Singular features of large fluctuations in oscillating chemical systems

Journal of Physical Chemistry

Volumn 100, Issue 49, 1996, Pages 19197-19209

  Dykman, M I ^a   Smelyanskiy, V N ^a   Maier, R S ^b   Silverstein, M ^a  

^a MICHIGAN STATE UNIVERSITY   (United States)

^b University of Arizona   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 7344224041     PISSN: 00223654     EISSN: None     Source Type: Journal    
DOI: 10.1021/jp962746i     Document Type: Article

References (59)

1. Epstein, I. R. J. Phys. Chem. 1984, 88, 187.
2. Hunt, K. L. C.; Hunt, P. M.; Ross, J. Annu. Rev. Phys. Chem. 1990, 41, 409.
3. Westerhoff, H. V.; Chen, Y. Proc. Natl. Acad. Sci. 1985, 82, 3222.
4. Blumenfeld, L. A.; Grosberg, A. Yu.; Tikhonov, A. N. J. Chem. Phys. 1991, 95, 7541.
5. Vance, W.; Ross, J. J. Phys. Chem. 1995, 103, 2472.
6. (a) Dykman, M. I.; McClintock, P. V. E.; Smelyanskiy, V. N.; Stein, N. D.; Stocks, N. G. Phys. Rev. Lett. 1992, 68, 2718.
7. (b) Dykman, M. I.; Luchinsky, D. G.; McClintock, P. V. E.; Smelyanskiy, V. N. Submitted for publication.
8. Hunt, K. L. C.; Hunt, P. M.; Ross, J. J. Chem. Phys. 1990, 92, 2572;
9. Hunt, K. L. C.; Hunt, P. M.; Ross, J. J. Chem. Phys. 1991, 96, 618.
10. Jauslin, H. R. J. Stat. Phys. 1986, 42, 573;
11. Physica 1987, 144A, 179.
12. Maier, R. S.; Stein, D. L. Phys. Rev. Lett. 1992, 69, 3691;
13. Phys. Rev. Lett. 1993, 71, 1783;
14. Phys. Rev. E 1993, 48, 931;
15. J. Stat. Phys. 1996, 83, 291.
16. Chinarov, V. A.; Dykman, M. I.; Smelyanskiy, V. N. Phys. Rev. E 1993, 47, 2448.
17. Dykman, M. I.; Mori, E.; Ross, J.; Hunt, P. M. J. Chem. Phys. 1994, 100, 5735.
18. Berry, M. V. Adv. Phys. 1976, 35, 1.
19. Schulman, L. S. Techniques and Applications of Path Integration; Wiley: New York, 1981.
20. Maslov, V. P.; Fedoriuk, M. V. Semi-Classical Approximation in Quantum Mechanics; Reidel: Boston/Dordrecht, 1981.
21. Delos, J. B. Adv. Chem. Phys. 1986, 65, 161.
22. Littlejohn, R. G. J. Stat. Phys. 1992, 68, 7.
23. (a) Haken, H. Synergetics: An Introduction, 2nd ed.; Springer-Verlag: New York/Berlin, 1978.
24. (b) van Kampen, N. G. Stochastic Processes in Physics and Chemistry; North-Holland: New York/Amsterdam, 1981.
25. Gardiner, G. W. Handbook of Stochastic Methods, 2nd ed.; Springer-Verlag: New York/Berlin, 1990.
26. Lax, M. In Statistical Physics, Phase Transitions and Superconductivity; Chrétien, M., Gross, E. P., Deser, S., Eds.; Gordon and Breach, New York, 1968.
27. Dykman, M. I.; Chu, X.; Ross, J. Phys. Rev. E 1993, 48, 1646;
28. Dykman, M. I.; Chu, X.; Ross, J. Phys. Rev. E 1995, 52, 6916.
29. Nicolis, G.; Turner, J. W. Physica A 1977, 89, 326.
30. Nicolis, G.; Malek-Mansour, M. Prog. Theor. Phys. Suppl. 1978 64, 249.
31. Fraikin, A.; Lemarchand, H. J. Stat. Phys. 1985, 41, 531.
32. Kubo, R.; Matsuo, K.; Kitahara, K. J. Stat. Phys. 1973, 9, 51.
33. Kitahara, K. Adv. Chem. Phys. 1973, 29, 85.
34. Wentzell, A. D. Theory Probab. Its Appl. 1976 21, 227, 499.
35. Maier, R. S. Random Struct. Algorithms 1991 2, 379;
36. In 1992 Lectures on Complex Systems; Addison-Wesley: New York, 1993.
37. Matkowsky, B. J.; Schuss, Z.; Knessl, C.; Tier, C; Mangel, M. Phys. Rev. A 1984, 29, 3359.
38. Knessl, C.; Mangel, M.; Matkowsky, B. J.; Schuss, Z.; Tier, C. J. Chem. Phys. 1984, 81, 1285.
39. Knessl, C.; Matkowsky, B. J.; Schuss, Z. J. Stat. Phys. 1986, 42, 169.
40. Hu Gang, Z. Phys. B 1986, 65, 103;
41. Phys. Rev. A 1987, 36, 5782.
42. Vlad, M.; Ross, J. J. Chem. Phys. 1994, 100, 7268;
43. Vlad, M.; Ross, J. J. Chem. Phys. 1994, 100, 7279;
44. Vlad, M.; Ross, J. J. Chem. Phys. 1994, 100, 7295.
45. Naeh, T.; Kbsek, M. M.; Matkowsky, B. J.; Schuss, Z. SIAM J. Appl. Math. 1990, 50, 595.
46. Wentzell, A. D.; Freidlin, M. I. Russ. Math. Surveys 1970 25, 1.
47. Freidlin, M. I.; Wentzell, A. D. Random Perturbations in Dynamical Systems; Springer-Verlag: New York/Berlin, 1984.
48. Landau, L. D.; Lifshitz, E. M. Mechanics; Pergamon: London, 1976.
49. Ludwig, D. SIAM Rev. 1975, 17, 605.
50. Dykman, M. I.; Krivoglaz, M. A. Soviet Phys. JETP 1979, 50, 30.
51. Graham, R.; Tél, T. Phys. Rev. Lett. 1984, 52, 9.
52. Graham, R.; Tél, T. J. Stat. Phys. 35, 729.
53. Graham, R.; Tél, T. Phys. Rev. A 1985, 31, 1109.
54. Dykman, M. I.; Millonas, M. M.; Smelyanskiy, V. N. Phys. Lett. A 1994, 195, 53.
55. Arnold, V. I. Mathematical Methods of Classical Mechanics; Springer-Verlag: New York/Berlin, 1978.
56. Guckenheimer, J.; Holmes, P. Nonlinear Oscillators, Dynamical Systems and Bifurcations of Vector Fields; Springer-Verlag: New York/ Berlin, 1983.
57. Smelyanskiy, V. N.; Dykman, M. I.; Maier, R. S. In preparation.
58. Whitney, H. Ann. Math. 1955, 62, 374.
59. Arnold, V. I. Catastrophe Theory; Springer-Verlag: New York/Berlin, 1984.