Generalized Mittag-Leffler relaxation of NH4H2PO4: Porous glass composite

Trzmiel, Justyna; Marciniszyn, T.; Komar, Jarosław

doi:10.1016/j.jnoncrysol.2011.01.032

Cited by 10 publications

(10 citation statements)

References 23 publications

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“…The modified Havriliak-Negami or JWS model. A modified version of the HN model has bee recently derived, in the diffusion framework, by A. Jurlewicz, K. Weron and A. Stanislavsky [58,113] with the aim of fitting with the Jonscher's URL some experimental data [119,120] exhibiting a less typical two-power-law relaxation pattern with frequency power law exponents m and n satisfying m < 1 − n.…”

Section: Main Models For Anomalous Dielectric Relaxationmentioning

confidence: 99%

See 1 more Smart Citation

Models of Dielectric Relaxation Based on Completely Monotone Functions

Garrappa

Mainardi

Maione

2016

FCAA

141

177

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The relaxation properties of dielectric materials are described, in the frequency domain, according to one of the several models proposed over the years: Kohlrausch-Williams-Watts, Cole-Cole, Cole-Davidson, Havriliak-Negami (with its modified version) and Excess wing model are among the most famous. Their description in the time domain involves some mathematical functions whose knowledge is of fundamental importance for a full understanding of the models. In this work, we survey the main dielectric models and we illustrate the corresponding time-domain functions. In particular, we stress the attention on the completely monotone character of the relaxation and response functions. We also provide a characterization of the models in terms of differential operators of fractional order

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Section: Main Models For Anomalous Dielectric Relaxationmentioning

confidence: 99%

“…The modified HN model proposed in [58,113], and termed as JWS in [120] earlier and in [112] later, is formulated according tô…”

Section: Main Models For Anomalous Dielectric Relaxationmentioning

confidence: 99%

Models of Dielectric Relaxation Based on Completely Monotone Functions

Garrappa

Mainardi

Maione

2016

FCAA

141

177

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“…Particularly, in the low-frequency regime. To improve a consistency between the experimental points and the fitting curve, formula (5), the mixture of the JWS and HN functions, have been applied. According to the fit quality analysis presented in Figure 2, such a mixture appears to be more appropriate fitting function for describing the data than the pure JWS function.…”

Section: Methodsmentioning

confidence: 99%

“…Indeed, the HN and CC formulas satisfy both power laws (1) and (2) To explain the less typical responses, the frequency-domain formula, termed Jurlewicz-Weron-Stanislavsky (JWS) function [5], has been derived recently in the framework of the stochastic scenarios for relaxation processes [6], [7]:…”

Section: Introductionmentioning

confidence: 99%

Two-power-law relaxation processes in semiconductors possessing metastable defects

Jurlewicz

Trzmiel

2013

2013 IEEE International Conference on Solid Dielectrics (ICSD)

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In this paper the two-power-law relaxation behavior of semiconducting materials possessing deep, metastable defects is analyzed in terms of a model leading to new power-law relaxation pattern being a mixture of the generalized MittagLeffler (GML) and Havriliak-Negami (HN) responses, which enlarges the class of physically well grounded fitting functions. Applying the probabilistic representation of the relaxation decay, we show that such a mixture can be derived from an extension of the stochastic model of correlated clusters.

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“…termed Jurlewicz, Weron and Stanislavsky (JWS) by Trzmiel et al (2011). The JWS function (1.3) satisfies the power-law properties (1.1) with n = 1 − a and m = ag fulfilling the relation m < 1 − n, and hence it is appropriate for description of less typical relaxation data.…”

Section: Introductionmentioning

confidence: 99%

Clustered continuous-time random walks: diffusion and relaxation consequences

et al. 2012

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We present a class of continuous-time random walks (CTRWs), in which random jumps are separated by random waiting times. The novel feature of these CTRWs is that the jumps are clustered. This introduces a coupled effect, with longer waiting times separating larger jump clusters. We show that the CTRW scaling limits are time-changed processes. Their densities solve two different fractional diffusion equations, depending on whether the waiting time is coupled to the preceding jump, or the following one. These fractional diffusion equations can be used to model all types of experimentally observed two power-law relaxation patterns. The parameters of the scaling limit process determine the power-law exponents and loss peak frequencies.

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Generalized Mittag-Leffler relaxation of NH4H2PO4: Porous glass composite

Cited by 10 publications

References 23 publications

Models of Dielectric Relaxation Based on Completely Monotone Functions

Models of Dielectric Relaxation Based on Completely Monotone Functions

Two-power-law relaxation processes in semiconductors possessing metastable defects

Clustered continuous-time random walks: diffusion and relaxation consequences

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