Multilevel simulation of hard sphere mixtures

Paul Rohrbach (U Cambridge)

May 03. 2022, 11:00 — 11:30

We present a self-consistent multilevel simulation method to estimate equilibrium properties of multiscale physical systems. Inspired by multilevel Markov chain Monte Carlo methods, we use an efficient but inexact coarse-grained approximation as the starting point of a hierarchical method to simulate the exact system of interest. We apply this method to highly size-asymmetric binary mixtures of hard spheres, where the scale separation between big and small particles poses a substantial challenge to standard Monte Carlo simulation methods. The big particles of this system display interesting collective behaviour, including a de-mixing transition at large size-ratios and high small-particle densities. To investigate this system, we first develop a two-level method that enables us to simulate the system up to this transition, providing the first computational evidence of its existence and locating the associated critical point. Subsequently, we discuss a generalisation of the two-level method that makes use of multiple levels of physical coarse-graining, and apply a three-level version to the binary mixture. For this example, we compare the numerical and asymptotic performance of the two- and three-level method. We show that taking an intermediate level into account can lower the variance of the method at fixed computational cost.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Computational Uncertainty Quantification: Mathematical Foundations, Methodology & Data (Thematic Programme)
Clemens Heitzinger (TU Vienna)
Fabio Nobile (EPFL Lausanne)
Robert Scheichl (U Heidelberg)
Christoph Schwab (ETH Zürich)
Sara van de Geer (ETH Zürich)
Karen Willcox (U of Texas, Austin)