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Localization-delocalization transition of a reaction-diffusion front near a semipermeable wall

B. Chopard·M. Droz·J. Magnin·Z. Racz
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Abstract

The A+B --> C reaction-diffusion process is studied in a system where the reagents are separated by a semipermeable wall. We use reaction-diffusion equations to describe the process and to derive a scaling description for the long-time behavior of the reaction front. Furthermore, we show that a critical localization-delocalization transition takes place as a control parameter which depends on the initial densities and on the diffusion constants is varied. The transition is between a reaction front of finite width that is localized at the wall and a front which is detached and moves away from the wall. At the critical point, the reaction front remains at the wall but its width diverges with time [as t^(1/6) in mean-field approximation].

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B. Chopard, M. Droz, J. Magnin, Z. Racz. 1997-06-30. Localization-delocalization transition of a reaction-diffusion front near a semipermeable wall. https://doi.org/10.1103/physreve.56.5343

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