Resonances in the Codimension-2 Bifurcations in the Couette–Taylor Problem

The investigation of codimension-2 bifurcations, in particular in systems with cylindric symmetry, enables us to deduce new types of secondary regimes branching-off from the symmetric regimes. This investigation also allows us the unique possibility of a rigorous treatment of chaotic solutions to Navier–Stokes and other nonlinear PDE’s. The central manifold approach combined with the reduction to the normal form lead to the so-called amplitude systems. These ODE systems describe the nonlinear interaction between the neutral modes, and always include several nonlinear terms due to so-called intrinsic resonances. However, sometimes additional resonances appear. In this paper we present the complete list of all possible resonances in dynamic systems with cylindric symmetry and the corresponding forms of the amplitude equations. Further, we present the results of extensive numerical investigation of the resonant codimension-2 bifurcations in the Couette–Taylor problem, thus creating an intriguing subject for further investigation.     

Photoinduced transformations in single crystals of 1,2-bis(2-[(<Emphasis Type="Italic">E</Emphasis>)-3-oxo-3-phenylprop-1-enyl]phenoxy)ethane and 1,5-bis(2-[(<Emphasis Type="Italic">E</Emphasis>)-3-oxo-3-phenylprop-1-enyl]phenoxy)-3-oxapentane

Differences in the parameters of pre-organization of chalcone podands to intermolecular photoinduced [2+2] cycloaddition (PCA) in crystals were discovered. As a result of PCA, the chalcone podand with two oxyethylene units forms stereoregular cyclobutane-containing polymer chains over the whole volume of the single crystal. In the case of the chalcone podand with one oxyethylene unit, the PCA reaction in single crystal becomes impossible; however, its mechanical destruction results in the formation of surface layers with stacking dimers. In these layers, photodimerization occurs due to a decrease in topochemical control from the molecular lattice.     

Mass spectrometric identification of multicage fullerene cycloadducts

Multicage fullerene cycloadducts have been detected by MALDI mass spectrometry; they have been found as admixtures in the products of reactions of the trifluoromethylation of fullerene samples doped with metallic sodium, the reaction between fullerenes and a mixture of trifluoromethylfullerenes, and the synthesis of fulleroproline esters. As a result, over 75 new compounds of this type have been identified. The optimization of the synthesis procedures and chromatographic fractionation allowed us to extract five compounds in the pure form: (C₆₀)₂(CF₂)₂(CF₃)₈, (C₆₀)₂(CF₂)₂(CF₃)₃C₂F₅, (C₆₀)₂(CF₂)₂(CF₃)₅C₂F₅, (C₆₀)₂(CF₂)₂(CF₃)₂O, and C₆₀CH₂N(CH₂C₆₀)CCOOtBu. Chemical structures of two of them, proposed on the basis of post source decay mass spectra, have been further confirmed by NMR spectra.     

Composition of magnetic layer and magnetotransport properties of electrodeposited layered nanostructures (Co-Cu)/Cu and (Ni-Co-Cu)/Cu

The magnetotransport characteristics of Co-Ni-Cu layered coatings containings 100 nanobilayers were measured at room temperature in a magnetic field of ±5 kOe. The coatings were deposited onto nickel sputtered on glass. It is shown that a decrease in the content of copper in the magnetic layer due to the conversion of copper ions in the solution into the multi-charge anionic complexes (by the example of sulfosalicylate electrolyte) leads to an increase in the giant magnetoresistance (GMR) effect. The stabilization of composition of Co-based magnetic layer by shifting the copper deposition potential to the equilibrium potential of Co or by introducing Ni, which assists the deposit passivation, leads to a decrease of the GMR effect. A benefit effect of partial dissolution of Co at the deposition potentials of nonmagnetic layer on the magnetotransport characteristics of multilayered coatings is first revealed. It is supposed that the effect is caused by the morphological factor of surface smoothing due to preferential dissolution of projecting areas of magnetic layer.     

A study of nicotinic acid synthesis on a pilot installation and its simulation

Technological process parameters of the nicotinic acid synthesis by oxidation of β-picoline on a vanadium-titanium catalyst in a unit tube of a pilot installation were determined: conversion of β-picoline, yield and selectivity for products, and parametric sensitivity of the "hot point" temperature to variation of parameters at the reactor inlet. A mathematical simulation of the process was carried using the model of heat-and-mass transfer in a bed of a tubular reactor and the kinetic model of oxidation of β-picoline.     

Metallic layer in the Earth’s lower mantle

We predict the insulator-metal-insulator transitions for the temperature and pressure of the lower mantle with the metal layer thickness Δh ≈ 400 km at the depth of 1400–1800 km. The insulator-metal transition has the Mott-Hubbard origin, while the second transition from metal to insulator results from spin crossover of the Fe²⁺ ions from high spin S = 2 to low spin S = 0 state. The conductivity in the metal layer may attain 250 S/m. The depth profile of the conductivity is also suggested.     

Molecular structures of chalcone podands: A prognosis of photoinduced transformations in the crystals

A series of chalcone podands with the propenone group in the ortho position of the bridging aryl substituent with respect to the oxyethylene fragment is synthesized. The influence of the preorganization of the chalcone podand molecules in crystals on their ability to participate in topochemical reactions is investigated. From analyzing the X-ray structural data, the highest probability of the solid-state photochemical [2 + 2]cycloaddition is predicted for podands with phenyl substituents and the oxyethylene fragment containing two or three oxygen atoms. The X-ray structural data for the chalcone podand C₃₂H₂₆O₄ (3a) are as follows: a = 7.904(9) Å, b = 14.92(2) Å, c = 21.30(3) Å, β = 91.7(1)°, monoclinic system, space group P2₁/c, Z = 4, V = 2510(5) ų, ρ = 1.26 g/cm³, and R = 0.046; C₃₄H₃₀O₅ (3b): a = 15.738(9) Å, b = 11.889(2) Å, c = 15.0830(15) Å, β = 105.47(14)°, monoclinic system, space group C2/c, Z = 4, V = 2720.0(9) ų, ρ = 1.266 g/cm³, and R = 0.0418; C₃₂H₂₄N₂O₈ (4a): a = 17.9416(18) Å, b = 10.9703(8) Å, c = 41.699(2) Å, β = 105.970(11)°, monoclinic system, space group P2₁/c, Z = 4, V = 2781.4(5) ų, ρ = 1.348 g/cm³, and R = 0.0426; C₃₆H₃₂N₂O₁₀ (4c): a = 7.6286(5)Å, b = 17.9398(10) Å, c = 11.5890(3)Å, β = 95.287(4)°, monoclinic system, space group P2₁/n, Z = 2, V = 1579.27(14) ų, ρ = 1.372 g/cm³, and R = 0.0377; and C₂₈H₂₂O₆ (5a): a = 15.6032(10) Å, b = 8.1131(5) Å, c = 17.7334(11) Å, β = 91.381(5)°, monoclinic system, space group C2/c, Z = 4, V = 2244.2(2) ų, ρ = 1.345 g/cm³, and R = 0.0309.     

A nonlinear response of the BiSrCaCuO single crystal in the microwave region

Third-harmonic microwave radiation of the BiSrCaCuO superconducting single crystal was studied. Two modes of microwave field-sample interactions were observed. In a weak field, a strong increase in the intensity of radiation after switching on a constant magnetic field, a hysteresis between opposite scan directions, and different harmonic amplitudes depending on the conditions of cooling (in the presence or absence of a magnetic field) were observed. These observations can be described by the generalized Ginzburg-Landau functional taking into account higher spatial derivatives of the order parameter. At a high intensity of incident waves, a magnetic field almost did not influence third-harmonic radiation, and, accordingly, hysteresis was absent. This is likely to be evidence that, at high powers, third-harmonic radiation arises as a result of generation of vortices under the action of a high-frequency magnetic field.