Numerically simulating sticky particles

Speaker: Miranda Holmes-Cerfon (New York University)
Occasion: Mathematical and Computational Materials Science
Date: February 18, 2021

Abstract: 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. One challenge in simulating such particles is that the range over which they interact attractively, is often much shorter than their diameters, so the SDEs describing the particles’ dynamics are stiff, requiring timesteps much smaller than the timescales of interest. I will introduce methods aimed at accelerating these simulations, which simulate instead 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 introduce methods that simulate such sticky diffusion processes directly, and discuss some ongoing challenges to extending these methods to high dimensions.