Stripe-hexagon competition in forced pattern-forming systems with broken up-down symmetry

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 71, Issue 4, 2005, Pages

  Peter, R ^a,b   Hilt, M ^a,b   Ziebert, F ^a,b   Bammert, J ^a   Erlenkamper C ^a   Lorscheid, N ^a   Weitenberg, C ^a   Winter, A ^a   Hammele, M ^a   Zimmermann, W ^a,b  

^a SAARLAND UNIVERSITY   (Germany)

^b UNIVERSITY OF BAYREUTH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

AMPLITUDE EQUATIONS; MODULATION AMPLITUDE; MODULATION WAVES; PATTERN-FORMING SYSTEM;

ANISOTROPY; BIFURCATION (MATHEMATICS); CHEMICAL REACTIONS; COMPUTER SIMULATION; DIFFUSION; HYDRODYNAMICS; NUMERICAL METHODS; PERTURBATION TECHNIQUES;

NONLINEAR SYSTEMS;

EID: 41349100412     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.71.046212     Document Type: Article

References (57)

1. R. E. Kelly and D. Pal, J. Fluid Mech. 86, 433 (1978).
2. M. Lowe, J. P. Gollub, and T. Lubensky, Phys. Rev. Lett. 51, 786 (1983).
3. M. Lowe, B. S. Albert, and J. P. Gollub, J. Fluid Mech. 173, 253 (1986).
4. P. Coullet, Phys. Rev. Lett. 56, 724 (1986).
5. P. Coullet and P. Huerre, Physica D 23, 27 (1986).
6. D. A. S. Rees and D. S. Riley, J. Fluid Mech. 166, 503 (1986).
7. P. Coullet and D. Walgraef, Europhys. Lett. 10, 525 (1989).
8. G. Hartung, F. H. Busse, and I. Rehberg, Phys. Rev. Lett. 66, 2742 (1991).
9. W. Zimmermann, in Defects, Singularities in Nematic Liquid Crystals: Mathematical and Physical Aspects, Vol. 332 of NATO ASI Series C, edited by J. M. Coron, J. M. Ghidaglia, and F. Helein (Kluwer, Dordrecht, 1991), p. 401.
10. W. Zimmermann et al., Europhys. Lett. 24, 217 (1993).
11. W. Zimmermann and R. Schmilz, in Spatio-Temporal Patterns in Nonequilibrium Complex Systems, edited by P. Cladis and P. Palffy-Muhoray (Addison-Wesley, New York, 1994), p. 273.
12. A. Ogawa, W. Zimmermann, K. Kawasaki, and T. Kawakatsu, J. Phys. II 6, 305 (1996).
13. W. Zimmermann and R. Schmilz, Phys. Rev. E 53, R1321 (1996).
14. R. Schmitz and W. Zimmermann, Phys. Rev. E 53, 5993 (1996).
15. R. Schmitz and W. Zimmermann, Phys. Lett. A 237, 405 (1997).
16. A. D. Stroock, R. F. Ismagilov, H. A. Stone, and G. M. Whitesides, Langmuir 19, 4358 (2003).
17. W. Zimmermann, B. Painter, and R. Behringer, Eur. Phys. J. B 5, 575 (1998).
18. Y. Hidaka, T. Fujimura, N. A. Mon, and S. Kai, Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 328, 565 (1999).
19. R. Neubecker and A. Zimmermann, Phys. Rev. E 65, 035205 (2002).
20. M. Dolnik, I. Berenstein, A. M. Zhabolinsky, and I. R. Epslein, Phys. Rev. Lett. 87, 238301 (2001).
21. I. Berenstein et al., Phys. Rev. Lett. 91, 058302 (2003).
22. M. Henriot, J. Burguette, and R. Ribotta, Phys. Rev. Lett. 91, 104501 (2003).
23. G. Ahlers, P. C. Hohenberg, and M. Lücke, Phys. Rev. Lett. 53, 48 (1984).
24. G. Ahlers, P. C. Hohenberg, and M. Lücke, Phys. Rev. A 32, 3493 (1985).
25. H. Riecke, J. D. Crawford, and E. Knobloch, Phys. Rev. Lett. 61, 1942 (1988).
26. D. Walgraef, Europhys. Lett. 7, 485 (1988).
27. I. Rehberg et al., Phys. Rev. Lett. 61, 2449 (1988).
28. P. Coullet and K. Emillson, Physica D 61, 119 (1992).
29. M. Silber, H. Riecke, and L. Kramer, Physica D 61, 260 (1992).
30. J. L. Rogers, M. L. Schatz, O. Brausen, and W. Pesch, Phys. Rev. Lett. 85, 4281 (2000).
31. A. L. Lin et al., Phys. Rev. Lett. 84, 4240 (2000).
32. A. L. Lin et al., Phys. Rev. E 62, 3790 (2000).
33. C. Utzny, W. Zimmermann, and M. Bär, Europhys. Lett. 57, 113 (2002).
34. S. Rüdiger et al., Phys. Rev. Lett. 90, 128301 (2003).
35. D. G. Miguez et al., Phys. Rev. Lett. 93, 048303 (2004).
36. S. Schuler, M. Hammele, and W. Zimmermann, Eur. Phys. J. B 42, 591 (2004).
37. F. H. Busse, J. Fluid Mech. 30, 625 (1967).
38. F. H. Busse, in Convection: Plate Tectonics and Global Dynamics, edited by W. R. Peltier (Gordon and Breach, Montreux, 1989), pp. 23-95.
39. A. Turing, Philos. Trans. R. Soc. London, Ser. B 237, 37 (1952).
40. J. D. Murray, Mathematical Biology (Springer, Berlin, 1989).
41. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals (Clarendon, Oxford, 1993).
42. S. Kai and W. Zimmermann, Prog. Theor. Phys. Suppl. 99, 458 (1989).
43. L. Kramer and W. Pesch, Annu. Rev. Fluid Mech. 27, 515 (1995).
44. A. Buka and L. Kramer, Pattern Formation in Liquid Crystals (Springer, Berlin, 1996).
45. R. Schmitz and W. Zimmermann, J. Phys. II 7, 677 (1997).
46. R. Friedrichs, Phys. Rev. E 66, 066215 (2002).
47. T. Ackemann, B. Giese, B. Schapers, and W. Lange, J. Opt. B: Quantum Semiclassical Opt. 1, 70 (1999).
48. V. K. Vanag and I. R. Epstein, Phys. Rev. E 67, 066219 (2003).
49. I. Lengyel and I. R. Epstein, Science 251, 650 (1990).
50. A. P. Munuzuri, M. Dolnik, A. M. Zhabotinsky, and I. R. Epstein, J. Am. Chem. Soc. 121, 8065 (1999).
51. A. Sanz-Anchelergues, A. M. Zhabotinsky, I. R. Epstein, and A. P. Munuzuri, Phys. Rev. E 63, 056124 (2001).
52. M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).
53. P. Manneville, Dissipative Structures and Weak Turbulence (Academic Press, London, 1990).
54. S. Ciliberto et al., Phys. Rev. Lett. 65, 2370 (1990).
55. M. Hilt and W. Zimmermann (unpublished).
56. I. Lengyel, S. Kádár, and I. R. Epstein, Science 259, 493 (1993).
57. M. Hammele and W. Zimmermann (unpublished).