Reaction-diffusion models from the Fokker-Planck formulation ofchemical processes

A Fokker-Planck-type model is proposed to describe the kineticsof certain chemical reactions. In particular, the competitionbetween transport and reaction processes is analysed. The studyis carried out considering various scalings of interaction,measured by the exponent of a small parameter related to themean free path. In the most significant case of competitionbetween both effects, the lowest-order density in the asymptoticexpansion obeys a reaction-diffusion equation. Such an equationwas earlier considered as the starting point in the study ofthese processes by other authors (e.g. by Schlgl). For otherinteraction scalings, the prevalence of chemical processes impliesthat the lowest-order density is determined by the (algebraic)equations of chemical equilibrium. In contrast, when transportprevails, the reaction terms affect only higher-orderdensities.