Averaging techniques

Most modeling codes are a time-averaging technique. Depending upon the process, a time-dependent technique may be more suitable. Time-dependent modeling requires much more computing power than does time averaging. 

Turn now to the flat-plate geometry. The coefficients A, B, and C, and the mixing-cup averaging technique must be revised. This programming exercise is left to the reader. Run the modified program with ki = I but without... 

The EMA method is similar to the volume-averaging technique in the sense that an effective transport coefficient is determined. However, it is less empirical and more general, an assessment that will become clear in a moment. Taking mass diffusion as an example, the fundamental equation to solve is... 

When more than two data points are available, the graphical method is much better to use than common averaging techniques. It gives one a visual picture of the fit of the data to 3.3.55. If one has several data points and estimates of the uncertainty in each point, a weighted least squares fit of the data would be appropriate. 

It should be emphasized that the enthalpy change includes not only sensible heat effects but also a heat-of-reaction term and in some cases pressure effects. If there are multiple inlet and outlet streams, appropriate averaging techniques must be used to employ this equation. 

Table 11,1.1 contains a workup of the data in terms of the above analysis. In the more general case one should be sure to use appropriate averaging techniques or graphical integration to determine both F(t) and T. When there is an abundance of data, plot it, draw a smooth curve, and integrate graphically instead of using the strictly numerical procedure employed above. 

Figure 11.13 (a) Enthalpy, (b) entropy and (c) Gibbs energy of mixing of MnO-MgO at 1000 K, all calculated using the configurational averaging technique. 

In the extended CFAR case a cell averaging technique is used in each part of the range window but with a greatest of selection (CAGO-CFAR). 

The early surface studies described above indicated that compounds were probably being formed with the first cycle and that the deposits had some degree of order. FEED, however, is an averaging technique. A surface can have significant amounts of disorder, relatively small domains, and still give a reasonable FEED pattern. STM was also used in those studies of compound monolayers, however the images collected were generally of very small areas of the deposits—5-15 nm on a side. Those STM studies... 

Of a class of moving average techniques that fall between Shewhart and CUSUM, the most popular is the EWMA method [12,13], The EWMA introduces yEWMAt, where... 

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