Linear stability analysis of bifurcations with a spatially periodic, fluctuating control parameter

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 55, Issue 6, 1997, Pages 7068-7078

  Röder, Joanna ^a,b   Röder, Heinrich ^a,b   Kramer, Lorenz ^a,b  

^a UNIVERSITY OF BAYREUTH   (Germany)

^b LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2542437380     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.55.7068     Document Type: Article

References (74)

1. S. Kai, J. Phys. Soc. Jpn.47, 1379 (1979).
2. T. Kawakubo, A. Yanagita and S. Kabashima, J. Phys. Soc. Jpn.50, 1451 (1981).
3. H R. Brand, S. Kai and S. Wakabayashi, Phys. Rev. Lett.54, 555 (1985).
4. S. Kai, H. Fukunuga and H R. Brand, J. Phys. Soc. Jpn.56, 3759 (1987).
5. S. Kai, H. Fukunuga and H R. Brand, J. Stat. Phys.54, 1133 (1989).
6. S. Wu and C D. Andereck, Phys. Rev. Lett.65, 591 (1990).
7. H. Amm, U. Behn, Th. John, and R. Stannarius, Proceedings of the 17th International Liquid Crystal Conference, Kent, 1996 [Mol. Cryst. Liq. Cryst. (to be published)].
8. A. Schenzle and H. Brand, Phys. Rev. A20, 1628 (1979).
9. R. Graham and A. Schenzle, Phys. Rev. A25, 1731 (1982).
10. R. Graham, Phys. Rev. A25, 3234 (1982).
11. A. Teubel, U. Behn and A. Kühnel, Z. Phys. B71, 393 (1988).
12. U. Behn and K. Schiele, Z. Phys. B77, 485 (1989).
13. J M. Deutsch, Physica A208, 433 (1994).
14. J M. Deutsch, Physica A208, 445 (1994).
15. W. Horsthemke, Phys. Rev. A31, 1123 (1985).
16. U. Behn and R. Müller, Phys. Lett.113A, 85 (1985).
17. R. Müller and U. Behn, Z. Phys. B69, 185 (1987).
18. R. Müller and U. Behn, Z. Phys. B78, 229 (1990).
19. A. Lange, Ph.D. thesis, University of Leipzig, 1993 (unpublished).
20. A. Lange, R. Müller and U. Behn, Z. Phys. B100, 477 (1996).
21. J. García-Ojalvo, A. Hernández-Machado and J M. Sancho, Phys. Rev. Lett.71, 1542 (1993).
22. C. Van Den Broeck, J.M.R. Parrondo, J. Armero and A. Hernández-Machado, Phys. Rev. E49, 2639 (1994).
23. J. Garciá-Ojalvo and J M. Sancho, Phys. Rev. E53, 5680 (1996).
24. J. Garciá-Ojalvo, J.M.R. Parrono, J J. Sancho and C. Van den Broeck, Phys. Rev. E54, 6918 (1996).
25. J. Garciá-Ojalvo and J M. Sancho, Int. J. Bifurcation Chaos4, 1337 (1994).
26. J. Garciá-Ojalvo, J M. Sancho and L. Ramírez-Piscina, Phys. Rev. A46, 4670 (1993).
27. L. Ramírez-Piscina, A. Hernández-Machado and J M. Sancho, Phys. Rev. B48, 119 (1993).
28. L. Ramírez-Piscina, J M. Sancho and A. Hernández-Machado, Phys. Rev. B48, 125 (1993).
29. A. Becker and L. Kramer, Phys. Rev. Lett.73, 995 (1994).
30. A. Becker and L. Kramer, Physica D90, 408 (1995).
31. A. Becker, Ph.D. thesis, University of Bayreuth, 1994 (unpublished).
32. R. Graham, Phys. Rev. A10, 1762 (1974);
33. R. Graham, Phys. Rev. A45, 4198(E) (1992).
34. J B. Swift and P C. Hohenberg, Phys. Rev. A15, 319 (1977).
35. M. San Miguel and F. Sagues, Phys. Rev. A36, 1882 (1987);
36. R F. Rodrigues, M. San Miguel and F. Sagues, Mol. Cryst.199, 393 (1991).
37. H. W. Müller, M. Lücke and M. Kamp, Europhys. Lett.10, 451 (1989);
38. H. W. Müller, M. Lücke and M. Kamp, Phys. Rev. A45, 3714 (1992).
39. W. Schöpf and W. Zimmermann, Phys. Rev. E47, 1739 (1993).
40. M. Treiber and L. Kramer, Phys. Rev. E49, 3184 (1994).
41. J B. Swift and P C. Hohenberg, Phys. Rev. Lett.60, 75 (1988).
42. J. Viñals, H. Xi and J D. Gunton, Phys. Rev. A46, 918 (1992).
43. M O. Caceres, A. Becker and L. Kramer, Phys. Rev. A43, 6581 (1991).
44. A. Becker, M O. Caceres and L. Kramer, Phys. Rev. A46, 4463 (1992).
45. P C. Hohenberg and J B. Swift, Phys. Rev. A46, 4773 (1992).
46. O. Stiller, A. Becker and L. Kramer, Phys. Rev. Lett.68, 3670 (1992).
47. C W. Meyers, G. Ahlers and D S. Cannell, Phys. Rev. Lett.59, 1577 (1987).
48. G. Ahlers, C W. Meyers and D S. Cannell, J. Stat. Phys.54, 1121 (1989).
49. K L. Babcock, G. Ahlers and D S. Cannell, Phys. Rev. Lett.67, 3388 (1991).
50. A. Tsameret and V. Steinberg, Phys. Rev. Lett.67, 3392 (1991).
51. I. Rehberg, S. Rasenat, M. de la Torre Juarez, W. Schöpf, F.H. Hörner, G. Ahlers and H. Brand, Phys. Rev. Lett.67, 596 (1991).
52. I. Rehberg, F.H. Hörner, L. Chiran, H. Richter and B L. Winkler, Phys. Rev. A44, R7855 (1991).
53. W. Schöpf and I. Rehberg, Europhys. Lett.17, 321 (1992);
54. W. Schöpf and I. Rehberg, J. Fluid Mech.271, 235 (1994).
55. G. Quentin and I. Rehberg, Phys. Rev. Lett.74, 1578 (1995).
56. M. Wu, G. Ahlers and D S. Cannell, Phys. Rev. Lett.75, 1743 (1995).
57. C. Van den Broeck, J. M. R. Parrondo and R. Toral, Phys. Rev. Lett.73, 3395 (1994).
58. C. Van den Broeck, J. M. R. Parrondo, R. Toral and R. Kawai, Phys. Rev. E55, 4084 (1997).
59. M. Lowe and J. Gollub, Phys. Rev. Lett.55, 2575 (1985).
60. S. Nasuno, S. Takeuchi and Y. Sawada, Phys. Rev. A40, 3457 (1989).
61. S. Chandrasekhar, Liquid Crystals (Cambridge University Press, Cambridge, 1992).
62. W. Helfrich, J. Chem. Phys.51, 4092 (1969).
63. Orsay Liquid Crystal Group, Phys. Rev. Lett.25, 1642 (1970);
64. E. Dubois-Violette, P.G. de Gennes and O. Parodi, J. Phys. (Paris)32, 305 (1971).
65. L. Kramer and W. Pesch, Annu. Rev. Fluid Mech.27, 515 (1995);
66. in Pattern Formation in Liquid Crystals, edited by A. Buka and L. Kramer (Springer, New York, 1996), Chap. 6.
67. See, e.g., C W. Gardiner, in Handbook of Stochastic Methods (Springer-Verlag, Berlin, 1983).
68. L D. Landau, Quantum Mechanics: Non-Relativistic Theory (Pergamon Press, Oxford, 1965).
69. M. Dennin, G. Ahlers, and D. S. Cannell, in Spatio-temporal Patterns in Nonequilibrium Complex Systems, edited by P. E. Cladis and P. Palffy-Muhoray, Santa Fe Institute Studies in the Sciences of Complexity Vol. XXI (Addison-Wesley, New York, 1994);
70. M. Dennin, M. Treiber, L. Kramer, G. Ahlers and D. Cannell, Phys. Rev. Lett.76, 319 (1995).
71. G. Grinstein, M. A. Muñoz and Y. Tu, Phys. Rev. Lett.76, 4376 (1996).
72. G. Schmidt, Physics of High Temperature Plasmas (Academic Press, New York, 1979), Chap. 9.4.
73. A P. Krekhov, L. Kramer, A. Buka and A N. Chuvyrov, J. Phys. (France) II3, 1387 (1993);
74. A. Krekhov and L. Kramer, Phys. Rev. E53, 4925 (1996).