Plotting program, computer

Wave functions can be visualized as the total electron density, orbital densities, electrostatic potential, atomic densities, or the Laplacian of the electron density. The program computes the data from the basis functions and molecular orbital coefficients. Thus, it does not need a large amount of disk space to store data, but the computation can be time-consuming. Molden can also compute electrostatic charges from the wave function. Several visualization modes are available, including contour plots, three-dimensional isosurfaces, and data slices. 

The plotting program is written on a Tektronix 1+051 graphics micro-computer which is coupled to a 1+662 plotter. 

The compositions of the polymers were determined by simulation of their spectra using a computer curve simulator-plotting program developed by B. L. Bruner at the University of Kentucky. An example of the output of the program is shown in Fig. 4. The input data are the positions, amplitudes, and... 

Table 4 shows the effect of monomer concentration, coinitiator concentration, and conversion on the composition of poly(4-methyl-1-pentene) using EtAlCl2 coinitiator at — 50° C. The 1,2-, 1,3-, and 1,4-repeat unit concentrations in the polymer have been determined from polymer spectra by use of a computer curve simulator-plotting program and are rounded to the nearest percent. No limits of error are indicated since none could be determined analytically. A reasonable error is thought to be +15% of the measured value. 

Dynamic light scattering, coupled with modern computer programs and auxiliary equipment, automatically graphs Zimm plots and computes Mw, Rg, , Cl, and flow rates. New techniques have expanded the method to the semidilute and concentrated regimes (Barth and Sun, 1991). 

Figure 10.2. Stacked plot rendering of computer-simulated spectra for an AB <=> A B exchanging system. [From A Simple Three Dimensional Perspective Plotting Program, by R. S. Macomber, Journal of Chemical Education, 53, 279 (1976). Reprinted by permission.]...

If a figrrre has been computer generated, many of the above concerrts may have been resolved automatically by the software plotting package. The user shotrld, however, be aware that the default plot scales are often not ideal. Most plot programs allow the user to control the aspect ratio, the scale ranges, and the shape of the symbols. You must also make sure that the plotted variables are correctly specified and their units clearly indicated. 

Examination of the properties of only the hydroxylic solvents was facilitated by a plotting program I wrote for the IBM personal computer. Data from two separate files may be read to an array for plotting. A third file is read to discriminate points for plotting as large or small circles. 

Three-dimensional drawings of normal modes, such as those shown in Chapter 2, can be made from the Cartesian displacement calculations obtained above. However, hand plotting of these data is laborious and complicated. Use of computer plotting programs greatly facilitates this process [95]. 

Note that distillation lines are generated by computer as easily as residue curves and,l -cause they do not involve any approximations to the operating line at total reflux, are preferred for the analyses to be performed in the remainder of this section. However, simulation programs compute and plot only residue curves. It can be shown that distillation lines have the same properties as residue curves at fixed points, and hence, both families of curves are sketched similarly. Their differences are pronounced in regions that exhibit extensive curvature. 

Plots of the bursting pressures of the Ni—Cr—Mo cylinders (EN 25) vs k derived from equations 16 and 17 show that neither equation is in such good agreement with the experimental results as is the curve derived from Manning s theory. Similar conclusions have been reached for cylinders made of other materials which have been tested (16). Manning s analytical procedure may be programmed for computation and, although torsion tests are not as commonly specified as tension tests, they are not difficult or expensive to carry out (20). 

Such programs generally concentrate on the technical parts of designing an experiment, and provide limited guidance on the important, softer aspects of experimental design stressed in this article. Also, most computer routines do not allow one to handle various advanced concepts that arise frequently in practice, eg, spHt plot and nested situations, discussed in the books in the bibhography. In fact, some of the most successful experiments do not involve standard canned plans, but are tailored to fit the problem at hand. 

Equations 5-118, 5-120, 5-121, and 5-122 are first order differential equations. A simulation exereise on the above equations using the Runge-Kutta fourth order method, ean determine the numher of moles with time inerement h = At = 0.2 hr for 2 hours. Computer program BATCH58 evaluates the numher of moles of eaeh eomponent as a funetion of time. Table 5-7 gives the results of the simulation, and Eigure 5-17 shows the plots of the eoneentrations versus time. 

The computer program PLUG51 used Equation 5-334 to determine the conversions and the compositions of the components. Table 5-13 illustrates the results of the computer program, and Figure 5-32 shows the plots of the rates of each reaction as a function of V/F. In both instances, the rates decrease toward zero as V/F increases. Figure 5-33 shows the plot of the total conversion versus V/F. 

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