Diffusion of ions in an electrostatic stochastic field and a space-dependent unperturbed magnetic field

Negrea, Marian

doi:10.1088/2058-6272/ab491e

Cited by 3 publications

(3 citation statements)

References 30 publications

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“…-Five six-parameter classes-( 27), ( 32) and ( 34) with ( 35), ( 36) and (53); -Three five-parameter classes-(55), ( 57) and (58); -At least three four-parameter classes-( 45) with ( 46), ( 49) and (51).…”

Section: Results and Discussion Of The Traveling Wave Solutionsmentioning

confidence: 99%

“…We are therefore able to conclude that this technique, with multiple auxiliary equations, does indeed provide a powerful and more effective mathematical tool. Applied here to the BD equation, it might also become applicable to a large variety of other choices of potentials in (1), obtaining information on phenomena from plasma physics [50,51], solidstate physics, chemical kinetics, fluid mechanics [52], population models, and so on.…”

Section: Discussionmentioning

confidence: 99%

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Solutions of the Bullough–Dodd Model of Scalar Field through Jacobi-Type Equations

2021

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A technique based on multiple auxiliary equations is used to investigate the traveling wave solutions of the Bullough–Dodd (BD) model of the scalar field. We place the model in a flat and homogeneous space, considering a symmetry reduction to a 2D-nonlinear equation. It is solved through this refined version of the auxiliary equation technique, and multiparametric solutions are found. The key idea is that the general elliptic equation, considered here as an auxiliary equation, degenerates under some special conditions into subequations involving fewer parameters. Using these subequations, we successfully construct, in a unitary way, a series of solutions for the BD equation, part of them not yet reported. The technique of multiple auxiliary equations could be employed to handle several other types of nonlinear equations, from QFT and from various other scientific areas.

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Section: Results and Discussion Of The Traveling Wave Solutionsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Solutions of the Bullough–Dodd Model of Scalar Field through Jacobi-Type Equations

2021

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“…In Refs. [12][13][14][15], the decorrelation trajectory (DCT) method was proposed as a method to calculate diffusion coefficients. In this method, a global ensemble is divided into many sub-ensembles.…”

Section: Introductionmentioning

confidence: 99%

Analysis of anomalous transport with temporal fractional transport equations in a bounded domain

Wu 吴,

Liu 刘,

Liu 刘

et al. 2023

Chinese Phys. B

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In this work, anomalous transport in magnetically confined plasmas is investigated using temporal fractional transport equations. The use of temporal fractional transport equations means that the order of the partial derivative with respect to time is a fraction. In this case, the Caputo fractional derivative with respect to time is utilized, because it preserves the form of the initial conditions. A numerical calculation reveals that the fractional order of the temporal derivative α (α∈(0,1), sub-diffusive regime) controls the diffusion rate. The temporal fractional derivative relates to the fact that the evolution of a physical quantity is affected by its past history, via what are termed memory effects. The magnitude of α is a measure of such memory effects. As α decreases, so does the rate of particle diffusion due to memory effects. As a result, if a system initially has a density profile without a source, then the smaller α is, the more slowly the density profile approaches zero. When a source is added, due to the balance of the diffusion and fueling processes, the system reaches a steady state and the density profile does not evolve. As α decreases, the time required for the system to reach a steady state increases. In magnetically confined plasmas, the temporal fractional transport model can be applied to off-axis heating processes. Moreover, it is found that the memory effects reduce the rate of energy conduction and that hollow temperature profiles can be sustained for a longer time in sub-diffusion processes than in ordinary diffusion processes.

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Advanced nonlinear control strategies for a fermentation bioreactor used for ethanol production

Petre

Selişteanu

Roman

2021

Bioresource Technology

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Diffusion of ions in an electrostatic stochastic field and a space-dependent unperturbed magnetic field

Cited by 3 publications

References 30 publications

Solutions of the Bullough–Dodd Model of Scalar Field through Jacobi-Type Equations

Solutions of the Bullough–Dodd Model of Scalar Field through Jacobi-Type Equations

Analysis of anomalous transport with temporal fractional transport equations in a bounded domain

Advanced nonlinear control strategies for a fermentation bioreactor used for ethanol production

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