Cross section anisotropic

Pack R T 1978 Anisotropic potentials and the damping of rainbow and diffraction oscillations in differential cross-sections Chem. Phys. Lett. 55 197... 

Fig. 7.2. The radial dependence of the anisotropic part of the intermolecular potential (a) variation of height of the librational barrier in any diametrical cross-section of the cage and its rectangular approximation (b) the corresponding rectangular approximation of F(r) separation between the region of libration and that of free rotation inside the cage.

Bonamy L., Bonamy J., Robert D., Temkin S. I. Consequences of angular momenta coupling on generalized spectroscopic relaxation cross-sections collisional narrowing in isotropic and anisotropic Raman CO2 branches, Proc. 13th ICORS. (Wiley Sons, New York) (1992). 

If these concepts of curve analysis shall be applied to the anisotropic scattering of polymer fibers, one should choose to study either the longitudinal or the transversal density fluctuations. According to the decision made, the fiber scattering must be projected either on the fiber axis or on the cross-sectional plane. This results in scattering curves with a one- or a two-dimensional Porod s law. Because modern radiation sources always feature a point-focus, the required plots for the separation of fluctuation and transition zone are readily established (cf. Table 8.3). 

Figure 23. Radial segment density profile through a cross-section of a highly curved spherical vesicle. The origin is at r = 0, and the vesicle radius is very small, i.e. approximately r = 25 (in units of segment sizes). The head-group units, the hydrocarbons of the tails and the ends of the hydrocarbon tails are indicated. Calculations were done on a slightly more simplified system of DPPC molecules in the RIS scheme method (third-order Markov approximation), i.e. without the anisotropic field contributions...

This statement is a priori obvious for isotropic PSs, but works also for anisotropic PSs as well. Essential here is the term representative, which means that the multiple measurements of ID or 2D porosities in a number of different directions (traverse lines for ID case, and cross sections for 2D case) are provided. In the case of anisotropic PSs, dependence of on a location (direction) of a corresponding cross section or traverse line in a PS gives a picture type of a rose of winds, which... 

Figure 1. Cross sections of films etched with liquid or plasma etchants. The isotropic profile represents no overetch, and can be generated with liquid or plasma etch techniques. The anisotropic profile requires plasma...

Both surfaces of the conventional membrane are quite similar in appearance, and the cross section is only slightly anisotropic with little difference in pore and cell size from one surface to the other (Figure 10). in contrast, a considerable difference is apparent between the pore sizes at opposite surfaces of the Tyrann-M/E membrane (Figure 11). The structure is highly anisotropic with an approximately five fold difference between the size of the pores at the two surfaces. Approximately... 

We noted in the preceding section that the polarizability of an ellipsoid is anisotropic the dipole moment induced by an applied uniform field is not, in general, parallel to that field. This anisotropy originates in the shape anisotropy of the ellipsoid. However, ellipsoids are not the only particles with an anisotropic polarizability in fact, all the expressions above for cross sections are valid regardless of the origin of the anisotropy provided that there exists a coordinate system in which the polarizability tensor is diagonal. 

We have discussed intrinsically anisotropic particles—ones with anisotropy originating in their optical constants rather than their shape—in previous chapters. In Section 5.6 we gave the solution to the problem of scattering by an anisotropic sphere in the Rayleigh approximation. From the results of that section and Section 5.5 it follows that the average cross section (C) (scattering or absorption) of a collection of randomly oriented, sufficiently small, anisotropic spheres is... 

For an isotropic medium such as a collection of many randomly oriented particles, which may themselves be anisotropic, the scattered irradiance and hence the differential scattering cross section is independent of . 

Hollow fiber membranes are primarily homogeneous. In use, their lower permeability is compensated for by large surface per unit volume of vessel. Fibers are 25-250 pm outside dia, wall thickness 5-50 pm. The cross section of a vessel for reverse osmosis may have 20-35 million fibers/sqft and a surface of 5500-9000 sqft/cuft of vessel. Recently developed hollow fibers for gas permeation processes have anisotropic structures. 

Anisotropic particles align with the flow streamlines to reduce their hydrodynamic cross-section. 

First, if the specimen is subjected to axial stress a as well as the twist then as Biot215 has shown, Eq. (2.1) needs to be modified so that M = M — al, where M is the applied torque and I the second moment of area of the cross section with respect to the twist axis. Second, the St. Venant principle needs to be modified, as shown above, if the material is highly anisotropic, and very high length to diameter ratios may be necessary (Folkes and Arridge125). 

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