The Edwards-Wilkinson equation with drift and Neumann boundary conditions

The well known scaling of the Edwards-Wilkinson equation is essentially determined by dimensional analysis. Once a drift term is added, more sophisticated reasoning is required, which initially suggests that the drift term dominates over the diffusion. However, the diffusion term is dangerously irrelevant and the resulting scaling in fact non-trivial. In the present article we compare the resulting scaling of the Edwards-Wilkinson equation with drift and Neumann boundary conditions to the published case with Dirichlet boundary conditions.