Approximate modeling of spherical membranes

Spherical symmetry is ubiquitous in nature. It is therefore unfortunate that simulation of spherical systems is so hard and require complete spheres with millions of interacting particles. Here, we introduce a method 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-layer and multilayer graphene. The 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.