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The unique features of flexoelectric and dielectric effects are investigated, and exploited for a variety of functions, in a wide range of helicoidal liquid crystal systems, including non-chiral, cholesteric and blue phases. Electrooptic techniques are developed to measure flexoelectric parameters in non-chiral and cholesteric liquid crystals using twisted nematic and Grandjean geometries respectively. A crystal rotation method, and using a lock-in amplifier, is used to enable the measurement of a very small e/K of 0.011 C/N^-1m^-1. Enhancement in chiral-flexoelectric switching is demonstrated theoretically in liquid crystals with negative dielectric anisotropy and in systems in which the pitch is constrained to be other than the natural pitch. A methodological framework for inducing stable Uniform Lying Helix alignment is developed based on weak homeotropic alignment conditions and a method to bias the helicoidal axis orientation; a series of approaches within this framework are demonstrated, including nano-grooved interfaces, periodic boundaries conditions, in-plane fields, and mould-templated micro-channels. The latter approach is potentially commercially viable for sub-millisecond electrooptic technology. The contribution to a cholesteric material's effective dielectric permittivity of flexoelectric polarization is formulated, and an ability to switch a cholesteric between Grandjean and lying-helix configurations based on the dispersion in the flexoelectric polarization and resultant relaxation in dielectric properties is demonstrated. The flexoelectric contribution to dielectric permittivity is exploited to enable switching in bistable reflective displays and alignment of the Uniform Lying Helix. The existence of a flexoelectric contribution to Kerr switching in blue phases is demonstrated, and a semi-empirical model for the effect is developed. The effect is the first known example of a non-polar flexoelectrooptic effect. Independent flexoelectric and dielectric contributions to Kerr switching in blue phases are measured experimentally by measuring the induced birefringence as a function of driving frequency in flexoelectric- and dielectric-dominated wide-temperature-range blue phase materials.

The thesis concerns the mathematical study of the calculus of variations and its application to liquid crystals. In the first chapter we examine vectorial problems in the calculus of variations with an additional pointwise constraint so that any admissible function <strong>n</strong> ε W^1,1(ΩM), and M is a manifold of suitable regularity. We formulate necessary and sufficient conditions for any given state <strong>n</strong> to be a strong or weak local minimiser of I. This is achieved using a nearest point projection mapping in order to use the more classical results which apply in the absence of a constraint. In the subsequent chapters we study various static continuum theories of liquid crystals. More specifically we look to explain a particular cholesteric fingerprint pattern observed by HP Labs. We begin in Chapter 2 by focusing on a specific cholesteric liquid crystal problem using the theory originally derived by Oseen and Frank. We find the global minimisers for general elastic constants amongst admissible functions which only depend on a single variable. Using the one-constant approximation for the Oseen-Frank free energy, we then show that these states are global minimisers of the three-dimensional problem if the pitch of the cholesteric liquid crystal is sufficiently long. Chapter 3 concerns the application of the results from the first chapter to the situations investigated in the second. The local stability of the one-dimensional states are quantified, analytically and numerically, and in doing so we unearth potential shortcomings of the classical Oseen-Frank theory. In Chapter 4, we ascertain some equivalence results between the continuum theories of Oseen and Frank, Ericksen, and Landau and de Gennes. We do so by proving lifting results, building on the work of Ball and Zarnescu, which relate the regularity of line and vector fields. The results prove to be interesting as they show that for a director theory to respect the head to tail symmetry of the liquid crystal molecules, the appropriate function space for the director field is S BV² (Ω,S<sup>2,/sup>). We take this idea and in the final chapter we propose a mathematical model of liquid crystals based upon the Oseen-Frank free energy but using special functions of bounded variation. We establish the existence of a minimiser, forms of the Euler-Lagrange equation, and find solutions of the Euler-Lagrange equation in some simple cases. Finally we use our proposed model to re-examine the same problems from Chapter 2. By doing so we extend the analysis we were able to achieve using Sobolev spaces and predict the existence of multi-dimensional minimisers consistent with the known experimental properties of high-chirality cholesteric liquid crystals.

<p>Designing an application specific integrated circuit (ASIC) must be starting with careful preparations, otherwise the chip will not be as good as possible. The theoretical studies must cover everything from the chip circuits to the application structure. In mobile applications there is extremely important that the current consumption becomes minimized because the battery power is limited. The power reductions studies must include the most power costing circuits on the chip. When the whole circuit or segments of the circuit is not in use, they must switch fast and simple into another mode that consume nearly none power. This mode is called sleep-mode. If the sleep-mode has very low leakage currents, the lifetime of the application will dramatically increase. </p><p>This report studies the most power costing circuits in smartcard application ASIC. The chip should be used to control a LCD display on the smartcard. The circuits that have been investigated are level shifters, charge pumps and LCD drivers, also sleep-mode configuration possibilities have been investigated. Other small preparing work is also included in the thesis.</p>

Designing an application specific integrated circuit (ASIC) must be starting with careful preparations, otherwise the chip will not be as good as possible. The theoretical studies must cover everything from the chip circuits to the application structure. In mobile applications there is extremely important that the current consumption becomes minimized because the battery power is limited. The power reductions studies must include the most power costing circuits on the chip. When the whole circuit or segments of the circuit is not in use, they must switch fast and simple into another mode that consume nearly none power. This mode is called sleep-mode. If the sleep-mode has very low leakage currents, the lifetime of the application will dramatically increase. This report studies the most power costing circuits in smartcard application ASIC. The chip should be used to control a LCD display on the smartcard. The circuits that have been investigated are level shifters, charge pumps and LCD drivers, also sleep-mode configuration possibilities have been investigated. Other small preparing work is also included in the thesis.

L’objectif de cette thèse est de réaliser une peau active pour le camouflage de véhicule terrestre à base de la technologie cristal liquide cholestérique. Après analyse de l’environnement, une texture est appliquée sur les écrans cristaux liquides afin de réduire la signature visuelle et thermique du véhicule. Les travaux ont consisté à proposer un dispositif trichrome cristal liquide permettant d’obtenir la colorimétrie définie par le cahier des charges. Les problèmes de tenue en température, de réflexion spéculaire, de niveaux de gris, niveaux de réflectivité, de réduction des tensions appliquées ont été traités au cours de cette thèse. La technologie proposée a permis la réalisation d’un démonstrateur sur un robot télécommandé qui a été présenté au salon Eurosatory 2018 sur le stand du ministère des armées. Des travaux ont été également engagés pour le développement de modulateur optique dans l’infrarouge, à base de cristaux liquides cholestérique, afin de moduler la réflectivité et donc de pouvoir limiter la signature thermique du véhicule. Plusieurs pistes ont été testées et proposées. / The objective of this thesis is to achieve an active skin for the camouflage of a land vehicle based on cholesteric liquid crystal technology. After analysis of the environment, a texture is applied on the LCDs to reduce the visual and thermal signature of the vehicle. The work consisted of proposing a trichrome liquid crystal device to obtain the colorimetry defined by the specifications. The problems of temperature resistance, specular reflection, gray scale, reflectivity levels, reduction of applied voltages were discussed during this thesis. The proposed technology enabled to realization of a demonstrator on a remote controlledrobot that was presented at Eurosatory 2018 on the stand of the Ministry of the Armed Forces. Work has also been started on the development of optical modulators in the infrared, based on cholesteric liquid crystals, in order to modulate the reflectivity and thus to be able to limit the thermal signature of the vehicle. Several tracks have been tested and proposed.

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