Range of stability

The nematic to smectic A phase transition has attracted a great deal of theoretical and experimental interest because it is tire simplest example of a phase transition characterized by tire development of translational order [88]. Experiments indicate tliat tire transition can be first order or, more usually, continuous, depending on tire range of stability of tire nematic phase. In addition, tire critical behaviour tliat results from a continuous transition is fascinating and allows a test of predictions of tire renonnalization group tlieory in an accessible experimental system. In fact, this transition is analogous to tire transition from a nonnal conductor to a superconductor [89], but is more readily studied in tire liquid crystal system. 

A reasonable approach for achieving long timesteps is to use implicit schemes [38]. These methods are designed specifically for problems with disparate timescales where explicit methods do not usually perform well, such as chemical reactions [39]. The integration formulas of implicit methods are designed to increase the range of stability for the difference equation. The experience with implicit methods in the context of biomolecular dynamics has not been extensive and rather disappointing (e.g., [40, 41]), for reasons discussed below. 

The primary phases all contain impurities. In fact these impurities stabilize the stmctures formed at high temperatures so that decomposition or transformations do not occur during cooling, as occurs with the pure compounds. For example, pure C S exists in at least six polymorphic forms each having a sharply defined temperature range of stability, whereas alite exists in three stabilized forms at room temperature depending on the impurities. Some properties of the more common phases in Portland clinkers are given in Table 2. 

The area source is assumed to be a rectangular shape, and the model can be used to estimate concentrations within the area. SCREEN examines a range of stability classes and wind speeds to identify the "worst case ... 

Here, we address the more general question of the relative stability of monomers, dimers and triangular trimers on the (111) surface of FCC transition metals of the same chemical species as a function of the d band filling Nd. All possible atomic configurations of the systems are considered monomers and dimers at sites N and F, triangles with A and B borders at sites N and F (Fig. 4). The d band-filling includes the range of stability of the FCC phase (Nd > 7.5e /atom). The densities of states are obtained from... 

It is seen that there exists a domain of d band-fillings Nchemical species. This domain narrows very rapidly when the cluster size increases. Consequently, outside this domain and in the range of stability of bulk FCC, i.e., when N 8.2e /atom, we predict that cluster adatoms sit always at normal sites irrespective of the size of the... 

It should be noted that relaxation effects play an important role on these results. Indeed it is found that, especially for monomers by also for dimers, the relaxation is larger at fault sites than at normal sites when Nd < 8e /atom while the opposite occurs for Nd 8e /atom. This tends to increase the range of stability of the fault site. It must be emphasized that second moment calculations (13) cannot account for this effect since they are quite insensitive to lateral relaxations. Actually, in such relaxation some distances are expanded whereas some others are compressed and the net effect on the second moment nearly cancels. 

Accordingly, the present survey is mainly concerned with constant temperature methods, though thermal analysis [730] has been shown to be most valuable in identifying the temperature range of stability and the compositions of decomposition intermediates. 

There seem to be many binary metallic systems in which there are phases of this sort. In the sodium-lead system there are two such phases. One of them, based on the ideal structure Na3Pb, extends from 27 to 30 atomic percent lead, with its maximum at about 28 atomic percent lead and the other, corresponding to the ideal composition NaPb3, extends from 68 to 72 atomic percent lead, with maximum at about 70 atomic percent. The intensities of X-ray reflection have verified that in the second of these phases sodium atoms occupy the positions 0, 0, 0, and the other three positions in the unit cell are occupied by lead atoms isomorphously replaced to some extent by sodium atoms (Zintl Harder, 1931). These two phases are interesting in that the ranges of stability do not include the pure compounds Na8Pb and NaPb3. 

Transition-metal complexes span an enormous range of stabilities. One of the principal aims of this chapter is to attempt to understand some of the factors which control these, and to determine the importance of ligand-field effects. Very extensive compilations of stability constants are available. 

Step 3. For each scaling level, m, and for each scaling episode, (a) determine the range of stability and (b) collect the wavelet coefficients at all scales in the range of the episode s stability. 

Efficient photoelectrochemical decomposition of ZnSe electrodes has been observed in aqueous (indifferent) electrolytes of various pHs, despite the wide band gap of the semiconductor [119, 120]. On the other hand, ZnSe has been found to exhibit better dark electrochemical stability compared to the GdX compounds. Large dark potential ranges of stability (at least 3 V) were determined for I-doped ZnSe electrodes in aqueous media of pH 0, 6.3, and 14, by Gautron et al. [121], who presented also a detailed discussion of the flat band potential behavior on the basis of the Gartner model. Interestingly, a Nernstian pH dependence was found for... 

The entire range of stability for x = 0.1 is 0 < Kc < 0.25. We will revisit this problem when we cover root locus plots we can make much better sense without doing any algebraic work ... 

An example is illustrated in Figure 8 for W/2.303 RT = 1.4. Two ranges of x values occur near the borders at x = 0 and x = 1, where the solid solutions are stable. The range of stability end at the x values which apply to the minima in the enthalphy curve, which are known as the limits of solid solubility Xgg. The two ranges of x values between the minima and the points of inflection in the enthalphy curve pertain to metastable solid solutions. The points of inflection occur at the so-called spinodal compositions X p (61). Between the two spinodal compositions any solid solution is unstable and will disproportionate into two solid solutions of the compositions Xgg. 

Table 3.1 shows a few examples of this notation. In this case, of course, the temperature and composition ranges of stability explicitly indicated for all the phases give additional or more detailed information. The Greek letters assigned to the phases of the systems may be considered as arbitrary ( pseudonyms of the formula or synonyms). Similarly to what can be observed for several common alloys of practical interest, these symbols often date back to the first investigation of the... 

Monosubstituted radicals. All substituents are stabilizing. The amount of stabilization for cyano-, ethynyl and, in particular, vinyl groups is smaller than in the Leroy scheme, but higher for carboxyl, hydroxyl and amino-groups. The total range of stabilization energies is compressed compared with Leroy s data. 

The activation parameters of the hydrolysis in aqueous dioxane of j -toluenesulfonyl bromide (336) pass through maxima at dioxane mole fractions of 0.01 and 0.12, which correspond to the range of stabilization of the solvent structure. 

No differences were found between the native and deglycosylated enzymes for the characteristics of pH range of stability, optimum pH, and adsorption to cellulose and milled wood. It can be concluded that the most important role of the carbohydrate chains in laccase III is the resistance to proteolysis in wood decay (15),... 

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