By Do D.D.
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Extra info for Adsorption analysis: Equilibria and kinetics
The functional Mi that relates the recorded experimental measurement Mi to the underlying species concentrations and other state variables could in principle be quite complicated, but often it is linearly dependent on just a few of the species concentrations at some time tmeasurement. As discussed in a later section, our estimate of the error bar in the model prediction for a ﬁxed x might depend on x, that is why ui(x) is written in Eq. (21). While this is conceptually simple, numerically it is very difﬁcult to ﬁnd the global maximum of P, because of the fact that the dependence of Y on x is only known implicitly through a complicated numerical procedure (solving the whole simulation).
Fraction of the grid points used by various models during a 1–d Adaptive Chemistry simulation of a premixed stoichiometric methane–air ﬂame. 0. Reduced models were accurate at about 80% of the grid points. made by approximating o not just at a single point Y, but over entire ranges of Y values that might be encountered by the solver in the process of solving Eq. (8). e. , does not guarantee that the approximation will be accurate at other points lying between Y1, Y2, etc. , 2001). Hence understanding the behavior of o and its approximations over intervals [Ylow,Yhigh] is critical to achieve effective error control.
The overall message is that PREDICTIVE KINETICS 47 predictive chemical kinetics looks very promising in the early 21st century, but very significant efforts, including changes in the day-to-day functioning of the kinetics community, will be required in order to achieve this promise. This manuscript certainly does not address all of the challenges to the advance of predictive chemical kinetics; for example it focuses only on homogeneous systems, and it is not even a complete review of efforts on any of the three sub-problems discussed in detail.