Miranda Holmes-Cerfon, CIMS

We propose a new way to look at particles interacting with short-ranged potentials (such as colloids), based on taking the limit as the range of the interaction goes to zero. In this limit, the landscape is entirely defined by geometrical manifolds plus a single control parameter, while the dynamics on top of the manifolds are given by a hierarchy Fokker-Planck equations coupled by "sticky" boundary conditions. We illustrate this theory with several applications, such as computing the low-dimensional manifolds, free energies, and transition rates for n<=8 identical particles, comparing these to experiments with colloids, and enumerating rigid packings of hard spheres.