Transverse instability of line defects of period-2 spiral waves

Physical Review Letters

Volumn 93, Issue 9, 2004, Pages

  Park, Jin Sung ^a   Woo, Sung Jae ^a   Lee, Kyoung J ^a  

^a Korea University   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); BOUNDARY CONDITIONS; CHAOS THEORY; CHEMICAL REACTORS; DEFORMATION; DIFFUSION; GRADIENT METHODS; MATHEMATICAL MODELS; OSCILLATIONS; REACTION KINETICS; WAVE PROPAGATION;

CHEMICAL REAGENTS; LINE DEFECTS; SPIRAL WAVES; TRANSVERSE INSTABILITY;

CRYSTAL DEFECTS;

EID: 19544369820     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevLett.93.098302     Document Type: Article

References (30)

1. P. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993); B. B. Plapp, D. A. Egolf, and E. Bodenschatz, Phys. Rev. Lett. 81, 5334 (1998); J. Lee, J. Kim, G. H. Lee, and K. J. Lee, Phys. Rev. E 65, 046207 (2002).
2. P. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993); B. B. Plapp, D. A. Egolf, and E. Bodenschatz, Phys. Rev. Lett. 81, 5334 (1998); J. Lee, J. Kim, G. H. Lee, and K. J. Lee, Phys. Rev. E 65, 046207 (2002).
3. P. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993); B. B. Plapp, D. A. Egolf, and E. Bodenschatz, Phys. Rev. Lett. 81, 5334 (1998); J. Lee, J. Kim, G. H. Lee, and K. J. Lee, Phys. Rev. E 65, 046207 (2002).
4. Chemical Waves and Patterns, edited by R. Kapral and K. Showalter (Kluwer, Dordrecht, 1995); V. K. Vanag and I. R. Epstein, Science 294, 835 (2001); Q. Ouyang and J. M. Flesselles, Nature (London) 379, 143 (1996); O. Steinbock, V. Zykov, and S. C. Müller, Nature (London) 366, 322 (1993).
5. Chemical Waves and Patterns, edited by R. Kapral and K. Showalter (Kluwer, Dordrecht, 1995); V. K. Vanag and I. R. Epstein, Science 294, 835 (2001); Q. Ouyang and J. M. Flesselles, Nature (London) 379, 143 (1996); O. Steinbock, V. Zykov, and S. C. Müller, Nature (London) 366, 322 (1993).
6. Chemical Waves and Patterns, edited by R. Kapral and K. Showalter (Kluwer, Dordrecht, 1995); V. K. Vanag and I. R. Epstein, Science 294, 835 (2001); Q. Ouyang and J. M. Flesselles, Nature (London) 379, 143 (1996); O. Steinbock, V. Zykov, and S. C. Müller, Nature (London) 366, 322 (1993).
7. Chemical Waves and Patterns, edited by R. Kapral and K. Showalter (Kluwer, Dordrecht, 1995); V. K. Vanag and I. R. Epstein, Science 294, 835 (2001); Q. Ouyang and J. M. Flesselles, Nature (London) 379, 143 (1996); O. Steinbock, V. Zykov, and S. C. Müller, Nature (London) 366, 322 (1993).
8. K. J. Lee, R. E. Goldstein, and E. C. Cox, Phys. Rev. Lett. 87, 068101 (2001); J. Davidenko, A. Pertsov, R. Salomonsz, W. Baxter, and J. Jalife, Nature (London) 355, 349 (1991); L. Glass, Phys. Today 49, No. 8, 40 (1996)
9. K. J. Lee, R. E. Goldstein, and E. C. Cox, Phys. Rev. Lett. 87, 068101 (2001); J. Davidenko, A. Pertsov, R. Salomonsz, W. Baxter, and J. Jalife, Nature (London) 355, 349 (1991); L. Glass, Phys. Today 49, No. 8, 40 (1996)
10. K. J. Lee, R. E. Goldstein, and E. C. Cox, Phys. Rev. Lett. 87, 068101 (2001); J. Davidenko, A. Pertsov, R. Salomonsz, W. Baxter, and J. Jalife, Nature (London) 355, 349 (1991); L. Glass, Phys. Today 49, No. 8, 40 (1996)
11. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer-Verlag, Berlin, 1984); S. Alonso, F. Saqués, and A. S. Mikhailov, Science 299, 1722 (2003); D. Barkley, Phys. Rev. Lett. 72, 164 (1994); M. Falcke and H. Levine, Phys. Rev. Lett. 80, 3875 (1998).
12. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer-Verlag, Berlin, 1984); S. Alonso, F. Saqués, and A. S. Mikhailov, Science 299, 1722 (2003); D. Barkley, Phys. Rev. Lett. 72, 164 (1994); M. Falcke and H. Levine, Phys. Rev. Lett. 80, 3875 (1998).
13. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer-Verlag, Berlin, 1984); S. Alonso, F. Saqués, and A. S. Mikhailov, Science 299, 1722 (2003); D. Barkley, Phys. Rev. Lett. 72, 164 (1994); M. Falcke and H. Levine, Phys. Rev. Lett. 80, 3875 (1998).
14. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer-Verlag, Berlin, 1984); S. Alonso, F. Saqués, and A. S. Mikhailov, Science 299, 1722 (2003); D. Barkley, Phys. Rev. Lett. 72, 164 (1994); M. Falcke and H. Levine, Phys. Rev. Lett. 80, 3875 (1998).
15. M. Yoneyama, A. Fujii, and S. Maeda, J. Am. Chem. Soc. 117, 8188 (1995).
16. A. Goryachev and R. Kapral, Phys. Rev. Lett. 76, 1619 (1996); Phys. Rev. E 54, 5469 (1996).
17. A. Goryachev and R. Kapral, Phys. Rev. Lett. 76, 1619 (1996); Phys. Rev. E 54, 5469 (1996).
18. A. Goryachev, H. Chaté, and R. Kapral, Phys. Rev. Lett. 80, 873 (1998).
19. J.-S. Park and K. J. Lee, Phys. Rev. Lett. 83, 5393 (1999); 88, 224501 (2002).
20. J.-S. Park and K. J. Lee, Phys. Rev. Lett. 83, 5393 (1999); 88, 224501 (2002).
21. A. Goryachev and R. Kapral, Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, 2243 (1999); A. Goryachev, R. Kapral, and H. Chaté, Int. J. Bifurcation Chaos Appl. Sci. Eng. 10, 1537 (2000).
22. A. Goryachev and R. Kapral, Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, 2243 (1999); A. Goryachev, R. Kapral, and H. Chaté, Int. J. Bifurcation Chaos Appl. Sci. Eng. 10, 1537 (2000).
23. -] is varied as a bifurcation parameter with other experimental parameter values fixed
24. The line defect's small curvature seems to be related with its slow rotation.
25. +] mostly affects the overall curvature of the line defect associated with a P-2 spiral wave.
26. A. Hagberg and E. Meron, Phys. Rev. Lett. 72, 2494 (1994).
27. An online movie for Fig. 4(b) is available at http:// turing.korea.ac.kr/download/exp.avi.
28. An online movie for Figs. 5(e) and 5(f) is available at http://turing.korea.ac.kr/download/sim.avi.
29. 2 = 1.526 to 1.530 in Fig. 5(c) is an artifact incurred by two factors: (i) the line defect, as it is determined by thresholding Δ V, has a finite width of approximately 0.3 pixels and (ii) the line defect is slightly deformed near the core area.
30. A. Goryachev, H. Chaté, and R. Kapral, Phys. Rev. Lett. 83, 1878 (1999).