Critical ratio

An alternative view (123) is that no single model can adequately explain why any given compound is sweet. This hypothesis derives from several features. First, there is the observation that all carbohydrates having a critical ratio of OH to C are sweet tasting. In other words, there are no stmctural constraints to the sweetness of carbohydrates. Second, not all sweeteners can be fit to the same SAR model. Rather, some fit one, others fit another. Third, studies on the transduction mechanisms of sweetness suggest more than a single mechanism for sweet taste, implying multiple receptors for sweeteners. 

If pressure drop is high enough to exceed the critical ratio, sonic velocity will be reached. When K = 1.4, ratio = 0.53. 

Since actual P2/P1 < critical ratio 0.528, the flow is sonic. 

In Figure 4.6 values of w2A i, u2/ Ptvi, and (A2/Cj) Jp v which are proportional to v2, u2, and A2 respectively are plotted as abscissae against P2jP. It is seen that the area A2 decreases to a minimum and then increases again. At the minimum cross-section the velocity is equal to the sonic velocity and P2/P1 is the critical ratio. is... 

Write a GA to investigate which arrangement is the more stable and investigate whether there is some critical ratio of the dimension of the quadrupole to the distance apart that determines which geometry is of lower energy. 

Weinstein, M.C. and R. Zeckhauser (1973), Critical ratios and efficient allocation , Journal of Public Economics, 2,147-57. 

Patel et al., 1974), but no effect is observed for neutral (Group IV) impurities in Ge or Si. Also, impurities that are electron-donors soften both Ge and Si at temperatures above about 450 °C whereas accepter type impurities soften Ge, but not Si. Another important point is that small impurity concentrations have little effect. The effects begin at concentrations of about 1018/cc. Since the atomic volume of Si is 20 A3, the critical ratio of impurity to Si atom is about 2 x 10 5. Therefore, the average lineal distance between impurity atoms is about one every 270 A. 

Differentiated fibres are not capable of proliferation, but a small population of myoblasts (satellite cells) persists in mature muscle. They can be stimulated to proliferate and fuse with existing fibres to increase the number of nuclei present and restore the critical ratio of nuclei to cytoplasm that has been reduced by fibre enlargement. 

A theoretical analysis of the stability of such colloidal crystals of spherical latex particles has been carried out by Marcel ja et al (28.). They employ the Lindemann criterion that a crystal will be stable if the rms thermal displacement of the particles about their equilibrium positions is a small fraction f of the lattice spacing R. Comparison with Monte Carlo simulations shows that f is about 0.1 for "hard crystals, and 0.08 for "soft crystals stabilized by long-ranged electrostatic forces. This latter criterion translates into a critical ratio... 

A modified law of corresponding states suitable for real gases was proposed in 1946 by Gouq-Jen Su of Univ of Peiping, China (Ref 1). A term called the "ideal critical volume was defined and the ratio of volume over the ideal critical volume was called the "ideal reduced volume . It was shown that for 17 gases within the temperature and pressure ranges studied, the over-all deviation was only 1%. The value of the critical ratio was not a restrictioh or a criterion for the applicability of the modified law... 

The result R /Rg = 6 is characteristic of all noninteracting chains. It holds in the limit of large n irrespective of the microstructurc as embodied in the chain part Vo- Tt is the first example of a universal critical ratio. Adding the excluded volume interaction, we will find that this ratio in the excluded volume limit of long chains again takes a universal -value, close to but different from (i. 

To summarize, strict e-expansion a priori seems to yield unambiguous results. Closer inspection, however, reveals that in low order calculations considerable ambiguity is hidden in the definition of the physical observables used as variables or chosen to calculate. What is worse, the e-expansion does not incorporate relevant physical ideas predicting the behavior outside the small momentum range or beyond the dilute limit. In particular, it does not give a reasonable form for crossover scaling functions. On the other hand, it can be used to calculate well-defined critical ratios, which are a function of dimensionality only, Even then, however, the precise definition of the ratio matters,... 

A similar determination of Co or qo based on appropriate critical ratios is presented in Appendix A 13.2. Summarizing the results we choose the theoretical parameters as... 

We should further stress that close to the above values our results are fairly insensitive to the theoretical parameters. This holds not only for the critical ratios explicitly considered in the determination of Co, but also for... 

Figure 13.7 shows that sixfold or octahedral coordination corresponds to the smaller ion at the center of an octahedron with the larger ions on the comers. The critical ratio corresponds to [2(r + i )]2 = 2R2, so... 

Figures 7.6 and 7.7 are useful graphs showing the critical ratios for two-phase flow and liquid flashing.

On the bais of an extensive review of experimental results of turbulence modulation in dilute suspension pipe flows and jet flows, Gore and Crowe (1989) proposed a critical ratio of particle diameter to a characteristic integral length scale of turbulence by the following relation... 

---