Wakes dimensions

For Re 300000 the resistance crisis occurs. The drag force depends on wake dimensions and these dimensions also depend upon the position of the separation line between the wake and the boundary layer. As Re increases, the turbulent separation point moves back as a consequence the wake dimensions diminish and the drag coefficient drops sharply from 0.4 to 0.1 (Fig. 20). All of these considerations are reported in detail by Torobin and Gauvin Boulos, Bhattacharyya and... 

Zukoski and Marble [70, 71] held that the wake of a flame holder establishes a critical ignition time. Their experiments, as indicated earlier, established that the length of the recirculating zone was determined by the characteristic dimension of the stabilizer. At the blowoff condition, they assumed that the free-stream combustible mixture flowing past the stabilizer had a contact time equal to the ignition time associated with the mixture that is, rw = ri( where rw is the flow contact time with the wake and r, is the ignition time. Since the flow contact time is given by... 

The length of the wake is proportional to the characteristic dimension of the stabilizer, the diameter d in the case of a rod, so that... 

The dimensions of the attached wake are shown in Figs. 5.6, 5.7, and 5.8. The various numerical solutions agree closely with flow visualization results of Taneda (T2), although other workers (K2) report separation slightly closer to the rear. The separation angle, measured in degrees from the front stagnation point, is well approximated by... 

Few observations have been reported on wakes of ellipsoidal bubbles and drops at Re > 1000. Yeheskel and Kehat (Y4) characterized shedding in this case as random. However, Lindt (L7, L8) studied air bubbles in water and distinguished a regular periodic component of drag associated with an open helical vortex wake structure. Strouhal numbers (defined as 2af/Uj, where / is the frequency and 2a is the maximum horizontal dimension) increase with Re, to level off at about 0.3 as bubbles approach the transition between the ellipsoidal and spherical-cap regimes. 

As mentioned in Chapter 1, psychiatrist William James touched on this extra dimension of reality and perception when he wrote, Our normal waking consciousness, rational consciousness as we call it, is but one special type of consciousness, whilst all about it, parted from it by the filmiest of screens, there lie potential forms of consciousness entirely different.... No account of the universe in its totality can be final which leaves these other forms of consciousness quite disregarded. 

Not at all. Imagine a 2-D man living in Flatland. Pretend his right eye is brown and his left eye is blue. He wakes up one day and his wife screams, because his eyes have switched places. What actually happened is that a 3-D being rotated him about the center of his body into the third dimension (Fig. 5.1). 

The three-dimensional AIM model is a first attempt to concretize and to visualize the state space concept. Because it has three dimensions, it is a space, not a plane, as are traditional representations of waking, sleeping, and dreaming. Furthermore, when realistic values are assigned to the three dimensions of the model—and with time as the fourth dimension—orbital trajectories of conscious state change emerge from the mapping. 

The net result is that in one brain-activated state, waking, the brain is in touch with the outside world and can act upon it, whereas in another equally activated state, REM sleep, it cannot do either. In both cases, the activation is real and important and must constitute a dimension of any model. But so diametrically opposed are the input-output conditions of waking and REM that they cannot possibly be dealt with by an activation-only model. We need the input-output (TO) dimension. 

In terms of the brain-mind paradigm and its 3-D map, the AIM model, SSRIs produce the equivalent of a stimulant effect as well as paradoxical sedation. The upward shift of the M dimension, caused by the elevation in aminergic drive, makes descent into deep sleep impossible, just as amphetamines make falling asleep at all more difficult. Because subjects spend much more time in light sleep at or near waking levels, they naturally experience more dreaming and they are more aware of it because they awaken more often. 

The first two parts of this book explain how scientists now understand normal alterations of consciousness in brain chemical terms. In part I, The Scope and Shape of Conscious States, I define the psychological components and dimensions of conscious experience. Chapter 1 shows how subjective experience can be conceptualized and measured in relation to brain science. It also introduces the notion of a unified brain-mind. Chapter 2 emphasizes the strategy of studying both spontaneous and experimental alterations in conscious state. Chapter 3 contrasts waking and dreaming by illustrating the way that we can measure these dramatic spontaneous changes in conscious state. 

In the wake of the commercial success of several liposome dmg products, lipid-based carriers are on the verge of becoming an accepted and versatile tool in drug delivery. Porter and Charman (Chapter 4) add an entirely new dimension to the usefulness of lipid-based carriers by showing that the systemic distribution... 

A characteristic transverse dimension d of the flame holder can be measured more easily than the length / of the recirculation zone. The ratio l/d experimentally has a practically constant value between 5 and 10, independent of flow conditions for hot turbulent wakes. Hence, I d in equation (65), so that d. Of greater interest than the dependence... 

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