Metric approach for sound propagation in nematic liquid crystals

TL;DR

This paper models sound propagation in nematic liquid crystals near topological defects using a geometric approach based on an effective metric, linking acoustics to differential geometry and proposing an experiment to measure elastic constants.

Contribution

It introduces a novel geometric framework for sound propagation in nematic liquid crystals and suggests an experimental method to determine elastic constants.

Findings

Ray trajectories are derived from the effective metric.

A diffraction experiment is proposed to measure elastic constants.

The geometric model successfully describes sound behavior near defects.

Abstract

In the eikonal approach, we describe sound propagation near to topological defects of nematic liquid crystal as geodesics of a non-euclidian manifold endowed with an effective metric tensor. The relation between the acoustics of the medium and this geometrical description is given by Fermat's principle. We calculate the ray trajectories and propose a diffraction experiment to retrieve informations about the elastic constants.