Discrepancy between the theory and experiments

Although the theory given in the previous section is largely in agreement 

Part of these discrepancies can be attributed to the molecular weight distribution, which seriously affects the value of On the other hand det led comparison with experimental results indicates that not all the discrepancy can be resolved by the molecular weight distribution.  

At present, a more consistent explanation seems to be that given by Graessley, who pointed out that the observed viscosity and the relaxation time are smaller than the calculated ones. Using eqns (7.32), (7.33), (7.46), and (7.47), one can show that 

On the other hand, a widely accepted empirical formula is 

Unfortunately since no data are available for molecular weights higher than SOOAfe, which is 3 x 10 for a polystyrene melt, the crucial test of Graessley s conjecture has not been given. However, it is obvious that 

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There is a significant scatter between the values of the Poiseuille number in micro-channel flows of fluids with different physical properties. The results presented in Table 3.1 for de-ionized water flow, in smooth micro-channels, are very close to the values predicted by the conventional theory. Significant discrepancy between the theory and experiment was observed in the cases when fluid with unknown physical properties was used (tap water, etc.). If the liquid contains even a very small amount of ions, the electrostatic charges on the solid surface will attract the counter-ions in the liquid to establish an electric field. Fluid-surface interaction can be put forward as an explanation of the Poiseuille number increase by the fluid ionic coupling with the surface (Brutin and Tadrist 2003 Ren et al. 2001 Papautsky et al. 1999). 

Another significant discrepancy between the theory and experiment is that even the computed values of the reorganization energy, to say nothing of its experimental estimation, are too small to be used for explaining the rate of the cathodic generation of solvated electrons (see Sect. 7). All this indicates that some factors affecting the electrochemical behaviour of solvated electrons are still unknown. 

The proportionality constant may be found by fitting the experimental value for Gd. For the other metals the 6p predicted from the scaling relation are compared with experimental values in tablq 3.8. The experimental values are taken from the review by Koehler (1972). In cases where the paramagnetic property is anisotropic, the average 0p is used for comparison. The small discrepancies between the theory and experiment should be viewed as evidence that the electronic structures of these metals are not identical. Applications of the RKKY theory to explain the magnetic behavior of rare-earth intermetallic compounds is discussed in ch. 14, sections 2.1.4 and 2.1.5. 

The observed build-up of TATB is similar to that found for Composition B described on page 101. The authors conclude Thus the experimental data obtained on 3 cm long IHE (Insensitive High Explosive) charges may underestimate the C-J pressure by about 20 percent. Attempts to extend the field of equation of state application, for example to model detonations of larger charges, overdriven detonations, or to calculate the sound velocity in the detonation products, will result in appreciable discrepancy between the theory and experiment. ... 

Thus, there is clearly a discrepancy between the theory and experiment, which exceeds the possible errors in calculations or in measurements. This discrepancy indicates that the process is essentially nonadiabatic (3 , = 10 for a mercury cathode and 10 - 10 for a silver cathode), i.e. the probability of a subbarrier transfer of a proton is rather low. It has been shown here that we could hardly explain the value Bg, << 1 for a barrierless discharge by assuming that the stretching of the 0-H bond is the decisive factor in the activation process. However, this value is natural for the quantum-mechanical theory. ... 

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. 

Motivated by the observed decay rate discrepancy between QED theory and experiment for At, numerous searches have been performed for forbidden, small or exotic decay modes. An exotic decay branch, besides o-Ps —> 37, with roughly 10-3 branching ratio could be causing the higher decay rate and is given by A 0bs = + A exotic- Many candidate decay branches have been proposed in... 

In Fig. 12 the comparison of experimental and calculated within the frameworks of fractal kinetics (according to the Eq. (24) and (25)) kinetic curves for DMDAACh is showa As one can see, excellent corresporrdence between the theory and experiment is obtained the discrepancy does not exceed 6%, i.e., it is not higher than Q definition error [1],... 

Several generations of chemists have been conditioned to accept the notorious discrepancy between the theory and practice of chemistry as the unquestionable norm. Sterically forbidden molecular rearrangements and phase transformations are routinely reported without comment, and the flow of electronic particles, postulated to rationalize the course of chemical reactions, is never subjected to critical scrutiny. In reality, practising chemists design their experiments in terms of the nineteenth-century notions of chemical affinity, never adequately explained by twentieth-century theories. The innocent belief that quanrnm physics explains all of chemistry is, like the rest of quantum theory, obediently respected as just another of its deep inscrutable mysteries. 

The results of the experiment depicted in Fig. 62 and others similarly obtained are summarized in Table XXXI. In every case the observed gel point is reached at higher than the theoretical extent of reaction. The discrepancies between the observed and calculated ojc s appear to be due to the failure of the theory to take into account a minor degree of intramolecular condensation. Since some of the interunit linkages... 

Next, one frequently would like to be able to make some assessment of the accuracy of a set of experimental vapor-liquid or activity coefficient measurements. Basic thermodynamic theory (as opposed to the solution modeling of Chapter 9) provides no means of predicting the values of liquid-phase activity coefficients to which the experimental results could be compared. Also, since the liquid solution models discussed in Chapter 9 only approximate real solution behavior, any discrepancy between these models and experiment is undoubtedly more a reflection of the inadequacy of the model than a test of the experimental results. 

This review is not presented from the historical point of view. Atomic and nuclear behavior and the theory and experiments backing it are discussed as we understand them today. Emphasis is given to the fact that the current picture of atoms, nuclei, and subatomic particles is only a model that represents our best current theoretical and experimental evidence. This model may change in the future if new evidence is obtained pointing to discrepancies between theory and experiment. 

Several recent papers have reported Density Functional Theory (DFT) calculations on the primary oxidation and reduction products observed in irradiated single crystals of the common nucleobases Thymine, Cytosine, Guanine, and Adenine. The theoretical calculations include estimates of spin densities and isotropic and anisotropic hyperfine couplings which can be compared with experimental results (obtained from detailed EPR/ENDOR experiments). In many cases the theoretical and experimental results agree rather well. In other cases there are discrepancies between the theoretical and experimental results. Herein the successes and failures of using DFT to calculate spin densities and hyperfine couplings of the primary radiation induced free radicals observed in the nucleobases will be discussed. 

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