Fluid mixing and optimal diffusion coefficients

Understanding the mechanisms of fluid mixing is crucial for many applications such as micro-fluids, oceanography, geophysical science, atmospheric science, and astronomy. I will introduce the field of fluid mixing and its main mechanisms: transport and diffusion. I also present my work on the diffusion operator. We will consider the spatially-dependent diffusion tensors that maximize the rate of convergence to equilibrium of solutions to the heat equation in inhomogeneous media.