Relative efficiency calculation

FIGURE 2.13 From measurements of the retention volume, Vr, and the peak width at half peak height, Wr, of a gaussian peak, an estimate of column efficiency N and relative efficiency, HETP, may be calculated. The last figure is for very well packed columns close to 2 X dp. [Reproduced from Sofer and Hagel (1997), with permission.]... 

It can be seen from Fig. 3.23 that the relation (3.6.16) yielded the highest efficiency of about 9.5% whereas the efficiency calculated using relation (3.6.13) employing a two-electrode geometry has a maximum value of about 7%. Although the relative values may vary with respect to the experimental setup and measurement conditions, this exercise demonstrates that a certain... 

It is not appropriate in this review to discuss the relative efficiency of minimization routines based on steepest descent procedures, but a few of the more important references are given. If the gradient can be evaluated analytically, and as McIver and Komomicki 25) have pointed out this is the case for many surfaces calculated by semi-empirical molecular orbital methods, then this is the best approach. The methods developed by Davidson 26), Fletcher and oweZZ (27), and AfurfagZz and Sargent 28) assume this to be the case. If the gradient has to be obtained numerically then the method developed by Powell 29) has found wide acceptance for its efficiency. 

We can answer these questions using Eq. (30.1), which defines relative efficiency. The calculated numerical value of relative efficiency means nothing The equation may be used only to compare two sets of operating data. The equation is not even thermodynamically correct. But it is sufficiently correct, provided the services represented by the two sets of data are reasonably similar. 

The relative efficiency with different rates of flow of the gas-mixture is illustrated by Fig. 40, where the speed of flow is expressed in litres per hour per c.c. of free space in the reaction chamber—calculated at room temp. 

Another example is the perturbing effect of eight calcium channel blockers on membranes prepared from two different lipids [68]. The authors used total lipids from rat brain and synaptosomal membranes. The spin probe was l-palmitoyl-2-stearoyl-phosphatidyl-choline labeled at the doxyl group at the carbon-16 position (16-PC). The apparent order parameter, S, is calculated from the apparent outer (Amax) and inner (Amin) splittings which were directly taken from the ESR spectra. It is used to describe the relative efficiency of the dmgs in perturbing the lipid membrane. 

There are two types of Hessian calculations semimimerical, using a finite difference of analytic gradients, and fully analytic. The analytic approach employed in our method is usually preferable due to the significantly increased accuracy of the calculated vibrational frequencies as well as its considerable time savings. The relative efficiency and accuracy of analytic Hessians increase with the size of the molecule. All calculations presented were performed with the quantum chemistry program GAMESS [70],... 

In the above procedure, errors in VLE are compensated by equivalent errors in tray efficiency. If the relative volatility calculated by the simulation is too high, fewer stages will be needed to match the measured test compositions, i.e., efficiency will be lower. Scaleup will be good as long as the VLE and efficiency errors continue to equally offset each other. This requires that process conditions (feed composition,... 

The relative efficiency per collision for deactivation of excited molecules in thermal reactions increases with the number of atoms in the collider, but reaches a constant limit when this number exceeds about 12. This has been demonstrated for many thermal reactions by studying the low pressure fall-off. It may be noted from eqn. (10) that plots of k /k against pressure for different inert gases should comprise a set of curves dispersed along the pressure axis according to the various efficiencies of deactivation per unit pressure. The relative efficiency per collision can be derived by calculating the collision frequency, Z, with a hard sphere or Lennard—Jones model. 

Efficiency calculations for impactors are often based on the assumption that a particle s location relative to other particles never changes so that all particles initially lying within some arbitrary distance from the impactor centerline will be collected, while all those outside... 

Here we consider the relative efficiencies of the different inverse update formula. The calculations take the initial inverse Hessian as a unit matrix and the initial in the line... 

The study showed that hair analysis identified approximately four times the number of cocaine users as urinalysis in each 3-month time frame and this with approximately one tenth the number of tests. This shows hair analysis to be 33 times more effective than urinalysis on a per-test basis. Considering the cost of urine testing, test scheduling, and observed collection, this translates into a considerable savings per identified drug user. If the relative efficiency of urinalysis is calculated on the basis of positive cocaine test results (since cocaine users in a 3-month interval were occasionally identified more than once by urinalysis), then hair analysis is 24 times more effective than urinalysis. Except for marijuana, the test results with the other drugs follow a similar pattern. 

Simple theoretical comparisons of relative efficiencies of AOPs may generate contradictory results, as is exemplified in Tab. 8-2, mainly depending on the basis of calculation (Bolton and Cater, 1994, Glaze et al, 1987). The method favored by Glaze et al. (1987) used the same molar concentrations of auxiliary oxidants... 

Figure 4 shows all the experimental Cq data for the short screws and the corresponding values calculated from Figure 2. Molecular diffusivities at the various temperatures were taken from Figure 3, and the equilibrium values from Figure 5. The scatter is not too bad, and indicates that the model fairly well predicts the effect of rotational speed, throughput rate, and molecular diffusivity on devolatilization performance. The data also indicate that the geometry efficiency, p (which were different for the two screws) has some merit, and provides a convenient means for comparing the relative efficiency of different screw designs.

E values for the intramolecular abstractions in the presence of Lewis bases were calculated with/s = 422 Jmol pm" that is, with C 10° higher than in the cyclohexane chair configuration, 111.4° [91] in benzene fsg = 406Jmol" pm" was used according to the criteria already discussed, which implies an angle 1.4° smaller than in the presence of Lewis bases. The reasons for these small changes in C were discussed in Section III.B.6. This adjustment of C predicts E > E, for reactions with relative efficiencies close to unity in the presence of added Lewis base, and E < E, for inefficient... 

Table 2.9. Numerically calculated optimum flip angles and the relative efficiency of the sequences after Amoureux and Fernandez (1998) for Vq/vi = 1.25.

The figures illustrate the high quality of the theoretical description. The predicted fall-off curves very well reproduce experiments performed at various temperatures and for different bath-gases. The calculated values of k,j0/[M] increase as He < Ar < N2 < SF6 < CH3COCH3 < C3H8, which is in agreement with the relative efficiencies of the bath-gases reported for other termolecular reactions.6... 

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