Scaling properties of diffusion-limited reactions: Simulation results

Abstract

In this Brief Report we present simulation-calculation results of the transient diffusion-limited reaction A+B→0 on Sierpinski gaskets embedded in Euclidean spaces of dimensions d between 2 and 13. We find that the asymptotic temporal behavior of the density decay follows the power-law relation ρ(t)∼${\mathit{t}}^{\mathrm{-}\mathrm{\alpha }}$, with α=d̃/4, d̃ being the spectral dimension. This result for Sierpinski gaskets contrasts with a recent general finding by Sheu, Lindenberg, and Kopelman [Phys. Rev. A 42, 2279 (1990)].