Stability analysis of mean-field-type nonlinear Fokker-Planck equations associated with a generalized entropy and its application to the self-gravitating system

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 67, Issue 5 2, 2003, Pages

  Shiino, Masatoshi ^a  

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; ENTROPY; FREE ENERGY; GRAVITATIONAL EFFECTS; LYAPUNOV METHODS; MATHEMATICAL TRANSFORMATIONS; NONLINEAR EQUATIONS;

FOKKER-PLANCK EQUATIONS; H THEOREM; LEGENDRE TRANSFORM; SELF-GRAVITATING SYSTEM; STABILITY ANALYSIS; THERMOSTATISTICS;

STATISTICAL MECHANICS;

EID: 42749105574     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (61)

1. H. Risken, The Fokker-Planck Equation (Springer-Verlag, Berlin, 1984).
2. C. W. Gardiner, Handbook of Stochastic Methods (Springer-Verlag, Berlin, 1985).
3. N. G. Van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981).
4. J. Schnakenberg, Rev. Mod. Phys. 48, 571 (1976).
5. F. Schlogl, Phys. Rep. 62, 267 (1980).
6. M. Shiino, J. Phys. Soc. Jpn. A 67, 3658 (1998).
7. L. Borland, A. R. Plastino, and C. Tsallis, J. Math. Phys. 39, 6490 (1998).
8. S. Kullback, Ann. Math. Stat. 22, 79 (1951).
9. M. Takatsuji, Bipl. Cybern. 17, 207 (1975).
10. H. Shimizu, Prog. Theor. Phys. 52, 329 (1974).
11. R. C. Desai and R. Zwanzig, J. Stat. Phys. 19, 1 (1978).
12. D. A. Dawson, J. Stat. Phys. 31, 29 (1983).
13. M. Shiino, Phys. Lett. A 111, 396 (1985).
14. M. Shiino, Phys. Lett. A 112, 302 (1985).
15. M. Shiino, Phys. Rev. A 36, 2393 (1987).
16. L. L. Bonilla, J. Stat. Phys. 46, 659 (1987).
17. A. N. Drozdov and M. Morillo, Phys. Rev. E 54, 3304 (1996).
18. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer, Berlin, 1984).
19. H. Sakaguchi, Prog. Theor. Phys. 79, 39 (1988).
20. A. Arenas and C. J. Perez Vicente, Europhys. Lett. 26, 79 (1994).
21. M. Yoshioka and M. Shiino, Phys. Rev. E 61, 4732 (2000).
22. M. Shiino and K. Yoshida, Phys. Rev. E 63, 026210 (2001).
23. T. D. Frank, A. Daffertshofer, C. E. Peper, P. J. Beck, and H. Haken, Physica D 150, 219 (2001).
24. H. C. Fogedby, Phys. Rev. E 50, 1657 (1994).
25. A. R. Plastino and A. Plastino, Physica A 222, 347 (1995).
26. C. Tsallis and D. J. Bukman, Phys. Rev. E 54, R2197 (1996).
27. L. Borland, Phys. Rev. E 57, 6634 (1998).
28. G. Kaniadakis and G. Lapenta, Phys. Rev. E 63, 3246 (2000).
29. S. Martinez, A. R. Plastino, and A. Plastino, Physica A 259, 183 (1998).
30. M. Shiino, J. Math. Phys. 42, 2540 (2001).
31. M. Shiino, J. Math. Phys. 43, 2654 (2002).
32. M. Shiino, J. Korean Phys. Soc. 40, 1037 (2002).
33. T. D. Frank and A. Daffertshofer, Physica A 285, 351 (2000).
34. T. D. Frank and A. Daffertshofer, Physica A 292, 392 (2001).
35. T. D. Frank and A. Daffertshofer, Physica A 295, 455 (2001).
36. A. Compte and D. Jou, J. Phys. A 29, 4321 (1996).
37. J. P. Bouchaud and A. Georges, Phys. Rep. 195, 127 (1990).
38. G. Zimbardo and P. Veltri, Phys. Rev. E 51, 1412 (1995).
39. G. M. Saslavsky, D. Stevens, and H. Weizner, Phys. Rev. E 48, 1683 (1993).
40. P. Rosenau, Phys. Rev. Lett. 74, 1056 (1995).
41. C. Tsallis, J. Stat. Phys. 52, 479 (1988).
42. E. M. F. Curado and C. Tsailis, J. Phys. A 24, L69 (1991).
43. C. Tsallis, R. S. Mendes, and A. R. Plastino, Physica A 261, 534 (1998).
44. T. Padmanabhan, Phys. Rep. 188, 286 (1990).
45. P. J. Klinko and B. N. Miller, Phys. Rev. E 62, 5783 (2000).
46. V. P. Youngkins and B. N. Miller, Phys. Rev. E 62, 4583 (2000).
47. J. J. Aly and J. Perez, Phys. Rev. E 60, 5185 (1999).
48. A. R. Plastino and A. Plastino, Phys. Lett. A 174, 384 (1993).
49. W. Thomson, Mathematical and Physical Papers (Cambridge University Press, Cambridge, 1911), Vol. 3, pp. 255-360.
50. S. Chandrasekher, An Introduction to the Theory of Stellar Structure (University of Chicago Press, Chicago, 1958).
51. J. Binney and S. Tremaine, Galactic Dynamics (Princeton University Press, Princeton, 1987).
52. A. Taruya and M. Sakagami, Physica A 307, 185 (2002).
53. Saslaw, Gravitational Physics of Stellar and Galactic Systems (Cambridge University Press, Cambridge, 1987).
54. M. Shiino, in Proceedings of the SID-8, New York, 2002, edited by H. Hara and S. Fujita (Nova Science, New York, 2002).
55. J. P. Cox, Theory of Stellar Pulsation, Princeton Series in Astrophysics (Princeton University Press, Princeton, 1980).
56. P. H. Chavanis, A&A 386, 732 (2002).
57. A. Taruya and M. Sakagami, Physica A (to be published).
58. B. D. Sharma and D. P. Mittal, J. Math. Sci. 10, 28 (1975).
59. P. H. Chavanis, A&A 386, 732 (2002).
60. P. H. Chavanis, C. Rosier, and C. Sire, Phys. Rev. E 66, 036105 (2002).
61. G. Kaniadakis, Physica A 296, 405 (2002).