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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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

References (8) Similar articles (20) ↓

V.M. Rozenbaum, I.V. Shapochkina, L.I. Trakhtenberg “Green's function method in the theory of Brownian motors” Phys. Usp. 62 496–509 (2019)
N.A. Vinokurov “Analytical mechanics and field theory: derivation of equations from energy conservation” Phys. Usp. 57 593–596 (2014)
E.V. Shuryak “Stochastic trajectory generation by computer” Sov. Phys. Usp. 27 448–453 (1984)
A.A. Snarskii “Did Maxwell know about the percolation threshold? (on the fiftieth anniversary оf percolation theory)” Phys. Usp. 50 1239–1242 (2007)
O.V. Rudenko “Nonlinear dynamics of quadratically cubic systems” Phys. Usp. 56 683–690 (2013)
V.D. Lakhno “Translation invariance and the problem of the bipolaron” Phys. Usp. 41 403–406 (1998)
A.V. Kukushkin “A technique for solving the wave equation and prospects for physical applications arising therefrom” Phys. Usp. 36 (2) 81–93 (1993)
G.A. Martynov “Nonequilibrium statistical mechanics, transport equations, and the second law of thermodynamics” Phys. Usp. 39 1045–1070 (1996)
V.V. Vasiliev, L.V. Fedorov “Spherically symmetric static problem of General Relativity for a continuum” Phys. Usp. 68 187–202 (2025)
S.P. Efimov “Coordinate space modification of Fock's theory. Harmonic tensors in the quantum Coulomb problem” Phys. Usp. 65 952–967 (2022)
A.G. Shalashov “Can we refer to Hamilton equations for an oscillator with friction?” Phys. Usp. 61 1082–1088 (2018)
V.G. Niz’ev “Dipole-wave theory of electromagnetic diffraction” Phys. Usp. 45 553–559 (2002)
S.L. Sobolev “Local non-equilibrium transport models” Phys. Usp. 40 1043–1053 (1997)
A.A. Andronov, Yu.A. Ryzhov “An infinity of the classical theory of fluctuations in a nondegenerate electron gas” Sov. Phys. Usp. 21 873–878 (1978)
E.D. Trifonov “On quantum statistics for ensembles with a finite number of particles” Phys. Usp. 54 723–727 (2011)
V.F. Kovalev, D.V. Shirkov “Renormalization-group symmetries for solutions of nonlinear boundary value problems” Phys. Usp. 51 815–830 (2008)
V.S. Popov “Feynman disentangling оf noncommuting operators and group representation theory” Phys. Usp. 50 1217–1238 (2007)
A. Loskutov “Dynamical chaos: systems of classical mechanics” Phys. Usp. 50 939–964 (2007)
A.I. Musienko, L.I. Manevich “Classical mechanical analogs of relativistic effects” Phys. Usp. 47 797–820 (2004)
A.V. Kukushkin “An invariant formulation of the potential integration method for the vortical equation of motion of a material point” Phys. Usp. 45 1153–1164 (2002)

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