Trap-controlled fractal diffusion model of an atypical dielectric response

Khamzin, A. A.; Никитин, А. А.

doi:10.1016/j.chemphys.2021.111163

Cited by 3 publications

(3 citation statements)

References 23 publications

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“…Prabhakar in 1971 in connection with weakly singular Volterra integral equations [18]. A subset of these functions is currently used in literature to describe anomalous dielectric relaxation [45,46]. These Havriliak-Negami models are also used to describe the dielectric and viscous properties of polymeric material [47].…”

Section: Three Parameter Fractional Relaxation Equation: Prabhakar Functionmentioning

confidence: 99%

Sinc Based Inverse Laplace Transforms, Mittag-Leffler Functions and Their Approximation for Fractional Calculus

Baumann

2021

Fractal Fract

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We shall discuss three methods of inverse Laplace transforms. A Sinc-Thiele approximation, a pure Sinc, and a Sinc-Gaussian based method. The two last Sinc related methods are exact methods of inverse Laplace transforms which allow us a numerical approximation using Sinc methods. The inverse Laplace transform converges exponentially and does not use Bromwich contours for computations. We apply the three methods to Mittag-Leffler functions incorporating one, two, and three parameters. The three parameter Mittag-Leffler function represents Prabhakar’s function. The exact Sinc methods are used to solve fractional differential equations of constant and variable differentiation order.

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Section: Three Parameter Fractional Relaxation Equation: Prabhakar Functionmentioning

confidence: 99%

Sinc Based Inverse Laplace Transforms, Mittag-Leffler Functions and Their Approximation for Fractional Calculus

Baumann

2021

Fractal Fract

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“…Prabhakar in 1971 in connection with weakly singular Volterra integral equations [19]. A subset of these functions is currently used in literature to describe anomalous dielectric relaxation [46,47]. These Havriliak−Negami models are also used to describe the dielectric and viscous properties of polymeric material [48].…”

Section: Three Parameter Fractional Relaxation Equation: Prabhakar Functionmentioning

confidence: 99%

Sinc Based Inverse Laplace Transforms, Mittag-Leffler Functions and their Approximation for Fractional Calculus

Baumann¹

2021

Preprint

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We shall discuss three methods of inverse Laplace transforms. A Sinc-Thiele approxi- mation, a pure Sinc, and a Sinc-Gaussian based method. The two last Sinc related methods are exact methods of inverse Laplace transforms which allow us a numerical approximation using Sinc methods. The inverse Laplace transform converges exponentially and does not use Bromwich contours for computations. We apply the three methods to Mittag-Leffler functions incorporating one, two, and three parameters. The three parameter Mittag-Leffler function represents Prabhakar’s function. The exact Sinc methods are used to solve fractional differential equations of constant and variable differentiation order.

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“…One of the possible scenarios for the emergence of localized states (traps) is the presence in system the mobile structural defects which block the hopping of charge carriers. Note that the MT model was successfully used to study the dielectric relaxation of hexagonal ice [32,33], hexagonal ice with impurities [34], atypical dielectric response of water in confined geometry [35] and derivation of Havrilyak-Negami dielectric response [36].…”

Section: Ion Trapping Model and Ac Conductivitymentioning

confidence: 99%

Ion trapping model of the ac conductivity in disordered solids

Khamzin,

Nikitin

2021

J. Phys.: Condens. Matter

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In this paper, we develop an approach based on ions trapping to describe the conductivity spectra in disordered solids. Applying the multiple trapping model and the diffusion equation for ions, we obtained a new expression for the ac conductivity, which allows us to describe the conductivity spectra in wide ranges of frequencies and temperatures. In the high-temperature region, the new expression for the ac conductivity reproduces the Jonscher behavior, and with decreasing temperatures transforms into an expression of the NCL-type. A new expression for the ac conductivity was successfully tested on the conductivity spectra of ion-conducting glasses.

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Trap-controlled fractal diffusion model of an atypical dielectric response

Cited by 3 publications

References 23 publications

Sinc Based Inverse Laplace Transforms, Mittag-Leffler Functions and Their Approximation for Fractional Calculus

Sinc Based Inverse Laplace Transforms, Mittag-Leffler Functions and Their Approximation for Fractional Calculus

Sinc Based Inverse Laplace Transforms, Mittag-Leffler Functions and their Approximation for Fractional Calculus

Ion trapping model of the ac conductivity in disordered solids

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