CSE Distinguished Seminar | Miranda Holmes-Cerfon

Abstract

Many problems in materials science and biology involve particles interacting with strong, short-ranged bonds, that break and form over experimental timescales. Simulating such particles is a challenge, because their stiff interactions require taking steps that are often much smaller than the scales of interest. I will introduce methods aimed at accelerating these simulations, which make progress by treating the interactions as distance constraints that can vary dynamically, and then moving on the manifolds that preserve the constraints. To this end I will describe (1) A Monte Carlo method that can generate samples from a probability distribution on a stratification: a collection of manifolds of different dimensions, where lower-dimensional manifolds form the boundaries of higher-dimensional manifolds; and (2) Ongoing work aimed at accurately simulating the stochastic dynamics of particles with distance constraints that can break and form. The latter harnesses the mathematical theory of sticky diffusions as well as novel discretizations of stochastic differential equations as Markov jump processes, to handle the unusual boundary conditions associated with such “sticky” particles.