Magnitude estimation data, analysis

Although a great deal of data analysis is needed to obtain a value of the optical nonlinearity from this measurement, we can estimate the order of magnitude of the value. The estimate comes from a comparison of this data with that taken on a similar experiment using Si as the nonlinear material. (15) The two experiments used approximately the same laser power and beam geometry, and the linear reflectivity curves were similar in shape and size (the minimum value of reflectivity). Neglecting differences... 

Layer of protection analysis (LOPA) is a simplified form of event tree analysis. Instead of analyzing all accident scenarios, LOPA selects a few specific scenarios as representative, or boundary, cases. LOPA uses order-of-magnitude estimates, rather than specific data, for the frequency of initiating events and for the probability the various layers of protection will fail on demand. In many cases, the simplified results of a LOPA provide sufficient input for deciding whether additional protection is necessary to reduce the likelihood of a given accident type. LOPAs typically require only a small fraction of the effort required for detailed event tree or fault tree analysis. 

The auto mode of analysis of the experimental J(t) versus t data provided magnitudes of model parameters that followed the experimental data better than those obtained in the manual mode of data analysis. The latter were very sensitive to estimates of instantaneous modulus and, in some instances, there were considerable differences between experimental data and model predictions (not shown here). Therefore, the results of auto mode data analysis are presented in Table 5-E the standard deviations of the parameters are also in Table 5-E in parentheses. The standard deviation of J was higher than those of the other parameters reflecting greater uncertainty in its estimation. 

In order to obtain some order of magnitude estimate of this diffusional process, the data of runs 1 and 2 were analyzed. The analysis assumed the presence of a continuous and unbroken, uniformly distributed film. Based on the analysis, a diffusivity coefficient for the conventional diffusion equation (Pick s law represented by dc/dt = D d c/dX ) was obtained. The value calculated was ... 

The first analysis of the ratings concerns their validity. Can panelists actually scale the relative sensory impressions of these odor stimuli by magnitude estimation Correct scaling of overall odor Intensity provides a validating measure of the panelist s sensory capabilities in this complicated study. Since panelists had the opportunity to scale unmixed odorants as well as the odor mixtures, and since the unmixed odorants comprised a graded intensity series (albeit presented at random in the set of 2k stimuli) it becomes a straightforward matter to determine whether panelists could pick out the k levels of each unmixed odorant, and scale them in the correct order of concentration. Panelists should do so. Table V shows linear and log-log (viz., power functions) relations between odor concentration in air, and rated overall odor intensity, for each pair of odorants in each study. Linear and power functions fit the data adequately. For power functions, the exponents are less than 1.0, confirming previously reported results in the literature. (2, 3)... 

Data analysis then fits a polynomial equation to the collected data. The magnitudes of the coefficient estimates in the equation indicate the importance of the variables. This equation can be simply viewed as a multidimensional French curve to illustrate the relationship between variables and responses. Those coefficient estimates with statistical significance are highlighted, and are used to select the axes for contour plots. 

The experimental and simulation results presented here indicate that the system viscosity has an important effect on the overall rate of the photosensitization of diary liodonium salts by anthracene. These studies reveal that as the viscosity of the solvent is increased from 1 to 1000 cP, the overall rate of the photosensitization reaction decreases by an order of magnitude. This decrease in reaction rate is qualitatively explained using the Smoluchowski-Stokes-Einstein model for the rate constants of the bimolecular, diffusion-controlled elementary reactions in the numerical solution of the kinetic photophysical equations. A more quantitative fit between the experimental data and the simulation results was obtained by scaling the bimolecular rate constants by rj"07 rather than the rf1 as suggested by the Smoluchowski-Stokes-Einstein analysis. These simulation results provide a semi-empirical correlation which may be used to estimate the effective photosensitization rate constant for viscosities ranging from 1 to 1000 cP. 

Figure 5A shows experimentally derived profiles of pH vs rate for reactions in H2O and D2O [30, 50, 71]. The magnitude of the apparent isotope effect (ratio of rate constants in H2O and D2O) is 4.4 and the profiles appear to support the possibility that a proton is transferred from (Mg -bound) water molecules. However, careful analysis led us to conclude that a metal ion binds directly to the 5 -oxygen. Since the concentration of the deproto-nated 2 -oxygen in H2O should be higher than that in D2O at a fixed pH, we must take into account this difference in pKa, namely ApKa (=pKa °-pKa ), when we analyze the solvent isotope effect of D2O [30, 50, 68, 71]. We can estimate the pKa in D2O from the pKa in H2O using the linear relationship shown in Fig. 5B [30, 68, 73-75]. If the pKa for a Mg -bound water molecule in H2O is 11.4, the ApKa is calculated to be 0.65 (solid line in Fig. 5B). Then, the pKa in D2O should be 12.0. Demonstrating the absence of an intrinsic isotope effect (kH2o/kD20=l)> the resultant theoretical curves closely fit the experimental data, with an approximate 4-fold difference in...

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