Smoothening out Disturbances: Why Diffusion Rocks

The diffusion equation plays an integral role modelling reality. Whenever there is a system containing a physical quantity that wants to smooth out and become homogeneously distributed then the diffusion term will model that happening. A temperature fluctuation in the atmosphere, a drop of dye in a pool of water, a magnetic field in a resistive fluid. All of these phenomena evolve according to the diffusion equation. Before going into the specifics of this equation, let’s take a quick look at it. If Q is a physical quantity (scalar, vector, or tensor) then the diffusion equation reads: