Gauge theory of disclinations on fluctuating elastic surfaces

TL;DR

This paper develops a gauge theory framework to describe disclinations on elastic surfaces that can change curvature and position, extending existing models to account for complex defect and surface behaviors.

Contribution

It introduces a novel gauge theory model for disclinations on fluctuating surfaces, generalizing the von Karman equations to include defect effects and surface variability.

Findings

Extended gauge theory for disclinations on Riemannian surfaces.

Recovery of von Karman equations with defect-induced sources.

Covariant equations for single disclinations on elastic surfaces.

Abstract

A variant of a gauge theory is formulated to describe disclinations on Riemannian surfaces that may change both the Gaussian (intrinsic) and mean (extrinsic) curvatures, which implies that both internal strains and a location of the surface in R^3 may vary. Besides, originally distributed disclinations are taken into account. For the flat surface, an extended variant of the Edelen-Kadic gauge theory is obtained. Within the linear scheme our model recovers the von Karman equations for membranes, with a disclination-induced source being generated by gauge fields. For a single disclination on an arbitrary elastic surface a covariant generalization of the von Karman equations is derived.