Effect of Anisotropy

There is no reason to believe that the off-diagonal Q integrals which yield this increase in U over I should be equal for longitudinal and transverse polarization but neither is there at present any basis for selecting different values. Hence we assume U1 = U2 and by use of the a values given above for the chlorine atom, the value of —El is calculated to be about 30 per cent smaller than was obtained in Table VI. Since the effect of anisotropy would be expected to be about the same for all of the halogens, the qualitative conclusions drawn from the results in Table VI are not affected. It is clear that anisotropy may be important, however, and must be considered in quantitative work. 

Figure 5. Effect of anisotropy on flow decay of 0.45pM Tyrann-M/E and conventional membranes with 0.01% Triton X-400 solutions. Relative pore size adjacent to feed 1 = Tyrann-M/E, large 2 — Tyrann-M/E, small 3 = conventional, large 4 = conventional, small.

For the hnear susceptibility, the zero-held specihc heat as well as the dipolar helds, the anisotropy dependence cancels out in the case of randomly distributed anisotropy (at least for sufficiently symmetric lathees). In other cases the anisotropy is a very important parameter as shown for the linear susceptibility in Figure 3.3 for an inhnite (macroscopic) spherical sample. The susceptibility is divided by Xiso = order to single out effects of anisotropy and dipolar... 

Figure 9.12—Effects of anisotropy and local inducedfields. The presence of it bonds is shown as zones in which there is a shielding (+)ora deshielding (—) effect. Ethylenic or aromatic protons are located outside a double cone of protection.

Knowles and Turan (2000) and Knowles (2005) have used the approach of Parsegian and Weiss (1972) to examine the effect of anisotropy on Hamaker constants. Such calculations are relevant for materials such as 7 -BN and rutile, Ti02, which exhibit strong anisotropy in their refractive indices because of their crystal structure. They make little difference to predicted values of Hamaker constants as a function of grain orientation for materials such as Si3N4 and SiC which, by comparison, exhibit modest values of birefringence. 

Now it is not difficult to calculate the amendment to formula (7.27) due to effect of anisotropy. At small velocity gradients, the tensor of anisotropy a is small, so that according to formulae (7.10) and (7.22), in linear approximation... 

However, the effect of anisotropy of the environment is expressed differently. One can see from formula (5.17), that the parameter ip is big in the case of strongly entangled system (y < y ), so that, according to equation (7.22),... 

The shear stress o 2 and the differences between the normal stresses o —0x2 and 022 — 033 are usually measured in the experiment (Meissner et al. 1989). The results of calculation of the stresses up to the third-order terms with respect to the velocity gradient will be demonstrated further on. For simplicity, we shall neglect the effect of anisotropy of the environment when the case of strongly entangled systems will be considered. 

One frequently deals with the linear effects of anisotropy which are induced by oscillatory velocity gradients or by oscillatory strains... 

If there is a systematic (i.e., highly ordered) tissue substructure such as in white matter, diffusion is usually more restricted in one than in another direction, i.e., the molecular mobility of water is not the same in all directions. In white matter, diffusion is less restricted parallel to than perpendicular to fiber tracts. If diffusion is different along various directions, then it is termed anisotropic diffusion. In stroke imaging the avoidance of the confounding effects of anisotropy is a common goal. However,... 

The big difference between normal isotropic liquids and nematic liquids is the effect of anisotropy on the viscous and elastic properties of the material. Liquid crystals of low molecular weight can be Newtonian anisotropic fluids, whereas liquid crystalline polymers can be rate and strain dependent anisotropic non-Newtonian fluids. The anisotropy gives rise to 5 viscosities and 3 elastic constants. In addition, the effective flow properties are determined by the flow dependent and history dependent texture. This all makes the rheology of LCPs extremely complicated. 

From this discussion it follows that all conclusions drawn for isotropic catalyst pellets hold for anisotropic catalyst pellets as well. In fact, with a single catalyst geometry, it is not possible to distinguish between isotropic and anisotropic pellets. The effect of anisotropy is lumped in with the effective diffusion coefficient. If the catalyst pellet is isotropic, then from Equation 7.128 it follows that we measure the effective diffusion coefficient D / = D J = D. For anisotropic pellets, we measure for pellets with a large height (0 large) and D H for flat pellets (0 small). For intermediate values of 0 the value of DeA is between De/iR and D H. 

C 7jfc/ is the average contrast factor, which accounts for the main effect of anisotropy." It can be shown that the contrast factor can be written in terms of the fourth order crystallographic invariant for the Laue group of the studied phase. In other words, can be written for any lattice symmetry, for instance using the invariants given by Popa. ... 

Favier used the USMP-1 opportunity to explore the interfacial breakdown in Bi-doped Sn, which, like most metals, solidifies as a plane front with little kinetic undercooling. His U.S. co-investigator, Abbaschian, investigated interfacial stability on the other side of the phase diagram i.e., Sn-doped Bi, which solidifies with a faceted interface. The purpose was to test the extension of the Mullins-Sekerka stability criterion to include the effects of anisotropy, which acts to stabilize the interface against breakdown into cellular and dendritic growth. " ... 

Fig. 1 Carbonyl group development in polymer samples exposed to UV illumination. The materials were an unpigmented polyethylene sample and similar samples pigmented with 5phr Ti02 pigment in the form of (i) anatase and (ii) rutile. (Data from Jin, C.Q. Ph.D. thesis. University of Newcastle upon Tyne, 2004. See also Jin, C. Christensen, P.A. Egerton, T.A. White, J.R. Effect of anisotropy on photomechanical oxidation of polyethylene. Polymer 2003, 44, 5969-5981.)...

The effects of anisotropy and anharmonicity in the atomic motions on the refinement of X-ray data for protein crystals are described in Chapt. XI. 

FIGURE 3.24 The effects of anisotropy in some actual molecules. 

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