Comparing experimental with theory

For the analysis of experimental data it is an important question how the different kinds of scattering processes contribute to the transport phenomena, especially since calculations are usually done for one kind of interaction. Therefore, to compare experiment with theory it is necessary to isolate from the experimental data the one contribution for which the calculation has been performed. 

In 1935, Frumkin and M. A. Proskumin [11] used ac measurements to measure the electric double layer capacitance. This permitted empirical values of the double layer capacitance to be compared rigorously with theory for the first time. The authors were successful because they carried out their experiments under conditions of exceptional cleanliness, such as glassware that had been acid-cleaned and water that had been multiply distilled. This work had an enormous impact internationally, because it demonstrated how reproducible measurements of the electrical double layer could be obtained. Indeed, Frumkin s experimental methods soon became legendary among western scientists. From that time forward, the ac method became the standard method of measuring interfacial capacitance. 

The quantitative data and observations discussed above appear to be consistent with the qualitative concepts put forward by Mosbach and others to explain the behavior of multistep enzyme systems. Mathematical modelling of gel entrapped, multistep, immobilized enzyme systems, using the collocation technique, is quite straightforward and provides the opportunity not only to compare experiment with theory but also to explore the effect of parameters of the system which are experimentally inaccessible. 

The changes of magnetic properties at surfaces can be investigated by a variety of experimental and theoretical techniques. Comparing experiment with theory, however, is not an easy task. First, the local measurements of the magnetic quantities (like magnetic moment or magnetic anisotropy) are quite difficult, and very often the information cannot be obtained directly. Second, calculations usually refer to simple model systems and therefore differ from real structures that are obtained experimentally. 

Fig. 5. Theory vs. experiment rupture forces computed from rupture simulations at various time scales (various pulling velocities Vcant) ranging from one nanosecond (vcant = 0.015 A/ps) to 40 picoscconds (vcant = 0.375 A/ps) (black circles) compare well with the experimental value (open diamond) when extrapolated linearly (dashed line) to the experimental time scale of milliseconds.

It should be noted that a comprehensive ELNES study is possible only by comparing experimentally observed structures with those calculated [2.210-2.212]. This is an extra field of investigation and different procedures based on molecular orbital approaches [2.214—2.216], multiple-scattering theory [2.217, 2.218], or band structure calculations [2.219, 2.220] can be used to compute the densities of electronic states in the valence and conduction bands. 

The above-cited values compare well with the results derived by solving numerically the system of Eqs. (7) to (13). As a further check, the value of Tgc, derived from the theory, Tgc = 119 °C, checked well with its experimental value equal to Tgc = 117 °C. The difference may be explained by the fact that relation (14) is only approximate and its results contain some error. 

A variety of studies can be found in the literature for the solution of the convection heat transfer problem in micro-channels. Some of the analytical methods are very powerful, computationally very fast, and provide highly accurate results. Usually, their application is shown only for those channels and thermal boundary conditions for which solutions already exist, such as circular tube and parallel plates for constant heat flux or constant temperature thermal boundary conditions. The majority of experimental investigations are carried out under other thermal boundary conditions (e.g., experiments in rectangular and trapezoidal channels were conducted with heating only the bottom and/or the top of the channel). These experiments should be compared to solutions obtained for a given channel geometry at the same thermal boundary conditions. Results obtained in devices that are built up from a number of parallel micro-channels should account for heat flux and temperature distribution not only due to heat conduction in the streamwise direction but also conduction across the experimental set-up, and new computational models should be elaborated to compare the measurements with theory. 

Numerous quantum mechanic calculations have been carried out to better understand the bonding of nitrogen oxide on transition metal surfaces. For instance, the group of Sautet et al have reported a comparative density-functional theory (DFT) study of the chemisorption and dissociation of NO molecules on the close-packed (111), the more open (100), and the stepped (511) surfaces of palladium and rhodium to estimate both energetics and kinetics of the reaction pathways [75], The structure sensitivity of the adsorption was found to correlate well with catalytic activity, as estimated from the calculated dissociation rate constants at 300 K. The latter were found to agree with numerous experimental observations, with (111) facets rather inactive towards NO dissociation and stepped surfaces far more active, and to follow the sequence Rh(100) > terraces in Rh(511) > steps in Rh(511) > steps in Pd(511) > Rh(lll) > Pd(100) > terraces in Pd (511) > Pd (111). The effect of the steps on activity was found to be clearly favorable on the Pd(511) surface but unfavorable on the Rh(511) surface, perhaps explaining the difference in activity between the two metals. The influence of... 

Tables 2.1 and 2.2 show that theory enables detonation velocities to be calculated in close agreement with those observed experimentally. This, unfortunately, is not a critical test of the theory as velocities when calculated are rather insensitive to the nature of the equation of state used. A better test would be to calculate the peak pressures, densities and temperatures encountered in detonation, and compare these with experimental results. The major difficulties here are experimental. Attempts to measure temperatures in the detonation zone have not been very successful, but better results have been obtained in the measurement of densities and pressures. Schall introduced density measurement by very short X-ray flash radiography and showed that TNT at an initial density of 1 -50 increased 22% in density in the detonation wave. More recently detonation pressures have been measured by Duff and Houston using a method (introduced by Goranson) in which the pressure is deduced from the velocity imparted to a metal plate placed at the end of the column of explosive. Using this method, for example, Deal obtains the detonation pressures for some military explosives recorded in Table 2.3. More...

In the theory of deuteron spin-lattice relaxation we apply a simple model to describe the relaxation of the magnetizations T and (A+E), for symmetry species of four coupled deuterons in CD4 free rotators. Expressions are derived for their direct relaxation rate via the intra and external quadrupole couplings. The jump motion between the equilibrium positions averages the relaxation rate within the same symmetry species. Spin conversion transitions couple the relaxation of T and (A+E). This mixing is included in the calculations by reapplying the simple model under somewhat different conditions. The results compare favorably with the experimental data for the zeolites HY, NaA and NaMordenite [6] and NaY presented here. Incoherent tunnelling is believed to dominate the relaxation process at lowest temperatures as soon as CD4 molecules become localized. 

The actual curve, however, is somewhat modified by Coulomb interaction between the electron or positron and the nucleus. This is allowed for by multiplication with a dimensionless function F(Z p), which leads to a correction factor / for the total decay rate, and it is the product ft that is used for purposes of comparing measured lifetimes with theory. The most rapid decays, with ft = 103 to 104 s, are known as super alio wed . These include 0+ to 0+ decays having A//, 2 = 2 and ft is found experimentally to be close to 3000 s, giving the coupling constant for the Fermi interaction... 

Table 3 collects the results obtained by different authors on the reaction of 0s04(NH3) with ethylene. Though the methods were not identical, the results are very similar, and in all cases there is a clear preference of the [3+2] over the [2+2] pathway. Additional confirmation was provided by a combined experimental and theoretical study using kinetic isotope effects (KIEs) to compare experiment and theory. Kinetic isotope effects were measured by a new NMR technique [25] and compared to values, which are available from calculated transition states. It showed that indeed only the [3+2] pathway is feasible [10]. 

Recent developments in the theory of interaction between ions or polar molecules and their nearest neighbors in the solution are summarized in the present review. Furthermore, new experimental data are presented as long as they can be compared reasonably with calculated results for isolated complexes. After collecting the material available we found it appropriate to divide the discussion of data and results into two parts ions and polar molecules. Most attention is given here to the ionic solvation since interactions between polar molecules, especially hydrogen bonding, have already been reviewed extensively 14-19). 

Calculations of isotope effects and isotopic exchange equilibrium constants based on the Born-Oppenheimer (BO) and rigid-rotor-harmonic-oscillator (RRHO) approximations are generally considered adequate for most purposes. Even so, it may be necessary to consider corrections to these approximations when comparing the detailed theory with high precision high accuracy experimental data. 

Chylek et al. (1983) showed that, by comparing experimental resonance spectra with spectra computed using Mie theory, the size and refractive index of a microsphere can be determined to about one part in 10. Numerous investigators have used resonance spectra to determine the optical properties of microspheres since Ashkin and Dziedzic observed resonances. A recent example is the droplet evaporation study of Tang and Munkelwitz (1991), who measured the vapor pressures of the low-volatility species dioctyl phthalate (DOP), glycerol, oleic acid, and methanesulfonic acid (MSA). This... 

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