Persistence of zero velocity fronts in reaction diffusion systems
| Autor: | Valentin Krinsky, Alain Pumir, Lorenz Kramer, Georg A. Gottwald, Viktor V. Barelko |
|---|---|
| Rok vydání: | 2000 |
| Předmět: |
Physics
Molecular diffusion Wave propagation Applied Mathematics Mathematical analysis Zero (complex analysis) General Physics and Astronomy Statistical and Nonlinear Physics Classical mechanics Reaction–diffusion system Range (statistics) Front velocity Effective diffusion coefficient Diffusion (business) Mathematical Physics |
| Zdroj: | Chaos: An Interdisciplinary Journal of Nonlinear Science. 10:731-737 |
| ISSN: | 1089-7682 1054-1500 |
| DOI: | 10.1063/1.1288709 |
| Popis: | Steady, nonpropagating, fronts in reaction diffusion systems usually exist only for special sets of control parameters. When varying one control parameter, the front velocity may become zero only at isolated values (where the Maxwell condition is satisfied, for potential systems). The experimental observation of fronts with a zero velocity over a finite interval of parameters, e.g., in catalytic experiments [Barelko et al., Chem. Eng. Sci., 33, 805 (1978)], therefore, seems paradoxical. We show that the velocity dependence on the control parameter may be such that velocity is very small over a finite interval, and much larger outside. This happens in a class of reaction diffusion systems with two components, with the extra assumptions that (i) the two diffusion coefficients are very different, and that (ii) the slowly diffusing variables has two stable states over a control parameter range. The ratio of the two velocity scales vanishes when the smallest diffusion coefficient goes to zero. A complete study of the effect is carried out in a model of catalytic reaction. (c) 2000 American Institute of Physics. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|