Freedom Analysis and Problem Formulation

The K j are the equilibrium ratios or K values for species i on stagey. Degrees-of-Freedom Analysis and Problem Formulation... 

The formulation of the NLP for application to large process design problems begins with the steady-state simulation of the process flowsheet for a nominal set of specifications or decision variables. As described in Section 4.2, during the creation of the simulation model (involving the material and energy balances, kinetic equations, etc., for the process units), a degrees-of-freedom analysis is performed. For the simulation model, the number of variables, normally exceeds the number of equations, N uaiions. with... 

Normalization expressions for molar fractions are additionally included in the problem formulation. The set of balance expressions 6.1 and 6.2 turns to be well-posed by specifying appropriate decision variables according to a degree of freedom analysis. Thus, for a given set [n-c, nteed, V] and an extent of reaction , the modeling... 

The vehicle for the analysis of the scattering problem will be the Wigner-Eisenbud R-matrix formulation. We consider a quantum system with two degrees of freedom represented by coordinates q for the nuclear motion and x for the electronic part. The domain for these variables will be such that the coupling between the two coordinates is considered only when q belongs to the interval [r,p]. The domain for the electronic coordinate is arbitrary, the space will instead be limited by a choice of two basis functions. 

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