MEIS application, examples

The lacking special description of the Gibbs phase rule in MEIS that should be met automatically in case of its validity is very important for solution of many problems on the analysis of multiphase, multicomponent systems. Indeed, without information (at least complete enough) on the process mechanism (for coal combustion, for example, it may consist of thousands of stages), it is impossible to specify the number of independent reactions and the number of phases. Prior to calculations it is difficult to evaluate, concentrations of what substances will turn out to be negligibly low, i.e., the dimensionality of the studied system. Besides, note that the MEIS application leads to departure from the Gibbs classical definition of the notion of a system component and its interpretation not as an individual substance, but only as part of this substance that is contained in any one phase. For example, if water in the reactive mixture is in gas and liquid phases, its corresponding phase contents represent different parameters of the considered system. Such an expansion of the space of variables in the problem solved facilitates its reduction to the CP problems. 

The examples of specifying the representation of individual expressions in system (7)-(12) and application of MEIS with variable parameters are presented in Section 5. 

In a third example of this methodology Mei et al. [65] produced a polymer containing the fibronectin-based peptide sequence GRGDS, a well-known cell adhesion sequence. This time, however, the polymerization of hydroxyethyl methacrylate was carried out on the sohd support in methyl ethyl ke-tone/propanol (7 3), resulting in a bio-hybrid with a polydispersity of 1.5. This peptide-polymer hybrid material was used as a support for the growth of mouse NIH-3T3 fibroblasts. It was shown that the cells adhered better to the polymer containing the peptide than to the unfunctionalized control polymer. This highhghts one of the many potential applications for protein-polymer hybrid materials. 

Studies on the specific features of MEIS made it possible to work out some modifications of mathematical programming methods that ensure effective application of the considered models. However, great difficulties are met even in the case when a problem solved can be reduced to a CP problem. For example, when applying MEIS of typ>e (8)-(13) they are 1) implicit setting of the constraints on monotony of characteristic functions (inequality (10)) and 2) large (up to 10-12 orders of magnitude) scatter in the values of sought variables, which happens in the analysis of environmental problems. 

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