Izvestiya of Saratov University.


ISSN 1817-3020 (Print)
ISSN 2542-193X (Online)

For citation:

Chetverikov A. P., Ebeling W., Velarde M. G. Solitons and clusters in one-dimensional ensembles of interacting brownian particles. Izvestiya of Saratov University. Physics , 2006, vol. 6, iss. 1, pp. 28-41. DOI: 10.18500/1817-3020-2006-6-1-2-28-41

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
Full text:
(downloads: 194)
Article type: 

Solitons and clusters in one-dimensional ensembles of interacting brownian particles

Chetverikov A. P., Saratov State University
Ebeling Werner, Humboldt University of Berlin
Velarde M. G., Institute of cross-disciplinary researches of the University of Madrid

The survey of the studies results of 1D ensembles dynamics of interacting Browniam particles is presented. Properties of both particles and the Fermi-Pasta-Ulam, Toda, Lennard-Jones, Morse interaction potentials are described. The Langevin equations are exhibited and structures and thermodynamic characteristics which may be extracted from data of a numerical integration of the equations are described. Excitations of phonons, cnoidal waves and solitons in dense ensembles and clusters in ensembles of low density are considered.

  1. Гардинер К.В. Стохастические методы в естественных науках. М.: Мир, 1986. 
  2. Климонтович Ю.Л. Нелинейное Броуновское движение // УФН. 1994. Т. 37. С.737-766.
  3. Молекулярная динамика ферментов / Под ред. Ю.М. Романовского, В. Эбелинга. М.: Изд-во Моск. ун-та, 2000.
  4. Stohastic Dynamics of Reacting Biomolecules / Eds. W. Ebeling, L. Schiraansky-Geier, Yu. Romanovsky. Singapore: World Scientific, 2002.
  5. Nekorkin V.I., Velarde M.G. Synergetic Phenomena in Active Lattices. Patterns, Waves, Solitons, Chaos. Berlin:Springer, 2002. 
  6. Scheweitzer F. Brownian Agents and Active Particles. Collective Dynamics in the Natural and Social Sciences. Berlin: Springer, 2003.
  7. Toda М. Теория нелинейных решеток. М.: Мир, 1984. 
  8. Анищенко B.C., Астахов В.В., Вадивасова Т.Е. и др. Нелинейные эффекты в хаотических и стохастических системах. М.; Ижевск, 2003.
  9. Никитин Н.Н., Разевич В.Д. Методы цифрового моделирования стохастических дифференциальных уравнений и оценка их погрешностей // Журн. вычисл. математики и мат. физики. 1978. Т.18, № 1. С. 106-117. 
  10. Toda M., Saitoh N. The classical specific heat of the exponential lattice // J. Phys. Soc. (Japan) 1983. V. 52. P. 3703-3705.
  11. Bolterauer H., Opper M. Solitons in the Statistical Mechanics of the Toda Lattice. // Condensed Matter. 1981. V. B42. P.155-161. 
  12. Jenssen M., Ebeling W. Distribution functions and excitation spectra of Toda systems at intermediate temperatures // Physica D. 2000. V. 141. P.I 17-132. 
  13. Ebeling W., Chetverikov A., Jenssen M. Statistical thermodynamics and non-linear excitations of Toda systems // Ukrain. Phys. J. 2000. V. 45. P. 479-Ш.
  14. Dunkel J., Ebeling W., Erdman II. Thermodynamics and transport in an active Morse ring chain // Eur. Phys. J. 2001. V. B24. P. 511-524. 
  15. Dunkel J., Ebeling W., Erdman U., Makarov V.A. Coherent motions and clusters in a dissipative Morse ring chain // Intern. J. Bif. and Chaos. 2002. V. 12, № 11. P. 2359-2377.
  16. Chetverikov A., Dunkel J. Phase behavior and collective excitations of the Morse ring chain // Eur. Phys. J. 2003. V. B35. P. 239-253.
  17. Chetverikov A., Ebeling W., Velarde M.G. Thermodynamic and phase transitions in dissipative and active Morse chain // Eur. Phys. J. 2005. V. 44. P. 509-519.
  18. Ланда П.С. Нелинейные колебания и волны. М., 1997.
  19. Shang-keng Ma. Calculation of entropy from data of motion // J. Stat. Phys. 1981. V. 26. P. 221.
  20. Четвериков А.П., Эбелинг В. Структурные свойства молекулярных цепочек с потенциалами Леннарда—Джонса и Морзе // Журн. структур, химии. 2004. Т. 45, № 3. С. 445-451.
  21. Makarov V.A., Ebeling W., Velarde A/. Soliton-like waves on dissipative Toda lattices // Intern. J. Bif. and Chaos. 2000. V. 10. P.1075-1089.
  22. Ebeling W., Erdman (J., Dunkel J., Jenssen M. Nonlinear Dynamics and Fluctuations of Dissipative Toda Chains // J. Stat. Phys. 2000. V. 101. P. 443-^57. 
  23. Makarov V.A., del Rio E., Ebeling W., Velarde M.G. Dissipative Toda-Rayleigh lattice and its oscillatory modes // Phys. Rev. E. 2001. V. E64. P. 036601-1/14. 
  24. Rio E. del, Makarov V.A., Velarde M.G., Ebeling W. Mode transitions and wave propagation in a driven-dissipative Toda-Rayleigh ring // Phys. Rev. E. 2003. V. E67. P. 056208-1/9. 
  25. Ebeling W., Schweitzer F., Tilch B. Active Brownian particles with energy depots modeling animal mobility // Biosystems. 1999. V. 49. P. 17-29.
  26. Schweitzer F., Ebeling W., Tilch B. Phys. Complex Motion of Brownian Particles with Energy Deports // Phys. Rev. Lett. 1998. V. 80. P. 5044-5047.
  27. Erdman V., Ebeling W., Schimansky-Geier L, Schweitzer F. Brownian particles far from equilibrium // Eur. Phys. J. B. 2000. V.B15. P. 105-113. 
  28. Velarde M.G., Ebeling W., Chetverikov A.P. On the possibility of electric conduction mediated by dissipative solitons // Intem. J. Bif. and Chaos. 2005. V. 15. № 1. P. 245-251