Numerical experiment result

Numerical Experiment We now present numerical results for non-zero Vi and V2- In particular, we take... 

In 1875 Alexander M Zaitsev of the University of Kazan (Russia) set forth a gen erahzation describing the regioselectivity of p eliminations Zaitsev s rule summarizes the results of numerous experiments m which alkene mixtures were produced by p elim matron In its original form Zaitsev s rule stated that the alkene formed in greatest amount is the one that corresponds to removal of the hydrogen from the f3 carbon hav mg the fewest hydrogens... 

The reaction between a Lewis acid R3M and a Lewis base ER3, usually resulting in the formation of a Lewis acid-base adduct R3M—ER3, is of fundamental interest in main group chemistry. Numerous experiments, in particular reactions of alane and gallane MH3 with amines and phosphines ER3, have been performed [14]. Several general coordination modes, as summarized in Fig. 2, have been identified by X-ray diffraction. 

The numerical simulations were performed at the same conditions as in Choo s experiments. It can be found from Fig. 18 that good agreements between the simulation and experiment results are achieved even at the film thickness less than 100 nm. 

Fig. 18—Comparison between numerical results and experiments by Choo et al. [45]. Line and symbol for experiment results and thin line for present results, (a) 74 mm/s (b) 53 mm/s (c) 37 mm/s and (d) 26 mm/s.

This book focuses on statistical data evaluation, but does so in a fashion that integrates the question—plan—experiment—result—interpretation—answer cycle by offering a multitude of real-life examples and numerical simulations to show what information can, or cannot, be extracted from a given data set. This perspective covers both the daily experience of the lab supervisor and the worries of the project manager. Only the bare minimum of theory is presented, but is extensively referenced to educational articles in easily accessible journals. 

The results from the model were compared semi-quantitatively with experimental measurements to validate the model. Because of both the extremely long time constants in the system and the variations in the ambient conditions in the laboratory where the extruder was placed, it was not possible to rigorously test the model against experimental data. To conserve demands of time and materials for experiments on the extruder, numerical experiments were used to provide data for developing an optimal control system. The goal of the numerical experiments was to develop a reduced-order model suitable for optimizing the control system. 

The reactor feed mixture was "prepared so as to contain less than 17% ethylene (remainder hydrogen) so that the change in total moles within the catalyst pore structure would be small. This reduced the variation in total pressure and its effect on the reaction rate, so as to permit comparison of experiment results with theoretical predictions [e.g., those of Weisz and Hicks (61)]. Since the numerical solutions to the nonisothermal catalyst problem also presumed first-order kinetics, they determined the Thiele modulus by forcing the observed rate to fit this form even though they recognized that a Hougen-Watson type rate expression would have been more appropriate. Hence their Thiele modulus was defined as... 

The principles of orbital symmetry conservation establish that concerted suprafacial [3, 3]-sigmatropic arrangements are allowed processes. Based on these principles and the results of numerous experiments their stereochemistry is highly predictable. 

The next series of numerical experiments was performed for the oxygen-dust mixtures with the values of governing parameters taken from Table 14.1. The dust concentration, initial turbulization, and the ignition duration were maintained constant pav = 0.21 kg/m , RMS = 1.4 m/s, to = 10 s. The results are shown in Table 14.4. It is seen that the increase of oxygen fraction in the oxidizer promotes the ignition and reduces the necessary ignition energy. 

It also shows just how sensitive are the results of explosive nucleosynthesis to the n/p ratio. A numerical experiment should convince us of this ... 

These globules, numerous experiments soon shewed to be the substance I was in search of, and a peculiar inflammable principle the basis of potash. I found that the platina was in no way connected with the result, except as the... 

From the numerous experiments performed by Che-vandier, with the view of determining the loss sustained by woods of different ages, and by the several parts of the same tree when exposed to the air during stated periods, it may be inferred, that so far as the abandoning of moisture to air was observed, the soil and locality where the trees grew did not affect the results. The samples submitted to examination were exposed in a shed, which protected them from rain as well as from the sun s rays,-and tho moisture was determined at the several stages, by drying a portion of the sample in the form of sawdust, at a temperature of 284°... 

It is known and has been demonstrated by several authors (by Sapozhnikov et al. [80] for nitrocellulose by Lukin [81] for nitroglycerine) that change of temperature alters the composition of the reaction products. As the result of numerous experiments, particular temperatures were chosen for definite nitric esters. Thus, owing to the greater ease of decomposition of nitroglycerine as compared with nitrocellulose the high temperature heat test for nitroglycerine is carried out at a temperature lower than that for nitrocellulose (120 and 132° C respectively). 

Finally, we tried a numerical experiment where 56Ni exists only in the outermost 0.2 M layer beneath the surface. The escape of X-rays and 7-rays are significant and the resulting optical light curve (the dash-dotted curve in Fig. 11) is as narrow as SN 1964L. Such a composition inversion is not realistic for helium stars but a natural outcome from the off-center detonation in accreting white dwarfs. 

We use a quasicubic model to try to describe the dependence of the flowing units on the distance, while using a Lennard-Jones potential. We use n = 6 for the attractive and m = 12 for the repulsive forces. The numeral agreement with the experiments resulting from these assumptions may not be overrated. 

Fig. 6.9 Dotted lines, experimental ionization rate curves for the (n,nt, n2, m ) states 1 (40,39,0,0) 2 (40,38,0,1) 3 (40,38,1,0) 4 (40,37,1,1) 5 (40,37,2,0) 6 (40,36,2,1). The tick marks represent the range of validity of the experiment. Solid line, theoretical curves calculated with Eq. (6) of ref. 22. Squares, numerical theoretical results from ref. 23 (from...

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