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

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 equilibria. 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 speedup 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 multistep nucleation of two classes of hard polyhedra.

Diffusional characteristics of a Newtonian event-chain Monte Carlo in hard disk systems

“…The NEC clearly improves the efficiencies of the diffusion coefficient, nucleation rate, and melting process [4]. This efficient algorithm has been extended to anisotropic hard particles (i.e., polygons) without the need for any approximations [7]. In the ECMC and variants thereof, the systems are driven by the sequential collisions of many particles that seem to behave as a chain; the optimal performance strongly depends on chain length, physical properties, and system size.…”

Simu-D: A Simulator-Descriptor Suite for Polymer-Based Systems under Extreme Conditions

“…Usually, the development of a commercial or open code, especially when built around Monte Carlo algorithms (moves), requires a major effort and programming in order to make it user-friendly, efficient, and of general applicability. Besides, it is very common that clever MC-based or general structure-optimization algorithms have and are being developed for specific applications or general classes of physical problems in continuous or lattice cells and in systems of varied chemical detail, in the bulk and under confinement [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52].…”