PCAF method

Attention should be drasvn to the microscopic examination of cast I N I. Thorpe and Connick (126) suggest polishing the cast sample with MgO powder and direct observation by reflected light. The previously suggested pcaF method by Williamson (i27) does not reveal sufficient structural detail. 

Another method for removing redundant reaction steps is the principal component analysis of matrix F PCAF), where V=[dfjdxk (Turmyi et al. 1989 Tomlin et al. 1992 Borger et al. 1992 Heard et al. 1998 Carslaw et al. 1999 Zsely and Turanyi 2001 Bahlouli et al. 2014). Here the sensitivity of the net rates of production of species to changes in the input parameters is investigated. Using the PCAF method, the objective function has the following form ... 

Although the PCAS and PCAF methods are similar in form, these two methods are fundamentally different. The objective function of PCAF contains the production rates of species, and the matrix F can be calculated from the right-hand side of ODE (2.9). The objective function of PCAS contains the concentrations of species [the solution of ODE (2.9)], and the matrix S has to be obtained from the solution of the sensitivity differential equations (5.7) and is therefore computationally more time consuming. Put another way, PCAS investigates the effect of parameter changes on the solution of the kinetic system of ODEs, whilst PCAF examines the effect of parameter changes on the right-hand sides of the kinetic system of ODEs (2.9). 

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