Solid angle average

Isotropization in the Case of Fiber Symmetry. If methods for the analysis of isotropic data shall be applied to scattering patterns with uniaxial orientation, the corresponding isotropic intensity must be computed. By carrying out this integration (the solid-angle average in reciprocal space) the information content of the fiber pattern is reduced. One should consider to apply an analysis of the longitudinal and the transversal structure (cf. Sect. 8.4.3). 

For a general, isotropic and condensed multiphase material with short-range order, the CLD offers the best possible model-free visualization of the nanostructure. Nevertheless, the image does not show many details because of the inherent solid-angle average. 

This is in 3D the solid-angle averaged intensity of the stack -stacks of layers) had been studied in a conventional setup. 

If the fluid stream is a gas, the last term in the above equation is essentially unity. Unless the cyclone itself is rotating or, for example, located on another planet, g can be taken as 32.2. If the bulk solids angle of internal friction is unknown, then taking an average value of 62 degrees, the equation reduces to ... 

In most experiments and observations we are confronted with a collection of very many particles unless special pains are taken to align the particles, or in the absence of a known alignment mechanism, we may reasonably assume that they are randomly oriented. Under these conditions the quantities of interest are the average cross sections (Cabs) and (Csca), which are independent of the polarization of the incident light provided that the particles are not intrinsically optically active. Let p(Cl) dti be the probability that one of the axes fixed relative to a particle, the x axis, say, lies within a solid angle dSl around the... 

In many cases 3 possible positions exist differing by a solid angle of 120° (tetrahedron angle 109°). We compute the average difference of the dipole energy 2 i4diei in an electric field to be... 

Q, where 2 is the solid angle determined by the directions of four pseudo-equatorial bonds and containing an axial ligand (A 2 = 0° for ideal octahedron) the average values for two virtually identical hypervalent bonds in each molecule are given. 

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