Instability region

Then the mixture with droplets is quenched into the spinodal instability region to some T < Ta (Concentration c(r) within droplets starts to evolve towards the value C(,(T) > C(,(T ), but the evolution type depends crucially on the value Act = cj(T) — Ch(Ta). At small Act we have a usual diffusion with smooth changes of composition in space and time. But when Act is not mall (for our simulations Act O.2), evolution is realised via peculiar wave-like patterning shown in Figs. 8-10. 

Figure 6.3 Instability regions for direct, constant condensation. (From Westendorf and Brown,...

Figure 5. Schematic representation of stability and instability regions.

We conclude that not only the a-particle but also the other fight clusters contribute significantly to the composition. Furthermore they also contribute to the baryon chemical potential and this way the modification of the phase instability region with respect to the temperature, baryon density and asymmetry can be obtained. As an example, for symmetric matter the baryon chemical potential as a function of density for T = 10 MeV is shown in Fig.3... 

We see that the instability region is reduced if cluster formation is taken into account. 

The boundary condition of instant annihilation when an interstitial atom finds itself in one of the unstable sites around vacancy reads w p) = 0, p, E / . (A shape and size of the instability region are discussed, e.g., by Schroder [3], Dzhumanov and Khabibullaev [16]). 

Fig. 8. The stability and instability regions of a polystyrene latex with added aluminum salt at different pH values (17).

The Villermaux criterion and the Da/Si criterion are dynamic stability criteria, meaning that with a cooling medium temperature above the limit level, 20 resp. 30 °C, the reactor will be operated in the instable region and present the phenomenon of parametric sensitivity. If instead of B12, B is used, both criteria lead to the same result. This should not be surprising since they derive from the same heat balance considerations, that is, the heat release rate of the reaction increases faster with temperature than the heat removal does. 

The site of the sharkskin distortion is again the die exit, and so is the screw thread pattern. The site of, and the mechanism for the gross extrudate distortion are problems that have no clear answers. The work of White and Ballenger, Oyanagi, den Otter, and Bergem clearly demonstrates that some instability in the entrance flow patterns is involved in HDPE melt fracture. Clear evidence for this can be found in Fig. 12.18. Slip at the capillary wall, to quote den Otter, does not appear to be essential for the instability region, although it may occasionally accompany it. ... 

Note the instability region of the small limit cycle. 

Clearly, since the FF indices of the two subsystems are closely related to the structure of the condensed hardness tensor n (l 12), these stability/instability regions can also be identified in terms of the ff and f% subsystem FF indices defining the orientation of the associated FF vector in the populational space of the two subsystems [25]. 

In the vast literature on melt flow instabilities in capillary extrusion, the most misleading information is the report that the material of construction of the capillary die has no effect on the flow curve of linear polyethylene, or, in particular, on the instability region [32, 68] - see a quotation by Tordella cited in Sect. 3. Experiments using screw-threaded dies have further led people to believe that the slip (at the flow discontinuity transition) with linear polyethylene therefore appears not to result from adhesive breakdown at the polymer-die in-... 

Fig. 17a—d. Details of the fracture surface on a CT-specimen of crystalline PETP a general view of notch (N), subcritical crack growth through crazes (A), transitional region (B), and brittle fracture part (C) b dimple pattern in the central part of the broken craze (region A) c patchwork structure in the transition zone to crack instability (region B) d brittle fracture part (region C)... 

Figure 5 shows that the leading exponents are positive and thus the 4>4 MTRS is chaotic. In addition, they varies depending on the time intervals We see relatively small instability regions, for example, around the intervals 9000-12,000 and 70,000-75,000. The variations of finite-time Lyapunov exponents have been related to the alternations between qualitatively different motions, such as (a) chaotic and quasi-regular, laminar motions in two-dimensional systems [11] and (b) random and cluster motions in high-dimensional systems [12], and they have been utilized for detecting these ordered motions. 

Above the threshold, that is, in the instability region v > y, the energy (or the number of photons) increases exponentially for (v — y)t 1... 

The stationary solution now presents a bistability [124]. This bistability is the reason for the existence of the instability region that was first described by Hoho [56] (see Section 2.1). Another consequence is a hysteresis in the stationary I—U characteristics (see Section 4.4.1). 

The region from the critical voltage U to the onset of field emission behaviour can be seen as an extent of the instability region beginning for... 

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