Kinetics of particles with short-range interactions
Particles in soft-matter systems (such as colloids) tend to have attractive interactions that are very short-ranged compared to their diameters, so traditional theories, that assume the energy landscape is smooth enough, will struggle to capture their dynamics. We propose a new framework to look at such particles, based on taking the limit as the range of the interaction goes to zero. In this limit, the energy landscape is a set of geometrical manifolds, while the dynamics on top of the manifolds are a diffusion process with “sticky” boundary conditions. This framework leads to new methods to compute dynamical quantities, such as transition rates between clusters of colloids, which give predictions agree quantitatively with our experiments. We propose a numerical method to simulate a sticky diffusion, which preliminary investigations suggest could be orders of magnitude faster than typical methods to simulate mesoscale particles.
Miranda Holmes-Cerfon received her PhD from the Courant Institute of Mathematical Sciences in 2010. She spent two years as an Applied Math Instructor at Harvard University, before returning to Courant in 2012 as a Courant Instructor and then Assistant professor. She is the recipient of several awards including the Department of Energy Early Career Award and the Alfred P. Sloan Research Fellowship in Mathematics.