X-Y plots

A mass spectrum is a graphic representation of the ions observed by the mass spectrometer over a specified range of m/z values. The output is in the form of an x,y plot in which the x-axis is the mass-to-charge scale and the y-axis is the intensity scale. If an ion is observed at an m/z value, a line is drawn representing the response of the detector to that ionic species. The mass spectrum will contain peaks that represent fragment ions as well as the molecular ion (see Figure 1.3). Interpretation of a mass spectrum identifies, confirms, or determines the quantity of a specific compound. 

Figure 2. (A)-(H) Equiline diagrams for areas of ridge from the global ridge system. Note that data from individual areas of ridge often form trends indicating a relationship between Th/U and ( °Th)/( U). The equihne diagram is an x-y plot with both axes normalized to ( Th). Therefore a likely explanation for the trends is that they reflect mixing of melts having distinct Th/U.

Solution To determine the location of the azeotrope for a specified pressure, the liquid composition has to be varied and a bubble-point calculation performed at each liquid composition until a composition is identified, whereby X = y,-. Alternatively, the vapor composition could be varied and a dew-point calculation performed at each vapor composition. Either way, this requires iteration. Figure 4.5 shows the x—y diagram for the 2-propanol-water system. This was obtained by carrying out a bubble-point calculation at different values of the liquid composition. The point where the x—y plot crosses the diagonal line gives the azeotropic composition. A more direct search for the azeotropic composition can be carried out for such a binary system in a spreadsheet by varying T and x simultaneously and by solving the objective function (see Section 3.9) ... 

Figure 4.5 x-y plot for the system 2-propanol (1) and water (2) from the Wilson equation at 1 atm. 

This equation is known as the q-line. On the x-y plot, it is a straight line with slope q/(q—1) and intersects the diagonal line at x p. It is plotted in Figure 9.8 for various values of q. 

There are three subroutines for making contour plots using various map projections and a subroutine for making x-y plots. The contour plotting routines are used with the Standard Pole Figure and Area Scan diffraction data files, while the x-y plot is used for data from x scans, scans, 28 scans, and layer line plots. 

Table 6.1 illustrates the calculation of skew angles for some reactions of interest. Figure 6.3a through c shows V(x,y) plots for several examples of collinear A + BC reactions. 

In the case where there is one design variable of interest, say percentage of lactose, the model of the response can be graphed as a curve on an x-y plot, as shown in Figure 2.1. 

Data Reduction. The spectral data can be collected on-line and stored directly on magnetic tape under control of a PDP-8 digital computer 11). Alternatively, they can be collected on a magnetic core memory, then transferred in bulk fashion (Figure 14). The choice of method is dictated by the length of counting required and by the method of treatment of the data (i.e., simple X-Y plot or complete channel information). 

Azeotropic and Partially Miscible Systems. Azeotropic mixtures are those whose vapor and liquid equilibrium compositions are identical. Their x-y lines cross or touch the diagonal. Partially miscible substances form a vapor phase of constant composition over the entire range of two-phase liquid compositions usually the horizontal portion of the x-y plot intersects the diagonal, but those of a few mixtures do not, notably those of mixtures of methylethylketone and phenol with water. Separation of azeotropic mixtures sometimes can be effected in several towers at different pressures, as illustrated by Example 13.6 for ethanol-water mixtures. Partially miscible constant boiling mixtures usually can be separated with two towers and a condensate phase separator, as done in Example 13.7 for n-butanol and water. 

The x-y plot like that of Figure 14.6 may be made with the tieline data of columns 5 and 2 expressed as fractions or by projection from the triangular diagram as shown. 

An effective but simple way of graphically illustrating the variability associated with the analytical data is to plot x—y plots of the duplicate and replicate pairs. Most statistical packages will have an option for plotting simple x—y plots. The G-BASE project uses MS Excel running a macro that will automatically plot duplicate-replicate and duplicate-duplicate results. Figure 5.8 shows three examples from the G-BASE East Midlands atlas area duplicate-replicate data for soils. This method gives an immediate visual appreciation of any errors present in an analytical batch and an indication of within site variability, as shown by the duplicate pairs, or the within sample variability, as indicated by the replicate pairs that demonstrate... 

Phase diagrams are used to describe binary systems by plotting two out of the three variables—composition, temperature, and pressure, at a constant value of the remaining one. The most popular of these plots are the T-x plot and the x-y plot, The x-y plot was described earlier (Sec. 1.2,1, Fig, 1.1). 

The most common graphic displays of interval and ratio information are X-Y plots, where distance in the display corresponds to distance on the relevant property or properties. Musical notation is a specialized interval scale that makes use of a limited visual alphabet corresponding to modes of execution of notes as well as a spatial scale corresponding to pitch. Finally, for displaying ratio information, pie charts can be useful,... 

Halve logarithmic x-y-Plot + Available Curves Available... 

Pseudoplastic liquids have a x-y plot that is concave downward. The simplest mathematical representation of such relations is a power law... 

Figure 2.7-1 shows several illustrative (x,y) plots. If the plot of a given data set looks like that shown in plot (a) or (b) of this figure, a straight line would probably be fitted to the data and used as the basis for subsequent interpolation or extrapolation. On the other hand, if the plot is distinctly curved as in plot (c), a curve could be drawn in by inspection and used as the basis of interpolation, or straight-line segments could be fitted to successive pairs of points, or a nonlinear function y(x) that fits the data could be sought. 

For quantitative validation of simulation results, it is often necessary to compare predicted profiles (of velocity or other variable of interest) with experimental data X-Y plotting facilities are useful for this purpose. Most post-processors allow the user to import tabulated data for comparison with simulation results. Facilities to calculate the usual global quantities of interest to reactor engineers, such as overall pressure drop, dispersed phase volume fraction, heat or mass transfer rates and so on, are necessary to address reactor engineering concerns. Most codes allow use of user-defined routines to evaluate different quantities of interest, which may then be displayed using the standard tools discussed above. 

The endpoints of the operating line on an X -Y plot (Fig. 15-23) are the points (X(, Y() and 0Cf, Y() where X and Y are the mass ratios for solute in the feed phase and extract phase, respectively, and subscripts /, r, s, and e denote the feed, raffinate, entering extraction solvent, and leaving extract streams. The number of theoretical stages can then be stepped off graphically as illustrated in Fig. 15-23. 

Figure 14-18 Simulated example with positive and negative differences in the low and high range, respectively A, Bland-Altman plot. B, An x-y plot with diagonal (dotted straight line) and estimated Deming regression line fso//d //ne) with 95% confidence curves (dashed lines).

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