Distribution in flowing reaction-diffusion systems.

A power-law distribution is found in the density profile of reacting systems A+B-->C+D and 2A-->2C under a flow in two and three dimensions. Different densities of reactants A and B are fixed at both ends. For the reaction A+B , the concentration of reactants asymptotically decay in space as x-1/2 and x-3/4 in two dimensions and three dimensions, respectively. For 2A , it decays as log(x)/x in two dimensions. The decay of A+B is explained considering the effect of segregation of reactants in the isotropic case. The decay for 2A is explained by the marginal behavior of two-dimensional diffusion. A logarithmic divergence of the diffusion constant with system size is found in two dimensions.