Director fluctuations in inhomogeneously ordered nematic liquid crystals: An extension of elastic molecular field

In order to describe the order director fluctuations in nematic liquid crystalline systems with inhomogeneous order parameter, the approach based on Frank elastic theory is extended by introducing spatially dependent rotational viscosity and elastic constants. Using the proposed model, eigenmodes of director fluctuations in the vicinity of a disclination line of strength 1 are examined. Particular attention is paid to the behaviour of fluctuations in the vicinity of the structural transition in a cylindrical cavity.