Velocity anisotropic

Results from the Western Superior wide-angle refraction experiment support an interpretation of azimuthal anisotropy. Musacchio et al. (1999) found evidence for a thin high-velocity anisotropic subcrustal layer, where the P-wave velocities in the east-west direction are faster than those in the north-south direction. The results from SKS splitting (see below) also indicate azimuthal anisotropy with a fast east-west direction. As a whole, the results are consistent with a preferred olivine a-axis aUgnment in a roughly east-west direction. 

Nonopaque materials, those that allow the transmission of light, can be optically classified as "isotropic" or "anisotropic." Isotropic materials (e.g., oil, water, epoxy, crystals in the isometric system) transmit light in all directions at the same velocity. Anisotropic materials (e.g., alite, calcite, quartz, all crystals in systems other than the isometric) divide the light into... 

Second corner reflection The first corner reflection appears as usual when the transducer is coupled to the probe at a certain distance from the V-butt weld. The second corner reflection appears if the transducer is positioned well above the V-hutt weld. If the weld is made of isotropic material the wavefront will miss (pass) the notch without causing any reflection or diffraction (see Fig. 3(a)) for this particular transducer position. In the anisotropic case, the direction of the phase velocity vector will differ from the 45° direction in the isotropic case. Moreover, the direction of the group velocity vector will no longer be the same as the direction of the phase velocity vector (see Fig. 3(b), 3(c)). This can be explained by comparing the corresponding slowness and group velocity diagrams. 

For defect sizing by TOED, use of L waves involves a penalty in resolution of almost a factor of two at a given frequency because of difference in velocity as compared to shear waves and use of SV waves runs into difficulties because of the mode conversion problems. Further, problems due to couplant thickness variations, surface roughness affects, beam skewing and distortion problems in anisotropic welds can also be expected. On the contrary, SH waves are not affected... 

In the following development we consider a plane wave of infinite lateral extent traveling in the positive Xj direction (the wave front itself lies in the Xj, Xj plane). When discussing anisotropic materials we restrict discussion to those propagation directions which produce longitudinal particle motion only i.e., if u is the particle velocity, then Uj = Uj = 0. The <100>, <110>, and <111 > direction in cubic crystals have this property, for example. The derivations presented here are heuristic with emphasis on the essential qualitative features of plastic flow. References are provided for those interested in proper quantitative features of crystal anisotropy and nonlinear thermoelasticity. 

If the magnitude of the fluctuating velocity component is the same in each of the three principal directions, the flow is termed isotropic. If they are different the flow is said to be anisotropic. Thus, if the root mean square values of the random velocity components... 

The coordinates (x, y, z) define the (velocity, gradient, vorticity) axes, respectively. For non-Newtonian viscoelastic liquids, such flow results not only in shear stress, but in anisotropic normal stresses, describable by the first and second normal stress differences (oxx-Oyy) and (o - ozz). The shear-rate dependent viscosity and normal stress coefficients are then [1]... 

Our determined anisotropy parameters for 226 nm photolysis agree favorably with the reported values of Syage, where a (3 value of 1.2 was measured for the fast 0(3P2) products. Syage observed a less anisotropic distribution for the slow 0(3P2) atoms, with a reported (3 value of 0.4. The f3 value of 1.2 for the high velocity component was rationalized by a prompt dissociation from the equilibrium ground state of ozone following an B I >2 <— X A i transition. 

Venneker et al. (2002) used as many as 20 bubble size classes in the bubble size range from 0.25 to some 20 mm. Just like GHOST , their in-house code named DA WN builds upon a liquid-only velocity field obtained with FLUENT, now with an anisotropic Reynolds Stress Model (RSM) for the turbulent momentum transport. To allow for the drastic increase in computational burden associated with using 20 population balance equations, the 3-D FLUENT flow field is averaged azimuthally into a 2-D flow field (Venneker, 1999, used a less elegant simplification )... 

---