Abscissa scale

The abscissa scale term is the same flow parameter used for plates (dimensionless) ... 

Relative density is usually determined at ambient temperature with speciahzed hydrometers. In the United States these hydrometers commonly are graduated in an arbitraiy scale termed degrees API. This scale relates inversely to relative density s (at 60°F) as follows (see also the abscissa scale of Fig. 27-3) ... 

Consecutive reactions involving one first-order reaction and one second-order reaction, or two second-order reactions, are very difficult problems. Chien has obtained closed-form integral solutions for many of the possible kinetic schemes, but the results are too complex for straightforward application of the equations. Chien recommends that the kineticist follow the concentration of the initial reactant A, and from this information rate constant k, can be estimated. Then families of curves plotted for the various kinetic schemes, making use of an abscissa scale that is a function of c kit, are compared with concentration-time data for an intermediate or product, seeking a match that will identify the kinetic scheme and possibly lead to additional rate constant estimates. 

Figure 12-32. ( uiiccnluiliuil dependence of llie hole nuibiliiy for UDAD ill pulysulfunc olMuincd from iransiciu absorption data. The abscissa scale shows ihc average distance between the UDAD molecules (Ref. (961). 

Fig. 6-4. Calculated curves showing relationship between intensity ratio and thickness for various values of exponent a. The abscissa scale is logarithmic. Circles = plated coatings squares = evaporated coatings. (Liebhafsky and Zemany, Anal. Chem., 28, 455.)...

The relation (103) will hold for any value of the scission yield, providing the macromolecules do not cross the boundary between the different streamlines, either by molecular diffusion or by flow turbulence. For samples having similar polydispersities and MWD, all the degradation data could be superimposed onto a single curve when plotted on a relative abscissa scale (e(0)/ef). 

Fig. 8. Transmittance versus time curves for the Co(C204)3 +Fe reaction. Upper curve shows disappearance of 00(0204)3 (wavelength, 600 m/t abscissa scale, 500 msec per major division). Lower curve shows formation and decay of the intermediate FeC204 (wavelength, 310 m/r abscissa scale, 2 sec per major division). [Co(C204)3 ] = 1.0x10" M [Fe ] = 2.5x10 A/ [HCIO4] = 0.92 M ionic strength = 1.0 Af temp., 25 °C. From Haim and Sutin -, by courtesy of The American Chemical Society.)...

Fig. 8. a) Non-least-motion approach of two methylenes. The sequence 1-2—3 shows the mutual orientation of the two fragments with decreasing distance, b) Energy variation along the least-motion path (i) and along the least-energy path (2). The abscissa scale is the C-C distance (A). The vertical bar is 1 eV on the ordinate energy scale. 

Fig. 17.15 The top panel shows the transient surface-state composition during catalytic ignition on a long time scale. The lower panel shows the transient response of the Stefan velocity and the pressure-curvature eigenvalue on a very short time scale during the ignition transient. The zero point for the abscissa scales is arbitrary.

Fig. 19. Results for the 63 °C curing study for R-45-M containing 8% ( ), 11% (O) and 16% (A) of curing agent IPDI. Diffusion of IPDI (top) and polymer molecules of weight Mn (bottom) is shown as function of curing time (abscissa scale is distorted). For IPDI diffusion after the first day, the upper error band corresponds to 16% concentration, the lower band to both 8 and 11 % (reprinted from Ref.110) with permission)...

The response curves were plotted by numerically solving the final equations at intervals of 0.01 or 0.04 or major divisions on the abscissa scale using a Tektronix 31 calculator and plotter. 

In Fig. 10.7 are reported two FT-IR spectra of C70 recorded respectively at -180°C and at +250°C as in the previous case of C60. In the wavelength (pm) abscissa scale it is difficult to appreciate the band shift due to temperature change occurred in C70 embedded in KBr. Therefore, Figs. 10.8 and 10.9 show the details of the spectra in wavenumbers putting in evidence the small band shift measured at the two temperatures employed. 

Figure 4.10 Transmission functions T(Usp) of an electrostatic deflection spectrometer for electrons with two different kinetic energies which differ by a factor of 2 n(2) = 2E°n(l) with , ( 1) = /l/°p(l) and E°ia(2) = /[/°p(2). Because these transmission functions are plotted on the same abscissa scale, the voltage range needed to produce the transmission function with jln(2) is twice as large as that needed for E in(l). As a consequence, the spectrometer function at l/°p(2) is twice as broad as that at l/ p(l), with fwhm(2) = 2 fwhm(l).

Figure 4.19. Static linear (a) and quadratic (b) susceptibilities for the dimensionless bias field E = 0.05 (1), 0.1 (2), 0.2 (3), 0.5 (4). Broken line shows the limiting behavior for H = 0. Note the threefold times difference between the abscissa scales of the (a) and (b) plots.

Figure 15.9 Spectrum for an elongated network (A, = 3.41, N = 51, Q = 0°) obtained by Monte-Carlo simulation. The abscissa scale denotes the reduced interaction A/vq, i.e. the orientational order parameter S. Ordinates are in linear arbitrary units...

Since T2 is readily determined from time-domain CARS with high accuracy (<2%), a combined analysis of frequency- and time-domain data was proposed and demonstrated (45), plotting the spontaneous Raman data in normalized frequency units, Aa> x T2 (note abscissa scale of Fig. 7b). In this way the bandshape only depends on the ratio rc/T2, and only this ratio has to be deduced from the wings of the Raman band. With respect to the experimental uncertainties (ordinate value of the baseline, overlap with neighboring combination tones), the approach is more reliable than the determination of two quantities, rc and T2, from the spectroscopic data. 

FIGURE 5.8 H NMR spectrum at 60 MHz of a sample with the molecular formula C10H6O4. Inset Abscissa scale, 1 Hz per division. 

Figure 14. /T as a function of Q tor R — 0.1 (experimental results). The parameters characterizing the system are do —222s , b—739s V", y —5070 s, and 0-0.054 s Note that the abscissa scale is so greatly contracted as to make it impossible to draw the decreasing behavior of /T with increasing Q which would be exhibited in the weak-Q region.

Figure 5.33. Adsorbed amount 0 of a strong negative polyelectrolytc as a function of the salt concentration on an uncharged surface = 0) and on a positively charged surface at two values of the surface charge density a° (indicated) U). Note that the abscissa scale is not linear in but in. c. Parameters N = 500, = 10, = L. IT =...

Figure 1. Tracer diffusion coefficients of CigTAC micelles in aqueous NaCl solutions at 35 °C. Cmc s are very close to zero in this abscissa scale.

An additional step is normally taken in the construction of plots of this type. The usual use of the plot is to determine p for a given T is only an intermediate quantity used to relate these variables. The necessity of looking up for each given temperature can be avoided if values of T(p" are shown on a second abscissa scale (see Figure 6.1-3). Now to find p T) you need only find T on the new abscissa scale the value of will be located at the same... 

Figure 7 Dependence of light-scattering efficiency of ammonium sulfate aerosol on the amount of material in the particle and RH. The scattering efficiency is expressed as a scattering coefficient cr p, here at wavelength 550 nm, per amount of sulfate. The auxiliary abscissa scale gives the particle radius (Nemesure et al., 1995) (reproduced by permission of American Geophysical Union from J. Geophys. Res.

Entrainment Corrections. Above about 80% of flood, the recirculation of liquid as entrainment between trays undermines the countercurrent action of the tray column, and efficiency therefore suffers. This is a particular problem in vacuum distillation where it may be optimum to allow a certain amount of liquid entrainment in initial design. Figure 13.41 shows an approximate method for entrainment correction to column efficiency or Murphree efficiency. The abscissa scale is the same parameter used for flooding prediction (Figure 13.32(b)). The ordinate value is used to correct from a dry to a wet efficiency (with entrainment) ... 

The iterative procedure for finding the optimal alignment starts (see Figure 1) by the request of some initial values of both The state parameters refined by the Kalman filter (i.e. X(0), the concentration of the components in the mixture, and P(0), the diagonal elements of the covariance matrix), and the parameters refined by the optimization procedure (i.e. the position parameters Tj, j=l,.,n, where n is the number of the componaits in the mixture). The Tj values represent the co-ordinates on the abscissa scale of the peak maximum of the components with respect to a fixed point on the composite spectrum, which is the beginning of the chosen spectral window. Moreover, the Tj are integer quantities expressed in terms of number of data points. 

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