Prediction discrepancies

These values enable many structures to be correctly predicted discrepancies arising mainly from the false assumption that ions behave entirely as rigid spheres. Some examples are given in Table 2.7. 

Mentre, F., Escolano, S. Prediction discrepancies for the evaluation of nonlinear... 

To assess the predictive ability of a QSAR in the frame of MTD method the cross-validation technique is used, in which one supposes that one or more of the known experimental values are in fact unknown . The analysis is repeated, excluding the temporarily unknown compotmds. The resulting equations are used to predict the experimental measurements for the omitted compound(s), and the resulting individual squared errors of prediction are accumulated. The cross-validation cycle is repeated, leaving one out (LOO) or more (LMO) different compotmd(s), until each compound has been excluded and predicted exactly once. The result of cross-validation is the predictive discrepancy sum of squares, sometimes called PRESS (Predictive REsidual Sum of Squares) ... 

Relaxations in the double layers between two interacting particles can retard aggregation rates and cause them to be independent of particle size [101-103]. Discrepancies between theoretical predictions and experimental observations of heterocoagulation between polymer latices, silica particles, and ceria particles [104] have promptetl Mati-jevic and co-workers to propose that the charge on these particles may not be uniformly distributed over the surface [105, 106]. Similar behavior has been seen in the heterocoagulation of cationic and anionic polymer latices [107]. 

A combination of equation (C2.6.13), equation (C2.6.14), equation (C2.6.15), equation (C2.6.16), equation (C2.6.17), equation (C2.6.18) and equation (C2.6.19) tlien allows us to estimate how low the electrolyte concentration needs to be to provide kinetic stability for a desired lengtli of time. This tlieory successfully accounts for a number of observations on slowly aggregating systems, but two discrepancies are found (see, for instance, [33]). First, tire observed dependence of stability ratio on salt concentration tends to be much weaker tlian predicted. Second, tire variation of tire stability ratio witli particle size is not reproduced experimentally. Recently, however, it was reported that for model particles witli a low surface charge, where tire DL VO tlieory is expected to hold, tire aggregation kinetics do agree witli tire tlieoretical predictions (see [60], and references tlierein). 

When the values of the BET monolayer capacity calculated from Type III isotherms are compared with independent estimates (e.g. from nitrogen adsorption) considerable discrepancies are frequently found. A number of typical examples are collected in Table 5.1. Comparison of the value of the monolayer capacity predicted by the BET equation with the corresponding value determined independently (columns (iv) and (v)) show that occasionally, as in line 6, the two agree reasonably well, but that in the majority... 

At the beginning of this section we enumerated four ways in which actual polymer molecules deviate from the model for perfectly flexible chains. The three sources of deviation which we have discussed so far all lead to the prediction of larger coil dimensions than would be the case for perfect flexibility. The fourth source of discrepancy, solvent interaction, can have either an expansion or a contraction effect on the coil dimensions. To see how this comes about, we consider enclosing the spherical domain occupied by the polymer molecule by a hypothetical boundary as indicated by the broken line in Fig. 1.9. Only a portion of this domain is actually occupied by chain segments, and the remaining sites are occupied by solvent molecules which we have assumed to be totally indifferent as far as coil dimensions are concerned. The region enclosed by this hypothetical boundary may be viewed as a solution, an we next consider the tendency of solvent molecules to cross in or out of the domain of the polymer molecule. 

A number of MO calculations has been carried out, and these have had mixed success in predicting chemical reactivity or spectroscopic parameters such as NMR chemical shifts and coupling constants. Most early calculations did not take into account the contribution of the sulfur 3d-orbitals to the ground state, and this accounts for some of the discrepancies between calculations and experimental observations. Of the MO methods used, CNDO/2 and CNDO/S have been most successful the INDO approximation cannot be used because of the presence of the sulfur atom. 

The discrepancies between the predictions of the JKR and DMT theories were first discussed by Tabor [41]. Tabor s discussion resulted in a rather heated exchange in the literature [42,43]. Subsequently, Muller et al. [44,45] attempted to... 

As with the maximum stress failure criterion, the maximum strain failure criterion can be plotted against available experimental results for uniaxial loading of an off-axis composite material. The discrepancies between experimental results and the prediction in Figure 2-38 are similar to, but even more pronounced than, those for the maximum stress failure criterion in Figure 2-37. Thus, the appropriate failure criterion for this E-glass-epoxy composite material still has not been found. 

The scaling dependence of the diffusion coefficient on N and Cobs Iso poses a number of questions. While the original scaling predictions, based on reptation dynamics [26,38], oc N, have been verified by some measurements [91,98], significant discrepancies have been reported too [95,96]. Attempts to interpret existing data in terms of alternative models, e.g., by the so-called hydrodynamic scaling model [96], fail to describe observations [100,101]. 

Their semi-empirical calculations also predicted a second transition below the A] which they did not observe they explained this discrepancy by noting that the missing band was probably obscured by the long-wavelength tail of the 206-nm band. ... 

We have found that for some alloys (e.g. Pt-Rh and Ni-Pt), the GPM yields pair interactions which are incorrect, because their values are either too large and would lead to overestimated transition temperatures (Ni-Pt), or they have even opposite sign than that expected from the experimental phase diagram and predicted by other theoretical methods (Pt-Rh). Various explanations of these discrepancies are conceivable ... 

Vermilyea" has adopted a thermodynamic approach to pitting, and considers that the critical pitting potential is the potential at which the metal salt of the aggressive ion (e.g. AICI3) is in equilibrium with metal oxide (e.g. AljOj). On the basis of this theory the critical pitting potential should decrease by 0-059V per decade increase in chloride ion concentration. Vermilyea s theory successfully predicts the values of the critical potentials for Al, Mg, Fe and Ni, but in the case of Zr, Ti and Ta there are large discrepancies. 

The electrical conductivity is proportional to n. Equation 1.168 therefore predicts an electrical conductivity varying as p. Experimental results show proportionality to p and this discrepancy is probably due to incomplete disorder of cation vacancies and positive holes. An effect of this sort (deviation from ideal thermodynamic behaviour) is not allowed for in the simple mass action formula of equation 1.167. 

It should be noted that it is extremely difficult to predict service lives of buried pipelines from the results of controlled trials with small specimens, whether in the laboratory or in the field. For example a study on the comparative corrosion resistances of ductile and grey iron pipes carried out jointly by European pipemakers in 1964-1973 indicated a mean pitting rate of 0 -35 mm/y for uncoated ductile iron pipe exposed in a typical heavy Essex clay of 500-900 ohm cm resistivity for 9 years. This is clearly at odds with the rate of 1 mm/y normally found on a corroded service pipe from such a soil. The discrepancy appears to be due to the use of specimens that were only a third of a pipe length each and were buried separately. It may reflect the contribution of the total surface area of the pipe as a cathode to the corrosion current at the anodic area at the pitting site. 

As for (ii), Mendeleev was, as indicated, quite ready to change atomic weight assignments from those accepted at his time to avoid significant discrepancies in his tables. This may sound ad hoc, but in fact, and as we already pointed out, some of these contra-predictions could be independently tested and their success in independent tests played an important evidential role—one which, as Brush allows, there is no reason (either historical or methodological) to suggest was any less significant than that played by the prediction of new elements. 

The fact that both heats of formation and equilibrium pressures of the hydrates of spherical molecules correctly follow from one model must mean that the L-J-D theory gives a good account of the entropy associated with the motions of these solutes in the cavities of a clathrate. That the heat of formation of ethane hydrate is predicted correctly, whereas the theoretical value of its vapor pressure is too low, is a further indication that the latter discrepancy must be ascribed to hindered rotation of the ethane molecules in their cavities. 

---