Numerical implementation of the asymptotic theory for classical diffusion in heterogeneous media


Based on the asymptotic theory of impurity transport developed by one of the authors (P.S.K.), numerical calculations of the concentration for classical diffusion in heterogeneous media in one and two dimensions are performed. In parallel, for the same media, a direct numerical solution of the diffusion equation was carried out. The results of the two calculations are highly consistent with each other at asymptotically far distances from the impurity source. The computation time according to the asymptotic theory turned out to be two orders of magnitude less than the time required for direct calculations.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: Data sharing not applicable to this article as no datasets were generated or analysed during the current study.]


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The authors are deeply grateful to Prof. L.V. Matveev for a fruitful discussion of the results. This work was financially supported by the Russian Science Foundation Grant no. 18-19-00533.

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PSK and ALM performed analytical calculations, ADV realized numerical computations. All authors contributed to writing the manuscript.

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Correspondence to Peter S. Kondratenko.

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Kondratenko, P.S., Matveev, A.L. & Vasiliev, A.D. Numerical implementation of the asymptotic theory for classical diffusion in heterogeneous media. Eur. Phys. J. B 94, 50 (2021).

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