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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Official URL: http://link.aps.org/doi/10.1103/PhysRevE.74.031116
Identification Number or DOI: doi: 10.1103/PhysRevE.74.031116
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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