DYNAMIC MULTISCALING OF THE REACTION-DIFFUSION FRONT FOR MA+NB-]O

We consider the reaction Bone that grows between separated regions of diffusing species A and B that react according to mA + nB --> 0, within the framework bf the mean-field-like reaction-diffusion equations. For distances from the center of the reaction zone much smaller than the diffusion length X(D) = root Dt, the particle density profiles are described by the scaling forms predicted by a quasistatic approximation, whereas they have a diffusive cutoff at a distance of order X(D). This cutoff, and the power-law decay of the quasistatic profiles, give rise to multiscaling behavior, with anomalous values for the exponents describing the moments of the density and reaction profiles. Numerical solutions of the reaction-diffusion equations are in good quantitative agreement with the predictions of this theory.