Theoretical criticisms

Hase W L 1972 Theoretical critical configuration for ethane decomposition and methyl radical recombination J. Chem. Rhys. 57 730-3... 

This method employs a theoretical critical mass flow based on an ideal nozzle and isothermal flow condition. For a pure gas, the mass flow can be determined from one equation ... 

Thus the theoretical critical distance can be calculated entirely on the basis of spectroscopic properties of the donor and acceptor. 

Fig. 14.4. Theoretical critical velocity as a function of separation distance for different values of solute radius/pore radius ratio (A). Solute radius (a) = 5 nm ko= 1.0 (k is the Debye parameter) membrane and solute surface potential = 50 mV. Values of A (a) 0.8 ...

I, Chapters 2 and 3 deal with the general backgrounds of industrial safety (e,g, models of accident causation and of human behaviour) and with the contributions that near miss reporting could make in understanding and controlling accidents and incidents, Also theoretical criticisms of the near miss reporting efforts are discussed here,... 

The SRK model has not been without theoretical criticism. Bainbridge (1984) summarizes two of the main points brought forward against it. Firstly, she mentions problems in interpretation of the words skill , rule , and... 

The point M(u = — 1) in the phase diagram, Fig. 22, represents the theoretical critical particle velocity. It is clear that... 

For crystals of reasonably pure, well-annealed metals at a given temperature, slip begins when the resolved shear stress reaches a certain critical value, which is characteristic of each metal. In the case of aluminum, for example, the observed critical shear stress Uco is usually about 4x10 N/m ( 4 bars = 0.4 MPa). Theoretically, for a perfect crystal, the resolved shear stress is expected to vary periodically as the lattice planes slide over each other and to have a maximum value that is simply related to the elastic shear modulus /t. This was first pointed out in 1926 by Frenkel who, on the basis of a simple model, estimated that the critical resolved shear stress was approximately equal to h/Itt (see Kittel 1968). In the case of aluminum (which is approximately elastically isotropic), = C44 = 2.7x10 N/m, so the theoretical critical resolved shear stress is about lO wco for the slip system <100>(100). 

The nucleus is assumed to have the same structure, density, etc. as the bulk phase, and have the same interaction energies with adjacent phases (surface tension, etc.). This conception has proved valuable in general, but a few of its assumptions are difficult to prove or incorrect on the molecular level (Talanquer and Oxtoby 1994). Other assumptions are practically impossible to test (ten Wolde and Frenkel 1997), as critical nucleus formation is a fleeting event that may not be amenable to any direct imaging method. However, as nanoparticles are of the same size domain as theoretical critical nuclei, an understanding of the nucleation process is essential to defining and possibly controlling the pathways for nanoparticle formation. 

The major theoretical criticisms of BET are concerned with the assumptions that the surface Is energetically uniform and that adsorbate-adsorbate Interactions are negligible. In case of carbon fibers, the first assumption does not apply. Edge effects, due to the finite size of carbon layers and the presence of hetero-elements on the surface, are sources of energetic heterogeneity. The second assumption, that adsorbed molecules do not Interact energetically, Is also unrealistic. In spite of these Inadequacies, the BET theory Is useful In a qualitative sense and remains the most widely used method for surface area measurements. 

Figure 5. Comparison between experimental (full line) and calculated (dashed line) demixing curves in the oil rich region of the hexanol and pentanol systems. is the experimental critical point. P-E is the theoretical critical point.

Moreover, a thorough comparison of the experimental results obtained from foils of metallic hydrides and polymers - both measured under identical experimental conditions - showed that the observed magnitudes of the anomalies are clearly dependent on the physical conditions the hydrogen atoms are involved in [Abdul-Redah 2003], This result contradicts completely the newest theoretical criticism of Ref. [Blostein 2001 Blostein 2003 (b)]. All the results of these tests prove unequivocally that the aforementioned criticism [Blostein 2001 Blostein 2003 (b)] is unjustified in the context of our NCS experiments. 

However, as noted in the discussion on the LRT (Section 12.6.1), the test tends to be conservative for fixed effects, suggesting that the actual critical value for the LRT statistic may be larger than 3.84. Moreover, the number of samples per subject and the sample size may also affect the theoretical critical value, as the likelihood ratio is asymptotically distributed. Previous work also indicated that the likelihood... 

The Type I error (rejection of the reduced model in favor of the full model) that would result from the use of the theoretical critical value was assessed for each of the designs considered, and for three alternative NONMEM linearization methods first-order (FO), first-order conditional estimation (FOCE), and first-order conditional estimation with interaction (FOCEI). Type I error rates were assessed by empirical determination of the probability of rejection of the reduced model, given that the reduced model was the correct model. Data sets were simulated with the reduced model (FO, 1000 data sets FOCE/FOCEI, 200 data sets) and fitted using the full and reduced models. The empirical Type I error was determined as the percentage of simulated data sets for which a LRT statistic of 3.84 or greater was obtained. The 3.84 critical value for the LRT statistic corresponds to a significance level of 5%, for a distribution with 1 degree of freedom (for the one extra parameter in the full model). The LRT statistic was calculated as the difference between the NONMEM objective function values of the reduced and full models. The results of these simulations were also used to determine an empirical critical value that would result in the Type I error rate equal to the nominal 5% value. 

A comparison of the power to determine DDI with theoretical and empirical critical values for the FO method is presented in Figure 12.6. As expected, the theoretical power to determine DDI is higher than the empirically determined power, given the inflated Type I error with the theoretical critical value. The empirical power is a more accurate representation of the true power. 

The effect of study design, IIV in PK parameters, and estimation method on power to detect DDI is presented in Figure 12.7. Much of the differences between the estimation methods seen with the theoretical critical value appear to have been eliminated, particularly differences between the FO and FOCE methods. The empirical power could not be determined with the FOCEI method due to failure of a sufficient number of estimation runs to converge. However, for cases in which the power with the FOCEI method could be determined, it was consistently greater than the power obtained with the other two methods. 

Lennard-Jones and Devonshire arrive at theoretical critical temperatures which are in good agreement with experimental values for argon, neon, nitrogen, etc. However, the theoretical critical volumes and pressures are off by factors of about 1.6 and 3.9, respectively. 

Equation 4-6 is the classical theoretical relationship for long thin cylinders under external pressures. These theoretical values for collapsing pressure are based on considerations of perfect geometry and perfect uniformity in the shell material. In any actual vessel, the idealized condition cannot be obtained and it was found that the collapse of commercial tubing and pipe occured at a critical pressure, approximately 27% less than the theoretical critical pressure. Using a safety factor of 4 for equation 4-5 we obtain... 

The most commonly used superconductor is NbTi,-an alloy, which is relatively ductile, and which can be extruded into wire In a relatively straightforward manner. Its theoretical critical field at the temperature of liquid helium is 11.8 T. 

A minimal micelle with peq = Pmm appears in the system at a certain (minimal) threshold concentration, Cmin, which can be identified as the theoretical critical micellization concentration . Below this threshold, c < Cmin, no micelles and only unimers are found in the solution. At amphiphile concentration c = Cmin, the number density of micelles, = exp [-Q(pmin)/for]. is negligible with respect to the unimer density,. A subsequent increase in the concentration of amphiphiles, c > Cmin, leads to an increase in both the concentration of micelles, Cmic, and the concentration of unimers, ci, and an increase in both the chemical potential of unimers and the aggregation number, peq-... 

Since A"(ni<) begins to depart from zero at ni< near unity, it follows from eq 4.6 that the theoretical critical contour length Lc for the onset of the excluded-volume effect on chain dimensions is approximately given by... 

If no stress and external pressure are loaded on the membrane at the temperature, Tq, considering a constant linear thermal expansion coefficient, the theoretical critical temperature for the membrane to buckle can be given as... 

A typical load out of plane displacement curve is shown in Figure 11. This indicates that the fracture load is well above the theoretical critical load to cause buckling. 

For the polystyrene-l-acetone system, the calculated phase separation region (a .sand clock ) proves to be more narrow than the experimental one, and the theoretical critical concentrations at the UCSl and LCST are twice as lower as the experimental ones (Siow et al., 1972). 

Table 8.2 summarizes the theoretical critical indices and their experimental values. The index s characterizes the divergence of the viscosity, and t characterizes the appearance of the elastic modulus. The index t is larger than because not all the chains in the connected network are elastically effective. There are many free ends near the percolation... 

PAXTON, H. C., Correlation of Experimental and Theoretical Criticality Data, Comparative Reliability, Safety Factors for Criticality Control, LAMS-2537 (March 1961). 

H. C. PAXTON, Correlations of Experimental, and Theoretical Critical Data," LAMS-2S37, p. 11, Los Alamos Scientific Laboratory (May 15, 1961). 

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