RSS feeds
РусскийEnglish
Issue 9, 2026
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

2025

 / 

June

←  →

Methodological notes


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

† , ‡ 
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.

Fulltext pdf (353 KB)
Fulltext is also available at DOI: 10.3367/UFNe.2024.09.039764
Correspondence should be addressed to
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/
001570951300005
2-s2.0-105011744881
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)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 14th, June 2024, revised: 2nd, September 2024, 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) ↓

  1. 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)
  2. E.V. Shuryak “Stochastic trajectory generation by computer” Sov. Phys. Usp. 27 448–453 (1984)
  3. A.A. Snarskii “Did Maxwell know about the percolation threshold? (on the fiftieth anniversary оf percolation theory)” Phys. Usp. 50 1239–1242 (2007)
  4. M.V. Davidovich “On energy and momentum conservation laws for an electromagnetic field in a medium or at diffraction on a conducting plate” Phys. Usp. 53 595–609 (2010)
  5. A.A. Logunov “The theory of the classical gravitational field” Phys. Usp. 38 179–193 (1995)
  6. V.I. Tatarskii “Example of the description of dissipative processes in terms of reversible dynamic equations and some comments on the fluctuation-dissipation theorem” Sov. Phys. Usp. 30 134–152 (1987)
  7. G.S. Golitsyn “A N Kolmogorov's 1934 paper is the basis for explaining the statistics of natural phenomena of the macrocosm” Phys. Usp. 67 80–90 (2024)
  8. S.V. Goupalov “Classical problems with the theory of elasticity and the quantum theory of angular momentum” Phys. Usp. 63 57–65 (2020)
  9. N.A. Vinokurov “Analytical mechanics and field theory: derivation of equations from energy conservation” Phys. Usp. 57 593–596 (2014)
  10. S.L. Sobolev “Local non-equilibrium transport models” Phys. Usp. 40 1043–1053 (1997)
  11. A.G. Shalashov, E.D. Gospodchikov “Structure of the Maxwell equations in the region of linear coupling of electromagnetic waves in weakly inhomogeneous anisotropic and gyrotropic media” Phys. Usp. 55 147–160 (2012)
  12. V.I. Klyatskin, K.V. Koshel’ “Simple example of the development of cluster structure of a passive tracer field in random flows” Phys. Usp. 43 717–723 (2000)
  13. V.I. Klyatskin “Statistical description of the diffusion of a passive tracer in a random velocity field” Phys. Usp. 37 501–513 (1994)
  14. M.A. Markov “Can the asymptotic freedom of gravitational interactions violate the energy dominance of classical cosmology?” Phys. Usp. 37 901–902 (1994)
  15. P.S. Landa, V.F. Marchenko “On the linear theory of waves in media with periodic structures” Sov. Phys. Usp. 34 (9) 830–834 (1991)
  16. I.V. Sokolov “The angular momentum of an electromagnetic wave, the Sadovskii effect, and the generation of magnetic fields in a plasma” Sov. Phys. Usp. 34 (10) 925–932 (1991)
  17. I.I. Abbasov, B.M. Bolotovskii, V.A. Davydov “High-frequency asymptotic behavior of radiation spectra of moving charges in classical electrodynamics” Sov. Phys. Usp. 29 788–796 (1986)
  18. L.A. Apresyan, Yu.A. Kravtsov “Photometry and coherence: wave aspects of the theory of radiation transport” Sov. Phys. Usp. 27 301–313 (1984)
  19. 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)
  20. D.E. Vakman, L.A. Vainshtein “Amplitude, phase, frequency—fundamental concepts of oscillation theory” Sov. Phys. Usp. 20 1002–1016 (1977)

The list is formed automatically.
© 1918–2026 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions