Aggregation efficiency, modeling

The actual calculation of such an efficiency is accomplished by methods demonstrated by Muralidhar et al (1988), referenced in footnote 28. The objective of the discussion herein has been to provide broad guidelines for modeling of the aggregation efficiency, since mechanisms and (hence details) in individual applications can vary rather diversely. Before concluding this discussion, we refer to one further aspect of modeling that can produce valuable simplifications in the foregoing treatment. Such simplifications arise from a consideration of times scales as in the treatment of Muralidhar and Ramkrishna (1986). 

The simplicity of this model allows an analytical solution to the boundary value problem (3.3.60)-(3.3.62) so that an explicit expression is possible for the aggregation efficiency. For details of such analytical solutions, the reader is referred to Das et al (1988). 

As noted earlier, environments such as water/methanol mixtures are useful models of membrane environments. These mixed solvents lead to a reduced efficiency of 02 quenching and the quenching becomes negligible at high water concentrations. Figure 14.2 shows an example of this behavior for zeaxanthin (ZEA), as the aggregation of ZEA is increased. 

Despite advances in MILP solution methods, problem size is still a major issue since scheduling problems are known to be NP-hard (i.e., exponential increase of computation time with size in worst case). While effective modeling can help to overcome to some extent the issue of computational efficiency, special solution strategies such as decomposition and aggregation are needed in order to address the ever increasing sizes of real-world problems. 

To conclude, the models proposed below are in good agreement with the empirical data and allow a first approach to an efficient rational design of homochiral bases. However, they only take the major NMR or X-ray observable solution HCLA complexes into consideration minor aggregates involving allylic alcoholate or protonated amine products, that might be reactive and contribute to the product formation, are ignored ... 

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