RESULTS OF CRITICALITY CALCULATIONS

Described herein are the results of criticality calculations for single-, four-, six-, and seven-cell gas core models. These beryllium-reflected and -moderated UFs systems all have potential merit relative to both the proliferation of weapons-grade materials and the con-servative/efflcient utilization of thorium and uranium resources. A brief investigation of the consequences of denaturing the with indicates neutronic feasibility for ratios up to 20 1 however, the practical-... 

The results of our calculations based on both the static and dynamic theories show that most of the nonbenzenoid cyclic conjugated systems examined exhibit in a greater or lesser degree a marked double-bond fixation. The static theory indicates that even in benzene there exists a hidden tendency to distort into a skewed structure and that such a tendency is actually realized in [4n-f-2] annulenes larger than a certain critical size. In nonalternant hydrocarbons bond distortion is a rather common phenomenon. Fulvenes, fulvalenes and certain peri-condensed nonalternant hydrocarbons undergo a first-order bond distortion, and... 

Using Eqs. (5-42)-(5-46) in Section 5.3.2.2 with iterative calculations, the predicted CHF were compared with Columbia University data (Fighetti and Reddy, 1983). The comparison was made by examining the statistical results of critical power ratios (DNBRs), where... 

Results of these calculations are given in Table 2 and in Figure 3. Also shown are results of calculations made assuming the mixture to be a perfect gas at the calculated critical temperature. (The pressure has no effect on the calculated ideal gas conversion in this reaction.)... 

The outputs can create consequences to personnel, structures, and equipment. There are different approaches for assessing consequences. Criteria can be developed that will allow the analyst to compare the results of the calculations to predetermined criteria. The results either meet or exceed the criteria. These criteria can be established based on a conservative approach of assuming a steady-state condition. Another approach is the use of more sophisticated heat transfer techniques, where a time-dependent onset of critical criteria is modeled. 

The results of the calculations of the spectra are illustrated by Figs. 18 and 19. The first figure refers to the temperature T = 133 K, which is near the triple point (131 K for CH3F). In this case the density p of a liquid, the maximum dielectric loss t j( in the Debye region, and the Debye relaxation time xD are substantially larger than those for T = 293 K (the latter is rather close to the critical temperature 318 K) to which Fig. 19 refers. The fitted parameters are such that the Kirkwood correlation factor is about 1 at T = 293 K. 

In this paper, the multiphonon relaxation of a local vibrational mode and the non-radiative electronic transitions in molecular systems and in solids are considered using this non-perturbative theory. Results of model calculations are presented. According to the obtained results, the rate of these processes exhibits a critical behavior it sharply increases near specific (critical) value(s) of the interaction. Also the usual increase of the non-radiative transition rate with temperature is reversed at certain value of the non-diagonal interaction and temperature. For a weak interaction, the results coincide with those of the perturbation theory. 

It should be noted that the same formula could be obtained if we consider only the Hamiltonian Hi specified by Eq. (30). It agrees with the results of numerical calculations, which show that the estimations of critical value of a are slightly modified if only Hi is taken into consideration. 

Vapor pressures over AlBrg(cr) and AlBr d) have been measured by Dunne and Gregory ( ), Fischer, Rahlfs and Benze (2) and Sulzmann ( ). The vapor pressures were corrected for vapor non-ideality by means of the equation AG /T=-RlnP-BP/T. The Bertholot equation of state and critical constants T =763 K and P =28.5 atm reported by Johnson, Silva and Cubicciotti (4) were used to calculate B. The corrected vapor pressures were used to calculate Aj,H"(298.15 K) by both 2nd and 3rd law methods. The results of the calculations are as follows with reaction (A) corresponding to 2 AlBrg(cr) Al2Brg(g) and reaction (B) corresponding to 2 AlBr (i)=Al Br (g). 

Figure 21 ALISS polar scans of a TiO2(110)-p(l x 1) surface taken along the (a) [001] direction and (b) [—110] direction using 1-keV Li" " ions backscattered at 160°. The solid circles are experimental data points and the solid curve is the result of theoretical calculations. Dotted lines demonstrate simulations for an error in critical angle by +1.0°. The dashed line shows the simulations for the bulk structure shown in Figure 20. (From Ref. 41.)...

The results of the calculation with these parameters are shown in Figure 5. The decarburisation reaction, the critical point and carbon content are modelled correctly,... 

Moreover, after calculating the critical exponent a, the critical exponent (v (X) is readily given by Eq. (68). The results of the calculations for the vW (A) series show oscillatory behavior. The data do not reach a limit at N... 

The metal hexacarbonyls have been investigated using both the simple Wolfsberg-Helmholz method, and several refinements designed to meet in part the criticisms (III—9) to which this open. Some results of these calculations are compared for Cr(CO)6 (Table 2) with those of the more exact calculation (70) and with experimental data. 

When the anisotropy is so large, the analysis is simplified, so that an analytic limiting expression can be derived. One asymptotic result of Fisher [53] has proved to be particularly useful for understanding the results of numerical calculations [30, 47—51]. The Fisher expression yields the critical temperature of an anisotropic lattice gas model, as follows ... 

The H/C ratio in eq. (2) is 1, whereas the ratio in eq. (1) is 3. The use of C02 instead of steam represents no change in overall reaction kinetics (ref. 2). However, the presence of CO, in the feedstock results in more critical conditions for carbon because of lower H/C ratio. The ratio of H2/CO in the reformer exit gas can be estimated by thermodynamic calculations knowing the atomic ratio 0/C and H/C in the feed stream, and the pressure and temperature at the reformer exit. The results of the calculations are presented in the equilibrium chart (ref. 3) shown in Fig. 2 for a given pressure and temperature. 

As device dimensions continue to shrink, pattern resolution becomes of critical importance. In this regard, the use of radiation sources with maximized output in the mid-UV region (300-350 nm) would permit increased resolution if an appropriate resist could be utilized. In this regard, commercial resist formulations function inefficiently in this region for a variety of reasons. Accordingly, we have used semiemipirical quantum mechanical techniques to calculate the electronic absorption spectra of two of the most commonly employed chromophores and to computationally assess the effect of a variety of substituents. The results of these calculations have been used to drive a synthetic program designed to produce an efficient sensitizer for use in the mid-UV. 

Results of thermodynamic calculations show (e.g. Dufour and Defay, 1963 E. Meszaros, 1969) that the critical supersaturation of solution droplets formed on water soluble particles (see Subsection 4.5.1) is less than values for insoluble particles of the same size.1 Furthermore, theory indicates that larger particles arc more active in condensation processes than smaller nuclei. These theoretical considerations are in good agreement with experimental findings (e.g. Twomey 1971 and 1972) which suggests that the majority of active condensation nuclei are composed of water soluble ammonium sulfate particles with dry radii greater than 0.01 0.05 /im. 

Since it s inception in 1967, the Advances in Quantum Chemistry series has attempted to present various aspects of atomic, molecular, and solid state theory at the cutting edge. The contributions have taken various forms, from longer review articles to conference proceedings, and most of them have been well received. In this issue, we continue in this trend, and address some of the fundamental issues in density functional theory (DFT). DFT is extremely popular these days in its applied form It is almost impossible to read an experimental article where explanation of the results does not involve a DFT calculation using one or another commercial program and implementing one or another parameterized potential scheme. However, the success of applied DFT seems to be that it works, rather than the result of critical analysis of the fundamentals of the theory. However, the community also needs to explore the limits of the theory itself, and it is with this that the first four contributions in this issue concern themselves. 

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