Diffusion-controlled reaction, A+B→C, with initially separated reactants

We review recent developments in the study of diffusion-reaction systems of the type A+B→C in which reactants are initially separated. We consider two initial boundary conditions: (i) the A and B particles are initially placed uniformly in Euclidean space at x>O and x<0 respectively, and (ii) the A particles are diffusing and inserted at a given site and the B particles are static and distributed uniformly in space. We present analytical and numerical results for both systems. We consider d = 1, 2, 3 dimensional systems as well as fractal lattices.