Rate equation of the A+A-> A reaction with probability of reaction and diffusion

MIGUEL LUIS HOYUELOS; HECTOR MÁRTIN,

PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS

AMER PHYSICAL SOC

Año: 1993 vol. 48 p. 3309 - 3313

1063-651X

We study the coagulation reaction A+A→A with probability p of reaction in a one-dimensional lattice. We show that dρ/dt=-pΓ1, where ρ(t) is the density of particles and Γ1(t) is the density of nearest-neighbor occupied sites. From the analysis of the crossover between the reaction-controlled-reaction and the diffusion-controlled-reaction regimes an approximate scaling ansatz for Γ1 and ρ for different values of p is proposed. Using this scaling, the collapse of Monte Carlo data improves when p decreases. From this scaling an analytical approximation of the density is found which agrees well with the numerical results of ρ(t) for different values of p.