Front propagation up a reaction rate gradient

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 motion of the front. 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 fluctuations in the system. For large density, the velocity is large, which allows for an approximate analytic treatment. We derive an analytic approximation for the dependence of the front velocity on bulk particle density, showing that the velocity indeed diverges in the infinite density limit. The form in which diffusion is implemented, namely nearest-neighbor hopping on a lattice, is seen to have an essential impact on the nature of the divergence.