We calculate renormalization-group functions in the developed turbulence model for infinite dimensional space d → ∞ using an operating method without renormalization constants. The renormalization fixed point and index ω, obtained within the considered three loop approximation, are in agreement with previous calculations. The results demonstrate the efficiency of the method and the possibility of its complete automation, which is crucially important in higher order perturbation theory computations.

The refraction of an extraordinary light wave in a layer of a chiral liquid crystal with the director rotated 90° has been studied. In this structure, if a light wave is incident on the surface of the liquid crystal at a large angle and the light passes through the whole layer, it refracts at the opposite boundary of the layer. The angular dependence of the light transmission through the liquid crystal layer has been researched. It has been demonstrated that the electric field changed the character of the refraction of the extraordinary wave and the light started to pass through the layer. The threshold voltage of the light transmission has been determined, as well as its dependence on the light incidence angle. The effect dynamics have been studied and the angular dependence of the light transmission decay time has been determined.

The equations describing the transient and steady stages of size and composition evolution for a gas bubble which grows or shrinks due to the diffusion of several gases dissolved in liquid solution have been derived. The diffusion fluxes for gases in the liquid mixture caused by the bubble growth or dissolution were assumed to be quasi-stationary and the mixture of the gases in the bubble was treated as ideal. The analytical solutions for the obtained evolution equations have been found for bubbles of any size with an arbitrary number of components in the case of equal products of diffusivities and solubilities of dissolved gases in the liquid solution, and for sufficiently large binary bubbles for which capillary effects can be neglected.

The uctuations of the director orientation in a freely suspended smectic-C* film were theoretically investigated. In the free energy expression of the film, not only were the elastic energy and the weak external electric field interaction considered, the interaction of polarization charges arising from uctuations of the polarization vector were also included. The correlation function of the director uctuations was obtained for a film of finite thickness. Calculations of light scattering intensity were provided. It has been found that due to the interaction of polarization charges, the angular dependence of the scattering intensity significantly depends on the magnitude of spontaneous polarization.

In this work we investigate the exact classical stochastic representations of many-body quantum dynamics. We focus on the representations in which the quantum states and the observables are linearly mapped onto classical quasiprobability distributions and functions in a certain (abstract) phase space. We demonstrate that when such representations have regular mathematical properties, they are reduced to the expansions of the density operator over a certain overcomplete operator basis. Our conclusions are supported by the fact that all the stochastic representations currently known in the literature (quantum mechanics in generalized phase space and, as it recently has been shown by us, the stochastic wave-function methods) have the mathematical structure of the above-mentioned type. We illustrate our considerations by presenting the recently derived operator mappings for the stochastic wave-function method.

The lattice model for a star-shaped polymer with a total number of up to 72 segments is considered. The number of arms varied, ranging from 2 to 6. Entropic sampling Monte Carlo simulation is used to obtain the equilibrium, thermal and structural properties of the considered systems over a wide range of temperatures. The coil-globule transition is observed and the transition temperature is shown to shift toward lower temperatures with an increase in the number of arms.

The scattering of elastic waves is studied in the vicinity of a vacuum-medium boundary. The Green’s function for a half-space is re-derived within the mixed 2D-Fourier representation, which is convenient for studying layered media. Monte-Carlo simulations of elastic wave scattering from random inhomogeneities within a simplified scalar model are performed, accounting for a boundary-induced term in the Green’s function. The multiply scattered elastic waves’ radiation is shown to decay with distance from the source much slower in vicinity of boundary than in an infinite medium, due to the boundary condition requirements.

The work of Knill et. al. (2001) established the possibility of nondeterministic realization of certain quantum logic operations using linear optical elements, ancilla photons and postselection techniques. It was also shown that any discrete unitary operator acting on N optical modes can be implemented by a triangular multiport device constructed from a series of beam splitters and phase shifters (see work of Reck, Zeilinger et. al., 1994). Here, we consider the rectangular linear optical multiport that is used for the probabilistic realization of unitary transformations on n qubits. This kind of linear optical scheme is suitable for probabilistic realization of unitary operators using ancilla photons and projective measurements. Qubits are encoded into the bosonic states of optical modes in two possible polarizations, and a number of ancilla photons and photodetectors are used for postselection of the qubits’ state, based on the output of the detectors. We derive a procedure of evolutionary operator calculation for schemes of the considered type and present algorithms for their efficient computation on symmetric state space. We also provide complexities for different algorithms for the computation of evolutionary operator and estimate demands of resources in each case. A destructive Toffoli gate, acting on three qubits, using one ancilla photon and a photodetector, is implemented using schemes of the presented type.

A method of thermal measurements has been proposed for determining the real surface contact area. Measurement of the true contact area is somewhat difficult. We propose here a method of contact area measurement, which is, in essence, an idealization of the well-known probe method employed in surface studies. In this study, to determine (estimate!) the fraction of the contact surface area projected onto the plane of a geometrical area of the section of the surface, it is proposed to use the electrothermal analogy. Considered in terms of this analogy, electrical conductance is assumed to correlate with heat transfer. As a result, the real contact area is found to be millions of times smaller than the area of the plane surface.

The mesokinetic model of the polymeric body formation was formulated, describing the nucleation, growth and aggregation of macromolecules followed by the aggregates’ assembly into the nanostructured body. According to this model, the near-surface nanostructure of the polymeric body retains the information on how it was formed, and this information can be extracted from the morphological characteristics of the microrelief of the body while maintaining its integrity, that is, body has the morphological memory. The mesokinetic model was used to study film formation by the evaporation of an o-xylene or toluene solution of polystyrene, which provided an opportunity to identify the kinetics of nanostructure formation found in the surface area of the film after completion of the process. It turned out that at the beginning of evaporation, a number of the primary macromolecules in the form of spheroidal nanoparticles were formed, and then, the primary aggregates coalesced into the secondary aggregates forming the ordered chains of nanoparticles.

The stimulated emission of a coherently excited atomic system was studied in the presence of a strong magnetic field.

The effect of fulleroid materials (fullerene C₆₀ and fullerene soot which is used for fullerenes production) on the mechanical properties of polymer nanocomposites based on polyamide 6 (PA6) was investigated. Composites were synthesized by direct mixing in an extruder. Dielectric spectroscopy was used to investigate the influence of nanoparticles on relaxation processes in the polymer matrix. It is found that the segmental relaxation processes becomes faster with the addition of fullerene C₆₀. In contrast, the secondary processes of PA6/fullerene C₆₀ nanocomposites were observed to slow down with the addition of fullerene C₆₀. This means that the local ‘molecular stiffness’ is increased, and a phenomenological link between the secondary relaxation times and the mechanical properties explains the increase in the Young’s modulus of the nanocomposites upon the addition of C₆₀. These observations suggest that nanoparticles can have a qualitatively different effect on the matrix polymer dynamics at different length scales, and caution must be taken in comparing the changes in the dynamics associated with different relaxation processes.

Despite having simple stoichiometry, NH₄V₃O₇ still remains an odd compound with poorly resolved structure among the series of known ammonium vanadates. Here, a new hydrothermal synthesis of the product with explicit NH₄V₃O₇ stoichiometry is evaluated. Intricate microstructure of the product is revealed as an aggregate of spherical microparticles consisting of microplatelets via scanning electron microscopy. To further guide the characterization of the NH₄V₃O₇ phase, X-ray diffraction analysis and first-principle calculations were carried out to refine the structure at an atomistic level and to predict electronic properties. The results suggest a complex structural hierarchy with consequent nanodomain organization of prepared NH₄V₃O₇ microplatelets.

The regularities of phase formation during oxidation of aqueous solutions of FeSO₄ and (or) suspensions of Fe(OH)₂ at quasi-constant temperature and pH values have been studied for wide intervals of temperature (20 – 85 ◦C) and (4.0 – 13.0) of the reaction medium. The produced nanodisperse materials have been examined by X-ray phase analysis, IR spectroscopy, scanning electron microscopy and X-ray fluorescence analysis, as well as by thermogravimetric analysis combined with thermal analysis and mass spectrometric analysis of released gases. The dependences of the phase, chemical and disperse compositions of the formed precipitates on the synthesis parameters have been revealed.