Model and reality

In this section we will discuss in some detail the relationship between molecular mechanics force field parameters and real physical parameters. As mentioned before, the fundamental difference between spectroscopic and molecular mechanics force fields is that the former are molecule-specific while the latter are general. Empirical force field parameters can be used for the calculation of unknown structures and their strain energies, and for the prediction of vibrational frequencies of new compounds. However, the parameters themselves generally have limited meaning. 

For example, the r0 value for the Co-N bond in cobalt(III)-amine complexes is smaller in parameterization schemes where 1,3-nonbonded interactions between the ligating atoms are included, than in force fields where only L-M-L angle bending functions are used. This is because the 1,3-nonbonded interactions in such complexes are highly repulsive, promoting an extension of the Co-N bonds. Thus, a smaller value for the ideal Co-N bond is required in order to reproduce the experimentally ob- 

Obviously, it would be of interest to know what the true ideal metal-ligand bond length is. Some studies, particularly some of those aimed at predicting metal ion se-lectivities based on hole size calculations, require accurate values for r0. The question 

As the bond lengths increase the difference between the r0 values for the two types of force fields decreases because the 1,3-nonbonded interactions become less repulsive. 

Another way to demonstrate this effect is shown in three sample calculations using the MOMEC force fieldt52-57 58 96 99-124-140 155) jn Table 3.5 the experimental M-N distances (r(obs)), the calculated bond lengths (r(calc)), the corresponding force constants (k) and ideal bond lengths (r0) are shown for some sample calculations of some hexaamminemetal complexes. 

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Effect of Transformation Processes The Role of Colloids in Pollutant Transport Models and Reality... 

Brown, J.H. 1994. Complex ecological systems. In Complexity Metaphors, Models, and Reality. Vol. XIX of Santa Fe Institute Studies in the Sciences of Complexity, G.A. Cowan, D. Pines and D. Meltzer, Eds. Addison-Wesley, Reading MA, pp. 419-433. 

Simulation has emerged as an important tool for extrapolating from scenarios that generated the data for model development activities into scenarios of potential interest for the drug development program (15). Similar to the model development process, effectiveness in the case of simulations is the correspondence between the model and reality. Efficiency hinges on the applicability of the results as the target scenarios step outside the boundaries of the initial model. Here we need to ask about the extensibility of the simulation results and how broadly applicable the results are. 

Before any further calculations, the water saturation in the microscopic model developed above should be calibrated to experimentally determined values. The saturation discrepancy between the model and reality results mainly from two sources that the microscopic model cannot address one is connate water saturation (Swc) and immobile oil saturation (Sd) the other is the wettability effect of irregular particle surfaces. If we assume that water saturation remains as a constant (S g) until water breakthrough occurs, the calibration can be carried out as... 

Ti the coefficient defined to balance porosity difference between the model and reality, dimensionless... 

These levels were used by Harrison Treagust (1996) whilst investigating students mental models of atoms and molecules. Most of the students in their sample (58%) were classified at Level 1 because they thought that there was a strong correlation between the structure of the models and reality. For instance, almost all of these students said that an atom is like a ball or sphere . The other 42% of the students were said to be at Level 2 because they were able to express some difference between... 

If we copy the time scale of the theoretical braking deceleration curve onto the figure which shows the measured abutment movements, we can also see, that the character of the movements is identical to the theoretical curve. Model and reality are corresponding. The maximum amplitude of the movement is about 0.5 mm during stopping the train. The accuracy is represented by the noise of the measurements and has a value of 0.1mm. This is the result if we use only an electronic camera as measuring instrument. All other brake tests show much the same results. So our example is representative for the selected test bridge. 

Figure 4.6 Model and reality tailored from [NUREG 0492 (Fig 1-3)].

All these simulations refer to the Ising model on the simple cubic lattice. Of course, also more comphcated lattices have been studied, and Fig. 2 shows a comparison of a hep simulation with solid helium. Again model and reality agree nicely. The Ising model has also been used to study oil-water systems where amphiphilic molecules may form membranes, micelles, and vesicles [15]. 

For operations as complex as the active runway example considered, a simulation model will always differ from reality. Hence, validation of the MC simulation results does not mean that one should try to show that the model is perfect. Rather one should identify the differences between the simulation model and reality, and subsequently analyse what the effects of these differences are in terms of bias and uncertainty at the assessed risk level of the model. If the bias and uncertainty fall within acceptable bounds, then the assesed risk levels are valid for the specified application. Otherwise one should improve the MC simulation model on those aspects causing the largest bias and uncertainty influence on the assessed risk level. Five types of differences between simulation model and the real operation can be distinguished (Everdij and Blom, 2002) ... 

Uncertainty. In addition to a systematic bias, the differences between simulation model and reality may induce uncertainty in the difference between the safety risk of the real operation and the safety risk resulting from the simulation model. 

Identify all differences between the simulation model and reality ... 

Zhang L, Diflert R, Bahnemann D, Votmoor M. Photo-induced hydrophilicity and self-cleaning models and reality. Energy Environ Sci 2012 5 7491-507. 

In this step the model is fitted to the measured data. Usually, the error between model and reality is minimized. 

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