Elliptic geometry

An important open question relates to whether an optimal AR exists with regard to entrainment enhancement. Laboratory jet experiments with pseudo-elliptical geometries [27] suggest that an optimal AR with regard to nozzle-geometry-enhanced entrainment might be at a value AR = 3. However, the experiments are not conclusive since they involved AR up to 3.5 and nonuniform momentum-thickness distributions, which are known to also affect the entrainment process [5]. Moreover, the possible effects on jet entrainment of other more complicated interactions such as vortex-ring bifurcation still need to be established. 

For a DNAPL pool with elliptic geometry as shown in Fig. 3b, assuming that NAPL pool dissolution is described by Eq. (l),the appropriate initial and boundary conditions are given by Eqs. (10)—(12), (14) and... 

Elliptic geometry uses a modification of Postulate II. Postulate II allows for lines of infinite length, which are denied in Elliptic geometry, where only finite lines are assumed. 

Fig. 9. Cartoon which reviews variations in the geometry of fault damage zones. The simple elliptical geometry (a) is likely to be modified in reality by strain flelds caused by (b), deviations away from a planar plane (c) at the fault splay points (d) from extensional tip strains and (e) variations in the strengths and architecture of lithologies present.

In this section the calculated moments of inertia of alkali metal clusters, whose structures have been derived from ab initio calculations have been used successfully to interpret distortions from sphericality for 3-dimensional structures. The analysis has proved successful in relating these distortions to simple models of cluster bonding, and provides a useful tool for the prediction of stable cluster structures for as yet uncharacterised species. Distortions from circular to elliptical geometries for planar structures can be evaluated using a similar methodology. 

The obvious intention is to use elliptic geometry (Section 1.2) as a model, which, however, identifies antipodal points and hence a common beginning and end of the proposed universe. 

The UV dryer consists of lamp housing and reflector assembly. The reflector itself may be of either parabolic or elliptical geometry. Elliptical reflectors are most often used with medium-pressure mercury lamps. Parabolic reflectors provide a parallel beam of radiation, while the elliptical reflectors produce a focused beam of radiation on the substrate (Figure 46.19). UV-curable coatings are 100% solids and solvent removal equipment is not required. 

At deformations lower than 300-400 %, the SAXS patterns tend to assume an elliptical geometry characterized by a concentration of intensity above and below the equatorial region (Fig. 11.9b, c, b, c ). The corresponding azimuthal intensity profiles show broad maxima centred on the meridian (j = 0° and 180°) for the... 

Flow Nozzles A simple form of flow nozzle is shown in Fig. 10-17. It consists essentially of a short cylinder with a flared approach section. The approach cross section is preferably elliptical in shape but may be conical. Recommended contours for long-radius flow nozzles are given in ASME PTC, op. cit., p. 13. In general, the length of the straight portion of the throat is about one-h f throat diameter, the upstream pressure tap is located about one pipe diameter from the nozzle inlet face, and the downstream pressure tap about one-half pipe diameter from the inlet face. For subsonic flow, the pressures at points 2 and 3 will be practically identical. If a conical inlet is preferred, the inlet and throat geometry specified for a Herschel-type venturi meter can be used, omitting the expansion section. 

There is no Kerr rotation or Kerr ellipticity for pure /flight or for mixed r- and p-light in the transverse geometry, but there is a magnetization induced change in the surface reflectivity. 

Figure 2. Schematic drawing of a control apparatus. A laser of frequency coi is focused by lens L into a cell containing a tripling medium such as Hg vapor. Mirrors Ml and M2 are mounted inside a phase tuning cell (not shown) containing a refractive medium such as H2. The folded mirror geometry produces a pair of elliptical astigmatic foci, one of which overlaps the molecular beam (MB) at a distance zm from the beam axis. (Reproduced with permission from Ref. 62, Copyright 2006 American Physical Society.)...

Geometry of a quadratic objective function of two independent variables—elliptical contours. If the eigenvalues are equal, then the contours are circles. 

PBDS will also be useful in a related area for the examination of catalysts which are opaque not because of high unit absorption but because they are physically large, i.e., entire catalyst pellets. This is made possible by the favourable geometry of the apparatus and detection device. As indicated schematically in Fig. 1, the sample is merely placed at the focus of the IR beam (an off-axis elliptical mirror is used to focus the IR beam about 1 cm from the edge of the mirror) and a laser beam grazes the surface. The "sample space of the spectrometer is thus of indefinite volume and can be made as large as needed to examine massive objects (in the present apparatus, a sphere of about 20 cm diameter could be accomodated). An example is shown in Fig. 8. 

Emission Models. Incident models do not make use of all the operating variables, such as radiant power or radiant exitance, diameter, and length of the light source, or dimensions and reflection coefficient of the elliptical cavity mentioned above. Models that describe the space of irradiation on the basis of geometry and process variables are known as emission models. 

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