title: Single species diffusion-influenced reaction A+A-->alphaA: validity of the smoluchowski approach
abstract: We investigate the single species diffusion-influenced reaction, A+A-->alphaA with a finite reactivity in all dimensions. The reaction model includes a pure coagulation (alpha=1) or a pure annihilation (alpha=0) model. We apply the hierarchical Smoluchowski approach to study the dimensional aspects of the fluctuation, reactivity, particle size, and alpha(0</=alpha</=1). The theoretical results are compared with those of the Monte Carlo simulations in one, two, and three regular dimensions. The simulation results reveal that the classical Smoluchowski approach is exact in the short time limit in all dimensions and in the long time limit in three dimensions. The hierarchical Smoluchowski approach is found to be numerically exact at all times in two and three dimensions. A numerical method to obtain the exact result of the annihilation for a finite reactivity in one dimension is presented. We also propose a quite accurate analytic solution for an arbitrary alpha for the infinite reactivity in one dimension.
authors.affiliation: Department of Chemistry and Center for Molecular Catalysis, Seoul National University, Seoul 151-742, Korea.
authors.initials: H
authors.lastname: Kim
authors.initials: KJ
authors.lastname: Shin