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

  • D. G. Vlachos
  • L. D. Schmidt
  • R. Aris
Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 37)


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.


Monte Carlo Method Heterogeneous System Attractive Interaction Nucleation Center Spatial Inhomogeneity 
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Copyright information

© Springer-Verlag New York Inc. 1991

Authors and Affiliations

  • D. G. Vlachos
  • L. D. Schmidt
  • R. Aris
    • 1
  1. 1.Department of Chemical Engineering and Materials ScienceUniversity of MinnesotaMinneapolisUSA

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