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.     

Structural hierarchy of rock masses and the mechanisms of its formation

The formation mechanisms for the structural hierarchy in geological media are discussed. It is shown that the formation of such a hierarchy is caused by certain external and internal circumstances. The first ones consist in the fact that, because of external actions, the Earth’s poles continuously execute the translational and rotational motions responsible for a regular structure of rock fracture and for the appearance of the scale factor √2. The second ones consist in the fact that, under the action of many random factors and because of external actions, during the formation of geological media there appear dissipative structures and, hence, some self-similar fractal structures are formed.     

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.     

New approach to processing of chlorine-containing wastes: Synthesis of 2,3-dichloropropene from 1,2,3-trichloropropane

Possibilities of utilization of by-products formed in manufacture of epichlorohydrin are considered. A promising way to utilize wastes from production of epichlorohydrin by synthesis of 2,3-dichloropropene from 1,2,3-trichloropropane is suggested.     

Influence of the composition of the polymer matrix on the electrooptical properties of films with a dispersed liquid crystal

Polymer films with a dispersed liquid crystal were prepared by photopolymerization of (meth)acrylic monomers. The electrooptical properties of these films were studied. The influence exerted by the composition of the monomer mixture, cross-linking agents, and chain-transfer agent on the liquid crystal drop size and on the transmission of the polymer-liquid crystal films was examined.     

Miscibility and phase structure of binary blends of polylactide and poly(methyl methacrylate)

Blends of amorphous poly(DL‐lactide) (DL‐PLA) and crystalline poly(L‐lactide) (PLLA) with poly(methyl methacrylate) (PMMA) were prepared by both solution/precipitation and solution‐casting film methods. The miscibility, crystallization behavior, and component interaction of these blends were examined by differential scanning calorimetry. Only one glass‐transition temperature (T_g) was found in the DL‐PLA/PMMA solution/precipitation blends, indicating miscibility in this system. Two isolated T_g's appeared in the DL‐PLA/PMMA solution‐casting film blends, suggesting two segregated phases in the blend system, but evidence showed that two components were partially miscible. In the PLLA/PMMA blend, the crystallization of PLLA was greatly restricted by amorphous PMMA. Once the thermal history of the blend was destroyed, PLLA and PMMA were miscible. The T_g composition relationship for both DL‐PLA/PMMA and PLLA/PMMA miscible systems obeyed the Gordon–Taylor equation. Experiment results indicated that there is no more favorable trend of DL‐PLA to form miscible blends with PMMA than PLLA when PLLA is in the amorphous state. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 23–30, 2003     

Study of the dynamic structure factor of strong glasses

The dynamic structure factors (DSFs) of several strong glasses (SF6, SF10, BK7, SUPRASIL) measured by Brillouin light scattering spectroscopy are reported. Spectra have been collected, at and above room temperature, at two scattering angles, θ=90° and θ=180° corresponding to exchanged wavevector q values ranging from 0.0256 to 0.0448 nm⁻¹. In particular we find that the isotropic spectral lineshapes are in all cases well described by the simple hydrodynamic theory of an amorphous solid. The width of the Brillouin peaks are found to be consistent with the predicted q² dependence at both investigated temperatures. This damping is however found to account only partially for the strong asymmetry of the Brillouin line clearly visible on a logarithmic intensity scale. As a matter of fact there is an excess intensity in the very low frequency plateau underlying the central component. The height of this plateau and hence the entire lineshape is well reproduced if a relaxation process is taken into account in the hydrodynamic equations. Owing to the intense elastic scattering we are able to determine unambiguously only the ratio between amplitude and characteristic time of this process which quantifies the sound dispersion to be of the order of a few percent in all samples. The temperature dependence of the parameters indicates that this relaxation cannot be attributed to thermally activated relaxation phenomena. These general findings favorably compare with molecular dynamics simulation results on similar systems.