Stability results for steady, spatially periodic planforms

Nonlinearity

Volumn 10, Issue 2, 1997, Pages 321-353

  Dionne, Benoit ^a   Silber, Mary ^b   Skeldon, Anne C ^c  

^a UNIVERSITY OF OTTAWA   (Canada)

^b Northwestern University   (United States)

^c CITY UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001686674     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/10/2/002     Document Type: Article

References (30)

1. Bosch Vivancos I, Chossat P and Melbourne I 1995 New planforms in systems of partial differential equations with Euclidean symmetry Arch. Rat. Mech. Anal. 131 199-224
2. Brattkus K and Davis S H 1988 Cellular growth near absolute stability Phys. Rev. B 38 11 452-60
3. Busse F H 1978 Non-linear properties of thermal convection Rep. Prog. Phys. 41 1929-67
4. Buzano E and Golubitsky M 1983 Bifurcation on the hexagonal lattice and the planar Bénard problem Phil. Trans. R. Soc. A 308 617-67
5. Coriell S R and McFadden G B 1993 Morphological stability Handbook of Crystal Growth vol 1, ed D T J Hurle (New York: Elsevier) 785-857
6. 2 mode interactions and hidden symmetry Nonlinearity 7 697-739
7. Dionne B 1990 Spatially periodic patterns in two and three dimensions PhD Thesis University of Houston
8. Dionne B and Golubitsky M 1992 Planforms in two and three dimensions Z. Angew. Math. Phys. 43 36-62
9. Dufiet V and Boissonade J 1992 Conventional and unconventional Turing patterns J. Chem. Phys. 96 664-73
10. Edwards W S and Fauve S 1994 Patterns and quasi-patterns in the Faraday experiment J. Fluid Mech. 278 123-48
11. Golubitsky M, Dionne B and Stewart I 1994 Coupled-cells, wreath products and direct products Dynamics. Bifurcations, Symmetry ed P Chossat (Dordrecht: Kluwer Academic) 127-38
12. Golubitsky M, Stewart I N and Schaeffer D G 1988 Singularities and Groups in Bifurcation Theory: vol 2 Appl. Math. Sci. Ser. vol 69 (New York: Springer)
13. Golubitsky M, Swift J W and Knobloch E 1984 Symmetries and pattern selection in Rayleigh-Bénard convection. Physica D 10 249-76
14. Gunaratne G H, Ouyang Q and Swinney H L 1994 Pattern formation in the presence of symmetries Phys. Rev. E 50 2802-20
15. Ihrig E and Golubitsky M 1984 Pattern selection with O(3) symmetry Physica D 12 1-33
16. Kirchgässner K 1979 Exotische Lösungen des Bénardschen Problems Math. Meth. in the Appl. Sci. 1 453-67
17. Knightly G H and Sather D 1987 Stability of cellular convection Arch. Rational Mech. Anal. 97 271-97
18. Knobloch E 1990 Pattern selection in long-wavelength convection Physica D 41 450-79
19. Marsden J E and McCracken M 1976 The Hopf Bifurcation and its Applications Appl. Math. Sci. Ser. vol 19 (Berlin: Springer)
20. Melbourne I 1996 Steady-state bifurcation with Euclidean symmetry Trans. AMS to appear
21. Ouyang Q and Swinney H L 1991 Transition from a uniform state to hexagonal and striped Turing patterns Nature 352 610-12
22. Sarocka D C and Bernoff A J 1995 An intrinsic equation of interfacial motion for the solidification of a pure hypercooled melt Physica D 85 348-74
23. Schlüter A, Lortz D and Busse F H 1965 On the stability of steady finite amplitude convection J. Fluid Mech. 23 129-44
24. Silber M and Knobloch E 1988 Pattern selection in fenofluids Physica D 30 83-98
25. Silber M and Knobloch E 1988 Pattern selection in steady binary-fluid convection Phys. Rev. A 38 1468-77
26. Sivashinsky G I 1983 Instabilities, pattern-formation, and turbulence in flames Ann. Rev. Fluid Mech. 15 179-99
27. Swift J W 1984 Bifurcation and symmetry in convection PhD Thesis University of California, Berkeley
28. Turing A M 1952 Chemical basis of morphogenesis Phil. Trans. R. Soc. B 327 37-72
29. Vanderbauwhede A 1980 Local bifurcation and symmetry Habilitation Thesis Rijksuniversiteit Gent
30. Wollkind D J, Sriranganathan R and Oulton D B 1984 Interfacial patterns during plane front alloy solidification Physica D 12 215-40