Entirely Incorrect Models

Although an important pioneering effort, this model proved to be entirely incorrect... 

In trying to obtain the term symbols for the [Ar]4s 4p excited state configuration of V, a professor obtains the 7/2 term symbol, among others. State two reasons why this is clearly incorrect, without attempting to solve the entire vector model. 

In this book, mathematical formulations are posed for well-defined physical problems and solved using rigorous solution methods. Assumptions are clearly stated and ad hoc analysis methods are avoided. In order to appreciate this philosophy, it is necessary to understand the proliferation of incorrect models and solutions in existing literature and software. A review of these formulations is imperative to teaching sound mathematics. But it is also important to petroleum engineers who purchase software responsible for field development and major financial commitments. For these reasons, we will explain common errors and their ramifications. To be entirely fair, only those problems that are actually solved in this book are listed and discussed here. 

The shortcomings of such investigations can be interpreted as (a) the starting fibrillar model is of insufficient accuracy to mimic the changes imposed by the mechanisms of distortion or (b) the emphasis, or even the entire basis, for the mechanisms of distortion is incorrect. 

No matter how rigorous the validation procedure of a model, it is important to realize that the model may give incorrect predictions for some chemicals because it is impossible to determine the entire chemistry space. Any QSAR model has to be considered as a living model that is improved when new data are available. 

To be sure, the first criterion, of conforming with all experimental results, is hardly ever met in practice. Where deviations show up, the design of the experiments, their evaluation, and the reproducibility of the results must be checked. Often, the disagreement can be traced to an artifact, an equipment malfunction, a calculation error, an incorrect entry in a lab record book, or some other extraneous source, and can then be safely disregarded. However, if a divergent result is confirmed, the proposed model is inadequate and must be refined or entirely rejected. 

Since charge compensation requires a modification of the charge density, changes of covalency at the surface are often assumed to heal the polarity. With the help of the bond transfer model, one can show that this statement is incorrect, as far as semi-infinite polar surfaces are concerned. It is useful to make a distinction between weakly polar surfaces, in which the dipole moment in the repeat unit is entirely due to covalent effects, and truely polar surfaces whose dipole moment contains an integer contribution. As already said, in the fully ionic limit, the first ones are considered as nonpolar, while the second ones are recognized as polar. 

Last note that the proper use of these QSAR models designed for molecules with a specific MOA requires that we can assign a molecule to its appropriate class. This task represents a major hurdle in ecological risk assessment, since incorrect mode-of-action-based QSAR selections can result in 10- to 1000-fold errors in toxicity predictions [66], Solutions have been proposed to overcome this problem [65,67-71], but in practice, none is entirely satisfying. The different modeling strategies proposed to solve this crucial problem are presented in the next section. 

In school, Bohr received his poorest marks in composition and struggled with writing during his entire life. In fact, he wrote so poorly that he was forced to dictate his Ph.D. thesis to his mother. Nevertheless, Bohr was a brilliant physicist. After receiving his Ph.D. in Denmark, he constructed a quantum model for the hydrogen atom by the time he was 27. Even though his model later proved to be incorrect, Bohr remained a central figure in the drive to understand the atom. He was awarded the Nobel Prize in physics in 1922. 

Water diffusion and solubility have been measured for a wide range of glass compositions, including a number of studies for vitreous silica, alkali silicates and aluminosilicates, soda-lime-silicates, and alkali borates and germanates. Early models for diffusion suggested that the diffusivity of water in melts was controlled entirely by the viscosity of the melt, as predicted by the Stokes-Einstein equation. This equation predicts that the diffusivity of a spherical particle in a liquid is inversely proportional to the viscosity. This hypothesis has been shown to be quantitatively incorrect by 4 orders of magnitude, to predict a much... 

One final concern with the use of the feature model is its central role in deciding what reusable artefacts are included. If the feature model is incorrect, it has consequences for the validity of the hazard assessment, the safety claims and the entire safety case. To offset this concern, we note our assumptions that ... 

This reservoir flow analysis and simulation book is unique beeause it brings two deeades of perspeetives and experience on the fluid mechanics of Darcy flows. Many commonly accepted recipes for flow evaluation are critiqued, and incorrect underlying assumptions are noted. This volume aims at a rigorous and scientifically correct approach to reservoir simulation. In each of dozens of difficult problems surveyed, the state of the art is examined, and analytical or numerical solutions are offered, with the exact physical assumptions always stated precisely. Industry common sense approaches are avoided once the correct model is formulated, the entire arsenal of analysis tools is brought to bear — we then focus on ways to extract formation information using the new solution or clever means to exploit the physics uncovered. 

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