Newtonian Event-Chain Monte Carlo and Collision Prediction with Polyhedral Particles

TL;DR

This paper introduces a Newtonian event-chain Monte Carlo method for simulating hard convex polyhedra, achieving significant speed-ups over traditional Monte Carlo and validating it on nucleation problems.

Contribution

We develop and implement Newtonian event-chain Monte Carlo for polyhedral particles, improving computational efficiency and accuracy in simulating phase behavior.

Findings

Speed-up of 10x for spherical polyhedra

Speed-up of 2x for highly aspherical polyhedra

Successful validation on nucleation processes

Abstract

Polyhedral nanocrystals are building blocks for nanostructured materials that find applications in catalysis and plasmonics. Synthesis efforts and self-assembly experiments have been assisted by computer simulations that predict phase equilibra. Most current simulations employ Monte Carlo methods, which generate stochastic dynamics. Collective and correlated configuration updates are alternatives that promise higher computational efficiency and generate trajectories with realistic dynamics. One such alternative involves event-chain updates and has recently been proposed for spherical particles. In this contribution, we develop and apply event-chain Monte Carlo for hard convex polyhedra. Our simulation makes use of an improved computational geometry algorithm XenoSweep, which predicts sweep collision in a particularly simple way. We implement Newtonian event chains in the open source general-purpose particle simulation toolkit HOOMD-blue for serial and parallel simulation. The speed-up over state-of-the-art Monte Carlo is between a factor of 10 for nearly spherical polyhedra and a factor of 2 for highly aspherical polyhedra. Finally, we validate the Newtonian event-chain algorithm by applying it to a current research problem, the multi-step nucleation of two classes of hard polyhedra.