Persistence of zero velocity fronts in reaction diffusion systems

Chaos
Lorenz KramerViktor V. Barelko

Abstract

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.

References

Aug 1, 1993·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·A Hagberg, E Meron
Apr 3, 1989·Physical Review Letters·P CoulletJ Lega

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Citations

Nov 6, 2009·Journal of Mathematical Biology·Sanjeeva Balasuriya, Georg A Gottwald
Oct 2, 2007·Chaos·Vladimir K Vanag, Irving R Epstein
Jun 5, 2003·Chaos·Jacques-Alexandre Sepulchre, Valentin I. Krinsky
Jan 24, 2008·Biophysical Journal·Yoichiro MoriLeah Edelstein-Keshet
Nov 5, 2014·The Journal of Chemical Physics·Jaime CisternasStefan Wehner
Nov 13, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·M A Miranda, J Burguete
Feb 1, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·R D BenguriaV Haikala

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