Selection of flow-distributed oscillation and Turing patterns by boundary forcing in a linearly growing, oscillating medium

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

Volumn 80, Issue 2, 2009, Pages

  Míguez, David G ^a   McGraw, Patrick ^b   Muñuzuri, Alberto P ^c   Menzinger, Michael ^b  

^a BRANDEIS UNIVERSITY   (United States)

^b UNIVERSITY OF TORONTO   (Canada)

^c UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL MODEL; BI-STABILITY; BOUNDARY FORCING; CHLORINE DIOXIDES; DIFFERENT FREQUENCY; DRIVING FREQUENCIES; DYNAMICAL SIMULATION; FLOW-DISTRIBUTED OSCILLATIONS; FORCING FREQUENCIES; GROWING DOMAINS; GROWTH BOUNDARIES; HARMONIC WAVE; LINEAR DISPERSION RELATIONS; MALONIC ACID; NUMERICAL PREDICTIONS; OSCILLATING MEDIUM; PERIODIC FORCING; PERTURBATION FREQUENCY; TRAVELING WAVE; TURING PATTERNS; TWO-DIMENSIONAL STRUCTURES;

CARBOXYLIC ACIDS; CHLORINE; PHASE VELOCITY;

FORECASTING;

EID: 69949180066     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.80.026208     Document Type: Article

References (45)

1. An open flow is characterized by an inflow and a corresponding boundary condition.
2. S. P. Kuznetsov, E. Mosekilde, G. Dewel, and P. Borckmanns, J. Chem. Phys. 106, 7609 (1997) 10.1063/1.473763
3. P. Andrésen, M. Bache, E. Mosekilde, G. Dewel, and P. Borckmanns, Phys. Rev. E 60, 297 (1999). 10.1103/PhysRevE.60.297
4. M. Kærn and M. Menzinger, Phys. Rev. E 60, R3471 (1999). 10.1103/PhysRevE.60.R3471
5. J. R. Bamforth, S. Kalliadasis, J. H. Merkin, and S. K. Scott, Phys. Chem. Chem. Phys. 2, 4013 (2000) 10.1039/b004552g
6. J. R. Bamforth, J. H. Merkin, S. K. Scott, R. Toth, and V. Gaspar, Phys. Chem. Chem. Phys. 3, 1435 (2001). 10.1039/b010094n
7. M. Kærn, M. Menzinger, and A. Hunding, J. Theor. Biol. 207, 473 (2000). 10.1006/jtbi.2000.2183
8. M. Kærn, M. Menzinger, R. Satnoianu, and A. Hunding, Faraday Discuss. 120, 295 (2002). 10.1039/b103244p
9. M. Kærn, D. G. Miguez, A. P. Munuzuri, and M. Menzinger, Biophys. Chem. 110, 231 (2004). 10.1016/j.bpc.2004.02.006
10. An open flow is related to an axially growing system by a Galilei transformation: the inflow is fixed and the medium flows in the former case, while in the latter, the growth boundary moves and the medium is fixed.
11. F. Giudicelli and J. Lewis, Curr. Opin. Genet. Dev. 14, 407 (2004). 10.1016/j.gde.2004.06.014
12. Y. Bessho and R. Kageyama, Curr. Opin. Genet. Dev. 13, 379 (2003). 10.1016/S0959-437X(03)00083-2
13. The somite size predicted from FDO agrees quantitatively with that in chick embryos.
14. R. A. Satnoianu and M. Menzinger, Phys. Rev. E 62, 113 (2000) 10.1103/PhysRevE.62.113
15. R. Satnoianu, P. K. Maini, and M. Menzinger, Physica D 160, 79 (2001). 10.1016/S0167-2789(01)00345-1
16. D. D. Miguez, R. A. Satnoianu, and A. P. Munuzuri, Phys. Rev. E 73, 025201 (R) (2006). 10.1103/PhysRevE.73.025201
17. D. G. Miguez, G. G. Izus, and A. P. Munuzuri, Phys. Rev. E 73, 016207 (2006). 10.1103/PhysRevE.73.016207
18. P. V. Kuptsov and R. A. Satnoianu, Phys. Rev. E 71, 015204 (R) (2005). 10.1103/PhysRevE.71.015204
19. P. V. Kuptsov, Physica D 197, 174 (2004). 10.1016/j.physd.2004.06.013
20. P. N. McGraw and M. Menzinger, Phys. Rev. E 68, 066122 (2003). 10.1103/PhysRevE.68.066122
21. P. N. McGraw and M. Menzinger, Phys. Rev. E 72, 026210 (2005). 10.1103/PhysRevE.72.026210
22. R. J. Briggs, Electron Stream Interactions with Plasmas (MIT, Cambridge, MA, 1964).
23. R. J. Deissler, J. Stat. Phys. 40, 371 (1985) 10.1007/BF01017180
24. R. J. Deissler, J. Stat. Phys. 54, 1459 (1989). 10.1007/BF01044729
25. In convectively unstable flows, perturbations are eventually washed out of a finite domain, while in an equivalent, growing, and stationary medium they grow in both directions.
26. P. N. McGraw and M. Menzinger, Phys. Rev. E 72, 027202 (2005). 10.1103/PhysRevE.72.027202
27. M. Kaern and M. Menzinger, Phys. Rev. E 61, 3334 (2000). 10.1103/PhysRevE.61.3334
28. M. Kærn and M. Menzinger, J. Phys. Chem. A 106, 4897 (2002). 10.1021/jp013095f
29. I. Lengyel, G. Rabai, and I. R. Epstein, J. Am. Chem. Soc. 112, 9104 (1990). 10.1021/ja00181a011
30. A. K. Horvath, M. Dolnik, A. P. Munuzuri, A. M. Zhabotinsky, and I. R. Epstein, Phys. Rev. Lett. 83, 2950 (1999). 10.1103/PhysRevLett.83.2950
31. D. G. Miguez, Ph.D. thesis, Universidad de Santiago de Compostela, 2005.
32. A. P. Munuzuri, M. Dolnik, A. M. Zhabotinsky, and I. R. Epstein, J. Am. Chem. Soc. 121, 8065 (1999). 10.1021/ja9910457
33. D. G. Miguez, M. Dolnik, A. P. Munuzuri, and L. Kramer, Phys. Rev. Lett. 96, 048304 (2006). 10.1103/PhysRevLett.96.048304
34. N. Kopell and L. N. Howard, Science 180, 1171 (1973). 10.1126/science.180.4091.1171
35. S. Y. Su, R. L. Armstrong, M. Menzinger, A. Cross, and C. Lemaire, J. Phys. Chem. 98, 2494 (1994). 10.1021/j100060a044
36. Q. Ouyang and H. L. Swinney, Nature (London) 352, 610 (1991). 10.1038/352610a0
37. A. M. Turing, Philos. Trans. R. Soc. London, Ser. B 237, 37 (1952). 10.1098/rstb.1952.0012
38. A. B. Rovinsky and M. Menzinger, Phys. Rev. Lett. 69, 1193 (1992). 10.1103/PhysRevLett.69.1193
39. M. R. E. Proctor, S. M. Tobias, and E. Knobloch, Physica D 145, 191 (2000). 10.1016/S0167-2789(00)00127-5
40. J. R. Bamforth, R. Toth, V. Gaspar, and S. K. Scott, Phys. Chem. Chem. Phys. 4, 1299 (2002). 10.1039/b107627b
41. R. Toth, A. Papp, V. Gaspar, J. H. Merkin, S. K. Scott, and A. F. Taylor, Phys. Chem. Chem. Phys. 3, 957 (2001). 10.1039/b009379n
42. M. Kaern, R. Satnoianu, A. Munuzuri, and M. Menzinger, Phys. Chem. Chem. Phys. 4, 1315 (2002). 10.1039/b109387h
43. P. Andrésen, E. Mosekilde, G. Dewel, and P. Borckmans, Phys. Rev. E 62, 2992 (2000). 10.1103/PhysRevE.62.2992
44. M. Kærn and M. Menzinger, Phys. Rev. E 62, 2994 (2000). 10.1103/PhysRevE.62.2994
45. R. A. Satnoianu, Phys. Rev. E 68, 032101 (2003). 10.1103/PhysRevE.68. 032101