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Noise-induced spatiotemporal patterns in a bistable reaction-diffusion system: Photoelectron emission microscopy experiments and modeling of the oxidation reaction on
Phys. Rev. E 73, 056123 – Published 23 May, 2006
DOI: https://doi.org/10.1103/PhysRevE.73.056123
Abstract
We use photoelectron emission microscopy (PEEM) measurements to study the spatiotemporal patterns obtained for the oxidation reaction on as a function of the noise strength we superpose on the and the oxygen fractions of the constant total reactant gas flux. The investigations are focused on the bistable regime this reaction displays including its monostable vicinity. Simultaneously we analyze numerically the underlying reaction-diffusion (RD) equations in two spatial dimensions. For intrinsic and/or small strength of the external noise we find transitions from the locally stable to the globally stable branch via slow nucleation and growth of islands of the globally stable state: oxygen or , respectively. With increasing noise strength the number of islands as well as their growth rate increases. These phenomena are very well reproduced by numerical calculations of the RD model. For sufficiently large noise strength we observe bursts from rich to oxygen rich and back as well as switching between the two states. While such phenomena are also obtained from the model calculations, their experimentally observed spatial scales were not satisfactorily reproduced using the same approach as for the lower noise strengths.
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References (34)
- A. N. Zaikin and A. M. Zhabotinskii, Nature (London) 225, 535 (1970); H. G. Busse, J. Phys. Chem. 73, 750 (1969).
- R. M. Noyes, R. J. Field, and E. Körös, J. Am. Chem. Soc. 94, 1394 (1972); R. J. Field, E. Körös, and R. M. Noyes, ibid. 94, 8649 (1972), R. M. Noyes, R. J. Field, H. D. Försterling, E. Körös, and P. Ruoff, J. Phys. Chem. 93, 270 (1989); A. L. Lin, A. Hagberg, E. Meron, and H. L. Swinney, Phys. Rev. E 69, 066217 (2004).
- Y. Hayase and T. Ohta, Phys. Rev. E 62, 5998 (2004); T. Ohta, Physica D 151, 61 (2001).
- R. A. FitzHugh, Biophys. J. 1, 445 (1961).
- J. Nagumo, S. Arimoto, and S. Yoshizawa, Proc. IRE 50, 2061 (1962).
- A. H. Hagberg, Ph.D. thesis, University of Arizona, Tucson, 1994.
- A. L. Lin, A. Hagberg, A. Ardelea, M. Bertram, H. L. Swinney, and E. Meron, Phys. Rev. E 62, 3790 (2000).
- C. Elphick, A. Hagberg, B. A. Malomed, and E. Meron, Phys. Lett. A 230, 33 (1997).
- P. Grindrod, The Theory and Applications of Reaction-Diffusion Equations (Clarendon Press, Oxford, 1996).
- A. Hagberg and E. Meron, Phys. Rev. Lett. 72, 2494 (1994).
- A. Hagberg and E. Meron, Phys. Rev. Lett. 91, 224503 (2003); F. Mertens, N. Gottschalk, M. Bär, M. Eiswirth, A. Mikhailov, and R. Imbihl, Phys. Rev. E 51, R5193 (1995).
- H. H. Rotermund, W. Engel, M. Kordesch, and G. Ertl, Nature (London) 343, 355 (1990).
- G. Ertl, Adv. Catal. 37, 213 (1990).
- R. Imbihl and G. Ertl, Chem. Rev. (Washington, D.C.) 95, 697 (1995).
- R. Imbihl, Prog. Surf. Sci. 44, 185 (1993).
- M. Berdau, G. G. Yelienin, A. Karpowicz, M. Ehsasi, K. Christmann, and J. H. Block, J. Chem. Phys. 110, 23 (1999).
- M. I. Monine, A. Schaak, B. Y. Rubinstein, R. Imbihl, and L. M. Pismen, Catal. Today 70, 321 (2001).
- A. Schaak and R. Imbihl, J. Chem. Phys. 116, 9021 (2002).
- M. Eiswirth, K. Krischer, and G. Ertl, Appl. Phys. A: Solids Surf. 51, 79 (1990).
- J. Hofmann, I. Meusel, J. Hartmann, J. Libuda, and H.-J. Freund, J. Catal. 204, 378 (2001).
- V. Johanek, M. Laurin, A. W. Grant, B. Kasemo, C. R. Henry, and J. Libuda, Science 304, 1639 (2004).
- S. Wehner, F. Baumann, M. Ruckdeschel, and J. Küppers, J. Chem. Phys. 119, 6823 (2003).
- S. Wehner, F. Baumann, and J. Küppers, Chem. Phys. Lett. 370, 126 (2003).
- S. K. Ma, Modern Theory of Critical Phenomena (Addison Wesley, Reading, MA, 1976).
- M. Baer, Ch. Zülicke, M. Eiswirth, and G. Ertl, J. Chem. Phys. 96, 8595 (1992).
- Y. Hayase, S. Wehner, J. Küppers, and H. R. Brand, Phys. Rev. E 69, 021609 (2004).
- S. Wehner, Y. Hayase, H. R. Brand, and J. Küppers, J. Phys. Chem. B 108, 14452 (2004).
- Y. Hayase, S. Wehner, J. Küppers, and H. R. Brand, Physica D 205, 15 (2005).
- A. S. Mikhailov, Foundations of Synergetics, 2nd ed. (Springer, Berlin, 1994), Vol. 1.
- S. Wehner, P. Hoffmann, D. Schmeisser, H. R. Brand, and J. Küppers, Phys. Rev. Lett. 95, 038301 (2005).
- P. Hoffmann, R. P. Mikalo, and D. Schmeisser, Solid-State Electron. 44, 837 (2000).
- W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran (Cambridge University Press, Cambridge, 1999).
- Physics of Covered Solid Surfaces. Adsorbed Layers on Surfaces, edited by H. P. Bonzel, Landolt-Börnstein, New Series, Group III (Springer-Verlag, Berlin, 2001), Vol. 42, Subvol. 1, Part 1, pp. 1–58, pp. 455–501, and references therein.
- J. Küppers and A. Plagge, J. Vac. Sci. Technol. 13, 259 (1976).