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

Bastien Chopard, Michel Droz, Jérôme Magnin, Z. Rácz

Research output: Contribution to journalArticle

27 Citations (Scopus)

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 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.

Original languageEnglish
Pages (from-to)5343-5350
Number of pages8
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume56
Issue number5 SUPPL. A
Publication statusPublished - Nov 1997

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Reaction-diffusion
reaction-diffusion equations
Mean-field Approximation
Long-time Behavior
Diverge
Reaction-diffusion Equations
Control Parameter
Diffusion Process
Mean Field
Critical Exponents
reagents
Critical point
critical point
Two Dimensions
exponents
Scaling
Fluctuations
scaling
approximation

ASJC Scopus subject areas

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

Cite this

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

In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 56, No. 5 SUPPL. A, 11.1997, p. 5343-5350.

Research output: Contribution to journalArticle

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