The General Three-Dimensional Calibration Model

The three-dimensional model of calibration and the spatial relationships of calibration, evaluation, and recovery is given in Fig. 6.3. 

It should be noted that the spatial model contains additionally to the calibration and evaluation functions the recovery function, too. These three functions represent the projection of the spatial C-E-R function onto the corresponding planes, as shown in Fig. 6.3. 

From the different character of xstandard and xsampie (Figs. 6.2 and 6.3) it can be seen that the relationship between the calibration function 

Consequences of various types of systematic deviations between xtest and xtruey and therefore, xstandard and xsampie are discussed in Danzer [1995]. 

The different statistical character of the three variables becomes most clear in the different uncertainties of the calibration and evaluation lines. Notwithstanding the fundamental differences between xstandard and xsampiey the calculation of the calibration coefficients is carried out by regression calculus. 

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Accuracy. In general, the accuracy of analytical results is assured by recovery studies (Wegscheider [1996] Danzer [1995] Burns et al. [2002]). According to the recovery function in the general three-dimensional calibration model (see Fig. 6.3), common studies on systematic deviations (Fig. 4.3), and Eqs. (4.2) and (4.3) the following recovery formulae... 

The general problem has been to extend the usefulness of the induction parameter model proposed by Oran et al. (1). This induction parameter model (IPM) is proposed as a means to enable one to estimate, relatively easily, the energy necessary to achieve ignition when using a thermal heating source Much of the calibration of this model, for example the effect of deposition volume (quench volume), can be done with one-dimensional models, and shock tube experiments. There are phenomena, however, which must be studied in two or three dimensions. Examples are turbulence and buoyancy. This paper discusses the effect of buoyancy and possible extensions to the IPM. 

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