Fractional Anomalous Diffusion

Evangelista, L. R.; Lenzi, E. K.

doi:10.1007/978-3-031-18150-4_5

Cited by 4 publications

(4 citation statements)

References 68 publications

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“…The values chosen for the parameters

and

are responsible for different behaviors of the mean square displacement for each case, as pointed out in the inset of Figure 1 . In particular, the diffusion present in this scenario is anomalous [ 51 , 52 ]. Figure 2 shows the behavior of Equation ( 41 ) for two different sets of

and

.…”

Section: The Problemmentioning

confidence: 99%

Nonlinear Fokker–Planck Equations, H-Theorem and Generalized Entropy of a Composed System

Evangelista,

Lenzi

2023

Entropy

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We investigate the dynamics of a system composed of two different subsystems when subjected to different nonlinear Fokker–Planck equations by considering the H–theorem. We use the H–theorem to obtain the conditions required to establish a suitable dependence for the system’s interaction that agrees with the thermodynamics law when the nonlinearity in these equations is the same. In this framework, we also consider different dynamical aspects of each subsystem and investigate a possible expression for the entropy of the composite system.

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“…The values chosen for the parameters

and

.…”

Section: The Problemmentioning

confidence: 99%

Nonlinear Fokker–Planck Equations, H-Theorem and Generalized Entropy of a Composed System

Evangelista,

Lenzi

2023

Entropy

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“…A generalization of the PNP-model involving fractional derivatives has been proposed by Evangelista and Lenzi, which is an intriguing approach . In this paper, however, we limit our analysis to the standard case, as the dependence of the fractional order of the time derivative on the trapping parameters has not yet been investigated.…”

Section: Introductionmentioning

confidence: 99%

Drift-Diffusion Phenomenon in the Presence of Reversible Trapping Reaction

Lelidis,

Alexe-Ionescu,

Barbero

2024

J. Phys. Chem. C

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The time evolution of the bulk density of particles in a fixed matrix within a cell in the shape of a slab is investigated in the presence of a reversible trapping reaction. The relaxation times are determined, and their dependence on the trapping parameters is explored. The analysis is performed for both neutral and charged particles. In the case of charged particles, such as ions in a solid electrolyte, ions in hydro-gels, or ions in porous electrodes, we assume that only the ions of a given sign contribute to the conduction current. We demonstrate that, besides the Debye's relaxation time τ D = Λ 2 /D, where Λ is the Debye length and D the diffusion coefficient, another relaxation time defined by τ = Λd/(2D), where d is the thickness of the sample, plays a significant role. The special case in which the exciting electric field is a simple harmonic function is also investigated. In this case, the electric impedance of the cell is determined, and its dc limit, as well as its high-frequency limit, are discussed. We investigate specific cases where the electrodes are blocking, transparent, or one is blocking while the other is transparent. As expected, in the high-frequency limit, the impedance becomes independent of the electrode characteristics. Both the resistance and reactance are bulk properties proportional to the sample's thickness. In contrast, in the low-frequency limit, interface resistance and reactance, localized over a thickness of the order of the Debye length, must be added to the bulk values, which still scale with the cell's thickness. The dependence of the interface properties on the trapping parameters is discussed.

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“…In recent decades, adsorption has been considered a promising wastewater treatment technique. − It is an efficient method of removing organic compounds and metals from water . Adsorption is a cost-effective and energy-efficient method that does not require much energy and has the potential to remove pollutants from water with minimal environmental impact. , Consequently, understanding adsorption kinetics is crucial for designing and operating adsorption equipment. − As a general rule, most literature uses two types of kinetic equations to describe adsorption phenomena: pseudo-first-order (PFO) and pseudo-second-order (PSO). , There have also been other models developed and applied to different situations of adsorption kinetics, such as Elovich, Brouers–Sotolongo, , fractal-like kinetics, and the mixed-order model …”

Section: Introductionmentioning

confidence: 99%

Fractional Kinetic Strategy toward the Adsorption of Organic Dyes: Finding a Way Out of the Dilemma Relating to Pseudo-First- and Pseudo-Second-Order Rate Laws

Tawfik,

Eltabey

2024

J. Phys. Chem. A

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Recently, there has been debate about using a pseudo-second-order model in adsorption kinetics and its ability to fit experimental data, especially at the initial stages. This paper introduces a generalized fractional kinetic model obtained via a fractional reaction–diffusion equation with a time-dependent reaction rate. This model is presented as a dependable approach to understanding chemical adsorption kinetics. It offers insights into the adsorbate history and extends classical kinetic models, such as pseudo-first-order and pseudo-second-order models. The generalized fractional kinetic model accounts for memory effects with long-range interactions, heterogeneity, and nonequilibrium dynamics, leading to more accurate predictions of adsorption rates, capacities, and equilibrium values. As an applied context, we use the fractional kinetic model to analyze experimental data on the adsorption of anionic acid yellow-17 and cationic brilliant green dyes in single and binary systems. The fractional kinetic model is employed to fit the data by incorporating waiting times into the adsorption process and correlating macroscopic properties, such as the pH, with adsorption dynamics.

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Fractional Anomalous Diffusion

Cited by 4 publications

References 68 publications

Nonlinear Fokker–Planck Equations, H-Theorem and Generalized Entropy of a Composed System

Nonlinear Fokker–Planck Equations, H-Theorem and Generalized Entropy of a Composed System

Drift-Diffusion Phenomenon in the Presence of Reversible Trapping Reaction

Fractional Kinetic Strategy toward the Adsorption of Organic Dyes: Finding a Way Out of the Dilemma Relating to Pseudo-First- and Pseudo-Second-Order Rate Laws

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