The European Physical Journal D

, Volume 62, Issue 1, pp 91–102 | Cite as

Carbon monoxide oxidation on Iridium (111) surfaces driven by strongly colored noise*

Article

Abstract.

The influence of external colored noise on the carbon monoxide oxidation on Iridium(111) surfaces is examined. The noise is introduced in the reaction by randomly varying the composition of the gas flow that keeps the reaction going on. Colored noise is studied using two models: a simple discrete time Markov chain, and the Ornstein-Uhlenbeck process. We compute the probability distribution and transition times, for medium and large correlation time of the noise. These results extend previous analyses that have been limited to small correlation times and the presence of a slow manifold, both assumptions that are not supported by experiments. As we will see, the correlation and intensity of the noise leads to qualitative changes in the stochastic behavior of the system.

Keywords

Correlation Time Iridium Exit Time Colored Noise Slow Manifold 

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References

  1. 1.
    K. Krischer, M. Eiswirth, G. Ertl, J. Chem. Phys. 96, 9161 (1992)CrossRefADSGoogle Scholar
  2. 2.
    K. Krischer, M. Eiswirth, G. Ertl, J. Chem. Phys. 97, 307 (1992)CrossRefADSGoogle Scholar
  3. 3.
    S. Jakubith, H. Rotermund, W. Engel, A. von Oertzen, G. Ertl, Phys. Rev. Lett. 65, 3013 (1990)CrossRefADSGoogle Scholar
  4. 4.
    J. Cisternas, P. Holmes, I. Kevrekidis, X. Li, J. Chem. Phys. 118, 3312 (2003)CrossRefADSGoogle Scholar
  5. 5.
    S. Wehner, F. Baumann, J. Küppers, Chem. Phys. Lett. 370, 126 (2003)CrossRefADSGoogle Scholar
  6. 6.
    Y. Hayase, S. Wehner, J. Küppers, H. Brand, Phys. Rev. E 69, 021609 (2004)CrossRefADSGoogle Scholar
  7. 7.
    S. Wehner, P. Hoffmann, D. Schmeisser, H. Brand, J. Küppers, Phys. Rev. Lett. 95, 038301 (2005)CrossRefADSGoogle Scholar
  8. 8.
    M. Pineda, R. Imbihl, L. Schimansky-Geier, C. Zülicke, J. Chem. Phys. 124, 044701 (2006)CrossRefADSGoogle Scholar
  9. 9.
    M. Pineda, L. Schimansky-Geier, R. Imbihl, Phys. Rev. E 75, 061107 (2007)CrossRefADSGoogle Scholar
  10. 10.
    P. Bodega, S. Alonso, H. Rotermund, J. Chem. Phys. 130, 1 (2009)CrossRefGoogle Scholar
  11. 11.
    M. Pineda, R. Toral, J. Chem. Phys. 130, 124704 (2009)CrossRefADSGoogle Scholar
  12. 12.
    S. Wehner, S. Karpitschka, Y. Burkov, D. Schmeisser, J. Küppers, H. Brand, Physica D 239, 746 (2010)CrossRefMATHADSGoogle Scholar
  13. 13.
    J. Cisternas, D. Escaff, O. Descalzi, S. Wehner, Int. J. Bif. Chaos 19, 3461 (2009)CrossRefMATHGoogle Scholar
  14. 14.
    F. De la Rubia, J. García-Sanz, M. Velarde, Surf. Sci. 143, 1 (1984)CrossRefADSGoogle Scholar
  15. 15.
    J. Cisternas, D. Escaff, O. Descalzi, S. Wehner, Int. J. Bif. Chaos 20, 243 (2010)CrossRefMATHGoogle Scholar
  16. 16.
    R. Stratonovich, Theory of Random Noise (Gordon and Breach, New York, 1963)Google Scholar
  17. 17.
    W. Horsthemke, R. Lefever, Noise Induced Transitions: Theory and Applications in Physics, Chemistry, and Biology (Springer, Berlin, 1984)Google Scholar
  18. 18.
    P. Jung, P. Hänggi, Phys. Rev. A 35, 4464 (1987)CrossRefADSGoogle Scholar
  19. 19.
    H. Malchow, L. Shimansky-Geier, Noise and Diffusion in Bistable Nonequilibrium Systems (B.G. Teubner Verlagsgesellschaft, Berlin, 1985)Google Scholar
  20. 20.
    P. Hänggi, P. Jung, in Advances in Chemical Systems, edited by I. Prigogine, S. Rice (John Wiley & Sons, New York, 1995), Vol. LXXXIXGoogle Scholar
  21. 21.
    T. Engel, G. Ertl, J. Chem. Phys. 69, 1267 (1978)CrossRefADSGoogle Scholar
  22. 22.
    T. Engel, G. Ertl, Adv. Catal. 28, 1 (1979)CrossRefGoogle Scholar
  23. 23.
    S. Wehner, Int. J. Bif. Chaos 19, 2637 (2009)CrossRefGoogle Scholar
  24. 24.
    T. Leiber, F. Marchesoni, H. Risken, Phys. Rev. Lett. 59, 1381 (1987)CrossRefADSMathSciNetGoogle Scholar
  25. 25.
    H. Risken, The Fokker-Planck Equation: Methods of Solutions and Applications (Springer, Berlin, 1989)Google Scholar
  26. 26.
    K. Lindenberg, B. West, J. Masoliver, First passage time problems for non-Markovian processes, in Noise in nonlinear dynamical systems, edited by F. Moss, P. McClintock (Cambridge University Press, Cambridge, 1989), Vol. 1, Chap. 4Google Scholar
  27. 27.
    C.W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences (Springer, Berlin, 1983)Google Scholar
  28. 28.
    L. Ferm, P. Lötstedt, P. Sjöberg, Bit Numerical Mathematics 46, 61 (2006)CrossRefGoogle Scholar
  29. 29.
    A. Hernández-Machado, M.S. Miguel, J. Sancho, Phys. Rev. A 29, 3388 (1984)CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Complex Systems Group, College of Engineering and Applied Sciences, Universidad de los AndesSantiagoChile
  2. 2.Department of Mathematical EngineeringUniversidad de ChileSantiagoChile
  3. 3.Institut für Integrierte Naturwissenschaften-Physik, Universität Koblenz-LandauKoblenzGermany

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