Phase velocities, TWiST

Fig. 3. Interstation phase velocities calculated from surface waves that traverse the TWiST array. The Rayleigh-wave phase velocities (plotted as error bars 2 SD either side of the mean) are clearly higher than those measured in an older study of the Canadian Shield (continuous lines Brune Dorman 1963), which was not confined to the Superior Craton.

Fig. 4. Inversion for shear-wave velocity model (continuous line) which best fits the Rayleigh-wave interstation phase velocities. The grey area shows range of acceptable solutions. Three other velocity models are shown for comparison dashed line, Brune Dorman (1963) dot-dashed line, Grand Helmberger (1984) dotted line, PREM (Dziewonski Anderson 1981). It should be noted that the TWiST model shows no indication of a low-velocity zone below a continental root.

Flow which fluctuates with time, such as pulsating flow in arteries, is more difficult to experimentally quantify than steady-state motion because phase encoding of spatial coordinate(s) and/or velocity requires the acquisition of a series of transients. Then a different velocity is detected in each transient. Hence the phase-twist caused by the motion in the presence of magnetic field gradients varies from transient to transient. However if the motion is periodic, e.g., v(r,t)=VQsin (n t +( )q] with a spatially varying amplitude Vq=Vq(/-), a pulsation frequency co =co (r) and an arbitrary phase ( )q, the phase modulation of the acquired data set is described as follows ... 

In order to analyze the atomization mechanism of the air-shrouded injector, the atomization characteristics of the fabricated atomizer was investigated using a phase Doppler particle analyzer (PDPA). The Sauter mean diameter (SMD) and mean velocity distribution at 5 ms ASI are shown in Fig. 34.8. As the air pressure increases, the air velocity increases and the air dispersion area is enlarged proportionally. The maximum velocity achieved is 55 m/s when the air pressure is 50 kPa. The degree of atomization is greater at the center flow because the air velocity at the center flow is greater. Spray patterns for various air pressures are shown in Fig. 34.9. It can be seen that as the air pressure increases, the atomization process transitions from varicose wave to sinuous wave mode. Atomization at low air pressure and low fuel pressure can be seen to be affected by a twisted or sinuous mode. The spray angle... 

The static theory discussed in the previous section describes the equilibrium situation in chiral nematics very well - in general, theory and experiment are in good accord. The dynamic situation is less clear. On the molecular scale, the chiral nematic and nematic phases are identical the question then becomes, how does the macroscopic twist or helicity modify the vector stress tensor of the achiral nematic phase defined by the so-called [109] Leslie friction coefficients a -a T Experimentally, viscosity coefficients that are then related to the Leslie coefficients are measured in a way that depends specifically on the experiment being used to determine them. The starting point for discussion of dynamic properties is to use classical mechanics to describe the time dependencies of the director field n (r, t), the velocity field v (r, t), and their interdependency. Excellent reviews of this, for achiral nematics, are to be found in [59,109,... 

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