Curved periodic switching

Periodic switching of helical flow in curved channels - chaotic advection... 

A simplified version of the model in Table IX, neglecting accumulation of mass and heat as well as dispersion and conduction in the gas phase, predicts dynamic performance of a laboratory S02 converter operating under periodic reversal of flow direction quite well. This is shown by Fig. 13 taken from Wu et al. (1996). Data show the temperature profiles in a 2-m bed of the Chinese S101 catalyst once a stationary cycling state is attained. One set of curves shows the temperature distribution just after switching direction and the second shows the distribution after a further 60 min. Simulated and experimental profiles are close. The surprising result is that the experimental maximum temperatures equal or exceed the simu-... 

Fig. 16. Variation in a stationary cycling state of catalyst temperature, S03, and complex concentrations in the melt phase and the concentration of gas phase species with time in a half cycle in the forward flow portion of a reactor operating under periodic reversal of flow direction with r = 40 min, SV = 900 h (Csodo = 6 vol%, (Co2)o = 15 vol%, Ta = 50°C. Curves 1, just after switching flow direction 2,1 min 3, 6.6 min 4, 13.3 min, and 5, 20 min after a switch in flow direction. (Figure adapted from Bunimovich et at., 1995, with permission, 1995 Elsevier Science Ltd.)...

Figure 7.7 Transitory changes in transmissivity by switching on and off the irradiation of 633 nm in a-Sb jSei t films 1 and 5 at.%. Thickness is 0.8 pm and intensity 0.5 W/cm. Sb concentration is 1 and 4 at.% (curves 1 and 2, respectively). On- and off-periods of illumination are shown by arrows.

In Figs. 5.4.1a and 5.4.2a, we present the steady VC curves, corresponding to Vcr — oo, computed, respectively, for e = 10-4, 10-6. For Vct finite the above procedure is carried out until V r is reached. At this point the modulation is switched on and the unsteady computation is performed for a few tens of periods T until the transients die out. The computed current density... 

The temperature rise of a coated probe follows the pattern illustrated in Figure 7 (curve a) [32,33]. When ultrasound is switched on there is an initial rapid rise (AT,) caused by heat generation at the interface between the thermocouple and the treated medium due to viscous forces acting between the probe and the fluid medium. This phase of heating rapidly reaches an equilibrium and this is followed by a period (A T2) when the temperature rises more slowly (AT2) due to absorption of the wave within the coating. However the temperature does not start increasing until several tens of milliseconds (time ,) after the sound was switched on. For castor oil this delay is 20 ms, for silicone rubber 20—30 ms, and for glue (UHU brand) 40-50 ms. 

The model thus shows how thresholds in the phosphorylation-dephosphorylation cascade controlling cdc2 kinase play a primary role in the mechanism of mitotic oscillations. The model further shows how these thresholds are necessarily associated with time delays whose role in the onset of periodic behaviour is no less important. The first delay indeed originates from the slow accumulation of cyclin up to the threshold value C beyond which the fraction of active cdc2 kinase abruptly increases up to a value close to unity. The second delay comes from the time required for M to reach the threshold M beyond which the cyclin protease is switched on. Moreover, the transitions in M and X do not occur instantaneously once C and M reach the threshold values predicted by the steady-state curves the time lag in each of the two modification processes contributes to the delay that separates the rise in C from the increase in Af, and the latter increase from the rise in X. The fact that the cyclin protease is not directly inactivated when the level of cyclin drops below C prolongs the phase of cyclin degradation, with the consequence that M and X will both become inactivated to a further degree as C drops well below C. ... 

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