Developed Smectics: When Exact Solutions Agree

TL;DR

This paper introduces a method to construct smectic layer configurations with complex dislocation textures by leveraging geometric connections, and extends these configurations to cases with finite bending modulus.

Contribution

It develops a novel geometric approach linking 2D layer arrangements and 3D developable surfaces to model smectic layers with arbitrary dislocation textures.

Findings

Constructed layer configurations with arbitrary dislocation textures.

Extended configurations to finite bending modulus cases.

Established a geometric connection between layers and developable surfaces.

Abstract

In the limit where the bending modulus vanishes, we construct layer configurations with arbitrary dislocation textures by exploiting a connection between uniformly-spaced layers in two dimensions and developable surfaces in three dimensions. We then show how these focal textures can be used to construct layer configurations with finite bending modulus.