Analysis of methods for calculating the static characteristics of dense Coulomb systems

[EN] In this paper, various methods for calculating static characteristics of plasma, such as HNC, MHNC, VMHNC, Percus-Yevik and analytical models were analyzed to satisfy a mathematical condition. Structural characteristics of a one-component plasma were reconstructed in a wide range of coupling parameters within the most requested various modern methods (HNC, MHNC, VMHNC, Percus-Yevik, and analytical models). All these methods were analyzed to fulfill the fundamental Cauchy ¿ Schwartz mathematical inequality. As a result a HNC method with the empirical expression of the bridge function and one of the recent methods for obtaining a structural factor based on a parameterized formula does not satisfy the inequality. The other methods for calculating static characteristics listed above beside the stated ones satisfy the condition. For the general analysis of a method, functional dependence was obtained expressing the Cauchy-Schwartz inequality. This dependence includes the frequency moments, which are defined within the framework of the method of moments. To satisfy the inequality, this relationship must be strictly positive. For each considered method of obtaining static structural characteristics, this relationship was calculated and analyzed. As a result, it was found that a number of methods do not satisfy the Cauchy-Schwartz inequality.Arkhipov, YV.; Askaruly, A.; Ashikbayeva, A.; Davletov, A.; Dubovtsev, D.; Santybayev, K.; Tkachenko Gorski, IM. (2018). Analysis of methods for calculating the static characteristics of dense Coulomb systems. Recent Contribution to Physics. 67(4):20-32. http://hdl.handle.net/10251/133778S203267

Static and dynamic structure factors with account of the ion structure for high-temperature alkali and alkaline earth plasmas

The electron-electron, electron-ion, ion-ion and charge-charge static structure factors are calculated for alkali (at T = 30 000 K, 60 000 K, n (e) = 0.7 x 10(21) A center dot 1.1 x 10(22) cm(-3)) and Be2+ (at T = 20 eV, n (e) = 2.5 x 10(23) cm(-3)) plasmas using the method described by Gregori et al. The dynamic structure factors for alkali plasmas are calculated at T = 30 000 K, n (e) = 1.74 x 10(20), 1.11 x 10(22) cm(-3) using the method of moments developed by Adamjan et al. In both methods the screened Hellmann-Gurskii-Krasko potential, obtained on the basis of Bogolyubov's method, has been used taking into account not only the quantum-mechanical effects but also the repulsion due to the Pauli exclusion principle. The repulsive part of the Hellmann-Gurskii-Krasko (HGK) potential reflects important features of the ion structure. Our results on the static structure factors for Be2+ plasma deviate from the data obtained by Gregori et al., while our dynamic structure factors are in a reasonable agreement with those of Adamyan et al.: at higher values of k and with increasing k the curves damp down while at lower values of k, and especially at higher electron coupling, we observe sharp peaks also reported in the mentioned work. For lower electron coupling the dynamic structure factors of Li+, Na+, K+, Rb+ and Cs+ do not differ while at higher electron coupling these curves split. As the number of shell electrons increases from Li+ to Cs+ the curves shift in the direction of low absolute value of omega and their heights diminish. We conclude that the short range forces, which we take into account by means of the HGK model potential, which deviates from the Coulomb and Deutsch ones, influence the static and dynamic structure factors significantly.The work has been realised at the Humboldt University at Berlin (Germany). One of the authors (S. P. Sadykova) would like to express sincere thanks to the Erasmus Mundus Program of the EU for the financial support and especially to Mr. M. Parske for his aid, to the Institute of Physics, Humboldt University at Berlin, for the support which made her participation at some scientific Conferences possible; I. M. T. acknowledges the financial support of the Spanish Ministerio de Educacion y Ciencia Project No. ENE2007-67406-C02-02/FTN and valuable discussions with Dr. D. Gericke.Sadykova, SP.; Ebeling, W.; Tkachenko Gorski, IM. (2011). Static and dynamic structure factors with account of the ion structure for high-temperature alkali and alkaline earth plasmas. 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Electrodynamic properties of dense high-temperature plasma

An expression for the longitudinal dielectric function of dense high-temperature isotropic plasma is obtained on the basis of the semiclassical approach and the linear density-response formalism. Spectrum and decrement of plasma waves, including quantum-mechanical effects, are derived. The linear and nonlinear stages of parametric two-plasmon instability, developing under the influence of electromagnetic radiation beam are studied. One of the possible saturation mechanism caused by nonlinear frequency shift is evaluated

THEORETICAL RESEARCH ON DETERMINING THE LENGTH OF THE SHOVELS OF A WHEEL OF CENTRIFUGAL FANS

Presents the results of theoretical research by scientists, carried out scientific work to determine the length of the shovel of a centrifugal fan wheel. A technological scheme for installing a shovel on a fan wheel disk has been developed Analyzes of these works are carried out, which show that the length of the wheel shovel has a significant dependence on the parameters of the wheel (R, R1), the angle of installation α and the radius of the arc R3 of the shovel. An analytical dependence is derived for determining the length of the shovel of a centrifugal fan wheel depending on the parameters of the wheel (R, R1), the angle of installation α and the radius of the arc R3 of the shovel. With the following values of the parameters of the fan wheel R=630 mm, R1=340 mm, angle of installation α0=100 and radius of the arc R3=200 mm, the length of the shovel is equal to L=154.29 mm. On the basis of the above mentioned dimensions, in the electronic version, the blades have been developed and the theoretical values and the difference that does not exceed 0.1% are compared

Unstable Asia: active deformation of Siberia revealed by drainage shifts

Regional incision and lateral shifts of rivers in the West Siberian Basin and surrounding areas show the action of long wavelength surface tilting, directed away from the Urals and Central Asian mountains and towards the Siberian Craton. In the north of the basin, surface uplift of individual folds is recorded by local lateral drainage migration. Lateral slopes of river valleys vary in gradient from 0.001 to 0.0001, generally decreasing with increasing river discharge. As a result of this surface deformation significant drainage shifts are taking place in three of the longest and highest discharge river systems on Earth: the Yenisei, Ob' and Irtysh. The deformation is most plausibly caused by subtle faulting at depth, below the thick basin fill of Mesozoic and Lower Cenozoic sediments. Active deformation of western Siberia appears to represent a previously unrecognised, far-field effect of the India–Eurasia collision, up to ∼1500 km north of the limit of major seismicity and mountain building. It adds ∼2.5 × 106 km2 to the region deformed by the collision, which is an area greater than the Himalayas and Tibet combined. It is also an analogue for the formation of low-angle unconformities in terrestrial sedimentary basins on the periphery of other orogenic belts

Energy loss of relativistic projectiles in non-ideal electron liquids

[EN] The energy loss of relativistic projectiles in collisional one-component plasmas is analyzed within the method of moments. Both the canonical and non-canonical solutions of the Hamburger moment problem corresponding to five convergent power frequency moments of the electron plasma loss function are employed with the static, purely imaginary, Nevanlinna parameter with the imaginary part iqual to the collision frequency calculated within the Green-Kubo formalism in terms of static structure factors evaluated in the HNC approximation using the Deutsch effective potential.Thus we take into account the dissipation processes in the plasma. It is pointed out that the correlations only slightly influence the deviation of the stopping power with the relativistic corrections taken into account from the classical Bethe-Bohr-Larkin asymptotic form.The financial support of the Spanish Ministerio de Educación y Ciencia Project # ENE2010-21116-C02-02 and the Ministry of education and science of the Republic of Kazakhstan projects #1128/GF, 1129/GF, 1099/GF are gratefully acknowledged. IMT acknowledges also the hospitality of the al-Farabi Kazakh National UniversityArkhipov, YV.; Ashikbayeva, A.; Askaruly, A.; Davletov, A.; Palací, D.; Tkachenko Gorski, IM. (2013). Energy loss of relativistic projectiles in non-ideal electron liquids. International Journal of Mathematics and Physics. 4(1):50-55. http://hdl.handle.net/10251/15511450554

ON THE COLLISIONAL ONE-COMPONENT PLASMA DIELECTRIC FUNCTION

[EN] Asymptotic properties of the collisional one-component plasma dielectric function in the random-phase (RPA) and Mermin approximation, with a constant collision frequency, are analyzed from the point of view of the verification of sum rules. The latter are the power frequency moments of the loss function, a positive even function of frequency directly related to the imaginary part of the inverse dielectric function. The zero moment is shown to coincide with that of the RPA, the f-sum rule is satisfied, and the fourth moment sum rule is verified only partly, without taking the correlations into account. These drawbacks of the Mermin model expression for the dielectric function define the realm of applicability of this approximation.Arkhipov, YV.; Ashikbayeva, A.; Askaruly, A.; Conde, L.; Davletov, A.; Tkachenko Gorski, IM. (2013). ON THE COLLISIONAL ONE-COMPONENT PLASMA DIELECTRIC FUNCTION. News of National Academy of Sciences of the Republic of Kazakhstan. Physico-mathematical series. 2:46-50. http://hdl.handle.net/10251/102259S4650

Statical structural properties of nonideal plasma

[EN] In this article radial distribution functions and static structure factors of nonideal plasma are investigated in the framework of Ornstein-Zernike equation with Percus-Yevick bridge function and Deutch micropotential. It is shown that short range symmetries appear in ionic subsystem of dense plasma and bridge contributions of electrons promote creation of symmetries in ionic subsystem of nonideal plasma.The financial support of the Ministry of education and science of the Republic of Kazakhstan projects # 1099/ GF is gratefully acknowledged.Arkhipov, YV.; Askaruly, A.; Voronkov, V.; Davletov, A.; Ashikbayeva, A.; Tkachenko Gorski, IM. (2013). Statical structural properties of nonideal plasma. International Journal of Mathematics and Physics. 4(1):80-84. http://hdl.handle.net/10251/148680S80844