EPJ Web Conf.
Volume 226, 2020Mathematical Modeling and Computational Physics 2019 (MMCP 2019)
|Number of page(s)||4|
|Section||Mathematical Modeling, Numerical Methods, and Simulation|
|Published online||20 January 2020|
Two-Species Reaction-Diffusion System: the Effect of Long-Range Spreading
Pavol Jozef Šafárik University,
2 Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, 040 01 Košice, Slovakia
3 Joint Institute for Nuclear Research, 141980 Dubna, Russia
★ e-mail: firstname.lastname@example.org
Published online: 20 January 2020
We study fluctuation effects in the two-species reaction-diffusion system A + B → Ø and A + A → (Ø, A). In contrast to the usually assumed ordinary short-range diffusion spreading of the reactants we consider anomalous diffusion due to microscopic long-range hops. In order to describe the latter, we employ the Lévy stochastic ensemble. The probability distribution for the Lévy flights decays in d dimensions with the distance r according to a power-law r−d−σ. For anomalous diffusion (including Lévy flights) the critical dimension dc = σ depends on the control parameter σ, 0 < σ ≤ 2. The model is studied in terms of the field theoretic approach based on the Feynman diagrammatic technique and perturbative renormalization group method. We demonstrate the ideas behind the B particle density calculation.
© The Authors, published by EDP Sciences, 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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