Anomalous diffusion with linear reaction dynamics: From continuous time random walks to fractional reaction-diffusion equations

Article

Henry, B. I., Langlands, Trevor and Wearne, S. L.. 2006. "Anomalous diffusion with linear reaction dynamics: From continuous time random walks to fractional reaction-diffusion equations." Physical Review E. 74 (3), pp. 1-15. https://doi.org/10.1103/PhysRevE.74.031116
Article Title

Anomalous diffusion with linear reaction dynamics: From continuous time random walks to fractional reaction-diffusion equations

ERA Journal ID1018
Article CategoryArticle
AuthorsHenry, B. I. (Author), Langlands, Trevor (Author) and Wearne, S. L. (Author)
Journal TitlePhysical Review E
Journal Citation74 (3), pp. 1-15
Number of Pages15
Year2006
PublisherAmerican Physical Society
Place of PublicationUnited States
ISSN1539-3755
1550-2376
2470-0045
2470-0053
Digital Object Identifier (DOI)https://doi.org/10.1103/PhysRevE.74.031116
Web Address (URL)http://link.aps.org/doi/10.1103/PhysRevE.74.031116
Abstract

We have revisited the problem of anomalously diffusing species, modeled at the mesoscopic level using continuous time random walks, to include linear reaction dynamics. If a constant proportion of walkers are added or removed instantaneously at the start of each step then the long time asymptotic limit yields a fractional reaction-diffusion equation with a fractional order temporal derivative operating on both the standard diffusion term and a linear reaction kinetics term. If the walkers are added or removed at a constant per capita rate during the waiting time between steps then the long time asymptotic limit has a standard linear reaction kinetics term but a fractional order temporal derivative operating on a nonstandard diffusion term. Results from the above two models are compared with a phenomenological model with standard linear reaction kinetics and a fractional order temporal derivative operating on a standard diffusion term. We have also developed further extensions of the CTRW model to include more general reaction dynamics.

Keywordsanomalous subdiffusion, fractional reaction-diffusion equations, linear kinetics
Contains Sensitive ContentDoes not contain sensitive content
ANZSRC Field of Research 2020340607. Reaction kinetics and dynamics
490410. Partial differential equations
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Byline AffiliationsUniversity of New South Wales
Icahn School of Medicine at Mount Sinai, United States
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