Tests of the Model

Fragments of the kinetic model may be tested by detailed simulation of the same experiments as have been used to determine the parameters in the model. Failure to reproduce these experiments is entirely possible if a wrong reaction mechanism has been assumed. 

A sensitive test can be made by simulation of a reactor through numerical integration of the rate expression. This will test the model at higher pressures, frequently at higher coverages, in the presence of all reactants, intermediates and products. 

The model can be further tested for internal consistency. Steps treated through kinetic equations should be slow at least under some conditions or the model may obviously be 

While the number of parameters may be large, only a few of the parameters are usually significant. The significant parameters are easily determined by calculation of the sensitivity of the calculated rate at typical conditions to a small variation in the value of each parameter. For the NH3 synthesis, for instance, the rate of dissociation of N2 and the binding energy for N are the most significant parameters and the kinetics of desorption of N2 in a TPD experiment is rather closely related to the kinetics of NH3-synthesis. 

Once the kinetic model passes the tests, the model may be used to understand details of the catalytic reaction, such as the origin of the macroscopic activation energy, the reaction orders or the structure of empirical kinetics. 

In order to decide whether this model is correct, we have been searching the ACD database of commercially available compounds by use of two-dimensional search techniques with visual inspection of the hits [6]. Possible candidates were optimized and compared to the model. By this method, one single compound (4) was found that fits into the model. The enantiomers of 4 were separated, and one enantiomer showed some in vitro inhibitory activity (see Table 1) the other was inactive. 

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There is nothing unique about the placement of this isolated segment to distinguish it from the placement of a small molecule on a lattice filled to the same extent. The polymeric nature of the solute shows up in the placement of the second segment This must be positioned in a site adjacent to the first, since the units are covalently bonded together. No such limitation exists for independent small molecules. To handle this development we assume that each site on the lattice has z neighboring sites and we call z the coordination number of the lattice. It might appear that the need for this parameter introduces into the model a quantity which would be difficult to evaluate in any eventual test of the model. It turns out, however, that the z s cancel out of the final result for, so we need not worry about this eventuality. 

It has been pointed out that analysis of terpolymerization data or copolymerization with chain transfer could, in principle, provide a test of the model. 5 However, to date experimental uncertainty has prevented this. 

Cornett RJ, Rigler FH (1980) The areal hypolimnetic oxygen deficit an empirical test of the model. Limnol Oceanogr 25 672-679... 

Thus, the basic tests of the model indicate reasonable fit to the data, randomly distributed errors, and a linear relationship. Therefore, this model can be used to predict the behavior of the electrochemical potential. 

An important issue is the reliability of the model over the entire United States. EPIC was tested for accuracy in estimating ET and Q by many investigators on data gathered from the United States and other countries. Numerous tests of the model are described by Sharpley and Williams70 and by others. Model tests by others are summarized below in each of these evaluations, EPIC produced accurate estimates of ET and Q. 

A more stringent test of the model is its ability to predict the histogram in Figure 10-5. 

The inverse problem to simulation from a reaction mechanism is the determination of the reaction mechanism from observed kinetics. The process of building a mechanism is an interactive one, with successive changes followed by experimental testing of the model predictions. The purpose is to be able to explain why a reacting system behaves the way it does in order to control it better or to improve it (e g., in reactor performance). 

This phase is intended as a final check of the model as a whole. Testing of individual model elements should be conducted during earlier phases. Evaluation of the model is carried out according to the evaluation criteria and test plan established in the problem definition phase. Next, carry out sensitivity testing of the model inputs... 

A very sensitive test of the model is the comparison of calculated and observed structure functions this is shown in Figs. F and G. Note that the central force model yields the characteristic double peak in sh(s) near 2.5 A-1. That the theoretical curve oscillates with greater amplitude than the experimental data indicates that the predicted distribution of near neighbor 00 separations is too narrow. The comparison with neutron diffraction data shows that the theoretical... 

The model was claimed to compute 5000-6000 molecules per min. The predictive ability of the model was validated by four approaches. In the first approach, a set of 20 compounds was randomly selected as an initial validation test set. A model was developed from the remaining 86 compounds with an MAE of 0.33, from which the test set values were then predicted. The results of this test prediction were very good and provided momentum for support of the three structure descriptors. In the second approach, a full cross-validation test of the model was investigated. The data set of 102 compounds was divided... 

See Samdahl, D. M., and R. Robertson. (1989). Social determinants of environmental concern A specification and test of the model. Environment and Behavior 21 57-81. 

However, the number of concentrations being fitted is fairly small, compared with the number of parameters going into the model. The computer calculations can be used to predict the concentrations of other trace compounds that should be present in smog chambers. If these compounds are later found at approximately the predicted concentrations, the model will be strengthened. If not, changes will have to be made in the model. A more stringent test of the model will occur when it becomes... 

Salt spray test. The model coatings of Table I are of the high solid type used in automotive top coats. Their primary function is not corrosion protection since this is first of all a matter of phosphate layer, electrocoat and/or primer. However, the topcoats may contribute to corrosion protection by their barrier function for water, oxygen and salts. Therefore their permeability is important as one of the factors in the corrosion protection by the total coating system. We feel that a salt spray test of the model coatings directly applied to a steel surface is of little relevance for their corrosion protection performance in a real system. 

When we talk about tracers, we generally mean conservative tracers with no sources or sinks. This is opposed to gas tracers, with gas transfer to the atmosphere, and reactive tracers, with a reaction occurring. Tracer studies typically use a conservative tracer, input to the system in a highly unsteady manner, such as a pulse or a front. The pulse and front are typically a more stringent test of the model than a steady-state process with any variety of reactions. Thus, a model that properly simulates the output concentration curve of a pulse or front is assumed to be sufficient for most real conditions with reactions. 

Residual oil combustion impact served as a test of the model s ability to predict point source emissions. Since vanadium and nickel emissions in Portland are almost totally associated with residual oil use, the CMB method was able to assign impacts with a high degree of confidence by using these two elements as chemical tracers. 

Even if it were possible to explain the cosmological redshift phenomenon by de Broglie s aging photon model, the practical feasible direct test of the model is not easy to perform because the minimum necessary distance for the aging effect to be noted is considerable. Let us make a rough estimate of this distance, assuming that the cosmological redshift is due only to the interaction of the photon with the subquantum medium. 

It might also be noted that K (Equation (62)) may be related to AG° for the adsorption process if the model applies to the experimental system. Therefore, from studies of adsorption at different temperatures, values of AH° and AS0 may be determined for the process described by Equation (61). It must be emphasized that compliance with the form predicted by the Langmuir isotherm is not a sensitive test of the model therefore interpretations of this kind must be used cautiously. 

Thus the mobility picture for water fully loaded into NaX zeolite fits together at least semiquantitatively. Further tests of the model based on newer NMR techniques have been proposed (9) and are in progress. Diffusion and other NMR data (45, 45) indicate on the one hand that the water mobility is greater at lower than maximum loadings, but on the other hand that the picture is not that simple. A theory based on fractionally filled cages in equilibrium with filled cages seems to be required. 

First, is the model or simulation designed in a way that it can be used by a key customer or key supplier Are you designing for accessibility The use of your model by others is an excellent test of the model s accessibility. When one of your key customers or key suppliers is using your model in a way that you never expected it to be used, your model has succeeded. It is tremendous to leam that your research and development has become market research. 

The first part of the present work describes the wind erosion model of a horizontal particle bed. A simple test of the model is presented in the second part, which reports the influence of a wide size distribution on the emitted mass flux of particles. 

The take-off test of the model developed in the present study allows to simulate the stochastic nature of the phenomenon. The establishment of the take-off criterion is detailed more precisely in the thesis of Descamps [12],... 

However, the test of the model becomes much more severe if it is required that this model, with its parameters unchanged, fit the spectra of neighboring nuclei as well. 

Example number 4, r. = 0.16, r2 = 0.82, shows the closest agreement with the experimentally observed values. A more rigorous test of the model is the prediction of the intermediate triad fractions. Figure 6 illustrates the change in triad probabilities as a function of conversion... 

The model overestimated final liver chromium concentrations, but bone and kidney concentrations were well-predicted. This was not a completely independent test of the model s validity since data from this study were used to set parameters for fractional uptake of chromium into bone. 

The purpose of the modeling was to examine the influence of the solution environment on the extent of dissociation of an organic acid. A series of studies was performed initially to establish the validity of the model in preparation for later work. An initial test of the model was to vary the PD value and monitor the concentration of products. As expected, an increase in the PD rule produced an increase in the calculated acid dissociation constant K. A second study examined the influence of acid concentration on the observed properties. As expected, the KA was approximately constant over a modest concentration range. A third study considered the effect of water temperature on the acid dissociation. As the modeled water temperature was increased by increasing the Pb(W) value, the value of the KA decreased, in agreement with a common, but not universal, observation of the effect of temperature on acid dissociation. These three preliminary studies thus revealed emerging attributes consistent with experimental observations. 

The text reviews the methodology of kinetic analysis for simple as well as complex reactions. Attention is focused on the differential and integral methods of kinetic modelling. The statistical testing of the model and the parameter estimates required by the stochastic character of experimental data is described in detail and illustrated by several practical examples. Sequential experimental design procedures for discrimination between rival models and for obtaining parameter estimates with the greatest attainable precision are developed and applied to real cases. 

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