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

Henry, B. I. and 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: Statistical, Nonlinear, and Soft Matter Physics, 74 (3). pp. 1-15. ISSN 1539-3755

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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.


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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. (American Physical Society)
Depositing User: Dr Trevor Langlands
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 31 Oct 2009 05:51
Last Modified: 02 Jul 2013 23:20
Uncontrolled Keywords: anomalous subdiffusion, fractional reaction-diffusion equations, linear kinetics
Fields of Research (FOR2008): 03 Chemical Sciences > 0307 Theoretical and Computational Chemistry > 030703 Reaction Kinetics and Dynamics
01 Mathematical Sciences > 0101 Pure Mathematics > 010110 Partial Differential Equations
Socio-Economic Objective (SEO2008): E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: doi: 10.1103/PhysRevE.74.031116
URI: http://eprints.usq.edu.au/id/eprint/5439

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