Comparison with experimental results

Extensive experiments on the stress relaxation for shear deformation have been done by Osaki et For convenience of comparison, 

In the limit of y- 0, this reduces to the relaxation modulus of linear viscoelasticity. 

Hiis relation, first found by Lodge and Meissner using a phenomenological argument, has been well confirmed. The ratio between the second normal stress difference N2(t, y) and the first normal stress difference Ni(t, y) is shown in Fig. 7.17. The experimental values are again in reasonable agreement with the theory. 

Uniaxial elongation. For uniaxial elongation, the tensile stress is given by ar(t. A) = [1 + (or(A) - l)cxpi-t/T )ffiX)G(t). (7.137) Here a(A) denotes a(E) of uniaxial elongation and 

The stress relaxation for uniaxial elongation has been studied by Ferry et ai. and the result has been well fitted by eqn (7.137) if the effect of the molecular distribution is taken into account.  

The range of applicability of the above theoretical approaches and numerical results can be estimated by comparing them with experimental results obtained, mostly, by direct optical microscope observation and for monodisperse polystyrene latex particles [8-10, 13, 14, 19, 21, 22, 34—36]. Several sets of experimental data have also been gathered using the AFM for latex [17, 20], colloid gold [62] or dendrimer suspensions [26]. One can also apply electron microscopy to determine particle 

Further experimental results pertinent to quasi-uniform surfaces, mostly kinetic data, have been discussed in review papers [36, 43, 44] and monographs [70, 71). 

The results obtained for quasi-homogeneous surfaces can be used for the interpretation of data derived for heterogeneous surfaces. 

Harley eto/., electron microscopy, diffusion [15] (open triangles) theoretical RSA simulations X= 10 ( ) theoretical RSA simulations T= 10. The solid and dashed lines represent the analytical approximation calculated from Equation 11.2 for ( )o= 100 and 10 kT, respectively. (From Ref. [44].) 

A different situation arises for lower ionic strength when the double layer thickness becomes comparable to the particle dimensions. In this case, because of the repulsion with the substrate, particles tend to adsorb preferentially on top of a site. As a result, one site can accommodate only one larger particle, whereas for high ionic 

This follows from expressions such as (16.60), and more generally from the hannonic medium representation of dielectric response (Section 16.9) in which Er is made of additive contributions of independent normal modes including intramolecular modes. 

Consider now the implications of (16.63) with regards to the four rates defined by the following rate diagrams 

The reorganization energy associated with either rate in (16.64) will be denoted 

Following Eq. (16.53) and assuming that the electronic coupling is the same for all these reactions we also have 

Therefore kba can be predicted from the equilibrium constant of the reaction (16.64) together with parameters that characterize the rates of the reactions (16.65). The 

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Obviously, the assumptions involved in the foregoing derivation are not entirely consistent. A transverse strain mismatch exists at the boundary between the fiber and the matrix by virtue of Equation (3.8). Moreover, the transverse stresses in the fiber and in the matrix are not likely to be the same because v, is not equal to Instead, a complete match of displacements across the boundary between the fiber and the matrix would constitute a rigorous solution for the apparent transverse Young s modulus. Such a solution can be found only by use of the theory of elasticity. The seriousness of such inconsistencies can be determined only by comparison with experimental results. 

P. Lehmann, R. Moreau, D. Camel, R. Bolcato. A simple analysis of the effect of convection on the structure of the mushy zone in the case of horizontal Bridgman solidification. Comparison with experimental results. J Cryst Growth 183 690, 1998. 

The MP2 treatment recovers the majority of the correlation effect, and the CCSD(T) results with the cc-pVQZ basis sets are in good agreement with the experimental values. The remaining discrepancies of 9cm , 13cm and lOcm are mainly due to basis set inadequacies, as indicated by the MP2/cc-pV5Z results. The MP2 values are in respectable agreement with the experimental harmonic frequencies, but of course still overestimate the experimental fundamental ones by the anharmonicity. For this reason, calculated MP2 harmonic frequencies are often scaled by 0.97 for comparison with experimental results. ... 

Since a considerable amount of review articles on both theoretical frameworks and calculated results have been reported[15-25], the main objective of the present study is placed on the comparisons with experimental results. The organization of the present report is as follows In the next section, for the sake of completeness, a brief theoretical description of the PPM is summarized from the previous articles. In the third section, disorder-LIq transition is focused and visualized atomic (spin) configuration is compared with recent high resolution electron micrograph. In the fourth section, ordering relaxation... 

Comparisons with experimental results 147) show that the reliability of this rule increases as the more the copolymerization system increasingly depends on the solvent. This is remarkable because the following crude approximations were used ... 

An alternative to the traditional approach is to generate the electronic states as needed during the dynamics. This has been done for atomic collisions, where detailed calculations and comparisons with experimental results are possi-ble.(4-8) General treatments of the coupling of electronic and nuclear motions in molecular systems can be done in a variety of formulations. In particular, Ohrn, Deumens and collaborators have implemented a general variational treatment in... 

Analysis of realistic aspects of fabrication and performance of plastic materials involves the combination of complex geometrical, material and physical factors. The identification of the material mechanisms responsible for a specific phenomenon requires the development of relatively complex numerical models which accommodate the critical factors. Once the model is in place, it is possible to simulate different material mechanisms and verify their predictions through a comparison with experimental results. 

N Konga,B., Fernandez, G.,Guillard,H.,and Larrouturou, B., Numerical investigations of the tulip flame instability—comparisons with experimental results, Combustion Science and Technology, 87, 69-89,1992. 

There are many facets to a successful quantum dynamics study. Of course, if comparison with experimental results is a goal, the underlying Bom-Oppenheimer potential energy surface must be known at an appropriately high level of electronic structure theory. For nonadiabatic problems, two or more surfaces and their couplings must be determined. The present chapter, however, focuses on the quantum dynamics of the nuclei once an adequate description of the electronic structure has been achieved. 

Differences in the structure of monocrystalline, threshold or bridge type polycrystalline adsorbents are to be manifested in the shape of adsorption - caused response of electrophysical characteristics [25]. The basic models of adsorption - induced response of monocrystalline and barrier poly crystal line adsorbents have been considered in Chapter 1. Here we describe various theoretical models of adsorption-induced response of polycrystalline adsorbents having intercrystalline contacts of the bridge type and their comparison with experimental results. 

Klima J, Frias-Ferrer A, Gonzalez-Garcy J, Ludvyk J, Saez V, Iniesta J (2007) Optimisation of 20 kHz sonoreactor geometry on the basis of numerical simulation of local ultrasonic intensity and qualitative comparison with experimental results. Ultrason Sonochem 14 19-28... 

FIGURE 8.5 Variation of the b-value of the gaussian thermalization distribution in n-hexane with excess electron energy. While the b values were obtained by comparison with experimental results, other forms of initial distribution are also possible. Reproduced from Hirata and Mataga (1991). 

Answer Chemical shift calculations for nanoscale semiconductors by DFT methods and comparison with experimental results have recently appeared [140], and while quite challenging hold much promise. 

Equation 13.5-2 is the segregated-flow model (SFM) with a continuous RTD, E(t). To what extent does it give valid results for the performance of a reactor To answer this question, we apply it first to ideal-reactor models (Chapters 14 to 16), for which we have derived the exact form of E(t), and for which exact performance results can be compared with those obtained independently by material balances. The utility of the SFM lies eventually in its potential use in situations involving nonideal flow, wheic results cannot be predicted a priori, in conjunction with an experimentally measured RTD (Chapters 19 and 20) in this case, confirmation must be done by comparison with experimental results. 

The random A1 siting method of reference (7) was used to compute 29Si NMR intensities for comparison with experimental results reported in reference (2). The results in Table II show clearly some discrepancy between the experimental and calculated results. The variance a2 ranges from 35 to 329. The discrepancy is greatest at higher Si/Al ratios where the experimental distribution is much sharper than is expected of the maximum probability distribution of silicon and aluminum atoms. These results imply some ordering of the aluminum atoms in the lattice. 

Here, [OH]0 and [NCO]0 are initial concentrations of OH and NCO groups, respectively. Figures 5.10 and 5.11 show the calculated dependences of the gel fraction, wg, and concentration of EANCs, ve on rH [30, 60-62] and their comparison with experimental results. 

The issue of the chemical nature of graphene edges, and thus of (re)active sites, was addressed head-on by Radovic and Bockrath [29]. Density functional theory was used to minimize problems that truly ab initio approaches such as Hartree-Fock are known to have, but careful comparison with experimental results in several seemingly unrelated fields was also performed. The key argument of relevance here is that, rather than being H-terminated, the sites that are most relevant for the chemical (re)activity of sp2 hybridized carbon materials are of carbene- and carbyne-type, as illustrated below for the zigzag (a) and armchair edges (b). 

The link between the long-chain branch structure and the properties of the polymer has to be established experimentally by means of model branched polymers. This link can also be derived theoretically or through computer modehng. As a result, a large sub-field of study has emerged. The methods and results of this theoretical work are systematically reviewed by J. Freire. Where available, comparisons with experimental results are made. 

In addition to the development of new methods, new applications of molecular dynamics computer simulation are also needed in order to make comparisons with experimental results. In particular, more complicated chemical reactions, beyond the relatively simple electron transfer reaction, could be studied. Examples include the study of chemical adsorption, hydrogen evolution reactions, and chemical modification of the electrode surface. All of the above directions and opportunities promise to keep this area of research very active ... 

Straight simulation of collision processes relevant to stopping by solution of the classical equations of motion has been common for about two decades [64]. Although the necessary computational effort is considerable, remarkable results have been found in comparisons with experimental results such as emitted-electron spectra [65]. The main application area of this method refers to very heavy ions at not too high speeds where the Bohr criterion is well satisfied yet relativistic effects are insignificant. 

Chapter 10 provides an exhaustive description of how these techniques can be applied to a large number of industrial alloys and other materials. This includes a discussion of solution and substance databases and step-by-step examples of multi-component calculations. Validation of calculated equilibria in multi-component alloys is given by a detailed comparison with experimental results for a variety of steels, titanium- and nickel-base alloys. Further selected examples include the formation of deleterious phases, complex precipitation sequences, sensitivity factor analysis, intermetallic alloys, alloy design, slag, slag-metal and other complex chemical equilibria and nuclear applications. 

Comparisons with experimental results show that vertical NOF-EAs are better than those predicted by the CCSD(T) method within the 6-31++G basis set. 

Equation (4.15) is important, it offers an atom-by-atom partitioning of the molecular binding energy. The nice thing about (4.15) is that it does not imply any spatial partitioning of the molecule. Equation (4.13) is instrumental in the theory of bond energies. AE is convenient for comparisons with experimental results. 

Kienzler, B., Luckscheiter, B. Wilhelm, S. 2001. Waste form corrosion modeling comparison with experimental results. Waste Management, 21, 741-752. 

Bourcier, W. L. 1994. Waste glass corrosion modeling Comparison with experimental results. Materials Research Society Symposium Proceedings, 333, 69 - 82. 

Such a calculation had to be made in determining the problem of interaction between a diatomic polar molecule and an atom with a closed electronic shell [1,2]. The solution of this problem was of special importance in connection with the nature of the hydrogen bond. Our investigations were based on a definite hydrogen bond model that was verified by mathematical treatment and comparison with experimental results. This model is essentially different from that criticized by Dr. Burawoy. Its main point can be explained as follows [2, 3]. 

Comparability What can we deduce from a comparison with experimental results characterizing the same system Are the calculations a realistic model of a real system ... 

In the first chapter, Bates and van Santen summarize the theoretical foundations of catalysis in acidic zeolites. Being the most important crystalline materials used as catalysts, zeolites have been the obvious starting point for applications of theory to catalysis by solids and surfaces. Impressive progress has been made in the application of theory to account for transport, sorption, and reaction in zeolites, and the comparisons with experimental results indicate some marked successes as well as opportunities for improving both the theoretical and experimental foundations. 

Alternatively, coupled diffusion equations with concentration-dependent diffusivities and comparison with experimental results can be solved with numerical methods (see Kirkaldy and Young [1] and Glicksman [4]). 

Most of the early theories of polymer adsorption were not concerned with the interaction between adsorbed polymers so that they have little relevance for a comparison with experimental results. In actuality, the adsorbed mass per unit area is very large even when adsorption of polymers occurs from a very dilute solution. In this section, some typical theories allowing for the interaction between adsorbed polymers are reviewed. 

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