Electronic spectrum of a two-dimensional Fibonacci lattice

The electronic spectrum and wave functions of a new quasicrystal structure—a two-dimensional Fibonacci lattice—are investigated in the tight-binding approximation using the method of the level statistics. This is a self-similar structure consisting of three elementary structural units. The “central” and “nodal” decoration of this structure are examined. It is shown that the electronic energy spectrum of a two-dimensional Fibonacci lattice contains a singular part, but in contrast to a one-dimensional Fibonacci lattice the spectrum does not contain a hierarchical gap structure. The measure of allowed states (Lebesgue measure) of the spectrum is different from zero, and for “central” decoration it is close to 1. The character of the localization of the wave functions is investigated, and it is found that the wave functions are “critical.” Zh. éksp. Teor. Fiz. 116, 1834–1842 (November 1999)     

Structures of Tris(2-hydroxyethyl)ammonium Salts of Succinic Acid

Succinic acid salts-tris(2-hydroxyethyl)ammonium succinate (C₆H₁₆NO₃) ₂ ⁺ C₄H₄O ₄ ^2? (monoclinic crystals, sp. gr. P2₁/c, Z = 4) and tris(2-hydroxyethyl)ammonium hydrogen succinate (C₆H₁₆NO₃)⁺C₄H₅O ₄ ^? (monoclinic crystals, sp. gr. P2₁/c, Z = 4)—were synthesized and structurally characterized. The specific features of the three-dimensional structures of tris(2-hydroxyethyl)ammonium salts of succinic acid are considered. The role of interionic electrostatic interactions in the structure stabilization and the formation of products of composition 1: 1 and 1: 2 derived from succinic acid is discussed.     

The first initial–boundary-value problem for a nonlinear model of the electrodynamics of vibrating elastic media

The first initial–boundary-value problem for nonlinear differential equations describing the interactions of a vibrating electroconductive body and the electromagnetic field is studied. We assume that the motion of the body occurs at velocities that are much smaller than the velocity of propagation of the electromagnetic waves through the elastic medium. The model under study consists of two coupled differential equations; one of them is the hyperbolic equation (an analogue of the Lamé system) and the other is the parabolic equation (an analogue of the diffusion Maxwell system). We prove an existence and uniqueness result. The proof is based on the classical Faedo–Galerkin method.     

Temperature dependence of the quadruple interaction and the diffusion of muonium atoms in α-quartz

The results of an experimental investigation of the quadrupole interaction of muonium atom in-quartz in the temperature region 75–300 K are presented. It is show that the observed temperature dependence of the quadrupole interaction parameters is fully determined by the diffusion of muonium.     

Steady-state wave flows of a weakly conducting gas in transverse electromagnetic fields

Gas flow in a MHD channel in transverse magnetic and electric fields is considered. The steady-state flows associated with the establishment of equilibrium between the hydraulic resistence and ponderomotive forces are investigated. The conditions of existence and the properties of such a steady-state flow regime are analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 123–129, July–August, 1990.     

Spectral kinetic properties of Yb3+:Na4Y6F22 and Yb3+:LiLuF4 crystals

Yb³⁺ (2.7 at.%):Na₄Y₆F₂₂ and Yb³⁺(1 at.%):LiLuF₄ crystals were grown by the Bridgman-Stockbarger method. We measured the temperature dependences of the thermal conductivity of the crystals and the absorption spectra. We determined the radiative lifetime of the Yb³⁺ ion in these crystals (1.94 msec and 2.13 msec) and calculated the stimulated emission cross section spectra. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 6, pp. 761–766, November–December, 2007.     

Identification of the convective instability in a multi-component solution by 3D simulations

Three-dimensional calculations have been done to simulate the onset of convective motion in ternary nondilute solution under phase transition conditions. The process is considered for Rayleigh number in the range $[1\times {10}^3,1.4\times {10}^4]$, where subcritical convective motion with hexagonal flow pattern is identified. The results are in good agreement with the linear and finite amplitude theory of hydrodynamics instability. To cite this article: V.V. Kolmychkov et al., C. R. Mecanique 333 (2005).     

Parametrization of semiempirical models against ab initio crystal data: evaluation of lattice energies of nitrate salts

A method to estimate the lattice energies E(latt) of nitrate salts is put forward. First, E(latt) is approximated by its electrostatic component E(elec). Then, E(elec) is correlated with Mulliken atomic charges calculated on the species that make up the crystal, using a simple equation involving two empirical parameters. The latter are fitted against point charge estimates of E(elec) computed on available X-ray structures of nitrate crystals. The correlation thus obtained yields lattice energies within 0.5 kJ/g from point charge values. A further assessment of the method against experimental data suggests that the main source of error arises from the point charge approximation.     

Synthesis of acylketene N,N-acetals and their E,Z-isomerism

A method was proposed for the synthesis of acylketene N,N-acetals (AKA) by the action of methanol in the presence of Co²⁺ acetate on diacylketene N,N-acetals. Using¹H and¹³C NMR spectroscopy, a restrainment of the internal rotation around the C=C bond of AKA was discovered, and the influence of solvation of the dynamic equilibrium of the E- and Z-isomers was studied.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 2, pp. 401–407, February, 1990.