Dashed lines

Figure 1 compares data reduction using the modified UNIQUAC equation with that using the original UNIQUAC equation. The data are those of Boublikova and Lu (1969) for ethanol and n-octane. The dashed line indicates results obtained with the original equation (q = q for ethanol) and the continuous line shows results obtained with the modified equation. The original equation predicts a liquid-liquid miscibility gap, contrary to experiment. The modified UNIQUAC equation, however, represents the alcohol/n-octane system with good accuracy. 

Figure 15 shows results for a difficult type I system methanol-n-heptane-benzene. In this example, the two-phase region is extremely small. The dashed line (a) shows predictions using the original UNIQUAC equation with q = q. This form of the UNIQUAC equation does not adequately fit the binary vapor-liquid equilibrium data for the methanol-benzene system and therefore the ternary predictions are grossly in error. The ternary prediction is much improved with the modified UNIQUAC equation (b) since this equation fits the methanol-benzene system much better. Further improvement (c) is obtained when a few ternary data are used to fix the binary parameters. 

Figure 16 shows observed and calculated VLE and LLE for the system benzene-water-ethanol. In this unusually fortunate case, predictions based on the binary data alone (dashed line) are in good agreement with the experimental ternary data. Several factors contribute to this good agreement VLE data for the mis-... 

Because the pseudo-inverse filter is chosen from the class of additive filters, the regularization can be done without taking into account the noise, (n). At the end of this procedure the noise is transformed to the output of the pseudo-inverse filter (long dashed lines on Fig. 1). The regularization criteria F(a,a) has to fulfill the next conditions (i) leading to an additive filter algorithm, (ii) having the asymptotic property a, —> a, for K,M... 

For the iteration algorithm (5) the optimal estimations (6) are directly used by a second back loop to block B (long dashed line in Fig. 1). 

In order to check the the validity of this method [8], 6 detection media Px where selected and applied on the reference pieces following the instructions of the standard (inclination angle 45° 3 applications of the detection medium and averaging). The arrangements of the cuts can be seen at Fig. 3. Indications or parts of indications are chosen for the valuation and marked by dashed lines. 

Fig. III-3. Comparison of Eq. III-18 (solid line) with experimental results for cyclohexane bridges formed between crossed mica cylinders the dashed line is the calculation including Eq. III-20 (from Ref. 19).

Fig. IV-13. Example of a p-polarized reflection spectrum from Ref. [154] for a stearyl alcohol monolayer on water. The dashed line is the baseline to be subtracted from the spectra. [Reprinted with permission from Joseph T. Buontempo and Stuart A. Rice, J. Chem. Phys. 98(7), 5835-5846 (April 1, 1993). Copyright 1993, American Institute of Physics.]...

Fig. IV-20. Film pressure-area plots for cerebronic acid (a long-chain a-hydroxy carboxylic acid) and cholesterol (see insert) and for an equimolar mixture. At low pressures the r-a plot is close to that of the average (dashed line), an unanticipated kink then appears, and finally, the horizontal portion probably represents ejection of the cholesterol. (From Ref. 239.)...

Fig. V-1. Variation of m / o and n /wo with distance for = 51.38 mV and 0.01 M uni-univalent electrolyte solution at 23°C. The areas under the full lines give an excess of 0.90 X 10 mol of anions in a column of solution of 1-cm cross section and a deficiency of 0.32 x 10 mol of cations. There is, correspondingly, a compensating positive surface charge of 1.22 x 10 " mol of electronic charge per cm. The dashed line indicates the effect of recognizing a finite ion size.

Fig. VI-7. The force between two crossed mica cylinders in dry OMCTS. The cylinder radii R were about 1 cm. The dashed lines show the presumed, experimentally inaccessible, transition between a repulsive maximum and an attractive minimum. (From Ref. 68.)...

Fig. X-3. Variation of contact angle with /oh. the fraction of the surface covered by HS(CH2)uOH in a mixture with HS(CH2)uCH3. Solid line is comparison with Eq. X-27, and dashed line is from Eq. X-28. (From Ref. 44.)...

Fig. X-7. Advancing and receding contact angles of octane on mica coated with a fluo-ropolymer FC 722 (3M) versus the duration of the solid-liquid contact. The solid lines represent the initial advancing and infinite time advancing and receding contact lines and the dashed lines are 95% confidence limits. (From Ref. 75.)...

Fig. XVII-22. Isosteric heats of adsorption for Kr on graphitized carbon black. Solid line calculated from isotherms at 110.14, 114.14, and 117.14 K dashed line calculated from isotherms at 122.02, 125.05, and 129.00 K. Point A reflects the transition from a fluid to an in-registry solid phase points B and C relate to the transition from the in-registry to and out-of-registry solid phase. The normal monolayer point is about 124 mol/g. [Reprinted with permission from T. P. Vo and T. Fort, Jr., J. Phys. Chem., 91, 6638 (1987) (Ref. 131). Copyright 1987, American Chemical Society.]...

Fig. XVIII-11. Calorimetric differential heat of adsorption of H2 on ZnO. Dashed line differential heat of desorption. (From Ref. 104.)...

In order to describe any electrochemical cell a convention is required for writing down the cells, such as the concentration cell described above. This convention should establish clearly where the boundaries between the different phases exist and, also, what the overall cell reaction is. It is now standard to use vertical lines to delineate phase boundaries, such as those between a solid and a liquid or between two innniscible liquids. The junction between two miscible liquids, which might be maintained by the use of a porous glass frit, is represented by a single vertical dashed line, j, and two dashed lines, jj, are used to indicate two liquid phases... 

Figure A2.5.1. Schematic phase diagram (pressure p versus temperature 7) for a typical one-component substance. The full lines mark the transitions from one phase to another (g, gas liquid s, solid). The liquid-gas line (the vapour pressure curve) ends at a critical point (c). The dotted line is a constant pressure line. The dashed lines represent metastable extensions of the stable phases.

R is the gas constant per mole, while K is the temperature unit Kelvin). The dashed lines represent metastable extensions of the stable phases beyond the transition temperatures. 

Figure A2.5.4. Themiodynamic fimctions (i, n, and C as a fimction of temperature T at eonstant pressure and eomposition x = 1/2) for the two-eomponent system shown in figure A2.5.3. Note the diflferenee between these and those shown for the one-eomponent system shown in figure A2.5.2. The fiinetions shown are dimensionless as in figure A2.5.2. The dashed lines represent metastable extensions (superheating or supereooling) of the one-phase systems.

Figure A2.5.10. Phase diagram for the van der Waals fluid, shown as reduced temperature versus reduced density p. . The region under the smooth coexistence curve is a two-phase liquid-gas region as indicated by the horizontal tie-lines. The critical point at the top of the curve has the coordinates (1,1). The dashed line is the diameter, and the dotted curve is the spinodal curve.

Figure A2.5.17. The coefficient Aias a fimction of temperature T. The line IRT (shown as dashed line) defines the critical point and separates the two-phase region from the one-phase region, (a) A constant K as assumed in the simplest example (b) a slowly decreasing K, found frequently in experimental systems, and (c) a sharply curved K T) that produces two critical-solution temperatures with a two-phase region in between.

Figure A2.5.22. The experimental heat eapaeity of a p-brass (CiiZn) alloy eontaining 48.9 atomie pereent Zn as measured by Moser (1934). The dashed line is ealeulated from the speeifie heats of Cu and Zn assuming an ideal mixture. Reprodueed from [6] Nix F C and Shoekley W 1938 Rev. Mod. Phy.s. 10 4, figure 4. Copyright (1938) by the Arneriean Physieal Soeiety.

Figure A2.5.25. Coexistence-curve diameters as functions of reduced temperature for Ne, N2, C2H4, and SFg. Dashed lines indicate linear fits to the data far from the critical point. Reproduced from [19] Pestak M W, Goldstein R E, Chan M H W, de Bniyn J R, Balzarini D A and Ashcroft N W 1987 Phys. Rev. B 36 599, figure 3. Copyright (1987) by the American Physical Society.

Figure A3.3.5 Tliemiodynamic force as a fiuictioii of the order parameter. Three equilibrium isodiemis (fiill curves) are shown according to a mean field description. For T < J., the isothemi has a van der Waals loop, from which the use of the Maxwell equal area constmction leads to the horizontal dashed line for the equilibrium isothemi. Associated coexistence curve (dotted curve) and spinodal curve (dashed line) are also shown. The spinodal curve is the locus of extrema of the various van der Waals loops for T < T. The states within the spinodal curve are themiodynaniically unstable, and those between the spinodal and coexistence...

Figure A3.4.5. Simple models for effeetive eollision eross seetions a hard sphere without tlireshold (dotted line) hard sphere with tlireshold (dashed line) and hyperbolie threshold (full eiirve). is the (translational) eollision energy and is the threshold energy. Oq is the hard sphere eollision eross seetion. The dashed-dotted eurve is of the generalized type E > q) Oq (1 - q/ j) exp[(l - j/ q)/(<3 q)] with the parameter...

Figure A3.10.25 Arrhenius plots of CO oxidation by O2 over Rli single crystals and supported Rli/Al203 at PCO = PO2 = 0.01 atm [43]. The dashed line in the figure is the predicted behaviour based on the rate constants for CO and O2 adsorption and desorption on Rli under UHV conditions.

Figure A3.13.2. Illustration of the analysis of the master equation in temis of its eigenvalues and example of IR-multiphoton excitation. The dashed lines give the long time straight line luniting behaviour. The fiill line to the right-hand side is for v = F (t) with a straight line of slope The intercept of the...

Figure Bl.2.3. Comparison of the hannonic oscillator potential energy curve and energy levels (dashed lines) with those for an anliannonic oscillator. The hannonic oscillator is a fair representation of the tnie potential energy curve at the bottom of the well. Note that the energy levels become closer together with increasing vibrational energy for the anliannonic oscillator. The aidiannonicity has been greatly exaggerated.

Figure B2.3.8. Energy-level sehemes deseribing various optieal methods for state-seleetively deteeting ehemieal reaetion produets left-hand side, laser-indueed fluoreseenee (LIF) eentre, resonanee-enlianeed multiphoton ionization (REMPI) and right-hand side, eoherent anti-Stokes Raman speetroseopy (CARS). The ionization oontinuiim is denoted by a shaded area. The dashed lines indieate virtual eleetronie states. Straight arrows indieate eoherent radiation, while a wavy arrow denotes spontaneous emission.

Figure B2.5.3. The fall-off curve of reaction (B2.5.14) with M = He between 0.3 bar and 200 bar. The dashed lines represent the extrapolated low- and high-pressure limits, /r r, = (2.1 0.2) x [He] cm moU s ...

Figure B3.3.8. Insertion probability for hard spheres of various diameters (indieated on the right) in the hard sphere fluid, as a fiinetion of paeking fraetion p, predieted using sealed partiele theory. The dashed line is a guide to the lowest aeeeptable value for ehemieal potential estimation by the simple Widom method.

Figure B3.3.11. The classical ring polymer isomorphism, forA = 2 atoms, using/ = 5 beads. The wavy lines represent quantum spring bonds between different imaginary-time representations of the same atom. The dashed lines represent real pair-potential interactions, each diminished by a factor P, between the atoms, linking corresponding imaginary times.

Figure B3.4.17. When a wavepacket comes to a crossing point, it will split into two parts (schematic Gaussians). One will remain on the same adiabat (difFerent diabat) and the other will hop to the other adiabat (same diabat). The adiabatic curves are shown by fidl lines and denoted by ground and excited die diabatic curves are shown by dashed lines and denoted 1, 2.

Dashed lines show tliat lasers are timed about one natural linewidtli to tire red of tire transition frequencies. 

A well-understood catalytic cycle is tliat of the Wilkinson alkene hydrogenation (figure C2.7.2) [2]. Like most catalytic cycles, tliat shown in figure C2.7.2 is complex, involving intennediate species in tire cycle (inside tire dashed line) and otlier species outside tire cycle and in dead-end patlis. Knowledge of all but a small number of catalytic cycles is only fragmentary because of tire complexity and because, if tire catalyst is active, tire cycle turns over rapidly and tire concentrations of tire intennediates are minute thus, tliese intennediates are often not even... 

Figure C2.7.2. Catalytic cycle (witliin dashed lines) for tire Wilkinson hydrogenation of alkene [2]. Values of rate and equilibrium constants are given in [2]...

The reactivities of tlie species witliin tlie Wilkinson cycle are so great tliat tliey are not observed directly during tlie catalytic reaction ratlier, tliey are present in a delicate dynamic balance during tlie catalysis in concentrations too low to observe easily, and only tlie more stable species outside tlie cycle (outside tlie dashed line in figure C2.7.2 are tlie ones observed. Obviously it was no simple matter to elucidate tliis cycle tlie research required piecing it togetlier from observations of kinetics and equilibria under conditions chosen so tliat sometimes tlie cycle proceeded slowly or not at all. 

Passivation is manifested in a polarization curve (figure C2.8.4) dashed line) by a dramatic decrease in current at a particular onset potential (the passivation potential, density, is lowered by several orders of magnitude. 

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