Reduced term value plot

Figure 3.1a Natural rotational quantum numbers for Hund s cases (a) and (b). Reduced term value plots for 2S (B = 1.0 cm-1) and 2nr (B = 1.0 cm-1, A = 20.0 cm-1), (a) Plot °f — BJ(J + 1) versus J(J + 1) displays case (a) limiting behavior for the 2II state at very low J. The dotted lines illustrate the B2/A corrections to the near case (a) effective B-values (See Section 3.5.4). The 2S state does not exhibit case (a) behavior even at low J (at J = 0 the limiting slopes of the 2S Fi and h l curves are —oo and +oo).

This technique reduces testing times significantly and provides reUable results for >20 years material. The values plotted in Figure 2 (25) are an illustration of the viabiUty of this technique as a means to provide reaUstic long-term thermal performance values (21). 

Figure 20. Time-dependent diffusion D(t) of a two-dimensional system calculated using different low-wavenumber cutoff plotted against reduced time. The different low-wavenumber cutoff (ka) values are indicated in the figure. The dotted line represents the D t) obtained neglecting the contribution from the current term. The plots are at p = 0.7932 and T — 0.7. The time is scaled by = y/mcr2/e. D(i) is scaled by Ixsc. This figure has been taken from Ref. 175.

Swalm found that most executives are conservative in their expenditure and that the patterns of utihty curves are very similar if plotted with an ordinate range of 1 unit. The unit, in this case, is the maximum authorized annual expenditure of the executive. Such curves may appear to differ quite widely when plotted in terms of absolute money values. The curves also show that executives tend to be more conservative when considering a loss than they do when considering a reduced gain. 

The curves represent a plot of log (h ) (reduced plate height) against log (v) (reduced velocity) for two very different columns. The lower the curve, the better the column is packed (the lower the minimum reduced plate height). At low velocities, the (B) term (longitudinal diffusion) dominates, and at high velocities the (C) term (resistance to mass transfer in the stationary phase) dominates, as in the Van Deemter equation. The best column efficiency is achieved when the minimum is about 2 particle diameters and thus, log (h ) is about 0.35. The optimum reduced velocity is in the range of 3 to 5 cm/sec., that is log (v) takes values between 0.3 and 0.5. The Knox... 

The term r Vf in Equation (3.71) can be interpreted as a reduced fiber-volume fraction. The word reduced is used because q 1. Moreover, it is apparent from Equation (3.72) that r is affected by the constituent material properties as well as by the reinforcement geometry factor To further assist in gaining appreciation of the Halpin-Tsai equations, the basic equation. Equation (3.71), is plotted in Figure 3-39 as a function of qV,. Curves with intermediate values of can be quickly generated. Note that all curves approach infinity as qVf approaches one. Obviously, practical values of qV, are less than about. 6, but most curves are shown in Figure 3-39 for values up to about. 9. Such master curves for various vaiues of can be used in design of composite materiais. 

Plot the observed e.m.f. values against the concentrations of the standard solutions, using a semi-log graph paper which covers four cycles (i.e. spans four decades on the log scale) use the log axis for the concentrations, which should be in terms of fluoride ion concentration. A straight line plot (calibration curve) will be obtained. With increasing dilution of the solutions there tends to be a departure from the straight line with the electrode combination and measuring system referred to above, this becomes apparent when the fluoride ion concentration is reduced to ca 0.2 mg L-1. 

The measured growth rates are illustrated by the circles in Fig. 7. The interface velocity is plotted versus the interface temperature T. The value of T is always greater than Tq because of the release of the latent heat at the interface. Dimensionless units for T and the velocity are used here. The maximum velocity corresponds to 80m /s for argon. The most surprising aspect is the rapid crystallization at low temperatures. Most materials exhibit sharply reduced rates at low temperatures, as expected for an activated growth process. That is, the kinetics can be represented as the product of an Arrhenius factor F(T) and a term that accounts for the net production of crystalline material as a result of the atoms ordering and disordering at the interface,... 

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