  Recently there has been interest in developing efficient ways to model
heterogeneous surface reactions with hybrid computational models that couple a
KMC model for a surface to a finite difference model for bulk diffusion in a
continuous domain. We consider two representative problems that validate a
hybrid method and also show that this method captures the combined effects of
nonlinearity and stochasticity. We first validate a simple
deposition/dissolution model with a linear rate showing that the KMC-continuum
hybrid agrees with both a fully deterministic model and its analytical
solution. We then study a deposition/dissolution model including competitive
adsorption, which leads to a nonlinear rate, and show that, in this case, the
KMC-continuum hybrid and fully deterministic simulations do not agree. However,
we are able to identify the difference as a natural result of the stochasticity
coming from the KMC surface process. Because KMC captures inherent
fluctuations, we consider it to be more realistic than a purely deterministic
model. Therefore, we consider the KMC-continuum hybrid to be more
representative of a real system.
