Table of contents

International Interdisciplinary Conference "Euler Readings MRSU 2017" Moscow, Russia, 22-24 November 2017

Philipp I Vysikaylo and Victor V Belyaev

Moscow Region State University, Radio street 10A, Moscow, 105005, Russia

E-mail: filvys@yandex.ru, vv.belyaev@mgou.ru

Preface

This volume of the IOP Conference Series: Materials Science and Engineering contains papers from the International Interdisciplinary Conference "Euler Readings MRSU 2017" which took place from the 22^nd to the 24^th November 2017 at the Moscow Region State University, Moscow, Russia.

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

In honor of the 250th anniversary of Euler's discovery of three libration points in Russia in 1767 in the area of two rotating gravitational attractors in 2017 an International Interdisciplinary Conference "Euler Readings MRSU 2017" was held in Moscow Region State University (MRSU). The Conference demonstrated that the Euler's ideas continue to remain relevant at the present time. This paper summarizes the main achievements on the basis of Leonard Euler's ideas presented at the Conference.

The analysis of energy balance equation for viscous laminar flow of fluid or gas in the cylindrical channel in the area (zone) of warm up bounded along the longitudinal coordinate is made. It was found that at laminar flow of fluid or gas in a round pipe, in each warm up area bounded along the longitudinal coordinate there are the areas of direct and reverse flows separated by a plane that is a locus of points where temperature is maximal for each fixed value of radial coordinate r.

The paper deals with investigation of the MHD-stability dependence on the depth of the anode immersion in the process of aluminium electrolysis. The proposed 3D three-phase mathematical model is based on the Navier-Stokes and Maxwell equation systems. This model makes it possible to simulate the distributions of the main physical fields both in horizontal and vertical planes. The suggested approach also allows to study the dynamics of the border between aluminium and electrolyte and the shape of the back oxidation zone.

The paper presents the investigation of the toroidal vortex structures (TVS) interaction in various media. The proposed mathematical model makes it possible to study in details the stages of interaction of the toroidal vortices and allows to conclude what processes occur in the real collision of vortex structures, and to predict the result of this collision.

In the paper it is briefly considered various aspects of stability concepts, which are used in physics, mathematics and numerical methods of solution. The interrelation between these concepts is described, the questions of preliminary stability research before the numerical solution of the problem and the correctness of the mathematical statement of the physical problem are discussed. Examples of concrete mathematical statements of individual physical problems are given: a nonlocal problem for the heat equation, the Korteweg-de Fries equation with boundary conditions at infinity, the sine-Gordon equation, the problem of propagation of femtosecond light pulses in an area with a cubic nonlinearity.

Are the main results of numerical research of the effect of high speed threshold Nonequilibrium activated kinetic processes in shock-compressed gases. In parallel to it are corresponding analytical results of the authors.

In the offered article, having used earlier constructed kinetic model for imperfect gas, the equation of state for such gas which takes place which is able in a thermodynamic equilibrium is received and also expression for critical temperature as functions is received from an interaction potential between molecules.

An influence of quantum and spatial dispersion properties of the non-degenerate electron plasma on the interaction of electromagnetic P-waves with one-dimensional photonic crystal consisting of conductor with low carrier electron density and transparent dielectric matter, is studied numerically. It is shown that at the frequencies of order of the plasma frequency and at small widths of the conducting and dielectric layers of the photonic crystal, optical coefficients in the quantum non-degenerate plasma approach differ from the coefficients in the classical electron gas approach. And also, at these frequencies one observes a temperature dependence of the optical coefficients.

The analysis of the analytical solution of the problem of the behavior of electron plasma in the AC electric field is fulfilled. Debye mode describes shielding of the external electric field in the plasma. The analysis of the region of existence of Debye mode, depending on the plasma parameters has been realized. A non-trivial dependence of the region of existence of Debye mode on the degree of degeneracy of the electron gas are revealed. For the case of nearly degenerate electron gas Debye mode has several areas of existence, depending on the frequency of the electric field.

Properties of channel in order to transport atoms (ions, molecules) is considered from point of its symmetry. Lagrange function of the transport channel is constructed. Properties of the Lagrange function and types of symmetry of the channel allow to estimate its inner size. Crystallographic channel of quartz and its dislocations are used as particular example.

The article describes the cases when ball lightning (BL) exhibited an extremely high specific energy store (up to 10¹⁰ J/m3), a presence of uncompensated electric charge (up to 10⁻³ C) and an ability to generate high frequency pulses (up to 10 MW). It is shown that the realization of a combination of these properties of BL is possible if to consider it as a heterogeneous system consisting of a unipolarly charged core and a dielectric shell. In the electric field of the core charge, arises a force owing to the polarization of the shell that opposes the Coulomb repulsion force of the charges. BL models constructed according to the indicated principle are described: the electrodynamic model and the chemical-thermal model, which treats BL as a hollow sphere filled with steam. The requirement to take into account the main three properties of BL makes it possible to reduce the number of models of this natural phenomenon. Detailed cases of observations of high-energy lightning are analyzed.

Gas dynamic modeling approach was applied to "plasmoid" formed in experimental electrical discharge breakdown in a cathode ceramic tube filled by a conductive liquid. Measured parameters were applied to the model in order to improve it. Qualitative agreement observed between behavior of the experimental "plasmoid" and model results. Temperature distribution results also agree with experiment in which temperature of 2000 K was registered.

Electrohydrodynamic effects over liquids under high voltage electrode are considered in experiments with corona discharge. Simple theory is applied for description of a funnel appearance over a liquid is presented. New types of electrohydrodynamic instabilities are revealed.

An analysis of the problem of so-called "abnormal" fast transfer of electrons in tokamak plasma, which turned out much faster than the result of accepted calculation, is given. Such transfer of hot electrons leads to unexpectedly fast destruction of the inner tokamak wall with ejection of its matter in plasma volume, what violates a condition of plasma confinement for controlled thermonuclear fusion. It is shown, taking into account real physics of electron drift in the gas (plasma) and using the conservation law for momentum of electron transfer (drift), that the drift velocity of elastically scattered electrons should be significantly greater than that of accepted calculation. The reason is that the relaxation time of the momentum of electron transfer, to which the electron drift velocity is proportional, is significantly greater (from 16 up to 4 times) than the electron free path time. Therefore, generally accepted replacement of the relaxation time, which is unknown a priori, by the electron free path time, leads to significant (16 times for thermal electrons) underestimation of electron drift velocity (mobility). This result means, that transfer of elastically (and isotropically) scattered electrons in the gas phase should be so fast, and corresponds to multiplying coefficient (16), introduced by D. Bohm to explain the observed by him "abnormal" fast diffusion of electrons.

The causes of the appearance of a solar wind consisting of protons, alpha particles and electrons arising as a result of ionization processes of atoms and molecules focusing to the Sun by gravitational forces are investigated. It is shown that a possible explanation of the occurrence of the solar wind is a slight violation of the neutrality of the Sun and the appearance of Coulomb mirrors for protons and alpha particles that reflect and accelerate light, positively charged particles. The parameters of the positively charged Sun are defined, allowing to estimate the reduced electric field in the photosphere, the chromosphere, the Sun's corona and to study the conditions necessary for reflection of positively charged particles from the positively charged Sun.

The report provides a review of the experimental material on superconductivity (SP) accumulated by 2017, a critical analysis of the Bardeen-Cooper-Schrieffer theory (BCS) has been given, and a new model of the super-conductivity effect proposed in works of V.A. Chizhov has been presented. The new model allows to understand the mechanism of the SP formation and to explain many experimental facts on the basis of the theory of pro-cesses occurring in the ideal defect of the crystal lattice – the twinning boundary (MSC-TB). Specific materials, including new ones, are described, which, in accordance with the theory of MSC-TB, should have improved properties of SC, promising directions for further research are formulated.

Astronomical data indicate a presence of dark matter (DM) in the space, what is necessary for explanation of observed dynamics of the galaxies within Newtonian mechanics. DM, at its very low density (∼10^-26kg/m³), constitutes main part of the matter in the Universe, 10 times the mass of all visible cosmic bodies. No doubt, namely properties of DM, which fills space, must determine its physical properties and fundamental physical laws. Taking into account observed properties of cosmic microwave background radiation (CMBR), whose energy is ∼90% of all cosmic radiation, and understanding that this radiation is produced by DM motion, conservation laws of classical physics and principles of quantum mechanics receive their materialistic substantiation. Thus, CMBR high homogeneity and isotropy (∼10^-4), and hence the same properties of DM (and space) justify momentum and angular momentum conservation laws, respectively, according to E. Noether's theorems. CMBR has black body spectrum at ∼2.7K with maximum wavelength ∼1.9·10^-3m, what allows calculate the value of mechanical action produced by DM thermal motion (∼7·10^-34 J·s). This value corresponds well to the Planck's constant, which is the mechanical action too, what gives materialistic basis for all principles of quantum mechanics. Obtained results directly confirm the reality of DM existence, and show that CMBR is an observed display of DM thermal motion. Understanding that namely from DM occur known creation of electron-positron pairs as contrarily rotating material vortexes (according to their spins) let substantiate positron nature of ball lightning what first explains all its observed specific properties.

Theoretical models developed in the MRSU group under leadership of Professor Artem Dadivanyan in area of the LC orientation and photo-induced effects are presented. Angular distribution functions of the dye and liquid crystal molecules under action of intensive light beam have been derived. The number of molecules in cluster is estimated. A model of dimers formation in the photoalignment dye is suggested that explains influence of the dye molecular structure on both polar and azimuthal anchoring energy.

We carried out the modeling orientation of the dyes CD–1 and SD–1 relative to the surface of oligodimethysiloxane using the atom–atom potentials method. We have discovered the dependence of the interaction energy in dyes molecules on the angles which characterizes their orientation relative to the surface of the oligodimethysiloxane crystal. It was found out that the obtained energy value of interaction with the surface can explain weak adhesive qualities of the dyes and the orientation type relative to the surface. We identified the break– loose force for the dyes on the oligodimethysiloxane crystal surface.

The variational calculus by Leonhard Euler is the basis for modern mathematics and theoretical physics. The efficiency of variational approach in statistical theory of liquid-crystal state and in general case in condensed state theory is shown. The developed approach in particular allows us to introduce correctly effective pair interactions and optimize the simple models of liquid crystals with help of realistic intermolecular potentials.

A design of an LED lamp with controllable shape and intensity of the light beam formed is described. The effect is achieved by dividing the light irradiating area for four section and their special fixation and fastening.

The article is an attempt to create a model built using Eulerian circles (Venn diagrams) to illustrate the methodological impact of recent Federal Law 283-FZ "On the independent evaluation of qualifications" and new Federal State Educational Standards of higher education of generation 3++ on educational process in Russia. In modern economic conditions, the ability to correctly assess the role of professional standards, as a matter of fact, some set, the degree of intersection with the approximate basic educational program and the Federal State Educational Standards becomes an important factor on which in the future will depend not only the demand of graduates in the labor market, but also the possibility of passing the professional and public accreditation of the proposed program.