Harmonic versus subharmonic patterns in a spatially forced oscillating chemical reaction

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

Volumn 73, Issue 6, 2006, Pages

  Hammele, Martin ^a,b   Zimmermann, Walter ^b  

^a UNIVERSITY OF BAYREUTH   (Germany)

^b SAARLAND UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

HARMONIC ANALYSIS; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; OSCILLATIONS;

OSCILLATING PATTERNS; OSCILLATION FREQUENCY; SPATIALLY PERIODIC FORCING; SUBHARMONIC PATTERN;

CHEMICAL REACTIONS;

EID: 33745024369     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.73.066211     Document Type: Article

References (39)

1. R. E. Kelly and D. Pal, J. Fluid Mech. JFLSA7 0022-1120 86, 433 (1978).
2. M. Lowe, J. P. Gollub, and T. C. Lubensky, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.51.786 51, 786 (1983).
3. M. Lowe and J. P. Gollub, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.31.3893 31, 3893 (1985).
4. M. Lowe, B. S. Albert, and J. P. Gollub, J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112086001167 173, 253 (1986).
5. P. Coullet, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.56.724 56, 724 (1986).
6. P. Coullet and D. Repaux, Europhys. Lett. EULEEJ 0295-5075 3, 573 (1987).
7. W. Zimmermann, Europhys. Lett. EULEEJ 0295-5075 24, 217 (1993).
8. A. Ogawa, W. Zimmermann, K. Kawasaki, and T. Kawakatsu, J. Phys. II JPAHER 1155-4312 10.1051/jp2:1996183 6, 305 (1996).
9. W. Zimmermann and R. Schmitz, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.53.R1321 53, R1321 (1996).
10. R. Schmitz and W. Zimmermann, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.53.5993 53, 5993 (1996).
11. W. Zimmermann, B. Painter, and R. Behringer, Eur. Phys. J. B EPJBFY 1434-6028 10.1007/s100510050500 5, 757 (1998).
12. A. Sanz-Anchelergues, A. M. Zhabotinsky, I. R. Epstein, and A. P. Muñuzuri, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.63.056124 63, 056124 (2001).
13. R. Peter, M. Hilt, F. Ziebert, J. Bammert, C. Erlenkamper, N. Lorscheid, G. C. Weitenber, A. Winter, M. Hammele, and W. Zimmermann, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.046212 71, 046212 (2005).
14. H. Riecke, J. D. Crawford, and E. Knobloch, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.61.1942 61, 1942 (1988).
15. D. Walgraef, Europhys. Lett. EULEEJ 0295-5075 7, 485 (1988).
16. I. Rehberg, S. Rasenat, J. Fineberg, M. de la Torre Juárez, and V. Steinberg, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.61.2449 61, 2449 (1988).
17. P. Coullet and D. Walgraef, Europhys. Lett. EULEEJ 0295-5075 10, 525 (1989).
18. P. Coullet and K. Emillson, Physica D PDNPDT 0167-2789 10.1016/0167-2789(92)90154-F 61, 119 (1992).
19. P. Coullet and K. Emillson, Physica A PHYADX 0378-4371 10.1016/0378-4371(92)90265-R 188, 190 (1992).
20. P. Coullet, K. Emillson, and D. Walgraef, Physica D PDNPDT 0167-2789 10.1016/0167-2789(92)90155-G 61, 132 (1992).
21. A. Amengual, D. Walgraef, M. San Miguel, and E. Hernández-García, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.1956 76, 1956 (1996).
22. C. Elphick, A. Hagberg, and E. Meron, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.5007 80, 5007 (1998).
23. V. Petrov, Q. Quyang, and H. L. Swinney, Nature (London) NATUAS 0028-0836 10.1038/41732 388, 655 (1997).
24. A. L. Lin, M. Bertram, K. Martinez, H. L. Swinney, A. Ardelea, and G. F. Carey, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.4240 84, 4240 (2000).
25. C. Utzny, W. Zimmermann, and M. Bär, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2002-00549-4 57, 113 (2002).
26. S. Rüdiger, D. G. Miguez, A. P. Munuzuris, F. Sagues, and J. Casademunt, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.128301 90, 128301 (2003).
27. I. Berenstein, L. Yang, M. Dolnik, A. M. Zhabotinsky, and I. R. Epstein, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.058302 91, 058302 (2003).
28. D. G. Míguez, E. M. Nicola, A. P. Munuzuri, J. Casademunt, F. Sagues, and L. Kramer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.048303 93, 048303 (2004).
29. M. Henriot, J. Burguete, and R. Ribotta, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.104501 91, 104501 (2003).
30. S. Schuler, M. Hammele, and W. Zimmermann, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2005-00019-5 42, 591 (2004).
31. I. Lengyel and I. R. Epstein, Science SCIEAS 0036-8075 251, 650 (1991).
32. I. Lengyel, S. Kádár, and I. R. Epstein, Science SCIEAS 0036-8075 259, 493 (1993).
33. A. P. Muñuzuri, M. Dolnik, A. M. Zhabotinsky, and I. R. Epstein, J. Am. Chem. Soc. JACSAT 0002-7863 10.1021/ja9910457 121, 8065 (1999).
34. I. Lengyel, G. Rábai, and I. R. Epstein, J. Am. Chem. Soc. JACSAT 0002-7863 10.1021/ja00181a011 112, 9104 (1990).
35. M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.65.851 65, 851 (1993).
36. M. Dolnik, I. Berenstein, A. M. Zhabotinsky, and I. R. Epstein, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.238301 87, 238301 (2001).
37. V. K. Vanag and I. R. Epstein, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.066219 67, 066219 (2003).
38. I. Aranson and L. Kramer, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.74.99 74, 99 (2002).
39. W. Schöpf and W. Zimmermann, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.47.1739 47, 1739 (1993).