Wave vectors selection at the threshold of a generic instability of a hexagonal stationary pattern

Physica D: Nonlinear Phenomena

Volumn 179, Issue 1-2, 2003, Pages 92-104

  Pirat, C ^a   Gil, L ^a  

^a UNIVERSITÉ CÔTE D'AZUR   (France)

Author keywords

Hexagonal pattern; Secondary instability; Wave vector selection

Indexed keywords

BIFURCATION (MATHEMATICS); EIGENVALUES AND EIGENFUNCTIONS; PARTIAL DIFFERENTIAL EQUATIONS; PHASE MODULATION; PROBLEM SOLVING; SYSTEMS ENGINEERING; VECTORS;

WAVE VECTORS;

SYSTEM STABILITY;

EID: 0037402177     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(03)00008-3     Document Type: Article

References (29)

1. Cross M.C., Hohenberg P.C., Rev. Mod. Phys. 65:1993;851.
2. E. Bodenschatz, W. Pesch, G. Ahlers, Annu. Rev. Fluid Mech. 32 (2000) 709.
3. Kolodner P., Physica D. 37:1989;319.
4. Moloney J.V., Gibbs H.M., Phys. Rev. Lett. 48:1982;1607 Grynberg G., Le Bihan E., Verkerk P., Simoneau P., Leite J.R.R., Bloch D., Le Boiteux S., Ducloy M., Opt. Commun. 67:1988;363.
5. Moloney J.V., Gibbs H.M., Phys. Rev. Lett. 48:1982;1607 Grynberg G., Le Bihan E., Verkerk P., Simoneau P., Leite J.R.R., Bloch D., Le Boiteux S., Ducloy M., Opt. Commun. 67:1988;363.
6. Castets V., Dulos E., Boissonade J., Kepper P.D., Phys. Rev. Lett. 64:1990;2953.
7. J.D. Murray, Mathematical Biology, Springer, Berlin, 1989 and 1993.
8. Buzano E., Golubitsky M., Philos. Trans. R. Soc. London A. 308:1983;617 Golubitsky M., Swift J.W., Knobloch E., Physica D. 10:1984;249.
9. Buzano E., Golubitsky M., Philos. Trans. R. Soc. London A. 308:1983;617 Golubitsky M., Swift J.W., Knobloch E., Physica D. 10:1984;249.
10. Kubstrup C., Herrero H., Perez-Garcia C., Phys. Rev. E. 54:1996;1560.
11. Dionne B., Silber M., Skeldon A.C., Nonlinearity. 10:1997;321.
12. Nuz A.E., Nepomnyaschy A.A., Golovin A.A., Hari A.A., Pismen L.M., Physica D. 135:2000;233.
13. Lauzeral J., Metens S., Walgraef D., Europhys. Lett. 24:1993;707.
14. Bestehorn M., Phys. Rev. E. 48:1993;3622.
15. Sushchik M.M., Tsimring L.S., Physica D. 74:1994;90.
16. Hoyle R.B., Phys. Rev. E. 61:2000;2506.
17. Christiansen B., Alstrom P., Levinsen M.T., Phys. Rev. Lett. 68:1992;2157.
18. W.S. Edwards, S. Fauve, Phys. Rev. E 47 (1993) R788.
19. Arbell H., Fineberg J., Phys. Rev. Lett. 81:1998;4384.
20. Elmer F.J., Phys. Rev. Lett. 70:1993;2028 Elmer F.J., Phys. Rev. B. 53:1996;14323.
21. Elmer F.J., Phys. Rev. Lett. 70:1993;2028 Elmer F.J., Phys. Rev. B. 53:1996;14323.
22. Herrero R., Westhoff E.G., Aumann A., Ackemann T., Logvin Y.A., Lange W., Phys. Rev. Lett. 82:2000;4627.
23. E.G. Westhoff, R. Herrero, T. Ackemann, W. Lange, Self-organized superlattice patterns with two slightly differing wave numbers, Phys. Rev. Lett., submitted for publication.
24. Daumont I., Kassner K., Misbah C., Valance A., Phys. Rev. E. 55(6):1997;6902.
25. Tse A.M., Rucklidge D.P., Hoyle R.B., Silber M., Physica D. 146:2000;367.
26. Coullet P., Iooss G., Phys. Rev. Lett. 64:1990;866.
27. Gil L., Europhys. Lett. 48:1999;156 Gil L., Physica D. 147:2000;300.
28. Gil L., Europhys. Lett. 48:1999;156 Gil L., Physica D. 147:2000;300.
29. M. Hamermesh, Group Theory and Its Application to Physical Problems, Addison-Wesley.