Uniform parallel

Louvers Baffles used for changing the direction of air flow into the tower in a uniform, parallel manner. They are also used in preventing water droplets from... 

FIGURE 10.52 Critical contamination region in a uniform parallel flow field. Qualitative solution of the difliision equation in a velocity field with the velocity equal to 0.45 m s, difliision coefficient equal to 2.4 cm s , and the distance between the working surface and the contamination source of 30 cm. 

The thickness of thin film layers separated by uniform, parallel interfaces can be determined from optical interference patterns that result. These measurements can be made from about 400 nm out through the visible spectrum and on into the near-infrared (NIR) region. Since film thickness measurements rely not on the absolnte magnitude of the reflected light, but on the variation of that signal with wavelength, the choice of nnits is less important. Typically %R is used, but in some cases raw intensity is also satisfactory. We will treat thickness determinations in more detail in the applications section of this chapter. 

The exposure-response surface (see Chapters 8 and 32) is rarely mapped in children, thus limiting extrapolation of therapy from adults to children. Models linking biomarkers to patient outcomes—outcomes link models—are virtually absent in pediatric pharmacometries. There is no reason to believe that PK/PD-biomarker-surrogate-outcomes linkage in children should uniformly parallel adults therefore, this is an area where there is a great need for further model development. Population methods can play an important role for filling in these critical pieces to determine optimal pediatric therapy. 

Problem 10-10. Mixing Layer. Two semi-infinite streams of the same fluid, but with different uniform, parallel velocities, Uand all, are brought into contact. Owing to the action of viscosity, a boundary layer will develop over which the initial discontinuity in velocity will be smoothed out as illustrated in the figure. Derive the boundary-layer equations for... 

Two types of porous electrodes can be considered two- and three-phase systems, where the latter is the special case of a triphasic interface in fuel cells, where the gas, liquid, and solid coexist. In the former, the liquid reactant is dissolved in the electrolyte and transported to the active sites of the electrocatalyst. In each case, we can consider uniform, parallel, cylindrical, or conical pores that are topped at the bottom by the metal substrate and at the top by the electrolyte [19,20],... 

The apparent mass factor m = a -pflcj) (a > 1) in Equation 2.16b considers that not all of the pore fluid moves along the maximum pressure gradient in case of tortuous, curvilinear capillaries. As a result the pore fluid seems to be more dense, with higher inertia, (a ) is called structure factor and is equal to 1 in case of uniform parallel capillaries. 

Linear macromolecules, either without substituents or with small ones regularly arranged, can juxtapose themselves at a microscopic level in uniform parallel aereas and form crystals. Plastics with crystalline regions always also contain more or less amorphous, unordered regions, for which reason they are termed semicrystalline. This macromolecular arrangement can be altered by a number of influences. 

The experimental evidence presented here indicates that anisotropic Si02 films can be deposited in a beam r.f. plasma system. The films cause parallel alignment for commonly used liquid crystal material and for appropriate beam incidence angles uniform parallel alignment is obtained in a single deposition. 

The value of 5op ranges from unity, if the dye transition moment is uniformly parallel to the director, through zero, if the dye orientation is completely randomized to if the dye transition moment is always perpendicular to the director. Note that op depends both on the underlying orientational order of the liquid crystal molecules and on the intrinsic molecular anisotropy of the dye. Suitable dyes have been called both pleochroic dyes and dichroic dyes (the latter is more exact) we call them simply anisotropic dyes. 

Within focal regions where fenestration of the alveolar wall and some confluence of air spaces were identified, Belton et al. (1977) found randomised electron dense collagen fibrils, whereas the normal alveolar septa contained uniformly parallel collagen fibrils. Many of the randomised fibrils had sufficient swelhng to display prominent internal spiralling. When the thickened fibrils were cut transversely, the appeared as a stack of flattened, electron dense lamellae. 

For low concentrations of polymer network, / external field, the liquid crystal is aligned uniformly parallel to the polymer fibers, as shown by in Figure 11.35(a). 

The nematogen used in the experiments was 5CB containing a small quantity of L-dye D81 (EM Chemicals). The glass sample cell spacing was 10 or 100 jum, (Hellma Cells). Uniform parallel alignment of the nematic was achieved by the rubbed PVA process. The glass sample cell was inserted into a temperature controlled aluminum block. 

Balakiishnan N, Kanet JJ, Sridhaian V (1999) Eaily/tardy scheduling with sequence dependent setups on uniform parallel machines. Comput Oper Res 26(2) 127-141 Coleman B (1992) Technical note a simple model for optimization the single machine early/tardy problem with problem with sequence-dependent setups. Prod Oper Manage l(2) 225-228 Davis JS, Kanet JJ (1993) Single-machine scheduling with early and tardy completion costs. Naval Res Logistics (NRL) 40(1) 85-101... 

REE patterns in bulk carbonaceous chondrites are fairly uniform, parallel to Cl, and show no dependence on volatility (e.g., no Eu or Yb anomalies). This uniformity also applies to the ordinary (H, E, EE classes) and enstatite (EL, EH classes) chondrite classes that show significant loss of their moderately and highly volatile elements (e.g., potassium, lead) and/or variations in their metal/silicate ratios. Accordingly, REE abundances in chondritic meteorites indicate no substantial cosmochemical fractionation (i.e., volatile related redox related) during their formation in the early stages of solar system evolution and indicate broad homogeneity in the solar nebula. 

From these considerations it appears plausible that by rubbing the substrate, in other words producing grooves in the surface, the liquid crystal molecules can be aligned uniformly parallel to the rubbed surface and brought into a stable position. Moreover it can be concluded that only in special cases the orientation of the liquid crystal molecules normal to the grooves (maximum deformation energy of the liquid crystal) is stable [41, 42]. 

Smectic A phases in which the layers are not uniformly parallel to the glass slides confining the sample (i.e. not in a planar orientation) are characterized by fan-like textures (Fig. 5.10b), made up of focal conics (Fig. 5.12). A focal conic is an intersection in the plane of a geometric object called a Dupin cyclide (Fig. 5.13), which results from lamellae forming a concentric roll (like a Swiss roll) being bent into an object based on an elliptical torus of non-uniform cross-section. The straight line that would define the rotation axis of the torus is distorted into a hyperbola in the Dupin cyclide. 

In thermoplastic materials, linear macromolecules can align themselves uniformly parallel to one another in microscopic regions and form crystallites, with or without regularly arranged substituents that are not too large. Polymer materials with crystalline regions invariably contain additional amorphous zones where the macromolecules cannot be ordered, which is why they are called semi-crystalline. Besides semi-crystalline materials there are also amorphous thermoplastics [1]. 

One optical feature of helicoidal structures is the ability to rotate the plane of incident polarized light. Since most of the characteristic optical properties of chiral liquid crystals result from the helicoidal structure, it is necessary to understand the origin of the chiral interactions responsible for the twisted structures. The continuum theory of liquid crystals is based on the Frank-Oseen approach to curvature elasticity in anisotropic fluids. It is assumed that the free energy is a quadratic function of curvature elastic strain, and for positive elastic constants the equilibrium state in the absence of surface or external forces is one of zero deformation with a uniform, parallel director. If a term linear in the twist strain is permitted, then spontaneously twisted structures can result, characterized by a pitch p, or wave-vector q=27tp i, where i is the axis of the helicoidal structure. For the simplest case of a nematic, the twist elastic free energy density can be written as ... 

In the above we have assumed that the lowest energy state is one of uniform parallel alignment of the director however, it is possible to modify these expressions for situations where the lowest energy state might be one of uniform splay, bend or twist. Of these, the last is important because it describes the helical liquid crystal phases that result from chiral molecules. Such states arise if there are terms in the free energy that are linear in the strain, and for a chiral nematic the free energy density becomes ... 

In Abbe s double prism method a thin ho-meotropically oriented nematic film is placed between the hypotenuse faces of two rectangular prisms. Using light polarized parallel and perpendicular to the optical axis, respectively, the principal refractive indices and can be obtained directly from the critical angle of total reflection, provided that the refractive index of the prism is greater than that of the liquid crystal [2, 8-10]. In some cases the director of the nematic phase was oriented uniformly parallel to the prism planes [11-14]. Special variants of the total reflection method have been described [3, 4, 15, 16]. A total reflection refractometer of the Abbe type has also been used to determine n, n and An in the infrared region between 2.5 and 14 p.m [17]. 

We now calculate the threshold of domain formation following the concepts of HelfrichJ We consider a thin planar cell with electrodes on the two surfaces. We assume that the dielectric anisotropy is negative (Ae = 6 — < 0) and that the liquid crystal is aligned uniformly parallel to the surface by suitable surface treatment. The geometry is that of Fig. 1 the director lies in the x-z plane and is parallel to the jc-axis at the surfaces. There is no variation in the y-direction and all variations in the jc-direction are periodic with period A. In this geometry, the electric field alone does not distort the liquid and any instability must be of hydrodynamic nature. 

There are two other examples of fluid orientation that are closely related to uniform parallel alignment. In the first case, the director also lies parallel to the cell surfaces. However, the director orientation in the plane parallel to the cell walls is not uniform rather, it changes randomly over dimensions on the order of micrometers. This orientation is known as random parallel alignment (see Fig. 4B). 

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