Abstract

In this talk I’ll introduce a rather general approach, motivated by statistical mechanics, to describe interacting `particles’ on the PDE level – Dynamic Density Functional Theory (DDFT). DDFT is primarily used in physics and engineering, but there is a recent push to extend its range of application to biology and social science. I’ll first motivate the viewpoint that (at least) some biological systems can be modelling as interacting particles, and describe why we would generally like to do this using techniques from statistical mechanics. I’ll then explain how a relatively simple version of (inertial) DDFT can be derived from the underlying Langevin equations for interacting particle dynamics, including highlighting the key assumptions. After outlining some extensions/modifications of this simple DDFT , I’ll briefly describe a robust, efficient, and accurate numerical method for their solution. Finally, I’ll present some applications, including oscillatory flow, droplet evaporation, sedimentation of yeast in the brewing industry, and control of infection through social distancing.