Theory and experiment, comparison

As in DC voltammetry, theory and experiment comparisons of AC voltammetric data have usually been undertaken heuristically, where the experimenter decides empirically whether a satisfactory agreement between the experiment data and the model has been achieved. However, an estimation of the quality of the fit between experimental and simulated data can be gained by examining the residual sum of squares (RSS) or by the mean percentage error (MPE) [34]. 

The Equation (8) and Equation (10) combination allows to estimate theoretically putting out a fire time The theory and experiment comparison in the form of the dependence of on organoclay mass contents (Figure 4) has shown their good correspondence. 

Comparison Between Theory and Experiment Comparisons between theory and experiment have been made for many materials. Shown in Fig. 2.20 are the graphs in stress space for the equations for the three theories given above. Also shown is experimental data on five different metals as well as four different polymers. It will be noted that cast iron, a very brittle material agrees well with the maximum normal stress theory while the ductile materials of steel and aluminum tend to agree best with the von Mises criteria. Polymers tend to be better represented by von Mises than the other theories. 

Skokov S and Bowman J M 1999 Variation of the resonance width of HOCI (6uq ) with total angular momentum comparison between ab /M/o theory and experiment J. Chem. Phys. 110 9789-92... 

P. Attard, J. L. Parker. Oscillatory solvation forces A comparison of theory and experiment. J Phys Chem 9(5 5086-5093, 1992. 

D. P. Landau, M. Krech. Spin dynamics simulations of ferro- and antiferromagnetic model systems comparison with theory and experiment. J Phys Condens Matter 77 R175-R213, 1999. 

Different Types of Proton Transfers. Molecular Ions. The Electrostatic Energy. The ZwiUertons of Amino Acids. Aviopro-tolysis of the Solvent. The Dissociation Constant of a Weak Acid. Variation of the Equilibrium Constant with Temperature. Proton Transfers of Class I. Proton Transfers of Classes II, III, and IV. The Temperature at Which In Kx Passes through Its Maximum. Comparison between Theory and Experiment. A Chart of Occupied and Vacant Proton Levels. 

Comparison between Theory and Experiment. The last column of Table 12 gave the difference between the value of J at 313°K and the value of J at 293°K. Since Jis independent of temperature, this difference is the increment in Jmv between these two temperatures—or if we use (140) it is the increment in J,t between these two temperatures. We see then that in class II the value of Jei increases by about 0.010 electron-volt in the 20° interval, while in class IV it increases by more than 0.03 electron-volt. In each case, according to (140), the increment in J,i is proportional to J,i itself for the increment is... 

The shapes of experimental and theoretical j(Fj curves are in mutual agreement. By comparison one arrives at injection barriers ranging from 0.4 eV (PPV imine) to 0.7 eV (PPPV). The agreement between theory and experiment is similarly good as far as the temperature dependence is concerned. Data shown in Figure 12-7 were taken with DASMB and confirm the analytic results for A=0.4eV. 

Jensen (J3) has conducted experimental studies in both laboratory and test motors to determine the value of the exponent g. The results obtained in a 3-in.-diameter test motor show that a value of g = 0.5 correlates the data. Using this correlation, experimentally observed propagation rates could be predicted with reasonable accuracy using Eqs. (21)—(24). A typical comparison between theory and experiment is shown in Fig. 12. 

Interest at Brookhaven was stirred by the contrast between the excellent agreement between theory and experiment for the D2+ + D2 reaction and the rather poor description provided for the H2-He and H2-Ne systems. The H2-He system is particularly interesting because of the relatively few particles involved in the reaction and its potential for accurate theoretical treatment. The reactions of H2 + or HD+ with He will be among the first to be treated in terms of a theoretically computed potential energy surface comparison of experiment and theory in this system is therefore of prime importance. 

In Spite of the existence of numerous experimental and theoretical investigations, a number of principal problems related to micro-fluid hydrodynamics are not well-studied. There are contradictory data on the drag in micro-channels, transition from laminar to turbulent flow, etc. That leads to difficulties in understanding the essence of this phenomenon and is a basis for questionable discoveries of special microeffects (Duncan and Peterson 1994 Ho and Tai 1998 Plam 2000 Herwig 2000 Herwig and Hausner 2003 Gad-el-Hak 2003). The latter were revealed by comparison of experimental data with predictions of a conventional theory based on the Navier-Stokes equations. The discrepancy between these data was interpreted as a display of new effects of flow in micro-channels. It should be noted that actual conditions of several experiments were often not identical to conditions that were used in the theoretical models. For this reason, the analysis of sources of disparity between the theory and experiment is of significance. 

Anion photoelectron spectroscopy [37, 38] amd photodetachment techniques [39] provide accurate information on electron detachment energies of negative ions. Ten closed-shell ainions considered here exhibit sharp peaks, indicative of minor or vanishing final-state nuclear rearrangements, in their photoelectron spectra. Comparisons between theory and experiment are straiightforward, for differences between vertical and adiabatic electron detachment energies (VEDEs and AEDEs, respectively) are small. 

Roth, CM Lenhoff, AM, Electrostatic and van der Waals Contributions to Protein Adsorption Comparison of Theory and Experiment, Langmuir 11, 3500, 1995. 

For some of the comparison of theory and experiment it is necessary to be specihc about the molecular length scale a (a very detailed discussion of this quantity can be found in Ref. [47]). The molecular scale denotes the lattice... 

A comparison of anisotropic Fe HFCs with the experimental results shows good agreement between theory and experiment for the ferryl complexes and reasonable agreement for ferrous and ferric complexes. Inspection reveals that the ZORA corrections are mostly small ( 0.1 MHz) but can approach 2 MHz and improve the agreement with the experiment. The SOC contributions are distinctly larger than the scalar-relativistic corrections for the majority of the investigated iron complexes. They can easily exceed 20%. 

Figure 15 Comparison of theory and experiment for the fractionation of oligoade-nylates on ion exchange materials, (a) Simulated chromatogram, (b) Observed chromatogram. An example of how theory is being used to attempt to optimize performance of ion exchange materials. The curve in (a) shows the nonlinear gradient development with a convex curvature. (Reproduced with permission of Elsevier Science from Baba, Y., Fukuda, M., and Yoza, N., J. Chromatogr., 458, 385, 1988.)...

Fig. 21. Comparison of theory and experiment for the thermal rate constant of the H+H2O — H2+OH reaction and the calculated contributions from individual vibrational states of H2O.

Figure 3.8 Comparison of theory and experiments (water-air horizontal flow at 25°C and 1 atm pressure with diameter of 2.5 cm). Solid lines theory. (From Dukler, 1978. Copyright 1978 by National Council of Canada. Reprinted with permission.) Fuzzy lines experimental data. (From Mand-hane et al., 1974. Copyright 1974 by Elsevier Science Ltd., Kidlington, UK. Reprinted with permission.)...

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