Type anisotropy coefficients

Foam type Volume weight 7 Gas-filling factor G (%) Parameter P Longitudinal Wave Velocity Anisotropy coefficients (Eq. 30 a) Effective anisotropy coefficient q (Eq. 29)... 

Einstein coefficient b, in (5) for viscosity 2.5 by a value dependent on the ratio between the lengths of the axes of ellipsoids. However, for the flows of different geometry (for example, uniaxial extension) the situation is rather complicated. Due to different orientation of ellipsoids upon shear and other geometrical schemes of flow, the correspondence between the viscosity changed at shear and behavior of dispersions at stressed states of other types is completely lost. Indeed, due to anisotropy of dispersion properties of anisodiametrical particles, the viscosity ceases to be a scalar property of the material and must be treated as a tensor quantity. 

From the form of Eq. (2.33) it becomes understandable why the anisotropy of polarization 7Z is sometimes called the degree of alignment. From the point of view of the determination of the magnitude of the polarization moments bPo the measurement of 71 is preferable, as compared with that of V, all the more so if one bears in mind that the population bPo appears only as a normalizing factor for all other bPQ and does not influence the shape of the probability density p(B,multipole moment dependence of V and 71 for various types of radiational transition (A = 0, 1) can be obtained using the numerical values of the Clebsch-Gordan coefficient from Table C.l, Appendix C. 

We shall now discuss in more detail the different phase types of polymers as far as data of birefringence, stress-optical coefficient and anisotropies in polarisability are available. 

Measurements. The anisotropy of the pair polarizability has been determined from three types of measurements depolarized CILS spectra, pressure dependent depolarization ratios, and second virial Kerr coefficients. 

These are expressed in terms of scalar products between the unit axis system vectors on sites 1 and 2 (on different molecules) and the unit vector 6. from site 1 to 2. The S functions that can have nonzero coefficients in the intermolecular potential depend on the symmetry of the site. This table includes the first few terms that would appear in the expansion of the atom-atom potential for linear molecules. The second set illustrate the types of additional functions that can occur for sites with other than symmetry. These additional terms happen to be those required to describe the anisotropy of the repulsion between the N atom in pyridine (with Zj in the direction of the conventional lone pair on the nitrogen and yj perpendicular to the ring) and the H atom in methanol (with Z2 along the O—H bond and X2 in the COH plane, with C in the direction of positive X2). The important S functions reflect the different symmetries of the two molecules.Note that coefficients of S functions with values of k of opposite sign are always related so that purely real combinations of S functions appear in the intermolecular potential. 

These surfaces were obtained subject to the two types of limiting behaviour constraints mentioned above (9,10). The limiting large-R behaviour was imposed by using reliable semi-empirical dispersion coefficients and their PgicosO) anisotropies, calculated as functions of the diatom bond length r (9,52), to define the values of the Cg coefficients for all (X,k). As the experimental data could only discern the k=0 and 1 components of the potential (5-7, 9,10), the collapsed diatom limit constraint was imposed by defining the k"2 functions by the requirements that at 5=-l (i.e., at r=0), the sum of (-1) times the A R, and constants for... 

The sensitivity of a piezoresistive pressure sensor depends on the piezoresistive coefficient. Silicon crystal face selection and gage layout on the crystal face are important because of the anisotropy of the piezoresistive effect. Silicon (100) and (110) are often used with P-type diffused resistors to achieve a desired sensitivity. The next consideration is the thermal stress effect originating from the silicon crystal face. Fig. 7.3.5 shows the stress-distribution maps for silicon (100) and silicon (110) by the finite element method (FEM). 

Anisotropic Hyperfine Interaction. The anisotropic component of the hyperfine coupling has two contributions a local anisotropy owing to spin density in p- or type orbitals on the atom of observation, and nonlocal dipolar coupling with spin on other atoms. The first type of interaction is proportioned to the orbital coefficient (squared) of the pid orbiteds. To a first approximation the second term can be considered as a classic point dipolar interaction between the nucleus and the electron spin on a nearby atom. This depends on the total electron spin density at the neighbor (p ), the distance between the spins (r,2), and the orientation of the vector between them with respect to the external magnetic field (denoted by angle 0). In the point dipole approximation,... 

Diffusion coefficient and surface exchange coefficient measurements have been reported for the K2MF4 type oxide materials by a number of authors [4-8, 13-19] and have been complemented by electrochemical permeation measurements [20-27] all of which demonstrate the fast oxide ion conduction of hyperstoichiometric K2NiF4 type oxides. Early reports also demonstrate the relatively poor oxide ion mobility in those materials found to be hypostoichiometric [28,29]. Initial reports of the fast oxide ion conduction in La2Ni04+s [4, 6-8] have generated a number of further studies [13-19] regarding the optimization of composition and determination of the effects of anisotropy on the conduction properties of these materials. Each of these features will be discussed in more detail below. 

Here the coefficients a and b characterize the surface-energy anisotropy and can be computed from the surface-energy dependence on the surface orientation. Naturally, the nonhnear operator Too i is invariant with respect to rotations by 7t/2, as well as any of the transformations x —s- —x, y — —y, x y, while Finis invariant with respect to rotations by 27t/3 as well as the transformation y —s- —y, b —b. The functions Wo 2,zih) are determined by the type of a wetting interaction model and can also differ for different orientations of the film surface. 

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