Scale power

Cell divider Temp, C Current Cell voltage. Product Current Power Scale Reference... 

Solution If power scales as N]D], then power per unit volume scales as N]D], To maintain constant power per unit volume. A/must decrease upon scaleup. Specifically, Nj must scale as When impeller speed is scaled... 

The frequency effects are studied in the cylindrical geometry (R = 0.08 m, L = 0.027 m) at a constant power of 25 W, which corresponds to a volume power density 46 mW cm . The pressure is 120 mTorr with 45% SiHa and 55% H2. It is found that the RF voltage at this power scales with the frequency as Vrfv p = C, with C a constant. Because the induced displacement current increases with the... 

Fig h. Diugr.i ii dI high-average power slab laser oscillator pumped by an array of diode lasers. Such an arrangement offers lower com, ease of power scaling, and long-ierm reliability. i Alter H er I... 

Solution If power scales as NjDj, then power per unit volume scales as NjDj. To maintain constant power per unit volume, IV/ must decrease upon scaleup. Specifically, Nj- must scale as DJ2 3. When impeller speed is scaled in this manner, the mixing time scales as D2J3and the impeller pumping rate scales as D7/3. To maintain a constant value for t, the throughput Q scales as Dj = S. Results for these and other design and operating variables are shown in Table 4.1. 

In the laboratory we can measure RF power in watts, but when we set up NMR experiments we use a relative power scale that is logarithmic the decibel scale. For comparison of power levels, we compare to a standard power level P0 that corresponds to zero on the decibel scale ... 

The decomposition of methyl chloroformate is a very convenient method to establish a nucleophilicity power scale of the chloride anion in onium chlorides, allowing thus to easily compare a priori the catalytic efficiency of different candidates. It is known that the decarboxylation of methyl chloroformate is catalyzed by Q Q type compounds thus producing only methyl chloride and carbon dioxide according to a pure 5N2 reaction (Ref. 7) [Scheme 10] ... 

When a system has long-time correlation, for which we expect fractional power scaling of excess heat, our assumption of the Boltzmann equilibrium distribution may always not be valid. Actually some power distributions such as the Tsallis distribution [14] have been reported at the edge of chaos [15]. A superstatistical equilibrium distribution is written as a superposition of Boltzmann distributions with different temperatures. Beck and Cohen [13] considered many types of distributions for the inverse of temperature. For example, they chose Gaussian, uniform, gamma, log-normal, and others. In particular, the Tsallis distribution is realized for gamma distribution. We will show that excess heat can be written as a superposition of correlation functions... 

In a separate article [10] we considered a modified version of a onedimensional intermittent chaotic system, the Manneville-Pomeau map [18]. We numerically confirmed the fractional power scaling of excess heat production. 

Before we close this section, we will comment on the area of the hysteresis loop. When the decay constant of a correlation functions depends on the inverse of temperature, we can expect various behavior for the area of the hysteresis loop. In the case of the Tsallis distribution, the inverse of temperature is distributed as a gamma distribution. If the decay constant is proportional to the temperature, the area of the histeresis loop decays as a modified Bessel function for the large period of external transformation. On the other hand, if the decay constant is proportional to the inverse of temperature, we can expect the fractional power scaling. 

Savage, V. M. et al. (2004). The predominance of quarter-power scaling in biology. Eunctional Ecology, 18, 257-82. 

Conical mixers are also known as Nauta mixers (Fig. 18-53). Material placed in the conical bin is lifted by the rotation of the helical screw, which in turn is rotated around the wall of the cone. The lifting actions of the screw combined with motion around the cone provide bulk mixing for flowable dry powders, paste materials, and even viscous fluids. The specific energy input is relatively small, and the large volume of the mixers can even provide storage capacity The mixers may have multiple screws, tapered screws, and high-speed dispersers for different applications. At constant speed, both the mixing time and power scale up with the square root of volume. Sizes from 0.1 to 20 m3 (3.3 to 700 ft3) are available. 

Some common terms used in preparative-scale liquid chromatography are summarized in Table 11.4, The production rate, specific production, or the recovery yield provide suitable objective functions to judge the relative success of individual methods. For efficient use of the separation system, the production rate and the recovery yield should be maximized. Invariably, this results in operating the column in an overloaded condition. Unfortunately, column operation under nonlinear conditions is complex, and optimum conditions are not as easy to predict as the less demanding, although less powerful, scale-up approach. To scale up an analytical separation, the same column packing, column length, and mobile phase velocity are used, and the column diameter increased... 

For data that resemble Pattern C, the researcher needs to up the power scale of X (x, r , etc.) or down the power scale of y y/y, log y, etc.) to linearize the data. For reasons previously discussed, it is recommended to transform the y values only, leaving the x values in the original form. In addition, once the data have been reexpressed, plot them to help determine visually if the reexpression adequately linearized them. If not, the next lower power transformation should be used, on the y value in this case. Once the data are reasonably linear, as determined visually, the F test for lack of fit can be used. Again, the smaller the Fc value, the better. If, say, the data are not quite linearized by y/y but are slightly curved in the opposite direction with the log y transformation, pick the reexpression with the smaller F value in the lack-of-fit test. 

For data that resemble Pattern D, the researcher can go up the power scale in reexpressing y or down the power scale in reexpressing x, or do both. Again, it... 

Recall from Chapter 2 the discussion on how to linearize curved data that exhibit patterns as seen in Figure 3.9. Data producing such a pattern are linearized by lowering the power scale of the x and/or y data. We lower the y data and retain the x values in their original form. 

With any waveform, the FAIMS separation power scales as the cube of peak field intensity. 

Because heat generation is the main limiting factor for power scaling of Nd lasers, a generalized figure of merit has been proposed to measure the effects of pump... 

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