A 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 /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 (2)^1/2 for large . Here, a two-particle representation is used to estimate the propagation velocity for finite . The results are in good agreement with numerical simulations of the lattice gas. Implications concerning front propagation in diffusion-reaction systems are discussed.