Feedback control of subcritical Turing instability with zero mode

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

Volumn 79, Issue 4, 2009, Pages

  Golovin, A A ^a   Kanevsky, Y ^b   Nepomnyashchy, A A ^b  

^a Northwestern University   (United States)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

CRITICAL VALUE; DAMPING COEFFICIENTS; GINZBURG-LANDAU EQUATIONS; MONOTONIC INSTABILITY; PARAMETERS CHARACTERIZING; PERIODIC PATTERN; SHORT WAVES; SOLITARY WAVE; STATIONARY STATE; TURING INSTABILITY; WAVE NUMBERS;

FEEDBACK CONTROL; STABILITY;

FEEDBACK;

EID: 66049128049     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.79.046218     Document Type: Article

References (51)

1. M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993). 10.1103/RevModPhys.65.851
2. D. Walgraef, Spatio-Temporal Pattern Formation: With Examples from Physics, Chemistry, and Materials Science (Springer-Verlag, Berlin, 1997).
3. I. S. Aranson and L. Kramer, Rev. Mod. Phys. 74, 99 (2002). 10.1103/RevModPhys.74.99
4. P. Coullet and S. Fauve, Phys. Rev. Lett. 55, 2857 (1985). 10.1103/PhysRevLett.55.2857
5. P. Coullet and G. Iooss, Phys. Rev. Lett. 64, 866 (1990). 10.1103/PhysRevLett.64.866
6. P. C. Matthews and S. M. Cox, Phys. Rev. E 62, R1473 (2000). 10.1103/PhysRevE.62.R1473
7. P. C. Matthews and S. M. Cox, Nonlinearity 13, 1293 (2000). 10.1088/0951-7715/13/4/317
8. S. M. Cox and P. C. Matthews, Physica D 175, 196 (2003). 10.1016/S0167-2789(02)00733-9
9. A. A. Golovin, A. A. Nepomnyashchy, and L. M. Pismen, Phys. Fluids 6, 34 (1994). 10.1063/1.868090
10. A. A. Golovin, A. A. Nepomnyashchy, and L. M. Pismen, J. Fluid Mech. 341, 317 (1997). 10.1017/S0022112097005582
11. D. Casini, G. DâAlessandro, and A. Politi, Phys. Rev. A 55, 751 (1997). 10.1103/PhysRevA.55.751
12. N. Komarova and A. C. Newell, J. Fluid Mech. 415, 285 (2000). 10.1017/S0022112000008855
13. A. A. Golovin, S. H. Davis, and P. W. Voorhees, Phys. Rev. E 68, 056203 (2003). 10.1103/PhysRevE.68.056203
14. W. SchÃpf and L. Kramer, Phys. Rev. Lett. 66, 2316 (1991). 10.1103/PhysRevLett.66.2316
15. Handbook of Chaos Control, 2nd ed., edited by, E. SchÃll, and, H. G. Schuster, (Wiley-VCH, Weinheim, 2008).
16. A. S. Mikhailov and K. Showalter, Phys. Rep. 425, 79 (2006). 10.1016/j.physrep.2005.11.003
17. J. Tang and H. H. Bau, Phys. Rev. Lett. 70, 1795 (1993). 10.1103/PhysRevLett.70.1795
18. P. K. Yuen and H. H. Bau, J. Fluid Mech. 317, 91 (1996). 10.1017/S0022112096000675
19. L. E. Howle, Phys. Fluids 9, 1861 (1997). 10.1063/1.869335
20. J. Tang and H. H. Bau, J. Fluid Mech. 363, 153 (1998). 10.1017/S0022112098008891
21. H. H. Bau, Int. J. Heat Mass Transfer 42, 1327 (1999). 10.1016/S0017-9310(98)00234-8
22. A. C. Or and R. E. Kelly, J. Fluid Mech. 440, 27 (2001). 10.1017/S0022112001004670
23. R. O. Grigoriev, Phys. Fluids 14, 1895 (2002). 10.1063/1.1476304
24. R. O. Grigoriev, Phys. Fluids 15, 1363 (2003). 10.1063/1.1566958
25. P. A. Monkewitz, E. Berger, and M. Schumm, Eur. J. Mech. B Fluids 10, 295 (1991).
26. D. S. Park, D. M. Ladd, and E. W. Hendriks, Phys. Lett. A 182, 244 (1993). 10.1016/0375-9601(93)91065-D
27. E. Lauga and T. R. Bewley, J. Fluid Mech. 512, 343 (2004). 10.1017/S0022112004009711
28. T. Sakurai, E. Mihaliuk, F. Chirila, and K. Showalter, Science 296, 2009 (2002). 10.1126/science.1071265
29. E. Mihaliuk, T. Sakurai, F. Chirila, and K. Showalter, Phys. Rev. E 65, 065602 (R) (2002). 10.1103/PhysRevE.65.065602
30. V. K. Vanag, A. M. Zhabotinsky, and I. R. Epstein, J. Phys. Chem. A 104, 11566 (2000). 10.1021/jp002390h
31. I. R. Epstein, ACS Symp. Ser. 827, 103 (2002).
32. D. Lebiedz and U. Brandt-Pollmann, Phys. Rev. Lett. 91, 208301 (2003). 10.1103/PhysRevLett.91.208301
33. M. Bertram and A. S. Mikhailov, Phys. Rev. E 63, 066102 (2001). 10.1103/PhysRevE.63.066102
34. M. Bertram and A. S. Mikhailov, Phys. Rev. E 67, 036207 (2003). 10.1103/PhysRevE.67.036207
35. C. Beta, M. Bertram, A. S. Mikhailov, H. H. Rotermund, and G. Ertl, Phys. Rev. E 67, 046224 (2003). 10.1103/PhysRevE.67.046224
36. R. Martin, A. J. Scroggie, G.-L. Oppo, and W. J. Firth, Phys. Rev. Lett. 77, 4007 (1996). 10.1103/PhysRevLett.77.4007
37. A. V. Mamaev and M. Saffman, Phys. Rev. Lett. 80, 3499 (1998). 10.1103/PhysRevLett.80.3499
38. T. V. Savina, A. A. Nepomnyashchy, S. Brandon, D. R. Lewin, and A. A. Golovin, J. Cryst. Growth 240, 292 (2002). 10.1016/S0022-0248(02)00859-X
39. A. A. Nepomnyashchy, A. A. Golovin, V. Gubareva, and V. Panfilov, Physica D 199, 61 (2004). 10.1016/j.physd.2004.08.004
40. D. Battogtokh and A. Mikhailov, Physica D 90, 84 (1996). 10.1016/0167-2789(95)00232-4
41. D. Battogtokh, A. Preusser, and A. Mikhailov, Physica D 106, 327 (1997). 10.1016/S0167-2789(97)00046-8
42. Y. Kawamura and Y. Kuramoto, Phys. Rev. E 69, 016202 (2004). 10.1103/PhysRevE.69.016202
43. K. A. Montgomery and M. Silber, Nonlinearity 17, 2225 (2004). 10.1088/0951-7715/17/6/011
44. C. M. Postlethwaite and M. Silber, Physica D 236, 65 (2007). 10.1016/j.physd.2007.07.011
45. B. Y. Rubinstein, A. A. Nepomnyashchy, and A. A. Golovin, Phys. Rev. E 75, 046213 (2007). 10.1103/PhysRevE.75.046213
46. A. A. Golovin and A. A. Nepomnyashchy, Phys. Rev. E 73, 046212 (2006). 10.1103/PhysRevE.73.046212
47. L. G. Stanton and A. A. Golovin, Phys. Rev. E 76, 036210 (2007). 10.1103/PhysRevE.76.036210
48. J. D. Murray, Mathematical Biology (Springer-Verlag, Berlin, 1989).
49. G. RÃder, G. Bordyugov, H. Engel, and M. Falcke, Phys. Rev. E 75, 036202 (2007). 10.1103/PhysRevE.75.036202
50. K. Pyragas, Phys. Lett. A 170, 421 (1992). 10.1016/0375-9601(92)90745-8
51. M. Dahlem, F. M. Schneider, and E. SchÃll, Chaos 18, 026110 (2008). 10.1063/1.2937120