Calculation speed

The models are applicable to large data sets with a rapid calculation speed, a wide range of compounds can be processed. Neural networks provided better models than multilinear regression analysis. 

Another variation on this technique is to hrst optimize the side chains and then keep the side chains hxed while optimizing the backbone. In an extreme case, representing these hxed side chains as large polygons with some net interaction potential can increase the calculation speed even more. 

Figure 11.25 Calculated speed of streamlines of (A) an HTE-multifold reactor (11 cm length and 7 mm diameter) with 1.5 mm pellets and (B) an industrial reactor (1.2 m length and 21 mm diameter) with 5 mm pellets.

Determine the pass-through time necessary for the different products available and compare the calculated speeds with the requirements fixed by the supplier. 

The calculated speed of sound in the gas can be thought of as that at the valve (i.e. its choke point). 

The predictive value of the theoretical treatment described above was verified experimentally [88,90]. The experimental results were in excellent agreement with the calculated speed point and characteristic curve of cross-linking photoresist. 

PROBLEM 11.26.1 Compute the Doppler recoil energy ER for 26pe57 and a linear speed vr needed to counteract the Doppler shift. Calculate also the speed of a free recoiling nucleus vr, and comment on why this calculated speed is too big. 

The estimated and calculated speeds do not match, and the pumping number is not constant for this Reynolds number range, so an iterative solution for the speed must continue. [In the turbulent range (/VRe. > 20,000), where pumping number is constant, no iteration is required and the calculated speed is correct for the design.]... 

In practice, the calculated speed should be used initially in the process and modified as required. 

An IBM 370/158 computer was used for all of the calculations. As would be expected, the calculation speed was different for each of the three dynamic models. The distance method of lines model ran at a speed of 0.23 times real time (4.3 times slower than real time) which was very slow. For short time transient calculations, the speed could be increased to real time speed, but long term numerical stability required the slower speed. The time method of lines model ran 3.92 times faster than real time. However, the calculated transient responses were incorrect and the model could not be used for that purpose. For a time slice of 1.5 minutes, the method of characteristics model ran 1.56 times faster than real time. If the time slice was increased to 5.0 minutes (fewer nodes), the speed increased to 4.75 times real time but the gas stream accuracy was reduced. Therefore, the 1.5 minute time slice was used for the calculations shown here. 

Concentration-time and temperature-time curves calculated from the polynomial approximation are in close agreement with the simulation results from the detailed kinetic model (see Fig. 4.19). Calculation of the curves with the polynomial approximation was 11,700 times faster. This gain in computer-time is unexpectedly high, although a lO -times increase in calculation speed has been reported in another application of repromodelling [230]. 

The estimated uncertainty in density is less than 0.02% for pressures up to 12 MPa and temperatures up to 340 K with the exception of the critical region and less than 0.03% for pressures up to 30 MPa and temperatures between 235 and 520 K. Elsewhere, the uncertainty in density is generally within 0.2%. In the region with densities up to one-half the critical density and for temperatures between 90 and 450 K, the estimated uncertainty of calculated speeds of sound is in general less than 0.02%. In the liquid and supercritical regions, the uncertainty is less than 1%. The uncertainty in heat capacities is within 0.3% for the vapor and 2% for the liquid. The formulation gives reasonable extrapolation behavior up to very high pressures (50 GPa) and temperatures (17,000 K). 

The time required to sediment particles depends on the rotor speed, the radius of the rotor, and the effective path length traveled by the sedimented particles, that is, the depth of the liquid in the tube. Duplication of conditions of centrifugation is often desirable. The following is a useful formula for calculating speed required of a rotor whose radius differs from the radius with which a prescribed RCF was originally defined ... 

Agitator speed calculate speed based on speed determined in pilot plant using volume ratio, impeller diameter in power correlation. 

The linear approach described here is expandable to multienzyme electrodes as well as multilayer electrodes. At least for the stationary case, multilayer models of bienzyme electrodes may be easily treated, too. The whole system is readily adaptable to potentiometric electrodes (Carr and Bowers, 1980). It must be noted, however, that the superiority over purely numerical solution procedures decreases with increasing number of enzyme species and in the multilayer model. The advantage in calculation speed using the sum formulas described (e.g., in Section 2.5.2) amounts to about two orders of magnitude. With multilayer electrodes and formulas containing double and triple sums it is reduced to one order of magnitude. 

We have shown, in agreement with the results presented in Ref. 21, that the method of classical trajectories gives very good predictions in the case of strong-field interactions (i.e., for the photon numbers larger than 10). The calculation speed of the method does not depend on numbers of interacting... 

This trend will grow in importance as calculation speed increases, experience expands, and a larger body of scientists graduate with these tools as part of their knowledge base. The interaction of the three disciplines is graphically represented in Fig. 4.1 in the preceding chapter. 

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