Mittag–Leffler Function as an Approximant to the Concentrated Ferrofluid’s Magnetization Curve

Ryapolov, P. A.; Postnikov, Eugene B.

doi:10.3390/fractalfract5040147

Cited by 10 publications

(4 citation statements)

References 32 publications

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“…To obtain the best fit to experimental data, using a generalized model of resistors and capacitors is an alternative, with a higher number of

elements, but an increase in the number of parameters. The poor description obtained when we use exponential function to fit experimental data can be improved using a Mittag–Leffler function [ 27 , 28 ]. The Mittag–Leffler function

of one parameter

is defined as Equation (7):

where

is the gamma function,

and

.…”

Section: Resultsmentioning

confidence: 99%

Electrical Conduction Mechanisms in Ethyl Cellulose Films under DC and AC Electric Fields

Puente-Córdova,

Luna-Martínez,

Mohamed-Noriega

et al. 2024

Polymers

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This work reports the dielectric behavior of the biopolymer ethyl cellulose (EC) observed from transient currents experiments under the action of a direct current (DC) electric field (~107 V/m) under vacuum conditions. The viscoelastic response of the EC was evaluated using dynamic mechanical analysis (DMA), observing a mechanical relaxation related to glass transition of around ~402 K. Furthermore, we propose a mathematical framework that describes the transient current in EC using a fractional differential equation, whose solution involves the Mittag–Leffler function. The fractional order, between 0 and 1, is related to the energy dissipation rate and the molecular mobility of the polymer. Subsequently, the conduction mechanisms are considered, on the one hand, the phenomena that occur through the polymer–electrode interface and, on the other hand, those which manifest themselves in the bulk material. Finally, alternating current (AC) conductivity measurements above the glass transition temperature (~402 K) and in a frequency domain from 20 Hz to 2 MHz were carried out, observing electrical conduction described by the segmental movements of the polymeric chains. Its electrical properties also position EC as a potential candidate for electrical, electronics, and mechatronics applications.

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“…To obtain the best fit to experimental data, using a generalized model of resistors and capacitors is an alternative, with a higher number of

of one parameter

is defined as Equation (7):

where

is the gamma function,

and

.…”

Section: Resultsmentioning

confidence: 99%

Electrical Conduction Mechanisms in Ethyl Cellulose Films under DC and AC Electric Fields

Puente-Córdova,

Luna-Martínez,

Mohamed-Noriega

et al. 2024

Polymers

View full text Add to dashboard Cite

show abstract

“…The expression for the AME in the magnetic fluid contains the magnetization, which, as shown in Section 4.2 , depends on the structural features of the magnetic fluid, namely, on the magnetic moments and the size of the MNPs, as well as the shape of the MNPs’ size distribution curve. This establishes the groundwork for developing a new method to study the structure and macroscopic properties of magnetic fluid using the acoustic method [ 185 , 186 , 187 ]. The method’s utility stems from its relative simplicity and non-invasive nature.…”

Section: Physical Properties and Structure Of Magnetic Fluidsmentioning

confidence: 99%

Magnetic Fluids: The Interaction between the Microstructure, Macroscopic Properties, and Dynamics under Different Combinations of External Influences

Ryapolov,

Vasilyeva,

Kalyuzhnaya

et al. 2024

Nanomaterials

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Magnetic fluids were historically the first active nano-dispersion material. Despite over half a century of research, interest in these nano-objects continues to grow every year. This is due to the impressive development of nanotechnology, the synthesis of nanoscale structures, and surface-active systems. The unique combination of fluidity and magnetic response allows magnetic fluids to be used in engineering devices and biomedical applications. In this review, experimental results and fundamental theoretical approaches are systematized to predict the micro- and macroscopic behavior of magnetic fluid systems under different external influences. The article serves as working material for both experienced scientists in the field of magnetic fluids and novice specialists who are just beginning to investigate this topic.

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“…𝑧 𝑘 Γ(𝛼𝑘 + 1) ∞ 𝑘=0 (11) Entonces, la solución analítica para la ecuación 5 resulta en la ecuación 12:…”

Section: 𝐸 𝛼 (𝑧) = ∑unclassified

Aplicación del cálculo fraccionario en el modelado de corrientes transitorias en polímeros

Puente-Córdova,

Segura-Méndez,

Rentería-Baltiérrez

et al. 2024

INGENIERIAS

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En este artículo se revisan las limitaciones de los modelos matemáticos comúnmente utilizados en la literatura para la descripción general del fenómeno de corrientes transitorias en materiales poliméricos mediante una ley de la potencia o una función exponencial negativa, y se propone la aplicación del cálculo fraccionario. De entre las limitaciones de los enfoques tradicionales destacan su fracaso en la asociación de este comportamiento eléctrico característico con parámetros físicos. Las causas de éstas provienen de la complejidad del comportamiento eléctrico en los polímeros. Dicho fenómeno ocurre a través de la relajación de carga eléctrica en función del tiempo, donde la viscoelasticidad del polímero influye ampliamente en el movimiento de dipolos eléctricos y en la conducción de portadores de carga eléctrica. Típicamente, el fenómeno de corrientes transitorias se describe a través de circuitos RC (resistor-capacitor), donde un resistor y un capacitor representan la habilidad de un polímero de disipar y almacenar carga eléctrica. El modelo matemático aquí construido mediante la aplicación del cálculo fraccionario proporciona una interpretación física a sus parámetros que describen comportamientos complejos en polímeros.

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Mittag–Leffler Function as an Approximant to the Concentrated Ferrofluid’s Magnetization Curve

Cited by 10 publications

References 32 publications

Electrical Conduction Mechanisms in Ethyl Cellulose Films under DC and AC Electric Fields

Electrical Conduction Mechanisms in Ethyl Cellulose Films under DC and AC Electric Fields

Magnetic Fluids: The Interaction between the Microstructure, Macroscopic Properties, and Dynamics under Different Combinations of External Influences

Aplicación del cálculo fraccionario en el modelado de corrientes transitorias en polímeros

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