Case Studies in Modeling

The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation. 

Modeling Material Parameters. In section 1.1.1, we argued that in many instances an extremely powerful idea is that of a material parameter. Whether 

Modeling Dislocation Cores. In an earlier section, we belabored the critical coupling of structure and properties, and this is another arena within which modeling can produce valuable insights. One of our insights concerning the importance of structure was that of the role of lattice defects in governing many 

Modeling Microstructure and its Evolution. Until this point, we have emphasized the virtues of modeling efforts built from the smallest scales up. However, as we have already noted, in many instances it is preferable to construct our theoretical vision on the basis of continuum models. We have already made reference to the critical role of microstructure in determining material properties and it is in this arena that we will consider a case study in continuum modeling. In particular, we consider the problem of a two-phase microstructure in which second-phase particles are dispersed through a matrix and the question under consideration concerns the temporal evolution of this microstructure. In particular, the modeler can ask questions both about the temporal history of particle size and shape as well as about its privileged terminal shape. 

The continuum basis of models of this type of microstructural evolution really amounts to a consideration of the competition between surface and elastic energies. Both the elastic and interfacial energies depend upon the shape and size of the second-phase particles, and may even depend upon the relative positions of 

---

Case Studies in Models with Internal Structure... 

Al7. Sanders, S.J., "Case Studies in Modeling Aqueous Electrolyte Solutions", CChemical Engineering, Accepted for Publication... 

For each of the stages of the model, Petersen (1985) provided a series of flow diagrams to assist analysts in using the model for incident analysis. These are given in Appendix 2B. The use of the model and the flow charts for detailed psychological analysis of incidents is illustrated by a case study in Appendix 2C. 

Leggett RW, Eckerman KF, Williams LR. 1982. Strontium-90 in bone A case study in age-dependent dosimetric modeling. Health Phys 43 3 07-322. 

There is some disagreement as to which parameter is most critical to gas blowout. Based on analysis of C02 phase behavior at different temperatures and pressures, Kamath and Salazar181 concluded that gas blowout becomes hazardous if the temperature of the injected HC1 exceeds 88°F. Panagiotopoulos and Reid182 concluded that HC1 concentration is the critical factor and that HC1 concentrations exceeding 6% will evolve C02 gas and create a blowout hazard. Both sets of investigators explained the circumstances of this case study in terms of their respective models. 

USEtox . In order to make sure that the results provided by USEtox are referred to China, the predicted emissions into the environmental compartments have been calculated using as a basis the information on the e-waste flow and presented in the chapter Tracking Global Hows of E-Waste Additives by Using Substance Flow Analysis, With a Case Study in China. Therefore these emissions are taken as inputs. Table 2 presents a summary with the main values extracted from the aforementioned chapter and used to run the USEtox model. 

In the second part, specific case studies in which the aforementioned models have been applied are presented. The results of such application as well as their reliability are discussed. Toxicological studies in Italy, risk assessment of electronic waste in China, or disposal of bearing lamps in India are some examples of selected scenarios.We hope that the scientific community finds in this book a source of information and inspiration to continue the research on chemical additives contained in products around the world. 

Table 4.4 is the summary of the mathematical model and the results obtained for the case study. The model for scenario 1 involves 637 constraints, 245 continuous and 42 binary variables. Seventy nodes were explored in the branch and bound algorithm. The model was solved in 1.61 CPU seconds, yielding an objective value (profit) of 1.61 million over the time horizon of interest, i.e. 6 h. This objective is concomitant with the production of 850 t of product and utilization of 210 t of freshwater. Ignoring any possibility for water reuse/recycle, whilst targeting the same product quantity would result in 390 t of freshwater utilization. Therefore, exploitation of water reuse/recycle opportunities results in more than 46% savings in freshwater utilization, in the absence of central reusable water storage. The water network to achieve the target is shown in Fig. 4.14. 

I can thank just a few of my colleagues and students who helped develop the case studies in this book. John Yecko and William Roy of the Illinois State Geological Survey first modeled degradation of the injection wells at Marshall, Illinois. Rachida Bouhlila provided analyses of the brines at Sebkhat El Melah, Tunisia. 

Finally, the model needs to prove its applicability in reality and its performance in an industry case study. The model is evaluated with comprehensive industry case data and the relevance of the end-to-end value chain planning approach is evaluated. Opportunities for model extensions are outlined at the end. 

The model is evaluated based on an industry case study in order to... 

Basak, S. C., Mills, D., Hawkins, D. M., Kraker, J. J. Proper statistical modeling and validation in QSAR A case study in the prediction of rat fat air partitioning. In Computation in Modem Science and Engineering, Proceedings of the International Conference on Computational Methods in Science and Engineering 2007 (ICCMSE 2007), Simos, T. E., Maroulis, G., Eds., American Institute of Physics, Melville, New York, 2007, pp. 548-551. 

The working hypotheses and the model were consulted in a multi-stage iterative working process, for the one part, for interpretation of the 13 case studies and, for the other part, were further developed on the basis of findings from the case studies. In addition, the contributions from the events relating to certain sectional subjects were integrated. 

Let us briefly examine modelling of solids, taking silicates as a case study. In order to model silicate structures, it is necessary to develop accurate potentials for the various silicate forms. Such potentials should be able to predict the known structures of zeolites and related materials accurately. Attempts have been made by a number of workers in this direction. The Si04 tetrahedron is the basic building block in silicates. While in... 

The influence of the stems, also studied in model solutions, is summarized in Table XIII (49). Stem extract and stems themselves are added to a solution of anthocyanins the anthocyanin concentration is the same in all cases. The stems decrease the anthocyanin levels and color intensity which is not observed with stem extract alone. These pieces exert their effects through absorption rather than through chemical reactions of one of their constituents. 

Viana M, Pandolfi M, Minguillon MC, Querol X, Alastuey A, Monfort E, Celades I (2008) Inter-comparison of receptor models for PM source apportionment case study in an industrial area. Atmos Environ 42 3820-3832... 

It shall be remarked that the application of PLS modeling for other case studies in the aquatic environment is also described in the literature. SEIP et al. [1994] applied PLS calibration to determine which physical factors determine the phytoplankton mass in lakes. 

The outputs of Step 1 illustrated for the case studies in a box on the next page include a list of the planning team members and their roles identification of decision makers a concise description and a conceptual model of the environmental problem in question and a summary of available resources and relevant deadlines for the project, such as the budget, personnel, and schedule. 

RS. Agachi, Z.K. Nagy, M.V. Cristea, and A. Imre-Lucaci. Model Based Control. Case Studies in Process Engineering. Wiley-VCH, Weinheim, 2006. 

McCarthur, S. (2000) Beyond carrying capacity Introducing a model to monitor and manage visitor activity in forests. In X. Font and J. Tribe (eds) Forest Tourism and Recreation Case Studies in Environmental Management (pp. 259-278). Wallingford CABI Publishing. 

C. Porcelli et al., Regulatory perspectives in the use and validation of QSAR. A case study DEMETRA model for daphnia toxicity. Environ. Sci. Technol. 42, 491 196 (2008)... 

---