Singular Twist Waves in Chromonic Liquid Crystals

TL;DR

This paper investigates the nonlinear twist-wave behavior in chromonic liquid crystals, demonstrating that smooth solutions can develop shock waves in finite time, with analytical estimates validated by numerical simulations.

Contribution

It introduces a nonlinear twist-wave equation for chromonic liquid crystals and shows the formation of shock waves from smooth solutions, providing analytical estimates validated numerically.

Findings

Smooth solutions to the twist-wave equation can break down in finite time.

Shock wave formation occurs under generic initial conditions.

Analytical estimates of critical time match numerical results.

Abstract

Chromonic liquid crystals are lyotropic nematic phases whose applications span from food to drug industries. It has recently been suggested that the elastic energy density governing the equilibrium distortions of these materials may be quartic in the measure of twist. Here we show that the non-linear twist-wave equation associated with such an energy has smooth solutions that break down in a finite time, giving rise to the formation of a shock wave, under rather generic assumptions on the initial profile. The critical time at which smooth solutions become singular is estimated analytically with an accuracy that numerical calculations for a number of exemplary cases prove to be satisfactory.