1994/07/08 by Dexin Zhong, Daniel ben‐Avraham, Daniel ben-Avraham · 23 citations
Chemistry · Mathematics · Physics and Astronomy · #Chemistry #Coalescence (physics) #Combinatorics #Computer science #Diffusion #Diffusion process #Dimension (graph theory) #Finite difference #Finite set #Limit (mathematics) #Markov Chains and Monte Carlo Methods #Mathematical analysis #Mathematics #Physics #Reaction rate #Reaction–diffusion system #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Thermodynamics #cond-mat
paper · pdf · doi:10.1088/0305-4470/28/1/010
published in Journal of Physics A Mathematical and General 28(1), 33-44 (Institute of Physics) · 13 pages (and 4 figures), plain TeX, SISSA-94-02
arxiv created 1994/07/08 · openalex publication_date 1995/01/07 · arxiv updated 2016/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We study the diffusion-limited process A+A to A in one dimension, with finite reaction rates. We develop an approximation scheme based on the method of inter-particle distribution functions (IPDF), which was used formerly for the exact solution of the same process with an infinite reaction rate. The approximation becomes exact in the very early time regime (or the reaction-controlled limit) and in the long-time (diffusion-controlled) asymptotic limit. For the intermediate time regime, we obtain a simple interpolative behaviour between these two limits. We also study the coalescence process (with finite reaction rates) with the back reaction A to A+A, and in the presence of particle input. In each of these cases the system reaches a non-trivial steady state with a finite concentration of particles. Theoretical predictions for the concentration time dependence and for the IPDF are compared with computer simulations.