Axis. Abscissa

Now we find intersection points of the curve ML(xf)with the abscissa axis. Assuming in Eq. (10.54) m/ 0 (at finite Xf), we obtain... 

The dependences ML(xf) for various Pe are plotted in Fig. 10.4b. The shape of these curves significantly depends on the value of the Peclet number. When Pe < 4 the raising and the falling branches of (((Xf) contain points (Xf)c and (xf)L on the abscissa axis and form canopy-shaped curves with characteristic maximum depending on Pe. Contrary to that, if Pe > 4, the curves ML(Xf) are not continuous. When Xf is large, the upper and lower branches have one (Pe = 4) or two (Pe > 4) asymptotes. 

The computed him thickness distribution of the cross line at the contact center is shown in Fig. 23. The abscissa axis is the dimensionless coordinate in the flow direction whereas the ordinate axis is the dimensionless him thickness. It is very clear that the him thickness distribution is similar to that of EHL predictions. 

Curves calculated from Eq. (8) for various values of the parameters ri and are shown in Figs. 24 and 25. The ordinate (Ei) represents the composition of the increment of copolymer formed from the monomer mixture having the composition (/i) given along the abscissa axis. Fig. 24 treats the case in which the two radicals display the same preference for one of the monomers over the other. That is... 

A. superior end point is obtained if the effects of dilution are compensated for by using an abscissa axis of V +AV/2. 

Figure 7.3 CaMgSi206-CaAl2Si208 (diopside-anorthite) system, after Bowen (1915) and Osborn (1942). Abscissa axis percentile weight of both components.

Note that the resulting fractional amounts are in weight percent, because the abscissa axis of the phase diagram reports the fractional weights of the two components (similar application of baricentric coordinates to a molar plot of type 7.2 would have resulted in molar fractions of phases in the system). Applying the lever rule at the various T, we may quantitatively follow the crystallization behavior of the system (i.e., atT = 1350 °C, = 0.333 and Xl = 0.666 atT = 1300... 

It may be noted in figure 10.3B that prolongation of the interpolant encounters the abscissa axis at X = j, which is exactly the proportion of the two structural sites where Rb/Na substitutions take place in nepheline. According to figure 10.3B and equation 10.20, it is plausible to admit that Rb is fixed almost exclusively in the larger of the two structural sites. 

From the relative positions of phases A, B, and C in figure 11.14, it is obvious that the last one is richest in Rb, so that the production of radiogenic Sr is highest in this phase. A hypothetical phase with no initial Rb at time = 0 would lie at zero on the abscissa axis and would maintain its initial ( Sr/ Sr)o unaltered. 

The first satisfactory definition of crystal radius was given by Tosi (1964) In an ideal ionic crystal where every valence electron is supposed to remain localised on its parent ion, to each ion it can be associated a limit at which the wave function vanishes. The radial extension of the ion along the connection with its first neighbour can be considered as a measure of its dimension in the crystal (crystal radius). This concept is clearly displayed in figure 1.7A, in which the radial electron density distribution curves are shown for Na and Cl ions in NaCl. The nucleus of Cl is located at the origin on the abscissa axis and the nucleus of Na is positioned at the interionic distance experimentally observed for neighboring ions in NaCl. The superimposed radial density functions define an electron density minimum that limits the dimensions or crystal radii of the two ions. We also note that the radial distribution functions for the two ions in the crystal (continuous lines) are not identical to the radial distribution functions for the free ions (dashed lines). 

Fig. 10.13 Effect of intensity of turbulence on the average Nusselt number for a sphere in an air stream. (Note scale change on abscissa axis.)...

Figure 1. Comparison of the Morse (dashed line) and Niketic-Rasmnssen (solid line) potentials. The abscissa axis is the bond length in A and the ordinate is the energy in kcal/mol.

As in Section IV for naphthalene vapor, the kinetic spectra of solids are presented by plotting on the abscissa axis the quantity Ep = (hv — incident photon,

work function of the solid (energy of electron abstraction). Ekin is the photoelectron kinetic energy, which is lower than the theoretical upper energy limit of kinetic energy because of internal energy... 

Fig. 13. Effect of the solvent solubility parameter 8 on the linear coefficient of thermal expansion 3 (1) and modulus of elasticity E (2) of films of linear SBS thermoelastoplastics with 28.3% PS obtained from solutions. The solvent is indicated on the abscissa axis I — n-heptane, II — tetra-hydrofurane, III — benzene, IV — chlorobenzene 119)...

Fig. 4.9. Discrimination of migration-controlled reactions [81]. D - diffusion (x < 1), I - intermediate regime (lies between abscissa axis and full line), and H - hopping reaction (below this line). The cases r = const and D = const are marked by lines--------------------------------and---------— respectively.

Numerical solution of a set of the kinetic equations (6.1.45) and (6.1.63) to (6.1.66) for the joint correlation functions is presented in Figs 6.11 and 6.12. (To make them clear, double logarithmic scale is used.) The auto-model variable 77 is plotted along abscissa axis in Fig. 6.11 showing the correlation function X(r, R). 

Fig. 7. 15. The joint correlation function of similar particles under their accumulation restricted by the tunnelling recombination [106], The dose rate p 5xl020 cm 5s 1 (curve a),6.7xl019 (curve b), 1.2 x 1018 (curve c), 2.2 x 1016 (curve d). The dotted line around the abscissa axis in (a) shows the case when there is no recombination.

Each monomer is ascribed with a two-dimensional coordinate, of which the abscissa dimension corresponds to the affinity to the polar (water) or the nonpolar phase (hexane) and the ordinate dimension corresponds to interfacial activity. The standard free energy of partition between water and hexane is used as a quantitative parameter for the abscissa axis (AFpart), whereas the standard energy of adsorption at the interface is used for the ordinate axis (AFa(js). Both parameters are normalized by the kT factor. The normalized values are denoted as A/part and A/ads, respectively. Thus,... 

Fig. 4.1.13(a-c) shows partial cross-sections for reactions with the reactant molecules in vibrational quantum states n = 0,1,2 and rotational quantum state J = 0 and products in vibrational states n = 0,1,2, respectively, and any rotational quantum state. Note that the abscissa axis in this plot is the translational energy and not the total energy as in Fig. 4.1.12. The translational energy is found in the latter plot by subtracting the molecular energy En

The order of integration is interchanged, as sketched in Fig. 11.2.1. The region covered in the integration is marked by the hatched region between the 45° line and the abscissa axis. This region may be spanned in two ways. We may choose an interval... 

Let Xi and Ab be the coordinates in a rectangular Cartesian coordinate system with X1 along the ordinate axis and X2 along the abscissa axis. One of the axes in the new coordinate system is now chosen to be collinear with the abscissa axis in the rectangular coordinate system, and we let the coordinate along this axis be the first term in the expression for X2 in Eq. (D.22), namely 2(ay — ay). The situation is sketched in Fig. D.1.1. The other axis with a coordinate proportional to the other distance ay — a 1 forms an angle 4> with the first. This angle is determined from the requirements that the projections of this coordinate on the X coordinate axis is a (a 2 — ay) and on the X2 coordinate axis is aym ay — ay )/.sy. If we let the proportionality constant of X2 — ay be / , then we have... 

Setting the values for order parameter p over the interval 0calculate temperature and subsequently construct the p = p(T) plot. This dependence is given in Fig. 3 for values of 8 (43) equal to 0,1 . 0,3. Fig. 3 shows that at 8>0 the order is increased with increasing temperature compared to its value at 8=0, the p(T) curve approximate asymptotically to the abscissa axis at T oo. At 8<0 the order parameter is descreased at each value of temperature, the p(T) curves pass below the curve at 8=0. 

Figure 3. The curve plots of the temperature dependence of order parameter constmcted by formula (42) for different values of energetic constant 5 (43), equal to 0,1 +0,15 0,2 0,25 0,3 (curves 1-5 for 5>0 and curves l -5 for 5<0). The dotted line corresponds to 5=0, i.e. for pure fullerite without platinum and hydrogen atoms. The temperature Tc of loss of fullerite stable state (somewhat below the ordering temperature) is marked with circle on the abscissas axis.

In Fig. 1 a conventional diagram is given for producing the X-shape junction between two nanotubes. Certain symbols for system states St and interstates transitions Bj are given in the bottom and top rows of the abscissa axis,... 

Figure 3. The curve plots of the temperature dependence of order parameters of fullerite of stoichiometric composition for sc (full curves rp) and fee (dotted curve r 2) phases. The order parameters rp (point 1 for kT) = 0,0285 eV, point 2 for kT) = 0,024 eV) and rp (point 0 for kT2 = 0,026 eV) at the phase transition temperature kT0 and also the temperatures kT0, kTi, kT2 on the abscissas axis are marked with circles.

The distribution function is presented graphically both as integral and differential distribution curves. In the integral distribution F(R) curve the abscissa axis depicts the size and the ordinate axis the fraction or percentage content of the total bubble number or the total volume of those bubbles whose size is bigger or smaller than R. In the differential distribution F(R) curve the abscissa axis depicts again the size but the ordinate axis the fraction content, i.e. number of bubbles entering a definite radius interval. The latter is more often employed. 

From Eq. (10.58) it is seen that can be defined as the cross point of the VF/Vg (c o) dependence with the abscissa axis (further in the text cl,o will be denoted as C). At large surfactant concentrations when the fraction of the dispersed gas retained in the foam strongly increases, the VF/Vg ratio tends to 1. In this case the whole initial solution is transformed into a foam and further increase in the expansion ratio becomes impossible, so a considerable part of the surfactant remains in the solution, i.e. reGVg =c-cLR cL0- cmn. As indicated by the experiments, at low concentrations ct,o - Cmm there is a region where the VF /Vg (C) dependence becomes linear. The extrapolation of this linear segment gives cmjn. The slope angle of this dependence, equal to VLOn / VtTe(ti -1), can be used to estimate the adsorption, needed for the formation of a stable foam with Pf > 1, in case the value of the specific foam surface area is known. 

In a NaDoS foam solution formed in the absence of an electrolyte, there is no linear segment that crosses the abscissa axis and the VF /Vg = f(C) curve is S-shaped without a clearly expressed emin> (Fig. 10.9, curve 3). 

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