Comparison with experimental data

The required input material parameters are as follows (see Yin et al. [3]) a, M, A, Oys N, Kc, and dr. The hardness a values at different strain levels and the strain rate exponent M were obtained empirically and are shown in Table 6.2 [3]. The values of a were obtained from a best-fit curve of a vs. s results at e = n (see, for example, Fig. 6.11). Values for other pertinent variables were derived or estimated by Yin et al [3] from other sources, and are summarized in Table 6.2. 

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Numerical Modeling of eddy current steam generator inspection Comparison with experimental data, P.O. Gros, Review of Progress in Quantitative Nondestructive Evaluation, Vol 16 A, D.O. Thompson D. Chimenti, Eds (Plenium, New York 1997) pp 257-261. 

Systems for evaluating electrolytes for metal electrowinning have been developed and are being used commercially in zinc production (96). Computerized mathematical models of zinc electrowinning cells have been developed and vaUdated by comparison with experimental data taken from pilot-plant cells (97). 

Comparison with experimental data confirmed efficiency of presented models, which enabled proper explanation of some unintepreted experiment facts. 

Hartree-Fock MO approach, the minimization of energy should provide the most accurate description of the electronic field. The mathematical problem is to define each of the terms, with being the most challenging. The formulation carmot be done exactly, but various approaches have been developed and calibrated by comparison with experimental data. The methods used most frequently by chemists were developed by A. D. Becke. " This approach is often called the B3LYP method. The computations can be done with... 

Middleton, J. C., Pierce, F., and Lynch, P. M., Computations of Flow Fields and Complex Reaction Yield in Turbulent Stirred Reactors and Comparison with Experimental Data, Chem. Eng. Res. Des., Vol. 64, pp. 18-21, 1986. 

This short outiine suggests that it is difficult to find Optimal design para-meters for air curtains. CFD may provide a more effective design method for air curtains (see Chapter 13). There are some published articles applying CFD to air jets, but comparison with experimental data is lacking. 

Here Tq are coordinates in a reference volume Vq and r = potential energy of Ar crystals has been computed [288] as well as lattice constants, thermal expansion coefficients, and isotope effects in other Lennard-Jones solids. In Fig. 4 we show the kinetic and potential energy of an Ar crystal in the canonical ensemble versus temperature for different values of P we note that in the classical hmit (P = 1) the low temperature specific heat does not decrease to zero however, with increasing P values the quantum limit is approached. In Fig. 5 the isotope effect on the lattice constant (at / = 0) in a Lennard-Jones system with parameters suitable for Ne atoms is presented, and a comparison with experimental data is made. Please note that in a classical system no isotope effect can be observed, x "" and the deviations between simulations and experiments are mainly caused by non-optimized potential parameters. 

The calculation of the proton affinities (PA) for a pair of tautomers and the comparison with experimental data [generally from ICR measurements (Section VII,F)] has been the subject of a series of publications with increasing sophistication (Table IV). Such calculations concerning the annular tautomerism of azoles and benzazoles have been reviewed [87AHC(41)187]. 

Fig. 10. Calculated sodium ion single channel currents for the malonyl Gramicidin channel and comparison with experimental data points using four different models all of which fit the data well but only one of which, B., is correct. The point to be made is that both the independent determination of rate constants and of the binding site locations are required.

With formulae (3.58), (3.59) and (3.66) Q-branch contours are calculated for CARS spectra of spherical rotators at various pressures and for various magnitudes of parameter y (Fig. 3.14). For comparison with experimental data, obtained in [162], the characteristic parameters of the spectra were extracted from these contours half-widths and shifts of the maximum subject to the density. They are plotted in Fig. 3.15 and Fig. 3.16. The corresponding experimental dependences for methane were plotted by one-parameter fitting. As a result, the cross-section for rotational energy relaxation oe is found ... 

Weislogel MM, Lichter S (1998) Capillary flow in an interior corner. 1 Eluid Mech 373 349-378 Wu PY, Little WA (1984) Measurement of the heat transfer characteristics of gas flow a fine channels heat exchangers used for microminiature refrigerators. Cryogenics 24 415 20 Xu X, Carey VP (1990) Film evaporation from a micro-grooved surface an approximate heat transfer model and its comparison with experimental data. J Thermophys 4(4) 512-520 Yarin LP, Ekelchik LA, Hetsroni G (2002) Two-phase laminar flow in a heated micro-channels. Int J Multiphase Flow 28 1589-1616... 

In this chapter the deposition of n-Si H by PECVD has been described. The chapter covers material as well as discharge issues. It tries to relate material and discharge properties in various ways. Plasma modeling provides a means to study in detail the physical and chemical processes that occur in the plasma. The presented models show a high degree of sophistication, but from the comparison with experimental data it is clear that especially the deposition model needs improvement. Also, a full 2D model most probably is not needed, as differences between ID and 2D modeling results are not very large. 

The first-principles calculation of NIS spectra has several important aspects. First of all, they greatly assist the assignment of NIS spectra. Secondly, the elucidation of the vibrational frequencies and normal mode compositions by means of quantum chemical calculations allows for the interpretation of the observed NIS patterns in terms of geometric and electronic structure and consequently provide a means of critically testing proposals for species of unknown structure. The first-principles calculation also provides an unambiguous way to perform consistent quantitative parameterization of experimental NIS data. Finally, there is another methodological aspect concerning the accuracy of the quantum chemically calculated force fields. Such calculations typically use only the experimental frequencies as reference values. However, apart from the frequencies, NIS probes the shapes of the normal modes for which the iron composition factors are a direct quantitative measure. Thus, by comparison with experimental data, one can assess the quality of the calculated normal mode compositions. 

Models have been formulated to enable the simulation of the concentration vs. radial distance profile as it develops with time, from which the time-dependent concentration vs. distance, d, profile, observed at the probe, can be extracted for comparison with experimental data. Models based on Eqs. (29) and (30) give similar results for conditions encountered practically. 

Blumenkrantz, A., and J. Taborek, 1971, Application of Stability Analysis for Design of Natural Circulation Boiling Systems and Comparison with Experimental Data, AlChE Paper 13, Natl. Heat Transfer Conf, Tulsa, OK. (6)... 

All solutions of Eqs. (3) such as that by Yu and Sparrow (Yl) yield the velocity profiles in each phase as a function of the interfacial position h and the pressure drop. The volumetric flow rates Qt and Q are obtained by integrating each velocity profile over the respective phase cross-sectional area. The ratio of the flow rates can then be determined as a function of only the interfacial position, and since the volumetric flow rates are known, this yields an implicit fourth order equation for the interfacial position h. The holdups Rt and Rn can be calculated once the interfacial position is known. Since each equation for the volumetric flow rates is linear with respect to the pressure drop, once the interfacial position is known the pressure drop may be easily computed. An analytical procedure for determining pressure drop and holdup for turbulent gas-laminar liquid flows has been developed by Etchells (El) and verified by comparison with experimental data in horizontal systems (A7). 

Reorientations produce characteristic maxima in the relaxation rate, which may be different for the various symmetry species of CD4. The measured relaxation rates exhibit dependence on two time constants at low temperatures, but also double maxima for both relaxation rates. We assume that molecules may move over some places (adsorption sites) on the cage walls and experience different local potentials. Under the assumption of large tunnelling splittings the T and (A+E) sub-systems relax at different rates. In the first step of calculation the effect of exchange between the different places was considered. Comparison with experimental data led to the conclusion that we have to include also a new relaxation process, namely the contribution from an external electric field gradient. It is finally quite understandable to expect that such effect appears when CD4 moves in the vicinity of a Na+ ion. 

In the IPCM calculations, the molecule is contained inside a cavity within the polarizable continuum, the size of which is determined by a suitable computed isodensity surface. The size of this cavity corresponds to the molecular volume allowing a simple, yet effective evaluation of the molecular activation volume, which is not based on semi-empirical models, but also does not allow a direct comparison with experimental data as the second solvation sphere is almost completely absent. The volume difference between the precursor complex Be(H20)4(H20)]2+ and the transition structure [Be(H20)5]2+, viz., —4.5A3, represents the activation volume of the reaction. This value can be compared with the value of —6.1 A3 calculated for the corresponding water exchange reaction around Li+, for which we concluded the operation of a limiting associative mechanism. In the present case, both the nature of [Be(H20)5]2+ and the activation volume clearly indicate the operation of an associative interchange mechanism (156). 

The research on the flow regimes in packed tubes suggests that laminar flow CFD simulations should be reasonable for Re <100 approximately, and turbulent simulations for Re >600, also approximately. Just as RANS models provide steady solutions that are regarded as time averages of the real time-dependent turbulent flow, it may be suggested that CFD simulations in the unsteady laminar inertial range 100 time-averaged picture of the flow field. As with wall functions, comparisons with experimental data and an improved assessment of what information is really needed from the simulations will inform us as to how to proceed in these areas. 

IGLO-HF 29Si NMR studies of silylated arenium ions 83 and 84 and comparison with experimental data have been reported.93,94... 

GIAO-MP2 calculated NMR chemical shifts for DFT optimized geometries and comparison with experimental data were used to study the site of protonation of dimethyl sulfoxide.139 The calculated 13C NMR chemical shift of O-protonated DMSO 107 (40.0 ppm) matches with the experimental value of 34.3 ppm. The calculated 13C NMR chemical shift of S-protonated DMSO 108 is 3 ppm deshielded compared to that calculated for 107. 

The variation of the defect species present as a function of dopant concentration, oxygen partial pressure, or temperature can then be determined by solution of the polynomial equations that connect the various defect populations. The Brouwer approximation may be satisfactory in many cases. As always, comparison with experimental data is essential. 

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