Ranks’ effect

At this stage it is enlightening to compare the results of this study with those obtained for hexane by MD simulations (figs. 2.10 and 13). The essential difference between the two approaches is the different part of the phase space that is sampled. Lattice theories give ensemble averages, MD simulations time-averages. Although in the present case the lattice results are more detailed, the results for y(T) are at least very similar. Further it is noted that the rank effect, established above, was also found by MD simulations for decane and eicosane (see reference to J.G. Harris, in sec. 2.7). 

As elaborated above, the Ericksen-Leslie theory takes into account only the first rank effect of the velocity gradient of liquid crystalline polymers. If the amplitude of the velocity gradient is high enough, these theories are no longer valid and the steady viscosity of liquid crystalline polymers... 

Keywords reducing uncertainty, cost-effective information, ranking sources of uncertainty, re-processing seismic, interference tests, aquifer behaviour, % uncertainty, decision tree analysis, value of information, fiscal regime, suspended wells, phased development. 

The most effective Lewis-acid catalysts for the Diels-Alder reaction are hard cations. Not surprisingly, they coordinate to hard nuclei on the reacting system, typically oxygen atoms. Consequently, hard solvents are likely to affect these interactions significantly. Table 1.4 shows a selection of some solvents ranked according to their softness. Note that water is one of the hardest... 

Also the arene-arene interactions, as encountered in Chapter 3, are partly due to hydrophobic effects, which can be ranked among enforced hydrophobic interactions. Simultaneous coordination of an aromatic oc amino acid ligand and the dienophile to the central copper(II) ion offers the possibility of a reduction of the number of water molecules involved in hydrophobic hydration, leading to a strengthening of the arene-arene interaction. Hence, hydrophobic effects can have a beneficial influence on the enantioselectivity of organic reactions. This effect is anticipated to extend well beyond the Diels-Alder reaction. 

After each of the effects is calculated, they are ranked from largest to smallest, without regard to sign, and those factors whose effects are substantially larger than the other factors are identified. The estimated standard deviation for the analysis is given by... 

Table 7.3 List of Some Substituents Ranked in Terms of Their Effects on Monomer and Radical Reactivity...

If resonance effects a/one are considered, it is possible to make some sense of the ranking of various propagation constants. 

Table 7.4 lists the Q and e values for an assortment of common monomers. The extremes in the column of e values in Table 7.4—which are listed in order-quantify the range of donor-acceptor properties which is used as the basis for ranking in Fig. 7.2. The Q values perform a similar ranking with respect to resonance effects. The eight different Q-e combinations in Table 7.4 allow the estimation of ri and values for 28 different copolymers. Of course, in these systems Q and e values were assigned to give the best fit to r values which had already been measured. As an illustration of the predictive values of the Q-e scheme, consider the following example ... 

The tiansition from a choice of multiple fossil fuels to various ranks of coal, with the subbituminous varieties a common choice, does in effect entail a fuel-dependent size aspect in furnace design. A controlling factor of furnace design is the ash content and composition of the coal. If wall deposition thereof (slagging) is not properly allowed for or controlled, the furnace may not perform as predicted. Furnace size varies with the ash content and composition of the coals used. The ash composition for various coals of industrial importance is shown in Table 3. 

Seam correlations, measurements of rank and geologic history, interpretation of petroleum (qv) formation with coal deposits, prediction of coke properties, and detection of coal oxidation can be deterrnined from petrographic analysis. Constituents of seams can be observed over considerable distances, permitting the correlation of seam profiles in coal basins. Measurements of vitrinite reflectance within a seam permit mapping of variations in thermal and tectonic histories. Figure 2 indicates the relationship of vitrinite reflectance to maximum temperatures and effective heating time in the seam (11,15). 

The effects of rank on both compressive and impact strength have been studied, and usual minima were found at 20—25% dry, ash-free volatile matter (88—90 wt % carbon). Accordingly, the Hardgrove grindabiUty index exhibits maximum values in this area. 

Fig. 11. Effect of coal rank on furnace sizing (constant heat output) (82), where W = width, D = depth, and h and H are the heights indicated. A represents medium volatile bituminous B, high volatile bituminous or subbituminous C, low sodium lignite D, medium sodium lignite and E, high...

Trace elements added to copper exert a significant influence on electrical conductivity. Effects on conductivity vary because of inherent differences ia effective atomic size and valency. The decrease ia conductivity produced by those elements appearing commonly ia copper, at a fixed atomic concentration, rank as follows Zn (least detrimental), Ag, Mg, Al, Ni, Si, Sn, P, Fe (most). Table 12 summarizes these effects. In the absence of chemical or physical interactions, the increase in electrical resistivity is linear with amounts of each element, and the effect of multiatom additions is additive. 

The efficiency ranking of desiccants in drying air is not always the same as that observed in drying other materials. Other materials may interact with the desiccants to reduce drying effectiveness. From a study of the efficiency of some 25 desiccants for drying several families of laboratory solvents and reagents it was concluded that molecular sieves are the desiccants of choice in most cases (9—17). 

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