Other Efficiency Criteria

So far, the discussions have dealt mainly with b, the most commonly used criterion of the fractionation efficiency. We shall now examine some of the other criteria mentioned before. 

As stated earlier, the shift of the average molecular weight of the fraction with respect to that of the parent distribution varies considerably with the type of distribution. For this is illustrated in Figs. 9 and 17. 

Huggins criteria and ( s. (14) and (15)) also depend on the shape of the initial distribution, as is witnessed by Fig. 22. However, the general shape of the (x) curves is not unlike that found by Huggins for binary potymers (Fig. 7). It indicates that an arbitrary decrease of x may well be harmful for the quality of the fraction. 

In fact, this conclusion is quite general it applies equally well to b, f and e. Generally, there exists a value for x below which a further decrease only leads away from the desired result, i.e. the lowest value of b (or highest value of f or e) attainable under the circumstances of the separation. 

In view of the remarks made in 1,4, examination of the remaining criterion a would not seem superfluous. Some examples of a x) curves are given in Fig. 23. The a (x) functions do not reveal any new aspect, and the a (x) curves are interesting only in so far as their minimum shifts towards lower ac-values than b [x). Further, they do not tend to descend 

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The quahty of incoming raw sugar is paramount for efficient operation. Polarization is a universal quaUty criterion. Color, ash (inorganic), invert sugar, moisture, dextran content, and grain size are other criteria that may be included in raw sugar purchase contracts. 

Any effect of Mach number is experienced by rotor and stator equally and thus neither (or both) are limiting, and this Mach number will be lower than for other degrees of reaction under the conditions stated. If equal lift and drag are assumed in both rotor and stator, then optimum efficiency is obtained with R = 0.5 and VJu = 0.5. Although the latter is not always true, it does provide a useful criterion. Furthermore, the blade angles are similar in rotor and stator, which may be an advantage in the... 

In the standard HMC method two ingredients are combined to sample states from a canonical distribution efficiently. One is molecular dynamics propagation with a large time step and the other is a Metropolis-like acceptance criterion [76] based on the change of the total energy. Typically, the best sampling of the configuration space of molecular systems is achieved with a time step of about 4 fs, which corresponds to an acceptance rate of about 70% (in comparison with 40-50% for Metropolis MC of pure molecular liquids). 

Another important issue that arises in the PDS method, as well as some other standardization methods, is the selection of the samples to use for standardization. It is critical that the standardization samples efficiently convey the magnitude and nature of instrument-to-instrument variability artifacts that are expected to be present in the analyzers while they are operating in the field. Note that this criterion is different than the criterion used for sample selection for calibration, which is to sufficiently cover the compositions of the process samples that the analyzer is expected to see during its operation. Sample selection strategies for instrument standardization have been given by many.73,77-79... 

For point particles governed by Stokes law, the Stokes number is the only criterion other than geometry that determines similitude for the shape of the particle trajectories. To ensure hydrodynamic similarity, in general, the collector Reynolds number also must be preserved, as well as the ratio I = R/a, called the interception parameter. Then, the collection efficiency of particles hitting an obstacle such as a cylinder has the form ... 

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