Graph three-dimensional

One of the most important uses of models is to show how electrons are distributed inside molecules The laws of quantum mechanics state that an electron s spatial location can not be precisely specified but the likelihood of detecting an electron at a particular loca tion can be calculated (and measured) This likelihood is called the electron density (see Chapter 1) and SpartanView can display three dimensional graphs that show regions of high and low electron density inside a molecule... 

Example of a two-factor response surface displayed as (a) a pseudo-three-dimensional graph and (b) a contour plot. Contour lines are shown for intervals of 0.5 response units. 

The abrasion loss as log (abrasion) of log (energy) and log (speed) is best presented either in tabular form filling out the table of Figure 26.67 or as a three-dimensional graph [52] as shown in Figure 26.68. Notice that the abrasion between the mildest condition (upper left) and the most severe condition (lower right) differs by a factor of about 1000. More important for practical use is the relative rating of an experimental compound to a standard reference compound. 

A two- or three-dimensional graph drawn with axes at right angles implies that each factor can take completely independent values and that a response exists for every point on the graph. This may be the case for many factors. If the effects of initial pH and time of an experiment are being studied, for example, it is probably acceptable to set the pH of the solution then allow the experiment to go for as long as required. However, if a simple water/ methanol mobile phase for liquid chromatography is used, it would be a waste of an axis to try to optimize both water and methanol concentration, because what is not water is methanol and vice versa. This is only a one-factor problem—the fraction of water (or methanol). 

Fig. 6.58. Three-dimensional graphs representing the surface excess (approximately equivalent to the number of adsorbed molecules) of fer-amyl alcohol calculated with respect to (a) the electrode potential and (b) the charge density. The electrical variable varies along the axis normal to the plane of the figure. The maximum surface excess corresponding to the plateau on both graphs is equal to 4.4 x 1(T10 mol cm-2. In this figure oM = qM. (Reprinted from J. Richer and J. Lipkowski, J. Electroanal. Chem. 251 217, copyright 1988, Fig. 12, with permission of Elsevier Science.)...

Figure 14.9 is a three-dimensional graph that shows the extension of (vapor + liquid) equilibrium isotherms or isobars to the critical region. Line ab at X2 = 0 is the vapor pressure line for pure component 1, with point b as the critical point. In a like manner, line cd at x2 = 1 is the vapor pressure line for pure component 2, with point d as the critical point. Note that at temperatures and pressures below points b and d, the isotherms and isobars (shown as the shaded areas) intersect the vapor pressure curves.k However,... 

Fig. 2. Base triangle of the three-dimensional graph representing the system QZg vs QY3 vs QTs.

When we introduce composition variables, we have more than three variables and consequently must apply certain restrictions in order to illustrate the behavior of the Gibbs energy in two- or three-dimensional graphs. Here we consider only binary systems at constant pressure. The three variables that we use are the molar Gibbs energy, the temperature, and the mole fraction of one of the components. We also limit the discussion to systems having a single phase or two phases in equilibrium. 

The relative entropy changes for all the processes discussed, pure equilibrium (C-E), pure frozen (C-F), kinetic rate controlling (C-I-G-A), modified Bray (C-B-R) and approximate Bray (C-T-S), are all shown on Fig. II. C. 1. In order to see somewhat more clearly the relative order of the performance for each procedure, the three-dimensional graph given in figure n. C. 2. is represented by... 

By using very thin samples, the oven aging of polypropylene can be appreciably accelerated. Specimens of definite and reproducible shape and thickness were made by using a microtome. The first phase of the work evaluated the influence of sample thickness from 0.2 to 12 mils on oven life at different temperatures. In the second phase, this modified technique was used to study the effectiveness of three anti-oxidant/DLTDP systems as thermal stabilizers for polypropylene. The results obtained over a wide spectrum of antioxidant/DLTDP combinations are shown in three-dimensional graphs. 

Figure 6.14 Three-dimensional graph of fraction dose absorbed vs. k a and k,i. Dose and cs mjn values [153] correspond to those of digoxin (A) and griseofulvin (B).

Figure 4.17. Three-dimensional graph for Cr in the NIST 8415 Whole Egg Powder SRM in the vicinity of the 357.87 nm line pyrolysis temperature 700°C, atomization temperature 2500°C direct solid sampling analysis.

Figure 4.20. Three-dimensional graphs for Se in the BCR 186 Pig Kidney CRM pyrolysis temperature 800°C, atomization temperature 2000°C Ir permanent modifier direct solid sampling analysis (a) in the vicinity of the 196.026 nm line (b) in the vicinity of the 203.985 nm line.

The minimum coagulation constant occurs for coagulation of equal-size particles. This can be seen in Fig. 18.1 which shows a three-dimensional graph of the coagulation constant matrix. The valley indicated on the plot represents the constants for coagulation of equal-size particles. 

Binary systems would require a three-dimensional graph, since composition, temperature, and pressure are all variable. However, with condensed binary systems, the pressure is hxed (normally to 1 atm) and the phase diagram can be reduced to a two-dimensional... 

Figure 5. Three-dimensional graph of lead isotope ratios for the Nigerian copper alloy objects listed in Table II.

Three Dimensional Graphs Demonstrating the Difference between Amperometric and Coulometric Detection Employing an Electrode Array Courtesy of the Analyst. 

The differential equations were solved for a variety of values of less than a. The program was run for considerable time and the last 100 points saved. If the limiting periodic orbit were asymptotically stable, these points would be near the periodic orbit - equal as well as the eye can determine. These periodic orbits, corresponding to different parameters and hence to different systems of differential equations, were then plotted on a single three-dimensional graph (Figure 8.1). This illustrates the stability. 

Three-dimensional graphs show the inter-relationships of three variables, (e.g. Fig. 32.21). 

Figure 3 Approaches to zeolite modeling depicted in a three-dimensional graph.

Figure 4. Three dimensional graph of the error function, eqn.(8), for different combinations of the two peak maxima co-ordinates in the Kalman filtering of the combined model [1A+2A]. The error function has been inverted for graphical enhancement. (From Fresenius J Anal. Chem(1993) 345 490, with permission)...

---