Approximate Modeling of Spherical Membrane

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.

4 pages, 2 figures, 1 table

References in corpus (10)

• The electronic properties of graphene
• The structure of suspended graphene sheets
• Ripple Texturing of Suspended Graphene Atomic Membranes
• Density-functional tight-binding for beginners
• Graphene: a perfect nanoballoon
• Graphene as an electronic membrane
• Rippling of Graphene
• Structural, chemical and dynamical trends in graphene grain boundaries
• Effects of Bending on Raman-active Vibration Modes of Carbon Nanotubes
• Electronic and optical trends in carbon nanotubes under pure bending

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• Atlas for the properties of elemental 2D metals
• Twisting Graphene Nanoribbons into Carbon Nanotubes
• Mechanics of nanoscale wrinkling of graphene on a non-developable spherical surface
• Stability limits of elemental 2D metals in graphene pores
• The Gaussian Stiffness of Graphene deduced from a Continuum Model based on Molecular Dynamics Potentials
• Revised Periodic Boundary Conditions: Fundamentals, Electrostatics, and the Tight-Binding Approximation
• Adhesion mechanics of graphene on textured substrates
• Designing electronic properties of two-dimensional crystals through optimization of deformations
• Graphene Cardboard: from Ripples to Tunable Metamaterial
• Graphene membrane as a pressure gauge
• On the bending of rectangular atomic monolayers along different directions: an ab initio study
• Quantum Simulations of One-Dimensional Nanostructures under Arbitrary Deformations
• Relative Stability and Local Curvature Analysis in Carbon Nanotori
• Rippling of two-dimensional materials by line defects
• Observation of increasing bending rigidity of graphene with temperature
• Electronic Structure Trends of Möbius Graphene Nanoribbons from Minimal-Cell Simulations
• Limits of Lateral Expansion in Two-Dimensional Materials with Line Defects
• Elastic Constants and Bending Rigidities from Long-Wavelength Perturbation Expansions