Surface plots

Many graphics packages allow for contour diagrams and surface plots. These are given above for the square of the LCAO plus combination, for any plane containing the intemuclear axis. 

Fig. 3. A 3-D surface plot for MUF resin curing period Fig. 4. A 3-D surface plot for MUF resin storage life...

Figure 9. Phase reconstruction of image reported in Figure 6 using the reference of image reported in Figure 8. The phase map is shown in (a), which includes a laterally averaged line-scan of 15 pixels, (b) A surface map of the two particles shape is displayed. The surface plot has been heavily noise filtered through Gaussian smoothing to better display the particles shape.

Fig. 4.12 Surface plots of the EFG tensor as determined from the angular dependence of the first-order quadrupole shift, Eq of high-field magnetic Mossbauer spectra. The plots visualize the value of the function (3cos 0 - 1 + rysin d cos20) for > 0 and ry = 0 (a), r] = 0.3 (b), and 77 = 1 (c)...

An example of a reaction cavity is illustrated by the van der Waals surface plots derived from the X-ray structures of di-2,6-dihydroxy-2,6-diphenylcyclohexanone 51 and its photodecarbonylation products, the cis- and tra i-2,6-diphenylcyclopen-tane-l,2-diols 52 and 53 (Scheme While the two products are formed in... 

The ESTM experiment provides actually five measurable quantities tunnelling current, / at the applied voltage, U, and three dimensions, x, y, z. The standard STM can therefore easily be modified by recording the local l-Uy U-zy or /-z characteristics (z is vertical distance of the tip from the electrode surface). Plot of dl/dU or d//dz versus x and y brings additional information on the electronic and chemical surface properties (local work functions, density-of-states effects, etc.), since these manifest themselves primarily as l-U dependences. The mentioned plots are basis of the scanning tunnelling spectroscopy (STS). 

Figures 5 and 6 show the response surfaces plotted for Property A and Property B, respectively. Note that two variables are plotted at once, with the values of the other variables fixed at levels chosen by the experimenter. The contours in the graph represent constant levels of the response. Fortunately, the computer allows rapid replotting for various levels of the fixed variables, as well as changing the identities of the fixed and floating variables, so that the entire design space can be investigated.

Similar overlaying of other response surface plots led to conclusions regarding the formulation variables and their effects on the properties of the copolymers. In addition, another (proprietary) computer program was used, which allowed the combination of several regression equations (for the various responses) and the calculation of variable values needed to achieve any desired combination of response values (if the models permit). 

Fig. 7.4 Surface plot of the contour diagram given in Fig. 7.3, illustrating the concept of torsional sensitivity. The numerical values were taken from M. Cao and L. Schafer, J. Mol. Struct., 284 (1993) 235.

Figure 8.28. Demonstration of a CDF. Data recorded during non-isothermal oriented crystallization of polyethylene at 117°C. Surface plots show the same CDF (a) Linear scale viewed from the top. (b) Linear scale viewed from the bottom, (c) Viewed from the top, logarithmic scale. Indicated are the determination of the most probable layer thickness, lt, and of the maximum layer extension, le. (d) Viewed from the bottom, logarithmic scale. The IDF in fiber direction is indicated by a light line in (a) and (b) (Source [56])...

The first graphical representation using MATLAB software is that of a two-dimensional contour surface plot of the data from Table 75-1 [2], This Figure 75-3 plot can represent multiple levels of j-axis data (absorbance) by the use of contours and color schemes. The MATLAB commands for generating this image are given in Table 75-2 where A represents the raster data matrix shown in Table 75-1. 

Table 75-3 MATLAB commands for generating a 3-D surface plot of data matrix A found in Table 75-1...

Figure 22. Electron emissions for 40-keV H+ ion impact on He. A CDW-EIS surface plot [38] for the double differential cross section d2a/dfidEk is plotted against k/v (see the caption of Fig. 20).

Figure 1.1 Surface plots of representative s, p, and d atomic orbitals (from the Kr valence shell).

The three quantum numbers may be said to control the size (n), shape (/), and orientation (m) of the orbital tfw Most important for orbital visualization are the angular shapes labeled by the azimuthal quantum number / s-type (spherical, / = 0), p-type ( dumbbell, / = 1), d-type ( cloverleaf, / = 2), and so forth. The shapes and orientations of basic s-type, p-type, and d-type hydrogenic orbitals are conventionally visualized as shown in Figs. 1.1 and 1.2. Figure 1.1 depicts a surface of each orbital, corresponding to a chosen electron density near the outer fringes of the orbital. However, a wave-like object intrinsically lacks any definite boundary, and surface plots obviously cannot depict the interesting variations of orbital amplitude under the surface. Such variations are better represented by radial or contour... 

Figure 1.2 (a) Lowest s- and p-type valence atomic orbitals of rare-gas atoms, showing radial profiles (left) and contour plots (right). (Each plot is 3 A wide, and only the four outermost contours are plotted see note 26.) (b) Similar to Fig. 1.2(a), for valence 4s, 4p, and 3d atomic orbitals of Kr, corresponding directly to the surface plots of Fig. 1.1. 

For simplicity throughout this text, we shall use the generic term NBO to refer both to the orbitals that appear in formulas such as Eq. (1.24) and to those displayed in surface plots and orbital-overlap diagrams. However, in case of confusion, it... 

To analyze response surface designs, a model is fitted to the data for each response. Usually the results are visualized in response surface plots, showing the change in response as a function of two factors. " These plots allow deciding on the optimal conditions. However, as already mentioned in Section IV, these response surfaces seem not so useful when only small variations around the nominal conditions are examined. 

In reference 20, a typical robustness test is not performed, but a study on the influence of peak measurement parameters is reported on the outcome. The study is special in the sense that no physicochemical parameter in the experimental runs is changed, but only data measurement and treatment-related parameters. These parameters can largely affect the reported results, as shown earlier, and in that sense they do influence the robusmess of the method. The different parameters (see above) were first screened in a two-level D-optimal design (9 factors in 10 experiments). The most important were then examined in a face-centered CCD, and conclusions were drawn from the response surfaces plots. 

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