Front velocity in models with quadratic autocatalysis

Journal of Chemical Physics

Volumn 117, Issue 18, 2002, Pages 8508-8514

  Vanag, Vladimir K ^a   Epstein, Irving R ^a  

^a BRANDEIS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BROMINE COMPOUNDS; CATALYSTS; COMPUTER SIMULATION; DIFFUSION; HYDROGEN INORGANIC COMPOUNDS; MATHEMATICAL MODELS; ORDINARY DIFFERENTIAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; PHASE TRANSITIONS; RATE CONSTANTS; VELOCITY; WAVE PROPAGATION;

AUTOCATALYST; BELOUSOV ZHABOTINSKY REACTION; FRONT PROPAGATION; FRONT VELOCITY; LINEAR STABILITY ANALYSIS; OREGONATOR MODEL; QUADRATIC AUTOCATALYSIS;

CATALYSIS;

EID: 0037044955     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1511728     Document Type: Article

References (26)

1. V. K. Vanag and I. R. Epstein, Phys. Rev. Lett. 87, 228301 (2001).
2. V. K. Vanag and I. R. Epstein, Science 294, 835 (2001).
3. V. K. Vanag and I. R. Epstein, Phys. Rev. Lett. 88, 088303 (2002).
4. R. J. Field and R. M. Noyes. J. Chem. Phys. 60, 1877 (1974).
5. L. J. Schwartz, C. L. DeCiantis, S. Chapman, B. K. Kelley, and J. P. Hornak, Langmuir 15, 5461 (1999).
6. R. A. Fisher, Ann. Eugen. 7, 355 (1937).
7. A. N. Kolmogorov, I. G. Petrovski, and N. S. Piskunov, Bull. Moscow State Univ., Series A 1, 1 (1937).
8. P. Gray and S. K. Scott, Chemical Oscillations and Instabilities: Non-linear Chemical Kinetics (Clarendon, Oxford University Press, Oxford, 1990).
9. A. G. Merzhanov and E. N. Rumanov, Rev. Mod. Phys. 71, 1173 (1999).
10. E. Ben-Jacob, H. Brand, G. Dee, L. Kramer, and J. S. Langer, Physica D 14, 348 (1985).
11. G. C. Paquette, L.-Y. Chen, N. Goldenfeld, and Y. Oono, Phys. Rev. Lett. 72, 76 (1994).
12. W. van Saarloos, Phys. Rev. E 37, 211 (1988).
13. W. van Saarloos, Phys. Rev. E 39, 6367 (1989).
14. V. A. Vasilev, Ju. M. Romanovskii, D. S. Chernavskii, and V. G. Yakhno, Autowave Processes in Kinetic Systems. Spatial and Temporal Self-Organization in Physics, Chemistry, Biology and Medicine (Deutscher Verlag, Berlin, 1987).
15. D. G. Aronson and H. F. Weinberger, in Partial Differential Equations and Related Topics, edited by A. Goldstein (Springer-Verlag, Berlin, 1975), pp. 5-49.
16. G. Dee and J. S. Langer, Phys. Rev. Lett. 50, 383 (1983).
17. W. van Saarloos, Phys. Rep. 301, 9 (1998).
18. P. Gray, S. K. Scott, and K. Showalter, Philos. Trans. R. Soc. London, Ser. A 337, 249 (1991).
19. V. K. Vanag and I. R. Epstein (unpublished).
20. X set to 0.01, the value used for simulation of the full system (2), (3).
21. FlexPDE, http://www.pdesolutions.com/flexpde.htm (2001).
22. 3. This version of the model has an additional, unphysical steady state at negative [X].
23. H. P. Breuer, W. Huber, and F. Petruccione, Physica D 73, 259 (1994).
24. J. Cook and B. Derrida, J. Stat. Phys. 61, 961 (1990).
25. B. Derrida and H. Spohn, J. Stat. Phys. 51, 817 (1988).
26. E. Brunet and B. Derrida, Phys. Rev. E 56, 2597 (1997).