were synthesized by polymer-derived method to obtain the integration of structure and functions, and the electromagnetic waves (EMW) absorption properties at X and Ku bands were investigated.

20 citations

Journal ArticleDOI
TL;DR: In this article, the one-dimensional structure of the as-prepared material was efficiently kept after partial nitridation, and the material exhibited good microwave absorption performances in X-band (8.2-12.4 GHz) with a minimum reflection loss (RL) of −−41.0 dB with an absorption bandwidth of 3.0 GHz.

10 citations

Journal ArticleDOI
TL;DR: In this article, errors in the reporting of the experimental data in the light of above issues are discussed which would be useful for researchers working in the area of dielectric properties of the materials.

10 citations

Journal ArticleDOI
TL;DR: The PDCs-SiCN(Fe) with negative permeability and permittivity were synthesized by polymer-derived method with ferric acetylacetonate as additive.

3 citations

References
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Book
01 Jan 1999

15,898 citations

Journal ArticleDOI
TL;DR: In this paper, the locus of the dielectric constant in the complex plane was defined to be a circular arc with end points on the axis of reals and center below this axis.
Abstract: The dispersion and absorption of a considerable number of liquid and dielectrics are represented by the empirical formula e*−e∞=(e0−e∞)/[1+(iωτ0)1−α]. In this equation, e* is the complex dielectric constant, e0 and e∞ are the ``static'' and ``infinite frequency'' dielectric constants, ω=2π times the frequency, and τ0 is a generalized relaxation time. The parameter α can assume values between 0 and 1, the former value giving the result of Debye for polar dielectrics. The expression (1) requires that the locus of the dielectric constant in the complex plane be a circular arc with end points on the axis of reals and center below this axis.If a distribution of relaxation times is assumed to account for Eq. (1), it is possible to calculate the necessary distribution function by the method of Fuoss and Kirkwood. It is, however, difficult to understand the physical significance of this formal result.If a dielectric satisfying Eq. (1) is represented by a three‐element electrical circuit, the mechanism responsible...

8,409 citations

Journal ArticleDOI
TL;DR: Fractional kinetic equations of the diffusion, diffusion-advection, and Fokker-Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns.

7,412 citations

Book
01 Jan 1983
TL;DR: In this paper, a broad-brush view of dielectric relaxation in solids is presented, making use of the existence of a universality of Dielectric response regardless of a wide diversity of materials and structures with dipolar as well as charge-carrier polarization.
Abstract: This review presents a wide-ranging broad-brush picture of dielectric relaxation in solids, making use of the existence of a `universality' of dielectric response regardless of a wide diversity of materials and structures, with dipolar as well as charge-carrier polarization. The review of the experimental evidence includes extreme examples of highly conducting materials showing strongly dispersive behaviour, low-loss materials with a `flat', frequency-independent susceptibility, dipolar loss peaks etc. The surprising conclusion is that despite the evident complexity of the relaxation processes certain very simple relations prevail and this leads to a better insight into the nature of these processes.

4,752 citations