Homotopy classification of director fields on polyhedral domains with tangent and periodic boundary conditions, with applications to bi-stable post-aligned liquid crystal displays

TL;DR

This paper provides a comprehensive topological classification of nematic liquid crystal states in complex geometries, with implications for designing bi-stable liquid crystal displays, using advanced algebraic topology methods.

Contribution

It introduces a complete topological classification framework for nematic liquid crystals on polyhedral domains with specific boundary conditions, surpassing traditional homotopy group approaches.

Findings

Classification applicable to periodic arrays of rectangular posts

Methods extend beyond relative homotopy groups

Results have practical implications for display technology

Abstract

We obtain complete topological classification of states of nematic liquid crystal in the geometry of periodic array of rectangular posts between two parallel slabs, with tangent or normal boundary conditions. This classification has applications in bi-stable pos-aligned liquid crystal display design and have technological significance. Methods used in classification are those of algebraic topology and go beyond relative homotopy groups.