Cite this article as:
??? S0LIT0NS AND CLUSTERS IN ONE-DIMENSIONAL ENSEMBLES OF INTERACTING BROWNIAN PARTICLES. Izvestiya of Saratov University. New series. Series Physics, 2006, vol. 6, iss. 1, pp. 28-?.
Heading:
UDC:
537.86
Language:
Russian
S0LIT0NS AND CLUSTERS IN ONE-DIMENSIONAL ENSEMBLES OF INTERACTING BROWNIAN PARTICLES
Abstract
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.
Key words:
References
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
Journal issue:
Full text (in Russian):
(downloads: 48)