Abstract
Motivated by experimental results of spatiotemporal pattern formation during heterogeneous chemical reactions on composite catalyst surfaces, we present a numerical study of such phenomena on model one-dimensional reactive media. Typical composite geometries employed in the simulations are in the form of alternating catalyst stripes with different reactivity (media with spatially varying kinetic constants). By varying the geometry and nature of the composite, and using the system size as bifurcation parameter, we explore a wealth of dynamic patterns, ranging from nonuniform steady states and effective travelling pulses to spatiotemporal chaos. We use simulation as well as numerical continuation, bifurcation and stability analysis techniques in an attempt to characterize and classify the nature and symmetry of these solutions and their transitions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. Graham, I.G. Kevrekidis,K.Asakura, J. Lauterbach, K. Krischer, H.H. Rotermund and G. Ertl, Effects of Boundaries on Pattern Formation: Catalytic Oxidation of CO on Platinum, Science, 264, 80 (1994).
M. Graham, M. BÄr, I.G. Kevrekidis, K. Asakura, J. Lauterbach, H.-H. Rotermund and G. Ertl, Catalysis on Microstructured Surfaces: Pattern Formation during CO Oxidation in Complex Pt Domains, Phys. Rev. E, 52, 76 (1995).
N. Hartmann, M. BÄr, I.G. Kevrekidis, K. Krischer, and R. Imbihl, Rotating Chemical Waves in Small Circular Domains, Phys. Rev. Lett. 76, 1384 (1996).
G. Haas, M. BÄr, I.G. Kevrekidis, P.B. Rasmussen, H.H. Rotermundand G. Ertl, Observation of Front Bifurcations in Controlled Geometries: From One to Two dimensions, Phys. Rev. Lett., 75, 3560 (1995).
H.H. Rotermund, W. Engel, M.E. Kordeschand G. Ertl, Imaging of Spatiotemporal Pattern Evolution during Carbon Monoxide Oxidation on Platinum, Nature 343, 355 (1990).
K. Asakura, J. Lauterbach, H.H. Rotermund and G. Ertl, Spatiotemporal Concentration Patterns Associated with the Catalytic Oxidation of CO on Au Covered Pt(110), J. Chem. Phys., 102, 8175 (1995).
M. BÄr, I.G. Kevrekidis, H.-H. Rotermund and G. Ertl, Pattern formation in Composite Excitable Media, Phys. Rev. E, 52, R5739 (1995).
M. BÄr, A.K. Bangia, I.G. Kevrekidis, G. Haas, H.-H. Rotermund, and G. Ertl, Composite Catalyst Surfaces: Effect of Inert and Active Heterogeneities on Pattern Formation, J. Phys. Chern., 100, 19106 (1996).
M. BÄr, A.K. Bangia, I.G. Kevrekidis, G. Haas, and H.-H. Rotermund, Pattern Formation in Nonuniform Media: CO Oxidation on Microstructured and Composite Pt Surfaces, TMS Symposium on Modern Methods for Modeling Microstructure Evolution in Materials, Cleveland OH, Oct. 1995.
A.K. Bangia, M. BÄr, I.G. Kevrekidis, M.D. Graham, H.H. Rotermund and G. Ertl, Catalysis on Microcomposite Surfaces, Chem. Eng. Sci., 51, 1757 (1996).
M.C. Cross and P.C. Hohenberg, Pattern Formation outside of Equilibrium, Rev. Mod. Phys., 65, 851 (1993).
A.S. Mikhailov, Foundations of Synergetics I(Springer-Verlag, Berlin, 1990).
R. Kapral and K. Showalter (Eds.), Chemical Waves and Patterns (Kluwer, Dordrecht, Netherlands, 1995).
K. Krischer, M. Eiswirth and G. Ertl, Oscillatory CO oxidation on Pt(110): Modeling of temporal self-organization, J. Chem. Phys., 96, 9161 (1992); K. Krlscher, M. Elswlrth and G. Ertl, Periodic Perturbations of the Oscillatory CO Oxidation on Pt(110): Model Calculations, J. Chem. Phys., 97, 303 (1992).
M. Bär, N. Gottschalk, M. Eiswirth and G. Ertl, Spiral Waves in a Surface Reaction: Model Calculations, J. Chem. Phys., 1001, 1202 (1994).
O. Steinbock, P. Kettunen and K. Showalter, Anisotropy and Spiral Organizing Centers in Patterned Excitable Media, Science, 269, 1857 (1995).
A. Hagberg, E. Meron, I. Rubinstein, and B. Zaltzman, Controlling Domain Patterns Far From Equilibrium, Phys. Rev. Lett. 76, 427 (1996).
A.M. Pertsov, E.A. Ermakova and E.E. Shnol, Diffraction ofAutowaves, Physica D, 44, 178 (1990); J.A. Sepulchreand A. Babloyantz, Motions of Spiral Waves in Oscillatory Media and in the Presence of Obstacles, Phys. Rev. E, 48, 187 (1993).
J.P. Voroney, A. Lawniczak and R. Kapral, Turing Pattern Formation in Heterogeneous Media, Physica D, in press.
M. Liauw, J. Ning and D. Luss, Pattern Formation on a Nonuniformly Active Ring, J. Chem. Phys., 104, 56–57 (1996).
M. Sheintuch, Spatiotemporal Patterns due to Local Nonuniformities, J. Phys. Chem., to appear.
O. Hess and E. Schöll, Spatiotemporal Dynamics in Twin-stripe Semiconductor Lasers, Physica D 70, 165 (1994); D. Merbach, O. Hess, H. Herzel and E. Schöll, Injection-induced Bifurcations of Transverse Spatiotemporal Patterns in a Semiconductor Laser Array, Phys. Rev. E 52, 1571 (1995); O. Hess and T. Kuhn, Spatio-temporal Dynamics of Semiconductor Lasers: Theory, Modelling and Analysis, Prog. Quant. Electr., 20, 85 (1996).
A.T. Winfree, Varieties of Spiral Wave Behavior: An Experimentalist’s Approach to the Theory of Excitable Media, Chaos,1, 303 (1991).
J.R. Leis and M.A. Kramer, ODESSA - an Ordinary Differential Equation Solver with Explicit Simultaneous Sensitivity Analysis, ACM Trans. Math. Software, 14, 61–67 (1988).
E. Doedel, H.B. Keller and J.P. Kernevez, Numerical Analysis and Control of Bifurcation Problems; Part I, Bifurcation in Finite Dimensions, Int. J. Bif. and Chaos, 1, 493 (1991).
J. Elezgaray and A. Arneodo, Crisis-induced Intermittent Bursting in Reaction-Diffusion Chemical Systems, Phys. Rev. Lett. 68, 714 (1992).
J. Ringland, N. Issa, and M. Schell, From U Sequences to the Farey Sequence: a Unification of One-Parameter Scenarios, Phys. Rev. A, 41, 4223 (1990).
F.N. Albahadily, J. Ringland and M. Schell, Mixed Mode Oscillations in an Electrochemical System. I and II, J. Chem. Phys., 90, 813 (1989).
M. Golubitsky and D.G. Schaeffer, Singularities and Groups in Bifurcation Theory, Vol. I, Springer-Verlag, 1985.
J.D. Crawford and E. Knobloch, Symmetry and Symmetry-breaking Bifurcations in Fluid Dynamics, Annu. Rev. Fluid Mech., 23, 341 (1991).
P. Chossat and M. Golubitsky, Symmetry-increasing Bifurcations of Chaotic Attractors, Physica D, 32 423 (1988).
E. Barany, M. Dellnitz and M. Golubitsky, Detecting the Symmetry of Attractors, Research Report UH/MD 143, Department of Mathematics, University of Houston (1992).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media New York
About this chapter
Cite this chapter
Shvartsman, S., Bangia, A.K., Bär, M., Kevrekidis, I.G. (1998). On Spatiotemporal Patterns in Composite Reactive Media. In: Golden, K.M., Grimmett, G.R., James, R.D., Milton, G.W., Sen, P.N. (eds) Mathematics of Multiscale Materials. The IMA Volumes in Mathematics and its Applications, vol 99. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1728-2_15
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1728-2_15
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7256-4
Online ISBN: 978-1-4612-1728-2
eBook Packages: Springer Book Archive