Exact Solution for Elastic Networks on Curved Surfaces

Abstract

The problem of characterizing the structure of an elastic network constrained to lie on a frozen curved surface appears in many areas of science and has been addressed by many different approaches, most notably, extending linear elasticity or through effective defect interaction models. In this paper, we show that the problem can be solved by considering non-linear elasticity in an exact form without resorting to any approximation in terms of geometric quantities. In this way, we are able to consider different effects that have been unwieldy or not viable to include in the past, such as a finite line tension, explicit dependence on the Poisson ratio or the determination of the particle positions for the entire lattice. Several geometries with rotational symmetry are solved explicitly. Comparison with linear elasticity reveals an agreement that extends beyond its strict range of applicability. Implications for the problem of the characterization of virus assembly are also discussed.

arXiv comment5 figures and 8 pages for the main paper. 4 figures and 11 pages for supplementary information

References in corpus (17)

• Virus shapes and buckling transitions in spherical shells
• Elastic theory of unconstrained non-Euclidean plates
• Interacting Topological Defects on Frozen Topographies
• Crystalline Order on a Sphere and the Generalized Thomson Problem
• Influence of Dislocations in Thomson's Problem
• In vitro protease cleavage and computer simulations reveal the HIV-1 capsid maturation pathway
• Geometry and Optimal Packing of Twisted Columns and Filaments
• Crystalline Order On Riemannian Manifolds With Variable Gaussian Curvature And Boundary
• The role of the encapsulated cargo in microcompartment assembly
• Ground States of Crystalline Caps: Generalized Jellium on Curved Space
• Elastic interactions between 2D geometric defects
• Statistical mechanics of thin spherical shells
• Emergent structure of multi-dislocation ground states in curved crystals
• Crystalline Particle Packings on Constant Mean Curvature (Delaunay) Surfaces
• Universality in the Screening Cloud of Dislocations Surrounding a Disclination
• Elasticity in Curved Topographies: Exact Theories and Linear Approximations
• A simple, general criterion for onset of disclination disorder on curved surfaces

Cited by in corpus (3)

• Hierarchical assembly is more robust than egalitarian assembly in synthetic capsids
• General Solution for Elastic Networks on Arbitrary Curved Surfaces in the Absence of Rotational Symmetry
• Geometry and dynamics of spring networks of spherical topology