2024/03/13 by E. S. Pikina, Pikina, E. S., A. R. Muratov +5
Computer Science · Engineering · Materials Science · #Advanced Materials and Mechanics #FOS: Physical sciences #Liquid Crystal Research Advancements #Nonlinear Dynamics and Pattern Formation #Soft Condensed Matter (cond-mat.soft)
paper · pdf · doi:10.48550/arxiv.2403.08325
openalex publication_date 2024/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Electro-hydrodynamic phenomena in liquid crystals constitute an old but still very active research area. The reason is that these phenomena play the key role in various applications of liquid crystals and due to the general interest of physical community to out-of-equilibrium systems. Nematic liquid crystals (NLCs) are ideally representative for such investigations. Our article aims to study theoretically the linear NLCs dynamics. We include into consideration orientation elastic energy, hydrodynamic motion, external alternating electric field, electric conductivity and flexoelectric polarization. We analyze the linear stability of the NLC film, determining dynamics of perturbations with respect to the homogeneous initial state of the NLC. For the purpose we compute eigen-values of the evolution matrix for a period of the external alternating electric field. These eigen-values determine the amplification factors for the modes during the period. The instability occurs when the principal eigen-value of the evolution matrix becomes unity by its absolute value. The condition determines the threshold (critical field) for the instability of the uniform state. It turns out that one might expect various types of the instability, only partially known and investigated in the literature. Particularly, we find that the flexoelectric instability may lead to two-dimensionally space modulated patterns exhibiting time oscillations. This type of the structures was somehow overlooked in the previous works.