Approximate Modeling of Spherical Membrane

TL;DR

This paper introduces a novel modeling approach for spherical membranes that significantly reduces computational costs, applicable to various membrane types and interaction methods, enabling efficient simulations of spherical systems.

Contribution

The paper presents a revised periodic boundary condition method tailored for spherical symmetry, applicable to both solid and liquid membranes with small curvature, improving simulation efficiency.

Findings

Method accurately calculates bending and Gaussian curvature moduli of graphene.

Approach reduces computational costs by orders of magnitude.

Applicable to diverse interactions and simulation techniques.

Abstract

Spherical symmetry is ubiquitous in nature. It's therefore unfortunate that spherical system simulations are so hard, and require complete spheres with millions of interacting particles. Here we introduce an approach to model spherical systems, using revised periodic boundary conditions adapted to spherical symmetry. Method reduces computational costs by orders of magnitude, and is applicable for both solid and liquid membranes, provided the curvature is sufficiently small. We demonstrate the method by calculating the bending and Gaussian curvature moduli of single- and multi-layer graphene. Method works with any interaction (ab initio, classical interactions), with any approach (molecular dynamics, Monte Carlo), and with applications ranging from science to engineering, from liquid to solid membranes, from bubbles to balloons.