Cross section normalization procedures

It is possible to develop a proper multigroup theory based upon group cross sections obtained by bilinear flux-adjoint weighting 40). It may even be more accurate in some applications than the normal procedure used here. But, in principle, provided the flux and adjoint spectra are accurately known for the purpose of obtaining group cross sections, either procedure is a valid one, and they will both give the same answer. 

The blends were prepared with two take-up speeds to achieve morphologies with different LCP fiber dimensions. The lower speed (L), leading to a draw ratio of 1 1, represents the normal blending procedure, which was what we used in our previous work [44]. The higher speed (H) resulting in a draw ratio of 6 1 was applied to form long highly oriented LCP fibers. The draw ratio for each strand was determined as the ratio between the die and strand cross-sections (Sq/Ss). 

For a while till now, our research group has been involved in studies of the properties of limit flames. Most of the results reported in this chapter were obtained for propane flames, under normal atmospheric conditions, in 300 mm long channels, with a square cross-section. The experimental procedure was described previously [25]. A flame propagating through a stationary mixture in a quenching tube or quenching channel can be characterized by the parameters defined in Figure 6.1.1. 

XPS Analysis. The ultrahigh vacuum (OHV) catalyst treatment-surface analysis system employed to characterize and treat the cobalt catalysts has been described previously ( 1, 2 The catalyst treatment and data analysis procedures have also been described (JJ. Briefly, the samples were treated in quartz reactors and then transferred under UHV into a modified Hewlett-Packard 5950A BSCA spectrometer for emalysis. Peak areas were normalized with theoretical cross-sections (Z) to obtain relative atomic compositions. 

Fig. 25. Comparison between the experimental abstraction reaction H + H2O(00)(0) cross-section (solid point with error bars), and the 5D QM calculations (solid line). The 6D QM cross-sections with the CS approximation (dotted line), and the QCT data using normal (o) and Gaussian (A) binning procedures are shown.

An early normalizing procedure, proposed by Kiselev (1957) to compare adsorption isotherms of hydrocarbons, water vapour, etc. on a series of different adsorbents, was simply to plot the surface excess concentration F (=n/A), obtained from a knowledge of the BET-nitrogen surface area, A (BET), versus p/p°. It is also possible to plot, instead of f, the reduced adsorption , n/nm, which still relies on the BET method to determine the monolayer capacity nm but does not require knowledge of the molecular cross-sectional area a. 

Momentum-transfer cross sections are normally determined by the electron swarm technique. A detailed discussion of the drift and diffusion of electrons in gases under the influence of electric and magnetic fields is beyond the scope of this book and only a brief summary will be given. The book by Huxley and Crompton (1974) should be consulted for a full description of the experimental methods and analysis procedures. 

To calculate the volumetric flowrate, q, of the fluid passing through a perpendicular surface. A, one must integrate the product of the component of the velocity that is normal to the area and the area over the whole cross-sectional area of the duct. This procedure is depicted in the equation... 

Intensity/wavelength/time cross-sectional diagrams (or time-resolved fluorescence "contour" diagrams) are generated using a weighted nonlinear least squares polynomial surface procedure (20). Area-normalized TRE spectra can be used for convenient pictorial representation, since the absolute emission intensity of individual time-resolved spectra vary substantially with time after excitation. 

There have been a number of review articles on TEM sample preparation techniques [4.2-4.5]. TEM samples of high Tc superconductors are mostly prepared either by crushing, cleaving or ion milling. These methods will be dealt with in Sections 4.2 and 4.3. Minor details frequently determine the success of a technique. To illustrate this, we will describe the normal preparation procedure for both techniques while we will concentrate on some tricks to obtain a good TEM sample reliably and fast. The method described here will mainly be focused on cross-section sample preparation. Finally, two new techniques will be introduced, (i) a simple TEM cross-section ion shadow... 

Choosing initial Cartesian coordinates for the polyatomic reactants follows the procedures outlined above for an atom + diatom collision and for normal-mode sampling. If the cross section is calculated as a function of the rotational quantum numbers J and K, the components of the angular momentum are found from... 

Downcomers smaller than 5 to 8 percent of the column cross-sectional area should therefore be avoided (73,123,144, 243,246,249, 409). Note that several of the cited designers expressed this rule as a minimum ratio of weir length or downcomer width to column diameter these ratios can be geometrically converted into the stated minimum area ratio. An alternative recommendation advocated by some designers (61, 138) is to set the minimum downcomer area to either twice the area calculated using the normal design procedure or 10 percent of the column cross-sectional area (whichever is smaller). 

Before entering the sample and reference cells, the output of the dye laser is spatially filtered by an iris that confines the beam to a cross-sectional area of approximately 2 mm. This procedure also reduces the amount of non-tunable amplified spontaneous emission (ASE) concentric to the laser beam. After emerging from the apparatus, the laser light is then monitored in two ways (1) power meter (Scientech calorimeter 36-0201, NBS traceable) from which a 5 % reflection is incident upon a (2) pyroelectric energy detector (Molectron J3-05) used for normalization of raw LPAS data. 

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