Skip to main content
SpringerLink
Log in
Book cover

Patterns and Dynamics in Reactive Media pp 187–206Cite as

Bifurcations and Global Stability in Surface Catalyzed Reactions Using the Monte Carlo Method

  • Conference paper

  • 263 Accesses

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 37))

Abstract

The vector of state variables characterizing the dynamics of heterogeneous systems is often spatially nonuniform. Ordinary differential equations (ODEs) or partial differential equations (PDEs) can describe spatial and temporal evolution of nonuniform field systems only under severe assumptions. The Monte Carlo method (MCM) is applied to model such heterogeneous systems. The conditions under which ODEs or PDEs fail are examined by studying generic model systems using the stochastic method. In the presence of nonlinearities in the governing deterministic equations, spatial inhomogeneities are observed. Multiplicities, cusp points, and periodic solutions are calculated by systematic investigation in parameter space and the global stability of solutions is presented. It is demonstrated that the presence of imperfections on surfaces introduces local nonuniformities in the adlayer (nucleation centers) and their interaction on the synchronization of the surface is discussed.

This research partly supported by NSF under grant No. CBT 9000117, a Graduate School Fellowship, the Minnesota Supercomputer Institute, and the Army High Performance Computing Research Center.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. L.F. Razon and R.A. Schmitz, Catal. Rev. — Sci. Eng., 28 (1986), p. 89.

    Article  CAS  Google Scholar 

  2. E. Wicke, P. Kummann, W. Keil, and J. Schiefler, Ber. Bunsenges. Phys. Chem., 84 (1980), p. 315.

    CAS  Google Scholar 

  3. P. Moller, K. Wetzl, M. Eiswirth, and G. Ertl, J. Chem. Phys., 85 (1986), p. 5328.

    Article  Google Scholar 

  4. M. Ehsasi, M. Matloch, O. Frank, J.H. Block, K. Christmann, F.S. Rys, and W. Hirschwald, J. Chem. Phys., 91 (1989), p. 4949.

    Article  CAS  Google Scholar 

  5. I. Kevrekidis, L.D. Schmidt, and R. Aris, Surface Sci., 137 (1984), p. 151.

    Article  CAS  Google Scholar 

  6. M.A. McKarnin, R. Aris, and L.D. Schmidt, Proc. R. Soc. Lond., A 415 (1988), p. 363.

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  8. D. G. Vlachos, L.D. Schmidt, and R. Aris, Surf. Science, (to be published).

    Google Scholar 

  9. R.M. Ziff, E. Gulari, and Y. Barshad, Phys. Rev. Letters, 56 (1986), p. 2553.

    Article  CAS  Google Scholar 

  10. Topics in Current Physics, Monte Carlo Methods in Statistical Physics, ed. K. Binder, (Springer, New York, 1986).

    Google Scholar 

  11. K. Fichthorn, E. Gulari, and R. Ziff, Chem. Eng. Sci., 44 (1989), p. 1403.

    Article  CAS  Google Scholar 

  12. K. Fichthorn, E. Gulari, and R. Ziff, Phys. Rev. Lett., 63 (1989), p. 1527.

    Article  CAS  Google Scholar 

  13. M. Kolb and Y. Boudeville, J. Chem. Phys., 92, (1990), p. 3935 and references therein.

    Article  CAS  Google Scholar 

  14. D.G. Vlachos, L.D. Schmidt, and R. Aris, J. Chem. Phys., 93 (1990), p. 8306.

    Article  CAS  Google Scholar 

  15. See. e.g., A.M. Zhabotinsky, Ber. Bunsenges. Phys. Chem., 84 (1980), p. 303.

    Google Scholar 

  16. P.C. Pawlicki and R.A. Schmitz, Chem. Eng. Prog., 83 (1987), p. 40.

    CAS  Google Scholar 

  17. R.A. Schmitz, G.A. D’Netto, L.F. Razon, and J.R. Brown, NATO ASI Ser., C (1984), 120(Chemical Instabilities, G. Nicolis and F. Baras (eds.)), p. 33.

    Google Scholar 

  18. R.J. Schwankner, M. Eiswirth, P. Moller, K. Wetzl, and G. Ertl, J., Chem. Phys., 87 (1987), p. 742.

    Article  CAS  Google Scholar 

  19. M.E. Kordesch, W. Engel, G. John Lapeyre, E. Zeitler, and A.M. Bradshaw, Appl. Phys., A 49 (1989), p. 399.

    Article  Google Scholar 

  20. G.A. Cordonier, F. Schuth, and L.D. Schmidt, J. Chem. Phys., 91 (1989), p. 5374.

    Article  CAS  Google Scholar 

  21. J.W. Cahn, Acta Metall., 9 (1961), p. 795.

    Article  CAS  Google Scholar 

  22. N. Metropolis and S. Ulam, J. Am. Stat. Ass., 44 (1949), p. 335.

    Article  CAS  Google Scholar 

  23. T.L. Hill, An Introduction to Statistical Thermodynamics, (Dover Publications, Inc., New York, 1986).

    Google Scholar 

  24. P. Grassberger and I. Procaccia, Physica, D9 (1983), p. 189.

    Google Scholar 

  25. Ruelle D., Proc. R. Soc. Lond., A 427 (1990), p. 241.

    Google Scholar 

  26. M. Eiswirth, P. Moller, K. Wetzl, R. Imbihl, and G. Ertl, J. Chem. Phys., 90 (1989), p. 510.

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN, 55455, USA

    R. Aris

Authors
  1. D. G. Vlachos
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. D. Schmidt
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. Aris
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Chemical Engineering and Material Science, University of Minnesota, Minneapolis, MN, 55455, USA

    Rutherford Aris

  2. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Donald G. Aronson

  3. Physics Department and the Center for Nonlinear Dynamics, University of Texas, Austin, TX, 78712, USA

    Harry L. Swinney

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag New York Inc.

About this paper

Cite this paper

Vlachos, D.G., Schmidt, L.D., Aris, R. (1991). Bifurcations and Global Stability in Surface Catalyzed Reactions Using the Monte Carlo Method. In: Aris, R., Aronson, D.G., Swinney, H.L. (eds) Patterns and Dynamics in Reactive Media. The IMA Volumes in Mathematics and its Applications, vol 37. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3206-3_12

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-3206-3_12

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7832-0

  • Online ISBN: 978-1-4612-3206-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation