Spatial anisotropy

The origin of stereofacial selectivity in electrophilic additions to methylene-cyclohexanes (2) and 5-methylene-l,3-dioxane (3) has been elucidated experimentally (Table 2) and theoretically. Ab initio calculations suggest that two electronic factors contribute to the experimentally observed axial stereoselectivity for polarizable electrophiles (in epoxidation and diimide reduction) the spatial anisotropy of the HOMO (common to both molecules) and the anisotropy in the electrostatic potential field (in the case of methylenedioxane). The anisotropy of the HOMO arises from the important topological difference between the contributions made to the HOMO by the periplanar p C-H a-bonds and opposing p C—O or C—C cr-bonds. In contrast, catalytic reduction proceeds with equatorial face selectivity for both the cyclohexane and the dioxane systems and appears to be governed largely by steric effects. ... 

The photodissociation process takes place most frequently at excitation of the molecule to a non-bonded state, with subsequent dissociation into products. Since the angular part of the transition probability, according to Chapter 2, is still dependent on the mutual orientation of the E-vector of the initiating light beam and on the transition dipole moment d, one may expect spatial anisotropy of angular momenta distribution both in the dissociation products and in the set of molecules which remains undestroyed. 

In the discussion of Kostelecky et al. on testing for Lorentz and CPT invariance using their extension of the standard model, the experiment on 7Li is designated as a clock comparison type experiment which tests for spatial anisotropy. Recent experiments of this type have greatly improved the bounds on parameters for Lorentz violation to 10-27 GeV for the proton (as indicated in Table 1), to 10 3° GeV for the neutron. 

A transition signal can then be detected in a straight forward way through a change in the spatial anisotropy of electrons from the decay p —> e Ve. ... 

In this paper it was very briefly demonstrated that the laser radiation in combination with external fields can be a powerful tool to prepare molecules in specific quantum state that can be characterized with a well pronounced spatial anisotropy of molecular axes (chemical bonds) and angular momentum. These states in past have been exploited in studies of molecuhu properties including dynamics of chemical reactions, but it seems that full capacity of this method still needs to be explored. 

For ordinary critical phenomena, such a spatial anisotropy is not very important — it gives rise to an anisotropy of the critical amplitude, of the correlation length in different lattice directions ( i = r[-1, fx = xffl 1 ), while the critical exponent dearly is the same for all spatial directions. Of course, this is no longer necessarily true at Lifshitz points There is no reason to assume that both functions / (p), K (p) in eq. (122) vanish for p = pt Let us rather assume that only ih(pl) — 0 while K (pO > 0 this yields the uniaxial Lifshitz point (Homreich et al., 1975). We then have to add a term f Ki (p)[32 (x)/9x ]2 to eq. (122) to find... 

Comparing the results from different techniques, such as SCLC or FET, each affected similarly by the contact effects, the temperature dependent mobility renders the expected spatial anisotropy of the transport in and normal to the (ab)-plane. The SCLC mobility at room temperature along the c -direction is found to be one order of magnitude smaller than the FET mobility along the (ab)-plane. 

To enable a microscopic analysis of the spatial anisotropy of the hole transport in diindenoperylen and to correlate the macroscopic observations quantitatively with the molecular orbital overlap, the purity of the samples as well as... 

Prestage J D, Bollinger J J, Itano W M and Wineland D J 1985, Limits for spatial anisotropy by use of nuclear-spin-polarized Be+ ions , Phys Rev Lett 5A, 2387-90... 

An external magnetic field creates a spatial anisotropy in the laboratory frame, and the AN — 1, AMn = 0 off-diagonal matrix elements of the linear term in the Zeeman effect Hamiltonian (Eq. (6.5.38)) destroy N (but not Mn) as a good quantum number. The external magnetic field causes a transition from the usual Hund s case (d) hIIrN+N) scheme to the uncoupled case (d)... 

In this paper, we concern another consequence of the light scattering into PAA membrane resulting in occurrence of spatial anisotropy of emergent light. 

In conclusion, the revealed maximum of light scattering in the direction parallel to pore axis resulting in spatial anisotropy of emergent 1 ight is coimected with non-isotropic distribution of DOPS. This effect may be utilized in creation of light sources with directed radiation based on PAA membranes. 

Dendrites form if solidification is limited by diffusion. The dissipation of latent heat can be the rate-determining factor. As heat conduction is better in the liquid than in the solid phase, there is spatial anisotropy in the solidification rate and the solid assumes a ramified shape. Latent heat is more easily disposed of at the end of the dendrites than in depressions on the growing solid surface, and the tops of dendrites grow faster than the depressions in the surface. This positive feedback yields the same type of morphology as diffusion-limited aggregation, which is... 

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