Difference plot

Consider two random initial configurations that differ at only one site, so that H t = 0) = 1. The difference plots shown in figure 3.16 suggest that for class cl and c2 rules, H t) rapidly approaches some small fixed value. Class c3 rules, on the other hand, are unstable with respect to such small perturbations H t) generally grows with time. The rate of growth of H t) depends on whether the rules are additive or nonadditive. 

Even more interesting are the difference plots, indicating the difference between the charge contours of the upper panel and the situation in which there would be no interaction between the adatom and the metal surface. Solid lines stand for an... 

Avdeef, A. pH-metric logP. Part 1. Difference plots for determining ion-pair octanol-water partition coefficients of multiprotic substances. Quant. Struct.-Aaiv. Relat. 1992, 11, 510-517. 

Fig. 19. Shear stress and first normal stress difference plotted as a function of shear rate for different molar masses, and b at different concentrations of polystyrene in toluene... 

Figure 3.1 Four-step construction of the Bjerrum difference plot for a three-pi molecule, whose constants are obscured in the simple titration curve (see text) (a) titration curves (b) isohydric volume differences (c) rotated difference plot (d) Bjerrum plot. [Avdeef, A., Curr. Topics Med. Chem., 1, 277-351 (2001). Reproduced with permission from Bentham Science Publishers, Ltd.]...

Operationally, such a plot can be obtained by subtracting a titration curve containing no sample ( blank titration left curve in Fig. 3.1a) from a titration curve with sample (right curve in Fig. 3.1a) at fixed values of pH. The resultant difference plot is shown in Fig. 3.1b. The plot is then rotated (Fig. 3. Id), to emphasize that % is the dependent variable and pH is the independent variable [163], The volume differences can be converted to proton counts as described in the preceding paragraph, to obtain the final form, shown in Fig. 3.Id. 

The authors express their gratitude to Drs. G. H. F. Diercksen and W, P. Kraemer for sending density and density difference plots of Li+(OH2) and F (HOH)B prior to publication and for the permission to print them in this review article. Several other groups sent their most recent... 

There are three different kinds of plots that are commonly used to show how magnitude ratio (absolute magnitude) and phase angle (argument) vary with frequency CO. They are called Nyquist, Bode (pronounced "Bow-dee ), and Nichols plots. After defining what each of them is, we will show what some common transfer functions look like in the three different plots. 

Fig. 13. The nuclear magnetic spin-lattice relaxation rate for water protons as a function of magnetic field strength reported as the proton Larmor frequency at 298 K for 5% suspensions of the particulate stabilized in a 0.5% agar gel presented as the difference plot (A) Zeolite 3A (B) Zeolite 13X (C) Zeolite NaY (D) kaolin with 7 s added to each point to offset the data presentation (E) Cancrinite with 9 s added to each point to offset the data presentation and (F) 0.5% agar gel profile with 10 s added to each point. The solid lines are fits to a power law (68).

The primary purpose of any quality control scheme is to identify ("flag") significant performance changes. The two-sample quality control scheme described above effectively identifies performance changes and permits separation of random and systematic error contributions. It also permits rapid evaluation of a specific analytical result relative to previous data. Graphical representation of these data provide effective anomaly detection. The quality control scheme presented here uses two slightly different plot formats to depict performance behavior. 

Fig. 3-15 Autoacceleration in benzoyl peroxide-initiated polymerization of methyl methacrylate in benzene at 50°C. The different plots represent various concentrations of monomer in solvent. After Schulz and Haborth [1948] (by permission of Huthig and Wepf Verlag, Basel).

Notice the attribute PUL5E=Un. This attribute determines the pulse width rather than the time constant of R4 and Cl. The results are shown on the following screen capture. To plot traces on different plots, add the first trace, select Plot and then Add Plot to Window to add a new plot add the second trace, select Plot and then Add Plot to Window to add a new plot and then add the third trace. Digital traces are automatically plotted on a separate section of the screen. 

Figure 10. Density difference plots for some excited states of bicyclo[l. 1. Ojbutane in each case the molecule is drawn to scale (reproduced from ref 102 with the permission of the American Chemical Society).

Figure 2.25. Charge density difference plot of N2 adsorbed on Ni(100). Regions of electron loss are indicated with dashed outer line and increase with full line. We have chosen a plane containing the interacting metal atom with one N2 molecule in the same plane. From Ref. [3].

Figure 2.44. Charge density difference plotted in a plane containing the metal atoms and the carbon skeleton of the ethylene molecule. The difference is taken between interacting and non-interacting molecules and metal cluster for the adsorbed cases. For the gas phase molecule (top), the difference between the singlet and triplet state is shown. From Ref. [85].

Figure 2.50. Charge density difference plotted along the —H plane (top) and the —H plane (bottom). From Ref. [95].

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