Modeling of many-body interactions between elastic spheres through symmetry functions

TL;DR

This paper develops a computationally efficient many-body model for elastic spheres using symmetry functions, enabling phase diagram exploration with Monte Carlo simulations.

Contribution

It introduces a systematic method to select symmetry functions for fitting complex elastic interactions in spherical particles.

Findings

The model captures the elastic energy of deformed spherical shells.

Simulations reveal fluid and hexagonal crystal phases.

The approach reduces computational cost for many-body interactions.

Abstract

Simple models for spherical particles with a soft shell have been shown to self-assemble into numerous crystal phases and even quasicrystals. However, most of these models rely on a simple pairwise interaction, which is usually a valid approximation only in the limit of small deformations, i.e. low densities. In this work, we consider a many-body yet simple model for the evaluation of the elastic energy associated with the deformation of a spherical shell. The resulting energy evaluation, however, is relatively expensive for direct use in simulations. We significantly reduce the associated numerical cost by fitting the potential using a set of symmetry functions. We propose a method for selecting a suitable set of symmetry functions that capture the most relevant features of the particle environment in a systematic manner. The fitted interaction potential is then used in Monte Carlo simulations to draw the phase diagram of the system in two dimensions. The system is found to form both a fluid and a hexagonal crystal phase.