Similarity actual distances

Here, d is the actual distance and u is the upper bound on that distance. The lower bound function can be similarly expressed ... 

Rather than using the distance distributions, which take no account of the actual distances, the second method calculates the degree of similarity between A and B on the basis of the number of components of DA and DB that are identical, i.e., it compares each element of DA in turn with each of the elements of DB to see if any of them match if so, then the matching element of DB is deleted from further consideration and the next element of DA used to initiate a further scan of DB. A distance match occurs if the distances are the same (to within any allowed tolerance such as plus or minus 0.5 A) and if the elemental t3rpes associated with this interatomic distance are the same this definition of a distance match also apphes to the third and fourth similarity methods discussed further below. The overall degree of similarity between A and B is then calculated from the number of distinct distances in common, COMMON. The specific similarity coefficient used here was the Tanimoto Coefficient which is defined by... 

Table 11.1 provides some general guidance for the minimum spacing between onshore equipment items. Actual distances will be adjusted according to local codes, company standards, area classification, and the findings of hazards analyses. Table 11.2 provides similar guidance for items located in the field. 

In the case of solids, there is no doubt that a lateral tension (which may be anisotropic) can exist between molecules on the surface and can be related to actual stretching or compression of the surface region. This is possible because of the immobility of solid surfaces. Similarly, with thin soap films, whose thickness can be as little as 100 A, stretching or extension of the film may involve a corresponding variation in intermolecular distances and an actual tension between molecules. 

Having established that these assumptions are reasonable, we need to consider the relationship between the parameters of the actual offset jet and the equivalent wall jet that will produce the same (or very similar) flow far downstream of the nozzle. It can be shown that the ratio of the initial kinematic momentum per unit length of nozzle of the wall jet to the offset jet,, and the ratio of the two nozzle heights,, depend on the ratio D/B, where D is the offset distance betw een the jet nozzle and the surface of the tank, and h, is the nozzle height of the offset jet. The relationship, which because of the assumptions made in the analysis is not valid at small values of D/hj, is shown in Fig 10.72. 

The main difference between the three functions is in the repulsive part at short distances the Lennard-Jones potential is much too hard, and the Exp.-6 also tends to overestimate the repulsion. It furthermore has the problem of inverting at short distances. For chemical purposes these problems are irrelevant, energies in excess of lOOkcal/mol are sufficient to break most bonds, and will never be sampled in actual calculations. The behaviour in the attractive part of the potential, which is essential for intermolecular interactions, is very similar for the three functions, as shown in... 

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