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<p dir="ltr">This dissertation encompasses my research work during my Ph.D. career, focusing on the controllability properties of liquid crystal flow. I have achieved two main results, which are as follows: Firstly, I have established the local exact controllability to the trajectory of the simplified Ericksen-Leslie model and its Ginzburg-Landau approximation. Secondly, I have successfully proven the global null controllability of the simplified Ericksen-Leslie model with Lions boundary condition for u and Neumann boundary condition for d, with the aid of a globally defined magnetic field which is independent of the spatial variable x. </p>

Autostereoscopic 2D/3D (two-dimension/three-dimension) switchable display has been attracting great interest in research and practical applications for several years. Among different autostereoscopic solutions, direction-multiplexed 3D displays based on microlens array or parallax barrier are viewed as the most promising candidates, due to their compatibility with conventional 2D display technologies. These 2D/3D switchable display system designs rely on fast switching display panels and photonics devices, including adaptive focus microlens array and switchable slit array. Polymer-stabilized blue phase liquid crystal (PS-BPLC) material provides a possible solution to meet the aforementioned fast response time requirement. However, present display and photonic devices based on blue phase liquid crystals suffer from several drawbacks, such as low contrast ratio, relatively large hysteresis and short lifetime. In this dissertation, we investigate the material properties of PS-BPLC so as to improve the performance of PS-BPLC devices. Then we propose several PS-BPLC devices for the autostereoscopic 2D/3D switchable display system designs. In the first part we evaluate the optical rotatory power (ORP) of blue phase liquid crystal, which is proven to be the primary reason for causing the low contrast ratio of PS-BPLC display systems. Those material parameters affecting the ORP of PS-BPLC are investigated and an empirical equation is proposed to calculate the polarization rotation angle in a PS-BPLC cell. Then several optical compensation methods are proposed to compensate the impact of ORP and to improve the contrast ratio of a display system. The pros and cons of each solution are discussed accordingly. In the second part, we propose two adaptive focus microlens array structures and a high efficiency switchable slit array based on the PS-BPLC materials. By optimizing the design parameters, these devices can be applied to the 2D/3D switchable display systems. In the last section, we focus on another factor that affects the performance and lifetime of PS-BPLC devices and systems: the UV exposure condition. The impact of UV exposure wavelength, dosage, uniformity, and photo-initiator are investigated. We demonstrate that by optimizing the UV exposure condition, we can reduce the hysteresis of PS-BPLC and improve its long term stability.

Recent research shows that liquid crystals can be used to report the presence of different types of substances through optical amplication of ligand-receptor binding. In this work, simulations based on a coarse-grained method have been performed to study a class of liquid-crystal-based sensors. A tensor order parameter was used to model the liquid crystalline system and the Beris-Edwards formulation was employed to obtain the time evolution of a liquid crystal medium containing particles. The simulation cases are built using three-dimensional unstructured meshes and the simulation geometries studied include simple models involving spheres as well as detailed modeling for a protein. The dynamics of a liquid crystal medium confined between two solid walls has been studied in the presence of spherical particles and a representative biological macromolecule. Comparisons of steady state and transient solutions from the present study with corresponding results from molecular dynamics based simulations in the literature yield good agreements.

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