# Mathematics Colloquia and Seminars

In this talk, I will discuss my joint work with Professor Steve Shkoller, Dr Rafael Granero-Belinch\'{o}n concerning new asymptotic models of the Rayleigh-Taylor (RT) instability and the mixing of two fluids. Granero-Belinch\'{o}n and Shkoller derived two new asymptotic models for the two-fluid Euler equations: the \emph{h-}model assumes that the interface $\Gamma(t)$ remains a graph and assumes smallness of the slope of $\Gamma(t)$; the \emph{z-}model has no smallness assumptions and allows for $\Gamma(t)$ to turnover and roll-up. We introduce the Gaussian noise on initial data and do an ensemble averaging procedure to formulate the mixing problem based on those two model equations. And we introduce the \emph{mixing norm} to measure the rate of mixing. We do numerical simulations mainly for \emph{z-}model for the rocket rig'' and the tilted rig'' experiments and find some interesting facts. I will conclude this talk with future work on the boundedness of the rate of mixing and other aspects of mixing.