Properties of the relaxation time distribution underlying the Kohlrausch–Williams–Watts photoionization of the DX centers in Cd1−xMnxTe mixed crystals

Trzmiel, Justyna; Weron, Karina; Janczura, Joanna; Płaczek‐Popko, E.

doi:10.1088/0953-8984/21/34/345801

Cited by 19 publications

(14 citation statements)

References 13 publications

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“…They have an almost equal crossing time t ≈ 1 s. Also, it is observed that of these three derivatives, the derivative of Atangana-Baleanu could describe a wider class of physical processes, becuase it is described in terms of Mittag-Leffler function. Finally, the conformable derivative gives as a solution the stretched exponential behavior, the crossing time is t conf ≈ 3 s. This behavior has been observed in a large number of complex physical processes [53][54][55][56][57][58][59]. Similar behaviors are observed in the case of alternating current AC, Figs.…”

Section: Comparisonsupporting

confidence: 67%

“…This derivative is a natural extension of the ordinary derivative, as a limit, and has the same properties as the ordinary one. This derivative can describe phenomena, such as relaxation processes in complex systems and so on [53][54][55][56][57][58]. As far as we know, the conformable derivative had not been applied to the RC circuit.…”

Section: Resultsmentioning

confidence: 99%

“…Much slower than the three previous cases. Stretched exponential functions are commonly observed in disordered systems [53][54][55][56][57][58][59]. The possible origen of the stretched exponential is given in [60].…”

Section: Rc With Conformable Fractional Derivativementioning

confidence: 99%

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A comparative analysis of the RC circuit with local and non-local fractional derivatives

García¹,

Filoteo²,

González

2018

Rev. Mex. Fís.

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This work is devoted to investigate solutions to RC circuits using four different types of time fractional diferential operators of order 0 < γ ≤ 1. The fractional derivatives considered are, Caputo, Caputo-Fabrizio, Atangana-Baleanu and the conformable derivative. It is shown that Atangana-Baleanu fractional derivative (non-local), and the conformable (local) derivative could describe a wider class of physical processes then the Caputo and Caputo-Fabrizio. The solutions are exactly equal for all four erivatives only for the case γ=1.

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Section: Comparisonsupporting

confidence: 67%

Section: Resultsmentioning

confidence: 99%

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A comparative analysis of the RC circuit with local and non-local fractional derivatives

García¹,

Filoteo²,

González

2018

Rev. Mex. Fís.

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“…The first derivative diverges when t → 0 for any β < 1. In addition, the corresponding response function expressed by the negative time derivative of g(t) exhibits short-time power-law properties and decays stretchedexponentially for long time [146] (see also [128]), namely…”

Section: Kohlrausch Function:properties and Approximationsmentioning

confidence: 99%

Response functions in linear viscoelastic constitutive equations and related fractional operators

Hristov

2019

Math. Model. Nat. Phenom.

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This study addresses the stress–strain relaxation functions of solid polymers in the framework of the linear viscoelasticity with aim to establish the adequate fractional operators emerging from the hereditary integrals. The analysis encompasses power-law and non-power-law materials, thus allowing to see the origins of application of the tools of the classical fractional calculus with singular memory kernels and the ideas leading towards fractional operators with non-singular (regular) kernels. A step ahead in modelling with hereditary integrals is the decomposition of non-power-law relaxation curves by Prony series, thus obtaining discrete relaxation kernels with a finite number of terms. This approach allows for seeing the physical background of the newly defined Caputo–Fabrizio time fractional derivative and demonstrates how other constitutive equations could be modified with non-singular fading memories. The non-power-law relaxation curves also allow for approximations by the Mittag–Leffler function of one parameter that leads reasonably into stress–strain hereditary integrals in terms of Atangana–Baleanu fractional derivative of Caputo sense. The main outcomes of the analysis done are the demonstrated distinguishes between the relaxation curve behaviours of different materials and are therefore the adequate modelling with suitable fractional operators.

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“…The KWW functional has been successfully applied to many out-ofequilibrium systems, with an anticorrelation between the disorder and β. 47,48 The fitting coefficients for a KWW analysis of the averaged piezoresponse over time for each composition and voltage are reported in Figs S4-S9 in the Supplementary Information (Figs S4 and S5 plot PMN's response to positive and negative applied voltages, respectively, Figs S6 and S7 plot PMN-0.36PT's response to positive and negative applied voltages, respectively; and Figs S8 and S9 plot PMN-0.40PT's response to positive and negative applied voltages, respectively). However, while such an approach benefits from the reduced statistical noise due to spatial averaging, it results in a loss of any spatial information and therefore possible local chemical heterogeneities.…”

Section: Discussionmentioning

confidence: 99%

Smart machine learning or discovering meaningful physical and chemical contributions through dimensional stacking

et al. 2019

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Despite remarkable advances in characterization techniques of functional materials yielding an ever growing amount of data, the interplay between the physical and chemical phenomena underpinning materials' functionalities is still often poorly understood. Dimensional reduction techniques have been used to tackle the challenge of understanding materials' behavior, leveraging the very large amount of data available. Here, we present a method for applying physical and chemical constraints to dimensional reduction analysis, through dimensional stacking. Compared to traditional, uncorrelated techniques, this approach enables a direct and simultaneous assessment of behaviors across all measurement parameters, through stacking of data along specific dimensions as required by physical or chemical correlations. The proposed method is applied to the nanoscale electromechanical relaxation response in (1 − x)PMN-xPT solid solutions, enabling a direct comparison of electric fieldand chemical composition-dependent contributors. A poling-like, and a relaxation-like behavior with a domain glass state are identified, and their evolution is tracked across the phase diagram. The proposed dimensional stacking technique, guided by the knowledge of the underlying physics of correlated systems, is valid for the analysis of any multidimensional dataset, opening a spectrum of possibilities for multidisciplinary use.npj Computational Materials (2019) 5:85 ; https://doi.

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Properties of the relaxation time distribution underlying the Kohlrausch–Williams–Watts photoionization of the DX centers in Cd_1−xMn_xTe mixed crystals

Cited by 19 publications

References 13 publications

A comparative analysis of the RC circuit with local and non-local fractional derivatives

A comparative analysis of the RC circuit with local and non-local fractional derivatives

Response functions in linear viscoelastic constitutive equations and related fractional operators

Smart machine learning or discovering meaningful physical and chemical contributions through dimensional stacking

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