Anomalous diffusion with linear reaction dynamics: From continuous time random walks to fractional reaction-diffusion equations
Article
Article Title | Anomalous diffusion with linear reaction dynamics: From continuous time random walks to fractional reaction-diffusion equations |
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ERA Journal ID | 1018 |
Article Category | Article |
Authors | Henry, B. I. (Author), Langlands, Trevor (Author) and Wearne, S. L. (Author) |
Journal Title | Physical Review E |
Journal Citation | 74 (3), pp. 1-15 |
Number of Pages | 15 |
Year | 2006 |
Publisher | American Physical Society |
Place of Publication | United States |
ISSN | 1539-3755 |
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. |
Keywords | anomalous subdiffusion, fractional reaction-diffusion equations, linear kinetics |
Contains Sensitive Content | Does not contain sensitive content |
ANZSRC Field of Research 2020 | 340607. Reaction kinetics and dynamics |
490410. Partial differential equations | |
Public Notes | File reproduced in accordance with the copyright policy of the publisher/author. |
Byline Affiliations | University of New South Wales |
Icahn School of Medicine at Mount Sinai, United States |
https://research.usq.edu.au/item/9z190/anomalous-diffusion-with-linear-reaction-dynamics-from-continuous-time-random-walks-to-fractional-reaction-diffusion-equations
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