That is a solution to a lattice random walk (LRW) in a confined space. It would likely find a better application to modeling epitaxial crystal growth for nanostructures. See [this research I did years ago](https://link.springer.com/chapter/10.1007/978-3-642-73632-2_2)

![](https://pbs.twimg.com/media/EZRsxVaWkAAnReW.png)

The diffusional confinement is very evident here, as the step edges provide the confinement boundary conditions. I have [a program in appendix F of my thesis](https://books.google.com/books?id=QbKN59MGbrUC&dq=pukite+thesis+diffraction&source=gbs_navlinks_s) to generate a diffusional concentration profile that can be compared to the closed-form solution. BCF stands for the Burton-Cabrera-Frank model. One issue I see is that these are absorbing boundary conditions and not reflecting boundary conditions (but then again isn't a contagion model absorbing?)

![](https://pbs.twimg.com/media/EZRxAAMXkAYWXSZ.png)

If someone wants to work on this at an applied level, I am up for it. I have other diffusion models that I was able to convert to an analytical closed-form solution, and it is a real benefit to do this because then the numerical iteration is not needed.