Comparison of the Two Models

It is not easy to directly compare the two models which were discussed in the previous sections. The only interactions which were studied with both techniques are those of a gramicidin A channel with Na+ and K+. In Fig. 6 the results of these studies 165 , I66,i89,i9i) are compare(j. The largest differences can be observed at the two ends of the channel. This is due to the fact that the ethanolamine tails were fixed in different con- 

The evaluation of pair potentials is much more time-consuming than the evaluation of the parameters in the model of Gresh et al. On the other hand, pair potentials are easy to transfer and corresponding interaction energy calculations are very fast. In contrast, the application of the model of Gresh et. al. includes always time-demanding ab initio calculations. 

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FIGURE 11.14 Data set consisting of a control dose-response curve and curves obtained in the presence of three concentrations of antagonist. Panel a curves fit to individual logistic functions (Equation 11.29) each to its own maximum, K value, and slope. Panel b curves fit to the average maximum of the individual curves (common maximum) and average slope of the curves (common n) with only K fit individually. The F value for the comparison of the two models is 2.4, df = 12,18. This value is not significant at the 95% level. Therefore, there is no statistical support for the hypothesis that the more complex model of individual maxima and slopes is required to fit the data. In this case, a set of curves with common maximum and slope can be used to fit these data. 

A comparison of the two models described by equations (9.4.7) and (9.4.8) with fractional crystallization for >j = 0.1 and Dt = 5 and assuming an erupted fraction Y of 50 percent is shown in Figure 9.5 (p. 493). Use of either equation (9.4.7) or equation (9.4.8) leads to quite different patterns of incompatible and compatible elements (Albarede, 1985 Caroff et al., 1993) which makes it possible to discuss the timing of replenishment and eruption events. 

A comparison of the two models with experimental data is given in Figure 12. In the figure, simulations were run with a simple agglomerate model and a... 

Figure 4 Comparison of the two models A (above reaction in the bulk of the liquid) and B (below reaction at the interfacial boundary) [13c],...

Comparison of the two models shows that the spring represents a systen storing energy that is recoverable, whereas the dashpot represents the dissipation of energy in the form of heat by a viscous matmal subjected to a deforming force. The dashpot is used to dmote the retarded nature of the response of a material to any applied stress. 

A comparison of the two models, shown in Fig. 4, indicates that the effect of axial dispersion on the conversion or temperature obtained is not significant. 

Fig. 5.30 Comparison of the two-phase frictional pressure gradient between micro-channel data and homogeneous flow model predictions using different viscosity formulations. Reprinted from Kawahara et al. (2002) with permission...

Finally, a comparison of the two-phase frictional pressure gradient data with the predictions of the Lockhart-Martinelli correlation using different C-values is shown in Fig. 5.32, including C = 5, C = 0.66, C calculated from the Lee and Lee model (2001), and C = 0.24. The conventional value of C = 5 again significantly over-... 

Alternatively, in order to better understand students mental model of particular content area(s), students can be presented with two concept maps which are constructed with the same concept labels and then probed for their interpretation and comparison of the two representations. This approach would help us to understand which organization of concepts students find easier to grapple with and the difficulties they face with respect to certain linkages of concepts. 

FIG. 19. Comparison of the two species model deposition rate as a function of N content with experimental results obtained from CiHi/Ns plasmas. (Reproduced from [74].)... 

In addition, mercury intrusion porosimetry results are shown together with the pore size distribution in Figure 3.7.3(B). The overlay of the two sets of data provides a direct comparison of the two aspects of the pore geometry that are vital to fluid flow in porous media. In short, conventional mercury porosimetry measures the distribution of pore throat sizes. On the other hand, DDIF measures both the pore body and pore throat. The overlay of the two data sets immediately identify which part of the pore space is the pore body and which is the throat, thus obtaining a model of the pore space. In the case of Berea sandstone, it is clear from Figure 3.7.3(B) that the pore space consists of a large cavity of about 85 pm and they are connected via 15-pm channels or throats. 

More recently, we have created full-bed periodic two-layer models for packings of cylindrical particles (Taskin et al., 2006). The geometry shown in Fig. 3b was created specifically for comparison of the WS model with cylindrical particles described in the following section, with the structures identical within a 120° segment of the bed. 

Sq and negative Hq (Figure 7.12), so the handedness of the polymers are correlated to those of the cholesteric phases and the apparent discrepancy depends only on the comparison of the two results at a single temperature. Also in these cases the most common model of Figure 1.9a seems to be followed.46 It should be remarked that in all these cases, Hq and Sq have opposite signs.41... 

The Zimm model is a little more complex to evaluate but is essentially a sum of Maxwell models with a dependence on the sum of the modes as p-i/2 Thjs applies to all but the first few modes. A comparison between the two models is shown in Figure 5.24a and b. 

The Hirshfeld functions give an excellent fit to the density, as illustrated for tetrafluoroterephthalonitrile in chapter 5 (see Fig. 5.12). But, because they are less localized than the spherical harmonic functions, net atomic charges are less well defined. A comparison of the two formalisms has been made in the refinement of pyridinium dicyanomethylide (Baert et al. 1982). While both models fit the data equally well, the Hirshfeld model leads to a much larger value of the molecular dipole moment obtained by summation over the atomic functions using the equations described in chapter 7. The multipole results appear in better agreement with other experimental and theoretical values, which suggests that the latter are preferable when electrostatic properties are to be evaluated directly from the least-squares results. When the evaluation is based on the density predicted by the model, both formalisms should perform well. 

Replicate samples were also excluded to avoid artificially increasing confidence in the classification functions. The subtraction of these seven replicate samples reduced the data set to 60 samples. For the interest of space and clarity, observations and elements excluded from DFA have been omitted from Tables III-V, but may be obtained from the primary author. After excluding limiting the data set to TMs and REEs common to hematite and without missing values, a subcomposition of 11 elements remained. This data set of 11 elements (Fe, Sc, Ti, V, Cr, Mn, Co, Sb, La, Sm, and Th) was transformed into 10 log-ratios for the remaining 60 non-replicate samples for discriminant analysis. The TM and REE model included all 10 log-ratios while the TM model excluded the log-ratios of Sb, La, Sm, and Th. Comparison of these two models... 

In Fig. 10 the operational fields of the two model systems are plotted together to make a comparison possible and assist in the explanation of the experimental findings. 

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