Asymptotic theory of classical tracer transport in inhomogeneous and nonstationary media. Hamilton's formalism

P.S. Kondratenko^†, L.V. Matveev^‡
Nuclear Safety Institute, Russian Academy of Sciences, ul. Bolshaya Tulskaya 52, Moscow, 115191, Russian Federation

We develop an asymptotic theory of tracer transport due to diffusion and advection, when the diffusivity and advection velocity vary slowly over space and time. The tracer concentration is expressed through a single time integral. The integrand is determined by solving first-order ordinary differential equations, which are similar to Hamilton's equations for a material point in classical mechanics.

Keywords: diffusion, advection, asymptotic form, Hamilton's equations
PACS: 05.60.Cd, 05.60.−k, 02.60.Cb (all)
DOI: 10.3367/UFNe.2024.09.039764
URL: https://ufn.ru/en/articles/2025/6/g/
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001570951300005
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2-s2.0-105011744881
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2025PhyU...68..627K
Citation: Kondratenko P S, Matveev L V "Asymptotic theory of classical tracer transport in inhomogeneous and nonstationary media. Hamilton's formalism" Phys. Usp. 68 627–630 (2025)

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Received: 14th, June 2024, revised: 2nd, September 2024, accepted: 13th, September 2024

Оригинал: Кондратенко П С, Матвеев Л В «Асимптотическая теория классического переноса примеси в неоднородных и нестационарных средах. Формализм Гамильтона» УФН 195 669–672 (2025); DOI: 10.3367/UFNr.2024.09.039764

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