Optimization, EMMS model

This is a nonlinear optimization problem with eight parameters and nine constraints, called energy-minimization multi-scale (EMMS) modeling, from which the parameter vector X and various energy consumptions can be calculated. 

The EMMS model is a nonlinear optimization problem involving eight parameters and nine constraints consisting of both equalities and inequalities,... 

A simphfied way is to decouple the two approaches first, the stabihty condition serves as the close law for the simphfied algebraic conservation equations, as described by the EMMS model for gas—hquid and gas—solid systems. The nonlinear optimization problem can therefore be solved to obtain the global or local structure parameters which are then be used to derive the closure law or correlations for the drag, bubble-induced turbulence and even the correction factors for the kernel functions of bubble coalescence and breakup for PBEs. 

The optimal combination of the EMM process parameters and their combined effect on MRR and accuracy is found out based on the developed second-order mathematical models, i.e., Eqns (8.2) and (8.3) for correlating the various process parameters effects with MRR and machining accuracy. Optimum factor levels that will maximize the MRR and minimize the accuracy related responses, i.e., WOCs are calculated and are listed in Table 8.4 for single optimization along with its predicted responses. MRR... 

These equations in principle solve the problem of combined geometry optimization. However, some interactions in Eq. (32) are counted twice, in the QM and in the MM terms (note that the MM layer contains the whole real system). Therefore the MM interactions in the model system which are fully taken into account in the QM calculations should be excluded from the Emm energy. This is just taken into aceount in Eqs. (27) and (28), according to which the difference... 

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