Stochastic and deterministic analysis of reactions: The fractal case

The transient diffusion-limited A+B→0, ${\mathit{A}}_0$=${\mathit{B}}_0$ annihilation on fractals is studied both via deterministic reaction-diffusion equations and via simulations of the stochastic many-particle problem. We show that the two approaches are not equivalent, yet the deterministic expressions capture the correct asymptotic behavior. For Sierpinski gaskets our analysis focuses on the overall decay law: ${\mathit{t}}^{\mathrm{-}\mathrm{\alpha }}$ with α=min(d̃/4,1) and on the superimposed hierarchical oscillations.