On the stability of homogeneous orientation in the plane-parallel cell of a liquid crystal doped with nanoparticles

We consider the problems of homogenous orientations stability of molecules in a nematic liquid crystal (NLC) doped with a small amount of cholesteric LC. We studied LC cells with homeotropic and twisted orientation of molecules on the cell boundaries. The problems are solved using the Noether theorem for LC. According to this theorem, invariance of free energy expression with respect to translation leads to conservation of the momentum flux, while invariance with respect to the rotation group leads to conservation of the angular momentum flux. These conservation laws are used to determine thresholds of stability of homogenous orientation of molecules in the above-mentioned mixture and the influence of nanoparticles on these thresholds.