Smoluchowski equation with a sink term: Analytical solutions for the rate constant and their numerical test

Journal of Chemical Physics

Volumn 109, Issue 11, 1998, Pages 4182-4189

  Berezhkovskii, A M ^a   D'yakov, Yu A ^a   Zitserman, V Yu ^b  

^a KARPOV INSTITUTE OF PHYSICAL CHEMISTRY   (Russian Federation)

^b JOINT INSTITUTE FOR HIGH TEMPERATURES   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; EIGENVALUES AND EIGENFUNCTIONS; INTEGRATION; PERTURBATION TECHNIQUES; RATE CONSTANTS; REACTION KINETICS; RELAXATION PROCESSES; VISCOSITY;

EXPONENTIAL SINK MODEL; FRACTIONAL POWER LAW; NUMERICAL TEST; SMOLUCHOWSKI EQUATION;

MATHEMATICAL MODELS;

EID: 0032529979     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.477024     Document Type: Article

References (43)

1. (a) G. Wilemski and M. Fixman, J. Chem. Phys. 58, 4009 (1973);
2. (b) 60, 866 (1074);
3. 60, 878 (1974).
4. M. Ya. Ovchinnikova, Teor. Eksp. Khim. 17, 651 (1981).
5. L. D. Zusman, Chem. Phys. 80, 29 (1983).
6. H. Sumi and R. A. Marcus, J. Chem. Phys. 84, 4894 (1986);
7. W. Nadler and R. A. Marcus, 86, 3906 (1987).
8. R. A. Marcus, J. Chem. Phys. 105, 5446 (1996).
9. H. Sumi, J. Mol. Liq. 65/66, 65 (1995).
10. N. Agmon and J. J. Hopfield, J. Chem. Phys. 78, 6947 (1983);
11. 79, 2042 (1983)
12. 80, 592 (1984).
13. R. Zwanzig, J. Chem. Phys. 97, 3587 (1992).
14. N. Eizenberg and J. Klafter, Chem. Phys. Lett. 243, 9 (1995);
15. J. Chem. Phys. 104, 6796 (1996);
16. Physica A (in press).
17. B. Bagchi, G. R. Fleming, and D. W. Oxtoby, J. Chem. Phys. 78, 7375 (1983);
18. B. Bagchi and G. R. Fleming, J. Phys. Chem. 94, 9 (1984).
19. A. M. Berezhkovskii and V. Yu. Zitserman, Physica A 166, 585 (1990).
20. A. M. Berezhkovskii and V. Yu. Zitserman, J. Phys. A 25, 2077 (1992).
21. A. M. Berezhkovskii, V. Yu. Zitserman, S.-Y. Sheu, D.-Y. Yang, J. Kuo, and S. H. Lin, J. Chem. Phys. 107, 10539 (1997).
22. R. Zwanzig, Acc. Chem. Res. 23, 148 (1990).
23. M. Pagitsas, J. Chem. Phys. 96, 8497 (1992).
24. (a) M. Morillo and R. I. Cukier, J. Chem. Phys. 89, 6736 (1988);
25. M. Morillo, D. Y. Yang, and R. I. Cukier, 90, 5711 (1989);
26. D. Y. Yang and R. I. Cukier, 91, 281 (1989);
27. D. Y. Yang, J. Stat. Phys. 74, 631 (1994);
28. (b) J. Zhu and J. C. Rasaiah, J. Chem. Phys. 95, 3325 (1991);
29. 96, 1435 (1992);
30. 98, 1213 (1993);
31. (c) S. Roy and B. Bagchi, 100, 8802 (1994);
32. (d) M. Kurzyński, 101, 255 (1994).
33. G. Weiss, J. Chem. Phys. 80, 2880 (1984).
34. S. Rabinovich and N. Agmon, Chem. Phys. 148, 11 (1990).
35. M. Gitterman and G. H. Weiss, Chem. Phys. 180, 319 (1994).
36. M. V. Basilevsky and G. V. Davidovitch, J. Chem. Phys. 102, 1607 (1995).
37. P. Pechukas and J. Ankerhold, J. Chem. Phys. 107, 2444 (1997).
38. H. Kramers, Physica (Amsterdam) 7, 284 (1940).
39. A. Nitzan, Adv. Chem. Phys. 70, 489 (1988).
40. P. Hänggi, P. Talker, and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990).
41. Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (Dover, New York, 1970).
42. C. W. Gardiner, Handbook of Stochastic Methods (Springer, Berlin, 1985).
43. S. E. Koonin, Computational Physics (Addison-Wesley, Cambridge, MA, 1986).