Lower critical value

Based on the above results and discussion, the mechanism for the rhythmic oscillations at the oil/water interface with surfactant and alcohol molecules may be explained in the following way [3,47,48] with reference to Table 1. As the first step, surfactant and alcohol molecules diffuse from the bulk aqueous phase to the interface. The surfactant and alcohol molecules near the interface tend to form a monolayer. When the concentration of the surfactant together with the alcohol reaches an upper critical value, the surfactant molecules are abruptly transferred to the organic phase with the formation of inverted micelles or inverted microemulsions. This step should be associated with the transfer of alcohol from the interface to the organic phase. Thus, when the concentration of the surfactant at the interface decreases below the lower critical value, accumulation of the surfactant begins and the cycle is repeated. Rhythmic changes in the electrical potential and the interface tension are thus generated. 

We compare results in the chiral limit (mo = 0) with those for finite current quark mass mo = 2.41 MeV and observe that the diquark gap is not sensitive to the presence of the current quark mass, which holds for all form-factors However, the choice of the form-factor influences the critical values of the phase transition as displayed in the quark matter phase diagram (/j,q — T plane) of Fig. 2, see also Fig. 1. A softer form-factor in momentum space gives lower critical values for Tc and at the borders of chiral symmetry restoration and diquark condensation. 

Several of these investigators have quoted an upper and lower critical value, enclosing a transition region, and Schoklitsch (S3) has given three values, the lowest, Nr = 144, at which turbulence could be first detected, the second, Nr0 = 389, at which the turbulent part of the flow became important, and an upper value, NRe = 900, at which the film became fully turbulent. ... 

Reaction (1) yields products of Br03 reduction (Br2, HOBr) which bro-minate MA to form its bromine derivatives (BMA). Reaction (2) produces an inhibitor for reaction (1) acting as a feedback. If the system contains much Ce4+, the amount of Br is also high and reaction (1) is hindered. Finally, the amount of Ce4+ falls to its lower critical value and the concentration of Br also decreases. Reaction (1) then proceeds at a high rate and everything begins again. 

The output of a sigmoid function, such as the logistic function, is not 0 or 1 but somewhere between. Therefore a decision must be made as to what value will be called on this value is called, by convention in this book, a critical value. Typically, if the output of the function is > 0.5, then the unit is said to be on (equivalent to the Heaviside function output of 1) otherwise it s off. Depending upon the application this can be changed to other critical values like 0.8 or 0.9. Higher critical values can be said to be less sensitive (it takes more input to turn them on) and lower critical values more sensitive (they turn on at lower input levels). 

Phase plane analysis thus readily accounts for the main experimental observation on the control of glycolytic oscillations by the substrate injection rate. Below the lower critical value of the substrate injection rate v, a stable steady state is estabUshed, corresponding to a low level of reaction product and to an enzyme predominantly in the inactive T state. Above the higher critical value of v, the stable steady state is associated with a higher level of product and with an enzyme predominantly in the active state R. Sustained oscillations, in the course of which the enzyme switches back and forth between the R and T states, occur in the range delimited by the two critical values of the substrate input. 

If the transport rate into the nucleus decreases below the lower critical value, equal to 0.02 h" in the case of fig. 11.7, sustained oscillations are suppressed. Such a situation could correspond to the loss of circadian rhythmicity in the recently characterized timeless (Jim) mutant in Drosophila (Sehgal et al, 1994) nuclear localization of PER appears to be blocked in that mutant (Vosshall et al, 1994). A key role for transport of PER into the nucleus is consistent with the view that the negative feedback exerted by PER on transcription is at the core of the mechanism of circadian rhythmicity. 

There is a lower critical value of the Pb02 powder density above which restoration of the active mass commences. For a pure lead electrode this critical density is slightly less than 3.80 g cm . Figure 6.24 evidences that there is but a very small difference between the capacity curves at d 4.15 and d — 4.50 g cm. This means that, at t/ = 4.15 g cm , the PbOi particles have reached their full capacity to interconnect into an active mass skeleton. 

The present model also predicts a lower critical value of chain degree of polymerization, Ncj below which the polymer chains are not entangled according to our definition of the tube. In references (8,9) we showed that the lower critical value satisfies... 

The confidence limits for the slope are given by fc where the r-value is taken at the desired confidence level and (A — 2) degrees of freedom. Similarly, the confidence limits for the intercept are given by a ts. The closeness of x to X is answered in terms of a confidence interval for that extends from an upper confidence (UCL) to a lower confidence (LCL) level. Let us choose 95% for the confidence interval. Then, remembering that this is a two-tailed test (UCL and LCL), we obtain from a table of Student s t distribution the critical value of L (U975) the appropriate number of degrees of freedom. 

Dielectric Strength. Dielectric failure may be thermal or dismptive. In thermal breakdown, appHed voltage heats the sample and thus lowers its electrical resistance. The lower resistance causes still greater heating and a vicious circle, leading to dielectric failure, occurs. However, if appHed voltage is below a critical value, a stabilized condition may exist where heat iaput rate equals heat loss rate. In dismptive dielectric failure, the sample temperature does not iacrease. This type of failure is usually associated with voids and defects ia the materials. 

Fig. 1. Phase diagram for mixtures (a) upper critical solution temperature (UCST) (b) lower critical solution temperature (LCST) (c) composition dependence of the free energy of the mixture (on an arbitrary scale) for temperatures above and below the critical value.

Equation 31 should not be used for densities greater than about half the critical value, nor equation 32 for densities exceeding 85% of the critical value. Substantially lower limits may apply for polar gases, particularly those that associate. 

The second class of anodic inhibitors contains ions which need oxygen to passivate a metal. Tungstate and molybdate, for example, requke the presence of oxygen to passivate a steel. The concentration of the anodic inhibitor is critical for corrosion protection. Insufficient concentrations can lead to pitting corrosion or an increase in the corrosion rate. The use of anodic inhibitors is more difficult at higher salt concentrations, higher temperatures, lower pH values, and in some cases, at lower oxygen concentrations (37). 

The critical values or value of t would be defined by the tabled value of t with (n — I) df corresponding to a tail area of Ot. For a two-tailed test, each tail area would be Ot/2, and for a one-tailed test there would be an upper-tail or a lower-tail area of Ot corresponding to forms 2 and 3 respectively. 

Chemical scaling is another form of fouling that occurs in NF and RO plants. The thermodynamic solubility of salts such as calcium carbonate and calcium and barium sulfate imposes an upper boundary on the system recovery. Thus, it is essential to operate systems at recoveries lower than this critical value to avoid chemical scaling, unless the water chemistry is adjusted to prevent precipitation. It is possible to increase system recovery by either adjusting the pH or adding an antisealant, or both. 

If an appropriate thermal feedback mechanism is not provided, the reaction occurs at the lower stationary state where the reaction rate may be negligible. The reaction could be extinguished, if the temperature of the feed entering the reactor drops below some critical value due to fouling of the heat exchange surface. 

The authors of [203-205] proposed a theory according to which the normal stresses of the matrix and filler may differ only under one condition i.e. the filler content by volume is above some critical value — when its concentration is sufficient to generate the so-called secondary network. In accordance with Privalko and Lipatov s classification [102], this concentration corresponds to the lower boundary of the high-filled class of composites. 

Figure 20 shows the plot of the surface tension vs. the logarithm of the concentration (or-lg c-isotherms) of sodium alkanesulfonates C,0-C15 at 45°C. In accordance with the general behavior of surfactants, the interfacial activity increases with growing chain length. The critical micelle concentration (cM) is shifted to lower concentration values. The typical surface tension at cM is between 38 and 33 mN/m. The ammonium alkanesulfonates show similar behavior, though their solubility is much better. The impact of the counterions is twofold First, a more polarizable counterion lowers the cM value (Fig. 21), while the aggregation number of the micelles rises. Second, polarizable and hydrophobic counterions, such as n-propyl- or isopropylammonium and n-butylammonium ions, enhance the interfacial activity as well (Fig. 22). Hydrophilic counterions such as 2-hydroxyethylammonium have the opposite effect. Table 14 summarizes some data for the dodecane 1-sulfonates.

At the beginning of sliding, the system is accelerated because the driven force must excess the resistance from lubricating film. For this reason, the system actually jumps from A to the point B, instead of B, to gain a shear stress lower than the critical value This phenomenon, so called velocity-weakening has been regarded widely in the literatures as the cause for instability and stick-slip motion in lubricated systems. 

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