Comparison Between Models and Experiments

There are a number of experiments directed at studying the incipience of nucleate boiling in heated channels of hydraulic diameter db = 0.04-20 mm. The overall 

Author Channel geometry Hydraulic diameter (mm) Mass flux (kg/m s) Fluid Heat flux (kW/m ) Pressure (MPa) 

Bergles and Rohsenow (1964) Cylindrical tube 2.387 (2.1-19.4) xlO Distilled water 1,890-18,900 0.261 

Hetsroni et al. (see this book) Cylindrical tube 1.07 49-146 Distilled water 62-162 0.1 

Stoddard et al. (2002) Annular channel 0.724-1.0 85-1,428 FuUy de-gassed water 124-1,000 0.344-1.034 

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Detailed quantitative analyses of the data allowed the production of a mathematical model, which was able to reproduce all of the characteristics seen in the experiments carried out. Comparing model profiles with the data enabled the diffusion coefficients of the various components and reaction rates to be estimated. It was concluded that oxygen inhibition and latex turbidity present real obstacles to the formation of uniformly cross-linked waterborne coatings in this type of system. This study showed that GARField profiles are sufficiently quantitative to allow comparison with simple models of physical processes. This type of comparison between model and experiment occurs frequently in the analysis of GARField data. 

Sequential steps are taken imtil the model provides a statistically adequate representation of the data to within the independently obtained stochastic error structure. The comparison between model and experiment can motivate modifications to the model or to the experimental parameters. 

The simplest and most appealing comparison between models and experiment is through the radial distribution function, which is here denoted by g r) and defined by the equation... 

The predicted results of models 1 and 2, calculated with optimum parameters determined on transient experiment, are compared to experimental results for the gas phase and the surface in Figures 5a and 5b, respectively. It must be pointed out that the periods invariance is not obtained simultaneously for ethylene and the surface ethoxides. The response of ethylene becomes reproducible after a different first cycle (not shown here), whereas the infrtu ed signal is not yet stable. Its value still increases during the following periods, due to a parallel slow adsorption of ethanol under a non-reactive form. This adsorption was also observed in the transient experiment, and consequently was included in the determination of a. Therefore the comparison between models and experiment can only be made on the last period in the case of the adsorbed species. 

Evaluation of Hydrodynamic Correlations - In contrast to mono-disperse systems, most of the hydrodynamic empirical correlations proposed for modelling the settling behaviour of poly-disperse systems (see for example Williams and Amarasinghe [6]) have been mainly confined to relatively concentrated systems (> 5% v/v). This is because as opposed to the dilute systems such as those encountered in the present study, these are easier to model since they are characterised by well defined interfaces the settling of which is largely representative of the bulk behaviour of the suspension. Accordingly all comparison between model and experiment presented here is confined to mono-disperse systems. 

Figure 2.8. Comparison between modeling and experiment for Young s modulus as a function of the hard segment chemistry and weight fraction. All calculations correspond to room temperature (T = 298 K) and PO equivalent weight of 1000 g/inol. Functionality fp= 2 for MDI-BDO-PO and MDI-DETDA-PO, and fp = Z for TDI-PU-PO elastomers [33]...

Figure S.11. Comparison between the predictions of a micro-kinetic model and measurements on a Cu(lOO) model catalyst with a real methanol synthesis catalyst. The full line represents the ideal match between model and experiment. [Adapted from P.B. Rasmussen, P.M. Holmblad, T. Askgaard,...

This makes a convenient point of contact with theory since models for adsorption inevitably subdivide the surface into an array of adsorption sites that gradually fill as the pressure increases. If 6 is defined as the fraction of sites filled, then 6 = 1 corresponds to monolayer coverage, with 8 < 1 or 6 > 1 to submonolayer and multilayer coverages, respectively. Theoretical isotherms predict how 6 varies with p in terms of some particular model for adsorption. It turns out that a set of experimental points can often be fitted by more than one theoretical isotherm, at least over part of the range of the data that is, theoretical isotherms are not highly sensitive to the model on which they are based. A comparison between theory and experiment with respect to the temperature dependence of adsorption is somewhat more discriminating than the isotherms themselves. 

As already described, the upper three portions of Figure 2 summarize the differences in the way the constraints are applied in the constrained-junction theory, constrained-chain theory, and the diffused-constraints theory, respectively [4], Additional comparisons between theory and experiment for a variety of elastomeric properties should be very helpful [20], Also, neutron-scattering measurements conducted on series of networks having different values of the junction functionality , which is the number of chains emanating from a junction (cross-link), would be extremely useful in suggesting how to position the constraints along a chain in refining such models, since should have a pronounced effect on the... 

A number of theoretical models for solvation dynamics that go beyond the simple Debye Onsager model have recently been developed. The simplest is an extension of Onsager model to include solvents with a non-Debye like (dielectric continuum and the probe can be represented by a spherical cavity. Newer theories allow for nonspherical probes [46], a nonuniform dielectric medium [45], a structured solvent represented by the mean spherical approximation [38-43], and other approaches (see below). Some of these are discussed in this section. Attempts are made where possible to emphasize the comparison between theory and experiment. 

This comparison never shows a perfect correspondence between models and experiments because of modeling and measurement errors. In fact, even if the presence of systematic experimental errors can be excluded, systematic errors generated by the inadequacy of the model must be added to random experimental errors for each measured variable (m = 1,..., Am) and each experimental time (j = 1,..., Ad), the errors generated by the model are defined as... 

OR and CD have for a long time been recognized as being very sensitive to the molecular environment. This hampers the comparison between theory and experiment, since the calculations are usually carried out for a single isolated molecule, whereas the measurements are usually conducted in liquid phase. Thus, attempts to account for solvent effects were undertaken at an early stage of theoretical modelling of natural optical activity. 

In spite of the previous comment, comparison between simulations and experiments (not presented here ) is fully convincing as far as the purpose of such a model is to allow predicting the burst pressure of a vessel when the thickness of the liner and the stacking sequence are known. It means for every burst pressure and consequently for any use pressure, one or several stacking sequences may be found to ensure the strength of the structure. 

These fits, although excellent, do not mle out the alternative exciton model. To judge which better describes the data, one needs a similar critical comparison between theory and experiment based on the exciton model. When such a quantitative comparison is made, one finds a fundamental discrepancy between the exciton model and the experimental results The exciton model predicts a symmetric absorption lineshape for oriented materials in which the conjugated polymer is chain aligned and chain extended. 

One major topic of the work is an extension of the CFD code with a post-processor for the fuel nitrogen to NOx conversion, A reduced kinetic scheme has been obtained which describes quite well the combustion emission behaviour with respect to NOx formation. Figure 9 shows a comparison between experimentally observed NH conversion to NO and modeling with this modified post processor. The agreement is reasonably good for experiments at 0.5 and 0.7 Mpa. Significant deviation between model and experiment is seen for an experiment at 0.4 MPa. This is attributed to a measurement error at that pressure, A recommendation is to perform more experiments at this or lower pressure. 

The quality of a regression can also be assessed by visual inspection of plots. Of course, some plots are more sensitive than others to the level of agreement between model and experiment. As will be demonstrated in this chapter, the plot types can be categorized as given in Table 20.1. The comparison of plot types is presented in the subsequent sections for regression of models to a specific impedance data set. 

Eigure 9 shows the comparison between theory and experiment for the missing-row model of the Ag(110)-(2 x l)-0 system. After consideration of all possible (2 X 1) reconstructions, the missing-row model has the lowest (best) R-factor, i.e., a one-parameter expression for the quality of ht between two curves. 

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