LOCALIZATION-DELOCALIZATION TRANSITION OF A REACTION-DIFFUSION FRONT NEAR A SEMIPERMEABLE WALL

The A+B-->C reaction-diffusion process is studied in a system where th e reagents are separated by a semipermeable wall. We use reaction-diff usion equations to describe the process, and to derive a scaling descr iption for the long-time behavior of the reaction front. Furthermore, we show that a critical localization-delocalization transition takes p lace as a control parameter which depends on the initial densities and on the diffusion constants is varied. The transition is between a rea ction front pf 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 ti me (as t(1/6) in the mean-field approximation). Below two dimensions, the fluctuations play an important role and the critical exponents hav e no longer their mean-field values.