Stability boundary and

The water stability boundaries and the locus of measured Eh and pH measurements in natural waters, as reported by Baas-Becking et al. (I960), are shown in Fig. 11.3 (see also Fig. 11.4). It has been observed that frequently the Eh values measured with a Pt electrode differ significantly from values computed from Gibbs free energies or standard potentials and solution concentrations. When they exist, there are two important reasons for such differences. These include (1) misbehavior of the Pt or other indicator electrode (2) the irreversibility or slow kinetics of most redox couple reactions and resultant di.sequilibrium between and among different redox couples in the same water and (3) the common existence of mixed potentials in natural waters (see below). 

Figure 9, Stability boundary and pH changes. Key O, initial pH measurements , pH of the same solution after storing at 20 C for 30 d.

We seek solutions near the stabihty threshold, i.e., when the parameter jj, is near the stability boundary, and the solution itself is close to the uniformly propagating wave. Therefore, we introduce the small parameter e by defining... 

Sugahara, T. Morita. K. Ohgaki, K. Stability boundaries and small hydrate-cage occupancy of ethylene hydrate system. Chem. Eng. Sci. 2000, 55, 6015-6020. 

Many features become more transparent when formulated in real (position) space in terms of ampbtude (envelope) or Ginzburg-Landau equations (GLE). Then one sees that the important information is really condensed in a few parameters and the universal aspects of the systems become apparent. By model calculations, which can often be performed analytically, stability boundaries and secondary bifurcation scenarios are traced out. The real space formulation is essential when it comes to the description of more complex spatio-temporal patterns with disorder and defects, which have been studied extensively in EHC slightly above threshold (Figs. 13.1b, 13.3b). One introduces a modulation ampbtude y4(x) defined as... 

Inequality (5.185) is a finite general stability boundary, and for this reason, the explicit Euler method is called conditionally stable. Any method with an infinite general stability boundary can be called unconditionally stable. 

We have already remarked that the problem concerning the loss of stability of periodic orbits in autonomous systems cannot always be reduced to a study of bifurcations of fixed points of the Poincare map. It may happen that the periodic orbit does not exist on the stability boundary and, therefore, the Poincare map is not defined at the critical parameter value. 

From polarization curves the protectiveness of a passive film in a certain environment can be estimated from the passive current density in figure C2.8.4 which reflects the layer s resistance to ion transport tlirough the film, and chemical dissolution of the film. It is clear that a variety of factors can influence ion transport tlirough the film, such as the film s chemical composition, stmcture, number of grain boundaries and the extent of flaws and pores. The protectiveness and stability of passive films has, for instance, been based on percolation arguments [67, 681, stmctural arguments [69], ion/defect mobility [56, 57] and charge distribution [70, 71]. 

Fig. 3. Stability boundary for impulse method applied to the 2-spring problem. Gamma is uiAt and Delta t is At.

The following mechanisms in corrosion behavior have been affected by implantation and have been reviewed (119) (/) expansion of the passive range of potential, (2) enhancement of resistance to localized breakdown of passive film, (J) formation of amorphous surface alloy to eliminate grain boundaries and stabilize an amorphous passive film, (4) shift open circuit (corrosion) potential into passive range of potential, (5) reduce/eliminate attack at second-phase particles, and (6) inhibit cathodic kinetics. 

Poor Weldability a. Underbead cracking, high hardness in heat-affected zone. b. Sensitization of nonstabilized austenitic stainless steels. a. Any welded structure. b. Same a. Steel with high carbon equivalents (3), sufficiently high alloy contents. b. Nonstabilized austenitic steels are subject to sensitization. a. High carbon equivalents (3), alloy contents, segregations of carbon and alloys. b. Precipitation of chromium carbides in grain boundaries and depletion of Cr in adjacent areas. a. Use steels with acceptable carbon equivalents (3) preheat and postheat when necessary stress relieve the unit b. Use stabilized austenitic or ELC stainless steels. 

Thus, the user can input the minimum site boundary distance as the minimum distance for calculation and obtain a concentration estimate at the site boundary and beyond, while ignoring distances less than the site boundary. If the automated distance array is used, then the SCREEN model will use an iteration routine to determine the maximum value and associated distance to the nearest meter. If the minimum and maximum distances entered do not encompass the true maximum concentration, then the maximum value calculated by SCREEN may not be the true maximum. Therefore, it is recommended that the maximum distance be set sufficiently large initially to ensure that the maximum concentration is found. This distance will depend on the source, and some trial and error may be necessary however, the user can input a distance of 50,000 m to examine the entire array. The iteration routine stops after 50 iterations and prints out a message if the maximum is not found. Also, since there may be several local maxima in the concentration distribution associated with different wind speeds, it is possible that SCREEN will not identify the overall maximum in its iteration. This is not likely to be a frequent occurrence, but will be more likely for stability classes C and D due to the larger number of wind speeds examined. 

Pourbaix s pioneering work on the graphical presentation of gas-metal equilibria and the concept of stability zones and their boundaries between the various stable compounds lead to the second type of diagrams. Figure 7.65 shows a Pourbaix plot of the log P02 system against the reciprocal... 

The numerical techniques of Chapter 8 can be used for the simultaneous solution of Equation (9.3) and as many versions of Equation (9.1) as are necessary. The methods are unchanged except for the discretization stability criterion and the wall boundary condition. When the velocity profile is flat, the stability criterion is most demanding when at the centerline ... 

These data indicate that thermal losses during unsteady flame-wall interactions constitute an intense source of combustion noise. This is exemplified in other cases where extinctions result from large coherent structures impacting on solid boundaries, or when a turbulent flame is stabilized close to a wall and impinges on the boundary. However, in many cases, the flame is stabilized away from the boundaries and this mechanism may not be operational. 

Figure 1.96. Log /oj-pH diagram constructed for temperature = 200°C, ionic strength = 1, ES = 10 m, and EC = 10 m. Solid line represents aqueous sulfur and carbon species boundaries which are loci of equal molalities. Dashed lines represent the stability boundaries for some minerals. Ad adularia. Bn bomite, Cp chalcopyrite, Ht hematite, Ka kaolinite, Mt magnetite, Po pyrrhotite, Py pyrite, Se sericite. Heavy dashed lines (1), (2), and (3) are iso-activity lines for ZnCOs component in carbonate in equilibrium with sphalerite (1) 4 co3=0-1- (2) 4 ,co3=0-01- (3) 4 co3 =0-001 (Shikazono, 1977b).

Figure 2. The classical stability of the map (dots) and the full differential dynamics (circles) was assessed by advancing the equations of motion 200 periods of the perturbation. If the trajectory returned to the vicinity of the nucleus a point was plotted in the (w — F) parameter plane. The dividing line a = 1.0 is indicated by the dotted line while the stability boundary is shown by the solid line.

At the stability boundary, ion motion is in resonance with this modulation voltage, and thus ion ejection is facilitated. Axial modulation basically improves the mass-selective instability mode of operation. 

We know the system is stable if all the roots of the characteristic equation are in the LHP and unstable if any of the roots are in the RHP. Therefore the imaginary axis represents the stability boundary. On the imaginary axis s is equal to some pure imaginary number s = ioi. 

These changes have significant effects on the solubility of metals in the KF solution. Firstly, the reduction in pE caused some reduction of Fe(OH)3 to Fe", increasing the Fe concentration in the digestion and lowering the stability boundary between Fe" and Fe(OH)3. Secondly, the higher pHs resulted in less adsorption of Pb and Zn, and possibly the precipitation of Pb and Zn hydroxides, resulting in less Pb and Zn in solution and more concentrations below detection. 

Hume-Rothery was to prove a fair, if demanding, editor, and the result was an important review on the stability of metallic phases as seen from the CALPHAD viewpoint (Kaufman 1969). The relevant correspondence provides a fascinating insight into his reservations concerning the emerging framework fiiat Kaufman had in mind. Hume-Rothery had spent most of his life on the accurate determination of experimental phase diagrams and was, in his words (Hume-Rothery 1968), ... not unsympathetic to any theory which promises reasonably accurate calculations of phase boundaries, and saves the immense amount of work which their experimental determination involves . 

Nakamura, T. Makino, T. Sugahara, T. Ohgaki, K. (2003). Stability boundaries of gas hydrates helped by methane—structure-H hydrates of methylcyclohexane and cis-... 

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