Diffusion-limited coalescence and annihilation in random media

Mandache, Catalin; ben‐Avraham, Daniel

doi:10.1063/1.481365

Cited by 13 publications

(19 citation statements)

References 39 publications

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“…To solve this problem, we generalized methods first applied to the reaction-diffusion A+A problem. For the A+A → A problem the method of intervals allows an exact formulation in terms of intervals on the line that are empty of A particles [4,6,7,9,10,11]. The distribution of intervals evolves linearly, and therefore one can find an exact solution.…”

Section: Introductionmentioning

confidence: 99%

“…For example, the reactions A + A → C (some selected references of many in the literature are [1,2,3,4,5,6,7,8,9,10,11]) and A + B → C (again, some of many references are [1,12,13,14,15,16,17,18,19,20,21,22,23]) under "normal" circumstances are described by secondorder rate laws, whereas the asymptotic rate law for the former reaction is of apparent order (1 + 2/d) for dimensions d < 2, and for the mixed reaction it is of apparent order (1 + 4/d) for d < 4. The slow-down implied by the higher order is a consequence of the rapid deviation of the spatial distribution of reactants from a random distribution.…”

Section: Introductionmentioning

confidence: 99%

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Reaction front in anA+B→Creaction-subdiffusion process

2004

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We study the reaction front for the process A + B → C in which the reagents move subdiffusively. Our theoretical description is based on a fractional reaction-subdiffusion equation in which both the motion and the reaction terms are affected by the subdiffusive character of the process. We design numerical simulations to check our theoretical results, describing the simulations in some detail because the rules necessarily differ in important respects from those used in diffusive processes. Comparisons between theory and simulations are on the whole favorable, with the most difficult quantities to capture being those that involve very small numbers of particles. In particular, we analyze the total number of product particles, the width of the depletion zone, the production profile of product and its width, as well as the reactant concentrations at the center of the reaction zone, all as a function of time. We also analyze the shape of the product profile as a function of time, in particular its unusual behavior at the center of the reaction zone.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reaction front in anA+B→Creaction-subdiffusion process

2004

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“…The problem of the coagulation dynamics in a discrete segment has been solved for the normal diffusive case [10][11][12][13]. Here we present the solution for the coagulation process of subdiffusive particles on a chain of L sites with periodic boundary conditions, which is described by the hierarchy (53) together with the additional boundary condition…”

Section: Coagulation In a Segmentmentioning

confidence: 99%

“…Not only may the actual physical system be discrete, but simulations usually involve discrete lattices, and finite reactant size effects (i.e., small distance scale effects) are more appropriately dealt with through discrete formulations [10][11][12][13]. Indeed, a discrete viewpoint was the starting point of the continuum equations considered in the previous section.…”

Section: Reactions In a Latticementioning

confidence: 99%

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Subdiffusion-limited reactions

2002

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We consider the coagulation dynamics A + A → A and the annihilation dynamics A+A → 0 for particles moving subdiffusively in one dimension, both on a lattice and in a continuum. The analysis combines the "anomalous kinetics" and "anomalous diffusion" problems, each of which leads to interesting dynamics separately and to even more interesting dynamics in combination. We calculate both short-time and long-time concentrations, and compare and contrast the continuous and discrete cases. Our analysis is based on the fractional diffusion equation and its discrete analog.

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Subdiffusion‐Limited Reactions

Yuste¹,

Lindenberg²,

Ruiz-Lorenzo³

2008

Anomalous Transport

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IntroductionAnomalous diffusion processes are ubiquitous in nature [1][2][3][4][5][6]. Their occurrence is usually associated with complex systems that induce spatial and/or temporal correlations in the diffusion process. The signature of normal diffusion is the linear asymptotic dependence of the mean-square displacement of the diffusing entity (hereafter called "the particle") on time, r 2 ∼ t, t → ∞. The signature of anomalous diffusion is a nonlinear dependence on time. In particular, if the growth with time is sublinear, so that(13.1) the particle is said to be subdiffusive. (The process is superdiffusive when the limit goes to infinity.) In this chapter, we focus on the important class of subdiffusive processes for whichand where the (anomalous) diffusion exponent γ satisfies 0 < γ < 1. An interesting class of diffusive processes are so-called diffusion-limited reactions. These are processes in which diffusion is the dominant mixing mechanism and, furthermore, where the time for reactants to find one another is much longer than the time it takes for a reaction to occur following such an encounter. Therefore, in these systems diffusion is the key factor that determines the spatial distribution of reactants and the resultant reaction rate. Since diffusion is not a particularly effective mixing mechanism, diffusionlimited reactions often present extremely interesting spatial as well as temporal characteristics. In this context, it is especially appropriate to point to the pioneering work of Turing on pattern formation in reaction-diffusion systems [7]. Diffusion-limited reactions show up in a vast number of applications including not only chemical (see, e.g., [8]) but also biological (e.g., [9]), ecological (e.g., [10]) and economic processes (e.g., [11]) that have been studied over many decades.

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Diffusion-limited coalescence and annihilation in random media

Cited by 13 publications

References 39 publications

Reaction front in anA+B→Creaction-subdiffusion process

Reaction front in anA+B→Creaction-subdiffusion process

Subdiffusion-limited reactions

Subdiffusion‐Limited Reactions

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