Fractional reaction-diffusion equation

By K. Seki, M. Wojcik, M. Tachiya. 2003

190 citations recorded by the source corpus.

A fractional reaction-diffusion equation is derived from a continuous time random walk model when the transport is dispersive. The exit from the encounter distance, which is described by the algebraic waiting time distribution of jump motion, interferes with the reaction at the encounter distance. Therefore, the reaction term has a memory effect. The derived equation is applied to the geminate recombination problem. The recombination is shown to depend on the intrinsic reaction rate, in contrast with the results of Sung et al. [J. Chem. Phys. 116, 2338 (2002)], which were obtained from the fractional reaction-diffusion equation where the diffusion term has a memory effect but the reaction term does not. The reactivity dependence of the recombination probability is confirmed by numerical simulations.

Subfields: Modeling and Simulation, Molecular Biology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/13334d5b581dc3f6f37d67e9b1a18ba69f6447e9

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Citations in the corpus

The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics (2004, methodology): “…was shown to be controlled by the fractional diffusion–reaction equation (Seki et al 2003a, 2003b) (compare Sung et al (2002)) ∂ ∂t C(r, t) = 0D1−αt ( Kα∇2 − kα δ(r − R) 4πR2 ) C(r, t) (74) for the concentration C(r, t), where we retained the spherical notation from Seki et al (2003a, 2003b).”
Existence and regularity results of a backward problem for fractional diffusion equations (2019, background): “Therefore, by applying (15), for any ε > 0 and t, s ∈ [ε,T] with s < t, it yields that ||2f (t, ·) − 2f (s, ·)||L2(Ω) ≤ M2T M1 ∫ T”
Semilinear Caputo time-fractional pseudo-parabolic equations (2021, background): “Many important physical models and practical problems require us to consider the pseudo-parabolic model with fractional derivative rather than classical one, like the physical model considering memory effects [18, 19, 13, 48] and some corresponding engineering problems [4, 5, 7, 44, 46, 50, 56], esp”