\subsection{Angular Momentum Transport: Homogeneous Case}
We will begin by evolving the MRI in the case of a chemically homogeneous, radially stratified Taylor-Couette geometry. Building on the previous experience of proposer Oishi in using Dedalus to study the MRI \cite{2016arXiv161001616C,2016arXiv161001603C}, we will perform a suite of simulations aimed at reproducing growth rates previously calculated by \citet{Menou_2004}.   

\subsection{Angular Momentum Transport: Mean Molecular Gradient}
Next, we will produce a series of simulations of increasing background mean molecular weight. We will quantify how this additional physics stabilizes (or doesn't) the MRI under conditions relevant to RGB stars. Using our findings, we will construct a parameterization of the turbulent viscosity $\nu_T$. This will allow us to characterize the torque from MRI driven turbulence in stellar interiors.

\subsection{Chemical Mixing}
Along with our MHD equations, we will consider the diffusion of a passive scalar. We will add this after the MRI reaches saturation in order to understand the nature of mixing induced by the instability. We will produce a measurement of the Schmidt number $\mathrm{Sc} = \nu_T/D_T$, 
  where $\nu_T$ is the turbulent viscosity and $D_T$  is the turbulent diffusion of mass. This will allow to further constrain the MRI mechanism, for example by comparing with the observed surface nitrogen enrichment in main sequence massive stars \citep{Hunter_2008}. 