Emerging Coherence of Oscillating Chemical Reactions on Arrays: Experiments and Simulations

Industrial and Engineering Chemistry Research

Volumn 43, Issue 2, 2004, Pages 315-326

  Zhai, Yumei ^a   Kiss, István Z ^a   Hudson, John L ^a  

^a University of Virginia   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARRAYS; COMPUTER SIMULATION; DISSOLUTION; ELECTRODES; NICKEL; NUMERICAL METHODS; OSCILLATORS (ELECTRONIC); SULFURIC ACID;

ELECTROCHEMICAL OSCILLATORS;

ELECTROCHEMISTRY;

NICKEL; SULFURIC ACID;

CHEMICAL ENGINEERING;

ARTICLE; CHEMICAL REACTION; DISSOLUTION; ELECTROCHEMISTRY; ELECTRODE; OSCILLATION; OSCILLATOR; PHASE TRANSITION; SIMULATION;

EID: 0347128031     PISSN: 08885885     EISSN: None     Source Type: Journal    
DOI: 10.1021/ie030164z     Document Type: Article

References (46)

1. Kuramoto, Y. Chemical oscillations, waves and turbulence; Springer: Berlin, 1984.
2. Mertens, F.; Imbihl, R.; Mikhailov, A. Breakdown of global coupling in oscillatory chemical-reactions. J. Chem. Phys. 1993, 99, 8668.
3. Slinko, M. M.; Ukharskii, A. A.; Jaeger, N. I. Global and non-local coupling in oscillating heterogeneous catalytic reactions: The oxidation of CO on zeolite supported palladium. Phys. Chem. Chem. Phys. 2001, 3, 1015.
4. Middya, U.; Luss, D. Impact of global interactions on patterns in a simple system. J. Chem. Phys. 1994, 100, 6386.
5. Lobban, L.; Luss, D. Spatial Temperature Oscillations During Hydrogen Oxidation on a Nickel Foil. J. Phys. Chem. 1989, 93, 6530.
6. Krischer, K. In Modern Aspects of Electrochemistry; Conway, B. E., Bockris, O. M., White, R. E., Eds.; Kluwer Academic/Plenum Press: New York, 1999; Vol. 32, p 1.
7. Mazouz, N.; Flätgen, G.; Krischer, K. Tuning the range of spatial coupling in electrochemical systems: From local via nonlocal to global coupling. Phys. Rev. E 1997, 55, 2260.
8. Mazouz, N.; Flätgen, G.; Krischer, K.; Kevrekidis, I. G. The impact of the operation mode on pattern formation in electrode reactions - From potentiostatic to galvanostatic control. J. Electrochem. Soc. 1998, 145, 2404.
9. Otterstedt, R. D.; Jaeger, N. I.; Plath, P. J.; Hudson, J. L. Global coupling effects on spatiotemporal patterns on a ring electrode. Chem. Eng. Sci. 1999, 54, 1221.
10. Bär, M.; Hildebrand, M.; Eiswirth, M.; Falcke, M.; Engel, H.; Neufeld, M. Chemical Turbulence and Standing Waves in a Surface Reaction Model: The Influence of Global Coupling and Wave Instabilities. Chaos 1994, 4, 499.
11. Middya, U.; Luss, D.; Sheintuch, M. Spatiotemporal Motions Due to Global Interaction. J. Chem. Phys. 1994, 100, 3568.
12. Kiss, I. Z.; Wang, W.; Hudson, J. L. Experiments on arrays of globally coupled periodic electrochemical oscillators. J. Phys. Chem. B 1999, 103, 11433.
13. Wang, W.; Kiss, I. Z.; Hudson, J. L. Experiments on arrays of globally coupled chaotic electrochemical oscillators: synchronization and clustering. Chaos 2000, 10, 248.
14. Liauw, M. A.; Plath, P. J.; Jaeger, N. I. Complex oscillations and global coupling during the catalytic oxidation of CO. J. Chem. Phys. 1996, 104, 6375.
15. Liauw, M. A.; Ning, J.; Luss, D. Pattern formation on a nonuniformly active ring. J. Chem. Phys. 1996, 104, 5657.
16. Winfree, A. T. The geometry of biological time; Springer-Verlag: New York, 1980.
17. Kiss, I. Z.; Zhai, Y.; Hudson, J. L. Collective dynamics of a weakly coupled electrochemical reaction on an array. Ind. Eng. Chem. Res. 2002, 41, 6363.
18. Kiss, I. Z.; Zhai, Y.; Hudson, J. L. Collective dynamics of chaotic chemical oscillators and the law of large numbers. Phys. Rev. Lett. 2002, 88, 238301.
19. Slinko, M. M.; Ukharskii, A. A.; Peskov, N. V.; Jaeger, N. I. Chaos and synchronisation in heterogeneous catalytic systems: CO oxidation over Pd zeolite catalysts. Catal. Today 2001, 70, 341.
20. Winfree, A. T. Biological Rhythms and the Behavior of Populations of Coupled Oscillators. J. Theor. Biol. 1967, 16, 15.
21. Kuramoto, Y. Cooperative Dynamics of Oscillator Community. Prog. Theor. Phys. Suppl. 1984, 79, 223.
22. Kuramoto, Y. In International Symposium on Mathematical Problems in Theoretical Physics, Lecture Notes in Physics; Araki, H., Ed.; Springer: New York, 1975; Vol. 39, p 420.
23. Daido, H. Intrinsic Fluctuation and Its Critical Scaling in a Class of Populations of Oscillators With Distributed Frequencies. Prog. Theor. Phys. 1989, 81, 727.
24. Daido, H. Onset of cooperative entrainment in limit-cycle oscillators with uniform all-to-all interactions: Bifurcation of the order function. Physica D 1996, 91, 24.
25. Mirollo, R. E.; Strogatz, S. H. Synchronization of Pulse-Coupled Biological Oscillators. SIAM J. Appl. Math. 1990, 50, 1645.
26. Strogatz, S. H. From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators. Physica D 2000, 143, 1.
27. York, R. A.; Compton, R. C. Quasi-Optical Power Combining Using Mutually Synchronized Oscillator Arrays. IEEE Trans. Microwave Theory Tech. 1991, 39, 1000.
28. Oliva, R. A.; Strogatz, S. H. Dynamics of a large array of globally coupled lasers with distributed frequencies. Int. J. Bifurcation Chaos 2001, 11, 2359.
29. Wiesenfeld, K.; Colet, P.; Strogatz, S. H. Synchronization transitions in a disordered Josephson series array. Phys. Rev. Lett. 1996, 76, 404.
30. Walker, T. J. Acoustic Synchrony: Two Mechanisms in the Snowy Tree Cricket. Science 1969, 166, 891.
31. Buck, J. Synchronous Rhythmic Flashing of Fireflies. II. Q. Rev. Biol. 1988, 63, 265.
32. Néda, Z.; Ravasz, E.; Brechet, Y.; Vicsek, T.; Barabási, A. L. The sound of many hands clapping-Tumultuous applause can transform itself into waves of synchronized clapping. Nature 2000, 403, 849.
33. Ghosh, A. K.; Chance, B.; Pye, E. K. Metabolic Coupling and Synchronization of NADH Oscillations in Yeast Cell Populations. Arch. Biochem. Biophys. 1971, 145, 319.
34. Danø, S.; Sørensen, P. G.; Hynne, F. Sustained oscillations in living cells. Nature 1999, 402, 320.
35. Danø, S.; Hynne, F.; De Monte, S.; d'Ovidio, F.; Sørensen, P. G.; Westerhoff, H. Synchronization of glycolytic oscillations in a yeast cell population. Faraday Discuss. 2001, 120, 261.
36. Wiener, N. Nonlinear Problems in Random Theory; MIT Press: Cambridge, MA, 1958.
37. Michaels, D. C.; Matyas, E. P.; Jalife, J. Mechanisms of Sinoatrial Pacemaker Synchronization: A New Hypothesis. Circ. Res. 1987, 61, 704.
38. Winfree, A. T. On emerging coherence. Science 2002, 298, 2336.
39. Kiss, I. Z.; Zhai, Y. M.; Hudson, J. L. Emerging coherence in a population of chemical oscillators. Science 2002, 296, 1676.
40. Lev, O.; Wolffberg, A.; Sheintuch, M.; Pismen, L. M. Bifurcations to Periodic and Chaotic Motions in Anodic Nickel Dissolution. Chem. Eng. Sci. 1988, 43, 1339.
41. Pikovsky, A. S.; Rosenblum, M. G.; Osipov, G. V.; Kurths, J. Phase synchronization of chaotic oscillators by external driving. Physica D 1997, 104, 219.
42. Gábor, D. J. Inst. Electr. Eng., Part 3 1946, 93, 429.
43. Haim, D.; Lev, O.; Pismen, L. M.; Sheintuch, M. Modeling Periodic and Chaotic Dynamics in Anodic Nickel Dissolution. J. Phys. Chem. 1992, 96, 2676.
44. Wang, W. Synchronization and Clustering of Arrays of Electrochemical Oscillators. Ph.D. Thesis, University of Virginia, Charlottesville, Virginia, 2001.
45. Newman, J. Electrochemical Systems; Prentice Hall: Engelwood Cliffs, NJ, 1973.
46. Sakaguchi, H.; Kuramoto, Y. A soluble active rotator model showing phase transition via mutual entrainment. Prog. Theor. Phys. 1986, 76, 576.