Molecular-dynamics studies of annihilation reactions

The validity of the reaction-diffusion formulation of annihilation kinetics, with randomly distributed initial conditions, is investigated by molecular-dynamics simulations of dense hard-disk fluids. For the reaction $A+B\rightarrow C+C$ quantitative agreement is found. Yet, this proves not to be the case for the reaction $A+A\rightarrow C+C$, where major discrepancies are observed. For this latter reaction, more sophisticated theories predict a logarithmic decay law of the form $\ln(t)/t$. The microscopic simulations essentially confirm this prediction