Profile plot

The wall thickness estimation in tangential projection technique is based on the evaluation of profile plots along the pipe diameter as shown in fig. 1 (lowest row). 

Profile Plot This window display the data (grey values, optical densities or wall thickness changes in mm after calibration) along the line shown in the image window. 

Fig. 4 Corrosion inside a pipe (bore 100 mm, wall thickness 6.3 mm), projection technique at 160 kV (double wall penetration), profile plot with calibrated wall thickness loss...

Fig. 5 Erosion pit inside a reducing pipe fitting, projection technique at 160 kV, profile plot with optical densities of the digitised film. The varying background caused by the geometrical set-up prevents a wall thickness calibration as in fig. 4...

Figure 6-12. (A) pH-rate profiles plotted at l -pH and (B) log l -pH for the hydrolysis of phthalamic acid. ...

Suppose you are marching down the infamous tube and at step j have determined the temperature and composition at each radial point. A correlation is available to calculate viscosity, and it gives the results tabulated below. Assume constant density and Re = 0.1. Determine the axial velocity profile. Plot your results and compare them with the parabolic distribution. 

The velocity profile plots show interruptions in the velocity profile, where the solid packing was located. In general, the data of the three different cases agreed very well qualitatively velocity highs and lows are shown at the same points in the bed. Quantitatively, the data of the two full-bed models are practically identical, indicating that the solutions were completely mesh independent. 

Closures of 3-, 4-, and 5-membered rings exhibit unusual behaviour when compared to higher homologues, as shown, for example, by observing the left-hand ends of the EM-profiles plotted in Fig. 10 these are reproduced very poorly by the calculated values shown in Fig. 26. 

Contour and amplitude profile plots of the ctHf bond (upper panels) and contour plots of the nF(a) and nF(7t) lone pairs (lower panels) are illustrated below ... 

Figure 4.96 Contour plots (left) and radial-profile plots (right) of overlapping hM and hH NHOs of ctMh bonds for group 10 dihydrides (NiH2, PdH2, and PtH2). Numerical (hM F, hH> Fock-matrix interaction elements are shown for each case.

Fig. 3 High backmixing [aL=5, ac = 5] flattens the steady state concentration profiles and therefore reduces extraction efficiency, as compared to zero backmixing conditions [aL=0, ac = 0], as seen in this axial profile plot.

Fig. 3 The substrate and product profiles plotted versus segment position for the steady state.

Fig. 17. Angular LEED beam profiles plotted for various values of the coverage for H on Fe(llO) at a temperature T = 200 K. From Imbihl et ol. .)...

Fig. 6. The profile plots of the eight samples. The peak of each plot represents the relative density of the band in each rectangle. The larger the area under the curve (AUC), the higher the intensity of the band.

Instead of 3-D plots, traces of the binding isotherm surface through a plane parallel to the [L]/[I] plane (contour diagrams) or profile plots (traces through the p./[L] or /x/[l plane can be used to explain certain special conditions. 

A typical reachon profile plotted with in-line FTIR is shown in Figure 5.4. The hydrogenation reachon starts as a slurry because of the low solubility of the sub-shate in MeOH. The concentrahon of enamine 27 in soluhon increases slowly as the reachon progresses. About 7h into the reaction, the reaction mixture becomes homogeneous. Most of substrate has been consumed and conversion is approximately 80% at this point. It takes another 8-10 h to reach the end point (>98% conversion). 

Fig. 10.1 (Continued), (c) Distribution of solutions within each local optimum for a basic amino acid dope (30% Arg, 30% Lys, 40% His). Each cluster consists of many different solutions, which are overlaid in die profile plots, revealing some trends. Each cluster emphasizes a different typical profile of solutions - and clusters 2 and 5 are especially different from die odier clusters. Comparing die mean values of each nucleodde between die clusters shows large differences, especially for die nucleotide fractions A1 and C3. The standard deviation for each nucleotide is 10%.

Figure 14 Distribution of natural fluorescence in an unstained oat kernel (a) Profile plot of distance (x-axis) Vs relative fluorescence intensity (y-axis) in scan through the mid-point of a kernel cross section, (b) Intensity profile showing fluorescence of phenolic constituents in an oat cross section.

Let us now revisit the modified example with the a-i and 7 parameter data as described on p. 195. We recall that for this system there are five steady states prior to feedback. Three of these are stable at the approximate (xa, xb, y) locations of (1, 0, 0), (0, 1, 0.41...), and (0, 0, 1). Of these three, the middle stable one yields the maximal amount of component B and therefore it is the most desirable steady state. Figure 4.41 shows a set of 3D profile plots with initial values from a neighborhood of the middle stable steady state xa,xb,v) = (0,1,0.41038) (taken from Figure 4.31) with xao = 0.1... 

In Figure 4.47, best viewed in color, we observe a parallel time-shifted behavior of the three profiles that start from our three different initial values after the first 50 time units. This seems to indicate that for infinite time, the solutions that start at any initial value will eventually travel with the same period along the same unique loop that is depicted in three dimensions in Figure 4.46, but time-shifted one from the other like trains on the same track. More specifically, the profiles plot of Figure 4.47 indicates that in 2,000 time units, this periodic attractor loop is traversed about five and a half times, or approximately once every 380 time units. The system reaches an explosive state eventually (after an early possible higher-level explosion, depending on the choice of the initial value) every 380 time units. These periodic explosions occur with temperature... 

We illustrate this reaction behavior further using our concentration and temperature profile plotting code plugflowxAy. m for a Damkohler number such as 107-456 just below ignition in Figure 5.16 and then for Da = 107 463 which indicates ignition and y uj) = 2 near the end of the tube for iv < 1 in Figure 5.17. 

Figure 1.12 shows the concentration profile plotted on Cartesian coordinates and semilog scales respectively. When a zero-order input has been left on for an amount of time equal to 3.3 to 5 half-lives, Cp is considered to be at steady state (90 and 96 percent of true steady state, respectively) and is designated as Cp ss. There is only one volume term, Vd, because the disposition is only one compartment. 

Profile plotting is a similar technique to the construction of star plots. Features are arranged as bars in single diagrams for each object. Bars may also be connected by lines. 

Figure 7.1 Spectral image for an observation line across five different polymer samples with different sizes (left to right polystyrene, PS polyoxymethylene, POM high density polyethylene, PE-HD polypropylene, PP acrylonitrile-butadiene-styrene, ABS). The left-side image shows the two-dimensional grey-scale image as delivered from the spectral imaging system, the right-hand image shows it as a three-dimensional profile plot to illustrate the spectral content.

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