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## Electrostatic Turbulence in Electron Temperature Jumps of the Solar Atmosphere

We discuss the connection of the formation and properties of solar atmosphere transition region

characterized by a steep electron temperature gradient with electrostatic turbulence, which provides a high

effective electron collision frequency and a low thermal conductivity of the medium. A simple dependence

of the noise electric field in the transition region on the effective collision frequency has been derived. Based

on known experimental models of the solar atmosphere, we have estimated the height dependence of the

thermal conductivity and the strength of the noise electric fields for a tube with a relatively weak magnetic

field passing from the chromosphere into the corona.

The possibility of using periodic pulsed laser radiation for spectral analysis of the thermal properties of multilayer metallic materials is studied. Pulse and frequency characteristics of samples are found. An expression for the transfer constant of a thermal signal in multilayer materials is obtained. A parametric model is used to determine the thermal conductivity of the interface in a three_layer Mo(1 μm)–W(48 μm)–Mo(1 μm) sample from the amplitude–frequency characteristic measured before and after irradiation by 9_MeV electrons.

We introduce a new asymptotic invariant of magnetic fields, namely, the quadratic (and polynomial) helicity. We construct a higher asymptotic invariant of a magnetic field. We also discuss various problems that can be solved by using the magnetic helicity invariant.

Gathering the proceedings of the 11th CHAOS2018 International Conference, this book highlights recent developments in nonlinear, dynamical and complex systems. The conference was intended to provide an essential forum for Scientists and Engineers to exchange ideas, methods, and techniques in the field of Nonlinear Dynamics, Chaos, Fractals and their applications in General Science and the Engineering Sciences.

The respective chapters address key methods, empirical data and computer techniques, as well as major theoretical advances in the applied nonlinear field. Beyond showcasing the state of the art, the book will help academic and industrial researchers alike apply chaotic theory in their studies.

Analytically and numerically calculations according to the original effective algorithms for largescale acoustic-gravity wave perturbations in the chromosphere from sources at the level of the photosphere are analyzed. Limitations to the energy flux of acoustic-gravity waves from the photosphere through the chromosphere are formulated. Structure of a narrow region with elevated pressure at the resonance altitude where the horizontal phase wave velocity is equal to the sound velocity is examined.

The system of equations for average velocity and Reynolds stresses are examined supposing the smallness of diffusive, relaxation and viscous processes. Such turbulent state is named ideal. It is shown that the spectrum of turbulence has the form of spectrum of absolutely black body.

Within the framework of model calculations the possibility of occurrence of the ion-acoustic oscillation instability in a plasma without current and particle fluxes, but with an anisotropic distribution function, which corresponds to heat flux is shown. The model distribution function was selected taking into account the medium conditions. The increment of ion-acoustic oscillation is investigated as functional of the distribution function parameters. The threshold condition for the anisotropic part of the distribution function, under which the build-up of ion-acoustic oscillation with the wave vector opposite to the heat flux begins is studied. The critical heat flux, which corresponds to the threshold of ion-acoustic instability, is determined. For the solar conditions, the critical heat flux proved to be close to the heat flux from the corona into the chromosphere on the boundary of the transition region. The estimations show that outside of active regions and even in active regions with weaker magnetic fields ion-acoustic turbulence can be responsible for the formation of the sharp temperature jump. The generalized Wiedemann-Franz law for a non-isothermic quasi-neutral plasma with developed ion-acoustic turbulence is discussed. This law determines the relationship between electrical and thermal conductivities in a plasma with well-developed ion-acoustic turbulence. The anomalously low thermal conductivity responsible to the formation of high temperature gradients in the zone of the temperature jump is explained. The results are used to explain some properties of stellar atmosphere transition regions.

A method based on the spectral analysis of thermowave oscillations formed under the effect of radiation of lasers operated in a periodic pulsed mode is developed for investigating the state of the interface of multilayered systems. The method is based on high sensitivity of the shape of the oscillating component of the pyrometric signal to adhesion characteristics of the phase interface. The shape of the signal is quantitatively estimated using the correlation coefficient (for a film–interface system) and the transfer function (for multilayered specimens).

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.

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.