An analysis of migration paths of Li+ cations in ternary oxygen-containing compounds Li p X q O r

A new method was developed for studying voids and channels in crystal structures based on the Voronoi-Dirichlet partition of crystal space, and 822 structurally characterized ternary compounds Li ^p X ^q O ^r were analyzed for the first time. For these compounds, the dimensionality was determined and the migration patterns of channel systems capable of providing lithium-ion transport were constructed. The calculated coordinates of lithium atoms in the centers of the voids are consistent (within 0.4 ?) with the known structural data. Among these compounds, 113 compounds have infinite channel systems, 60 compounds (18 structural types, STs) have been described earlier in the literature as solid electrolytes, and 53 compounds (23 STs) can be considered as potential one-, two-, or three-dimensional ionic conductors (13, 3, and 7 STs, respectively). Original Russian Text ? N.A. Anurova, V.A. Blatov, G.D. Ilyushin, O.A. Blatova, A.K. Ivanov-Shitz, L.N. Dem’yanets, 2008, published in Kristallografiya, 2008, Vol. 53, No. 6, pp. 987–993.     

Parametric oscillations and stability of systems with large modulation coefficient

We study parametric oscillations of linear systems with one degree of freedom for large values of the modulation coefficient. We use the classical analytic Lyapunov-Poincaré perturbation methods and an original numerically-analytic method of accelerated convergence to construct periodic solutions and the corresponding eigenvalues. We find the boundaries of stability and instability domains. We use specific models to illustrate the main properties of parametric oscillations of systems with singular character of the perturbation dependence on the modulation coefficient. We consider periodic boundary value problems for the modified Mathieu equation and the Kochin equation modeling crankshaft torsional vibrations and show that there are significant differences between weakly and essentially perturbed periodicmotions both for the lowest and arbitrary oscillation modes. We also describe the unusual properties of the boundaries in the domain of the system determining parameters.     

Stress concentration and effective stiffness of aligned fiber reinforced composite with anisotropic constituents

The paper addresses the problem of calculation of the local stress field and effective elastic properties of a unidirectional fiber reinforced composite with anisotropic constituents. For this aim, the representative unit cell approach has been utilized. The micro geometry of the composite is modeled by a periodic structure with a unit cell containing multiple circular fibers. The number of fibers is sufficient to account for the micro structure statistics of composite. A new method based on the multipole expansion technique is developed to obtain the exact series solution for the micro stress field. The method combines the principle of superposition, technique of complex potentials and some new results in the theory of special functions. A proper choice of potentials and new results for their series expansions allow one to reduce the boundary-value problem for the multiple-connected domain to an ordinary, well-posed set of linear algebraic equations. This reduction provides high numerical efficiency of the developed method. Exact expressions for the components of the effective stiffness tensor have been obtained by analytical averaging of the strain and stress fields.     

Chlorination of aromatic substrates catalyzed by the phthalocyanine complexes

The chlorination of benzene, toluene, and o-xylene with molecular chlorine in the presence of the phthalocyanine complexes of different structures was studied. The transformations of the catalysts during the reaction were investigated. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1644–1647, August, 2008.     

Thermodynamic parameters of urethane formation reactions and concomitant processes

Thermodynamic parameters of reactions of methyl and phenyl isocyanates with a series of compounds were determined by quantum-chemical calculations. The products of these reactions model for various functional groups present in commercial polyurethanes. The thermodynamic stability series for compounds formed from aliphatic and aromatic isocyanates were constructed.     

The honors class: hilbert’s problems and their solvers

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Time structure of iodine laser pulse in the free running mode of operation

Time structure of iodine laser pulse in the free running mode of operation was studied using the power amplifier of laser system PERUN as the laser oscillator. Two characteristic shapes of laser pulse correspond to different regimes of laser operation, the existence of which is ascribed to the critical concentration of I₂ molecules. Simultaneously an additional chemical pumping was proved at least in the initial phase of photodissociation and in a late-time lasing after the end of flashlamps pumping light.     

Thermal expansion of a rig

Summary We have estimated and measured the daily thermal expansion of an oceanographic platform. This has been found negligible as far as the calibration of a satellite altimeter is concerned.