Two-particle representation of front propagation in diffusion-reaction systems

A two-particle model is formulated which approximates the motion of the forwardmost particle in a lattice gas, which has recently been analyzed and numerically simulated. The lattice gas, which evolves on a linear chain, consists of particles which jump to each vacant nearest neighbor site with rate γ/2 and also create new particles at these sites with rate 1/2. This model is known to exhibit statistically steady propagation of the forwardmost particle, with mean propagation velocity converging to (2γ)/sup 1/2/ for large γ. Here, a two-particle representation is used to estimate the propagation velocity for finite γ. The results are in good agreement with numerical simulations of the lattice gas. Implications concerning front propagation in diffusion-reaction systems are discussed