CHANGES IN THE EFFECTIVE PARAMETERS OF AVERAGED MOTIONS IN NONLINEAR SYSTEMS SUBJECT TO NOISE OR VIBRATION


Cite this article as:

Landa P. S. CHANGES IN THE EFFECTIVE PARAMETERS OF AVERAGED MOTIONS IN NONLINEAR SYSTEMS SUBJECT TO NOISE OR VIBRATION. Izvestiya VUZ. Applied Nonlinear Dynamics, 2008, vol. 16, iss. 3, pp. 33-55. DOI: https://doi.org/10.18500/0869-6632-2008-16-3-33-55


An important problem of the change in the effective parameters of averaged motions in nonlinear systems is described. This problem is known in physics for a long time. It is concerned with the derivation of bodies motion equations taking into account the collisions with the molecules of the surrounding gas. Many researchers believe implicitly that this problem is essential only for the transfer from microscopic equations to macroscopic ones. However this problem reveals often itself in the present-day macroscopic physics. Below we give a number of the examples of such the change.

DOI: 
10.18500/0869-6632-2008-16-3-33-55
Literature

1. Boltzmann L. Лекции по теории газов. М.: Гостехиздат, 1956.

2. Климонтович Ю.Л. Статистическая физика. М.: Наука, 1982.

3. Prandtl L. Bericht uber Untersuchungen zur ausgebildeten Turbulenz // Zs. angew.  ̈ Math. Mech. 1925. Vol. 5, No 2. P. 136.

4. Ландау Л.Д., Лифшиц Е.М. Гидродинамика. М.: Наука, 1986.

5. Prandtl L. Fuhrer durch die Str  ̈ omungslehre. 3 ed. / F. Vieweg. Braunschweig, 1949.  ̈

6. Гиневский А.С., Колесников А.В. Теория идеального плота // Доклады АН. 1980. Т. 251, No 2. C. 312.

7. Brillouin L. Can the rectifier become a thermodynamical demon // Phys. Rev. 1950. Vol. 78. P. 627.

8. MacDonald D.K.C. Brownian movement // Phys. Rev. 1957. Vol. 108. P. 541.

9. Alkemade C.T.J. On the problem of Brownian motion of nonlinear systems // Physica. 1958. Vol. 24. P. 1029.

10. Van Kampen N.G. Thermal fluctuations in a nonlinear system // Phys. Rev. 1958. Vol. 110. P. 319.

11. Marek A. A note to recent theories of Brownian motion in nonlinear systems //

Physica. 1959. Vol. 25. P. 1358.

12. Стратонович Р.Л. О парадоксе в теории тепловых флуктуаций нелинейных сопротивлений // Вестник МГУ. 1960. No 4. C. 99.

13. Фейнман Р., Лейтон Р., Сэндс М. Фейнмановские лекции по физике // М.: Мир, 1965. Т. 4, гл. 46.

14. Peskin C., Odell G., and Oster G. // Biophys. J. 1993. Vol. 65. P. 316.

15. Svoboda K., Schmidt C.F., Schnapp B.J. and Block S.M. // Nature. 1993. Vol. 365. P. 721.

16. Magnasco M.O. Forced thermal ratchets // Phys. Rev. Lett. 1993. Vol. 71. P. 1477.

17. Astumian R. Dean and Bier M. Fluctuation driven ratchets: molecular motors // Phys. Rev. Lett. 1994. Vol. 72. P. 1766.

18. Doering C.R. Randomly rattled ratchets // Nuovo Cimento Soc. Ital. Fiz. 1995. Vol. 17D. P. 685.

19. Hanggi P. and Bartussek R.  ̈ // in Nonlinear Physics and Complex Systems – Current Status and Future Trends, Lect. Notes in Physics Vol. 476 / Ed. by J. Parisi, S.C. Muller, and W. Zimmermann. Berlin: Springer-Verlag, 1996. P. 294.  ̈

20. Landa P.S. Noise-induced transport of Brownian particles with consideration for their mass // Phys. Rev. E. 1998. Vol. 58. P. 1325.

21. Gammaitoni L. // Rev. Mod. Phys. 1998. Vol. 70. P. 223.

22. Landa P.S. Regular and chaotic oscillations. Berlin-Heidelberg: Springer-Verlag, 2001.

23. Ланда П.С. Механизм стохастического резонанса // ДАН. 2004. Т. 399, No 4. C. 1.

24. Стратонович Р.Л. Избранные вопросы теории флуктуаций в радиотехнике. М.: Сов. Радио, 1961.

25. Блехман И.И. Вибрационная механика. М.: Наука, 1994.

26. Блехман И.И., Ланда П.С. Сопряженные резонансы в нелинейных системах при двухчастотном воздействии. Виброиндуцированные бифуркации // Изв. вузов. ПНД. 2002. Т. 10, No 1-2. C. 44.

27. Blekhman I.I. and Landa P.S. Conjugate resonances and bifurcations in nonlinear systems under biharmonical excitation // Int. J. of Non-linear Mechanics. 2004. Vol. 39. P. 421.

28. Блехман И.И., Ланда П.С. Эффект сопряженности резонансов и бифуркаций при двухчастотном воздействии на маятник с вибрирующей осью подвеса // ДАН. 2004. Т. 395, No 2. C. 192.

Status: 
одобрено к публикации
Short Text (PDF): 
Full Text (PDF): 

BibTeX

@article{Ланда-IzvVUZ_AND-16-3-33,
author = {Polina S. Landa},
title = {CHANGES IN THE EFFECTIVE PARAMETERS OF AVERAGED MOTIONS IN NONLINEAR SYSTEMS SUBJECT TO NOISE OR VIBRATION},
year = {2008},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {16},number = {3},
url = {https://old-andjournal.sgu.ru/en/articles/changes-in-the-effective-parameters-of-averaged-motions-in-nonlinear-systems-subject-to},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2008-16-3-33-55},pages = {33--55},issn = {0869-6632},
keywords = {ИЗМЕНЕНИЕ ЭФФЕКТИВНЫХ ПАРАМЕТРОВ УСРЕДНЕННЫХ ДВИЖЕНИЙ НЕЛИНЕЙНЫХ СИСТЕМ ПОД ДЕЙСТВИЕМ ШУМА И ВИБРАЦИЙ},
abstract = {An important problem of the change in the effective parameters of averaged motions in nonlinear systems is described. This problem is known in physics for a long time. It is concerned with the derivation of bodies motion equations taking into account the collisions with the molecules of the surrounding gas. Many researchers believe implicitly that this problem is essential only for the transfer from microscopic equations to macroscopic ones. However this problem reveals often itself in the present-day macroscopic physics. Below we give a number of the examples of such the change. }}