Joint density closure schemes for a diffusion-limited reaction

Abstract We study the macroscopic particle concentration in the diffusion-limited reactions A + A→A, A + A⇌A, A + A→A with particle input, and A + A⇌A with particle input, in one spatial dimension using different schemes for truncating the hierarchy of kinetic equations for the joint density functions. Our goal is to evaluate the quality of some nonsystematic approximations by comparing with the exact solution. The approximate results for the asymptotic behavior of particle concentrations, and the particle concentrations of the equilibrium and nonequilibrium steady states are in good agreement with exact results. For the irreversible reactions, the results of Kirkwood's superposition approximation are better than those of a simpler approximation. The superposition approximation yields better results far from equilibrium, while the simpler closure gives excellent predictions near equilibrium.

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