Global feedback control for pattern-forming systems

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

Volumn 76, Issue 3, 2007, Pages

  Stanton, L G ^a   Golovin, A A ^a  

^a Northwestern University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; STATISTICAL MECHANICS;

HEXAGONAL PATTERN; NONLINEAR REGIME; ROLL PATTERNS; SUPERCRITICAL SH EQUATION;

FEEDBACK CONTROL;

EID: 34748873798     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.76.036210     Document Type: Article

References (62)

1. H. Haken, Advanced Synergetics: Instability Hierarchies of Self-Organizing Systems and Devices (Springer-Verlag, Berlin, 1983).
2. A. S. Mikhailov, Foundations of Synergetics (Springer-Verlag, Berlin, 1990).
3. M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.65.851 65, 851 (1993).
4. D. Walgraef, Spatio-Temporal Pattern Formation: With Examples from Physics, Chemistry, and Materials Science (Springer-Verlag, Berlin, 1997).
5. H. G. Schuster, Handbook of Chaos Control: Foundations and Applications (Wiley-VCH, Weinheim, 1999).
6. A. S. Mikhailov and K. Showalter, Phys. Rep. PRPLCM 0370-1573 10.1016/j.physrep.2005.11.003 425, 79 (2006).
7. J. Tang and H. H. Bau, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.70.1795 70, 1795 (1993).
8. P. K. Yuen and H. H. Bau, J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112096000675 317, 91 (1996).
9. L. E. Howle, Phys. Fluids PHFLE6 1070-6631 10.1063/1.869335 9, 1861 (1997).
10. J. Tang and H. H. Bau, J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112098008891 363, 153 (1998).
11. H. H. Bau, Int. J. Heat Mass Transfer IJHMAK 0017-9310 10.1016/S0017-9310(98)00234-8 42, 1327 (1999).
12. A. C. Or, R. E. Kelly, L. Cortelezzi, and J. L. Speyer, J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112099004607 387, 321 (1999).
13. A. C. Or and R. E. Kelly, J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112001004670 440, 27 (2001).
14. P. Kolodner and G. Flätgen, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.61.2519 61, 2519 (2000).
15. R. O. Grigoriev, Phys. Fluids PHFLE6 1070-6631 10.1063/1.1476304 14, 1895 (2002).
16. R. O. Grigoriev, Phys. Fluids PHFLE6 1070-6631 10.1063/1.1566958 15, 1363 (2003).
17. P. A. Monkewitz, E. Berger, and M. Schumm, Eur. J. Mech. B/Fluids 10, 295 (1991). 0997-7546
18. D. S. Park, D. M. Ladd, and E. W. Hendriks, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(93)91065-D 182, 244 (1993).
19. E. Lauga and T. R. Bewley, Proc. R. Soc. London, Ser. A PRLAAZ 0950-1207 10.1098/rspa.2002.1116 459, 2077 (2003).
20. E. Lauga and T. R. Bewley, J. Fluid Mech. 512, 343 (2004). 0022-1120
21. T. Sakurai, E. Mihaliuk, F. Chirila, and K. Showalter, Science SCIEAS 0036-8075 10.1126/science.1071265 296, 2009 (2002).
22. E. Mihaliuk, T. Sakurai, F. Chirila, and K. Showalter, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.065602 65, 065602 (R) (2002).
23. V. K. Vanag, A. M. Zhabotinsky, and I. R. Epstein, J. Phys. Chem. A JPCAFH 1089-5639 10.1021/jp002390h 104, 11566 (2000).
24. I. R. Epstein, ACS Symp. Ser. ACSMC8 0097-6156 827, 103 (2002).
25. D. Lebiedz and U. Brandt-Pollmann, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.208301 91, 208301 (2003).
26. M. Bertram and A. S. Mikhailov, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.63.066102 63, 066102 (2001).
27. M. Bertram and A. S. Mikhailov, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.036207 67, 036207 (2003).
28. C. Beta, M. Bertram, A. S. Mikhailov, H. H. Rotermund, and G. Ertl, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.046224 67, 046224 (2003).
29. R. Martin, A. J. Scroggie, G.-L. Oppo, and W. J. Firth, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.4007 77, 4007 (1996).
30. A. V. Mamaev and M. Saffman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.3499 80, 3499 (1998).
31. T. V. Savina, A. A. Nepomnyashchy, S. Brandon, D. R. Lewin, and A. A. Golovin, J. Cryst. Growth JCRGAE 0022-0248 10.1016/S0022-0248(02)00859-X 240, 292 (2002).
32. A. A. Nepomnyashchy, A. A. Golovin, V. Gubareva, and V. Panfilov, Physica D PDNPDT 0167-2789 10.1016/j.physd.2004.08.004 199, 61 (2004).
33. B. Echebarria and A. Karma, Chaos CHAOEH 1054-1500 10.1063/1.1501544 12, 923 (2002).
34. D. Battogtokh and A. Mikhailov, Physica D PDNPDT 0167-2789 10.1016/0167-2789(95)00232-4 90, 84 (1996).
35. D. Battogtokh, A. Preusser, and A. Mikhailov, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(97)00046-8 106, 327 (1997).
36. Y. Kawamura and Y. Kuramoto, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.016202 69, 016202 (2004).
37. K. A. Montgomery and M. Silber, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/17/6/011 17, 2225 (2004).
38. A. A. Golovin and A. A. Nepomnyashchy, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.73.046212 73, 046212 (2006).
39. A. A. Nepomnhyashchy, Physica D PDNPDT 0167-2789 10.1016/0167-2789(95) 00090-Q 86, 90 (1995).
40. G. I. Sivashinsky, Acta Astronaut. AASTCF 0094-5765 10.1016/0094-5765(77) 90096-0 4, 1177 (1977).
41. A. Novick-Cohen, Physica D PDNPDT 0167-2789 10.1016/0167-2789(87)90240-5 26, 403 (1987).
42. M. L. Frankel, Physica D PDNPDT 0167-2789 10.1016/0167-2789(87)90017-0 27, 260 (1987).
43. A. Umantsev and S. H. Davis, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.45.7195 45, 7195 (1992).
44. G. M. Homsy, Lect. Appl. Math. ZZZZZZ 0075-8485 15, 191 (1974).
45. A. A. Nepomnyashchy, Fluid Dyn. FLDYAH 0015-4628 10.1007/BF01025515 9, 354 (1975).
46. Y. Kuramoto and T. Tsuzuki, Prog. Theor. Phys. PTPKAV 0033-068X 55, 536 (1976).
47. A. Armaou and P. D. Christophides, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(99)00175-X 137, 49 (2000).
48. T. Kobayashi, Int. J. Syst. Sci. 33, 175 (2002). 0020-7721
49. Y. Lou and P. D. Christophides, IEEE Trans. Control Syst. Technol. 11, 737 (2003). 1063-6536
50. A. A. Nepomnyashchy and A. A. Golovin, in Self-Assembly, Pattern Formation and Growth Phenomena in Nano-Systems, edited by, A. A. Golovin, and, A. A. Nepomnyashchy, (Springer-Verlag, Berlin, 2006), pp. 1-54.
51. J. Swift and P. C. Hohenberg, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.15.319 15, 319 (1977).
52. F. H. Busse, J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112067001661 30, 625 (1967).
53. D. Bensimon, B. I. Shraiman, and V. Croquette, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.38.5461 38, 5461 (1988).
54. H. Sakaguchi and H. R. Brand, Physica D PDNPDT 0167-2789 10.1016/0167-2789(96)00077-2 97, 274 (1996).
55. A. Handel and R. Grigoriev, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.066208 72, 066208 (2005).
56. G. H. Gunaratne, Q. Ouyang, and H. L. Swinney, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.50.2802 50, 2802 (1994).
57. E. A. Kuznetsov, A. A. Nepomnyashchy, and L. M. Pismen, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(95)00568-N 205, 261 (1995).
58. R. Graham, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.2185 76, 2185 (1996).
59. A. A. Golovin, A. A. Nepomnyashchy, and L. M. Pismen, J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112097005582 341, 317 (1997).
60. B. Y. Rubinstein, A. A. Nepomnyashchy, and A. A. Golovin, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.75.046213 75, 046213 (2007).
61. K. Pyragas, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(92)90745-8 170, 421 (1992).
62. C. M. Postlethwaite and M. Silber, Physica D (to be published). 0167-2789