Calculations distribution

Figure 4-18. Calculated distribution for ternary liquid-liquid systems show good agreement with experiment except very near the plait point.

Figure C2.13.2. Electron energy distributions/(U) for a mean electron energy of 4.2 eV, Maxwell distribution (M), Dmyvesteyn distribution (D) and a calculated distribution (Ar) for an Ar plasma [12].

Note that the calculated distribution shows some deviation from the measured values because of the small departure of the actual sample from the theoretical coefficient of variation (i.e., 47.5 versus 52 percent). 

At the conclusion of the calculation, a fragment size distribution as well as fragment number is provided. A cumulative number distribution is shown in Fig. 8.22 and compared with aluminum ring data acquired at = lO s (Grady and Benson, 1983). With the assumed fracture site nucleation law, the calculated distribution appears to agree reasonably well with the data. The calculation better predicts the tails of the distribution which have trends which deviate from strict exponential behavior as was noted in the previous section. 

It can be seen from Table 4.3 that there is no positive or foolproof way of determining the distributional parameters useful in probabilistic design, although the linear rectification method is an efficient approach (Siddal, 1983). The choice of ranking equation can also affect the accuracy of the calculated distribution parameters using the methods described. Reference should be made to the guidance notes given in this respect. 

To extract the agglomeration kernels from PSD data, the inverse problem mentioned above has to be solved. The population balance is therefore solved for different values of the agglomeration kernel, the results are compared with the experimental distributions and the sums of non-linear least squares are calculated. The calculated distribution with the minimum sum of least squares fits the experimental distribution best. 

The distribution function of the vectors normal to the surfaces,/(x), for the direction of the magnetic field B, in accord with the directions of the crystallographic axis (100) for the P, D, G surfaces, is presented in Fig. 6. The histograms for the P, D, G are practically the same, as they should be the differences between the histograms are of the order of a line width. The accuracy of the numerical results can be judged by comparing the histograms obtained in our calculation with the analytically calculated distribution function for the P, D, G surfaces [29]. The sohd line in Fig. 6(a) represents the result of analytical calculations [35]. 

Figure 15-23. Calculalcil value ol ihc square of (lie normalized electrical field i 2 at the Cw/PEOPT interface lor PEOPT thickness of 30 nm (solid line) and 40 nm (dashed line) versus thickness of the CM layer at a wavelength of 460 nin. The inset shows the calculated distribution of the square of Ihc normalized opiical field E ] inside an 1TO (120 mn)/PEDOT-PSS (110 iini)/PEOPT(30 nm)/CW) (32 nm) device at the same wavelength (reproduced by permission of Wilcy-VCH from Ref. 92 ).

Step polymerisation Monomer concentration drops rapidly to zero early in the reaction. Polymer molar mass rises steadily during reaction. Long reaction times increase molar mass and are essential to obtain very high molar masses. At all stages of the reaction every possible molecular species from dimers to polymers of large degrees of polymerisation are present in a calculable distribution. 

To generate the necessary distribution functions, the ratio of is used to approximate the true molecular weight distribution by a Schulz-Zimm distribution. It is also assumed that the reactive functional groups are distributed randomly on the polymer chain. The Schulz-Zimm parameters used to calculate distribution functions and probability generating functions (see below) are defined as follows ... 

The introduction of vectors of constant displacement length to represent the individual elements, which actually vary in length, is rendered more plausible by inquiry into the effect of incorporating this artifice in the treatment of the freely jointed chain. In this case V = m H. Upon substitution of this expression together with n nlm in Eq. (17), the previous expression for / , Eq. (6), is recovered. Hence the calculated distribution is unaff ected by an arbitrary subdivision of the chain in this manner. We conclude that the value chosen for m in the reduction of the real chain to an equivalent freely jointed chain likewise is inconsequential (within the limits on m stated above). 

Fig. 128.—Calculated distribution for each of eight fractions separated from the initial distribution shown by the uppermost curve. Dotted lines represent distribution of polymer remaining in the dilute phase after each successive precipitation with =10 in each case. The distribution for each fraction, obtained as the differences between successive dotted curves, is shown by a solid curve. (Schulz. )...

For both foam systems, the calculated distribution functions of the cell size from the SEM images are presented in Figure 9.20. The nanocomposite foams nicely obeyed a Gaussian distribution. In the case of PLA/ODA foamed at 150 °C under a high pressure of 24 MPa, we can see that the width of the distribution peaks, which indicates the dispersity for cell size, became narrow, accompanied by a finer dispersion of silicate particles. 

Fig. 3. Calculated distribution of beryllium hydroxo species in acid conditions, (a) CBe = 0.2 M, (b) CBs = 0.002 M.

Fig. 7. Calculated distribution diagram of beiyllium hydroxo species, CBb = 0.002 M.

Fig. 15. 9Be NMR spectra and calculated distribution diagram for the system BeS04-malonate 1 1 (CBe = CL = 0.1 M) (95).

The complex scattering wave function can be specified by nodal points at which u = 0,v = 0. They have great physical significance since they are responsible for current vortices. We have calculated distribution functions for nearest distances between nodal points and found that there is a universal form for open chaotic billiards. The form coincides with the distribution for the Berry function and hence, it may be used as a signature of quantum chaos in open systems. All distributions agree well with numerically computed results for transmission through quantum chaotic billiards. 

Pyridinecarboxaldehyde, 3. Possible hydration of the aldehyde group makes the aqueous solution chemistry of 3 potentially more complex and interesting than the other compounds. Hydration is less extensive with 3 than 4-pyridinecarboxaldehyde but upon protonation, about 80% will exist as the hydrate (gem-diol). The calculated distribution of species as a function of pH is given in Figure 4 based on the equilibrium constants determined by Laviron (9). 

Fig. 2.1. Formula representation (left), calculated geometries (middle) and calculated distributions of formal charge (right) in the pnra-tolyl ion, [C7H7]. Reproduced from Ref. [26] with permission. American Chemical Society, 1977.

One method proposed for estimating the cost of fuel cell power plants is to calculate distributive (bulk) costs as a function of the equipment cost using established factors based on conventional generating technologies. When applied in such a way as to compensate for the differences associated with a fuel cell plant, this approach can yield reasonable results. NETL has elected, based on the international prominence of the Association for the Advancement of Cost Engineering (AACE), to utilize this approach in estimating the costs for fuel cell/turbine power plant systems currently under study. 

Huggenberger, F., Letey, J., and Farmer, W.J. Observed and calculated distribution oflindane in soil columns as influenced by water movement. Soil Sci. Soc. Am. Proa, 36 544-548, 1972. 

Figure 3.2a. The effect of pH on the initial rate of hydrogenation of maleic acid (MA) catalyzed by [RhCI(TPPMS)j] in aqueous solution. [Rh]=0.001 M, [MA]=0.05 M, 60 C, Hj, I bar total pressure. The calculated distribution (a%) of nondissociated (H2A) and dissociated (HA, A ) maleic acid is also shown. Reprinted with pennission from Ckem. Eur. J. 2001, 7, 193. Copyright (2001) Wiley-VCH Verlag GmbH.

Fig. 4.22 Comparison of measured and calculated distribution ratios of americi-um(III)-terpyridine-decanoic acid complexes between 0.05 M HNOj and various organic solvent combinations. The calculated values are obtained with the Hansen partial solubility parameters. (From Ref. 45.)... 

The binodal curve has been calculated and is shown in Fig. 10.2 as a solid line. Furthermore, the calculated distribution of acetic acid between both phases is shown in Fig. 10.3. From these figures, it can be seen that the fitting to experimental data is good. 

To detain an nnpaired electron and facilitate the azocoupling, the o-dinitrobenzene anion-radical was tested in the reaction (Todres et al. 1988). Such an anion-radical yielded an azo-coupled prodnct according to Scheme 1.2 (the nitrogen oxide evolved was detected). The reaction led to a para-snbstitnted prodnct, entirely in accordance with the calculated distribution of spin density in the anion-radical of o-dinitrobenzene (Todres 1990). It was established, by means of labeled-atom experiments and analysis of the gas prodnced, that azo-coupling is accompanied by the conversion of one of the nitro gronps into the hydroxy gronp and the liberation of nitric monoxide. In other... 

Reaction system contains various stages, or chain lengths, of product present in a calculable distribution... 

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