  We expand on a previous study of fronts in finite particle number
reaction-diffusion systems in the presence of a reaction rate gradient in the
direction of the front motion. We study the system via reaction-diffusion
equations, using the expedient of a cutoff in the reaction rate below some
critical density to capture the essential role of fl uctuations in the system.
For large density, the velocity is large, which allows for an approximate
analytic treatment. We derive an analytic approximation for the front velocity
depe ndence on bulk particle density, showing that the velocity indeed diverge
s in the infinite density limit. The form in which diffusion is impleme nted,
namely nearest-neighbor hopping on a lattice, is seen to have an essential
impact on the nature of the divergence.
