Three-dimensional plots

Figure Bl.22.11. Near-field scanning optical microscopy fluorescence image of oxazine molecules dispersed on a PMMA film surface. Each protuberance in this three-dimensional plot corresponds to the detection of a single molecule, the different intensities of those features being due to different orientations of the molecules. Sub-diffraction resolution, in this case on the order of a fraction of a micron, can be achieved by the near-field scaiming arrangement. Spectroscopic characterization of each molecule is also possible. (Reprinted with pennission from [82]. Copyright 1996 American Chemical Society.)...

Note These equations are from Doming, S. N. Morgan, S. L. Experimental Design A Chemometric Approach. Elsevier Amsterdam, 1987, and pseudo-three-dimensional plots of the response surfaces can be found in their figures 11.4, 11.5, and 11.14. The response surface for problem (a) also is shown in Color Plate 13. 

RgureS Three-dimensional plot of predicted ellipsometric parameter data versus angle of incidence and wavelength. 

Figure 12 Three-dimensional plot of the tear energy of a viscoelastic composite as a function of temp, and strain rate. Source Ref. 39.

Figure 3. Three-dimensional plot of the room-temperature fluorescence of a mixture of 500 ng each of benzo(a)pyrene and benzo(e)pyrene on 80% q-cyclodextrin-NaCl. Numbers along dashed lines show the approximate wavelengths (nm) represented by these lines. The excitation wavelength was varied from 250 nm (front spectrum) to 370 nm (back spectrum) at 2-nm increments. Benzo(a)pyrene emitted from approximately 380 nm to 540 nm, and benzo(e)pyrene emitted from 365 nm to 505 nm.

Fig. 1.6 Three-dimensional plot of X2 and X3 versus virtual log P as obtained from MD simulation of acetylcholine in water. Reproduced from Ref [16] with kind permission of American Chemical Society 2005.

Figure 2.38a. Three-dimensional plot of the REVTEMP optimisation.

Fig. 23. The three-dimensional plot of the product flux contour diagram for the 0(1D) + H2 —> OH + H reaction at the collision energy of 1.3 kcal/mol.

Figure 3.7 (a) Plot of the angular function (0) = constant for an s orbital in plane through the z axis, (b) Plot of (00) = constant (cos 8) for a p orbital in a plane through the z axis, (c) Three-dimensional plots of the angular function (00) for the s and p orbitals. (Adapted with permission from P. A. Cox, Introduction to Quantum Theory and Atomic Structure, 1996, Oxford University Press, Oxford, Figure 4.4.)... 

Figure 2. Schematic three-dimensional plot showing various planes of AB polymer/polymer composition. From left to right homopolymer blends blends containing 50 weight percent diblock copolymer diblock copolymers. 

Figure 7.8 (a) Molecular structures of two LnW30 [107]. (b) Three-dimensional plots of... 

A number of factors must be taken into account when the diagrammatic representation of mixed proton conductivity is attempted. The behavior of the solid depends upon the temperature, the dopant concentration, the partial pressure of oxygen, and the partial pressure of hydrogen or water vapor. Schematic representation of defect concentrations in mixed proton conductors on a Brouwer diagram therefore requires a four-dimensional depiction. A three-dimensional plot can be constructed if two variables, often temperature and dopant concentration, are fixed (Fig. 8.18a). It is often clearer to use two-dimensional sections of such a plot, constructed with three variables fixed (Fig. 8.18h-8.18<7). 

Figure 8.18 Schematic representation of defect concentrations in mixed proton conductors on a Brouwer diagram (a) three-dimensional plot with two variables fixed (b)-(d) two-dimensional plots with three variables fixed.

Fig. 6. A high level of interpixel noise seen in a three-dimensional plot of Fig. 5. 

Figure 2. Three-dimensional plots of the CO oxidation transients determined in the single potential step experiments on the Pt(100) electrode in 0.10 M HC10., solution. The potential step was applied from E = +0.40 V to Ep displayed on the third axis of the figure.

Computation of this function results in a three-dimensional plot for which one axis is time delay (or range), the second is Doppler frequency or radial velocity and the third is the output power of the matched filter (usually normalised to unity). The extent of the ambiguity function peak in the Tr and the fd dimensions determines the range and Doppler resolutions respectively. As we are using the directly received signal only we term this self-ambiguity as there is no inclusion of any system geometry dependence on the transmitter and receiver locations. 

Graphical display of response over time (as two- or three-dimensional plots). 

All of our calculations were performed with the Gaussian98 suite [11] of codes on AMD Athlon 2000+ 1.6 GHz and Pentium IV 1.7 GHz computers, as well as on SGI 0rigin2000 and Compaq Sierra systems. The three-dimensional plots of molecular orbitals were generated with the MOLDEN program [12]. 

The multipole model reduces the crystal electron density to a number of parameters, which can be fitted to experimental structure factors. For CU2O, structure factors for the (531) and higher-order reflections out to (14,4,2) were taken from X-ray measurements. Weak (ooe) (with o for odd and e for even) and very weak (eeo) reflections were also taken from X-ray work. Fig. 6 shows a three-dimensional plot of the difference between the static crystal charge density obtained from the multipole fitting to... 

Figure 2.22 A three-dimensional plot of the diffracted intensity as a function of specimen rotations both parallel ( ) and perpendicular ( j to the dispersion plane. The larger peak is that from the substrate GaAs and the smaller from the GaAIAs layer. CuK i, slit-limited from a single GaAs beam conditioner...

A new analyzer based on ion mobihty has been introduced in 2005 and combines DMS and IMS analyzers in tandem, hence ions are first separated in a DMS drift tube and then characterized by twin IMS drift tubes [62]. Because the DMS is comparatively slow (0.1—1 Hz) and the mobihty spectrometer operates at 30 Hz, mobility spectra can be obtained throughout a DMS sweep of compensation voltage, creating a three-dimensional plot as shown in Figure 12 for DNT and TNT (unpublished experimental results provided by C.R. White et al. at New Mexico State University, September 2005). As shown in the topographic plots of Figure 12, a benefit of ion characterization for K and AK is seen in the improved separation of peaks over DMS and IMS alone. The tandem DMS-IMS was described at the 2005 International Symposium on IMS and is under development requiring detailed evaluation as drift tube improvements are made. 

Figure 12.34 Pseudo-three-dimensional plot of response as a function of composition for a three-component mixture.

For purposes of illustration only, to circumvent the problem of a zero determinant but still show the distributions of uncertainty and information in this design, a seventh experiment was added at a factor combination just slightly removed from one of the hexagonal points (at jc, = 2.000, X2 = 0.001). The hexagonal points were also adjusted somewhat to coincide with the grid lines in the pseudo-three-dimensional plots (this is equivalent to a minor adjustment of scale in the X2 dimension). Neither of these modifications significantly affects the overall conclusions to be drawn from this example. The actual design is... 

The first results from the use of PLS were reported by Dunn fit al (6) who estimated the composition of PCB contaminated waste oil in terms of Aroclor mixtures. Stalling gt al (13), who reported on the characterization of PCB mixtures and the use of three-dimensional plots derived from principal components, demonstrated that the fractional composition of TCDD and other PCDD residues were related to their geographical origins. These two reports (6,13) described the application of an advanced chemometric tool in residue studies and illustrated the... 

We thank Michael Koehler (University of Illinois at Chicago) for developing the combined two- and three-dimensional plotting program to display the sample component scores. 

The need for multivariate techniques is apparent when one considers that each measured parameter contributes one dimension to the representation. Thus examining two parameter interactions requires a two dimensional plot. Such graphical representations are effective in identifying significant relationships among the variables. A three variable system requires a three dimensional plot to simultaneously represent all potential bivariate interactions. However, as the number of variables increases the dimensionality of the required representation exceeds man s ability to perceive significant patterns in the data. Indeed, humans do not conceptualize comfortably beyond three dimensions. Without assistance one would be restricted to considering only problems that are characterized by three factors. 

Figure 3. Pseudo-three-dimensional plots of the canonical orbitals for CHj, 1 (A = C). The atom labels are only indicated for the lowest lying carbon 1 s orbital otherwise they are left out for clarity.

A general assembly for a SEC-MALLS instrument is given in Figure 3.16. A typical three-dimensional plot obtained from such an assembly is shown in Figure 3.17. 

FIGURE 3.17 Three-dimensional plot of scattering intensity as a function of scattering angle and elution volume for a broad molecular weight distribution (MWD) polystyrene (PS) (NITS standard reference 706). (Courtesy of Wyatt Technology Corporation, Santa Barbara, CA 93117 wyatt wyatt.com. With permission.)... 

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