Points and curves

A convenient way to illustrate the behavior of the model for the example of ZnS deposition is to plot the measured deposition rate, r(d, ZnS), as a function of the incident-flux rate of one element when the incident-flux rate of the second element is fixed. An example is shown in Figure 13 for the deposition of ZnS as a function of the incident-flux rate of sulfur at a substrate temperature of 200 °C. Experimental data points and curves representing the best-fit model predictions are shown for each of four zinc incident-flux rates. A nonlinear least-square procedure was used to obtain the following values for the model parameters that best fit equation 40 to the experimental data 8(Zn) = 0.6-0.7, 8(S) = 0.5-0.7, and K(ZnS) > 1015 cm2-s/ZnS. 

Fig. 50. Number of monomer units Si 2 in a Kuhn segment of copolymer molecules of cyclohexanamide and caprolactam vs. relative content Z of cyclohexanamide units in the chain according to flow birefringence data Points and Curve 1 experimental data Curves 2 and 3 plotted according to Eqs. (74) and (75)...

Figure 2,5 (a) An Arrhenius plot of log k versus I/TXK) for the dissolution rates of various silicate rocks and minerals. The data points and curves for rhyolite, basalt glass, and diabase are from Apps (1983), as is the curve labeled silicates, which Apps computed from the results of Wood and Walther (1983). Curves for the S1O2 polymorphs are based on Rimstidt and Barnes (1980). Modified from Langmuir and Mahoney (1985). Reprinted from the National Well Water Assoc. Used by permission, (b) An Arrhenius plot of log k versus 1 /T(K) for the precipitation of quartz and amorphous silica based on Rimstidt and Barnes (1980). Reprinted from Geochim. Cosmochim. Acta, 44, J.D. Rimstidt and H.L. Barnes, The kinetics of silica water reactions, 1683-99, 1980, with permission from Elsevier Science Ltd, The Boulevard. Langford Lane. Kidlington OXS 1GB, U.K. 

Instead of employing the prism, the change in the composition of the ternary solutions can also be indicated by means of the projections of the curves A2K, and on the base of the prism, the particular temperature being written beside the different eutectic points and curves. This is shown in Fig. 103. 

Fig. 11. Auger sputter profiles (Auger amplitude vs. ion-bombardment time) for unreduced (open points, dashed curves) and reduced (solid points and curves) Rh/(single crystal) Ti02 model catalysts. Curves for Ti and O have been shifted up for clarity. (After Ref. 27.)...

Figure 2. Equation of state of the 6 12 fluid. The points and curves give computer simulation and the second-order perturbation theory results for seven isotherms that are labelled with the appropriate values of kT/e. For the Lennard-Jones fluid the triple-point reduced temperature ana density are about 0.7 and 0.85, respectively, and the critical-point reduced temperature and density are about 1.30 and 0.30, respectively.

Fig. 9.6 Nonlinear rate of neuronal loss. The graph is derived from the imaging data shown in Fig. 9.5. The number of neurons lost is based on the DWl lesion volume at each time point and the assumptions of neurons per unit volume given by Saver. Each patient has three data points, and curves were fitted to go through the three data points. The red dashed line is the neuronal loss estimated by Saver. The black dashed line is the mean neuronal loss of all 14 patients...

C. M. Singal, Analytical expressions for the series-resistance-dependent maximum power point and curve factor for solar cells, Solar Cells 3 (1981) 163-177. 

The broken lines in Figure 4.2 represent metastable conditions. If orthorhombic sulphur is heated rapidly beyond 95.5 °C, the change to the monoclinic form does not occur until a certain time has elapsed curve BB, a continuation of curve AB, is the vapour pressure curve for metastable orthorhombic sulphur above the transition point. Similarly, if monoclinic sulphur is cooled rapidly below 95.5 °C, the change to the orthorhombic form does not take place immediately, and curve BA is the vapour pressure curve for metastable monoclinic sulphur below the transition point. Likewise, curve CB is the vapour pressure curve for metastable liquid sulphur below the 115 °C transition point, and curve B E the melting point curve for metastable orthorhombic sulphur. Point B, therefore, is a fourth triple point (110 °C and 1.7 N m ) of the system. 

On the right of Figure 2-4, the shape of a part is visualized. Any point and curve can be computed in the model coordinate system using the mathematical description of the shape. The shape in this example is covered by flat surfaces it does not contain any curved surfaces or curves on its boundary. Lines and flat surfaces constitute a complete closed boundary of the body. The shape model is based on the principle of boundary representation with surfaces covering the shape and lines at the intersection of surfaces. 

Figure 7.29. Experimental kinetic curves (points) and curves calculated using equation (7.40) (lines) for glycidyl methacrylate postpolymerization at Co=3.0% (by mass), q=37.4 W/m and 7=20T.

Figure 7.30. Experimental kinetic curves (points) and curves calculated using equation...

Fig. tr.1-80 GaAs. Coefficient of linear thermal expansion. Experimental data points, and curves from an ah initio pseudopotential calculation [1.77]... 

Let us examine the curve for Cp, i vs. at fixed Cj,..., Q, X<,+2-Figure 4.22 shows three curves for each curve, the Q,..., C., variables are fixed. The fixed variables for each curve are selected in such a way that curve I is in the two-phase region, curve II passes through the critical point, and curve III stays in the singe-phase region. For curve J, B and C are the stability limits these two points are... 

In contrast, the errors of the polarization-resistance technique have been very thoroughly and quantitatively evaluated, and the reported errors are the smallest among the four techniques for all error categories. On the other hand, this technique has two more error possibilities (in linearization and Tafel-slope estimate) than the other techniques. Consequently, the overall error may be comparable to those of the three-point and curve-fitting techniques, and it has to be evaluated for each experimental situation. The systematic errors can be avoided by using the appropriately corrected polarization equations in the data evaluation however, that requires numerical values for the appropriate parameters, such as mass transport, double layer, solution resistance, equi-... 

Figure 3. Variation of band gap as a function ofZn (O) concentration, x. Lower points and curve (solid) calculated BGs and smoothed Efx) curve using the estimated bowing parameter, b. Upper points and curve (dashed) experimental data for (Gaj.xZnJ(Nj.xOJ solid solution (38,71) and predicted experimental Eg(x) behavior using the estimated b and the limiting GaN and ZnO band gaps (71).

The surface curve is a single scoped entity which contains in its scope the complete data structure that defines the curve geometry, hence, in wireframe models the surface-curve behaves as a single three-dimensional curve entity (see "Points and curves" on page 56 and "Geometry on surfaces"). The curve attribute refers to the top of that data structure. The surface entities which are referred from within the curve on surface entities may lie within the scope of the same surface-curve or outside. 

These entities represent any curves on a surface. The curves are represented in exactly the same way as two-dimensional curves in the xy-plane. This means that the algorithms described for the evaluation of two-dimensional curves in "Points and curves" on page 56 apply here as well. However, the curve points are all defined in the two-dimensional parameter space associated with the referenced surface. Hence, after application of the curve evaluation algorithm the resulting (x,y) values have to be treated as (u,v) coordinates in the parameter space of the referenced surface. 

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