In nanoscale thin films, the thermal fluctuations of fluid particles have macroscopic effects on the dynamics of the flow, including the development of surface waves, and the rupture of the film. The focus of this project is on using stochastic PDEs to model the effect of these fluctuations. The report covers implicit numerical schemes for solving these stochastic PDEs. These schemes are then used to model rupture of the films, comparing computational results for mean rupture time to those derived from rare event theory.

A short document outlining the basics of Fourier spectral methods and how to get a basic Navier-Stokes solver working from scratch.