Comparison of different models

S. Altmeyer, V. Mathieu, S. Jullemier, P. Contal, N. Midoux, S. Rode, J.-P. Leclerc, Comparison of different models of cyclone prediction... 

Comparison of Different Models with the Experimental Data of Wagner and Kerker (12) ... 

Diepold, R., Kreuter, I, Himber, J., Gurny, R., Lee, V. H., Robinson, J. R., et al. (1989), Comparison of different models for the testing of pilocarpine eyedrops using conventional eyedrops and a novel depot formulation (nanoparticles), Graefes Arch. Clin. Exp. Ophthalmol., 227(2), 188-193. 

Figure 3 Comparison of different models for the trace-element composition of the upper-continental crust. All values normalized to the new composition provided in Table 3. Gray shaded field represents 20% variation from this value for all panels except (f), in which gray field represents a factor of two variation. Trace elements are divided into the following groups (a) transition metals, (b) high-field strength elements, (c) alkali, alkaline-earth elements, (d) REEs, (e) actinides and heavy metals, and (f) highly siderophile and chalcophile elements (note log scale). Data from Tables 1 and 2 lanthanum estimate from Eade and Fahrig (1973) is omitted from panel D.

Table 2.8 Comparison of Different Models for Estimating the Substituent Effect in Aniline (Adapted from Murrell, 1963)...

Depending on the purpose of the data analysis, several different models maybe appropriate. Choosing which model is better is therefore part of the overall validation procedure. For calibration problems, different models can be compared in terms of how well they predict the dependent variables. Sometimes a priori knowledge of the structure of the data is available (e.g., that fluorescence data can be well approximated by a trilinear model), but often this is not the case. If no external information is available on which comparison of different models can be based, other approaches have to be used. In the following, a discussion is given of how to assess the appropriateness of the model based on the mathematical properties of the data and the model. No exact rules will be given, but rather some guidelines that may be helpful for the data analyst. 

Alonso, E.E, and J. Alcoverro, FEBEX benchmark test case definition and comparison of different modelling approaches, this volume, 2004,... 

AD-equation a Peclet number of Pe=10 is used. This gives a spread in the RTD (dispersion) that is within the range of observed values in the field. The standard deviation of the transmissivities of the channels in the network model was chosen such that the RTD of a nonsorbing tracer also has a Pe=10. In the time scale presented there seem not be dramatic differences between the model results for the Network and the AD-models. It should be noted, however, that the early arrival times are of special interest for radionuclides that decay. There the differences are considerable. Similar results were obtained in comparisons of different models using very similar data bases (Selroos et a. 2002). In that comparison a discrete fracture network model, a channel network model and a stochastic continuum model were used. 

THE FEBEX BENCHMARK TEST. CASE DEFINITION AND COMPARISON OF DIFFERENT MODELLING APPROACHES... 

Figure 3-9. Comparison of different models of non-equilibrium vibrational energy distribution funetions in nitrogen Ty = 3000 K, To = 800 K.

The distributions of D values are displayed in Figure 10. The means of these three distributions are -0.0041 (Plot A), -0.0305 (Plot B) and -0.0264 (Plot C), respectively. Using a two-side t test, it is shown that all these three distributions of D values have a mean value that is significant not zero with P values equal to 0, 0 and 0 for Plot A, Plot B and Plot C. To conclude, this section provides illustrative examples for the comparison of different modeling methods. Our example demonstrates that PIS (an ECR model associated with a 1) performs better than PCR (an ECR model associated with a = 0) and a specific transitional ECR model associated with a = 0.5 has the moderate performance. 

Figure 1. Comparison of different models for elastic modulus, r =2.

Table 5 Comparison of different models and equations describing the deformation behavior of materials... 

K. R. Ward, N. S. Lawrence, R. S. Hartshorne, and R. G. Compton. The theory of cychc voltammetry of electrochemically heterogeneous surfaces Comparison of different models for surface geometry and applications to highly ordered pyrolytic graphite, Phys. Chem. Chem. Phys. 14, 7264-7275 (2012). 

Comparison of different models for risk analysis to estimate the manpower in the case of roughly defined project s tasks... 

Figure 5.29. Comparison of different model approaches to endogenous metabolism and maintenance by showing the validity of the different model parameters k, and mg.

Xu, C., Xu, X.W., Dai, F.C., Saraf, A.K. 2012b. Comparison of different models for susceptibility mapping of earthquake triggered landslides related with the 2008 Wenchuan earthquake in China. Computers Geosciences 46 317—329. 

Schweisfurth, T., Raasch, C., and Herstatt, C. (2011), "Free revealing in open innovation A comparison of different models and their benefits for companies," International Journal of Product Development, 13 (2), 95 -118. 

Zhao M, Zhou XH, Jiang Q (2001) Comparison of different models for melting point change of metallic nanocrystals. J Mater Res 16(ll) 3304-3308... 

Wood (2002) has recently made an extensive comparison of different models for predicting mixture adsorption from single-component D-R isotherms. The data of a total of 93 binary mixtures of organic vapors on activated carbon were compared. Despite the simplicity of the model (Eqs. 3.11 and 3.12), predictions were among the best. 

Mosche M, Jordening HJ (1999) Comparison of different models of substrate and product inhibition in anaerobic digestion. Water Res 33 2545-2554... 

Tian, L. and Ahmadi, G. (2007). Particle Deposition in Turbulent Duct Flows - Comparisons of Different Model Predictions, J. Aerosol Science, Vol. 38, pp. 377-397. 

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