Contours of constant

Fig. XVII-18. Contours of constant adsorption energy for a krypton atom over the basal plane of graphite. The carbon atoms are at the centers of the dotted triangular regions. The rhombuses show the unit cells for the graphite lattice and for the commensurate adatom lattice. (From Ref. 8. Reprinted with permission from American Chemical Society, copyright 1993.)...

Note that r locus and r locf ind works for both continuous and discrete systems. The statement squar e provides square axes and so provides a round unit circle. The command zgr id creates a unit circle together with contours of constant natural frequency and damping, within the unit circle. When examp76.m has been run, using r locf ind at the MATLAB prompt allows points on the loci to be selected and values of K identified (see Figure 7.20)... 

The higher heating value is plotted on the composition coordinate in Figure 6. These curves are for 50 atm and 700 °K. The contours of constant heating value increase uniformly in the direction of pure methane. These contours, of course, are very similar to the contours of CH4 concentration which are plotted in Figure 7 for the same conditions, 50 atm and 700°K. 

FIG. 13 Gel data contours of constant swelling factor from experimental data. Dashed line indicates the composition of an ideal gel. (Reprinted with permission from Ref. 313, Copyright 1971, Nature.)... 

One has to keep in mind that STM images show contours of constant tunnel probability rather than height contours directly. Nevertheless, for simple cases such as a metal surface, both quantities are closely related to each other. The dependence of the tunnel current IT on the tunnel voltage UT and on other parameters is given for the ideal case in Eq. (5.1) ... 

Figure 6.10 The topological map of an idealized mountain represented by the circular contours of constant height on a topological map. Two gradient paths or lines of steepest ascent (a) are shown, together with a path (b) that is not a line of steepest ascent but is an easier route up the mountain. The lines of steepest ascent—gradient paths—cross the contours at right angles.

One has to keep in mind, that STM images show contours of constant tunnel probability rather than height contours directly. Nevertheless, for simple cases such... 

Contours of constant value of the objective function/are defined by the linear equation... 

The geometry of this problem is shown in Figure 8.11. The linear equality constraint is a straight line, and the contours of constant objective function values are circles centered at the origin. From a geometric point of view, the problem is to find the point on the line that is closest to the origin at x = 0, y = 0. The solution to the problem is at x = 2, y = 2, where the objective function value is 8. 

Contours of constant signal to noise ratio follow the lines of ovals of Cassini as the signal to noise ratio is inversely proportional to the product of the squares of the transmitter to target and target to receiver ranges. In monostatic radar contours of constant signal to noise ratio are circles. 

Since the standard deviations are unity and the variables are independent (zero covariance), the covariance-matrix of X is the identity matrix / and the contours of constant probability in the space 9T are given by... 

Contours of constant probability density in the space 91" are such as... 

Figure 12.15 Contours of constant response as functions of jr, and for the response surface of Figure 12.14.

Figure 12.17 Upper left panel contours of constant response in two-dimensional factor space. Upper right panel a subset of the contours of constant response. Lower left panel canonical axes translated to stationary point of response surface. Lower right panel canonical axes rotated to coincide with principal axes of response surface.

Assuming the same s] as was used to draw Figure 12.24, the uncertainty surface for the rotatable design of Equation 12.81 is shown in Figure 12.26. The uncertainty depends only on the distance from the center of the design i.e., the contours of constant uncertainty are circular about the center of the design. 

However, it is not possible to add °C and min In a normalized factor space the factors are unitless and there is no difficulty with calculating distances. Coded rotatable designs do produce contours of constant response in the uncoded factor space, but in the uncoded factor space the contours are usually elliptical, not circular. 

Figure 12,31 Contours of constant composition for each of the three mixture components (x, Xj, and X3), individually and superimposed. The single design point corresponds to 25% x 50% Xj, and 25% X3.

Fig. 6.7 Regimes of motion for disks in free fall or rise. Contours of constant Strouhal number Sr and constant Reynolds number are also shown.

Fig. 4.15. Contours of constant charge density for Si(lll). The occupied portion of the dangling-bond surface state on Si(lll) is shown. Dots locate nuclei of surface atoms, the vacuum is above, and the charge density is in a.u.X lOL (Reproduced from Appelbaum and Hamann, 1976, with permission.)...

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