Compare situation description

A point that deserves attention is the contribution of the electronic solvent polarization to the solvatochromic shifts. Most force fields use atomic point charges that include the effect of electron polarization in an implicit way. The main problem with the use of this implicit description of the electronic polarization is that it gives a vanishing contribution when one compares situations where the solvent structure is fixed, for instance when the Franck-Condon principle is applied in vertical transitions. In these situations it is convenient to have a model to compute explicitly... 

The fluid mechanics origins of shock-compression science are reflected in the early literature, which builds upon fluid mechanics concepts and is more concerned with basic issues of wave propagation than solid state materials properties. Indeed, mechanical wave measurements, upon which much of shock-compression science is built, give no direct information on defects. This fluids bias has led to a situation in which there appears to be no published terse description of shock-compressed solids comparable to Kormer s for the perfect lattice. Davison and Graham described the situation as an elastic fluid approximation. A description of shock-compressed solids in terms of the benign shock paradigm might perhaps be stated as ... 

For some applications, for example, human reliability analysis, a situation needs to be rated on a numerical scale. In these cases, values such as those shown in the left-hand column of Table 3.1 can be generated by comparing the situation being evaluated with the descriptions in the second, third, and subsequent columns which represent other PIFs relevant to the situation being assessed. These represent the worst, average, and best conditions that are likely to occur in chemical plants in general and correspond to ratings of 1,5, and 9 on the numerical scale in the left hand colunrm of Table 3.1. Obviously,... 

The reason for this becomes apparent when one compares the shapes of the localized it orbitals with that of the ethylene 7r orbital. All of the former have a positive lobe which extends over at least three atoms. In contrast, the ethylene orbital is strictly limited to two atoms, i.e., the ethylene 7r orbital is considerably more localized than even the maximally localized orbitals occurring in the aromatic systems. This, then, is the origin of the theoretical resonance energy the additional stabilization that is found in aromatic conjugated systems arises from the fact that even the maximally localized it orbitals are still more delocalized than the ethylene orbital. The localized description permits us therefore to be more precise and suggests that resonance stabilization in aromatic molecules be ascribed to a "local delocalization of each localized orbital. One infers that it electrons are more delocalized than a electrons because only half as many orbitals cover the same available space. It is also noteworthy that localized it orbitals situated on joint atoms (n 2, it23, ir l4, n22 ) contribute more stabilization than those located on non-joint atoms, i.e. the joint provides more paths for local delocalization. 

It is important to emphasize that the similarity behavior is not the result of approximations or assumptions where certain physical effects have been neglected. Instead, these are situations where the full two-dimensional behavior can be completely represented by a one-dimensional description for special sets of boundary conditions. Of course, in all finite-dimensional systems there are edge effects that violate that similarity behavior. By way of contrast, however, one may consider the difference between the governing equations used here and the boundary-layer equations for flow parallel to a solid surface. The boundary-layer equations are approximations in which certain terms are neglected because they are small compared to other terms. Thus terms are dropped even though they are not exactly zero, whereas here the mathematical reduction is accomplished because certain terms vanish naturally over nearly all of the domain (excluding edge effects). 

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