Anisotropy coefficient

Crystallographic orientation Hardness 77v Polar anisotropy coefficient 77m a. jKh = TTmln Anisotropy ceofficient Mean hardness ... 

One can see that dependence of the steady-state values of the moments on the anisotropy coefficients appears in terms of the second order, as was assumed previously. 

The anisotropy of the coil has been calculated for other models of the macromolecule. Expressions for the anisotropy coefficient are known in the case where the macromolecule has been represented schematically by a continuous thread (the persistence length model) (Gotlib 1964 Zgaevskii and Pokrovskii 1970) and also in the case where the microstructure of the macromolecules has been specified. In the latter case, the anisotropy coefficient of the macromolecule is expressed in terms of the bond polarisabilities and other microcharacteristics of the macromolecule (Flory 1969). 

When account is taken of the excluded volume effects, one has also to take into account the possible effect of the shielding of the inner segments of the macromolecular coil, the latter effect being the greater the longer the macromolecule, so that the expression for the anisotropy coefficient, which has to be covariant in relation to subdivisions into subchain, assumes the form... 

In Table 11 are compiled the results concerning 2-D Heisenberg systems a is the anisotropy coefficient and the perpendicular susceptibility is calculated from the relationship ... 

Let us consider the hyperlattice anisotropy coefficient Oh as the ratio of the hyperlattice temporal to the spatial scale... 

The cellular anisotropy of plastic foams may be evaluated by e.g. an anisotropy coefficient q which is equal to the ratio between average cell dimensions along the major symmetry axes of the respective model. An isotropic material Is characterized by only one anisotropy coefficient (q = 1), a transversally anisotropic material by two(qj = q and q ) and an orthotropic medium by three coefficients (q q q ). 

The effective anisotropy coefficient q which characterizes the anisotropy of the whole material is given by ... 

As G. and S, Olive correctly indicated, the definition of the effective anisotropy coefficient q in Eq. (29) is unfortunate because the case q = 1 may be given not only for isotropic foamed polymers but also for anisotropic ones (for example, if... 

As shown by Karapetyan the structural anisotropy coefficients differ very... 

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)... 

Elastic Properties [1.30,1.31,1.35]. In regard to elasticity, at least below room temperature, tungsten behaves nearly isotropically the anisotropy coefficient at 24 °C is = 1.010 [1.35]. The elastic constants for polycrystalline tungsten at 20 °C are given below. Their temperature dependence as well as the respective values for singlecrystal elastic constants are shown in Fig. 1.10 [1.40], based on ultrasonic measurements [1.30,1.31]. 

Figure 4. Calculated properties vs. temperature and anisotropy coefficient (p) elastic modulus, MPa, along Y/Z-axes (a) and its relative difference, %, to X-axis (b) thermal conductivity, W/mK, along Y/Z-axes (c) and its relative difference, %, to X-axis (d).

The main bottleneck in this case will be in relaxation on the Y-Z plane (perpendicular to gradient), since there will be the most property mismatch and restricted movement of the parts of the whole specimen. Interesting, that relative anisotropy in elastic module between X and Y/Z components is not large (2-3%), but depends on temperature and anisotropy coefficient in a complicated way (Fig.4a and b). On the other hand, differences in values of thermal conductivity between X and Y/Z are almost the same for different anisotropy, but change strongly with the temperature (Fig.4c and d). The results for Y/Z-plane could be summarised in Table 1. 

Dependence of anisotropy coefficient on ratio (T2/01 ueja —> 0). Curve... 

For large values of the anisotropy coefficient both components of the field become the same at the range of small parameters ... 

Therefore, at the late stage of the transient response for relatively small values of anisotropy coefficient the field is inversely proportional to A. ... 

First consider the behavior of the field when the formation is more resistive than the surrounding medium (Figs. 11.7-11.8). In measuring the field in a relatively resistive formation of a small thickness the influence of a change in the conductivity of the surrounding medium exceeds the influence due to a change of anisotropy coefficient of the formation. 

It is natural that with an increase of the formation thickness the influence of parameter A2 becomes stronger, specially it is noticeable within the intermediate part of the frequency response, the low boundary of which corresponds to the frequency, when due to the skin effect the influence of the surrounding medium is small, ft is obvious that in measuring the anisotropy coefficient in formations of a small thickness, it is reasonable to increase significantly the frequency. 

Anisotropy requirements are usually characterized by the anisotropy coefficient, which is the etching rate ratio in vertical and horizontal directions ... 

For conventional sizes (1 = 1 pm, 1 = 0.5 qm, d = 2 qm), the required anisotropy coefficient should be at least 10. Small trench width can obviously be achieved by using a... 

The maximum value of the anisotropy coefficient for the ion energy-driven etching is equal to... 

In the opposite regime of limited flux of active neutral etching species, Kd [Pg.519]

The film wets the substrate if F < or fs/ffo > e + 1. In this case, the nonlinear anisotropy coefficient a in eq.(32) is always positive. The faceting instability requires a negative surface stiffness that can be achieved only if... 

The situation is different for [111] orientation when the firee-energy functional has anisotropic cubic terms leading to anisotropic quadratic terms in the evolution equation for the surface shape and the complex quadratic resonant interaction coefficient. In this case, the imaginary part of the resonant interaction coefficient depends on the surface-energy anisotropy coefficient, q, and the pattern orientation within the [111] plane (angle po). As one can see from... 

Figure 1. Thickness dependence of the critical temperature (left scale, full circles) and of the anisotropy coefficient (right scale, empty circles) in Nb/Cuo.42Nio.5s/Nb trilayers.

Let us consider the effect of the degree of elastic anisotropy of the lattice of, for example, a diamond-t3 e crystal on the form of the frequency spectrum and on the temperature dependence of the specific heat and pther thermodynamic functions. In order to see the effect of such an anisotropy, we will vary the anisotropy coefficient A - 2c44/(cu - C42) 2y when the ratios of the bulk moduli to the shear moduli are constant ... 

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