Calculated and experimental concentrations

In this example the number of measured variables is less than the number of state variables. Zhu et al. (1997) minimized an unweighted sum of squares of deviations of calculated and experimental concentrations of HPA and PD. They used Marquardt s modification of the Gauss-Newton method and reported the parameter estimates shown in Table 16.24. 

Figure 4 shows a comparison of experimental and calculated concentration-time profiles for HCHO, NO, NO, and ozone for the experiment performed with exhaust from the biodiesel fuel together with the base VOC mixture in the presence of NO,. The concentration of formaldehyde is slightly underestimated by the model for reaction times after 13 00 GMT. However, this deviation reaches only a few ppb and is within the experimental error of the HCHO concentration (typically 20%). In total, the calculated and experimental concentration-time profiles are in good agreement. 

The values of the adsorption parameters used in this study were obtained as a result of the minimization of the sum of least squares deviation of calculated and experimental concentration profiles in a batch experiment [20]. The experimental concentration curve is given along with the calculated profiles (based on either the first-order or Langmuir kinetics) in Eigure 15.2. 

Figure 12.6. (a) Calculated (a + a) phase boundary for Fe-V together with experimental boundaries (After Spencer and Putland 1973). (b) Comparison between calculated and experimental values of the concentration of Al, V and Fe in the two phases in Ti-6AMV alloy (after Saunders and... 

Knowing the experimental retention times, the previous equation allows the calculation of experimental concentration on the solid phase. Parameters of adsorption isotherms, can then be determined by fitting experimental and calculated concentrations. 

Both calculations and experimental data indicate that at a reasonably small volume concentration of active particles and small degree of particle deposition on the film surface the following relationship [6] is rather strictly obeyed (see Fig. 3.1.) ... 

Fig. 8.20 Calculated and experimental burning rates for HMX-CMDB propellants, showing that the burning rate decreases with increasing HMX concentration (average HMX particle size = 200 pm).

Figure 10.20 Comparison between calculated and experimental values for the concentration of Al, V and Fe in the a and 0 phase in Ti-6At-4V alloys.

Baumy et al. (27) determined the binding constants for two 3,4-dihydro-2//-l-benzopyran derivatives of /3-CD. These binding constants were then used to calculate the optimal concentration of chiral selector for the enantioseparation of the two compounds. The calculation of the optimal concentration of the chiral selector was performed according to Eq. (18). Good agreement was found between the calculated and experimentally observed optimum concentrations for the two compounds. 

At the lowest concentrations of 2-propanol, 10"2 M, there is reasonable agreement between calculated and experimental results. These results then are consistent with the assumption that acetone is the only oxidation product from the radical produced from 2-propanol in aqueous solution containing oxygen. It has similarly been shown (23) that acetaldehyde is the only organic oxidation product in the radiation-induced oxidation of aqueous ethanol. However, our experiments indicate that in... 

The reported block function was adopted to improve the overall correlation between calculated and experimental pICso at the two different concentrations. As reported previously (25, 36), in the lower range of inhibition, below 5%, a stronger correlation between plCgjj computed at 10 xM concentration and experimental pICgQlc was found, when compared to 1 xM. An opposite trend was present in the upper range of inhibition (above 99%), where pICgQlc computed at 1 xM concentration tended to correlate better with experiment than that at 10 xM. For inhibition values between the previously defined cut-offs, we used the average pICso. 

In some polymer-nonpolar solvent systems, % has been calculated as a function of concentration on the basis of the statistical-thermodynamical theory called the equation of state theory [13,14]. This semiempirical theory takes into account not only the interaction between solute and solvent, but also the characteristics of pure substances through the equations of state of each component. At present, however, we cannot apply this approach to such a complex case as the NIPA-water system. Thus, at the present stage, we must regard % as an empirical parameter to be determined through a comparison between calculated and experimental results. The empirical estimation of % for the NIPA-water system will be described in the next section. 

Calculated and experimental values are in good agreement and consistent with the isomorphous substitution of Siiv by Tiiv. The concentration of titanium measured along the axis of the crystals was found to be constant. A simple... 

Fig. 20. Calculated and experimental (dotted and solid curves respectively) values of (1) elastic modulus (E) and (2) ultimate compression strength (crj versus phenolic microsphere concentration (C) in an epoxy syntactic foam at 23 °C 162)...

The influence of molar mass, charge density as well as chain branching was also determined in the presence of low molecular mass salt. As seen in Fig. 16, the differences between theory and experiment are more important to low molar masses. In Fig. 16 the concentration dependence of the activity of the low molecular salt has been taken into account when calculating fac=fexp/fo [H4, 126], where fac and fexp are calculated and experimentally determined counterion activity coefficients, respectively f0 is the activity coefficient of the added low molecular salt in aqueous solution without polyelectrolyte. 

This equation can be solved numerically. At concentrations of oxygen below 0.2%, the limiting current plateau becomes narrow and the onset of another electrode process contributes to positive error. It has been attributed to the reduction of CO2 or to the increase of unspecified electronic current (Pham and Glass, 1997). Excellent agreement between the calculated and experimental values has been observed for a wide range of temperatures (Fig. 7.20). 

Figure 36.10. Comparison between calculated and experimental results for the detection of alkaline phosphatase in polyimide microchannels at various concentrations, namely (A) 0, 0.1 and lpM and (B) 10 and 100 pM...

Fig. 3.21. Percent difference between model-calculated and experimental carbon dioxide gas concentrations for NaCl systems in equilibrium with CO26H2O, where % Diff. = [model — expt./expt.] x 100. Reprinted from Marion et al. (2006) with permission...

A good agreement between Prophy calculations and experimental results is observed for H20. HI and I2 concentrations are underestimated. 

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