Formation of traveling waves in nematics due to material parameter ramps

Abstract

We propose a simple one-dimensional linear model to describe the formation of localized traveling waves due to material parameter ramps in nematic liquid crystals. We assume that due to some external perturbation the material parameters (conductivity, dielectric constants, viscosity, elasticity) of the liquid crystal become slowly varying functions of position. Temperature gradient in localized regions induced by a laser beam could be one such perturbation. We obtain a 4x4 system of electrohydrodynamic equations [partial derivative equations (PDE) with respect to time and position]. At first we assume that all parameters change from their nonperturbed value by the same ramp function. Then, to reveal the parameters which slowly change are predominant in the formation of localized traveling waves, we obtain four more systems of equations. Each time we assume that just one of the material parameters changes while the others are held constant. Accordingly, by reducing 4x4 systems of equations into one equation and using a WKB-like approach for nonuniform media, we obtain the relevant dispersion relations. We show that ramps of elasticity and dielectric parameters play the dominant role in the formation of localized traveling waves in nonuniform nematic media.

Propagation of periodic director and flow patterns in a cholesteric liquid crystal under electroconvection

“…In addition to the fluid-structure interaction, the migration of the charge carriers should be analysed as they interact with both flow and structure. Therefore, it is generally complicated and challenging to describe the mechanisms of the phenomena related to electroconvection, as seen in the generation of travelling waves including solitons [4][5][6][7][8][9][10][11][12][13][14], bifurcation between turbulent states [15][16][17][18], and the appearance of negative viscosity [19,20].…”