Parameters experimental versus calculated

Fig. 3 (a) Experimental versus calculated toxicity (Log (LC50)) values as obtained using one-parameter chemical potential (ji) regression model for the complete set of Fluorine and Sulfur compounds (b) same for electrophilicity index (co) (c) same for net electrophilicity (Aco ) from Eqs. (9), (10) and (13) (d) same for net electrophilicity (Act)" ") from Eqs. (11), (12) and (13) (Reprinted with permission from [350]. Copyright 2011 IGI Global)... 

Fig. 1. a) Standard protonation enthalpy in secondary carbenium ion formation on H-(US)Y-zeolites with a varying Si/Al ratio, b) Effect of the average acid strength for a series of H-(US)Y zeolites experimental (symbols) versus calculated results based on the parameter values obtained in [11] (lines) for n-nonane conversion as a function of the space time at 506 K, 0.45 MPa, Hj/HC = 13.13 (Si/Al-ratios 2.6, 18, 60)... 

NH4NH2C00, DNH4HC03.NH3. D(NH4)2C03,NH3,and DNH4NH C00,NH3 as adjustable parameters. Experimental data and calculated results are shown in Figure 2. The average percent deviation of calculated versus measured partial pressure is 11% for CO2 and 3.9% for NH3. The same system and the same least squares objective function have been studied by Beutier and Renon (9J. Their results, on the same basis, were 16% for C02 and 5% for NH3. Edwards, et al. (10) also studied vapor-liquid equilibrium of a NH3 C02 aqueous system at 373.15°K. 

Table II gives an example of the fixed parameters used in calculating the model-predicted values of conversion for the a-methylstyrene-hexane solvent system and 0.5% Pd catalyst. These, along with the experimental conversion versus liquid superficial velocity data, were input to a computer program for data reduction. Similar data files were developed for each series of experiments and reduced in a similar fashion.

Fig. 14 - Experimental and calculated absolute values of S7Fe quadrupolar splitting in R(Nio.99Feo.oi)2B2C versus ratio of lattice parameters c/a.

The computing problem is concerned with calculating the maximum number of unknown parameters of a proposed reaction system from available experimental data. This data can be any combination of values for constant parameters (rate and equilibrium constants) and variable parameters (concentration versus time data). Moreover, data for different variable parameters need not have the same time scale. When the unknown parameters are calculated, it is important that the mathematical validity of the proposed model be determined in terms of the experimental accuracy of the data. Also, if it is impossible to solve for all unknown parameters, then the model must be automatically reduced to a form that contains only solvable parameters. Thus, the input to CRAMS consists of 1) a description of a proposed reaction system model and, 2) experimental data for those parameters that were measured or previously determined. The output of CRAMS is 1) information concerning the mathematical validity of the model and 2) values for the maximum number of computable unknown parameters and, if possible, the associated reliabilities. The system checks for model validity only in those reactions with unknown rate constants. Thus a simulation-only problem does not invoke any model validation procedures. 

The assumptions of competitive and non-competitive adsorptions of the reactants (Eqs. (9) and (16) respectively) can be discriminated by plotting (PNc/r) and P c/r versus Pno and PcQ. The valid equation should give a linear plot. Moreover, the specific rate constant for the dissociation of NO, k , and the equilibriiun adsorption constants of NO and CO (X,jo and X o) can be estimated from the slopes and intercepts of the straight lines. A mathematical procedure based on the least square method was also carried out in order to calculate these different parameters, in particular when the rate law cannot be linearized, as for Eqs. (14) and (15). The adjustment of the values for k , Xnq and Xco was achieved when the summation of the square deviations between experimental and calculated rates, a tends towards the lowest value. 

FIGURE 1.7 Plots of viscomelric branching parameter, g, versus branch functionahty, p, for star chains on a simple cubic lattice (unfilled circles), together with experimental data for star polymers in theta solvents , polystyrene in cyclohexane , polyisoprene in dioxane. Solid and dashed lines represent calculated values via Eqs. (1.70) and (1.71), respectively. (Adapted... 

Figure 2.43 The full optimized Leu-enkephalin structure with enlarged parts of both systems. Selected interatomic distances are indicated. (A) The plots show the correlation of experimental isotropic chemical shift values (5 so) and calculated nuclear shielding values ( 7 so). (B)The plots represent the correlation of experimental chemical shift tensor values Sii) and calculated nuclear shielding parameters of the enkephalin peptides. (C) The correlations of the experimental versus the computed parameters are shown for Leu-enkephalin. Reprinted from Ref. [96]. Copyright 2014 American Chemical Society.

Fig. 10.7 Blast wave positive phase relative amplitude (a) and non-dimensional scaled impulse (b) versus non-dimensional scaled distance. Bands of parameter values contain experimental and calculation data [2, 3, 11,17, 20, 21, 26, 27, 32]...

Fig. 4. Solvation free energy and entropy from simulations compared with experimental values, (a) and (b) Comparison between experimental and calculated solvation free energies using different parameter sets for anions (a) and cations (b). (c) and (d) Comparison between experimental and calculated solvation entropies using different parameter sets for anions (c) and cations (d). Plotted are the simulated solvation free energies/entropies versus the experimental solvation free energies/entropies. The experimental solvation free energies and entropies are taken from Marcus/ leading to the solid lines. The dashed Knes show the experimental single-ion properties shifted in such a way that (i) the shifts of an anion and a cation cancel each other, and (ii) the Dang chloride ion exactly reproduces the experimental data.

In many process-design calculations it is not necessary to fit the data to within the experimental uncertainty. Here, economics dictates that a minimum number of adjustable parameters be fitted to scarce data with the best accuracy possible. This compromise between "goodness of fit" and number of parameters requires some method of discriminating between models. One way is to compare the uncertainties in the calculated parameters. An alternative method consists of examination of the residuals for trends and excessive errors when plotted versus other system variables (Draper and Smith, 1966). A more useful quantity for comparison is obtained from the sum of the weighted squared residuals given by Equation (1). 

Though a powerfiil technique, Neutron Reflectivity has a number of drawbacks. Two are experimental the necessity to go to a neutron source and, because of the extreme grazing angles, a requirement that the sample be optically flat over at least a 5-cm diameter. Two drawbacks are concerned with data interpretation the reflec-tivity-versus-angle data does not directly give a a depth profile this must be obtained by calculation for an assumed model where layer thickness and interface width are parameters (cf., XRF and VASE determination of film thicknesses. Chapters 6 and 7). The second problem is that roughness at an interface produces the same effect on specular reflection as true interdiffiision. 

Another surprising result of these calculations was that they suggested the relationship between the magnitude of the secondary a-deuterium KIE and transition state structure that had been based on experimental results (Streitwieser et al., 1958 Bartell, 1961 Kaplan and Thornton, 1967) was incorrect. Wolfe and Kim plotted the calculated secondary a-deuterium KIE at various levels of theory versus a looseness parameter, L, for the transition state. The L parameter was defined as the sum of the percentage extension of the C—X and the C—X bonds on going from the reactant (product) to... 

The simultaneous solution of the equations for ai, 02, and K will yield an a versus X curve if all the underlying parameters were known. To this end, Futerko and Hsing fitted the numerical solutions of these simultaneous equations to the experimental points on the above-discussed water vapor uptake isotherms of Hinatsu et al. This determined the best fit values of x and X was first assumed to be constant, and in improved calculations, y was assumed to have a linear dependence on 02, which slightly improved the results in terms of estimated data fitting errors. The authors also describe methods for deriving the temperature dependences of x and K using the experimental data of other workers. 

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