The approximate conformal mapping of a disk onto domain with an acute angle

The method of boundary curve reparametrization is applied to construction of the approximate analytical conformal mapping of the unit disk onto an arbitrary given finite domain with a boundary smooth at every point but fininte number of acute angle points. The method is based on both the Fredholm equation solution and spline-interpolation. This approach consists of approximate solution of a linear system with unknown Fourier coefficients and construction of correction splines. The approximate mapping function has the form of a Cauchy integral. The method presentation is supported by demonstration of some examples. This method is applicable to the case of multiply connected domains with boundary angle points.Comment: Accepted for publication in IJACM 11.01.2

The exact solution of a shock wave reflection problem from a wall shielded by a gas suspension layer

The paper is devoted to solving the shockwave reflection problem from a wall shielded by a gas suspension layer. The dynamics of the gas suspension are described in a two-speed two-temperature formulation. In contrast to the known approximate models of dusty gas based on the application of classical self-similar solutions by correcting gas dynamic parameters and physical constants, an asymptotically exact solution is obtained. The analytical solution to the problem is constructed in the form of a composition of elementary decays discontinuities. The nonequilibrium solution converges to the exact one with a decrease in the characteristic times of dynamic and thermal relaxation of the carrier gas and suspended particles of arbitrary concentration. Calculations based on the nonequilibrium model are performed by the hybrid large-particle method of the second-order approximation in space and time. Both for the exact and calculate profiles of the relative values of the pressure and density of the mixture, the normalized velocity of the dispersed phase obtained from the nonequilibrium model are given. The influence of the intensity of the incident shock wave, as well as the concentration of particles in the gas suspension layer on the parameters of the impact of the shock wave pulse on the wall, is studied. The presence of a shielding layer leads to an increase in the reflection pressure from the wall compared to the reflection of the shock wave in a pure gas. The analysis of the influence of the relaxation properties of the gas suspension layer with a change in particle sizes from 1 to 8 μm is carried out. For sufficiently small particles of 1 micron and the accepted scales of the problem, the nonequilibrium solution reproduces the shock-wave structure well and corresponds to the asymptotics. With the increase in the size of dispersed inclusions, the spatial relaxation zones, smoothing the profiles of the parameters, increase. The error in calculating the velocity and other parameters for a nonequilibrium gas suspension with particles of 1 μm compared to the exact solution is in the range from 10–7 to 10–5. The results obtained are of practical importance in substantiating the influence of inert particle impurities on the dynamic loading of structures. The analytical solution to the problem may be in demand when testing various numerical schemes

The Discourse Personality of Politician Sergey Mikheyev with Regards to his Speech Behaviour

This paper presents the results of research into the linguistic personality of politician Sergey Mikheyev when viewed as a discourse personality. Special consideration has been given to the speech behaviour characteristic of a discourse personality. The paper presents the results of the cognitive-discursive and linguo-rhetorical description of a discourse personality.The relevance of this research is based on the growing interest for linguistic personality typology with regards to discourse (K. F. Sedov, V. I. Karasik, N. D. Golev, A. V. Bolotnov, et al.). A mixed type of political discourse that actualises both the personal and status factors of its formation was chosen as the object of analysis. The research focuses on semantic dominants and semantic constructs of the discourse behaviour of the Russian politician Sergey Mikheyev, as well as on the cognitive and linguo-rhetorical mechanisms of the interpretation of speech acts when viewed as elements of individual discourse behaviour. We define the linguo-rhetorical competence of the politician’s personality. The study is novel in that it identifies semantic dominants and semantic constructs found in Mikheyev’s discourse and uses an integrative approach to analysis (cognitive-discursive and linguo-rhetorical). It is proven that semantic dominants, constructs, and presuppositions manifest inventive mechanisms of individual discourse activity. We suggest defining the status of Mikheyev’s discourse personality as a mixed type of elitist linguistic personality that is pragmatically oriented. We prove that the discourse personality of Sergey Mikheyev is a prototype of a future successful politician’s linguistic personality. The paper presents the author’s original communicative competence system of S. Mikheyev’s discourse personality

On approximate conformal mapping of a disk and an annulus with radial and circular slits onto multiply connected domains

The method of boundary curve reparametrization is generalized to the case of multiply connected domains. We construct the approximate analytical conformal mapping of the unit disk with m circular slits and n-m radial slits and an annulus with (m-1) circular slits and n-m radial slits onto an arbitrary given (n+1) multiply connected finite domain with a smooth boundary. The method is based on extension of the Lichtenstein-Gershgorin equation to a multiply connected domain. The proposed method is reduced to the solution of a linear system with unknown Fourier coefficients. The approximate mapping function has the form of a Cauchy integral. Numerical examples demonstrate that the proposed method is effective in computations

The experimental and theoretical investigations of damage development and distribution in double-forged tungsten under plasma irradiation-initiated extreme heat loads

The influence of extreme heat loads, as produced by a multiple pulses of non-homogeneous fl ow of slow plasma (0.1-1 keV) and fast ions (100 keV), on double-forged tungsten (DFW) was investigated. For generation of deuterium plasma and fast deuterons, plasma-focus devices PF-12 and PF-1000 are used. Depending on devices and conditions, the power flux density of plasma varied in a range of 107-1010 W/cm2 with pulse duration of 50-100 ns. Power flux density of fast ions was 1010-1012 W/cm2 at the pulse duration of 10-50 ns. To achieve the combined effect of different kind of plasmas, the samples were later irradiated with hydrogen plasma (105 W/cm2, 0.25 ms) by a QSPA Kh-50 plasma generator. Surface modification was analysed by scanning electron microscopy (SEM) and microroughness measurements. For estimation of damages in the bulk of material, an electrical conductivity method was used. Investigations showed that irradiation of DFW with multiple plasma pulses generated a mesh of micro- and macrocracks due to high heat load. A comparison with single forged tungsten (W) and tungsten doped with 1% lanthanum-oxide (WL10) reveals the better crack-resistance of DFW. Also, sizes of cells formed between the cracks on the DFW’s surface were larger than in cases of W or WL10. Measurements of electrical conductivity indicated a layer of decreased conductivity, which reached up to 500 μm. It depended mainly on values of power flux density of fast ions, but not on the number of pulses. Thus, it may be concluded that bulk defects (weakening bonds between grains and crystals, dislocations, point-defects) were generated due to mechanical shock wave, which was generated by the fast ions flux. Damages and erosion of materials under different combined radiation conditions have also been discussed