I am trying to find resources on the Gillespie stochastic simulation algorithm for my system which happens on a surface. The original algorithm was developed for a reactor of volume $V$, but my system is a flat surface of area $A$. My questions are as follows:
- Are there any publications that do stochastic simulation on surfaces?
- Is extending the SSA from a volume to a surface trivial? For example, consider the following second order reaction: $$R_1+R_2 \rightarrow P_1$$ and suppose that the rate constant is $k$. The stochastic and deterministic constants ($k^{stoc}$ and $k^{det}$) for a reactor of volume $V$ are related as follows $$k^{det}=\frac{N_aV}{2}k^{stoch}$$ where $N_a$ is Avogadro's number. Can I simply replace $V$ with the surface area $A$ to get $$k^{det}_{area}=\frac{N_aA}{2}k^{stoch}_{area}$$
Please note that I am not looking to discretize space for diffusion. Just like the SSA does not discretize volumes, I should like to summarize the surface by one number (i.e, the surface area).