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## Глобальная структура гелиосферы: трёхмерная кинетико-магнитогидродинамическая модель и анализ данных космических аппаратов

We investigate quasi-adiabatic dynamics of charged particles in strong current sheets (SCSs) in the solar wind, including the heliospheric current sheet (HCS), both theoretically and observationally. A self-consistent hybrid model of an SCS is developed in which ion dynamics is described at the quasi-adiabatic approximation, while the electrons are assumed to be magnetized, and their motion is described in the guiding center approximation. The model shows that the SCS profile is determined by the relative contribution of two currents: (i) the current supported by demagnetized protons that move along open quasi-adiabatic orbits, and (ii) the electron drift current. The simplest modeled SCS is found to be a multi-layered structure that consists of a thin current sheet embedded into a much thicker analog of a plasma sheet. This result is in good agreement with observations of SCSs at ∼1 au. The analysis of fine structure of different SCSs, including the HCS, shows that an SCS represents a narrow current layer (with a thickness of ∼104 km) embedded into a wider region of about 105 km, independently of the SCS origin. Therefore, multi-scale structuring is very likely an intrinsic feature of SCSs in the solar wind.

We developed a numerical model of the interstellar dust distribution in the global heliosphere including the heliospheric interface, where the solar wind plasma interacts with the local interstellar plasma. The model is based on the plasma distributions obtained by the 3D kinetic-magnetohydrodynamic model of the heliospheric interface developed by Izmodenov & Alexashov (2015). This paper explores how the dust particles with different initial charge-to-mass ratios (*q*∞/*m*) are filtered and deflected in the outer heliosheath. It is shown that the Lorentz force caused by the interstellar magnetic field leads to formation of specific features of the distribution of dust especially in the case of intermediate gyroradius (∼several AU). We also study the characteristics of the dust flow at the entrance to the heliosphere. We show that more than 70 per cent of particles with *q*∞/*m* ≤ 2 C kg−1 penetrate to the heliosphere. At the nose part of the heliopause, these dust particles are decelerated up to 15 per cent and deflected from the interstellar wind direction by up to 35°. This deflection depends on polarity of the interstellar magnetic field. Distribution of particles with *q*∞/*m* > 0.5 C kg−1 upstream of the heliopause is not uniform and even not axisymmetric due to the assumed inclination of the interstellar magnetic field with respect to the interstellar wind direction.

Recent NuSTAR and XMM–Newton observations of the molecular cloud around the Arches stellar cluster demonstrate a dramatic change both in morphology and intensity of its nonthermal X-ray emission, similar to that observed in many molecular clouds of the Central Molecular Zone at the Galactic Center. These variations trace the propagation of illuminating fronts, presumably induced by past flaring activities of SgrA. In this paper, we present results of a long NuSTAR observation of the Arches complex in 2016, taken a year after the previous XMM+NuSTAR observations which revealed a strong decline in the cloud emission. The 2016 NuSTAR observation shows that both the non-thermal continuum emission and the Fe Kα 6.4 keV line flux are consistent with the level measured in 2015. No significant variation has been detected in both spectral shape and Fe Kα equivalent width EW6.4 keV, which may be interpreted as the intensity of the Arches non-thermal emission reaching its stationary level. At the same time, the measured 2016 non-thermal flux is not formally in disagreement with the declining trend observed in 2007–2015. Thus, we cannot assess whether the non-thermal emission has reached a stationary level in 2016, and new observations, separated by a longer time period, are needed to draw stringent conclusions. Detailed spectral analysis of three bright clumps of the Arches molecular cloud performed for the first time showed different EW6.4 keV and absorption. This is a strong hint that the X-ray emission from the molecular cloud is a mix of two components with different origins.

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.

Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.