Isotropic nature

B in support of their contention that Ou varies appreciably for supposedly equivalent samples. However, this contention seems logical for the highly non-isotropic nature of an explosive sample consisting, as it does, of a variety of different sizes and shapes of explosive grains. 

A similar relationship can be observed with promoted M0S2. Each family of catalysts has its own linear correlation, which cannot be compared to each other directly because of the corrosivity problem. More recently, low-temperature oxygen chemisorption has been claimed to be more reliable, but it also lacks a well-determined stoichiometry (52). Oxygen chemisorption has also been applied to tungsten and rhenium sulfides, as well as promoted molybdenum and tungsten sulfides. In the isotropic class, it has been applied only to ruthenium sulfide, in which case it gives approximately the same result as a BET measurement due to the isotropic nature of this sulfide (41). 

Due to the isotropic nature of the liquid, the linearized hydrodynamic equations are easily solved when written in the Fourier (wave number) plane. Thus, the basic equations in fluid mechanics in the wavenumber and Laplace frequency (z) plane are written as... 

Amorphous metals can be prepared in a wide variety of stable and metastable compositions with all catalyti-cally relevant elements. This synthetic flexibility and the isotropic nature of the amorphous state with no defined surface orientations and no defect structure (as no long-range ordering exists) provoked the search for their application in catalysis [21]. The drastic effect of an average statistical mixture of a second metal component to a catalytically active base metal was illustrated in a model experiment of CO chemisorption on polycrystalline Ni which was alloyed by Zr as a crystalline phase and in the amorphous state. As CO... 

The isotropic form of the nuclear Zeeman interaction was discussed in detail in Section 1.2.3.1. This interaction is observed in isotropic media, and also in cases where the molecular orbital hosting the unpaired electron has substantial s character. The resulting isotropic hyperfrne couphng is related to the finite probability of the unpaired electron being at the nucleus. The spherical symmetry of the s orbital explains the isotropic nature of the interaction which is given by ... 

In studies that involve the CFD analysis of turbulent fluid flow, the k-t model is most frequently used because it offers the best compromise between width of application and computational economy (Launder, 1991). Despite its widespread popularity the k-e model, if used to generate an isotropic turbulent viscosity, is inappropriate for simulation of turbulent swirling flows as encountered in process equipment such as cyclones and hydrocyclones (Hargreaves and Silvester, 1990) and more advanced turbulence models such as the ASM or the RSM should be considered. Because these models are computationally much more demanding and involve an increased number of empirical parameters compared to the k-e model, other strategies have been worked out (Boysan et al, 1982 Hargreaves and Silvester, 1990) to avoid the isotropic nature of the classical k-e model. 

Transmission electron microscopy of deformed SB diblocks with spherical PB domains showed clear evidence for PB sphere cavitation in the crazed zones In fact, in contr t to the thick crazes of the cylindrical morphology materials, the crazes in the spherical morphology were exceedingly thin, approaching the dimension of the PB sphere diameter. Because of the simplifications offered by the isotropic nature of the spherical morphology, it was possible to develop a precise model for the rate of growth of crazes for this system. 

The isotropic nature of a liquid implies that any structure factor, S(k), obtained from a scattering experiment (typically X-ray or neutron) on that liquid will contain no angular dependence (of the molecules). Thus, the Fourier transform of any S(k) will yield a radial distribution function. Recently developed techniques of isotopic substitution [5-7] have been utilized in neutron diffraction experiments in order to extract site-site partial structure factors, and hence site-site radial distribution functions, gap(r). Unfortunately, because g p(r) represents integrals (convolutions) over the full pair distribution function, even a complete set of site-site radial distribution functions can not be used to reconstruct unambiguously the full molecular pair distribution function [2]. However, it should be mentioned at... 

Compressive-strength values are generally of the same order as the tensile strengths in the 2.0- to 3.0-pcf overall-density region. More important is the isotropic nature of the foam, which indicates rounded cells which have almost the same compressive strengths in both parallel and perpendicular directions to foam rise. This is very important in providing dimensionally stable foams. 

In order to derive these we will consider an adiabatic evacuated enclosure, like that shown in Fig. 5.19, with walls of any material. In this enclosure a state of thermodynamic equilibrium will be reached The walls assume the same temperature T overall and the enclosure is filled with radiation, which is known as hollow enclosure radiation. In the sense of quantum mechanics this can also be interpreted as a photon gas in equilibrium. This equilibrium radiation is fully homogeneous, isotropic and non-polarised. It is of equal strength at every point in the hollow enclosure and is independent of direction it is determined purely by the temperature T of the walls. Due to its isotropic nature, the spectral intensity L x of the hollow enclosure radiation does not depend on / and universal function of wavelength and temperature L x = L x X,T), which is also called Kirchhoff s function. As the enclosure is filled with the same diffuse radiation, the incident spectral intensity Kx for every element of any area that is oriented in any position, will, according... 

Figure 2 shows a generalized view of reverse osmosis/ultra-filtration. You will note that the artist has purposely shown the membrane having an isotropic nature, i.e., a dense topskin with small pores with a very porous support layer. The feed... 

Figure 2. A generalized view of RO/UF. Note that the artist purposely has shown the membrane having an isotropic nature, i.e., a dense topskin with small pores with a very porous support layer. The feed solution flows between the two membranes and as the pressurized feed solution passes over the membranes, permeate passes through the membranes and concentrate exits from between the membranes. The artist has made an effort to show that the impurities in the water are being concentrated as the permeate is being removed.

Metallic glasses have been used in catalysis in two ways, namely, in investigations carried out on as-quenched glassy metals and in those where the glassy metals were subjected to different pretreatments and served merely as precursors to catalytically active materials. The use of glassy metals as catalyst precursors has been shown to open up new possibilities for the preparation of supported metal catalysts with unusual chemical and structural properties. This potential resides mainly on the high reactivity and isotropic nature of these materials compared to their crystalline counterparts. Several efficient supported metal catalysts are compared to conventionally prepared supported metal catalysts in Chap. 3. 

The total yield of secondary electrons will increase as the specimen is tilted but the angular distribution remains the same. This is a consequence of the isotropic nature of secondary electron generation where the path direction of the secondary electrons is independent of the direction of the initiating high energy electrons. 

A similar analysis may be applied to the partially ordered nematic fluids composed of molecules comprising the mesogenic unit and flexible chain segments. In the LC state, one must consider the orientation-dependent interactions in addition to those of the isotropic nature. As mentioned earlier, the volume dependence (1/V ) incorporated in the Maier-Saupe expression may be replaced by MV. In its modified form, Maier-Saupe potential can easily be accommodated by introducing an additional term in the conventional van der Waals expression ... 

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