Hysteresis zone

In general, the Bl-type actinide compounds show a large difference between the transition pressure on pressure increase and the transition pressure on pressure decrease (Dabos-Seignon and Benedict 1990). This hysteresis is probably due to delayed establishment of thermodynamic equilibrium. It has been shown in some lanthanide metals (Kruger et al. 1990) that a slight temperature increase reduces the width of this hysteresis zone and that the equilibrium transition pressure has some intermediate value. 

The hysteresis zones, i.e. the pressure ranges between transitions at increasing and decreasing pressure, have a tendency to widen with increasing atomic number of the actinide. PuAs has the largest hysteresis zone of these compounds, of the order of... 

Figure 6.5 Dynamic inversion locus showing the hysteresis zones (shaded). The arrows indicate the direction of change...

Fig. 9.4. (a) The dependence of the stationary-state concentration of reactant A at the centre of the reaction zone, a (0), on the dimensionless diffusion coefficient D for systems with various reservoir concentrations of the autocatalyst B curve a, / = 0, so one solution is the no reaction states a0i>8 = 0, whilst two other branches exist for low D curves b and c show the effect of increasing / , unfolding the hysteresis loop curve d corresponds to / = 0.1185 for which multiplicity has been lost, (b) The region of multiple stationary-state profiles forms a cusp in the / -D parameter plane the boundary a corresponds to the infinite slab geometry, with b and c appropriate to the infinite cylinder and sphere respectively. 

Typical values for the parameters D and x u might be D = 0.05 and ku = 0.01. We now examine how the stationary-state concentration profiles ass(p) and /Jss(p) depend on the dimensionless concentration of the precursor reactant, p0. Figure 9.10 shows the stationary-state concentrations at the centre of the reaction zone ass(0) and / ss(0) as functions of p0. These loci each draw out a hysteresis loop, with a range of corresponding multiplicity of solutions. 

For the five mixtures, the cumulative mesoporous volume, Feds, and mesoporous surface area, S edB, and are both linear decreasing functions of the micropore content y (Figure 2b). The cumulative specific surface area SedB is definitely a better estimator of the mesoporous surface than the specific surface S xt computed Ifom the t-plot. The lUPAC classification states that mesopores are pores whose width is larger that 2 nm. In the case of the cylindrical pore model retained for the pore size distribution, this is equivalent to radii larger than 1 nm. It should however be stressed that the calculation of the cumulative surface and volume of the mesopores must not be continued at lower pressures than the closing of the hysteresis loop (gray zones of Figures 3a and 3b). If a black box analysis tool is used and if the calculation is systematically continued down to 1 nm, severe overestimation of the mesopores surface and volume may occur. 

For non-transparent specimens, as shown by Bucknall and Stevens useful information relative to the deformation mode can be obtained by recording hysteresis loops as a function of cycles. Figure 6 shows hysteresis loops obtained at 0.2 Hz at various N values for PS tested at a stress amplitude of 24.1 MPa and Fig. 7 for HIPS tested at 17.2 MPa. For PS, with Nf = 1,451 cycles, there is no detectable change in loop area at this stress amplitude up to the final cycle. This illustrates the highly localized nature of the fatigue-induced damage zone in PS and indicates that, for this polymer, hysteresis loop observations are not an effective method for detecting craze... 

Wind Effects and Hysteresis. Advected salt is presumably the hardest to predict from local observations. Yet, this mechanism seems to be the best to explain the parts of our time series that show salt peaks when the wind is low or steady. Apparently, either the ship is approaching a zone of generation, or a previously more active air parcel has slowed and the observations are of residual salt in the process of settling out. 

---