Surprisal

Comparing this solution with that based on a sharp phase separation in Example 4.2, the errors are surprisingly small. However, looking at the K... 

Hexane is an easy example. The variations in acentric factors are much more pronounced for heavy polar or polarizable components. It comes as no surprise that the values reported from different sources are not identical. 

Not surprisingly, costs are several times higher than conventional wells. Nevertheless, overall project economics may favour ERD over other development options. For example, BP developed the offshore part of the Wytch Farm Oilfield (which is located under Poole Harbour in Dorset, UK) from an onshore location. The wells targeted the reservoir at a vertical depth of 1,500 meters with a lateral displacement of over 8,000 meters (Fig. 3.20). The alternative was to build a drilling location on an artificial island in Poole Bay. ERD probably saved a considerable amount of money and advanced first oil by several years. 

The problem of invariant pattern recognition is recognized as being a highly complex and difficult one. It is not surprising, therefore, that a wide variety of techniques have been invented to deal with specific or general instances of this problem. 

Studying modem approaches for such schemes, one can see that knowledge of operational conditions and potential degradation mechanisms play a prominent role. Surprisingly, the role of NDT is often limited to tlie use of conventional methods such as ultrasonic wall thickness measurements, ultrasonic inspection, radiography, and last but not least visual inspection. 

Since scanning tunneling microscopy requires flat conducting surfaces, it is not surprising that most of its early application was to study inorganic materials [17, 19, 20, 29-34]. These studies include investigations of catalytic metal surfaces [24, 35-37], silicon and other oxides [21], superconductors [38], gold... 

Substances in this category include Krypton, sodium chloride, and diamond, as examples, and it is not surprising that differences in detail as to frictional behavior do occur. The softer solids tend to obey Amontons law with /i values in the normal range of 0.5-1.0, provided they are not too near their melting points. Ionic crystals, such as sodium chloride, tend to show irreversible surface damage, in the form of cracks, owing to their brittleness, but still tend to obey Amontons law. This suggests that the area of contact is mainly determined by plastic flow rather than by elastic deformation. 

The HLB system has made it possible to organize a great deal of rather messy information and to plan fairly efficient systematic approaches to the optimiza-tion of emulsion preparation. If pursued too far, however, the system tends to lose itself in complexities [74]. It is not surprising that HLB numbers are not really additive their effective value depends on what particular oil phase is involved and the emulsion depends on volume fraction. Finally, the host of physical characteristics needed to describe an emulsion cannot be encapsulated by a single HLB number (note Ref. 75). 

It is not surprising, in view of the material of the preceding section, that the heat of chemisorption often varies from the degree of surface coverage. It is convenient to consider two types of explanation (actual systems involving some combination of the two). First, the surface may be heterogeneous, so that a site energy distribution is involved (Section XVII-14). As an example, the variation of the calorimetric differential heat of adsorption of H2 on ZnO is shown in Fig. 

It is interesting and surprising to note that, although the molar entlialpy molar volume of... 

This simple mo l contiimes to ignore the possibility of volume changes on mixing, so for simplicity the molar volumes and are taken as those of the pure components. It should come as no surprise that in... 

Exponent values derived from experiments on fluids, binary alloys, and certain magnets differ substantially from all those derived from analytic (mean-field) theories. Flowever it is surprising that the experimental values appear to be the same from all these experiments, not only for different fluids and fluid mixtures, but indeed the same for the magnets and alloys as well (see section A2.5.5). 

The astrochemistty of ions may be divided into topics of interstellar clouds, stellar atmospheres, planetary atmospheres and comets. There are many areas of astrophysics (stars, planetary nebulae, novae, supemovae) where highly ionized species are important, but beyond the scope of ion chemistry . (Still, molecules, including H2O, are observed in solar spectra [155] and a surprise in the study of Supernova 1987A was the identification of molecular species, CO, SiO and possibly ITf[156. 157]. ) In the early universe, after expansion had cooled matter to the point that molecules could fonn, the small fraction of positive and negative ions that remained was crucial to the fomiation of molecules, for example [156]... 

As with the other surface reactions discussed above, the steps m a catalytic reaction (neglecting diffiision) are as follows the adsorption of reactant molecules or atoms to fomi bound surface species, the reaction of these surface species with gas phase species or other surface species and subsequent product desorption. The global reaction rate is governed by the slowest of these elementary steps, called the rate-detemiming or rate-limiting step. In many cases, it has been found that either the adsorption or desorption steps are rate detemiining. It is not surprising, then, that the surface stmcture of the catalyst, which is a variable that can influence adsorption and desorption rates, can sometimes affect the overall conversion and selectivity. 

Surprisingly, the origin of the eomplex oseillations and ehaos in the CO + O2 system (where traee quantities of Ft-eontaming speeies have a major infliienoe on the reaetion and, eonsequently, many of the reaetions of the Fl2 + O2 system predominate) are far from established to date. 

Clearly the broad survey of current activity in Raman spectroscopy revealed by this simple snapshot promises an exciting flitiire tiiat is likely to find surprising new applications, even as present methods and applications become refined. 

The simplifying approximation of a linear response is now made, by which it is assumed that rotations about different axes may be decoupled. This is only strictly valid for small rotations, but is surprisingly good for larger rotations too. This means that Mo(r)constant. Accordingly, at the end of the pulse the... 

The need for such large CSF expansions should not be surprising considering (i) that each electron pair requires at least two CSFs to fomi polarized orbital pairs, (ii) there are of the order of N N - 1 )/2 = X electron pairs for N electrons, hence (iii) the number of temis in the Cl wavefiinction scales as 1. For a molecule containing ten electrons, there could be 2 =3.5x10 temis in the Cl expansion. This may be an overestimate of the number of CSFs needed, but it demonstrates how rapidly the number of CSFs can grow with the number of electrons. 

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