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The forced phase locking in a system of the oscillating electroconvective rolls that form in a nematic liquid crystal layer in a dc electric field is studied. As a result of the action of an additive ac electric field with a small amplitude, the system of oscillators is found to be divided into clusters, where oscillations are fully phase locked. The electroconvective rolls in neighboring clusters oscillate in antiphase and the clusters are separated by Ising walls. The phase locking is shown to be maximal at the forcing frequency that is close to the double frequency of the natural oscillations of rolls. A model is proposed to describe spatially distributed phase oscillators, and it takes into account the symmetries of a system of electroconvective rolls and external forcing. The results of numerical simulations agree well with the experimental data.

The structural transformations in a nematic liquid crystal (NLC) layer with a hybrid orientation (planar director orientation is created on one substrate and homeotropic director orientation is created on the other) are studied. In the case of a dc voltage applied to the NLC layer, the primary instability is flexoelectric. It causes the appearance of flexoelectric domains oriented along the director on the substrate with a planar orientation. When the voltage increases further, an electroconvective instability in the form of rolls moving almost normal to flexoelectric domains develops along with these domains. Thus, the following spatially periodic structures of different natures coexist in one system: equilibrium static flexoelectric deformation of a director and dissipative moving oblique electroconvection rolls. The primary instability in the case of an ac voltage is represented by electroconvection, which leads to moving oblique or normal rolls depending on the electric field frequency. Above the electroconvection threshold, a transition to moving “abnormal” rolls is detected. The wavevector of the rolls coincides with the initial director orientation on the substrate with a planar orientation, and the projection of the director at the midplane of the NLC layer on the layer plane makes a certain angle with the wavevector. The results of numerical calculations of the threshold characteristics of the primary instabilities agree well with the obtained experimental data.

The nonsingular soliton-like defects in plane nematic liquid crystal (NLC) layers and spherical NLC drops are experimentally detected and studied when the interaction of NLC molecules with a bounding surface is varied. The dynamics and the annihilation of nonsingular defects of opposite signs on a plane surface are investigated. Periodic transformations of the soliton-like defects in NLC drops in an electric field are detected. The theory of elasticity is used to show that the surface energy taken into account in the total free energy of NLC in the case of weak anchoring leads to the possibility of nonsingular solutions of a director equilibrium equation. The calculated pictures of director distribution in a plane NLC layer and in a spherical NLC drop characterized by weak surface anchoring agree well with the results of polarized light optical observations.

The spatiotemporal dynamics of oscillating electroconvective structures appearing in a nematic liquid crystal (NLC) under the combined action of applied alternating (ac) and direct (dc) electric voltages has been experimentally studied. It is established that an increase in the dc component of the applied voltage leads to synchronization of the hydrodynamic mode with the orientational twist mode of the NLC director. The synchronization parameter and the phase shift of the modes are determined as function of the applied dc voltage. The results confirm the flexoelectric mechanism of synchronization.

We describe the dynamics of zigzag oscillations in a system of convective rolls in a nematic liquid crystal above the electroconvection threshold under the action of an ac voltage with a biased position of the mean value. It is found that an increase in the contribution from the constant component leads to a substantial increase in the spatiotemporal ordering of zigzag rolls and their synchronization with the homogeneous twist mode. The results confirm the flexoelectric mechanism of locking.

It has been confirmed that the flexoelectric polarization model can provide an adequate interpretation of the temperature behavior of the electrical response of homeotropically oriented samples of n-methoxybenzylidene-n-butylaniline nematic liquid crystals at twice the excitation frequency. The temperature dependence of samples with different director orientations has been investigated experimentally.