Transitional value

As indicated in Section 3.7.9, this definition of ReMR may be used to determine the limit of stable streamline flow. The transition value (R ur)c is approximately the same as for a Newtonian fluid, but there is some evidence that, for moderately shear-thinning fluids, streamline flow may persist to somewhat higher values. Putting n = 1 in equation 3,140 leads to the standard definition of the Reynolds number. 

In this discussion, two mutually canceling simplifications have been made. For the transition value of the radius ratio the phenomenon of double repulsion causes the inter-atomic distances in fluorite type crystals to be increased somewhat, so that R is equal to /3Rx-5, where i has a value of about 1.05 (found experimentally in strontium chloride). Double repulsion is not operative in rutile type crystals, for which R = i M + Rx- From these equations the transition ratio is found to be (4.80/5.04)- /3i — 1 = 0.73, for t = 1.05 that is, it is increased 12%. But Ru and Rx in these equations are not the crystal radii, which we have used above, but are the univalent crystal radii multiplied by the constant of Equation 13 with z placed equal to /2, for M++X2. Hence the univalent crystal radius ratio should be used instead of the crystal radius ratio, which is about 17% smaller (for strontium chloride). Because of its simpler nature the treatment in the text has been presented it is to be emphasized that the complete agreement with the theoretical transition ratio found in Table XVII is possibly to some extent accidental, for perturbing influences might cause the transition to occur for values a few per cent, higher or lower. 

Other high performance polymer backbones have been explored as PEM materials in addition to poly-(arylene ether)s and polyimides. Ductile copolymers with high modulus and glass transition values are desirable PEM candidates. The hydrolytic and oxidative stability of many of these materials remains to be determined. Nevertheless, interesting synthetic methodologies have been employed to investigate these materials, which have been instructive in the search for new PEM candidates. 

Thus digestion of the rock phosphate would be undertaken above the transition temperature to form hemlhydrate crystals. The crystallizers however would be operated at a temperature below the transition value and so gypsum crystals are produced. 

A more detailed spectroscopic study of the T Cl ion has been reported by Cotton et al. (70). Of particular interest is the band in the near infrared, between 6000 and 8000 cm, which the authors assign as the 6 - 6 transition. Values for absorption energies were calculated from SCF-Xa analysis, and numerical agreement with assigned bands was superior to the agreement attained in related even-electron calculations for Re2Cll (194) and Mo2Clg (199). 

Glass-transition values reported rounded to nearest 5°C. 

If fractionation were perfect, f(M) would be zero below some value of M representing the transition between supernatant and precipitate and unity for all higher values of M. It is shown (8) that the most readily determined value of the z(x) curve is its maximum, H, occurring at the point where this transition value of M is Mw. Adopting the use of an asterisk to denote quantities calculated with the above assumption of perfect fractionation... 

Thus, the kind and quantity of relativistic corrections to the length and velocity forms of 1-radiation are different. From this point of view the concept of the equivalency of these forms must be improved both forms will lead to coinciding transition values for the accurate (exact) wave functions only if we account for the relativistic corrections of order v2/c2 to the transition operators (in practice, only for the velocity form). The other conclusion accounting for the relativistic effects leads to qualitatively new results, namely, to new operators, which allow not only improved values of permitted transitions, but also describe a number of lines, which earlier were forbidden. These relativistic corrections usually are very small, but they are very important for weak intercombination lines of light neutral atoms (see Chapter 30). 

It is clear that in the low-temperature part, the introduction of MGI units decreases the dissipation relative to what should be expected from the MMA content. However, this effect gradually disappears along the high-temperature part to reach, at the end of the /3 transition, values equal to or slightly higher than those expected. 

Guo and coworkers (29) examined the chemical stability of lyophilized quinapril HC1 as a function of initial solution pH. Lyophilization of different quinapril solutions produces mixtures of amorphous quinapril and its neutralized form, with glass transition values between the Tg values of quinapril and neutralized quinapril. As the fraction of quinapril increases the rate of chemical degradation increases relative to that of quinapril HC1 alone. This is most likely caused by the plasticizing effects of neutralized quinapril. 

The parameter R is the laminar-turbulent transition value of R and has the numerical value 183.3 for Newtonian fluids. For non-Newtonian fluids it would have to be computed from the various results presented above. 

We now examine more carefully the lineshape in the low-energy part far from the 0-0 transition value.52 53 From a perturbational point of view, this absorption may be visualized as a successive absorption of many phonon energy quanta up to the excitonic band, where a density of excitonic final states exists. In this scheme, the low-energy absorption wing exists only at finite temperature. If v phonons are necessary to reach the excitonic band, the dominant term in originates from the consecutive absorption of v phonons following the diagram... 

Phosphorescence of s-triazine has been observed by Ohta et al. following excitation of the 6o band of the Si — So transition. Values for the phosphorescence lifetime and quantum yield were reported. The effects of rotational excitation on the yields and decays of the fast and slow components of Si state s-triazine fluorescence have been studied. Excitation along the rotational contours of the 6j and 6o bands revealed that the fast component showed little rotational level dependence in contrast to the slow component. This behaviour was interpreted in terms of an increase in the number of triplet levels coupled to the optically prepared singlet levels with increasing angular momentum quantum number, J. A broad emission feature present in addition to narrowline fluorescence from rovibronic levels of 6 or 6 in S, s-triazine has been observed and the rotational level dependence of its quantum yield and decay over a range of pressures reported... 

This indicates that we need 0ad > 4 for there to be real roots. The roots correspond to the critical temperature excess at the points of ignition (lower root) and extinction (upper root) respectively. As 0ad is decreased towards the transitional value ad.trans = 4, so the two turning points approach each other and merge as the hysteresis loop unfolds (Fig. 5.6). 

However, a critical value is found for the applied stress intensity factor, K ic, below which the environmental stress-cracking agent accelerates fracture initiation below this transition value, the slope of the stress intensity factor vs. initiation time plot is higher but still similar for the two materials. 

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