Cones of optical axes in gyrotropic crystals with scalar permittivity

A theory is constructed for the degeneracy of electromagnetic waves in gyrotropic crystals near their isotropy points (in temperature and other parameters), in which permittivity ? becomes scalar due to dispersion and optical anisotropy is entirely determined by gyrotropy. It is shown that closed lines of intersection of sheets of the refraction surface, which correspond to the cones and, in particular, planes of the optical axes, are formed for isotropic ?. The polarization characteristics of wave fields experience a jump upon a transition through such lines. The conditions for the existence and geometry of the degeneracy cones under investigation are analyzed for crystals of all symmetry classes permitting optical activity. It is shown that the degeneracy lines disappear for a small deviation of ? from isotropy, while polarization anomalies persist. Isolated (one or two) degeneracy points may retain in place of the lines in the case when the optical axes of a perturbed crystal with “switched-off” gyrotropy belong to the initial cone.     

Copper(I) complexes with phenylphosphonous acid diamide

Copper(I) halide complexes with phenylphosphonous diamide ligand (L), C₅₆H₁₀₀Br₄Cu₄N₈P₄ (II) and C₅₆H₁₀₀Cu₄I₄N₈P₄ (III), were synthesized and studied by X-ray diffraction to determine their molecular and crystal structures (CIF files CCDC nos. 1426622 (II), 1426623 (III)). The prepared coordination compounds are cubane-like tetramers like L₄Cu₄X₄. During the reaction, copper(I) is coordinated to the phosphorus atom of ligand L. The stability of the complexes depends considerably on the halogen atom. The iodide complexes are most stable during storage.     

The use of a new carboranylamidophosphite ligand in the asymmetric Pd-catalysed allylic alkylation in organic solvents and supercritical carbon dioxide

A novel P-monodentate ligand based on carboranyl alcohol and (S)-2-(anilinomethyl)pyrrolidine provides high enantioselectivities (ee’s up to 95%) in the Pd-catalyzed allylic alkylation of (E)-1,3-diphenylallyl acetate. The first example of the Pd-catalysed allylic alkylation in supercritical carbon dioxide is also described.     

Generation of an average flow by a pulsating stream near a curved free surface

The generation of an average flow near a curved free surface under the action of small-amplitude harmonic translational vibrations is studied. It is found that, in contrast to the case of a flat non-deformable free surface, an average flow is generated in the viscous boundary layer. This flow, propagating in the bulk fluid, can be described by the steady-state Navier-Stokes equations with effective boundary conditions for the shear stresses. It is shown that, in contrast to the flow generation near a solid surface, the flow generated near the free surface depends on the fluid viscosity and the curvature of the surface.     

Opportunities of the elastometry method for investigating the elastic properties of the eyeball shell

On the basis of a maximally simple mechanical model, the possibility to estimate the stiffness of the eyeball shell using the intraocular pressures measured in the presence of different weights applied to the cornea (elastometry method) is investigated. On the basis of general considerations of dimensional theory, it is shown that the pressure difference used in ophthalmology for estimating the rigidity of the eye ball and determined in the elastometry procedure depends on the ratio E/p ₀, where E is a quantity characterizing the shell stiffness and p ₀ is the intraocular pressure in the unloaded eye. An experimental procedure, which can be treated as a development of the elastometry method and makes it possible to estimate a certain parameter dependent only on the eyeball shell stiffness, is proposed. The practical realization of the method proposed needs to be checked experimentally.     

Noise effect on convection generation in a modulated gravity field

The noise effect on the stability of equilibrium in systems with slowly varying parameters is investigated. With reference to some model examples and for the case of convection in a closed region in the presence of gravity modulation it is shown that taking the noise into account is of key importance at low modulation frequencies, since it can even change the sign of the effect: modulation leads to equilibrium stabilization in the absence of the noise and to destabilization in its presence.