SFU Applied & Computational Math Seminar Series: Miranda Holmes-Cerfon

Particles with diameters of nanometres to micrometres form the building blocks of many of the materials around us, and can be designed in a multitude of ways to form new ones. Such particles commonly live in fluids, where they jiggle about randomly because of thermal fluctuations in the fluid, and interact with each other via numerous mechanisms. One challenge in simulating such particles is that the range over which they interact attractively is often much shorter than their diameters, so the equations describing the particles’ dynamics are stiff, requiring timesteps much smaller than the timescales of interest. I will introduce methods to accelerate these simulations, which instead solve the limiting equations as the range of the attractive interaction goes to zero. In this limit a system of particles is described by a diffusion process on a collection of manifolds of different dimensions, connected by “sticky” boundary conditions. I will describe our progress in simulating low-dimensional sticky diffusion processes, explain how these algorithms give us insight into sticky diffusions’ unusual mathematical properties, and then discuss some ongoing challenges such as extending these methods to high dimensions, incorporating friction and hydrodynamic interactions, and capturing the anomalous diffusion that is sometimes observed experimentally.