Instability strip

In the Galaxy, we know 93 (3 Cephei (Stankov Handler 2004) and about 100 SPB-type stars (De Cat et al. 2004). They fall within the instability strips predicted by the theory. The K-mechanism driving pulsations in (3 Cephei and SPB stars strongly depends on the abundance of the iron-group ions in the driving zone at temperatures around 2 x 105 K (Dziembowski Pamyatnykh 1993, Dziembowski et al. 1993). Theoretical models predict that pulsations of (3 Cephei and SPB-type vanish for Z = 0.01 and Z = 0.006, respectively (Pamyatnykh 1999). 

PN nucleus, horizontal-branch and white-dwarf regions. The dotted line shows a schematic main sequence and evolutionary track for Population II, while various dashed lines show roughly the Cepheid instability strip, the transition to surface convection zones and the helium-shell flashing locus for Population I. After Pagel (1977). Copyright by the IAU. Reproduced with kind permission from Kluwer Academic Publishers. 

Fig. 5.19. Evolutionary track in the HR diagram of an AGB model of total mass 0.6 Mq, initial composition (Y, Z) = (0.25, 0.001 Z /20). Heavy dots marked 2 to 11 indicate the start of a series of thermal pulses (see Fig. 5.20), which lead to excursions along the steep diagonal lines. Numbers along the horizontal and descending track indicate times in years relative to the moment when an ionized planetary nebula appears and (in parentheses) the mass of the envelope in units of Mq. R = 0.0285 indicates a line of constant radius (R in solar units) corresponding to the white-dwarf sequence. Shaded areas represent earlier evolutionary stages for stars with initial masses 3,5 and 7 Mq and the steep broken line marks the high-temperature boundary of the instability strip in which stars pulsate in their fundamental mode. The y-axis gives log L/Lq. Adapted from Iben and Renzini (1983).

Stars less massive than about 8 M0 will avoid the supernova fate. In the 3-8 Mq range, helium ignition occurs in a non-degenerate core, so is not explosive. Core helium burning is associated with a blueward loop through the Cepheid instability strip, after which the star develops a double shell structure and becomes an asymptotic giant branch star. 

Early models suggest at least two phases of mass transfer necessary to explain the very low surface hydrogen abundances e.g. [J27]. The current best model for the evolution of v Sgr [9] is that it began as a f 0+3 Mq, f 50 d binary in which the envelope was blown to infinity, with little change of orbit, as the more massive star approached both Roche Lobe overflow and the Cepheid instability strip simultaneously. 

As a star undergoes post-main sequence evolution, it may make several passes through the instability strip in the H-R diagram. There the star becomes variable, i.e. a Cepheid variable which alternately blows up and shrinks again causing an observable brightness variation. 

As described previously, in the atomization sub-model, 232 droplet parcels are injected with a size equal to the nozzle exit diameter. The subsequent breakups of the parcels and the resultant droplets are calculated with a breakup model that assumes that droplet breakup times and sizes are proportional to wave growth rates and wavelengths obtained from the liquid jet stability analysis. Other breakup mechanisms considered in the sub-model include the Kelvin-Helmholtz instability, Rayleigh-Taylor instability, 206 and boundary layer stripping mechanisms. The TAB model 310 is also included for modeling liquid breakup. 

Breakup of water drops due to strong electrical forces has been studied in connection with rain phenomena [e.g. (A4, L8, L9, M4, M7)]. As a strong electrical field is imposed on a freely falling drop, marked elongation occurs in the direction of the field and can lead to stripping of charge-bearing liquid. A simple criterion derived by Taylor (T6) can be used to predict the critical condition for instability. It has also been shown (W6) that soap bubbles can be rendered unstable by electric fields. 

Membrane instability results in partial mixing of feed and stripping phases, which deteriorates the selectivity. In addition, raffinate and product are contaminated by the extractant, leading also to extractant losses. Economy of separation and hence industrial application of LM for separation of cephalosporins are strongly dependent on membrane stabilization. 

These processes are considerably more complex in actual CMOS fabrication. First, the lower layers of a CMOS structure typically have a twin-tub design which includes both PMOS and NMOS devices adjacent to each other (see Fig. 3b). After step 1, a mask is opened such that a wide area is implanted to form the -well, followed by a similar procedure to create they>-well. Isolation between active areas is commonly provided by local oxidation of silicon (LOCOS), which creates a thick field oxide. A narrow strip of lightly doped drain (LDD) is formed under the edges of the gate to prevent hot-carrier induced instabilities. Passivation sidewalls are used as etch resists. A complete sequence of fabrication from wafer to packaged unit is shown in Figure 10. 

Atoms are first stripped of their electrons at very high temperatures this creates a plasma (ionized gas) of positive ions. Then the positive ions must be brought into close enough proximity, so that the strong attractive force between nucleons can overwhelm the Coulomb repulsion between them. Magnetic fields can confine hot plasmas of ions, provided that collective instabilities of these plasmas can be controlled. For a successful nuclear fusion reactor, three requirements must be met (1) The density of the plasma must exceed some critical value p. (2) The plasma confinement time must exceed some critical value t. (3) The temperature of the plasma must exceed some critical value 9... 

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