A novel technique to initiate and investigate scroll waves in thin layers of the photosensitive Belousov-Zhabotinsky reaction

Abstract.

While free scroll rings are non-stationary objects that either grow or contract with time, spatial confinement can have a large impact on their evolution reaching from significant lifetime extension (J.F. Totz, H. Engel, O. Steinbock, New J. Phys. 17, 093043 (2015)) up to formation of stable stationary and breathing pacemakers (A. Azhand, J.F. Totz, H. Engel, EPL 108, 10004 (2014)). Here, we explore the parameter range in which the interaction between an axis-symmetric scroll ring and a confining planar no-flux boundary can be studied experimentally in transparent gel layers supporting chemical wave propagation in the photosensitive variant of the Belousov-Zhabotinsky medium. Based on full three-dimensional simulations of the underlying modified complete Oregonator model for experimentally realistic parameters, we determine the conditions for successful initiation of scroll rings in a phase diagram spanned by the layer thickness and the applied light intensity. Furthermore, we discuss whether the illumination-induced excitability gradient due to Lambert-Beer’s law as well as a possible inclination of the filament plane with respect to the no-flux boundary can destabilize the scroll ring.

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References

  1. 1

    A.T. Winfree, Science 175, 634 (1972)

    ADS  Article  Google Scholar 

  2. 2

    N.A. Goroleva, J. Bures, J. Neurobiol. 14, 353 (1983)

    Article  Google Scholar 

  3. 3

    S. Jakubith, H.H. Rotermund, W. Engel, A. von Oertzen, G. Ertl, Phys. Rev. Lett. 65, 3013 (1990)

    ADS  Article  Google Scholar 

  4. 4

    F. Siegert, C.J. Weijer, Physica D 49, 37 (1991)

    Article  Google Scholar 

  5. 5

    J.M. Davidenko, A.M. Pertsov, R. Salomonsz, W. Baxter, J. Jalife, Nature 355, 349 (1992)

    ADS  Article  Google Scholar 

  6. 6

    T. Frisch, S. Rica, P Coullet, J.M. Gilli, Phys. Rev. Lett. 72, 1471 (1994)

    ADS  Article  Google Scholar 

  7. 7

    G. Kastbereger, E. Schmelzer, I. Kranner, PLOS One 3, e3141 (2008)

    ADS  Article  Google Scholar 

  8. 8

    M.R. Tinsley, D. Collison, K. Showalter, J. Phys. Chem. A 117, 12719 (2013)

    Article  Google Scholar 

  9. 9

    A.T. Winfree, Science 181, 934 (1973)

    ADS  Article  Google Scholar 

  10. 10

    A.B. Medvinsky, A.V. Panfilov, A.M. Pertsov, in Self-Organization: Autowaves and Structures Far From Equilibrium, edited by V.I. Krinsky (Springer, Heidelberg, 1984) p. 195

  11. 11

    J.P. Keener, Physica D 31, 269 (1988)

    ADS  MathSciNet  Article  Google Scholar 

  12. 12

    V.N. Biktashev, A.V. Holden, H. Zhang, Philos. Trans. R. Soc. A 347, 611 (1994)

    ADS  MathSciNet  Article  Google Scholar 

  13. 13

    A.V. Panfilov, A.N. Rudenko, Physica D 28, 215 (1987)

    ADS  MathSciNet  Article  Google Scholar 

  14. 14

    T. Bánsági, O. Steinbock, Phys. Rev. E 76, 045202(R) (2007)

    ADS  Article  Google Scholar 

  15. 15

    V.N. Biktashev, Int. J. Bifurcat. Chaos 8, 677 (1998)

    MathSciNet  Article  Google Scholar 

  16. 16

    S. Alonso, F. Sagues, A.S. Mikhailov, Science 299, 1722 (2003)

    ADS  Article  Google Scholar 

  17. 17

    A.T. Winfree, Sci. Am. 230, 82 (1974)

    Article  Google Scholar 

  18. 18

    B. Welsh, J. Gomatam, A. Burgess, Nature 304, 611 (1983)

    ADS  Article  Google Scholar 

  19. 19

    A.T. Winfree, W. Jahnke, J. Phys. Chem. 93, 2823 (1989)

    Article  Google Scholar 

  20. 20

    T. Bánsági, O. Steinbock, Phys. Rev. Lett. 97, 198301 (2006)

    ADS  Article  Google Scholar 

  21. 21

    L.V. Yakushevich, Stud. Biophys. 100, 195 (1984)

    Google Scholar 

  22. 22

    H. Dierckx, H. Verschelde, Phys. Rev. E 88, 062907 (2013)

    ADS  Article  Google Scholar 

  23. 23

    P.J. Nandapurkar, A.T. Winfree, Physica D 35, 277 (1989)

    ADS  MathSciNet  Article  Google Scholar 

  24. 24

    A. Azhand, J.F. Totz, H. Engel, EPL 108, 10004 (2014)

    ADS  Article  Google Scholar 

  25. 25

    J.F. Totz, H. Engel, O. Steinbock, New J. Phys. 17, 093043 (2015)

    ADS  Article  Google Scholar 

  26. 26

    H. Dierckx, H. Verschelde, Ö. Selsil, V.N. Biktashev, Phys. Rev. Lett. 109, 174102 (2012)

    ADS  Article  Google Scholar 

  27. 27

    I.V. Biktasheva, H. Dierckx, V.N. Biktashev, Phys. Rev. Lett. 114, 068302 (2015)

    ADS  Article  Google Scholar 

  28. 28

    H. Ke, Z. Zhang, O. Steinbock, Chaos 25, 064303 (2015)

    ADS  MathSciNet  Article  Google Scholar 

  29. 29

    I. Aranson, L. Kramer, A. Weber, Phys. Rev. E 47, 3231 (1993)

    ADS  Article  Google Scholar 

  30. 30

    I. Aranson, D. Kessler, I. Mitkov, Phys. Rev. E 50, R2395 (1994)

    ADS  Article  Google Scholar 

  31. 31

    H. Brandtstädter, M. Braune, I. Schebesch, H. Engel, Chem. Phys. Lett. 323, 145 (2000)

    ADS  Article  Google Scholar 

  32. 32

    H. Henry, V. Hakim, Phys. Rev. E 65, 046235 (2002)

    ADS  MathSciNet  Article  Google Scholar 

  33. 33

    I.V. Biktasheva, V.N. Biktashev, Phys. Rev. E 67, 026221 (2003)

    ADS  Article  Google Scholar 

  34. 34

    I.V. Biktasheva, D. Barkley, V.N. Biktashev, G.V. Bordyugov, A.J. Foulkes, Phys. Rev. E 79, 056702 (2009)

    ADS  MathSciNet  Article  Google Scholar 

  35. 35

    D. Kupitz, M.J.B. Hauser, J. Phys. Chem. A 117, 12711 (2013)

    Article  Google Scholar 

  36. 36

    H.-J. Krug, L. Pohlmann, L. Kuhnert, J. Phys. Chem. 94, 4862 (1990)

    Article  Google Scholar 

  37. 37

    H. Linde, H. Engel, Physica D 49, 13 (1991)

    ADS  Article  Google Scholar 

  38. 38

    T. Amemiya, S. Kádár, P. Kettunen, K. Showalter, Phys. Rev. Lett. 77, 3244 (1996)

    ADS  Article  Google Scholar 

  39. 39

    T. Amemiya, P. Kettunen, S. Kádár, T. Yamaguchi, K. Showalter, Chaos 8, 872 (1998)

    ADS  Article  Google Scholar 

  40. 40

    S. Kádár, T. Amemiya, K. Showalter, J. Phys. Chem. A 101, 8200 (1997)

    Article  Google Scholar 

  41. 41

    O.-U. Kheowan, V. Gáspár, V.S. Zykov, S.C. Müller, Phys. Chem. Chem. Phys. 3, 4747 (2001)

    Article  Google Scholar 

  42. 42

    A.P. Muñuzuri, V. P. Pérez-Villar, M. Markus, Phys. Rev. Lett. 79, 1941 (1997)

    ADS  Article  Google Scholar 

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Correspondence to Arash Azhand.

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Azhand, A., Buchholz, R., Totz, J. et al. A novel technique to initiate and investigate scroll waves in thin layers of the photosensitive Belousov-Zhabotinsky reaction. Eur. Phys. J. E 39, 61 (2016). https://doi.org/10.1140/epje/i2016-16061-2

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Keywords

  • Topical Issue: Nonequilibrium Collective Dynamics in Condensed and Biological Matter