Abstract:
In the paper we prove the existence results for initial-value boundary value problems for compressible isothermal Navier-Stokes equations. We restrict ourselves to 2D case of a problem with no-slip condition for nonstationary motion of viscous compressible isothermal fluid. However, the technique of modeling and analysis presented here is general and can be used for 3D problems.

Abstract:
The Navier-Stokes equations for compressible barotropic flow in the stationary three dimensional case are considered. It is assumed that a fluid occupies a bounded domain and satisfies the no-slip boundary condition. The existence of a weak solution under the assumption that the adiabatic exponent satisfies $\gamma>1$ is proved. These results cover the cases of monoatomic, diatomic, and polyatomic gases.

Abstract:
Various astrophysical studies have motivated the investigation of the transport of high energy particles in magnetic turbulence, either in the source or en route to the observation sites. For strong turbulence and large rigidity, the pitch-angle scattering rate is governed by a simple law involving a mean free path that increases proportionally to the square of the particle energy. In this paper, we show that perpendicular diffusion deviates from this behavior in the presence of a mean field. We propose an exact theoretical derivation of the diffusion coefficients and show that a mean field significantly changes the transverse diffusion even in the presence of a stronger turbulent field. In particular, the transverse diffusion coefficient is shown to reach a finite value at large rigidity instead of increasing proportionally to the square of the particle energy. Our theoretical derivation is corroborated by a dedicated Monte Carlo simulation. We briefly discuss several possible applications in astrophysics.

Abstract:
We consider doubly-periodic travelling waves at the surface of an infinitely deep perfect fluid, only subjected to gravity $g$ and resulting from the nonlinear interaction of two simply periodic travelling waves making an angle $2\theta $ between them. \newline Denoting by $\mu =gL/c^{2}$ the dimensionless bifurcation parameter ($L$ is the wave length along the direction of the travelling wave and $c$ is the velocity of the wave), bifurcation occurs for $\mu =\cos \theta$. For non-resonant cases, we first give a large family of formal three-dimensional gravity travelling waves, in the form of an expansion in powers of the amplitudes of two basic travelling waves. "Diamond waves" are a particular case of such waves, when they are symmetric with respect to the direction of propagation.\newline \emph{The main object of the paper is the proof of existence} of such symmetric waves having the above mentioned asymptotic expansion. Due to the \emph{occurence of small divisors}, the main difficulty is the inversion of the linearized operator at a non trivial point, for applying the Nash Moser theorem. This operator is the sum of a second order differentiation along a certain direction, and an integro-differential operator of first order, both depending periodically of coordinates. It is shown that for almost all angles $\theta $, the 3-dimensional travelling waves bifurcate for a set of "good" values of the bifurcation parameter having asymptotically a full measure near the bifurcation curve in the parameter plane $(\theta ,\mu ).$

Abstract:
The physics of instabilities in the precursor of relativistic collisionless shocks is of broad importance in high energy astrophysics, because these instabilities build up the shock, control the particle acceleration process and generate the magnetic fields in which the accelerated particles radiate. Two crucial parameters control the micro-physics of these shocks: the magnetization of the ambient medium and the Lorentz factor of the shock front; as of today, much of this parameter space remains to be explored. In the present paper, we report on a new instability upstream of electron-positron relativistic shocks and we argue that this instability shapes the micro-physics at moderate magnetization levels and/or large Lorentz factors. This instability is seeded by the electric current carried by the accelerated particles in the shock precursor as they gyrate around the background magnetic field. The compensation current induced in the background plasma leads to an unstable configuration, with the appearance of charge neutral filaments carrying a current of the same polarity, oriented along the perpendicular current. This ``current-driven filamentation'' instability grows faster than any other instability studied so far upstream of relativistic shocks, with a growth rate comparable to the plasma frequency. Furthermore, the compensation of the current is associated with a slow-down of the ambient plasma as it penetrates the shock precursor (as viewed in the shock rest frame). This slow-down of the plasma implies that the ``current driven filamentation'' instability can grow for any value of the shock Lorentz factor, provided the magnetization \sigma <~ 10^{-2}. We argue that this instability explains the results of recent particle-in-cell simulations in the mildly magnetized regime.

Abstract:
We report the first comparative study of the properties of two-dimensional arrays and single superconducting film - normal wire - superconducting film (SNS) junctions. The NS interfaces of our SNS junctions are really high transparent, for superconducting and normal metal parts are made from the same material (superconducting polycrystalline PtSi film). We have found that the two-dimensional arrays reveal some novel features: (i) the significant narrowing of the zero bias anomaly (ZBA) in comparison with single SNS junctions, (ii) the appearance of subharmonic energy gap structure (SGS), with up to n=16 (eV=\pm 2\Delta/n), with some numbers being lost, (iii) the transition from 2D logarithmic weak localization behavior to metallic one. Our experiments show that coherent phenomena governed by the Andreev reflection are not only maintained over the macroscopic scale but manifest novel pronounced effects as well. The behavior of the ZBA and SGS in 2D array of SNS junctions strongly suggests that the development of a novel theoretical approach is needed which would self-consistently take into account the distribution of the currents, the potentials, and the superconducting order parameter.

Abstract:
The mechanical properties and microstructure formation processes in Si3N4+3% AI2O3+5% Y2O3(Yb2O3) ceramic compacts sintered under microwave heating (MWH) and under traditional heating (TH) were investigated. The initial ceramic materials were powder blends of silicon nitride with oxides. The mean powder particle sizes were 0.5-1.0 mim. The content of alfa-phase in the Si3N4 powder was more than 95 %. The samples were sintered at 1800BC in nitrogen at normal pressure, the heating rate in all experiments was 60BC/min. The Vickers hardness (HV), fracture toughness (K1C) and bending strength (on) were determined. The microstructures of fracture surfaces of samples were studied by SEM. Quantitative microstructure analysis was carried out. It was shown that the values of HV and Kic of ceramic samples sintered under MWH at 1800BC rose steadily with the sintering time. This caused an increase in density, which reached maximum as fast as after 30 min of the MWH sintering; the mass loss at that time amounted to 3-4 %. The porosity of sintered samples with an addition of yttria was less than 1 %, that of ytterbia was greater, 2.4 %. For similar values of relative density, the hardness and fracture toughness of ceramic samples produced under MWH were higher as compared with those of samples sintered under TH. The microstructure of samples had the form of elongated grains in a matrix of polyhedral grains of the beta-Si3N4 phase. Measurements showed the mean size of grains in samples produced by MWH to be greater that in samples produced by TH. A larger number of elongated grains were formed. It was concluded that for sintering under MWH of Si3N4-based ceramics the growth of elongated beta-Si3N4 grains and formation of a "reinforced" microstructure were promoted and thereby improved the mechanical properties of such ceramics.

Abstract:
The human body is constantly under attack from free radicals that occur as part of normal cell metabolism, and by exposure to environmental factors such as UV light, cigarette smoke, environmental pollutants and gamma radiation. The resulting “Reactive Oxygen Species” (ROS) circulate freely in the body with access to all organs and tissues, which can have serious repercussions throughout the body. The body possesses a number of mechanisms both to control the production of ROS and to cope with free radicals in order to limit or repair damage to tissues. Overproduction of ROS or insufficient defense mechanisms leads to a dangerous disbalance in the organism. Thereby several pathomechanisms implicated in over 100 human diseases, e.g., cardiovascular disease, cancer, diabetes mellitus, physiological disease, aging, etc., can be induced. Thus, a detailed investigation on the quantity of oxygen radicals, such as hydroxyl radicals (OH ●) in human serum blood, and its possible correlation with antioxidant therapy effects, is highly topical. The subject of this study was the influence of schizophrenia on the amount of OH ● in human serum blood. The radicals were detected by fluorimetry, using terephthalic acid as a chemical trap. For all experiments the serum blood of healthy people was used as a control group.

Abstract:
The dependence of the dynamic range of the phase generated carrier (PGC) technique on low-pass filters passbands is investigated using a simulation model. A nonlinear character of this dependence, which could lead to dynamic range limitations or measurement uncertainty, is presented for the first time. A detailed theoretical analysis is provided to verify the simulation results and these results are consistent with performed calculations. The method for the calculation of low-pass filters passbands according to the required dynamic range upper limit is proposed. 1. Introduction Fiber optic interferometric sensors have been intensively developed for the past few decades. Fiber-optic interferometers are used as a sensitive element in fiber optic gyroscopes, hydrophones, and so forth [1]. As a result, many special data acquisition methods, digital signal processing algorithms, and demodulation techniques have been invented to recover measured phase signals. One of the most popular demodulation techniques is phase generated carrier (PGC) demodulation technique [2]. This technique has been used in many applications such as hydroacoustics [3–5], vibration [6], and pipeline leakage detection [7], and its main properties have been thoroughly studied [8–10]. However, implementation methods of demodulation techniques have changed with the advent of high performance field programmable gate arrays (FPGAs). FPGAs allow realizing complex real-time digital signal processing algorithms, and therefore they are ideally suitable for the multichannel PGC technique implementation to demodulate signals from fiber-optic sensor arrays [11]. Unfortunately, the usage of FPGAs for such purposes has got some problems caused by sampling frequency restrictions and finite passbands of digital schemes. This paper is devoted to the detailed analysis of the PGC technique taking into account its practical implementation problems and digital design restrictions. The dependence of the dynamic range of the PGC technique on low-pass filters passbands is investigated for the first time and the nonlinear character of this dependence is shown and explained. 2. Simulation The PGC demodulation scheme is presented in Figure 1 [11]. Its functional model was implemented using MATLAB to investigate dependences of output signals on various parameters. Filter Design and Analysis Tool (FDATool) was used for generating necessary finite impulse response digital filters. Figure 1: PGC demodulation scheme. Several parameters were constants in this model:(i)the duration of simulated signals was 1

Abstract:
We have investigated low-temperature transport properties of two-dimensional arrays of superconductor--normal-metal--superconductor (SNS) junctions. It has been found that in two-dimensional arrays of SNS junctions (i) a change in the energy spectrum within an interval of the order of the Thouless energy is observed even when the thermal broadening far exceeds the Thouless energy for a single SNS junction; (ii) the manifestation of the subharmonic energy gap structure (SGS) with high harmonic numbers is possible even if the energy relaxation length is smaller than that required for the realization of a multiple Andreev reflection in a single SNS junction. These results point to the synchronization of a great number of SNS junctions. A mechanism of the SGS origin in two-dimensional arrays of SNS junctions, involving the processes of conventional and crossed Andreev reflection, is proposed.