### 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 the mean-field approximation). Below two dimensions, the fluctuations play an important role and the critical exponents have no longer their mean-field values.

Original language | English |
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Pages (from-to) | 5343-5350 |

Number of pages | 8 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 56 |

Issue number | 5 SUPPL. A |

Publication status | Published - Nov 1997 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Condensed Matter Physics
- Statistical and Nonlinear Physics

### Cite this

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*56*(5 SUPPL. A), 5343-5350.

**Localization-delocalization transition of a reaction-diffusion front near a semipermeable wall.** / Chopard, Bastien; Droz, Michel; Magnin, Jérôme; Rácz, Z.

Research output: Contribution to journal › Article

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 56, no. 5 SUPPL. A, pp. 5343-5350.

}

TY - JOUR

T1 - Localization-delocalization transition of a reaction-diffusion front near a semipermeable wall

AU - Chopard, Bastien

AU - Droz, Michel

AU - Magnin, Jérôme

AU - Rácz, Z.

PY - 1997/11

Y1 - 1997/11

N2 - 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 t1/6 in the mean-field approximation). Below two dimensions, the fluctuations play an important role and the critical exponents have no longer their mean-field values.

AB - 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 t1/6 in the mean-field approximation). Below two dimensions, the fluctuations play an important role and the critical exponents have no longer their mean-field values.

UR - http://www.scopus.com/inward/record.url?scp=0000826644&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000826644&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0000826644

VL - 56

SP - 5343

EP - 5350

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 5 SUPPL. A

ER -