Distributed approximating functional approach to the Fokker-Planck equation: Eigenfunction expansion

Journal of Chemical Physics

Volumn 106, Issue 12, 1997, Pages 5216-5224

  Zhang, D S ^a   Wei, G W ^a   Kouri, D J ^a   Hoffman, D K ^b  

^a University of Houston   (United States)

^b IOWA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; DIFFUSION; EIGENVALUES AND EIGENFUNCTIONS; KINETIC THEORY; PARTIAL DIFFERENTIAL EQUATIONS; POLYNOMIALS;

ANHARMONIC RESONATING SYSTEM; BISTABLE DIFFUSION MODEL; DISTRIBUTED APPROXIMATING FUNCTIONAL METHOD; FOKKER-PLANCK EQUATION; LORENTZ GAS;

MOLECULAR PHYSICS;

EID: 0031099196     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.473520     Document Type: Article

References (55)

1. N. G. van Kampen, J. Stat. Phys. 17, 71 (1977); H. Dekker and N, G. van Kampen, Phys. Lett. 73A, 374 (1979).
2. N. G. van Kampen, J. Stat. Phys. 17, 71 (1977); H. Dekker and N, G. van Kampen, Phys. Lett. 73A, 374 (1979).
3. R. Kubo, K. Matsuo, and K. Kitahara, J. Stat. Phys. 9, 51 (1973).
4. M. Suzuki, Adv. Chem. Phys. 46, 195 (1981).
5. B. Caroli, C. Caroli, and B. Roulet, J. Stat. Phys. 21, 26 (1979).
6. B. Caroli, C. Caroli, and B. Roulet, J. Stat. Phys. 26, 83 (1981).
7. R. S. Larson and M. Kostin J. Chem. Phys. 69, 4821 (1978).
8. R. Indira, M. C. Valsakumar, K. P. N. Murthy, and G. Ananthakrishna, J. Stat. Phys. 33, 181 (1981).
9. M. F. Wehner and W. G. Wolfer, Phys. Rev. A 27, 2663 (1983).
10. H. Brand, A. Schenzle, and G. Schröder, Phys. Rev. A 25, 2324 (1982).
11. R. Blackmore and B. Shizgal, Phys. Rev. A 31, 1855 (1985).
12. E. M. Epperlein, J. Comput. Phys. 112, 291 (1994).
13. H. L. Frisch and B. Nowakowski, J. Chem. Phys. 98, 8963 (1993).
14. M. A. Muñoz and P. L. Garrido, Phys. Rev. E 50, 2458 (1994).
15. T. H. Kho, Phy. Rev. A 32, 66 (1985).
16. H. Risken, The Fokker-Planck Equation: Methods of Solution and Application (Springer-Verlag, Berlin, 1984).
17. B. Shizgal, J. Comput. Phys. 41, 309 (1981).
18. B. Shizgal and R. Blackmore, J. Comput. Phys. 55, 313 (1984).
19. D. K. Hoffman, N. Nayar, O. A. Sharafeddin, and D. J. Kouri, J. Phys. Chem. 95, 8299 (1991).
20. D. K. Hoffman and D. J. Kouri, J. Phys. Chem. 96, 1179 (1992).
21. W. Zhu, Y. Huang, D. J. Kouri, C. Chandler, and D. K. Hoffman, Chem. Phys. Lett. 217, 73 (1993).
22. B. Shizgal and H. Chen, J. Chem. Phys. 104, 4137 (1996).
23. K. Andersen and K. E. Shuler, J. Chem. Phys. 40, 633 (1964).
24. B. Shizgal, J. Chem. Phys. 70, 1948 (1979).
25. M. Henon and C. Heiles, Astron. J. 69, 73 (1964).
26. G. H. Walker and J. Ford, Phys. Rev. 188, 416 (1969).
27. D. W. Noid and R. A. Marcus, J. Chem. Phys. 62, 2119 (1975).
28. D. W. Noid, M. L. Koszykowski, M. Tabor, and R. A. Marcus, J. Chem. Phys. 72, 6169 (1980).
29. K. S. J. Nordholm and S. A. Rice, J. Chem. Phys. 61, 203 (1974).
30. M. D. Feit, J. A. Fleck, Jr., and A. Steiger, J. Comput. Phys. 47, 412 (1982).
31. A. Einstein, Ann. Phys. 17, 549 (1905); 19, 371 (1906).
32. A. Einstein, Ann. Phys. 17, 549 (1905); 19, 371 (1906).
33. P. Langevin, Comptes Rend. 146, 530 (1908).
34. A. D. Fokker, Ann. Phys. 43, 810 (1914).
35. M. Planck, Sitzber. PreuB. Akad. Wiss. 324 (1917).
36. H. A. Kramers, Physica 7, 284 (1940).
37. S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943).
38. K. Itô, Proc. Imp. Acad. 20, 519 (1944).
39. H. Haken, Synergetics, An Introduction, 3rd ed. Springer Ser. Synergetics (Springer, Berlin, 1983), Vol. 1.
40. N. G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdamn 1981).
41. D. J. Kouri, W. Zhu, X. Ma, B. M. Pettitt, and D. K. Hoffman, J. Phys. Chem. 96, 9622 (1992).
42. D. J. Kouri and D. K. Hoffman, J. Phys. Chem. 95, 9631 (1992).
43. D. K. Hoffman, M. Arnold, and D. J. Kouri, J. Phys. Chem. 96, 6539 (1992).
44. D. K. Hoffman, M. Arnold, and D. J. Kouri, J. Phys. Chem. 97, 1110 (1993).
45. D. K. Hoffman, M. Arnold, W. Zhu, and D. J. Kouri, J. Phys. Chem. 99, 1124 (1993).
46. D. K. Hoffman and D. J. Kouri, J. Phys. Chem. 97, 4984 (1993).
47. D. K. Hoffman and D. J. Kouri, J. Phys. Chem. 99, 1124 (1993).
48. D. K. Hoffman and D. J. Kouri, in Time-Dependent Quantum Molecular dynamics, edited by J. Broeckhove and L. Lathouwers, NATO ASI Series B 1992, Vol. 299, p. 117.
49. D. K. Hoffman, T. L. Marchioro, II, M. Arnold, Y. Huang, W. Zhu, and D. J. Kouri, J. Math. Chem. 20, 117 (1996).
50. R. Dutt, A. Khare, and U. P. Sukhatme, Am. J. Phys. 56, 163 (1988).
51. A. Comtet, A. D. Bandrauk, and D. K. Campbell, Phys. Lett. B 150, 159 (1985).
52. M. R. Hoare and C. H. Kaplinsky, J. Chem. Phys. 52, 3336 (1970).
53. M. R. Hoare, Adv. Chem. Phys. 20, 135 (1971).
54. C. S. Shapiro and N. Corngold, Phys. Rev. A 137, 1686 (1970).
55. H. Oser, K. E. Shuler, and G. Weiss, J. Chem. Phys. 41, 1661 (1964).