Predictions compared with interpolation

Table III also includes on line (d) for each composition the interpolated experimental result obtained from a computer fit to the 29si NMR data (11). The predicted distributions (b) in Table III are compared with the experimental data in Figure 4.

In order to check if the predictions are interpolations or extrapolations, the simplest test is to compare the values of the PPs on the predicted compounds with those in the training series, or simply inspect the position of the predicted compounds in a score plot together with the compounds in the training series. Other, more sophisticated methods have been suggested elsewhere [13],... 

Figure 2.20 Predictions using extrapolation compared to the prediction obtained with the unmodified interpolation (first row of Tables 2.4 to 2.6).

Comparisons between observed data and model predictions must be made on a consistent basis, i.e., apples with apples and oranges with oranges. Since models provide a continuous timeseries, any type of statistic can be produced such as daily maximums, minimums, averages, medians, etc. However, observed data are usually collected on infrequent intervals so only certain statistics can be reliably estimated. Validation of aquatic chemical fate and transport models is often performed by comparing both simulated and observed concentration values and total chemical loadings obtained from multiplying the flow and the concentration values. Whereas the model supplies flow and concentration values in each time step, the calculated observed loads are usually based on values interpolated between actual flow and sample measurements. The frequency of sample collection will affect the validity of the resulting calculated load. Thus, the model user needs to be aware of how observed chemical loads are calculated in order to assess the veracity of the values. 

With porous membrane DS devices of this geometry and for thin membranes with low-tortuosity pores (i.e., where the diffusion distance within the pores is very small compared to the radial diffusion distance in the DS), good predictions for the collection efficiencies can be obtained if the nominal X and dfd0 values are both multiplied by the fraction of the surface that is porous. For example, with a diffusion scrubber based on such a membrane tube (L = 40 cm, dQ = 0.5 cm, d = 0.045 cm, fractional porosity 0.4), the corrected X values for H20.2 as sample gas are 0.32, 0.16, 0.11, and 0.08, respectively for Q = 0.5, 1.0, 1.5, and 2.0 L/min, and the corrected djda value is 0.036. The collection efficiencies predicted from Figure 1 (interpolating between dfdQ values of 0.02 and 0.05) are in good agreement with... 

Table 1 compares the dimensionless coagulation coefficient predicted by the present model with other models. Since the Hamaker constant for most of the aerosol systems is of the order of 10"12 eig, this value is used in the calculation of the lower bound. Particle diffusion coefficients based on Philips slip correction factor for an accommodation coefficient of unity are used for the calculation of the coagulation coefficients ft (the Fuchs interpolation formula) and fts (the Sitarski... 

Figure 15.7 shows that models 1-3 perform equally well for the prediction of polymerization rate (Fig. 15.7a) and molecular weight development (Fig. 15.7b). However, the predictions of monomer and solvent concentrations in both phases differ significantly (Fig. 15.8). Moreover, when interpolating the parameters of these three models to consider a system with lower pressure, and now comparing models 1, 2, and 4, it is observed that models 1 and 2 perform poorly, and model 4 reproduces reasonably well the behavior of this system (Fig. 15.9).

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