Anomalous subdiffusion with multispecies linear reaction dynamics

Article


Langlands, Trevor, Henry, B. I. and Wearne, S. L.. 2008. "Anomalous subdiffusion with multispecies linear reaction dynamics." Physical Review B: Covering condensed matter and materials physics. 77, pp. 1-9. https://doi.org/10.1103/PhysRevE.77.021111
Article Title

Anomalous subdiffusion with multispecies linear reaction dynamics

ERA Journal ID1131
1018
Article CategoryArticle
AuthorsLanglands, Trevor (Author), Henry, B. I. (Author) and Wearne, S. L. (Author)
Journal TitlePhysical Review B: Covering condensed matter and materials physics
Physical Review E
Journal Citation77, pp. 1-9
Number of Pages9
Year2008
PublisherAmerican Physical Society
Place of PublicationUnited States
ISSN1098-0121
1550-235X
2469-9950
2469-9969
1539-3755
1550-2376
2470-0045
2470-0053
Digital Object Identifier (DOI)https://doi.org/10.1103/PhysRevE.77.021111
Web Address (URL)http://link.aps.org/doi/10.1103/PhysRevE.77.021111
Abstract

We have introduced a set of coupled fractional reaction-diffusion equations to model a multispecies system undergoing anomalous subdiffusion with linear reaction dynamics. The model equations are derived from a mesoscopic continuous time random walk formulation of anomalously diffusing species with linear mean field reaction kinetics. The effect of reactions is manifest in reaction modified spatiotemporal diffusion operators as well as in additive mean field reaction terms. One consequence of the nonseparability of reaction and subdiffusion terms is that the governing evolution equation for the concentration of one particular species may include both reactive and diffusive contributions from other species. The general solution is derived for the multispecies system and some particular special cases involving both irreversible and reversible reaction dynamics are analyzed in detail. We have carried out Monte Carlo simulations corresponding to these special cases and we find excellent agreement with theory.

Keywordsanomalous subdiffusion, fractional reaction-diffusion equations, multi-species reactions
ANZSRC Field of Research 2020490510. Stochastic analysis and modelling
340607. Reaction kinetics and dynamics
490410. Partial differential equations
Public Notes

File reproduced in accordance with the copyright policy of the publisher/author.

Byline AffiliationsUniversity of New South Wales
Icahn School of Medicine at Mount Sinai, United States
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