Orientation sphere

The Poisson kernel is the Lorentzian on the orientation sphere (cf. Sect. 9.8). 

Figure 9.2. Reflection 4m (s) smeared by misorientation of the ensemble of crystallites (structural entities). The center of gravity is found at s/jd- Definitions of polar coordinates Dashed lines indicate the radial direction of the integration that leads to a projection onto the orientation sphere resulting in the pole figure g kl ([Pg.208]

History. Wilke [129] considers the case that different orders of a reflection are observed and that the orientation distribution can be analytically described by a Gaussian on the orientation sphere. He shows how the apparent increase of the integral breadth with the order of the reflection can be used to separate misorientation effects from size effects. Ruland [30-34] generalizes this concept. He considers various analytical orientation distribution functions [9,84,124] and deduces that the method can be used if only a single reflection is sufficiently extended in radial direction, as is frequently the case with the streak-shaped reflections of the anisotropic... 

Pathway to the Solution. All orientation functions are defined on the orientation sphere. At the best, their period is n. Thus the mapping of an analytical function h (x) on the orientation sphere is equivalent to... 

Figure 9.9. Infinite functions in a periodic world. Using a function (black line) as an orientation function means to wrap it around the orientation sphere. Only one branch of a LORENTZ distribution at the right side of the equator is sketched. Shape change occurs... 

G5b. Goldman, A. J., Cox, R. G., and Brenner, H., Slow viscous motion of two identical arbitrarily oriented spheres through a viscous fluid. Chem. Eng. Sci. (in press) see also Goldman, A. J., Investigations in low Reynolds number fluid-particle dynamics. Ph.D. Dissertation, New York University, New York, 1966. 

Apart from product- and production-oriented spheres of application, VR technologies are also used in product modeling and control. Research approaches can also be encountered in information technology, for the analysis and maintenance of communication networks, and in the modeling of production engineering processes. 

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