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Pattern formation in the Schlögl model of nonlinear kinetics

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  • Dung, Mei Hsu
  • Kozak, John J.

Abstract

To study the effect of a local, spatial inhomogeneity on the progress of a chemical reaction which may exhibit a nonequilibrium phase transition, we have studied a (slightly) generalized version of a model proposed originally by Schlögl. Focusing on that regime of parameter space where the reaction sequence A + 2X[lrarr2]3X and B + X[lrarr2]C allows a first-order transition, we consider the consequences of introducing a spatially-varying diffusion coefficient characterized by a correlation length which calibrates the region over which the spatial inhomogeneity persists. We find that if the inhomogeneity is localized, only small quantitative differences are found between the exact solution reported earlier by Schlögl and the solutions generated here. However, as the correlation length becomes larger, abruptly at a certain critical value, a qualitative change in the nature of the solutions is found, with apparent oscillations produced in the concentration variable of the problem. We interpret this behavior as indicating the onset of pattern formation, and suggest that this behavior may be of importance in those radiation-induced phenomena where high-energy intermediates are produced.

Suggested Citation

  • Dung, Mei Hsu & Kozak, John J., 1981. "Pattern formation in the Schlögl model of nonlinear kinetics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 108(1), pages 63-76.
    • Handle: RePEc:eee:phsmap:v:108:y:1981:i:1:p:63-76
    DOI: 10.1016/0378-4371(81)90165-5
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    References listed on IDEAS

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    1. Streissler Erich, 1977. "Zu W. Rall, „Stärkere Inflation bei stetigerem Wachstum?," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 191(5-6), pages 557-558, February.
    2. Magee, Rp, 1975. "Cost-Volume-Profit Analysis, Uncertainty And Capital-Market Equilibrium," Journal of Accounting Research, Wiley Blackwell, vol. 13(2), pages 257-266.
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