Continuous time random walk with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e25" altimg="si3.svg"><mml:mi>A</mml:mi><mml:mo>→</mml:mo><mml:mi>B</mml:mi></mml:math> reaction in flows

Li, G.H.; Zhang, H.; Zhang, B.

doi:10.1016/j.physa.2019.121917

Cited by 4 publications

(2 citation statements)

References 23 publications

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“…The fractional dynamic approach is emerging as a novel description of anomalous transport processes [4][5][6]. Numerous researchers have applied the fractional derivative models to describe the turbulent flow [7], non-Darcian flow [8][9][10], transient flow [11], atmospheric pollutant dispersion [12,13], solute transport [14], and contaminant migration [15,16].…”

Section: Introductionmentioning

confidence: 99%

Fractional Advection Diffusion Models for Radionuclide Migration in Multiple Barriers System of Deep Geological Repository

2022

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Based on the multiple barriers concept of deep geological disposal of high-level waste, fractional advection diffusion equations for radionuclide migration in multiple layers low-permeability porous media are proposed in this work. The presented fractional advection diffusion models in terms of different definitions of fractional derivative are analytically addressed via the Laplace integral transform method. This work provides a theoretical foundation for further simulations of radionuclide migration in the multiple barriers system of the high-level waste repository.

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Section: Introductionmentioning

confidence: 99%

Fractional Advection Diffusion Models for Radionuclide Migration in Multiple Barriers System of Deep Geological Repository

2022

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“…A fundamental and now longstanding question is how to model reaction kinetics for subdiffusive molecules (see the review [12] and [13][14][15][16][17][18][19][20][21][22]). In the classical case of normal diffusion, reaction terms can simply be added to the evolution equations describing spatial movement.…”

Section: Introductionmentioning

confidence: 99%

Anomalous reaction-diffusion equations for linear reactions

Lawley

2020

Preprint

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Deriving evolution equations accounting for both anomalous diffusion and reactions is notoriously difficult, even in the simplest cases. In contrast to normal diffusion, reaction kinetics cannot be incorporated into evolution equations modeling subdiffusion by merely adding reaction terms to the equations describing spatial movement. A series of previous works derived fractional reactiondiffusion equations for the spatiotemporal evolution of particles undergoing subdiffusion in one space dimension with linear reactions between a finite number of discrete states. In this paper, we first give a short and elementary proof of these previous results. We then show how this argument gives the evolution equations for more general cases, including subdiffusion following any fractional Fokker-Planck equation in an arbitrary d-dimensional spatial domain with time-dependent reactions between infinitely many discrete states. In contrast to previous works which employed a variety of technical mathematical methods, our analysis reveals that the evolution equations follow from (i) the probabilistic independence of the stochastic spatial and discrete processes describing a single particle and (ii) the linearity of the integro-differential operators describing spatial movement. We also apply our results to systems combining reactions with superdiffusion.

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Anomalous reaction-diffusion equations for linear reactions

Lawley

2020

Phys. Rev. E

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Continuous time random walk with A→B reaction in flows

Cited by 4 publications

References 23 publications

Fractional Advection Diffusion Models for Radionuclide Migration in Multiple Barriers System of Deep Geological Repository

Fractional Advection Diffusion Models for Radionuclide Migration in Multiple Barriers System of Deep Geological Repository

Anomalous reaction-diffusion equations for linear reactions

Anomalous reaction-diffusion equations for linear reactions

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