The Optimum Value of

It can be shown that, in terms of overall stresses in a converter and size, r 0.4 represents an optimum of sorts. We will now try to understand why this is so, and later we will try to point out exceptions to this reasoning. 

Therefore, in general, a current ripple ratio of around 0.4 is a good design target for any topology, any application, and any switching frequency. 

we will discuss some reasons/considerations for not adhering to this r 0.4 rule-of-thumb (under certain conditions). 

---

The rule of thumb to determine the ground loop impedance is to consider the ground fault current as one and a halftimes that of the overcurrent setting of the circuit breaker for breaker-controlled systems (a fault condition for a breaker) or three times the rating of the fuses, for fuse-protected systems (an overcurrent condition for the fuses). Based on this rule. Table 21.2 suggests the optimum values of ground loop impedances for circuits of different... 

An extruder is coupled to a die, the output of which is given by (KP/ij) where P is the pressure drop across the die, i] is the visco.sity of the plastic and is a constant. What are the optimum values of screw helix angle and channel depth to give maximum output from the extruder. 

The rest of the gaseous stream, (i — )G, is bypassed, and the net effect is that a fraction a of the VOC contained in the whole gaseous waste is recovered. Hence, the identification of the optimum value of is part of the system optimization. 

As can be seen from the plots, the minimum TAC is about 55,OOQ/yr. The opdmal permeate composition is about 0.0005 kmol/m which conesponds to a feed pressure of 48 atm. It is interesting to note that the optimum value of Cp is significantly less than the required target composition (0.0012 kmol/m ). In other words, more separation can be obtained for less cost It is also worth mentioning that in some cases, environmental regulations tnay allow the bypass of a fraction of the feed and later mix it with the over-separated permeate to attain the requited target composition. In such cases, lower costs than the ones shown in Figs. 11.5 and 11.6 can be accomplished. 

Fig. 6.4 then shows a more complete calculation of plant efficiency for varying S. The optimum condition of maximum efficiency is reached at 5 = 0.208. The picture changes for a gas turbine with a higher pressure ratio, for which the increase to maximum efficiency is less, as is the optimum value of S 2]. 

The optimum values of die oq and a coefficients are determined by the variational procedure. The HF wave function constrains both electrons to move in the same bonding orbital. By allowing the doubly excited state to enter the wave function, the electrons can better avoid each other, as the antibonding MO now is also available. The antibonding MO has a nodal plane (where opposite sides of this plane. This left-right correlation is a molecular equivalent of the atomic radial correlation discussed in Section 5.2. 

The optimum value of c is determined by the variational principle. If c = 1, the UHF wave function is identical to RHF. This will normally be the case near the equilibrium distance. As the bond is stretched, the UHF wave function allows each of the electrons to localize on a nucleus c goes towards 0. The point where the RHF and UHF descriptions start to differ is often referred to as the RHF/UHF instability point. This is an example of symmetry breaking, as discussed in Section 3.8.3. The UHF wave function correctly dissociates into two hydrogen atoms, however, the symmetry breaking of the MOs has two other, closely connected, consequences introduction of electron correlation and spin contamination. To illustrate these concepts, we need to look at the 4 o UHF determinant, and the six RHF determinants in eqs. (4.15) and (4.16) in more detail. We will again ignore all normalization constants. 

Optimum Pump Output. In harder formations where drilling rates are limited by maximum available bit weight and rotary speed, the optimum value of... 

The same procedure is then adopted for obtaining the optimum value of P,2 and hence ... 

A primary goal of this chapter is to learn how to achieve control over the pH of solutions of acids, bases, and their salts. The control of pH is crucial for the ability of organisms—including ourselves—to survive, because even minor drifts from the optimum value of the pH can cause enzymes to change their shape and cease to function. The information in this chapter is used in industry to control the pH of reaction mixtures and to purify water. In agriculture it is used to maintain the soil at an optimal pH. In the laboratory it is used to interpret the change in pH of a solution during a titration, one of the most common quantitative analytical technique. It also helps us appreciate the basis of qualitative analysis, the identification of the substances and ions present in a sample. 

When an analytical method is being developed, the ultimate requirement is to be able to determine the analyte(s) of interest with adequate accuracy and precision at appropriate levels. There are many examples in the literature of methodology that allows this to be achieved being developed without the need to use complex experimental design simply by varying individual factors that are thought to affect the experimental outcome until the best performance has been obtained. This simple approach assumes that the optimum value of any factor remains the same however other factors are varied, i.e. there is no interaction between factors, but the analyst must be aware that this fundamental assumption is not always valid. 

Factorial design One method of experimental design that allows interactions between factors to be investigated, i.e. whether changing one experimental variable changes the optimum value of another. 

The absorbances at 1730, 1630, 1460, 1379, 1260, 1120, and 1019 cm follow an upward trend with concentration in the case of the bulk-modified samples also (Figure 31.4a through g) in line with the gel content, due to the reasons, pointed out above. Since the surface concentration of TMPTA per unit volume of EPDM is lower in the case of bulk modification as compared to surface modification, the optimum value of the concentration of TMPTA is not observed in these plots. 

Equation (1.5) then allows us to deduce the optimum value of Tads of the Sabatier maximum rate. It can be deduced from Eq. (1.12a). The latter depends on the CO pressure through A. 

The optimum values of AF and AF must be chosen such as to minimize the total activation free energy in Eq. (34.38) with the constraint... 

The interval of the batch time is split in two equal intervals. Temperature and feed rate at the boundaries of sub-intervals are subjected to optimization together with the other variables. Temperature and feed rate between the boundaries of sub-intervals are assumed to be straight lines connecting the initial and final values. The optimum values of variables obtained in step two are taken as initial guesses for optimization. The new profiles consist of two ramps joining optimized points. 

The A term represents the contribution from eddy diffusion, the B term the contribution from longitudinal diffusion, and the C terms the contributions from mass transfer in the mobile and stationary phases to the total column plate height. By differentiating equation (1.31) with respect to the mobile phase velocity and setting the result equal to zero, the optimum values of mobile phase velocity (u ) and plate height (HETP ) can be obtained. 

The optimum values of the first and second entropies, and the steady rates of production of these by the reservoirs may readily be obtained. The maximum value of the total first entropy is... 

The third step is to find the values of the variables that give the optimum value of the objective function (maximum or minimum). The best techniques to be used for this step will depend on the complexity of the system and on the particular mathematical model used to represent the system. 

The one-at-a-time method is to pick one of the variables and make a number of tests until the optimum for that variable is obtained at a constant level of the other variables. If the temperature is held constant at 250°F in Figure 14-1, the optimum value of the pressure would be 51 psia (point B). 

It is desired to determine the optimum values of the constants in the van der Waals equation ... 

Using the following methods, obtain the optimum values of a and b ... 

Er has dropped to five standard deviations, the optimum transmittance has dropped to 3.2, and then drops off quickly below that value. Surprisingly, the optimum value of transmittance appears to reach a minimum value, and then increase again as Er continues to decrease. It is not entirely clear whether this is simply appearance or actually reflects the correct description of the behavior of the noise in this regime, given the unstable nature of the variance values upon which it is based. In fact, originally these curves were computed only for values of Er equal to or greater than three due to the expectation that no reasonable results could be obtained at lower values of Er. However, when the unexpectedly smooth decrease in the optimum value of %T was observed down to that level, it seemed prudent to extend the calculations to still lower values, whereupon the results in Figure 45-11 were obtained. 

The resulting plot is presented in Figure 51-29. From the plot, and from examining the list of values from which the plot was made, there appears to be no shift in the transmittance corresponding to the optimum value of relative absorbance, as the reference reading varies. 

For EMG peaks, peak skew increases with the ratio xG/oG. Figure 16-32 illustrates the characteristics of such a peak calculated for xG/aG = 1.5. In general, with xG/aG > 1 (peak skew > 0.7), a direct calculation of the moments is required to obtain a good approximation of the true value of N , since other methods give a large error (Yau et al., Modems Size-Exclusion Liquid Chromatography, Wiley, New York, 1979). Alternatively, Eq. (16-165) can be fitted to experimental peaks to determine the optimum values of fG, aG, and xG. 

---