Standard computed curves

Fig. 12. Schematic curves (top, bottom) of the calculated free energy of hydration AGhydr of two hypothetical HT materials (top Si-rich/Ca-poor bottom Si-poor/Ca-rich) as a function of the pH. The shaded areas are the actual ranges of computed AGhydr of HT materials, categorized as a function of the HT process from which they originate. For comparison, the computed curve for the standard HLW glass SON68 is also shown (dotted curve).

First of all, let us discuss the case of equal concentrations nA(t) = nB(t) = n t) when two kinds of similar correlation functions coincide Xjj r,t) = X r,t), u = A,B. In Fig. 5.2 the concentration development in the one-dimensional case is presented [26]. The curve (a) gives averaged (over 10 simulations) computer-calculated density. Stripped lines demonstrate dispersion of results they correspond to the curves n t)) s t), where ( (0) is standard deviation. Curve (b) shows the numerical solution of a set (4.1.19), (4.1.28), and (5.1.14) to (5.1.16) derived in the framework of the superposition approximation. Curve (c) gives results of the linear approximation (4.1.41) and (4.1.42). At last, the additional curve (d) is drawn Just to illustrate concentration behaviour at short times. In the linear approximation we neglect similar reactant correlation, X r,t) — 1, whereas in curve (d) dissimilar (AB) reactant correlations (4.1.40) are also... 

Figure 9. Computed curves of pC02 vs. time after mixing equal volumes of a 5% erythrocyte suspension (pco 0) and standard buffer solution (Pco2 65 torr) at 37°C (15)...

For research applications, where maximal accuracy is desirable even at the expense of time and effort, two maneuvers are possible. The first involves derivation of the initial dissociation curve using the standard calibration curve. A second computation follows, using the derived curve for calibration. This process is repeated until the derived and calibrating dissociation curves match each other. This method requires considerable calculations, but it is theoretically valid even for abnormal hemoglobins. The other technique for accurate dissociation curve analysis is simply a variation on the traditional method of carefully equilibrating aliquots... 

Here Rcp = dp ug — Up //ig is the droplet Reynolds number. The above correlation is valid for Re < 800. The constants a = 0.15 and b = 0.687 yield the drag within 5% from the standard drag curve. Modifications to the solid particle drag are applied to compute the drag on a liquid drop and are given below. 

Dubinin et al. evaluated the amount surface area from the benzene isotherm measured for the nonporous reference adsorbent /7/, we, however estimated the specific surface area Sme of the mesopores from the adsorption isotherm studied /8/, In calculations of the mesopore size distribution and the specific surface area Sme it has been assumed that the parallel - sided slits are rigid and the size distribution does not extend continuously from the mesopore into both the macropore and micropore range. We have used the desorption branch of the hysteresis loop of the isotherm for the computation. The procedure of B.F. Roberts /9/ has been applied. In this computation, which is a rigorous application of the concept of simultaneous capillary condensation and multilayer adsorption, the adsorbed volume is first expressed as a function of pore size then it is converted to pore volume. A standard t - curve /lO/, which represents the benzene adsorption onto nonporous carbon blacks, has been used for correction for multilayer thickness. 

Understanding how the force field was originally parameterized will aid in knowing how to create new parameters consistent with that force field. The original parameterization of a force field is, in essence, a massive curve fit of many parameters from different compounds in order to obtain the lowest standard deviation between computed and experimental results for the entire set of molecules. In some simple cases, this is done by using the average of the values from the experimental results. More often, this is a very complex iterative process. 

Curve-Fitting Methods In the direct-computation methods discussed earlier, the analyte s concentration is determined by solving the appropriate rate equation at one or two discrete times. The relationship between the analyte s concentration and the measured response is a function of the rate constant, which must be measured in a separate experiment. This may be accomplished using a single external standard (as in Example 13.2) or with a calibration curve (as in Example 13.4). 

To quantitate proteins from staining, a densitometer aided by computer software is used to evaluate band areas of samples compared to band areas of a standard curve. Amido black, Coomassie Brilliant Blue, and silver stains are all appHcable for use in quantification of proteins. 

The RMDB consists of two mayor sections computer data storage and retrieval system, and backup microfilm data bank file. The computer data storage and retrieval system is used for die standard reliability and maintainability data listing, special calculations, and searches. This data bank system has been established to facilitate remote terminal access compatible with the GIDEP remote terminal programs. The microfilm data bank file is used for storage and distribution of supplier s documents, failure analysis curves, description of methods used in the collection of the data, and additional background information too extensive to include in the computer data bank. 

Recorded kinetic curves were fitted to the five-parameter Equation (1). The parameters pj with their errors and the standard deviation of regressions are summarized in Tables 1-6. Comparison of the data confirm the previously reported (refs. 8,12) similarity in the behavior of the two isomers in the presence of strong bases in spite of the different shape of the kinetic curves. The relatively good agreement of exponents p2, P4 computed for the diastereomers at the same temperature and amine concentration demonstrates the validity of the model used. From comparison of Equations (4) and (7) it follows that both reaction must give the same exponent. 

In order to do this, a simple calculator may be used to aid in the mathematical manipulations. A desktop computer into which the data is entered may be used to generate a standard curve automatically along with the unknown values which are automatically read from the curve. If a paper tape print out... 

Quantitative XRF analysis has developed from specific to universal methods. At the time of poor computational facilities, methods were limited to the determination of few elements in well-defined concentration ranges by statistical treatment of experimental data from reference material (linear or second order curves), or by compensation methods (dilution, internal standards, etc.). Later, semi-empirical influence coefficient methods were introduced. Universality came about by the development of fundamental parameter approaches for the correction of total matrix effects... 

The calibration process then involves measurement of the complete scattering curve of the secondary standard and the evaluation26 of k by determination of Porod s law with its asymptote Ap and the density fluctuation background Ipi, numerical extrapolation of the function s2 (/ (s) - Ipi) towards s = 07 and finally computation of the scattering power... 

Er has dropped to five standard deviations, the optimum transmittance has dropped to 3.2, and then drops off quickly below that value. Surprisingly, the optimum value of transmittance appears to reach a minimum value, and then increase again as Er continues to decrease. It is not entirely clear whether this is simply appearance or actually reflects the correct description of the behavior of the noise in this regime, given the unstable nature of the variance values upon which it is based. In fact, originally these curves were computed only for values of Er equal to or greater than three due to the expectation that no reasonable results could be obtained at lower values of Er. However, when the unexpectedly smooth decrease in the optimum value of %T was observed down to that level, it seemed prudent to extend the calculations to still lower values, whereupon the results in Figure 45-11 were obtained. 

Fig. 2. Abundance of 3He vs. main-sequence masses (determined by Galli et al. 1997) for the six PN of the sample of Balser et al. (1997) and Balser, Rood, Bania (1999). The curves labeled Pop I and Pop II show the standard abundance of 3He computed by Weiss, Wagenhuber, Denissenkov (1996) for two metallicities. The curves labeled with extra-mixing show the results of stellar nucleosynthesis calculations with deep mixing by Boothroyd Sackmann (1999) (upper curve) and the equilibrium value 3He/H = 10-B for M < 2.5 M (lower curve).

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