Langlands, Trevor and Henry, B. I. and Wearne, S. L. (2008) Anomalous subdiffusion with multispecies linear reaction dynamics. Physical Review E: Statistical Nonlinear and Soft Matter Physics, 77. pp. 1-9. ISSN 1539-3755
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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.
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| Item Type: | Article (Commonwealth Reporting Category C) |
|---|---|
| Refereed: | Yes |
| Item Status: | Live Archive |
| Additional Information: | Author's version deposited in accordance with the copyright policy of the publisher. http://forms.aps.org/author/copytrnsfr.pdf |
| Faculty/School / Institute/Centre: | Historic - Faculty of Sciences - Department of Maths and Computing (Up to 30 Jun 2013) |
| Faculty/School / Institute/Centre: | Historic - Faculty of Sciences - Department of Maths and Computing (Up to 30 Jun 2013) |
| Date Deposited: | 29 Oct 2009 12:47 |
| Last Modified: | 29 Aug 2014 04:26 |
| Uncontrolled Keywords: | anomalous subdiffusion, fractional reaction-diffusion equations, multi-species reactions |
| Fields of Research (2008): | 01 Mathematical Sciences > 0104 Statistics > 010406 Stochastic Analysis and Modelling 03 Chemical Sciences > 0307 Theoretical and Computational Chemistry > 030703 Reaction Kinetics and Dynamics 01 Mathematical Sciences > 0101 Pure Mathematics > 010110 Partial Differential Equations |
| Fields of Research (2020): | 49 MATHEMATICAL SCIENCES > 4905 Statistics > 490510 Stochastic analysis and modelling 34 CHEMICAL SCIENCES > 3406 Physical chemistry > 340607 Reaction kinetics and dynamics 49 MATHEMATICAL SCIENCES > 4904 Pure mathematics > 490410 Partial differential equations |
| Socio-Economic Objectives (2008): | E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences |
| Identification Number or DOI: | https://doi.org/10.1103/PhysRevE.77.021111 |
| URI: | http://eprints.usq.edu.au/id/eprint/5449 |
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