Azimuthal anisotropy

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. 

Anisotropy in the upper mantle is primarily attributed to the preferred alignment of olivine and, to a lesser extent, the alignment of other upper-mantle minerals. Evidence comes from measurements on mantle xenoliths (Mainprice Silver 1993 Ben Ismail Mainprice 1998) and ophiolites (Nicolas Christensen 1987) and laboratory deformation studies (Zhang Karato 1995). These measurements help guide the interpretation of seismic observations. It is conventionally assumed that the anisotropy is c.4-5% in magnitude and has hexagonal symmetry with a horizontal synunetry axis (azimuthal anisotropy) (Mainprice Silver 1993). Numerical simulations of the lattice preferred orientation... 

Simons, F. J., van der Hilst, R. D., Montagner J.-P. ZiELHUls, A. 2001. Multimode Rayleigh wave inversion for shear wave speed heterogeneity and azimuthal anisotropy of the Australian upper mantle. Geophysical Journal Interrmtional, 203, 1-17. 

Vinnik, L. P., Makeyeva, L. L, Milev, A. Usenko, Y. 1992. Global patterns of azimuthal anisotropy and deformation in the continental mantle. Geophysical Journal International, 111, 433-447. 

Yu, Y. Park, J. 1994. Hunting for azimuthal anisotropy beneath the Pacific Ocean region. Journal of Geophysical Research, 99, 15399-15421. 

Debayle, E. 1999. SV-wave azimuthal anisotropy in the Australian upper mantle preliminary results from automated Rayleigh waveform inversions. Geophysical Journal International, 137, 747-754. 

K. Ichimura, Y. Hayashi, Y. Kawanishi, T. Seki, T. Tamaki, and N. Ishizuki, p-Cyanoazobenzene as a command molecule for azimuthal anisotropy regulation of a nematic liquid crystal upon exposure to linearly polarised visible light, Langmuir 9, 857-860 (1993). 

For instance, at the present, by optical measurements (by in situ electroreflectance) it was shown that the symmetry properties of the crystal faces were not perturbed by contact with aqueous solutions. For copper, all faces studied present their azimuthal anisotropy with respect to the plane of polarization of the incident light, except for (100), (111), (211), and some neighboring faces of (111) for which no azimuthal anisotropy is observed. " For silver, the twofold symmetry of the (110) face was observed the electroreflectance spectra at normal incidence differ markedly when the electric field vector of light is parallel or perpendicular to the surface atomic rails. This is not the case for the (111) and (100) faces which have higher symmetry. For gold, no azimuthal anisotropy was observed for the (111) and (100) faces with respect to the plane of polarization of the incident light, while the (110) and (311) faces present an azimuthal anisotropy. It does not necessarily mean that the outermost layer of surface atoms is 1 x 1, because a surface reconstruction such as 1 x2 for Au (110) would have the same symmetry order as 1x1. These are already studies of the metal surface in the presence of the electrochemical dl. 

Inversions of body wave arrival times for three-dimensional velocity structures are common practice at volcanoes using teleseismic waves, local earthquake sources, and active seismic sources. These inversions can also account for 3D Vp azimuthal anisotropy, which is parameterized with a percent anisotropy and an orientation of the fast axis. Seismic anisotropy can be detected using inversions of Love and Rayleigh surface waves from large earthquakes in the same manner. 

Jordan, C., Marowsky, G., and Rubahn, H.-G. (1995). Coverage dependent changes in the azimuthal anisotropy of second harmonic generated from Na/Si(lll) 7x7 interfaces. Opt. Comm., 120 98 -102. 

S. P. Holland, B. J. Garrison, and N. Winograd, Azimuthal anisotropies of dimer ions ejected from ion bombarded Ni(OOl), Phys. Rev. Lett. 44 756 (1980). 

Frederick B G, Power J R, Cole R J, Perry C C, Chen Q, Flaq S, Bertrams T, Richardson N V and Weightman P 1998 Adsorbate azimuthal orientation from reflectance anisotropy spectroscopy P/rys. Rev. Lett. 80 4490-3... 

Frequent malpractice is the application of the azimuthal averaging algorithm to anisotropic scattering data for the purpose of isotropization. The result appears isotropic, but the chosen integration is incorrect. Only in the case of low anisotropy this procedure is permitted, because then the introduced error is kept small. 

Let us consider a population of N molecules randomly oriented and excited at time 0 by an infinitely short pulse of light polarized along Oz. At time t, the emission transition moments ME of the excited molecules have a certain angular distribution. The orientation of these transition moments is characterized by 0E, the angle with respect to the Oz axis, and by (azimuth), the angle with respect to the Oz axis (Figure 5.5). The final expression of emission anisotropy should be independent of

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Using the same method that led to Eq. (5.27), it is easy to establish the rule of multiplication of depolarization factors when several processes inducing successive rotations of the transition moments (each being characterized by cos2 C,) are independent random relative azimuths, the emission anisotropy is the product of the depolarization factors (3 cos2 c, — l)/2 ... 

Assuming an axially symmetric potential, the anisotropy energy of n) will be an even function of the longitudinal component of the magnetic moment s n. The averages we need to calculate are aU products of the form = (n =i (cn ))a> where the c are arbitrary constant vectors. Introducing the polar and azimuthal angles of the spin d, tp), we can write as... 

An applied field in the xy-plane can tune the tunnel splittings Amm. via the Sx and Sy spin operators of the Zeeman terms that do not commute with the spin Hamiltonian. This effect can be demonstrated by using the Landau-Zener method (Section 3.1). Fig. 8 presents a detailed study of the tunnel splitting A 10 at the tunnel transition between m - +10, as a function of transverse fields applied at different angles (p, defined as the azimuth angle between the anisotropy hard axis and the transverse field (Fig. 4). 

A standard TN-LCD consists of a nematic liquid crystal mixture of positive dielectric anisotropy contained in a cell with an alignment layer on both substrate surfaces, usually rubbed polyimide, crossed polarisers and a cell gap of 5- 0fim, see Figure 3.7. The nematic director is aligned parallel to the direction of rubbing in the azimuthal plane of the device. The alignment layer induces a small pretilt angle (6 1-3°) of the director in the zenithal plane. The... 

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