Diffusion-limited coalescence with finite reaction rates in one dimension

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Abstract
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.
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