Differential flow instability in the Ginzburg-Landau and Swift-Hohenberg approximations

Physica D: Nonlinear Phenomena

Volumn 95, Issue 3-4, 1996, Pages 306-318

  Rovinsky, Arkady ^a   Malevanets, Anatoly ^a   Menzinger, Michael ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0342452439     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/0167-2789(96)00053-X     Document Type: Article

References (31)

1. A.B. Rovinsky and M. Menzinger, Phys. Rev. Lett. 69 (1992) 1193.
2. A.B. Rovinsky and M. Menzinger, Phys. Rev. Lett. 70 (1993) 778.
3. A.B. Rovinsky and M. Menzinger, Phys. Rev. Lett. 72 (1994) 2017.
4. H. Haken, Advanced Synergetics (Springer, Berlin, 1983).
5. V.I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations (Springer, Berlin, 1983);
6. B.D. Hassard, B.D. Kazarinoff and Y.-H. Wan, Theory and Application of Hopf Bifurcation, London Math. Soc. Lecture Notes 41 (Cambridge University Press, Cambridge, 1981).
7. M.C. Cross and P.C. Hohenberg, Rev. Modern Phys. 65 (1993) 851;
8. W. van Saarlos and P.C. Hohenberg, Physica D 56 (1992) 303.
9. A.B. Rovinsky, S. Nakata, V.Z. Yakhnin and M. Menzinger, Phys. Rev. E (submitted).
10. T.B. Benjamin and J.E. Feir, J. Fluid Mech. 27 (1967) 417.
11. A. Turing, Philos. Trans. Roy. Soc. B 237 (1952) 37.
12. I.G. Aramanovich, L.E. Elsgolts and G.L. Lunts, Functions of Complex Variables [Funktzii compleksnogo peremennogo] (Nauka, Moskwa, 1968) [In Russian].
13. L. Segel and J.L. Jackson, J. Theoret. Biol. 37 (1972) 545;
14. H. Meinhardt, Models of Biological Pattern Formation (Academic Press, New York, 1982);
15. G. Nicolis and I. Prigogine, Self-Organization in Noneqilibrium Systems (Wiley, New York, 1977).
16. R.J. Deissler, J. Stat. Physics 40 (1985) 371;
17. J.M. Chomaz, Phys. Rev. Lett. 69 (1992) 1931.
18. P. Ortoleva, Nonlinear Chemical Waves (Wiley, New York, 1992).
19. P. Kolodner, R.W. Walden, A. Passner and C.M. Surko, J. Fluid Mech. 163 (1986) 195;
20. F.H. Busse and R.M. Clever, J. Fluid Mech. ibid. 91 (1979) 319;
21. F.H. Busse, Rep. Progr. Phys. 41 (1978) 1929;
22. E.W. Bolton, F.H. Busse and R.M. Clever, Bull. Amer. Phys. Soc. 28 (1983) 1399.
23. A.H. Nayfeh, Introduction to Perturbation Methods (Wiley, New York, 1981).
24. A.C. Newell, Lectures in Applied Mathematics, Vol. 15 (American Mathematical Society Providence, RJ, 1974) 157.
25. J.-J. Perraud, A. De Witt, E. Dulos, P. De Kepper, G. Dewel and P. Borckmans, Phys. Rev. Lett. 71 (1993) 1272;
26. A. De Witt, G. Dewel and P. Borckmans, Phys. Rev. E 48 (1993) 4191;
27. A. Rovinsky and M. Menzinger, Phys. Rev. A 46 (1992) 6315;
28. M. Sangali and H.-C. Chang, Phys. Rev. E 49 (1994) 5207.
29. A. Malevanets, A. Careta and R. Kapral, Phys. Rev. E, in press.
30. V. Yakhnin, A. Rovinsky and M. Menzinger, Chem. Engrg. Sci. 50 (1995) 2835.
31. A. Weber, L. Kramer, I.S. Aranson and L. Aranson, Physica D 61 (1992) 279.