Director distribution modeling

We should note that an important role of the flexoelectric effect in a nonuniform field was first discovered by Prost et al. [165] and then developed in [155, 157, 163, 164]. Neglecting flexoelectric terms in equilibrium equations for the director distribution is one of the drawbacks of some recent models [158-161]. 

Before outlining the effect of fields on the orientation of the director, it must be emphasized that surface interactions and boundary conditions are usually of importance. The models applied here assume that there is a well-defined director distribution in the absence of any external field, and in practice this can only be provided by suitable treatment of boundary surfaces. The strength of surface interactions must also be considered as this will influence the equilibrium director configuration in the presence of a field. For the simplest description of field effects in liquid crystals it is usual to assume an infinite anchoring energy for... 

Experiments by Muller et al. [17] on the lamellar phase of a lyotropic system (an LMW surfactant) under shear suggest that multilamellar vesicles develop via an intermediate state for which one finds a distribution of director orientations in the plane perpendicular to the flow direction. These results are compatible with an undulation instability of the type proposed here, since undulations lead to such a distribution of director orientations. Furthermore, Noirez [25] found in shear experiment on a smectic A liquid crystalline polymer in a cone-plate geometry that the layer thickness reduces slightly with increasing shear. This result is compatible with the model presented here as well. 

Within the dielectric continuum model, the electrostatic interactions between a probe and the surrounding molecules are described in terms of the interaction between the charges contained in the molecular cavity, and the electrostatic potential these changes experience, as a result of the polarization of the environment (the so-called reaction field). A simple expression is obtained for the case of an electric dipole, /a0, homogeneously distributed within a spherical cavity of radius a embedded in an anisotropic medium [10-12], by generalizing the Onsager model [13]. For the dipole parallel (perpendicular) to the director, the reaction field is parallel (perpendicular) to the dipole, and can be calculated as [10] ... 

James M. Mason is Director of the Hydrogen Research Institute in Farmingdale, New York. He received his PhD at Cornell University in 1996. His research interests are the economic modelling of centralized hydrogen production and distribution systems using renewable energy sources. 

Doi molecular theory adds a probability density function of molecular orientation to model rigid rodlike polymer molecules. This model is capable of describing the local molecular orientation distribution and nonlinear viscoelastic phenomena. Doi theory successfully predicts director tumbling in the linear regime and two sign changes in the first normal stress difference,as will be discussed later. However, because this theory assumes a uniform spatial structure, it is unable to describe textured LCPs. 

Larson and Doi introduced a mesoscopic polydomain model based on LE theory. This model includes a domain orientation distribution function and incorporates director tumbling, distortional elasticity, and texture size. Larson-Doi model can qualitatively predict the steady flow behavior and transient behavior. However, discrepancies between the theoretical predictions and the experiments of model systems were observed, especially when the shear history includes rest periods. ° This model is restricted to low shear rates without perturbing the molecular orientation distribution function in each domain.f ... 

Electrically driven convection in nematic liquid crystals [6,7,16] represents an alternative system with particular features listed in the Introduction. At onset, EC represents typically a regular array of convection rolls associated with a spatially periodic modulation of the director and the space charge distribution. Depending on the experimental conditions, the nature of the roll patterns changes, which is particularly reflected in the wide range of possible wavelengths A found. In many cases A scales with the thickness d of the nematic layer, and therefore, it is convenient to introduce a dimensionless wavenumber as q = that will be used throughout the paper. Most of the patterns can be understood in terms of the Carr-Helfrich (CH) mechanism [17, 18] to be discussed below, from which the standard model (SM) has been derived... 

Values of macroorder parameters S, , (see Sect. 3.3), obtained for the LCPs 4 and model compounds 7 and 8, using various orientation methods, are listed in Table 8. For a random distribution of director axes S, , = 0. In case of a complete alignment we expect = 1.0 or S, , = —0.5, depending on the sign of the diamagnetic or dielectric anisotropy of die system. 

The Mission Director and ACE also did not have the information necessary to exercise their responsibility. The ACE had an inaccurate model of where the Black Hawks were located in the airspace. He testified that he presumed the Black Hawks were conducting standard operations in the Security Zone and had landed [159]. He also testified that, although he had a radarscope, he had no knowledge of AWACS radar symbology I have no idea what those little blips mean. The Mission Director, on the ground, was dependent on the information about the current airspace state sent down from the AWACS via JTIDS (the Joint Tactical Information Distribution System). 

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