## Conference submissions

#### Mathematical and computer modeling of the nonlinear dynamics of particle beams in cyclic accelerators

Evgenii Krushinevskii1 , Sergei Andrianov2

1Saint-Petersburg State University, Faculty of Applied Mathematics and Control Processes , Russian Federation
2Saint-Petersburg State University, Faculty of Applied Mathematics and Control Processes , Russian Federation

###### Abstract

The article explores the methods of mathematical and computer modeling of the nonlinear dynamics of particle beams in cyclic accelerators in terms of the matrix formalism using both numerical and symbolic representations of the corresponding nonlinear differential equations. This paper shows how the matrix formalism approach allows the use of modern computational algorithms and artificial intelligence methods for more efficient and flexible modeling of particle beam dynamics in accelerators. Also, the article proposes a method of representing control elements using LEGO objects, which makes it possible to increase the efficiency of using control elements from a computational point of view and to facilitate the process of modeling particle dynamics.

#### Model for assessing the influence of factors on a country's competitiveness in the global economy

1Kazan Federal Universitu, Institute of International Relations, Russian Federation

###### Abstract

In the work, based on the analysis of the countries-leaders of competitiveness, it was revealed that all of them among the most developed sectors of the economy had components of the competitiveness index related to innovative development and infrastructure. This suggests that it is the sectors of innovation and infrastructure that can be considered strategically important and make efforts for their development. Therefore, it makes sense to build models related to these areas. The paper presents two macroeconomic models for assessing the influence of factors on competitiveness, one of which will be innovation-oriented, and the second - infrastructure-oriented. These models use spatial data reflecting the assessments of 111 countries for a number of indicators produced by international organizations such as the World Economic Forum, the World Bank, and the World Intellectual Property Organization. Data for the Russian Federation are not included in the sample, since they will be used later to verify the results of the models.

#### Model for assessing the influence of factors on a country's competitiveness in the global economy

1Kazan National Research Technological University, Institute for Innovation Management, Russian Federation

###### Abstract

In the work, based on the analysis of the countries-leaders of competitiveness, it was revealed that all of them among the most developed sectors of the economy had components of the competitiveness index related to innovative development and infrastructure. This suggests that it is the sectors of innovation and infrastructure that can be considered strategically important and make efforts for their development. Therefore, it makes sense to build models related to these areas. The paper presents two macroeconomic models for assessing the influence of factors on competitiveness, one of which will be innovation-oriented, and the second - infrastructure-oriented. These models use spatial data reflecting the assessments of 111 countries for a number of indicators produced by international organizations such as the World Economic Forum, the World Bank, and the World Intellectual Property Organization. Data for the Russian Federation are not included in the sample, since they will be used later to verify the results of the models.

#### Model for assessing the influence of factors on a country's competitiveness in the global economy

1Kazan National Research Technological University, Institute for Innovation Management, Russian Federation

###### Abstract

In the work, based on the analysis of the countries-leaders of competitiveness, it was revealed that all of them among the most developed sectors of the economy had components of the competitiveness index related to innovative development and infrastructure. This suggests that it is the sectors of innovation and infrastructure that can be considered strategically important and make efforts for their development. Therefore, it makes sense to build models related to these areas. The paper presents two macroeconomic models for assessing the influence of factors on competitiveness, one of which will be innovation-oriented, and the second - infrastructure-oriented. These models use spatial data reflecting the assessments of 111 countries for a number of indicators produced by international organizations such as the World Economic Forum, the World Bank, and the World Intellectual Property Organization. Data for the Russian Federation are not included in the sample, since they will be used later to verify the results of the models.

#### On the two-component generalization of the (2+1)-dimensional Davey-Stewartson I equation

Nurzhan Serikbayev1 , Gulgassyl Nugmanova2 , Ratbay Myrzakulov3

1L.N.Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
2L.N. Gumilyov Eurasian National University, Mathematical and computer modeling, Kazakhstan
3L.N. Gumilyov Eurasian National University, Department of General and Theoretical Physics, Kazakhstan

###### Abstract

The geometric-gauge equivalent of the famous Ishimori spin equation is the (2+1)-dimensional Davey-Stewartson equation, which in turn is one of the (2+1)-dimensional generalizations of the nonlinear Schrodinger equation. Multicomponent generalization of nonlinear integrable equations attract considerable interest from both physical and mathematical points of view. In this paper, the two-component integrable generalization of the (2+1)-dimensional Davey-Stewartson I equation is obtained based on its one-component representation, and the corresponding Lax representation is also obtained.

#### A discrete Nambu bracket for 2D extended Magnetohydrodynamics

Dimitrios Kaltsas1 , Michael Kraus2 , George Throumoulopoulos3

1University of Ioannina, Physics Department, Greece
2Max-Planck-Institut für Plasmaphysik and Technische Universität München, , Germany
3University of Ioannina, Physics Department, , Greece

###### Abstract

In this note we propose a trilinear bracket formulation for the Hamiltonian extended Magnetohydrodynamics (XMHD) model with homogeneous mass density. The corresponding two-dimensional representation is derived by performing spatial reduction on the three-dimensional bracket, upon introducing a symmetric representation for the field variables. Subsequently, the trilinear bracket of the resulting two-dimensional, four-field model is discretized using a finite difference scheme, which results in semi-discrete dynamics that involve the Arakawa Jacobian. Simulations of planar dynamics show that this scheme respects the desired conservation properties to high precision.

#### Generalized susceptibility of a screw dislocation in ferroelastics near structural phase transition

1Voronezh State Technical University, Higher mathematics and physical and mathematical modeling, Russian Federation
2Voronezh State Technical University, Higher mathematics and physical and mathematical modeling, Russian Federation

###### Abstract

Small amplitude bending vibrations of a screw dislocation in ferroelastic crystal is considered. Based on the full set of equations describing the vibrations of a crystal with a dislocation near the structural phase transition, written equations for the dynamics of linear sсrew dislocation in the linear approximation of the dislocation displacement. Fourier transform of the Peach-Koehler force projection on the dislocation slip plane is obtained. Linear response function of a screw dislocation in ferroelastics to an external force is found.

#### Scenario of the evolution of the universe with equation of state of the Weierstrass type gas

Pyotr Tsyba1 , Zinaida Barkova2 , Sabit Bekov3 , Olga Razina4 , Ratbay Myrzakulov5

1L N Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
2L.N. Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
3L.N. Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
4L N Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
5L.N. Gumilyov Eurasian National University, Department of General and Theoretical Physics, Kazakhstan

###### Abstract

In this article, we examined the Starobinsky gravity model in homogeneous and isotropic space-time described by the Friedman-Robertson-Walker metric. In the framework of this model, cosmological parameters were described that describe it in the early and late evolutionary times, such as the slow roll parameters, perturbation of curvature, scalar-tensor ratio, equation of state parameter and deceleration parameter. For reconstruction, an ansatz of a special type was chosen, which can be considered a generalization of the Chaplygin type of gas. The energy conditions are also calculated for this model. Dependencies of these parameters on cosmological time are plotted graphically.

#### Cosmological solutions of F(R,T) gravity model with k-essence

Koblandy Yerzhanov1 , Bekdaulet Meirbekov2 , Gulnur Bauyrzhan3 , Ratbay Myrzakulov4

1L.N.Gumilyov Eurasian National University, Department of general and theoretical physics, Kazakhstan
2L.N.Gumilyov Eurasian National University, , Kazakhstan
3L.N.Gumilyov Eurasian National University, Department of general and theoretical physics, Kazakhstan
4L.N. Gumilyov Eurasian National University, Department of General and Theoretical Physics, Kazakhstan

###### Abstract

Now exist several alternative cosmological models that describe observable properties of our universe. In particular, it is such models as $F(R)$ and $F(T)$ gravity. We consider properties of their generalization as $F(R,T)$ model of gravity with k−essence. We obtained some exact solutions of particular cass of scale factor $a$ for general formof the $F(R,T)$ functions with scalar field. These solutions describe the accelerated/deccelerated periods of the universe.

###### Acknowledgements:

The work was carried out with the financial support of the Ministry of Education and Science of the Republic of Kazakhstan, Grant No. 0118RK00935.

#### Cosmological Yang-Mills model with k-essence

Olga Razina1 , Pyotr Tsyba2 , Ratbay Myrzakulov3 , Bekdaulet Meirbekov4 , Zamzagul Shanina5

1L N Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
2L N Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
3L.N. Gumilyov Eurasian National University, Department of General and Theoretical Physics, Kazakhstan
4L.N.Gumilyov Eurasian National University, , Kazakhstan
5L.N.Gumilyov Eurasian National University, Department of General & Theoretical Physics , Kazakhstan

###### Abstract

The possibility of explaining the accelerated expansion of the universe based on a modification of Einstein's equations is considered. In this paper we consider the $f(R)$ model of gravity with Yang-Mills field $F^a_{\mu\nu}F^{\mu\nu a}$ and $k$-essence in four dimensions together with a homogeneous, isotropic and flat Friedman-Robertson-Walker universe. The introduction of the Yang-Mills field for $f(R)$ gravity makes it possible to consider new models for studying the observed accelerated expansion of the universe. For this model, a system of equations of motion is found, an exponential solution is constructed and scalar potential is reconstructed. Using the slow roll parameters, we studied the inflationary period and the possibility of getting out of it. For later times, the parameter of the equation of state $\omega$ and the deceleration parameter $q$ are found, the value of which corresponds to the accelerated expansion of the universe.

#### Cosmological model of F(T) gravity with fermion fields via Noether symmetry

Nurgissa Myrzakulov1 , Sabit Bekov2 , Shamshyrak Myrzakulova3 , Ratbay Myrzakulov4

1LN Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
2L.N. Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
3LN Gumilyov Eurasian National University, General and theoretical physics, Kazakhstan
4L.N. Gumilyov Eurasian National University, Department of General and Theoretical Physics, Kazakhstan

###### Abstract

In this article, we investigate the modified F(T) gravity, which is non-minimally coupled with the Dirac (fermion) field in Friedmann-Robertson-Walker space-time. Point-like Lagrangian is derived and modified Friedmann equations and Dirac equations for the fermion field are obtained by using the Lagrange multiplier. The Noether symmetry method related to differential equations is a useful tool for studying conserved quantities. In addition, this method is very useful for determining the unknown functions that exist in the point-like Lagrangian. Using this method, the form of the coupling between gravity and matter, the self-consistent potential, the symmetry generators, the form of F(T) gravity and the first integral (Noether charge) or a conserved quantity for this model are determined. Cosmological solutions that have a power-law form and describe the late time accelerated expansion of the Universe are obtained.

###### Acknowledgements:

This work was supported by the Ministry of Education and Science of Kazakhstan under grants 011800935 and 011800693.

#### Traveling wave solutions for the (3+1)-dimensional Davey-Stewartson equations

Nurzhan Serikbayev1 , Gaukhar Shaikhova2 , Kuralay Yesmakhanova3 , Ratbay Myrzakulov4

1L.N.Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
2L. N. Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
3L. N. Gumilyov Eurasian National University, Department of Mathematical and Computer Modeling, Kazakhstan
4L.N. Gumilyov Eurasian National University, Department of General and Theoretical Physics, Kazakhstan

###### Abstract

In this work, the extended tanh method is used to construct traveling wave solutions for the (3+1)-dimensional Davey–Stewartson equations. The extended tanh method is a powerful solution method for obtaining different kind solutions of nonlinear evolution equations. This method can be applied to nonintegrable equations as well as to integrable ones.

#### Noether symmetry approach in f(T,B) gravity with fermionic field

Kairat Myrzakulov1 , Aziza Altaibayeva2 , Duman Kenzhalin3 , Ratbay Myrzakulov4

1Eurasian National University, Department of General & Theoretical Physics, Kazakhstan
2LN Gumilyov Eurasian National University, , Kazakhstan
3L.N. Gumilyov Eurasian National University, Kazakhstan, Department of General & Theoretical Physics, Kazakhstan
4L.N. Gumilyov Eurasian National University, Department of General and Theoretical Physics, Kazakhstan

###### Abstract

In this paper, we consider a model with a fermionic field that is non-minimally coupled to f(T,B) gravity for the flat Friedman-Robertson-Walker metric. Friedmann equations are derived for our model. By using the Noether symmetry approach forms of the function f(T,B), the coupling function F(Ѱ) and the potential function V(Ѱ) are determined. Finally, we obtain the cosmological solution for scale factor, which to describe the late-time expansion of the Universe.

###### Acknowledgements:

This work was supported by the Ministry of Education and Science of Kazakhstan under grants 011800935 and 011800693.

#### Cosmology of f-essence with inhomogeneous viscous fluid

Shynaray Myrzakul1 , Moldir Arzimbetova2 , Musat Imankul 3 , Ratbay Myrzakulov4

1L. N. Gumilyov Eurasian National University, Genaral and teoretical physics, Kazakhstan
2al-Farabi Kazakh National University, Teoretical and nuclear physics, Kazakhstan
3al-Farabi Kazakh National University, Teoretical and nuclear physics, Kazakhstan
4L.N. Gumilyov Eurasian National University, Department of General and Theoretical Physics, Kazakhstan

###### Abstract

F-essence is a generalized form of fermion fields. In this paper, we study the dynamics of f-essence with a viscous fluid in the flat Friedmann-Robertson-Walker universe. Various types of viscous fluids are analyzed and the possibility of reproducing the current accelerating expansion of the Universe is investigated. The cosmological parameters of this model are determined. It is shown that accelerated expansion can also be obtained with a viscous fluid of the fermion field, as in the case of non-interacting perfect fluid considered in most modern models of accelerated expansion of the Universe.

#### Flood estimation for Zhabay River Basin in Akmola region

Berik Rakhimzhanov1 , Abylaikhan Murat2 , Gaukhar Shaikhova3

1JSC «National company «Kazakhstan Gharysh Sapary, JSC «National company «Kazakhstan Gharysh Sapary, Kazakhstan
2JSC «National company «Kazakhstan Gharysh Sapary, JSC «National company «Kazakhstan Gharysh Sapary, Kazakhstan
3L. N. Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan

###### Abstract

This paper presents results of a study carried in Akmola region, aimed at analyzing the flood frequency of Zhabay River Basin. The estimate has been carried out on the Zhabay river employing flood frequency analysis method.

#### Geometric characteristics for Camassa-Holm equation

Assem Mussatayeva1 , Nurgissa Myrzakulov2 , Aziza Altaibayeva3

1L.N.Gumilyov Eurasian National University, Department of General and Theoretical Physics, Kazakhstan
2LN Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
3LN Gumilyov Eurasian National University, , Kazakhstan

###### Abstract

One of the actual problems of mathematical physics is to relate differential geometry and nonlinear differential equation. Research in this direction is very important, as the results are a theoretical and practical application. In this paper, we investigate the Camassa-Holm equation. It is well known that the integrable nonlinear Camassa-Holm equation plays an important role in the study of wave propagation. We present the relationship between the Camassa-Holm equation and soliton surfaces. The first and second fundamental forms, surface area and curvature for the Camassa-Holm equation are found.

###### Acknowledgements:

The authors would like to thank the organizers of the 8th International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) for the kind invitation to present this talk. This work was supported by the Ministry of Education and Science of Kazakhstan under grants 011800935 and 011800693.

#### Numerical modeling of Liesegang structures formation process under an electric field influence

Victor Kireev1 , Bakyt Shalabayeva2 , Nurbolat Jaichibekov3 , Adelina Nizamova4 , Zhanserik Kozhabay5

1Bashkir State University, Applied Physics, Russian Federation
2L.N. Gumilyov Eurasian National University, Faculty of mechanics and mathematics, Kazakhstan
3L.N.Gumilyov Eurasian National University, Faculty of mechanics and mathematics, Kazakhstan
4Mavlutov Institute of Mechanics, Mechanics of Multiphase Systems, Russian Federation
5L.N.Gumilyov ENU , Kazakstan, Faculty Mechaniks and mathematics , Kazakhstan

###### Abstract

In the present paper the formation of Liesegang structures, i.e. the process of periodic deposition with the mutual diffusion of two reacting chemicals in the presence of an external constant electric field, is studied using numerical modeling. The mathematical model of the process consists of three differential equations of diffusion-reaction for the concentrations of the initial components and the resulting precipitate. The kinetics of sedimentation is described in accordance with the Ostwald’s supersaturation theory. The equations of the mathematical model in one-dimensional and two-dimensional statements were solved numerically using the control volume method using computer code written by the authors in the C ++ language. As a result of numerical simulation in the absence of an electric field, periodic structures were obtained formed of the precipitate, which qualitatively corresponds to the patterns observed in the experiments. It is shown that numerically obtained Liesegang rings satisfy the well-known laws: the ratio of the distances to neighbouring rings remains constant and there is a power dependence between the distances to the rings and the time of their formation. The influence of the ratio of the concentration of the starting substances and the electric field strength on the nature of the structures formed is investigated. It also has been shown that an increase in the electric field strength leads to anincrease in the number of structures formed.

###### Acknowledgements:

The research was executed by the grant of the Ministry of education and science of the Republic Kazakhstan: The authors were supported by the grant AP05134098 of SC of the MES of RK.

#### Probabilistic estimate of indoor radon distribution in Abruzzo (central Italy)

Antonio Pasculli1 , FABIO RIZZO2

1University of G. D’Annunzio, Department of Engineering and Geology (InGeo), Italy
2G. D'ANNUNZIO UNIVERSITY, ENGINEERING AND GEOLOGY, Italy

###### Abstract

Since some years ago in Abruzzo, a region located in the middle part of Italy, the Environment Protection Regional Agency (ARTA), within a national program framework, has been carrying out studies aimed to assess the geographic hazard distribution of indoor radon concentrations and to estimate the possible existence of high concentrations areas (radon prone areas). Radon in buildings can reach relatively high concentrations, depending on a number of factors (ground and housing characteristics, ventilation rates and so on). Through a number of monitoring campaigns a set of more than 1900 measures has been acquired. Thus, on the basis of these public experimental data, different statistical approaches, aimed to estimate the probability to exceed the level of 200 Bq/m3 (lower than 300 Bq/m3, threshold value currently recommended by the Euratom commission for indoor radon risk acceptability), taken just as a working reference value, have been selected and discussed in this paper. Essentially, ‘Monte Carlo Empirical Bayesian approach’, ‘Bootstrap’ and ‘Gibbs samplers’ methods have been applied and the results have been partially compared. Moreover, some insights on the minimum number of samples, needed to assess the probability distribution as reasonable as possible, are provided.

#### Evaluating the connectivity, continuity and distance norm in mathematical models for community ecology, epidemiology and multicellular pathway prediction.

Wilfried Allaerts1

1Biological Publishing A&O and Erasmus MC, Rotterdam, Immunology, Netherlands

###### Abstract

The main global threats of the biosphere on our planet, such as a global biodiversity impairment, global health issues in the developing countries, associated with an environmental decay, unnoticed in previous eras, the rise of greenhouse gasses and global warming, urge for a new evaluation of the applicability of mathematical modelling in the physical sciences and its benefits for society. In this paper, we embark on a historical review of the mathematical models developed in the previous century, that were devoted to the study of the geographical spread of biological infections. The basic notions of connectivity, continuity and distance norm as applied by successive bio-mathematicians, starting with the names of Volterra, Turing and Kendall, are highlighted in order to demonstrate their usefulness in several new areas of bio-mathematical research. These new areas include the well-known fields of community ecology and epidemiology, but also the less well-known field of multicellular pathway prediction. The biological interpretation of these abstract mathematical notions, as well as the methodological criteria for these interpretative schemes and their corroboration with empirical evidence are discussed. In particular, we will focus on the boundedness norm in polynomial Lyapunov functions and its application in Markovian models for community assembly and in models for cellular pathways in multicellular systems. Finally, the usefulness of hybrid mathematical modelling in miscellaneous biological, environmental and public health issues will be discussed.

#### Eu-induced lattice vibrations in Gd2O3 crystals

Anatoly Zatsepin1

1Ural Federal University, Institute of Physics and Technology, Russian Federation

###### Abstract

The effect of trivalent Eu ion on the atomic structure and the vibrational spectrum of cubic Gd2O3 is investigated. This study was performed by means of computer modeling within the framework of a shell model. The equilibrium structures and the phonon symmetrized local densities of states have been calculated. In addition, frequencies of localized vibrations induced by Eu impurity have been determined. These frequencies are compared with the available experimental data in literature.

###### Acknowledgements:

The work was supported partially by the Ministry of Education and Science of the Russian Federation (Government Task No. 3.1485.2017/4.6) and by Act 211 of Government of the Russian Federation, contract № 02.A03.21.0006

#### Simulation of AlGaP heterostructures and LEDs

Oleg Rabinovich1

1NUST MISIS, Semiconductor devices, Russian Federation

###### Abstract

Changing LED performance characteristics, depending on Indium atoms concentration and at different temperatures were simulated. It was suggested that a heterostructure having p-n junction area S0 can be considered as a sum of “SmallLED” electrically connected in parallel. Good correlation in simulation and experimental results has been obtained. It was determined that the best AlGaP heterostructure contains 5 wide QW (width 10 nm each) in active region. The main thing is that in central ones there is maximum radiation and at the both ends of active region are “barriers” which help to concentrate electrons/holes in active region and additionally “protect” QW from different defects.

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#### Simulation of tandem solar cell based on perovskite

Oleg Rabinovich1

1NUST MISIS, Semiconductor devices, Russian Federation

###### Abstract

In this paper we present p-i-n GaAs & perovskite PV cells comparison of in-series or in-parallel connection. It is made based on the two tandems types with a non-monolithic connection and experimental sub-cells. The results based on tandems simulation are discussed. It is shown that the in-parallel connection is preferable than in-series even when the sub-cell photocurrents are not balanced and the open circuit voltages (Voc) are close to each other. In-parallel connection cell efficiency more than 22 % is demonstrated for the GaAs shading effect by MAPbI3 film, with an achieved short-circuit current density (Jsc) - 39 mA/cm2.

###### Acknowledgements:

The work was carried out with the financial support of the Ministry of Education and Science of the Russian Federation within the framework of the state task to the university № 3.2794.2017/4.6

#### DEVELOPMENT OF MATHEMATICAL MODELS OF CHEMICAL-TECHNOLOGICAL SYSTEMS OF BENZENE PRODUCTION

Yerbol Ospanov1

1Shakarim University, cathedra “Automation and Computer Engineering“, Kazakhstan

###### Abstract

This paper proposes a method for development of model systems based on various information considering example of technological system of benzene production and researching problems of combined model construction, i.e. sets of mathematical models that enable to extensively describe work of complex chemical-technological systems (CTS). Mathematical models are built for fractionating and benzene columns, CTS primary units on benzene production of Atyrau refinery. On the basis of proposed method, it has been established that it is optimum to design combined models for these units, i.e. volumes of target products at the exit are defined using regression models, whereas quality indicators of product are determined using fuzzy models. Influence of aromatic hydrocarbons in reformatte on average octane number of benzene is determined based on logical rules of conditional proof and linguistic models according to knowledge base.

#### Application the random matrix theory to vibrational properties of amorphous solids

Dmitry Conyuh1 , Yaroslav Beltukov2

1Ioffe Physical-Technical Institute of the Russian Academy of Sciences, , Russian Federation
2Ioffe Institute, , Russian Federation

###### Abstract

In this work, we apply the random matrix theory to the study of vibrational properties of disordered systems with a big number of degrees of freedom, such as amorphous solids. The random matrix theory is applied in many fields, for example, in theoretical neuroscience, computer, and social networks. Different random matrix ensembles are used to identify properties of complex systems with different intrinsic symmetries. Mechanical stability of amorphous solids implies the Wishart ensemble with the positive definite dynamical matrix of the form $\hat{M} = \hat{B}\hat{B}^T$. The translational invariance in amorphous solids leads to the sum rule $\sum_i B_{ij} = 0$, which means non-zero correlations of the matrix elements $B_{ij}$. The proposed correlated Wishart ensemble has many universal properties of amorphous solids. One of these properties is the boson peak in the reduced vibrational density of states $g(\omega)/\omega^2$. The boson peak has been observed in many experiments on amorphous solids, but its nature was not clear so far. We show that the boson peak naturally occurs in the proposed model and find its analytical form.

###### Acknowledgements:

This work is supported by the Russian Federation President Grant no. MK-3052.2019.2.

#### Eu-induced lattice vibrations in Gd2O3 crystals

Alexey Kislov1 , Anatoly Zatsepin2

1Ural Federal University, Institute of Physics and Technology, Russian Federation
2Ural Federal University, Institute of Physics and Technology, Russian Federation

###### Abstract

The effect of trivalent Eu ion on the atomic structure and the vibrational spectrum of cubic Gd2O3 is investigated. This study was performed by means of computer modeling within the framework of a shell model. The equilibrium structures and the phonon symmetrized local densities of states have been calculated. In addition, frequencies of localized vibrations induced by Eu impurity have been determined. These frequencies are compared with the available experimental data in literature.

###### Acknowledgements:

The work was supported partially by the Ministry of Education and Science of the Russian Federation (Government Task No. 3.1485.2017/4.6) and by Act 211 of Government of the Russian Federation, contract № 02.A03.21.0006

#### Modeling the process of wheel drive slipping with anti-skid devices

Rustem Sakhapov1 , Muhammat Gatiyatullin2 , Regina Nikolaeva3 , Marat Makhmutov4

1Kazan State University of Architecture and Engineering, ROAD CONSTRUCTION MACHINERY, Russian Federation
2Kazan State University of Architecture and Engineering, Road construction machinery, Russian Federation
3Kazan State University of Architecture and Engineering , Road construction machinery, Russian Federation
4Kazan State University of Architecture and Engineering , Road construction machinery, Russian Federation

###### Abstract

This article investigates the increase of traction-coupling properties of propellers, patency of machine-tractor units and decrease of soil compaction. For a propulsor equipped with anti-skid devices, the slippage process is formed due to factors of soil compression by the soil-tread and shear of the soil by tire hooks. With the decrease in the number of detachable hooks, the period when the first hook disengaged and the second has not yet entered in interaction with the ground, increases. At the moment, traction and coupling properties of the wheel are formed only due to the tire hooks. When the detachable hook engages with the soil, the traction capacity of the wheel is made up of the forces of shear of soil "bricks" sandwiched between tire hooks and the forces of soil deformation by detachable hooks. As a result of integrating the dependence of the shear stress and deformation of the soil, a formula was obtained to determine the tangential traction force of the tractor. If the skidding of the wheel assembly depends on the pulling force, then the drag force from the anti-skid device. Using the known dependencies of the slippage of wheeled propellers, dependences are obtained to determine the slippage of the propulsion unit with the anti-skid device. With the increase in the number of anti-skid devices on the wheel, slippage is reduced, however, according to the research, the time required for the assembly and disassembly of the device reduces the interchangeability of the wheel assembly. We calculated he number of anti-skid devices at which the maximum exchange capacity will be reached. The penetration depths at which the maximum efficiency of the wheel assembly running system will be reached are obtained and the results are tabulated.

#### MODELING THE OPERATION OF CLIMATE CONTROL SYSTEM IN PREMISES BASED ON A FUZZY CONTROLLER

Lazzat Sansyzbay1 , Batyrbay Orazbayev2

1L.N.Gumilyov Eurasian National University, Faculty of Information Technology, Kazakhstan
2L.N.Gumilyov Eurasian National University, Faculty of Information Technology, Kazakhstan

###### Abstract

Background. People spend a long period in premises during their life. The parameters of the microclimate, established in the room, directly affect the health of the person and his performance. Therefore, when designing modern buildings, there are increased requirements for creating and providing comfortable conditions for human life and activity. Maintaining the microclimate at a given level is carried out using various automated control systems necessary to regulate specific parameter (temperature, humidity, carbon dioxide concentration). Most of the currently existing microclimate control systems operate on the basis of traditional P, PI, PID controllers. But the work of such systems is effective only in a narrow operating range. With significant fluctuations in environment, it is required to reconfigure the parameters of these regulators each time. In such cases, maintaining comfortable conditions in the room is recommended by using intelligent control technologies, so-called fuzzy control systems, operating in terms of fuzzy logic. Objective. The aim of the paper is to research the possibility of implementation of intelligent control systems to maintain the comfortable microclimate in the premises and checking the adequacy of the system through simulation. Methods. The climate control system is based on fuzzy inference and provides forming the base of fuzzy production rules, fuzzification of input values, aggregation of truth of sub conditions of each rule, activation of conclusions and defuzzification process that generates an output signal to control the smart home functional devices. Procedures of the fuzzy inference and simulation are implemented in the Matlab programming environment using the Fuzzy Logic Toolbox and Simulink packages. Conclusions. The results of the paper showed that the developed intelligent microclimate control system for premises based on fuzzy logic provides a flexible self-tuning of the engineering equipment and maintaining the microclimate parameters at the required level.

#### Mathematical model of the motion of suspended particles in a turbulent flow and their influence on the motion of an unmanned aerial vehicle

Bakyt Shalabayeva1 , Nurbolat Jaichibekov2 , Zarina Kutpanova3 , Altynbek Toleu4

1L.N. Gumilyov Eurasian National University, Faculty of mechanics and mathematics, Kazakhstan
2L.N.Gumilyov Eurasian National University, Faculty of mechanics and mathematics, Kazakhstan
3L.N.Gumilyov Eurasian National University, FACULTY OF INFORMATION TECHNOLOGY, Kazakhstan
4L.N.Gumilyov Eurasian National University, Faculty of Information Technology, Kazakhstan

###### Abstract

A mathematical model of turbulent motion of a non-homogeneous flow is constructed. Based on the pulsation energy balance method, a closed system of equations is obtained for calculating the average velocity and turbidity of a non-uniform flow. The calculation of the pulsation characteristics of the flow with a transverse shift is carried out and the analysis of the effect of the impurity on the pulsation structure of the turbulent flow and its effect on the motion of an unmanned aircraft is carried out. Since the safety assessment and service lifetime of an unmanned aerial vehicle cannot exclude the influence of disturbances in the atmosphere when calculating characteristics.

#### Shortcuts to adiabaticity for a qubit using detuning control

Dionisis Stefanatos1 , Nikos Iliopoulos2 , Vasilios Karanikolas3 , Emmanuel Paspalakis4

1University of Patras, Department of Materials Science, Greece
2University of Patras, School of Natural Sciences, Materials Science Department, Greece
3University of Patras, School of Natural Sciences, Materials Science Department, Greece
4University of Patras, School of Natural Sciences, Materials Science Department, Greece

###### Abstract

In this work we derive novel ultrafast shortcuts for adiabatic rapid passage for a qubit where the only control variable is the longitudinal $z$-field, while the transverse $x$-field remains constant. This restrictive framework is pertinent to some important tasks in quantum information processing, for example the design of a high fidelity controlled-phase gate can be mapped to the adiabatic quantum control of such a qubit. We study this problem in the adiabatic reference frame and with appropriately rescaled time, using as control input the derivative of the total field polar angle (with respect to rescaled time). We first show that a constant pulse can achieve perfect adiabatic rapid passage at only specific times, corresponding to resonant shortcuts to adiabaticity. We next show that, by using on-off" pulse-sequences with appropriate characteristics (amplitude, timing, and number of pulses), a perfect fidelity can be obtained for every duration larger than the limit $\pi/\Omega$, where $\Omega$ is the constant transverse $x$-field. The proposed methodology exploits the advantages of composite pulses in the rescaled time, while the corresponding control $z$-field varies continuously and monotonically in the original time.

###### Acknowledgements:

The research is implemented through the Operational Program Human Resources Development, Education and Lifelong Learning'' and is co-financed by the European Union (European Social Fund) and Greek national funds (project E$\Delta$BM34, code MIS 5005825).

#### Development of the formalism of the discrete element method for the study of the mechanical behavior of liquid-saturated porous materials on a pore scale

Evgeny Shilko1 , Alexandr Grigoriev2 , Alexander Lotkov3

1Institute of Strength Physics and Materials Science SB RAS, Laboratory of computer-aided design of materials, Russian Federation
2(Institute of Strength Physics and Materials Science SB RAS, , Russian Federation
3Institute of Strength Physics and Materials Science SB RAS, , Russian Federation

###### Abstract

Various implementations of the discrete element method (DEM) are widely used for computer modeling of the behavior of solid-phase brittle materials under complex loading conditions and on different spatial scales from microscopic to macroscopic one. A well-known advantage of DEM is the possibility of explicit modeling of the processes of multiple fracture, accompanied by intensive mass transfer and mixing of fragments, as well as of the contact problems. This makes the formalism of discrete elements attractive as an effective tool for studying the evolution of the pore structure of permeable materials with different rheological properties of the solid skeleton. Nevertheless, the use of discrete elements for modeling mechanical processes in liquid-saturated materials at the scale of pores with explicit consideration for the geometry of the pore space and taking into account redistribution of filling liquid faces a number of limitations. The key limitation is the need to develop “hybrid” computational algorithms, in which the liquid phase is modeled by another numerical method (hydrodynamic continuous methods, the Lattice Boltzmann method, smoothed particles hydrodynamics, etc.). The most important problems are connected with the need to match domains modeled by different numerical methods, to correctly specify their interaction and so on. A promising way to solve these principal problems is to develop a generalized formalism of DEM, which allows the simulation of both solid-phase materials and soft matter and their interaction within the framework of a single (unified) particle-based formalism. To solve this problem, we developed a discrete-element model of the mechanical behavior of a liquid in the micropore space of a solid-phase material. The developed model combines the key features of the two particle-based methods: the discrete element method and the dissipative particle dynamics (DPD) method. The latter is widely used to model soft matter (including liquid) at the nano- and microscopic scales. In the framework of the proposed model, the liquid is modeled by an ensemble of elements (particles). Each of them simulates some volume of fluid that interacts with the surrounding volumes of fluid (particles) and the walls of the solid-phase material. The main features of this model are: 1) The liquid is assumed to be linearly compressible, which is modeled in the approximation of homogeneously deformable elements. By the analogy with the DPD method, elements do not resist shear deformation (only the central potential interaction is taken into account). 2) Pairs of liquid elements are able to maintain adhesion under tension conditions (element-element interaction takes into account surface energy). We take this effect into account by using the adhesive interaction force. This attractive force models the attractive van der Waals force. Two approximations to the specifying of this force are proposed: a conventional power function (the force decreases with increasing distance) and a constant force acting up to a certain threshold value of tensile strain in a pair (analogous to the Dugdale cohesive model). 3) By analogy with the DPD method, dissipative and random (Brownian) contributions to the forces of interaction of particles are taken into account. A special relationship is used to determine the necessary values of the Brownian force amplitude and dynamic viscosity coefficient to maintain the specified temperature of the modeled liquid. Using the developed model, we performed a test computer simulation of water filtration in a slit-shaped micropore, which is part of an interconnected micropore network (filtration volume of the carrier), under the pressure gradient. Both the solid-phase and liquid-phase domains were modeled in the framework of a unified approach (by the method of discrete elements). We considered solid walls of the micropore as linear-elastic and isotropic. The mechanical characteristics of the material of micropore walls were specified in accordance with the typical values of the mechanical characteristics of hydroxyapatite (HAP), which is a biocompatible material used in different biomedical applications including transplantology. The physical-mechanical characteristics of liquid particles correspond to the hydromechanical properties of fresh water. The values of adhesion stress and characteristic distance of the action of the adhesion potential in the pairs of liquid particles were estimated based on the magnitude of the surface energy. The results of the test simulation showed the adequacy of the proposed model of the mechanical behavior of a liquid in the solid-phase skeleton and its applicability for solving various problems concerning fluid-solid interaction at the microscale. One of the promising applications of the developed formalism is the modeling of drug transport in the pore space of microporous drug carriers.

###### Acknowledgements:

The work was financially supported by the Russian Federation via the Ministry of Science and Higher Education of the Russian Federation (project identifier RFMEFI60718X0202).

#### Development of cognitive competences in physics in students of Health Sciences and Biology

Jesús González1 , José Escobar2 , Laury García3

###### Abstract

A computational method that contributes to the development of cognitive competences, in students of health sciences and biology of Magdalena University, is based on the use of a novel environment of virtual experiences of physical systems. This article investigates the level of learning achieved through the implementation of virtual laboratories that can be used by the user to work in web environments and mobile devices. Conceptual tests were administered to evaluate students' competences before, during and after instruction. We present some perceptions and comments of the students regarding the virtual laboratories of Newtonian mechanics and we conclude on their effectiveness in the development of cognitive competences.

###### Acknowledgements:

This work was financed by the Universidad del Magdalena (Fonciencias)

#### Micromagnetic simulation of thickness-dependent magnetization reversal processes in elongated iron nanodots

Donlawat Sudsom1 , Christoph Döpke2 , Tomasz Blachowicz3 , Andrea Ehrmann4

1Bielefeld University of Applied Sciences, , Germany
2Bielefeld University of Applied Sciences, , Germany
3Silesian University of Technology, , Poland
4Bielefeld University of Applied Sciences, Faculty of Engineering and Mathematics, Germany

###### Abstract

Micromagnetic simulations were used to investigate magnetization reversal processes in elongated ferromagnetic nanodots, prepared by combining two half-circles with a rectangle. The micromagnetic simulation program OOMMF is based on dynamically solving the Landau-Lifshitz-Gilbert equation of motion. Material parameters were chosen as typical for Fe (iron). Lateral dimensions were in most simulations chosen as 730 nm x 133 nm, while the dot height was varied between 3 nm and 54 nm. For different in-plane angles of the external magnetic field, varying magnetization reversal processes were found with changing dot thickness, offering a possibility to tailor magnetic states by modifying the thickness of the nanodot.

#### Advanced methods of low cost mission design for the Galilean moons exploration

Alexey Grushevskii1

1Keldysh Institute of Applied Mathematics of Russian Academy os Sciences, Department of Space flight mechanics and motion control, Russian Federation

###### Abstract

Design of low-energy space missions using gravity assist maneuvers is a key and pressing research field in modern astrodynamics. By their complexity and popularity, the problems addressing the flights to Jovian moons and other outer planets of the Solar system using gravity maneuvers are of particular interest. The reduction of the spacecraft’s asymptotic velocity and the radiation hazard are really main problems for low-cost Delta V - tours for the Galilean moons exploration. In this work multibody flow adaptive synthesis algorithms to overcome ballistic determinism expressed by exist of the Jacobi integral in the restricted three body problem are developed. It is shown that the diversity of the gravity of the ensemble in the Jovian system, not only complicates the accurate ballistic mission analysis, but, when its multibody effective use, allowing you to tailor flowed algorithms for the constructing scenarios of gravity assist maneuvers for interplanetary missions design, including circumvention of dangerous radiation areas, as well as landing at selected Galilean moon at a reasonable cost, resources and time.

#### Geneva Mechanism Geometric Resolution

Eduardo Martinez1

1Universidad de Monterrey, Industrial Design, Mexico

###### Abstract

Geneva mechanisms have been used to obtain an output intermittent circular motion by the means of a continuous circular motion. It offers the option of having a rest time with between motions in the output link. This paper is intended to provide the geometric resolution of this mechanisms via number of steps and diameter of output link.

#### Simultaneous Ionization Of Projectile And Target In Ortho Positronium - Sodium atom system

DIPALI GHOSH1

1MICHAEL MADHUSUDAN MEMORIAL COLLEGE, DURGAPUR, BURDWAN, WESTBENGAL, INDIA, PHYSICS, India

###### Abstract

As an impact of enhanced advancement of the experimental techniques for the study of Positronium (Ps) impact collisional processes, interest has been created among theoreticians to revise the understanding of fundamental particle- antiparticle -matter interactions. In the present study, sodium atom and ortho positronium (Ps) have been considered as the target and projectile respectively. From the theoretical point of view, the quasi-one electron models of the loosely bound outermost electron and a stationary effective potential due to frozen inner shell electrons are the appealing features of sodium atom where as the neutral Ps atom by virtue of its light mass provides an advantage over charged particles and heavy projectiles. The present calculations have been done with Distorted Eikonal Approximation [1] and in the frame work of model potential formalism [2, 3]. Since this complete breakup process becomes a four body problem, from the theoretical perspective, it is a bit difficult task. The complexity mainly arises due to the internal degrees of freedom of the projectile Ps which must be taken into account. Furthermore, the present study of simultaneous target and projectile ionization in Ps- Sodium system is different from the complete fragmentation of Ps - H system, as the effective model potential of sodium has been considered. The present triple differential cross sections (TDCS) additionally carries the information about the influence of the Ps on the target electron distributions in a static screened potential. Cross sections for positronium impact simultaneous ionization of isolated Na and Ps for the equal energy sharing and the velocity matching between the ejected electrons and the positron, shows that the kinematics depend on both incident energy and collision geometry. References: [1] S. Roy , D. Ghosh and C. Sinha , J. Phys.B, J. Phys. B 38 2145 (2005) [2] G.A. Hart, and P.L. Goodfriend. J. Chem. Phys, 53 448 (1970) [3]. M K Pandey, Y-C Lin and Y K Ho, J. Phys.B, 49 034007 (2016)

#### A Case Study of Closed Universe that Fits the Cosmological Data of Supernovae of Type Ia

1Community College of Qatar, Department of Maths and Sciences, Qatar

###### Abstract

In this paper a case study of an homogeneous and isotropic expanding space-time that expand via expansion of its basic element raises a fundamental distinction between recession movement of matter and space expansion. We prove that observing matter recession at an accelerating rate is not an indication for the acceleration of the universe expansion. More precisely, we show that the observed acceleration in the recession movement of galaxies is naturally due to the space-time deceleration. The case study provides us with a possible space-time with independent movement that might produce the observed behavior of galaxies registered for the redshift $z<0.5$ as well as for the redshift $z>0.5$. This case study calls into question the recent interpretation of the accelerating recession movement of galaxies as indication for the universe acceleration.

#### The Imitation Model Self-Organization Percolation Systems with a History of Genesis.

Alexander Herega1

1Odessa Research and Production Center, Research Department , Ukraine

###### Abstract

It was proposed the imitation computer model of percolation clusters, which are self-organized in the process of genesis. It is investigated two- and three-dimensional cluster systems constructed by the Monte Carlo method. Authors studied how properties of model clusters depend on the interaction parameters and the history of it creation. It is shown how a property of clusters depends on the number of acts of particle interaction, aggregation distance, and on system generation speed. It was obtained the analytical dependences of a number of parameters of the cluster system on the level of self-organization, the characteristic values of the correlation length, and the generation rate of the system.

#### Unifying approach to score based statistical inference in physical sciences

Václav Kůs1 , Richard Finger2

1Czech Technical University in Prague, Department of Mathematics, Czech Republic

###### Abstract

In this contribution the statistical inference based on score functions is developed with the aim of future utilization throughout different fields of physics, for example in detector collision data processing or neutrino prongs matching. New score functions are defined by $$M_\rho (P,P_n)=\sum_{A\in\mathcal{D}_n} P_n(A) \, \rho\left(\frac{P_n(A)-P(A)}{P(A)}\right),$$ where $\mathcal{D}_n$ is a sequence of finite or countable partitions, $P$ and $P_n$ are theoretical and empirical probability measures, while the {\em score kernel} $\rho(\cdot)$ is any function with $\rho(0)=0$, nonincreasing on $(-1,0)$ and nondecreasing on $(0,\infty)$. The corresponding minimum score estimators are also presented. We find that consistency of different estimators in various score functions leads to the well-known consistency in commonly used statistical distances or disparity measures between probability distributions. Conditions under which a specific score function pass to $\phi$--divergence of theoretical and empirical distribution are formulated. Conversely, each $\phi$--divergence is a score function. Furthermore, the minimization of arbitrary divergence score function leads to the classical histogram density estimator and thus can be used to alternative interpretation of histogram based calculations in (high energy) physics. From the score function setup, the Kolmogorov-Smirnov testing statistics can be achieved through absolute score function under the class of mutually complement interval partitioning of the real line. It means that the most popular statistical methods, such as histogram estimation and Kolmogorov goodness of fit testing used in physics, can be covered by one unifying score based statistical approach. Also, these methods were previously successfully applied to data sets originated from the particular material elasticity testing (nondestructive defectoscopy) within Preisach-Mayergoyz space modeling.

###### Acknowledgements:

These results were supported by the research grants SGS18/188/OHK4/3T/14 (MEYS), LTT180001 (MEYS), and GA16-09848S (GACR held at Department of Adaptive Systems, UTIA AV CR).

#### Entropy production rate of diffusivity fluctuations under diffusing diffusivity equation

Yuichi Itto1

1Aichi Institute of Technology, Science Division, Center for General Education, Japan

###### Abstract

A recent experimental study has elucidated, for RNA-protein particles exhibiting anomalous diffusion in cytoplasm of a living cell, that the distribution of diffusivity fluctuations (i.e., fluctuating diffusion coefficient) obeys an exponential law. There, it has been pointed out that this exponential distribution is the maximal entropy distribution. Here, time evolution of entropy associated with diffusivity fluctuations is discussed. The entropy production rate under the diffusing diffusivity equation, which offers a description of the dynamical behavior of the fluctuations, is explicitly shown to be positive. The time-dependent solution of the equation makes it possible to see how the entropy approaches its maximum value. Thus, the exponential law of the fluctuations is dynamically realized as the maximum entropy distribution. The lower bound on a rate that suppresses the entropy production is also presented.

#### Group analysis comparison results for linear evolution equations

Jean-Claude Ndogmo1

1University of Venda, Mathematics, South Africa

###### Abstract

The lie group classification of second order linear evolution equations is performed and the results are compared with those of the ordinary differential equation counterpart. An emphasis in this comparison is placed on the number of equivalence classes and their canonical forms, the transformation reducing equations in a given equivalence class to the canonical form, and the iterative properties of the equations.

#### MATHEMATICAL EVALUATION OF MANAGING THE INVESTMENT ACTIVITY (The Example of Food Industry In The Republic Of Tatarstan)

Tina Vakhitova1 , Landish Gadelshina2 , Liliya Zulfakarova3 , Liliya Garifova4 , Sergei Mokichev5

1Kazan Federal University, Institute of Management, Economics and Finance, Russian Federation
2Kazan Federal University, Institute of Management, Economics and Finance, Russian Federation
3Kazan Federal University, Institute of Management, Economics and Finance, Russian Federation
4Kazan Federal University, Institute of Management, Economics and Finance , Russian Federation
5Institute of Management, Economics and Finance, Kazan Federal University, Economics and Econometrics, Russian Federation

###### Abstract

Now, when the Russian economy entered a positive phase of the cycle in 2017-2018, with minimal losses to adapt to external shocks arising in previous years. Against the background of improving quantitative indicators in Russia and its individual regions, there is a deterioration in the structural parameters that characterize the quality of economic growth. There are certain methodological and organizational bases of regulation of investment activity in the region, making possible to research the investment efficiency evaluation, considering the time lag on the example of the food industry of the Republic of Tatarstan. The article discusses various mathematical approaches and methods of managing the selection of investment projects, macroeconomic factors that are forming the investing appeal of regions and industries.

#### Simulation of disruptions triggered by Vertical Displacement Events (VDE) in tokamak and potential leading edge effect in plasma energy deposition to in-vessel material surfaces

Calin Atanasiu1 , Leonid Zakharov2 , Xujing Li3

1National Institute for Laser, Plasma and Radiation Physics, Bucharest, Romania, Plasma Phyics and Nuclear Fusion, Lab. 22, Romania
2National Institute for Laser, Plasma and Radiation Physics, , Romania
3Hangzhou Normal University, Department of Mathematics, China

###### Abstract

C.V. Atanasiu$^1$, L.E. Zakharov$^{2,3}$ $^1$National Institute for Laser, Plasma and Radiation Physics, Atomistilor 409, MG-36, 077125 Magurele-Bucharest, Romania $^2$LiWFusion, Princeton, NJ 08543, USA, $^3$Department of Physics, University of Helsinki, Finland The key basis for tokamak plasma disruption modeling is to understand how currents flow to the plasma facing surfaces during plasma disruption events [1]. Disruptions on JET were capable of melting the plasma facing beryllium tiles. Similar wall damage in ITER should be assessed. Accordingly, this paper will address two important disruption effects in both mitigated and non-mitigated disruptions in JET and ITER: (a) excitation of vertical disruption during the current quench (i.e., abnormal plasma current ramp down) and (b) calculation of the wetting zone of plasma and plasma facing surfaces and of potential leading edge effect in power deposition to the in-vessel tiles during disruptions. Our work is based on the theory of current sharing between plasma and the wall, revealing Hiro currents as the main leading inductive effect in disruptions [2] and the new mathematical model, called Tokamak MHD (TMHD) [3] specially formulated for disruptions simulation as a replacement of conventional MHD. TMHD considers disruption as fast equilibrium evolution by emphasizing the force balance when the plasma inertia plays no role, while conventional MHD uses the plasma inertia (which is 8-9 orders lower than electromagnetic forces in JET VDEs) as a driver of time evolution causing numerical instabilities. We have found that the most important element of the power deposition is the geometry of the wetting zone and together with 3-D equilibrium can be calculated based on TMHD model. [1] L.E. Zakharov, C.V. Atanasiu, K. Lackner, M. Hoelzl, and E. Strumberger, J. Plasma Phys., 81 515810610 (2015). [2] L.E. Zakharov, Phys. of Plasmas, 15 062507 (2008). [3] L.E. Zakharov, X. Li, Phys. Plasmas 22, 6, 062511, (2015).

#### The differential-q-difference 2D Toda equation: bilinear form and soliton solutions

Bayan Kutum1 , Kuralay Yesmakhanova2 , Gaukhar Shaikhova3

1L.N.Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
2L. N. Gumilyov Eurasian National University, Department of Mathematical and Computer Modeling, Kazakhstan
3L. N. Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan

###### Abstract

In this paper, the differential-q-difference 2D Toda lattice is studied. Hirota’s bilinear technique is applied to it. Soliton solutions are constructed through the resulting bilinear form for the differential-q-difference 2D Toda equation. Interactions between soliton solitons are displayed with different choices of variable coefficients.

#### GEANT4 simulation of the ionization chambers part of complex EAS installation

Nurzhan Saduev1 , Vladimir Oskomov2 , Sergey Shaulov3 , Orazaly Kalikulov4 , Askhat Zhumabayev5 , Yerzhan Mukhamejanov6 , Inesh Kenzhina7 , Nurzhan Yerezep8 , Shinbolat Utey9 , Aleksander Sedov10

1al-Farabi Kazakh National University, Physics and Technology Department, Kazakhstan
2KazNU, , Kazakhstan
3Lebedev Physical Institute, , Russian Federation
4KazNU, , Kazakhstan
5KazNU, PhysTech, Kazakhstan
6KazNU, , Kazakhstan
7KazNU, , Kazakhstan
8KazNU, , Kazakhstan
9KazNU, , Kazakhstan
10KazNU, , Kazakhstan

###### Abstract

It is planned to expand the existing installation for the registration of extensive air showers (EAS) at the Tian-Shan mountain cosmic rays station located near Almaty, Kazakhstan at altitude of 3340 meters above sea level, in collaboration between Lebedev Physical Institute of the Russian Academy of Sciences (Moscow, Russia), Kazakh National University (Almaty, Kazakhstan), Institute of Physics and Technology (Almaty, Kazakhstan), Institute of Ionosphere (Almaty, Kazakhstan). At present, the system for registration of electromagnetic shower component consists of ∼ 100 detector points built on the basis of plastic scintillator plates with the sensitive area of 0.25m2 and 1 m2, spread equidistantly over ∼104 m2 space. The extension of the installation is planned by adding ionization chambers, 3000x70x130 mm in size. The purpose of adding ionization chambers is to register the hadron component of the shower, in order to determine the lateral distribution of the of EAS cores. Ionization chambers are assembled into a section of two mutually perpendicular layers of 25 ionization chambers in each layer. Such an arrangement of ionization chambers allows us to estimate the size of the EAS core. At the preliminary stage, the aforementioned section of the ionization chambers was modeled on GEANT4. Based on the obtained simulation results, the installation is planned to be created.

###### Acknowledgements:

This work was supported by the MES RK PTF program “Fundamental and applied studies in related fields of physics of terrestrial, near-earth and atmospheric processes and their practical application” (IRN: #BR05236494).

#### Properties of the network of semantic relations in the Russian language based on the RuWordNet data

1Kazan Federal University, Institute of Physics, Russian Federation
2Kazan Federal University, Institute of Philology and Intercultural Communication, Russian Federation

###### Abstract

It was previously shown that the WordNet thesaurus has a small-world structure. We obtained a similar result for RuWordNet, a recently created thesaurus of the Russian language, and determined the main characteristics of the network of semantic relations in the Russian language. They are the average length of the path between the vertices, the maximum path length between the vertices, the cluster coefficient and the assortativity coefficient. The distribution of the vertices degrees was also considered. We compared the values of the structural parameters of the networks for WordNet and RuWordNet. A significant difference between RuWordNet and WordNet is that RuWordNet has many semantic relations of the 'POS-synonymy' type (synonymy between words of different parts of speech) that are hardly found in WordNet. The values of structural constants were determined for RuWordNet both regarding this type of relations and without taking into account these relations, which allows one to estimate the influence of relations between parts of speech on the structure of the words network.

#### A Novel Simple Miniaturization Technique for Microstrip Couplers

Denis letavin1

###### Abstract

This paper analyzes the new compact design of couplers based on the use of microstrip lowpass filters. The proposed design achieves significant reduction in coupler size while obtaining the same characteristics as of the conventional coupler. Prototype of the coupler with the central frequency of 1 GHz was produced on the substrate with dielectric permittivity of 4.4. The experimental results showed good agreement with numerical simulations. The size of the rat-race coupler was reduced by 83.7%.

#### Reduced directional coupler through the use of artificial cells

Denis letavin1 , Nikolay Knyazev2

2Ural Federal University, , Russian Federation

###### Abstract

This paper presents the topology of the directional coupler that carries out the power division of 1 to 3. The area of the proposed device was reduced by 72.5% due to the use of artificial cells, whose characteristics are equivalent to quarter-wave segments, with smaller dimensions. Using the NI-AWR Environment 14 program, the topology of the proposed device was developed, with an operating frequency of 1 GHz and on the FR-4 material. Then, using a photolithography, a prototype of the coupler was made and its characteristics were measured using a R&amp;S vector network analyser.

###### Acknowledgements:

Author are grateful for the simulation software NI-AWR Design Environment provided by the National Instruments Company. The research was executed by the grant of the Ministry of education and science of the Russian Federation (project № 8.2538.2017/4.6). The research was performed on equipment of the Urals Federal University common use center.

#### Modelling an experiment to measure the speed of gravity in short distances

Carlos Frajuca1 , Fabio Bortoli2

1IFSP, Mechanics, Brazil
2Instituto Federal de Educação, Ciência e Tecnologia de São Paulo - Campus São Paulo, Department of Mechanics, Brazil

###### Abstract

An experiment to measure the speed of gravitational signals in short distances is been developed with the goal to study its behavior as traveling through a medium. The experiment is composed of 3 sapphire devices suspended in vacuum and cooled down to 4.2 Kelvin. The amplitudes of the central device (detector) is monitored by an ultralow phase noise microwave signal using resonance in the whispering gallery modes. The other two sapphire devices are excited by piezoelectric crystals which make the two devices vibrate at the same frequency and phase. Between the two vibrating devices and the detector, a different medium will placed, then the speed is measured and compared with the case where the medium is pure air. The modeling of the experiment is made assuming the detector as a spring-mass system. The results shows that the detection is possible.

###### Acknowledgements:

The authos acknowledge CNPq and FAPESP.

#### Soliton surfaces for complex modified Korteweg–de Vries equation

Gulnur Bauyrzhan1 , Kuralay Yesmakhanova2 , Koblandy Yerzhanov3 , Sveta Ybyraiymova4

1L.N.Gumilyov Eurasian National University, Department of general and theoretical physics, Kazakhstan
2L. N. Gumilyov Eurasian National University, Department of Mathematical and Computer Modeling, Kazakhstan
3L.N.Gumilyov Eurasian National University, Department of general and theoretical physics, Kazakhstan
4Al-Farabi Kazakh National University, Pre-University Training, Kazakhstan

###### Abstract

In mathematics and physics, one of the main tasks is to relate differential geometry and non-linear differential equations, it means that the study of particular cases of subvarieties, curves, and surfaces are of great importance. Soliton surfaces associated with integrable systems to play an essential role in many problems with the physical application. In this paper, we study the complex modified Korteweg–de Vries (cmKdV) equation. It is well known that the cmKdV equation is a very important integrable equation. We present the relationship between an integrable system and soliton surfaces and namely Lax representation of the cmKdV equation was used to obtain the first and second fundamental forms.

#### Bianchi type-I cosmological model with non-minimally coupled fermion fields via Noether symmetry

Duman Kenzhalin1 , Kairat Myrzakulov2

1L.N. Gumilyov Eurasian National University, Kazakhstan, Department of General & Theoretical Physics, Kazakhstan
2Eurasian National University, Department of General & Theoretical Physics, Kazakhstan

###### Abstract

A cosmological model where a fermion field is non-minimally coupled with the gravitational field in Bianchi type I spacetime is studied. By applying Noether symmetry the possible functions for the coupling and for the potential density of the fermion field are determined. Cosmological solutions are found showing that the non-minimally coupled fermion field behaves as an dark energy describing an accelerated expansion scenario.

#### Numerical simulation of the XXZ Heisenberg magnet

Nurgul Suikimbayeva1 , Pyotr Tsyba2 , Olga Razina3

1L.N.Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
2L N Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
3L N Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan

###### Abstract

We consider the XXZ model of a magnet with spin-1/2. Depending on the configuration of the system for a finite number of spins N in the chain we obtained possible values of energy and momentum.

#### Neural net clustering in the study of electrical grids failures in relation to geomagnetic storms

Agnieszka Siluszyk1 , Agnieszka Gil2 , Renata Modzelewska3 , Szczepan Moskwa4 , Marek Siluszyk5 , Anna Wawrzyńczak6

1Siedlce University of Natural Sciences and Humanities, Faculty of Sciences, Poland
2Siedlce University, , Poland
3Siedlce University, , Portugal
4AGH University of Science and Technology in Krakow, , Poland
5Siedlce University, , Poland
6Siedlce University, Science Faculty, Poland

###### Abstract

Abstract. The space weather and space climate problem is well-known, in specially, for all which deal with investigations of disturbances of satellites operation, failures in ground-based electrical and electronic systems caused by geomagnetic storms. In spite of many studies on the changeable Sun and the uctuations in the interplanetary space triggered by solar-driven disturbances, the question, which of the components of magnetic storms in uences the strongest the electrical and electronic systems is still open. Here, we consider this matter for the data of electrical grids breakdowns having unidenti ed reasons, as well as failures connected to the aging of the infrastructure elements and breakdowns of electronic devices, which occurred during the periods of an increased geomagnetic activity. Mathematical and statistical methods, among them neural net clustering, demonstrate that there exist connections between the groups of the coecients characterizing the state of Earths vicinity during magnetic storms and the number of failures in electrical network in southern Poland.

#### Dispersionless limit of generalized Landau-Lifshitz equation

Zhanna Sagidullayeva1 , Gulgassyl Nugmanova2 , Ratbay Myrzakulov3

1L.N. Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
2L.N. Gumilyov Eurasian National University, Mathematical and computer modeling, Kazakhstan
3L.N. Gumilyov Eurasian National University, Department of General and Theoretical Physics, Kazakhstan

###### Abstract

In this paper, we present the dispersionless limit (quasiclassical limit) of the generalized Landau-Lifshitz equation with a self-consistent vector potential. Using the scale transformation we also obtained the Lax representation, the compatibility condition of which give us the considering system. The results can be used to describe spin waves in magnets and ferromagnets in the absence of dispersive properties of the medium.

#### In search of an efective Monte Carlo method for identi cation of atmospheric contamination source

Piotr Kopka1

1National Centre for Nuclear Research (NCBJ) , Laboratory for Nuclear Energy and Environmental Analyses, Poland

###### Abstract

We present the Bayesian framework able to identify the source of the airborne contaminant. We compare the effectiveness of framework utilizing the three popular Monte Carlo algorithms with the use of data from the full-scale field experiment - Copenhagen Tracer Experiments. The input data ta are the on-line arriving concentrations of released substance registered by sensors, while the output are the posterior probabilities of four parameters characterizing the contamination source, i.e.: contamination source position (x,y,z) and release rate (q). As the forward model to predict the concentrations at the sensors locations, we use fast response Second-order Closure Integrated Puff model. The performer study present that among the Markov Chain Monte Carlo (MCMC), Sequential Monte Carlo (SMC) and Sequential Monte Carlo Approximate Bayesian Computation (SMC ABC) the last algorithm performed the best in the proposed framework localizing the airborne contaminant source parameters.

#### Soliton surfaces associated with the WDVV equation for n = 3 case

1L.N.Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
2Nazarbayev University, Mathematics, Kazakhstan

###### Abstract

This paper describes the soliton surfaces approach. We constructed the surface associated with the Witten-Dijkgraaf-E.Verlinde-H.Verlinde (WDVV) equations using Sym-Tafel formula, which gives a connec- tion between the classical geometry of manifolds immersed in R_m and the theory of solitons. The so-called Sym-Tafel formula simplifies the explicit reconstruction of the surface from the knowledge of its fundamen- tal forms, unifies various integrable nonlinearities and enables one to apply powerful methods of the soliton theory to geometrical problems. The soliton surfaces approach is very useful in construction of the so-called integrable geometries. Indeed, any class of soliton surfaces is integrable. We consider the geometry of sur- faces immersed in Euclidean spaces. Such soliton surfaces for the WDVV equation for n = 3 case with an antidiagonal metric η_11 = 0 are considered, and first and second fundamental forms of soliton surfaces are found for this case. Also, we study an area of surfaces for the WDVV equation for n = 3 case with an antidiagonal metric η_11 = 0.

#### Soliton surfaces induced by the coupled integrable dispersionless equation with self-consistent sources

Zamzagul Shanina1 , Ratbay Myrzakulov2

1L.N.Gumilyov Eurasian National University, Department of General & Theoretical Physics , Kazakhstan
2L.N. Gumilyov Eurasian National University, Department of General and Theoretical Physics, Kazakhstan

###### Abstract

The coupled integrable dispersionless equations have a significant interest because of structure, integrability, and the possibility of obtaining a soliton solution. In this paper, we construct soliton surfaces for integrable dispersionless equation with self-consistent sources in Riemann space. The surfaces, arising from M-XXXII equation and their reduction in R^3, are studied. We obtain Gaussian and mean curvatures and also evaluate the area of surface parametrically defined with the Riemannian metric. Using the scale transformation and transformation of dependent and independent variables of the coupled dispersionless equations we obtain the equation that describes a current-fed string interacting with an external magnetic field in three-dimensional Euclidean space.

#### Size dependence of the dislocation segment vibration spectrum for various types of dislocations

Igor Bataronov1 , Viktor Dezhin2

1Voronezh State Technical University, Higher mathematics and physical and mathematical modeling, Russian Federation
2Voronezh State Technical University, Higher mathematics and physical and mathematical modeling, Russian Federation

###### Abstract

The vibration spectra of the edge, mixed and screw dislocations, depending on the dislocation segment length, are considered. The value of Poisson's ratio 1/3 is assumed. The normalized values of the eigenfrequencies and damping coefficients for different frequency numbers by equating the inverse matrix of dislocation oscillators generalized susceptibilities [1] to zero were found. It is seen from the dependences obtained that in the case of a screw dislocation the transformation of the dislocation oscillators generalized susceptibility poles occurs. For edge and mixed dislocations the transformation of the poles was not observed. This agrees with the results of the vibration spectrum orientation dependence study. The authors suggest that these differences are due to the presence of a screw dislocation quasilocal vibration branches [2]. 1. Bataronov I.L. and Dezhin V.V. J. Phys.: Conf. Ser. V. 738. 012108. (2016). 2. Bataronov I.L. and Dezhin V.V. J. Phys.: Conf. Ser. V. 936. 012035. (2017).

#### Modelling the control of the motor for a experiment to measure the gravity speed.

Carlos Alberto Junior1 , Carlos Frajuca2 , Davinson Silva3 , Eduardo Sanchez4 , Fabio Bortoli5

1IFSP, , Brazil
2IFSP, Mechanics, Brazil
3FATEC, , Brazil
4IFSP, , Brazil
5Instituto Federal de Educação, Ciência e Tecnologia de São Paulo - Campus São Paulo, Department of Mechanics, Brazil

###### Abstract

Brushless DC motors (BLDCM) are recognized for their high efficiency and low maintenance cost and are continuously subject to change in applications without motion control. The BLDCM can be used as an option to traditional switched reluctance motors. For the control of the speed of permanent magnet motors the more common is an integral proportional control (PI). The PI drivers are widely used because of a simple, easy-to-implement control structure, but they are presented as control complexities, such as non-linearity, parametric load perturbations and protection. The use of this method of pulse control (PWM) using a SIMULINK / MATLAB simulation to obtain the values ​​necessary to control the speed of the brushless motor used in the gravitational wave calibrator prototype. SIMULINK / MATLAB is used to become a reliable and flexible simulation. The command will be used for precision accuracy of a ten thousand version of the calibrator.

###### Acknowledgements:

The authors thanks CNPq and FAPESP.

#### Analysis of the probability distribution of time series of word frequencies

1Kazan Federal University, Institute of Physics, Russian Federation
2Kazan Federal University, Institute of International Relations, Russian Federation

###### Abstract

Knowledge of probability distribution of frequency of words and phrases is important in solving many practical problems such as estimation of semantic similarity between words, detection of semantic changes and others. It is assumed by many researchers that frequencies of words obey the Poisson law. However, there is much evidence that the Poisson distribution describes empirical data unsatisfactory. The analysis of the probability law in this case is greatly complicated by the fact that series of frequencies in most cases are non-stationary. This paper discusses the distribution law of time series of word frequencies based on the Google Books Ngram corpus data. It is shown that the correlation between the first moments of the frequencies differs from that expected in the assumption of the Poisson distribution. In particular, anomalously high values of frequency dispersion are observed for words with high frequency. To check the significance of deviations from the Poisson law, statistical modeling of frequency series was performed. Alternative assumptions about the probability distribution of word frequencies are also considered.

#### Particle-based modeling of the mechanical behavior of porous fluid-saturated viscoelastic solids

Evgeny Shilko1 , Andrey Dimaki2 , Valentin Popov3

1Institute of Strength Physics and Materials Science SB RAS, Laboratory of computer-aided design of materials, Russian Federation
2Institute of Strength Physics and Materials Science of SB RAS, Laboratory of computer-aided design of materials, Russian Federation
3Berlin University of Technology, , Germany

###### Abstract

The regularities of the nonlinear behavior of viscoelastic materials and the related non-stationarity of mechanical characteristics (namely, their dependence on the loading rate) are the issues in a wide range of analytical and computational studies as these features determine the peculiarities of functioning of critical elements of various technical and natural structures including biological ones. A broad subgroup of materials of this class comprises materials with the high contrast of local mechanical properties that contain viscous soft matter phases as structural constituents. Well-known examples are porous fluid-saturated materials, such as rocks, bone and soft tissues, other natural and synthesized biomedical and engineering materials. Interstitial fluid can change the behavior of a material dramatically. In particular, the mechanical interaction of solid-phase and liquid-phase components can determine a strongly pronounced non-linear dependence of the mechanical behavior and effective mechanical characteristics of the material on the loading rate even in a quasistatic region in which the substance of the solid-phase skeleton is insensitive to strain rate. Moreover, at higher loading rates the material response is determined by the ratio of the relaxation times of the skeleton and the characteristic time of redistribution of interstitial fluid in the pore space. The above said determines the relevance of conducting theoretical studies of crucial aspects of nonlinear dynamic behavior (including fracture) of fluid-saturated viscoelastic materials under complex loading conditions. A useful tool for carrying out these studies is computer modeling using the discrete element method (DEM). A key advantage of this particle-based numerical method is the ability to explicitly model fracture processes (including multiple fractures) on various scales from micro- to macroscopic. This makes DEM attractive, in particular, for studying contact interaction, friction and wear in viscoelastic contact pairs of different nature, including articular joints. In this work, we developed a DEM-based model, which allows describing the mechanical behavior of porous fluid-saturated materials with a viscoelastic skeleton. To build the model we used an implementation of DEM, which is called the method of movable cellular automata (MCA). The main feature of this implementation is the use of a generalized many-body formulation of relations for the forces of element-element interaction. Within this formalism, we developed three-dimensional models of permeable fluid-saturated materials with solid skeleton characterized by viscoelastic rheological properties (including Kelvin and Maxwell models and the standard model of elastomers). The influence of the pore fluid on the stress state of the skeleton is taken into account based on the Biot model of poroelasticity. Fluid transport in the pore space is modeled using the finite-volume implementation of the classical equation of fluid mass transfer. Using computer modeling, we obtained the generalized relations, which describe the dependences of uniaxial compressive strength and effective Young's modulus of some kinds of viscoelastic fluid-saturated materials on the strain rate, the relaxation times of the skeleton and the characteristic time of redistribution of fluid in the pore space. We showed for the first time that these dependences are logistic and can be described by common sigmoid “master” functions of the special dimensionless parameter. The relevance of the simulation results is determined by the possibility of their application for assessing and predicting the mechanical response of fluid-saturated viscoelastic technical and natural materials (including bone tissue) under dynamic loading.

###### Acknowledgements:

This research was supported by the Russian Science Foundation (grant No. 17-11-01232).

#### Mathematical models for identifying of individual buyers based on the analysis of large panel data of sales in supermarket

Yuriy Dimitrienko1 , Olga Dimitrienko2 , Alexandra Dobrynina3

1Bauman Moscow State Technical University, Computational Mathematics and Mathematical Physics, Russian Federation
2Bauman Moscow State Technical University, , Russian Federation
3Bauman Moscow State Technical University, Computational Mathematics and Mathematical Physics, Russian Federation

###### Abstract

The problem of identifying individual buyers in a supermarket based on a large amount of data on cashier's checks in a supermarket over a long period of time is considered. A complex of mathematical models for solving this problem using automated numerical data analysis is proposed. A special product space has been built, the concept of the trajectory of the movement of customers in the product space has been introduced A computational algorithm has been developed for solving the problem of identifying individual customers using panel data of cash vouchers. The algorithm is universal because it does not use any personal data. As an example of specific input data, commodity checks from the supermarket chain were used for a certain period of time.

###### Acknowledgements:

Identifying of individual buyers, analysis of large panel data

#### Asymptotic analysis of elastic thin two-layer plates with the slippage of layers

Yuriy Dimitrienko1 , Elena Gubareva2

1Bauman Moscow State Technical University, Computational Mathematics and Mathematical Physics, Russian Federation
2Bauman Moscow State Technical University, Computational Mathematics and Mathematical Physics, Russian Federation

###### Abstract

The problem of the deformation of thin two-layer plates, in which the slip condition is given at the interface between the layers, instead of the classical case of ideal contact, is considered. The method of asymptotic analysis of the 3-dimensional elasticity theory equations is applied to solve this problem when exposed to lateral pressure, longitudinal and shear forces on the end surfaces. Asymptotic analysis is performed on a small geometrical parameter representing the ratio of the thickness to the characteristic length of the plate. Recurrent formulations of local quasi-one-dimensional problems of the theory of elasticity with slippage are obtained. An explicit analytical solutions are obtained for these tasks. The averaged equations of elastic equilibrium of a two-layer plate with slipping layers are derived. It is shown that due to slippage, the order of averaged equations of the theory of plates rises to 5 orders of magnitude, in contrast to the classical 4-th order, which takes place in the theory of Kirchhoff-Love plates. Additional boundary conditions for this system of order 5 are formulated and its analytical solution is obtained for the case of a rectangular plate under the action of uniform pressure. A numerical analysis of the solution of the averaged problem is carried out. It is shown that the presence of slippage of layers significantly increases the plate deflection compared with the conditions of ideal contact of layers

###### Acknowledgements:

The reported study was funded by Ministry of Education and Science of the RF according to the research project (Goszadanie) No. 9.3602.2017/ПЧ

#### Econometric assessment of the world energy market impact on the incomes of the consolidated budget of Russia

Svetlana Absalyamova1 , Liliya Zulfakarova2 , Natalya Ivanova3 , Chulpan Mukhametgalieva4

1Kazan Federal University, Institute of Management, Economics and Finance, Russian Federation
2Kazan Federal University, Institute of Management, Economics and Finance, Russian Federation
3Kazan Federal University, Institute of Management, Economics and Finance, Russian Federation
4Kazan Federal University, Institute of Management, Economics and Finance, Russian Federation

###### Abstract

The article is devoted to the study of modern trends in energy resources megamarket. The results of the study reveal a system of factors affecting the production and consumption of energy resources in the global economy. The authors make a forecast of the development of traditional and alternative energy in the coming decades. The paper assess the degree of influence of the changing conjuncture of the world energy market on the Russian economy. The study shows the presence of high closeness of communication on the Chaddock scale and the direct linear dependence of Russia's GDP at current prices on the volume of oil and gas revenues of the consolidated budget of the Russian Federation, confirmed by calculating the Pearson correlation coefficient. The article proposes a set of measures that reduce the dependence of the Russian budget on the world energy market.

#### NUMERICAL MODELING OF LIESEGANG STRUCTURES FORMATION PROCESS UNDER AN ELECTRIC FIELD INFLUENCE

Nurbolat Jaichibekov1

1L.N.Gumilyov Eurasian National University, Faculty of mechanics and mathematics, Kazakhstan

###### Abstract

Oscillatory chemical reactions, in which the concentrations of reacting substances change periodically, have been the subject of study by scientists of various specialties for more than one hundred years: chemists, physicists, biologists, geologists, physicians, mathematicians [1]. The best-known examples of oscillatory chemicals reactions are Bray-Liebhafsky reaction (1921), Belousov-Zhabotinsky reaction (1958) and Briggs-Rauscher reaction (1972). Liesegang rings (or layers), representing spatial periodic structures, were first discovered by the German chemist Raphael Edward Liesegang in 1896, but a theory has not yet been created that can explain all the mechanisms underlying this periodic reaction [2-3]. Further theoretical and experimental study of the patterns of formation of Liezegang structures can, in particular, contribute to a deeper understanding of the characteristics of sedimentation in various technological processes in petrochemical production. In the present paper the formation of Liezegang structures, i.e. the process of periodic deposition with the mutual diffusion of two reacting chemicals in the presence of an external constant electric field, is studied using numerical modeling. The mathematical model of the process consists of three differential equations of diffusion-reaction for the concentrations of the initial components and the resulting precipitate. The kinetics of sedimentation is described in accordance with the Ostwald’s supersaturation theory. The equations of the mathematical model in one-dimensional and two-dimensional statements were solved numerically using the control volume method using computer code written by the authors in the C ++ language. As a result of numerical simulation in the absence of an electric field, periodic structures were obtained formed of the precipitate , which qualitatively correspond to the patterns observed in the experiments. It is shown that numerically obtained Liesegang rings satisfy the well-known laws: the ratio of the distances to neighboring rings remains constant and there is a power dependence between the distances to the rings and the time of their formation. The influence of the ratio of the concentration of the starting substances and the electric field strength on the nature of the structures formed is investigated. It also has been shown that an increase in the electric field strength leads to a decrease in the number of structures formed.

###### Acknowledgements:

2010 Mathematics Subject Classification: 37N10, 65N08, 80A32

#### Sensivity analysis of impact ionization coefficients in a electronic device

Hugo Aya Baquero1

###### Abstract

Terminal current in a device increases when energetic carriers create additional carriers by impact ionization. Okuto and Crowell suggested an empirical model for describe this phenomenon. In this paper, Monte Carlo techniques were used to observe the effect of variability in the impact ionization coefficients on the results obtained from a computational model for electrons and holes transport. The model was implemented in FEM simulation tool, in order to study avalanche current in a MOSFET including uncertainty of the impact ionization coefficients of material.

###### Acknowledgements:

This project is partially founded by Engineering Faculty of the Universidad Distrital Francisco José de Caldas de Bogotá, inside the Proyecto Curricular de Ingeniería Electrónica.

#### Hodge Ranking as a quantitative tool in social representations theory

Ana Lúcia Pereira1

1State University of Ponta Grossa, Department of Mathematics and Statistics, Brazil

###### Abstract

Social representations were introduced in the social psychology by Moskovici in 1961, and consists in a framework of ideas, concepts, beliefs or feelings shared by individuals in a given group, regarding some social object. Since then, social representations theory evolved both in its conceptual aspects and in the development of methodological tools to analyse data. In the last decades a great effort was made in the development of quantitative tools, as complementary to the most usual qualitative analysis. For instance, graphs of similarity, several techniques of clustering and statistical analysis of frequency and evocation order are often used to analyse the structure of a social representation. In this work we propose to use the technique of Hodge ranking to rank the vertices in a graph as a complementary quantitative tool to reveal the structure of a social representation. This technique provides an ordering of the data elements (ideas, concepts, feelings, etc.), based on the relative importance individuals associate to them, and has the advantage of working fine with imbalanced data, that is often the case in social representations in which individuals evoque ideas spontaneously, sometimes inconsistently. Another advantage of this technique is that it provides measures of the global inconsistencies in the ranking results.

#### Synthesis of Optimal Control for Affine Nonlinear Dynamic System

Armen Bagdasaryan1

1American University of the Middle East, Mathematics, Kuwait

###### Abstract

The problem of synthesis of optimal control of complex nonlinear and multidimensional systems oriented on the building of integrated control systems with the adaptation and selforganization properties is of much current interest. The further development of optimization methods employed in control problems demonstrated their effectiveness and has led to the construction of algorithms of approximate solution of optimization problems that significantly extends the class of control problems that can be set. In this work we consider a synthesis of optimal control for affine nonlinear system, in which a special emphasis is placed on the degenerate problems of optimal control. Our approach is based on the extension of the method of minimization of generalized work function by properly transforming the initial nondegenerate problem of optimal control into degenerate problem of optimal control synthesis. The search for the solution is based on the suboptimal strategy that includes the construction of minimizing sequences that converge intervalwise to the optimal solution of the initial problem. We obtain some optimality conditions as well as the necessary and sufficient conditions of existence of optimal solution.

#### Distribution of ionization times in a model for strong field ionization

1State University of Ponta Grossa, Mathematics & Statistics, Brazil

###### Abstract

The quantum tunneling phenomenon is one of the most counter-intuitive features of quantum mechanics, and the problem of determining the time a particle takes to cross a classically forbidden region has been a very controversial subject since the early days of the theory. Recently, advances in ultrafast physics opened the possibility to measure times of ionization of atoms, induced by the application of a strong laser field, at the scale of attoseconds. However, the intrinsic experimental difficulties associated both with the measurements and the interpretation of the results have, so far, prevented an elucidation of the problem and, in fact, contradictory results still persist, with some experiments obtaining a finite non-zero result and others being compatible with instantaneous tunneling. In this work we consider a simple model for the strong field ionization of an electron that, at $t=0$, is in the bound state of a Dirac delta potential well; immediately after $t=0$ the potential is deformed by the application of a strong linear laser field. We use this model to obtain a probability distribution, recently proposed by the authors, for some times associated to the ionization process, including barrier exit times and tunneling times. Although simple, our model shares qualitative features with real attoclock experiments, and we explore these similarities to discuss the possibility of interpreting the time measurements in those experiments as being tunneling times.

#### The linear responce function of a mixed dislocation in ferroelectrics

1Voronezh State Technical University, Higher mathematics and physical and mathematical modeling, Russian Federation
2Voronezh State Technical University, Higher mathematics and physical and mathematical modeling, Russian Federation

###### Abstract

Bending vibrations of a mixed dislocation in a uniaxial ferroelectrics are considered, the dislocation line is located along the ferroelectric axis. Based on the complete system of equations describing the vibrations of a ferroelectric crystal with a dislocation, system of equations for the mixed dislocation dynamics in a linear approximation in the dislocation displacement is written. An expression for the Peach–Koehler force acting on the dislocation is obtained, and the linear response function of the mixed dislocation is found.

#### DISPERSIONLESS LIMIT OF THE (1+1)-DIMENSIONAL FOKAS-LENELLS EQUATION

Meruyert Zhassybayeva1 , Kuralay Yesmakhanova2 , Ratbay Myrzakulov3

1L.N. Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
2L. N. Gumilyov Eurasian National University, Department of Mathematical and Computer Modeling, Kazakhstan
3L.N. Gumilyov Eurasian National University, Department of General and Theoretical Physics, Kazakhstan

###### Abstract

Nonlinear dispersionless equations can be obtained as dispersionless limits (quasiclassical limits) of integrable hierarchies of equations or by constructing a system of hydrodynamic type. In this paper, the dispersionless limit of the (1+1)-dimensional Fokas-Lenells equation is found. We present Lax pair for this dispersionless equation. As well known, the Fokas-Lenells equation characterizes the propagation of ultrashort nonlinear light pulses in optical fibers. Exact solutions of the dispersionless version of the Fokas-Lenells equation describe nonlinear shock waves in optical fiber systems. By using the obtained results, one can find “shock” wave solutions of the dispersionless equation, which have different physical applications.

#### Optical properties of biological tissues evaluation with a hybrid goniometer and integrating-sphere technique and Monte Carlo mathematical modelling

Nikita Kovalenko1 , Georgii Aloian2 , Denis Mukhankov3 , Oleg Ryabushkin4

1Moscow Institute of Physics and Technology, The School of Electronics, Photonics and Molecular Physics, Russian Federation
2Moscow Institute of Physics and Technology, Electronics, Photonics and Molecular Physics, Russian Federation
3FIRE RAS, Photonics, Russian Federation
4FIRE RAS, Photonics, Russian Federation

###### Abstract

For the morphological study of biological tissues, diagnostics and laser irradiation application in medicine, optical properties of the tissue, such as optical absorption (μa), scattering (μs), scattering anisotropy (g), are necessary to be known. The most common technique for measuring optical properties is based on measurements of diffusion reflection and collimated and diffusion transmittance. These values are usually measured with integrating-spheres technique. Experimental data is afterward fitted with mathematical modeling of the irradiation propagation in the tissue thus tissue optical properties can be evaluated. Usually, samples of different thickness are used, but its preparation is not always possible. For example, when studying thin tissue is it impossible to obtain samples with greater thickness. An alternative approach is based on goniometer measurements that require measurements of the angular dependence of the scattered light. However, such measurements require high precision instruments as scattered power in a small solid angle is measured. Such methods are sensitive to local inhomogeneities of the sample. Another limitation is the long duration of the experiment during which the biological tissue can change its properties. We propose a novel technique for measuring the optical properties of biological tissue samples. The dependence of the scattered radiation power at different solid angles is measured experimentally by changing the distance from the sample to the inlet of the integrating sphere. The Monte Carlo method for multilayer tissues is used for modeling of the radiation propagation in the sample. The optical properties of the sample μa, μs, g are determined by comparing the results of mathematical modeling with the experimental angular dependence of scattered and transmitted light. This approach allows obtaining a larger volume of input data for the model thus increasing the accuracy of calculations even with measurement of only one sample of fixed thickness. The use of integrating spheres virtually eliminates the limitations of classical goniometer measurements. Using this method, the optical properties of the pulp of the aloe arborescens leaf at a wavelength of 589 nm were investigated in this work.

#### Equivalent temperature concept in laser physics and its correspondence with thermodynamic temperature

Georgii Aloian1 , Denis Mukhankov2 , Nikita Kovalenko3 , Oleg Ryabushkin4

1Moscow Institute of Physics and Technology, Electronics, Photonics and Molecular Physics, Russian Federation
2FIRE RAS, Photonics, Russian Federation
3Moscow Institute of Physics and Technology, The School of Electronics, Photonics and Molecular Physics, Russian Federation
4FIRE RAS, Photonics, Russian Federation

###### Abstract

Recently it was proposed to use impedance spectroscopy for the measurement of low optical absorption coefficients of nonlinear-optical crystals, which possess piezoelectric properties. Piezoelectric resonance laser calorimetry (PRLC) determines the equivalent temperature of the sample interacting with laser irradiation by measuring the heating induced frequency shifts of its eigenmodes, noncontactly excited by an external radiofrequency electric field. Temperature calibration of the piezoelectric resonance frequencies of the sample is preliminarily performed during uniform heating. During laser radiation nonuniform heating, the equivalent temperature of the sample is determined by measuring the shifts of its piezoelectric resonance frequencies in accordance with the temperature calibration data. Optical absorption coefficients can be determined by solving the heat conduction problem relying on measured equivalent temperature kinetics of the sample. As a rule, the sample temperature is measured using external thermal sensors. However, absorption of scattered radiation inevitably leads to the additional heating of the sensor and subsequent measurement errors. PRLC approach has certain advantages as in this case the sample itself acts as a temperature detector. One of the possible ways is to use crystals with large apertures so that the radiation intensity does not exceed the optical damage threshold. In order to use PRLC for the investigation of large-size crystals, it is necessary to take into account the presence of considerable temperature gradient inside the sample during laser radiation propagation. However, it is essential to build an accurate theoretical model of the crystal heating by laser radiation in order to establish the correct correlation between the thermodynamic and equivalent temperatures of the crystal. This leads to the problems of matching the experimental data with simulation results. In this paper, we have proved experimentally and theoretically that the equivalent temperature with good accuracy coincides with the average thermodynamic temperature of the crystal interacting with laser radiation and thus PRLC can be used. The lithium niobate crystal sample was placed between two metal electrodes forming a capacitor. Two Peltier elements were attached to the bottom electrode at the opposite sides. By adjusting the temperature of the Peltier elements, it was possible to make a linear temperature gradient inside the bottom electrode and consequently inside the crystal, which was in good thermal contact with it. The dependence of the equivalent temperature of the crystal determined using several piezoelectric resonances, coincide with corresponding average temperatures. This fact was also confirmed in simulation experiments conducted for the samples of different shapes having even more complex longitudinal and transverse temperature gradients. Thus, low optical absorption coefficients of large crystals with a complex shape can be measured with high accuracy using PRLC.

#### Study of Geologically-Consistent History Matching Peculiarities by Means of Gradient-Free Optimization Methods

Ivan Shiryaev1 , Ernest Zakirov2 , Ilya Indrupskiy3

1Oil and Gas Research Institute of the Russian Academy of Sciences (OGRI RAS), , Russian Federation
2Oil and Gas Research Institute of the Russian Academy of Sciences (OGRI RAS), , Russian Federation
3Oil and Gas Research Institute of Russian Academy of Sciences, Gas, Oil and Condensate Recovery Lab, Russian Federation

###### Abstract

This paper presents some results and distinctive features of the algorithm for automated history matching of 3D reservoir flow models using gradient-free methods. Widely used Nelder-Mead method was chosen for optimization. In order to preserve geological consistency of a model within the history matching process, control parameters are comprised of “porosity-to-permeability” relation parameters, anisotropic (semi)variogram parameters, and reservoir properties at pilot points. The control parameters are used at each iteration of the history matching process to generate porosity and permeability distributions based on static well data and perform flow simulations. Test studies were conducted for a specially developed synthetic model representing a inhomogeneous five-spot well pattern element. Oil flow rates at production wells and water flow rate at the injection well, as well as bottomhole pressures of all wells were chosen as measured dynamic data in the objective function. The influence of initial guess of parameter values and relative weights in the objective function on the quality of reconstruction of the ‘true’ solution and convergence rate were evaluated. Problems of gradient-free optimization methods application and specific features of residuals normalization in the objective function, as well as influence of pilot points are discussed.

###### Acknowledgements:

The results presented in the paper were obtained under the OGRI RAS state research contract

Jan Glasa1 , Lukas Valasek2 , Peter Weisenpacher3

1Institute of Informatics, Slovak Academy of Sciences, Department of Parallel Computational Methods and Algorithms, Slovakia (Slovak Republic)
2Institute of Informatics, Slovak Academy of Sciences, , Slovakia
3Institute of Informatics, Slovak Academy of Sciences, , Slovakia

###### Abstract

Road tunnels are specific underground structures constructed in order to shorten transport routes and improve environment and road safety. They solve critical traffic problems caused by enormous increase of the number of vehicles on roads and higher demands for passenger transport and cargo traffic capacity. Fires belong to the most dangerous and destructive incidents in road tunnels producing large amount of toxic smoke and causing extreme increase of temperature resulting in huge damages. For assurance of safe tunnel operation, teaching and training of tunnel operators is necessary to increase their preparedness for potential incidents including incidents with fire. According to European legislation this task is fully in competence of tunnel safety officer and tunnel administrator. For periodic annual teaching and training of existing and new tunnel operators, a unique TTOS (Tunnel Traffic & Operation Simulator) device has been used in Slovakia since 2013. TTOS is a simplified version of operator control centre of 1 km long virtual twin-tube highway tunnel with unidirectional traffic. The system is implemented to operate the tunnel by two operators: operator for the tunnel technology and operator for the tunnel traffic management. Their work is changeable. It means that one operator can control entire tunnel and handle all technological equipment (ventilation, lighting, variable traffic signs, power supply, etc.). All alarms, faults, incidents detections, warnings, responses as well as interventions of Central Control System (CCS) and operators are recorded. The technological equipment implemented in TTOS is in accordance with national and European regulations and technical directives. Various car accident scenarios and CCS reactions can be simulated in TTOS allowing verification of operator’s actions. The TTOS fire simulation is based on fast simple smoke spread models which do not provide any relevant information about the simulated fire dynamics and smoke stratification. Advances in fire research have led to the development of simulation systems capable to simulate complex physical and chemical processes related to fire. Some of these systems have achieved high level of reliability and acceptance. In this paper, we describe the development of a series of 3D visualizations created using the CFD-based Fire Dynamics Simulator. These visualizations have been implemented into the TTOS environment in the form of videos as a didactic tool available for tunnel operators. They provide information about the smoke spread and stratification as well as about the evolution of selected physical quantities describing fire such as temperature, air flow velocity and visibility. A short discussion about potential of autonomous vehicles in the case of road tunnel fire is also included.

#### Replacement of Numerical Simulations with Machine Learning in the Inverse Problem of Two-Phase Flow in Porous Medium

Yu Goncharova1 , Ilya Indrupskiy2

1National University of Oil and Gas «Gubkin University», , Russian Federation
2Oil and Gas Research Institute of Russian Academy of Sciences, Gas, Oil and Condensate Recovery Lab, Russian Federation

###### Abstract

A possibility to replace full-physics numerical simulations with machine-learning-based algorithms in inverse problems of multiphase flow in porous media is studied on an example of specialized oil-well tests. The performance function is computed at each iteration of the inverse problem solution using an artificial neural network (ANN) instead of forward numerical simulations. Proper ANN structure, training set, and learning algorithm are established and implemented. Achieved approximation quality for the performance function on a test sample is well suitable for the inverse problem solution. Further improvements and alternative ANN formulations are proposed for practical applications.

###### Acknowledgements:

The results presented in the paper were obtained under the OGRI RAS state research contract

#### Development of Carrier Dynamics and Optimization Model for Extracting Optoelectronic Properties from Time-Resolved Photoluminescence Measurements

1Qatar Environment and Energy Research Institute, Computational Materials, Qatar
2King Fahd University of Petroleum & Minerals, Electrical Engineering, Saudi Arabia
3Qatar Environment and Energy Research Institute, , Qatar
4University of Sharjah, , United Arab Emirates

###### Abstract

Time-resolved Photoluminescence (TRPL) has been used extensively by experimentalists to investigate the carrier extraction at the interfaces of solar cells. The contactless nature and its application for both complete and non-complete device make it an ideal tool for characterizing limitations in solar cells. Conventionally, TRPL transient decays are analyzed by performing curve-fitting and extracting the associated lifetimes. Due to the complex quasi-exponential shape of the TRPL; one exponent, two exponent and stretched exponential functions for fitting have often been employed. However, the main limitation arising from this method is the extraction of arbitrary lifetime constants without consistent consideration of the physical processes involved in TRPL dynamics. Moreover, as the carrier diffusion and varied recombination pathways are occurring at comparable time scales, there is a high likelihood that the extracted parameters may be convoluted with other properties. To properly understand the photophysics and obtain meaningful insights, charge transport governing PL transients must be taken into consideration. In this work, an extensive model is developed to extract the physical features characterizing carrier dynamics in the solar cell bulk and at the interfaces of transport layers. The numerically modeled PL decay is capable of tracing temporal variation of optoelectronic properties along with the transport of minority carriers spatially. By coupling the model with the experimental measurements, the proposed method aims to go beyond the conventional fitting parameters of lifetimes and extract the parameters with physical significance such as surface recombination/interface recombination velocity, defect-assisted recombination constant, radiative recombination frequency, mobility, injection level, and doping density. Excellent conformity of fits to experimental data is found by coupling multi-start optimization algorithm with carrier dynamics model. The resulted physical parameters from thin films and single crystals of perovskites clarified the distinct nature of both materials and provided hints for possible improvements. The ability of the proposed charge dynamics model to swiftly extract meaningful optoelectronic parameters from TRPL signal makes it a standard characterization tool for acquiring in-depth knowledge of the material.

#### Quantitative analysis of lexical complexity in contemporary Russian novels

Yulia Maslennikova1 , Alexey Abramov2

1Kazan Federal University, radiophysics, Russian Federation
2K(P)FU, Institute of Physics, Russian Federation

###### Abstract

The study of literary complexity has a long history. But especially in the modernist period, the complexity has come to be stronger identified with literature, and literature became synonymous with difficulty. At this historical moment, the first strictly formalized approaches to the quantitative study of language arise. Their aims included an attempt to identify such lexical attributes as complexity, readability, or difficulty. But literature complexity can be defined as an intersection of these terms because of the problem is that complexity itself is like a moving target: what at first feels forbiddingly new can come to seem familiar to the reader of tomorrow. This research presents a set of methods for measuring the lexical complexity of a text, which measures the lexical content of individual texts against the culture at large. We applied a range of statistical measures upon a set of texts. For the analysis, we selected 50 famous Russian novels of the 20th century based on their historical and generic variety. The main approach consists of the comparison of the relative frequency of a work’s words against the Google Books dataset. This dataset represents a remarkable resource, with the Russian Google Books corpus in the period 1800–2012, containing approximately 4.7 billion 1-grams. This corpus has the advantage of providing a huge volume of text from which to estimate word frequency or rarity in the period that a text was written. Relative frequencies distribution for a novel’s words were compared with frequencies of Google Books corpus of different years using Jensen–Shannon divergence, L1-norm (also known as Manhattan Distance), Spearman’s rank correlation. Also, so-called a Zipf score was calculated, such measure was proposed by authors of similar research of modern English fiction. It was shown that the lexical complexity of individual texts should be measured against the culture at large. It was found that a writer who commonly seems to be difficult, verbose or notional, can in fact use language that is more ‘common’ (relative to the culture at large) than any other texts.

#### A self-consistent model of second harmonic generation of laser radiation in periodically poled nonlinear-optical crystal conditioned by its nonuniform heating

Gregory Ivanov1 , Evgeniy Kogut2 , Aleksey Konyashkin3 , Oleg Ryabushkin4

1Moscow Institute of Physics and Technology (State University), The School of Electronics, Photonics and Molecular Physics, Department of Photonics, Russian Federation
2Moscow Institute of Physics and Technology, Physical and quantum electronics, Russian Federation
3Kotelnikov Institute of radio-enginiering and electronics of RAS, Quantum electronics, Russian Federation
4FIRE RAS, Photonics, Russian Federation

###### Abstract

Nowadays frequency conversion of laser radiation in nonlinear-optical crystals is widely used for generation in visible and middle infrared spectral ranges. Interaction of laser radiation with nonlinear-optical crystals results in its nonuniform heating due to both linear and nonlinear absorption of pump and generated photons. Along with the violation of phase matching conditions followed by the decrease of the conversion efficiency another one detrimental effect of the crystal nonuniform heating is the formation of defects, which are precursors of crystal laser damage. Eventually, the control of the crystal temperature distribution in processes of nonlinear-optical frequency conversion are of great importance. We have developed a self-consistent theoretical model that describes the process of the second harmonic generation (SHG) of the laser radiation in a nonlinear-optical crystal in conditions of its nonuniform heating induced by optical absorption. A periodically poled crystal pumped by the pulse laser radiation focused into its center was considered Along with the absorption of pump and generated waves the diffraction effect was also taken into account. The Iteration procedure of solving the SHG problem relied onto the interrelated solution of two equation systems describing the temperature dependent SHG and the heat conduction processes. The heat sources were represented by the absorbed power of both pump and generated radiation. Eventually the resulting distribution of the crystal temperature should correspond to the radiation intensity distributions of pump and second harmonic. The introduced theoretical model was verified experimentally by performing SHG of the radiation of the Yb-doped fiber laser (central wavelength 1064 nm). In the periodically poled lithium niobate crystal (PPLN). Simulated temperature distributions of PPLN at given values of SHG output power were in a good agreement with measured ones. A theoretical model that correctly describes the SHG process will help to prevent the violation of phase matching conditions by compensating induced temperature gradients in nonlinear-optical frequency conversion experiments.

#### Fractal Interpolation and Integration over Two-Dimensional Triangular Meshes

Zekeriya Sarı1 , Gizem Kalender2 , Serkan Günel3

1Dokuz Eylül University, Electrical and Electronics Engineering, Turkey
2Dokuz Eylül University, Electrical and Electronics Engineering, Turkey
3Dokuz Eylül University, Electrical and Electronics Engineering, Turkey

###### Abstract

The fractal interpolation techniques are powerful alternatives to classical interpolation methods in case of complex irregularly data such as financial time series, seismic data and biological signals. The main goal of this study is to apply fractal interpolation techniques over two-dimensional irregular meshes. We partition the polygonal interpolation domain into triangular regions. We consider affine contraction mappings from triangular regions to triangular patches of the mesh. Calculation of the fractal interpolation coefficients is reduced to solving a linear system of equations. Freely chosen scaling variables of the iterated function system transformations provide flexibility. Additionally, the constructed iterated function system coefficients for the interpolation can be used directly to evaluate two-dimensional numerical integrals over the domain. We provide basic error results via numerical simulations.

#### Fractal Interpolation and Integration over Two-Dimensional Triangular Meshes

Gizem Kalender1

1Dokuz Eylül University, Electrical and Electronics Engineering, Turkey

###### Abstract

The fractal interpolation techniques are powerful alternatives to classical interpolation methods in case of complex irregularly data such as financial time series, seismic data and biological signals. The main goal of this study is to apply fractal interpolation techniques over two-dimensional irregular meshes. We partition the polygonal interpolation domain into triangular regions. We consider affine contraction mappings from triangular regions to triangular patches of the mesh. Calculation of the fractal interpolation coefficients is reduced to solving a linear system of equations. Freely chosen scaling variables of the iterated function system transformations provide flexibility. Additionally, the constructed iterated function system coefficients for the interpolation can be used directly to evaluate two-dimensional numerical integrals over the domain. We provide basic error results via numerical simulations.

#### Model of the polarization extinction ratio change due to multiple reflection of laser radiation from the faces of the terbium-gallium garnet crystal in Faraday rotator

Aleksandr Seleznev1 , Evgeniy Kogut2 , Renat Shaidullin3 , Oleg Ryabushkin4 , Gregory Ivanov5

1Moscow Institute of Physics and Technology (State University), The School of Electronics, Photonics and Molecular Physics, Department of Photonics, Russian Federation
2Moscow Institute of Physics and Technology, Physical and quantum electronics, Russian Federation
3FIRE RAS, Photonics, Russian Federation
4FIRE RAS, Photonics, Russian Federation
5Moscow Institute of Physics and Technology (State University), The School of Electronics, Photonics and Molecular Physics, Department of Photonics, Russian Federation

###### Abstract

The variety of laser sources with different wavelengths were developed due to the nonlinear frequency conversion of the polarized radiation. The efficiency of this conversion depends on the polarization extinction ratio and the direction of polarization, which is controlled by the terbium-gallium garnet (TGG) magneto-optical crystal, placed in a magnetic field. TGG crystals are widely used for optical isolators, rotators and modulators, based on Faraday effect. When linearly polarized optical radiation passes through this crystal in a magnetic field, the polarization plane rotates by an angle which is proportional to the magnitude of the magnetic field and the length of the crystal. However, after passing the TGG crystal radiation can partially depolarize, what can lead to the malfunction of the optical element. In the literature the mechanisms of radiation depolarization due to the effect of photoelasticity and temperature dependence of the Verdet constant under conditions of inhomogeneous heating of the crystal by laser radiation were described in detail. This paper for the first time presents an analysis of change in the extinction ratio of the polarization of radiation passing through a TGG crystal placed in a constant magnetic field, taking into account the effect of multiple reflections from the crystal faces. We propose that the radiation passing through the TGG crystal will have components rotated by different angles due to non-reciprocity of the Faraday effect what can lead to depolarization of the output radiation. The mathematical model, describing the polarization state of the output radiation, taking into account the presence of radiation components that have experienced multiple reflections from the faces, was developed. The decrease in the polarization extinction ratio depends on the reflection coefficient from the faces and varies from 23 dB for the crystal without anti-reflective coating to 0.5 dB for a crystal with anti-reflective coating with a reflection coefficient of 0.1%. Also the dependences of the polarization extinction ratio of the output radiation on the polarization rotation angle and the phase shift between components rotated by different angles were calculated. Experimental measurements of the extinction ratio of the polarized radiation passing through the TGG crystal demonstrated compliance with the calculations of the proposed model. The influence of the laser beam offset from the center of the magneto-optical crystal on the radiation depolarization value was also estimated.

#### Software Environment for Computer-Aided Heuristic Optimization of Hydraulic Systems for Synchronous Movement of Actuators of Various Functional Purposes

Alexander Bushuev1 , Mikhail Ivanov2 , Dmitrii Korotaev3 , Georgy Resh4

1Bauman Moscow State Technical University, Computational Mathematics and Mathematical Physics Department, Russian Federation
2JSC Military Industrial Corporation NPO Mashinostroyenia, Bauman Moscow State Technical University, Computational Mathematics and Mathematical Physics Department, Russian Federation
3Bauman Moscow State Technical University, Computational Mathematics and Mathematical Physics Department, Russian Federation
4JSC Military Industrial Corporation NPO Mashinostroyenia, Bauman Moscow State Technical University, Aerospace Systems Department, Russian Federation

###### Abstract

A software environment was developed for computer-aided design of optimal throttle hydraulic synchronization systems of actuators of various functional purposes operating under conditions of external alternating-sign force effects. The criterion of an optimization procedure was the minimization of a mismatch time of relative movement of actuators during operation. A compute core of an object-oriented code was constructed on the basis of a dynamic mathematical model of a synchronization system consisting of four power cylinders. A model problem was solved with the help of the created software environment. This model problem demonstrated the efficiency of the proposed multidimensional optimization process. The methodology was based on the use of the well-known heuristic method (binary coded genetic algorithm) and the subsequent improvement (in the sense of a given objective functional) of the obtained solution by a method on the basis of the Hooke-Jeeves algorithm. Recommendations on the practical application of the software and mathematical support for achieving the best convergence to the extreme value of a vector of controlled parameters were formulated.

#### Numerical Simulation of Non-Equilibrium Isochoric Phase Transitions in Hydrocarbon Mixtures

Ayguzel Aglyamova1 , Ilya Indrupskiy2

1National University of Oil and Gas «Gubkin University», , Russian Federation
2Oil and Gas Research Institute of Russian Academy of Sciences, Gas, Oil and Condensate Recovery Lab, Russian Federation

###### Abstract

Numerical simulations of phase behavior in multicomponent hydrocarbon mixtures is an essential part of petroleum reservoir engineering practice. Almost all industry-adopted models are based on equilibrium assumptions. The condition of Gibbs energy minimum, or equality of chemical potentials, combined with equation of state (EoS), e.g. the Peng-Robinson EoS, for each phase and with balance conditions for concentrations are used to compute phase mole fractions and compositions (component concentrations in the phases). However, experimental and field data show that in a number of important real situations equilibrium assumptions are not valid. In the previous study of Indrupskiy et al. (Computational Geosciences, 21(5), 2017, P. 1173-1188. DOI: 10.1007/s10596-017-9648-x) a unified model and numerical algorithms were presented for isothermal non-equilibrium phase behavior simulations in petroleum engineering applications. The model is based on the relaxation equation for the component chemical potentials difference between phases. It was verified on field data, however, only integral behavior of the system (a gas-condensate reservoir) was available to be matched. In the current study, we extended the non-equilibrium model to isochoric processes and developed a numerical algorithm which allowed to perform direct simulation of laboratory experiments with a multicomponent hydrocarbon mixture and validate the non-equilibrium model. The experimental data were successfully matched with the model simulations. The model and algorithm are suitable for equilibrium and non-equilibrium isochoric phase behavior simulations with synthetic and real multicomponent hydrocarbon mixtures (oils and gas-condensates).

###### Acknowledgements:

The results presented in the paper were obtained under the OGRI RAS state research contract

#### A two-stage opinion formation model based on an extended XY-magnet interaction and socio-dynamic update mechanisms.

Dod Prenga1

1University of Tirana, Physic, Albania

###### Abstract

Abstract. In this work we propose a two stage model for opinion formation in a special case where the society is assumed as made up of duos of strongly interacting individuals. The first stage is driven by interests or merely satisfaction fulfilling conducts and therefore the opinion is calculate via statistical mechanics approach. The energy-like function named the utility, is derived from the XY magnet Hamiltonian by simply adding a third term entailing the copulation of two classical energy terms to count for nonlinear interaction between opinion agents. In the second stage those pre-formed opinions start to interact with others ones based on pure sociological mechanisms. Here we performed the updates based on Deffuant model by considering the starting opinion values calculated in the first stage. Scalar and vector addition have been considered in separate analyses. The resulting pattern of scalar-opinion update shows the dependence of final society attitude toward an issue F acting as exterior field on the magnet-like model. Compared to some standard approaches which use random opinion value in starting step, our approach impose diversity in the initial conditions resulting variations outcomes depending on model parameters. It shows a higher consensus level and less clustering for small confidence bounds. The vector model shows varieties of results which finally were compared and discussed in the reference of the real human behaviour.

#### Case study in which the Deutsch-Jozsa algorithm responds with pure states

Eraldo Marinho1

###### Abstract

A theoretical essay is presented on a particular type of balanced functions that allow the Deutsch-Jozsa algorithm to produce pure state instead of mixed states. Such results occur if and only if the balanced functions are linear combinations (modulo 2) of a set of balanced clock functions, that is, clock functions with periods that are power of 2.

###### Acknowledgements:

The author thanks Geysa de Oliveira Marinho for the critical reading of the manuscript and helpful suggestions.

#### PERCEPTIONS IN STUDENTS OF DEGREE IN COMPUTERS ON THE USE OF ROBOTICS IN THE TEACHING PROCESSES

Jesús González1 , Liliana Martínez2 , Henry Sánchez3

###### Abstract

The teaching of robotics in a properly planned and controlled environment has allowed its incursion into academic stages both in secondary and higher education. So it should be added that the teaching process in this area, motivates and enhances the creativity and cooperative work of the students, connecting it directly with mathematics, physics, computers and electronics, I feel this the foundations that underpin and consolidate as you progress in the teaching process. Therefore, one of the objectives of this tool is to create an interest in science and engineering in students. This study was carried out to answer the question: How do professors and undergraduate students describe the usefulness, effectiveness and efficiency of using a robot as a face-to-face education technology for a learning experience? Therefore, one of the objectives of this tool is to create an interest in science and engineering in students. This study was carried out to answer the question: How do professors and undergraduate students describe the usefulness, effectiveness and efficiency of using a robot as a face-to-face education technology for a learning experience? For this study, two surveys developed by researchers were conducted to evaluate the perceptions of professors and undergraduates in computer science in a learning experience. The results of this study indicate that the teachers and students of degree in computer of the Universidad del Magdalena, consider the use of robots as a facilitator of teaching processes as a highly motivating tool to undertake new teaching strategies and suggest a greater exploration due to the versatility that Robotics offers today.

#### Virtual laboratories of electromagnetism for education in engineering: A perception

Jesús González1 , Jhon De la Hoz2 , Laury García3 , Jesús Beltrán4 , José Escobar5

###### Abstract

The influence of virtual tools as didactic means towards the study of electromagnetism phenomena takes greater relevance every day at the Universidad del Magdalena due to the inclusion of a visual and dynamic element beyond the reading of physical text books and even the development of laboratories real electromagnetism. This article shows a very positive perception on the part of the engineering students regarding the advanced virtual laboratories of electromagnetism, influencing the learning of physical concepts and the development of cognitive competences. Students' understanding of the concepts of physics in the domain of electromagnetic physics was evaluated in a pre- and post-test design involving 60 participants assigned to four experimental groups and 30 participants assigned to the control group. There were two experimental conditions, namely, experimentation with manipulation of real material, experimentation with virtual manipulation, as well as a condition of control (ie, traditional instruction with no virtual experimentation). Conceptual tests were administered to assess students' comprehension before, during and after the application of the virtual laboratories. The analyzes revealed that even though the two experimental conditions promote the conceptualization and correct interpretations of the students' physical concepts in the domain of electromagnetism better than in the control group as expected; we see that, the use of the virtual tool obtains a greater acceptance as this study shows.

#### Remarkable effects of dirty limit on superconducting condensate

Jader González1 , Fernando Durán2 , Jesús González3

###### Abstract

Using heterostructures that combine a two superconductor (Nb-Pb). We demonstrate the modulation of the superconducting condensate at the nanoscale via variation of mean-free path. The modulation of superconductivity can be obtained not only for chosing smaller superconducting lengths comparing with bulk superconducting length or considering several geometric shapes, but also whether strong local dopping effect can be produced over the superficial area of the superconductor. Through this mechanism, a nanoscale pattern of two condensates regions can be created in the superconductor. This yields a magenetization curves that has no counterpart in the literature. We show that this form of modulation based on the possibity of change mean-free path represent a groundbreaking prospects in the study of the effects that might exploit unique superconducting properties, due to allows the manipulation of magnetic flux quanta.

###### Acknowledgements:

This work was financed by the University of Magdalena (Fonciencias) and Direcci´on de Investigaci´on y Transferencia (DIT) Universidad Pontificia Bolivariana.

#### In search of an effective Monte Carlo method for identification of atmospheric contamination source

Piotr Kopka1

1National Centre for Nuclear Research (NCBJ) , Laboratory for Nuclear Energy and Environmental Analyses, Poland

###### Abstract

We present the Bayesian framework able to identify the source of the airborne contaminant. We compare the effectiveness of framework utilizing the three popular Monte Carlo algorithms with the use of data from the full-scale Field experiment - Copenhagen Tracer Experiments. The input data ta are the on-line arriving concentrations of released substance registered by sensors, while the output are the posterior probabilities of four parameters characterizing the contamination source, i.e.: contamination source position (x,y,z) and release rate (q). As the forward model to predict the concentrations at the sensors locations, we use fast response Second-order Closure Integrated Puff model. The performer study present that among the Markov Chain Monte Carlo (MCMC), Sequential Monte Carlo (SMC) and Sequential Monte Carlo Approximate Bayesian Computation (SMC ABC) the last algorithm performed the best in the proposed framework localizing the airborne contaminant source parameters.

#### The SAPBC method on local, non-cluster updates algorithms of Monte Carlo simulation: A study on more convergence of spin correlation at the critical temperature

Amin Najafi1

1Technical and Vocational University, Shahid Mofateh of Hamedan, Iran, physics, Iran (Islamic Republic of)

###### Abstract

In this method, we propose the computational technique of Screw-Antisymmetric Periodic Boundary Condition (SAPBC Method) on local, non-cluster update algorithms of Isotropic square Ising model of Monte Carlo Simulations. The SAPBC Method, actually, is an extended mixed method of Screw (helical) and Antisymmetric periodic boundary conditions beyond connection from of nearest neighbor spin of the main lattice to even far away block of the foreign neighbor spin arrays. While describing of the exact geometry of the method, it applies to the critical slowing down to achieve more convergence of spin correlation at the critical temperature. Algorithms performed by using the SAPBC Method have faster correlation and much shorter autocorrelation time than algorithms performed by using the PBC Method. We will also see that the Autocorrelation function for the typewriter Metropolis algorithm was found to be zero at high temperatures. For low temperatures it fell to zero and stayed there. The SAPBC Method also confirms the law of the spatial correlation length with its dynamical critical exponent. Therefore, it can be used as a trenchant method applied to boundary conditions of Monte Carlo simulation problems extending on a variety of other models such as XY-Pots-Heisenberg model and also cluster algorithms such as Wolf, Swendsen-Wangas, Hoshen-Koppelman as well.

#### Modeling of Wind Setup Effects for Stratified Flows in Open Channels: A Model for the Istanbul Strait (Bosphorus)

Ayse Humeyra Bilge1

1Kadir Has University, Industrial Engineering, Turkey

###### Abstract

In previous work, we presented wind effects on stratifies flows in open channels, in the specific case of the Istanbul Strait (Bosphorus). In that work, we studied changes in the flow regime, due to strong winds in the direction of the upper layer’s flow. In the present talk, we will discuss the effect of winds in the direction opposite to the direction of the upper layer’s flow. We consider the case of two basins with different density, temperature or surface level characteristics and a narrow channel connecting these basins. The gravity, temperature or density gradients give rise to stratified flows in the channel. These flow regimes may also be complicated by tidal effects. Typical examples of channels with stratified flows are the Gibraltar Strait connecting the Atlantic Ocean and the Mediterranean Sea, the Canakkale Strait (Dardanelles) connecting the Mediterranean Sea to the Marmara Sea, the Istanbul Strait (Bosphorus) connecting the Black Sea and the Marmara Sea, and the Kerch Strait connecting the Azov Sea to the Black Sea. It is known that persistent winds in the flow direction the along a channel lead to a decrease of the flow height. In previous work we gave a model for the decrease in the height of the upper layer, in the case of a stratified flow. The decrease in the upper level height affects the thickness of the mixing layer and may have environmental adverse effects. In the case of Istanbul Strait, winds in the direction opposite to the flow of the upper layer have a more drastic effect. The surface level difference between the northern and southern entrances is about 30-40 cm. The southern entrance of the channel has a funnel topology and strong southerly winds give rise a "wind setup" effect that increases the water level at the entrance of the channel and leads to a blockage of the upper layer and a reversal of the current regime. This effect is observed a couple of times in a year, mostly in fall where the Black Sea’s surface height is at its lowest, hence the gravity gradient is minimal. It might be expected that even minor changes in the gravity gradient between the entrances of the Istanbul Strait would increase the frequency of flow reversals. In this work, we present a model for the simulation of various factors that would lead changes in the gravity difference at both ends of the Istanbul Strait and calculate their effects on the probability of flow reversals. References Andersen A., Jakobsen F. and Alpar B. 1997 The water level in the Bosphorus Straight and its dependence on atmospheric forcing, Deutsche Hydrographische Zeitschrift German Journal of Hydrography 49 Bilge A.H., G. Kirkil, S.Burak, M. Incegul, 2016 Modeling of Wind Effects on Stratified Flows in Open Channels: A Model for the Istanbul Strait (Bosphorus) J. Phys.: Conf. Ser. 738 012069 Chanson H. 2004 The Hydraulics of Open Channel Flow: An Introduction Jarosz E.W., Teague J. and Book J.W. and Beiktepe 2011b Observed volume fluxes in the Bosphorus Strait Geophys. Res. Lett. 38 L21608 http://dx.doi.org/ Plate E.J. and Goodwin C.R. The influence of wind on open channel flow, Coastal Engineering Report Yuce H. 1996 Mediterranean water in the Strait of Istanbul (Bosphorus) and the Black Sea exit Estuar. Coast. Shelf Sci. 43 597616

###### Acknowledgements:

This is joint work with G. Kirkil, M. Hekimoglu (Kadir Has University) and S. Burak (Institute of Marine Sciences and Management, Istanbul University)

#### Modeling the process of attracting foreign investment in the Russian economy

Gulnaz Galeeva1

1Kazan Federal Universitu, Institute of Management, Economics and Finance, Russian Federation

###### Abstract

In the paper, on the basis of an assessment of the development of the Russian economy, the sectors most in need of an investment are identified, taking into account the depreciation rate of basic production assets. Depreciation of fixed assets reflects the demand for investment in order to modernize and reconstruct production. Based on the data of the Federal State Statistics Service of Russia, a rating of economic sectors in terms of the degree of depreciation of fixed assets at the end of the year by type of economic activity for 2013-2018 is built. In addition, the paper presents a model for predicting the inflow of foreign direct investment in Russia, developed using the classical approach to estimating linear regression criteria, which is based on the least squares method (OLS). In compiling this regression model, the applied software package for econometric modeling GRETL (GNU Regression, Econometrics and Time-series Library) was used to predict the inflow of foreign investment. Forecasting the inflow of foreign investment in the Russian Federation is aimed at solving the following tasks: to determine the most competent direction of investment policy and activity using forecast estimates, as well as to assess the country's investment attractiveness. However, a significant role in predicting this indicator is played by the determination of factors that have an impact on the future volume of foreign investment. In addition, the analysis of foreign investments, depending on the influence of various factors, can tell about those or other motives that guide foreign investors when investing their own capital.

#### Model for assessing the influence of factors on a country's competitiveness in the global economy

1Kazan Federal Universitu, Institute of Management, Economics and Finance, Russian Federation
2Kazan Federal Universitu, Institute of International Relations, Russian Federation
3Kazan National Research Technological University, Institute for Innovation Management, Russian Federation
4Kazan National Research Technological University, Institute for Innovation Management, Russian Federation

###### Abstract

In the work, based on the analysis of the countries-leaders of competitiveness, it was revealed that all of them among the most developed sectors of the economy had components of the competitiveness index related to innovative development and infrastructure. This suggests that it is the sectors of innovation and infrastructure that can be considered strategically important and make efforts for their development. Therefore, it makes sense to build models related to these areas. The paper presents two macroeconomic models for assessing the influence of factors on competitiveness, one of which will be innovation-oriented, and the second - infrastructure-oriented. These models use spatial data reflecting the assessments of 111 countries for a number of indicators produced by international organizations such as the World Economic Forum, the World Bank, and the World Intellectual Property Organization. Data for the Russian Federation are not included in the sample, since they will be used later to verify the results of the models.

#### Pole representation of the dislocation segment generalized susceptibility diagonal matrix elements

Igor Bataronov1 , Viktor Dezhin2

1Voronezh State Technical University, Higher mathematics and physical and mathematical modeling, Russian Federation
2Voronezh State Technical University, Higher mathematics and physical and mathematical modeling, Russian Federation

###### Abstract

Diagonal elements of the generalized susceptibility matrix in the form of expansion in a series of poles are presented. Screw dislocation segment is considered. The calculation of the series coefficients for different values of the dislocation segment normalized lengths has been carried out. The real and imaginary parts of the diagonal matrix elements are calculated. The results of the calculations are presented in the figures. The figures show a good agreement of the diagonal matrix elements direct calculation results with the calculation carried out in this work.

#### On the hamiltonian formulation of an octonionic integrable extension for the Korteweg-de Vries equation

Mercedes Fernandez1 , Alvaro Restuccia2 , Adrian Sotomayor3

1Universidad de Antofagasta, Departamento de Matematicas, Chile
2University of Antofagasta, Department of Physics, Chile
3University of Antofagasta, Department of Mathematics, Chile

###### Abstract

We present in this work the hamiltonian formulation of an octonionic extension of Korteweg-de Vries equation with a non-trivial interaction term. The formulation should to take into account the non commmutativity and non associativity of the implicit algebra which defines the equation. We also analize the hamiltonian structure of the equation.

###### Acknowledgements:

AS and AR are partially supported by Project Fondecyt 1161192, Chile.

#### Procedure of the mathematical simulation of the subsonic detached flow around the bodies with the application of an equivalent surface of simplex form and semi-infinite tailed section.

Valery Timofeev1

1BAUMAN MOSCOW STATE TECHNICAL UNIVERSITY, FN-11, Russian Federation

###### Abstract

The basic condition of the procedure of the mathematical simulation of the subsonic flow around bodies with the flow breakaway in the ground region are represented. It is proposed to compose the surface of equivalent body from the collection of the sections of the simplex form, which in the totality form equivalent surface. Brief description of approach to the selection of the configuration of individual sections is given. It is recommended supply the tail section of the equivalent surface with the section, which downstream becomes infinite. It is proposed for this semi-infinite section to keep permanent mold and dimensions of cross section. For the selection of the significant dimensions of some sections are used the relationships of the boundary-layer theory, theory of viscous jets and tracks, and also the data about the aerodynamic coefficients of base pressure and resistance. Numerical simulation is carried out by the method of single vortices. The results of the mathematical simulation of the flow around axisymmetrical cylindrical bodies with the head part and the ground shear with the zero and nontrivial angles of attack are represented.

#### On Convergence of Difference Approximations to Problems of Optimal Control in the Coefficients of Elliptic Equations with Mixed Derivatives and Unbounded Non-Linearity

Aigul Manapova1

1Bashkir State University, Department of Mathematics and IT, Russian Federation

###### Abstract

This paper deals with optimization problems for elliptic PDEs with mixed derivatives and unbounded nonlinearity in coefficients (i.e. the conditions imposed on the equation coefficients are assumed to hold only in a neighborhood of the exact solution to the original problem). The controls are contained in the coefficients multiplying the highest derivatives. Convergence and approximation analysis for the optimization problems is investigated. The convergence of the approximations with respect to the state, functional and control is established, the approximations are regularized.

#### Reduction of inhomogeneous boundary conditions to homogeneous in partial differential equations

Tatiana Oblakova1

1Bauman Moscow State Technical University, the Computational Mathematics and Mathematical Physics Department of BMSTU, Russian Federation

###### Abstract

A universal replacement of the variable is proposed, which allows reducing the problem with inhomogeneous boundary conditions of any type to a problem with homogeneous ones. It is shown that due to this replacement the structure of the obtained analytical solutions is significantly simplified. The question of the existence of such a replacement is investigated, examples are given that demonstrate the performance and advantages of the proposed approach for solutions obtained by the Fourier method.

#### Boss Tower and Baseplate Flange Optimization

joompon bamrungwong1

1KING MONGKUT'S UNIVERSITY OF TECHNOLOGY NORTH BANGKOK, Faculty of Applied Science, Thailand

###### Abstract

The swaging process is commonly used in head stack assembly, which is a process that is undertaken to either reduce or increase the diameter of tubes or rods. In the head stack assembly process, a swage boss engages with an arm hole of E-Block. Current hard disk drives have very small tolerances, requiring the swage effect of new hard disk drives to be reduced to as little as possible. In this study, finite element analysis (FEA) was used to reduce the swage effect. At present, FEA and investigative tests indicate that a significant portion of gram changing through swaging is caused by E-block tip deformation due to swaging. Deformation of the E-block tip is the result of unbalanced swage forces between the tension and compression suspension. Achieving optimization concepts leads to a new swage plate design to reduce the gramload change of the target and to equalize the swage forces. The FEA results found that gramload change of the target decreased by 35% on the tension side, and by 65% on the compression side through swage by boss tower. The HGA torque out was not different. The suspension flange was also studied. Subsequently, suspension manufacturing is able to bias the suspension as incoming HGA. The flange deformation might be closer to zero after the swaging process.

###### Acknowledgements:

I would like to thank the Department of Industrial Physics and Medical Instrumentation, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, as well as Seagate Technology (Thailand) Co., Ltd. for supporting this research.

#### Deformation and Smoothing of Cusp Singularities

1Hamad Bin Khalifa University, College of Science and Engineering, Qatar
2Hamad Bin Khalifa University, , Qatar

###### Abstract

A cusp singularity (CS), is a point at which the slope of a continuous curve changes abruptly in sign and magnitude. A particular type of CS, which is the focus of this paper, is where only the sign of the slope is altered while the magnitude of the slope is unchanged. This type of CSs occur in many natural phenomena such as Kato's cusp and particular plasmonics. Solving such problems numerically can be challenging because of the discontinuity in the derivatives. In this paper, we present an efficient spectral method incorporated with transformation (mapping) to handle the cusp problem. The transformation is based on functions that are locally odd around all the cusp points. The idea is to transform functions from C$^0$ continuity to C$^{\text{N}}$ continuity ($\text{N}>1$), and then implement a spectral method to solve the mapped problem without any domain decomposition. The final solution is obtained with inverse mapping.

###### Acknowledgements:

This work is supported by Qatar National Research Fund (QNRF) under project NPRP X-107-1-027.

#### Generating efficient basis sets for unbounded domains

1Hamad Bin Khalifa University, College of Science and Engineering, Qatar
2Hamad Bin Khalifa University, , Qatar

###### Abstract

The treatment of the problems involving unbounded domains (UDs) with vanishing boundary conditions is always challenging. For spectral methods, in particular, very limited basis sets are commonly used for such domains, in which the ranges of the decay rates with acceptable computational efficiency, are very small. Furthermore, maintaining high level of analyticity becomes burdensome. Developing efficient mapped basis tailored for such problem is one of the main strategies to overcome these difficulties. In this work, we present a technique to generate efficient basis sets for UDs. This approach allows using basis sets defined for bounded domains (BDs) for problems in UDs, and hence, providing more freedom to choose from a variety of basis sets. To ensure computational efficiency, the designed transformations cover a wide range of decay rates and allow solving integrals analytically. The method is applied to solve many differential equations encountered frequently in many physics related problems. The results illustrate the efficiency of the developed technique and mapped basis sets.

###### Acknowledgements:

This work is supported by Qatar National Research Fund (QNRF) under project NPRP X-107-1-027.

#### Optimal Control Models of Einstein's Field Equations

Salah Haggag1

1The Egyptian Russian University, Department of Basic Sciences, Egypt

###### Abstract

It is shown that some problems of Einstein's field equations of General Relativity can be modeled as optimal control problems. The advantages of adopting such an approach are explained. Some examples are given for problems in relativistic astrophysics and cosmology. Extension to other problems is explored, and difficulties in the formulation of optimal control problems in General Relativity are indicated.

#### Mathematic Model on Conversion of Monochromatic Light

Chen-Wu Wu1

1Chinese Academy of Sciences, Institute of Mechanics, China

###### Abstract

The technology of Laser power beaming is conceptualized to supply power for an aerostat, for which the interactions between monochromatic light (Laser) and atmosphere as well as semiconductor device are modeled. Firstly, an empirical mathematic model is developed on the atmospheric attenuation of Laser and numerical examples presented for typical situations. Then on, a transient coupled mathematic model is established to analyze the thermo-mechanical effects on light-electricity conversion in the photovoltaic cell. Finally, the overall energy efficiency is estimated based on the model for such system of Laser power beaming.

###### Acknowledgements:

This work was supported by the National Natural Science Foundation of China (Grant No. 11572327 and No. 11332011) and the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDA17030100).

#### Inverse problems of restoring the geometric dimensions of a construction defects by thermal fields analysis

Anna Salnikova1

1BMSTU, FN11, Russian Federation

###### Abstract

The proposed work is devoted to the study of a defect in a rectangular plate with a cavity, based on the analysis of thermal fields.

###### Acknowledgements:

The work was carried out with support of state task of Ministry for Science and Education № 9.5387.2017/БЧ

#### Computer modeling of analytical algorithms of digital treatment of signals

1L.N.Gumilev Eurasian National University, Faculty of Mechanics and Mathematics, Kazakhstan

###### Abstract

This work is aimed at the study of mathematical algorithms of digital signal processing. Digital signal processing is a set of methods of signal processing based on numerical methods using digital computers and software. Any continuous (analogue) signal s (t) can be sampled in time and frequency-digitized, i.e. represented in digital form. The frequency-time transformations are definitely determined through mathematical Fourier transforms. Fourier transform is a transformation that allows decomposing the signal spectrum into harmonic wave functions. They describe the phase or amplitude of each sine wave corresponding to a particular frequency. The phase is the starting point of the curve and the amplitude is its height. Nowadays processing of discrete signals is carried out in frequency area, which considerably reduce the size of the digital equipment and time of processing. The fast Fourier transform algorithm allows reducing the number of operations to calculate the coefficients of the harmonic terms of the signals for a smaller number of operations. In this work, the main aim is to calculate the phase component of analog signals.

#### Scientometric Study of Superconductivity Research in South America from 1980 to 2019

Jhon De la Hoz1 , Jesús Beltrán2 , Jesús González3

###### Abstract

This paper presents scientometric analysis of superconductivity research output in South America from 1980 to 2019 and compares it with Global output as reported in Web of Science. The study shows that superconductivity research in South America had a steep growth between 1980 and 2000, particularly an abrupt hike in 2005 is noticeable followed by a more or less steady pattern thereafter up to 2019. South America superconductivity papers are analysed bibliometrically to indicate the authorship, collaboration pattern, to identify the major institutions and most relevant journals; apart from identifying the research field or application area of research in superconductivity.

###### Acknowledgements:

This work was financed by the Universidad del Magdalena (Fonciencias)

#### Modeling and research of influence of the external magnetic field on processes in a metal melt, received in the heavy current arc furnace

Mikhail Dokukin1

1Bauman Moscow State Technical University, Department of Physics, Russian Federation

###### Abstract

Need of a research of processes of hashing of liquid metal fusion for receiving homogeneous alloys is proved in this work. The mathematical model of processes of electromagnetic hashing of the fusions received the arc furnace is given. Statement of a special experiment for check of the offered model is considered. Results of calculations and the made experiments on the small-sized arc furnace are given. In the conclusion good coincidence of the offered theory and an experiment is emphasized and recommendations for improvement of the available processing equipment are made.

#### Study of the fundamental interactions in the bounded states of the systems: Earth-Moon, Proton - Electron (hydrogen atom), positronium (process e- e+→e- e+), and quarkonium, ( QQ)

Jesús Beltrán1 , José Escobar2 , Jesús González3

###### Abstract

The bound states of two particles such as the Earth-Moon system, bounded by the gravitational interaction, the hydrogen atom and the positron-electron system, bounded by the electromagnetic interaction, and the quark-antiquark system (whose union is due to the strong interaction), provide physicists with a natural laboratory for the study of fundamental interactions. The interaction potential of these systems is determined and the results are discussed. We approach the study of the Earth-Moon system, reviewing the effects of gravitational interaction and the details of Newton's theory on universal gravity. Also, the Theory of Relativity formulated by Albert Einstein, at the beginning of the 20th century. With regard to the hydrogen atom, the Schrödinger equation is used to calculate the spectrum of energy levels, and Feynman diagrams are used to obtain in detail this interaction potential between a proton and an electron (Breit-Fermi potential) calculating the energy spectrum again and commenting on the results. Then we apply the same method for positronium (process e- e+→e- e+), which consists of an electron linked to a positron (antiparticle of the electron), and establish the similarities and differences between these two systems. In the framework of the non-relativistic quark model (MQNR) the quarks-antiquarks (heavy) linked states are studied and using the theory of time-independent perturbations, the Hamiltonian for this system is obtained in order. This potential is analyzed term by term, to observe its validity in the study of the spectra of the systems, comparing the theoretical results obtained with the experimental ones. Then we apply the same method for positronium (process e- e+→e- e+), which consists of an electron linked to a positron (antiparticle of the electron), and establish the similarities and differences between these two systems. Within the framework of the non-relativistic quark model (MQNR) the quarks-antiquarks (heavy) linked states are studied and using the theory of time-independent perturbations, the Hamiltonian is obtained for this system to order . This potential is analyzed term by term, to observe its validity in the study of the spectra of the systems, comparing the theoretical results obtained with the experimental ones.

###### Acknowledgements:

This work was financed by the Universidad del Magdalena (Fonciencias)

#### NUMERICAL EVALUATION OF LOW FREQUENCY SOUND PROPAGATION IN TWO LAYERED MEDIA

Dorin Bibicu1 , Simona Moldovanu2 , Luminita Moraru3

1Dunarea de Jos University of Galati, Faculty of Economics and Business Administration, Romania
2Dunarea de Jos University, Computer Science and Information Technology, Romania
3University Dunarea de Jos of Galati, Chemistry, Physics and Environment, Romania

###### Abstract

This paper presents the simulation results of the infrasound sound energy transfer through various interfaces and discusses on the acoustic transparency of different media as a function of refraction index. Acoustic transparency is defined as the ratio of acoustic power radiated into the structure to the acoustic power emitted by a wave source. The effect of various surfaces on the transmission of infrasound has been studied by numerical simulation. To examine the transmitted homogeneous and inhomogeneous plane waves at the air - textile interface, we used MATLAB 2016 to calculate and plot the contributions of homogeneous and inhomogeneous plane waves as a function of frequency ranging from 3 to 5 Hz. Textiles (composed of natural or synthetic fibers) such as 100%cotton, 50% cotton – 50% flax, 100% wool (felt), nylon1 and nylon2 and flax showing various wave propagation properties were investigated. We found that almost the entire acoustic power passes through the interface of layered structure in the case of wool, cotton and flax, therefore the reflected power can be neglected. In the case of nylons, an amount of acoustic power ranging from 2% to 25% is reflected into air.

###### Acknowledgements:

The authors acknowledge funding under the Project MESMERISE 700399 from the European Union’s Horizon 2020 research and innovation programme – the Framework Programme for Research and Innovation (2014-2020).

#### USE OF ROBOTIC SIMULATION IN THE TRAINING OF NURSING STUDENTS OF THE FACULTY OF HEALTH SCIENCES: PERCEPTIONS

Angela Romero1 , Damaris Valderrama2 , Jesús González3

###### Abstract

Clinical simulation is rapidly becoming an important tool in the training of students who pursue a career in nursing as a viable complement or a substitute for practice with living patients. Although simulation can never replace real clinical practice, it is a useful tool to create realism before performing practical skills during patient care. Robotic simulation can create real scenarios that not only test knowledge, but also provide a safe environment for practicing advanced concepts and difficult patient situations. Members of the nursing faculty often have the challenge of preparing nurses for complex environments and working with interdisciplinary teams. In addition, health care administrators expect a basic competency from new nursing graduates who are prepared to function in the complex work environment independently after orientation. An exploratory and descriptive study was conducted using surveys among the students of the nursing program on the use of a humanoid robot for teaching nursing in the laboratory of practices of the Universidad del Magdalena. The results of this study indicate that, in the program and students are positively motivated about the use of technology as a teaching strategy (especially humanoid robots), which suggests a greater exploration of its use in education Nursing.

###### Acknowledgements:

This work was financed by the ”Universidad del Magdalena (Fonciencias)”

#### Robots in nursing education: a bibliometric analysis

Angela Romero1 , Liliana Martínez2 , Jesús González3

###### Abstract

Laboratory experimentation using robotics plays an essential role in nursing education. This research to answer the question, How do the use of robots by the nursing students influence the effectiveness, the usefulness, and user friendliness of, their satisfaction with, this kind of education technology for a clinical experience. Furthermore, this technology provide additional benefits such as supporting distance learning, improving lab accessibility to handicapped people, and increasing safety for dangerous experimentation. This paper analyzes the literature on robotics labs in nursing education from its beginnings to 2019, identifying the most influential publications, the most researched topics, and how the interest in those topics has evolved along the way. To do so, bibliographical data gathered from ISI Web of Science, Scopus and MedLine have been examined using two prominent bibliometric approaches: science mapping and performance analysis prominent bibliometric approaches: science mapping and performance analysis.

###### Acknowledgements:

This work was financed by the Universidad del Magdalena (Fonciencias).

#### Modeling of stress state of a perforated cement sheath in a production well

Timur Kireev1 , Guzel Bulgakova2

1USATU, Mathematics, Russian Federation
2Ufa State Aviation Technical University, mathematics, Russian Federation

###### Abstract

Modeling of stress state of a perforated cement sheath in a production well is performed. Long-term well operation is considered. The slightly compressible fluid flow model is used to calculate the pore pressure of a fluid. The linear-elastic body model and finite volume method with multipoint stress approximation are used to calculate the stress state of the cement sheath and production casing. The numerical model was verified by comparing the calculation results with a calculation in the Fenics open-source computing platform. It is shown that the maximum Mises stress value falls on the perforation zone at the junction of the cement sheath and production casing. Stresses are shown to slightly decrease during long-term well operation. It is also shown that an increase in the Young's modulus of the production casing leads to a decrease in the Mises stress in the cement sheath.

#### Differences in the properties of fused silica and silicon dioxide films: results of the atomistic simulation

Fedor Grigoriev1 , Vladimir Sulimov2 , Alexander Tikhonravov3

1M.V. Lomonosov MSU, RCC, Russian Federation
2M.V. Lomonosov MSU, RCC, Russian Federation
3M.V. Lomonosov MSU, RCC, Russian Federation

###### Abstract

The study of differences in the structural and mechanical properties of the substrate and the growing on this substrate film is important for improving the technology of optical coatings production - in particular, to reduce the mechanical stresses in the coatings. Experimental study of these differences may be still a great challenge. At the same time, due to the progress in high performance computing, it is possible to perform the atomistic simulation of thin films deposition process on the length of about a several tens nanometers that is close to the technologically sensible thicknesses. In the presented investigation the previously developed method of atomistic simulation of the film deposition process, based on classical molecular dynamics, is used to study the structural and mechanical properties of deposited silicon dioxide thin films and fused silica which is often used as a substrate for film deposition. Structural properties are analyzed using the radial distribution function and cumulative function. It is found that the excess of the density of a high-energy deposited silicon dioxide film above the fused silica density is explained by differences in the structure in the third and subsequent coordination spheres. At the same time the parameters of the first coordination sphere: bond lengths, valence angles - are almost the same for the film and the fused silica substrate. The bulk modulus, Young modulus and Poisson’s ratio are calculated for high- and low-energy deposited films and fused silica. It was founded that the all calculated parameters are higher for high-energy deposited film than for low-energy deposited film and fused silica. The reasons for these differences are discussed.

###### Acknowledgements:

The work is supported by the Russian Science Foundation (grant number 19-11-00053).

#### ANALYSIS AND NUMERICAL SIMULATION OF A VIRUS-RESISTANT HIV-1 MODEL WITH INFECTIVE IMMIGRATION.

MUSA RABIU1

1UNIVERSITY OF KWAZULU-NATAL, MATHEMATICS, South Africa

###### Abstract

In this paper, we developed a new finite dimensional virus -resistant HIV-1 model with infective immigration on the population. The basic analysis of the model was carried out. Originally, the basic reproduction number $\mathcal{R}_o$ and disease-free equilibrium doesn't exist unless a certain condition $q_1=q_2=0$ is satisfied. Asymptotic stability analysis of the endemic equilibrium was yielded using the geometric method and compound matrix theory while it became apparent that the model doesn't exhibit bifurcation. The sensitivity analysis of the model was verified to comprehend parameters that can possibly eradicate the virus. Numerical simulation of the model concludes that in the context of a virus-resistant HIV-1 model which is the most sensitive phenomenon in disease eradication, the influx of infective immigrants must be at minimal point

###### Acknowledgements:

We really acknowledge the effort of all the unknown reviewers for their effort.

#### NUMERICAL SIMULATIONS OF GASEOUS FLAMES IN COMBUSTION CHAMBER APPLICATIONS

Cosmin Katona1 , Carmen Safta2 , Florin Frunzulica3 , Marcel Goemans4

1Polytechnic University of Bucharest, Power Engineering Faculty, Romania
2Polytechnic University of Bucharest, Power Engineering Faculty, Romania
3Polytechnic University of Bucharest, Aerospace Engineering Faculty, Romania
4NUTARA Environmental BV, Process Research Department, Belgium

###### Abstract

Recent developments and assessments of combustion models, numerical schemes and high-power computing allow simulations to be applied to real industrial thermal oxidizers and burners. In this paper, two type concepts in a complex geometry of a burner and combustion chamber is reviewed by means of measurements data from on-site during operations compared with the numerical simulation's analysis. The combustion models as Flamelet, Flamelet Generated Manifolds (FGM) and Hybrid BML/Flamelet are performed to assess modeling and fundamental flow aspects of combustion instabilities in a swirl concept in the context of the Reynolds-averaged Navier Stokes (RANS) equations for gaseous flames. Simulations in real thermal oxidizers illustrate the prospective of the approach but the combustion modeling and chemistry sub-grid models are limited cases in terms of validations due to the lack of available advanced set of measurements. Specific issues associated to real thermal oxidizer are presented: on-site measurements during operations, multi-perforation of heat in the combustor walls and flame instabilities. The examples are assigned as mean flow predictions (velocity, temperature and species) and transient phenomena (ignition and flame instabilities). Finally, the conceptual differences of the potential perspectives are discussed in detail from a theoretical and practical point of view.

#### Measurement of Natural Radioactivity Using NaI (Tl) Detector in Soil Samples from Fault Regions of Mizoram, India

Rosangliana Chawngthu1

1Govt Zirtiri Residential Science College, Department of Physics, India

###### Abstract

Measurement of natural radioactivity in soil samples collected from Fault regions of Mizoram, India has been carried out using 5”X 4” NaI (Tl) Detector. Soil samples were collected from different sites located in various parts of Mizoram. The activity concentrations were measured for three specific radionuclides viz, Uranium-238, Thorium-232 and Potassium-40. The activity concentrations collected from the soil samples are found to be in the range of 12.45 Bq/kg to 58.83 Bq/kg for 238U, 34.24 Bq/kg to 161.79 Bq/kg for 232Th and 175.56 Bq/kg to 1190.25 Bq/kg for 40K. The average natural activity concentrations of 238U, 232Th and 40K collected from the soil samples are 37.4 Bq/kg, 102.86 Bq/kg and 691.47 Bq/kg which are much higher than the corresponding worldwide values of 35 Bq/kg, 30 Bq/kg and 400 Bq/kg respectively. The Radium equivalent activity concentrations levels obtained from the soil samples are within the range of 108.76 Bq/kg to 346.93 Bq/kg with an average of 237.74 Bq/kg. Radium equivalent activity concentration levels for the different regions have been found to be within the safe limit of 370 Bq/kg recommended by UNSCEAR 2000.

#### Data Encryption Based on Exponential Numbers

Ho-Hsuan Chang1

1I-Shou University, Department of Communication Engineering, Taiwan, Province Of China

###### Abstract

A novel data encryption scheme using a set of exponential numbers is proposed in this paper which aims at achieving secure communications over public networks. The study begins with the definition of pattern of exponential number, where the decimal pattern of an exponential number $g^e$ is the result of taking e-1 times multiplication the base element g by itself. The multiplication operation of two large integers involves the complicated carry conditions in each step, which is digit-dependence and can only be analyzed case by case. This implies that the pattern of a large exponential number is unpredictable. Next, we prove that nature number can be spanned by a set of exponential numbers, and there exists numerous spanning sets for one nature number, demonstrating that the expression of nature number using a set of exponential numbers is not unique. The unpredictable nature of exponential patterns and the abundant available sets of exponential numbers can contribute the concealment of information when data streams are encrypted by the exponential numbers. In addition, we prove that the base elements of a set of exponential numbers applied for spanning a nature number can be arbitrarily assigned. With this property, we can distribute a secret key sequence in advance as the base elements for data encryption, or this secret key can be shared using the Diffie-Hellman Key-Exchange system over public network. Finally, the encrypted message consists of a sequence of exponents and the index data, which indicates the relationship between the base elements and the secret key for decryption. The ciphertext is transmitted via the public channel to the receiver end; however, it can only be decrypted by those who own the secret key. Some examples are shown for demonstration the feasibility of the proposed encryption scheme.

#### NUMERICAL STUDY OF COHERENT INTERACTION OF LASER WAVES IN А NONLINEAR SPECTROSCOPY OF THE DEGENERATE ATOMIC TRANSITIONS

Aleksandr Chernenko1 , Edward Saprykin2

1Rzhanov Institute of Semiconductor Physics, Laboratory of nonlinear resonance processes, Russian Federation
2Institute of Automation and Electrometry SB RAS, , Russian Federation

###### Abstract

The results of the development of the theory of nonlinear resonances in spectroscopy of saturated absorption of degenerate atomic transitions based on the numerical solutions of systems of kinetic equations describing the resonance interaction of an atom with coherent optical fields, and the inclusion of their induced incoherent fields of spontaneous emission of excited atoms (the SIR effect [1]) are presented. This approach allows us to analyze the system of kinetic equations with a high degree of accuracy for arbitrary values of the total moments of the lower and upper atomic states, the degree of openness of the atomic transition, the intensities of both saturating and probe fields, as well as the orientation of their polarization and propagation directions [2, 3]. The specific features of the influence of these parameters on the shapes of nonlinear resonances are revealed. Some details of the approach used are demonstrated here with respect to the atomic transition between levels with the full moments J = 0, 1, 2. References: 1. S.G. Rautian, E.G. Saprykin and А.А. Chernenko. Optics and spectr.,98, 292, (2005). 2. E.G. Saprykin, А.А. Chernenko and A.M. Shalagin. JETP, 146, 229, (2014); JETP, 150, 238, (2016); JETP, 154, 223, (2018). 3. E.G. Saprykin, А.А. Chernenko. QE, 49, 479 (2019).

#### Influence of real cracks on chloride penetration in reinforced concrete

Corina Sosdean1

1Politehnica” University of Timisoara, Department Strength of Materials, Romania

###### Abstract

Due to the fact that real cracks in concrete have a complex 3D geometry and their influence on transport and degradation mechanisms is not straightforward, very limited investigation of the influence of chloride diffusion on samples with real cracks can be found in literature. With regards to the durability and service life of reinforced concrete structures (RC), this research paper, presents a 3D macro scale model with crack and rebar representation that can realistically simulate chloride penetration in RC samples with real cracks. The numerical simulation was conducted considering only diffusion, while other mechanisms are neglected, by using the mass diffusion modulus in Abaqus based on an extended form of Fick’s law. The model is validated by comparing the data obtained by numerical simulation with the experimental data previously obtained by [2]. The simulation results show that both cracking and the presence of rebars have a significant effect on chloride penetration.

#### Eight-vertex model over Grassmann algebra

Tolkyn Kassenova1 , Pyotr Tsyba2 , Olga Razina3

1L.N.Gumilyov Eurasian National University, Department of General and Theoretical Physics, Kazakhstan
2L N Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
3L N Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan

###### Abstract

An eight-vertex model on a square lattice over a Grassmann algebra is investigated using an equation that is a three-dimensional generalization of the Yang-Baxter equation. Anticommuting quantum spin systems are studied, where the quasiclassical limit leads to some abstract classical physics with anticommuting variables. The solution of the quantum Yang-Baxter equation is the $R$ - matrix, which corresponds to the transfer $R$ - matrix of the eight-vertex model of statistical mechanics.

#### Soliton surfaces associated with the (1+1)-dimensional Yajima-Oikawa equation

Zhanbala Umbetova1 , Kuralay Yesmakhanova2 , Tolkynay Myrzakul3

1L.N. Gumilyov Eurasian National University, General and theoretical physics, Kazakhstan
2L. N. Gumilyov Eurasian National University, Department of Mathematical and Computer Modeling, Kazakhstan
3al-Farabi Kazakh National University, physical-technical department, Kazakhstan

###### Abstract

Soliton surfaces associated with integrable systems play a significant role in physics and mathematics. In this paper, we investigate the relationship between integrable equations and differential geometry of surface by the example of the Yajima-Oikawa equation. The integrability of nonlinear equations is understood as the existence their Lax representations. Using the connection between classical geometry and soliton theory, we have found the soliton surface related with the Yajima-Oikawa equation. The surface area, curvature, the first and second fundamental forms are found.

#### Asymmetry of the structure of the Lorenz Attractor Equations in the basis of physical coordinates

Vadim Petrov1 , Veronika Mazulina2 , Alexander Bushuev3 , Yury Litvinov4

1Saint Petersburg State University of Information Technologies, Mechanics and Optics, Department of Computer Technologies and Control Systems, Russian Federation
2Saint-Petersburg National Research University of Information Technologies, Mechanics and Optics, Department of Computer Technologies and Control Systems, Russian Federation
3Saint Petersburg State University of Information Technologies, Mechanics and Optics, Department of Computer Technologies and Control Systems, Russian Federation
4Saint Petersburg State University of Information Technologies, Mechanics and Optics, Department of Computer Technologies and Control Systems, Russian Federation

###### Abstract

In the report, the system of Lorenz Attractor equations is considered only in the LT-basis of physical coordinates, where L is space T is time. The simulating scheme of equations is made. The blocks of the scheme are integrators, multipliers and dimensional gains. For the input and output of the blocks, only the type of physical quantity is known, for example, pressure, temperature, volume, speed, flow. For simulation, we introduce the square matrices of block inputs and outputs as well as the transfer matrix of the block. Dimensions of physical quantities form the elements of the matrices. The Euclidean norm of the matrix is the numerical value of the input or output or blocks resource consumption. The graphical representation of the structure with transfer matrices allows to find the vertical axis of the attractor symmetry and to determine the degree of asymmetry in the relations of resource consumption of the left and right parts. The method is used to simulate the solution of an inventive problem, which involves the transition from a prototype to a technical contradiction between two alternative properties. Therefore, the process is considered as a homeostatic binary division of a biological cell. The mother cell determines the prototype, and the daughter cells determine two alternative properties of the contradiction. The asymmetry brings a numerical estimate of the resource difference for alternative properties. The greater asymmetry gives a greater degree of novelty to the inventive problem, but the more difficult it is to resolve the contradiction. An example of convection is considered in a closed loop known as Benard cells.

#### Anisotropic electromagnetic string cosmological model in Brans-Dicke theory of gravitation

MUKUNDA DEWRI1

1BODOLAND UNIVERSITY, KOKRAJHAR, MATHEMATICAL SCIENCES, India

###### Abstract

This paper deals with the study of Bianchi type-I string cosmological model with electromagnetic field in B-D theory of gravitation. In this paper a new set of exact solutions of Einstein field equations in B-D theory for spatially homogeneous and anisotropic Bianchi type-I space-time have been obtained. The solutions of the Brans-Dicke field equations are found considering time dependent deceleration parameter of the form $q=-1+\frac{1}{\sqrt{t}}$. The physical and dynamical behaviors of the model has been discussed.

#### Numerical and statistical modeling based investigation of the detection efficiency of high-spectral-resolution lidars at different laser radiation wavelengths

Tsvetina Evgenieva1 , Vladimir Anguelov2 , Ljuan Gurdev3

2Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, , Bulgaria
3Institute of Electronics, Bulgarian Academy of Sciences, , Bulgaria

###### Abstract

In the present work, a numerical and statistical modeling approach is developed for estimating the operation efficiency of high-spectral-resolution lidars (HSRLs), when determining the atmospheric aerosol extinction profiles along the lidar line of sight (LOS) at different sensing (laser) radiation wavelengths from the UV, VIS and NIR spectral ranges. The efficiency estimation is based on numerical modeling of the lidar signal profile along the LOS and the corresponding profile of the signal-to-noise ratio (SNR) of its measurement. The optimally efficient wavelength (at certain distances along the LOS) is that ensuring maximum signal strength and SNR and, consequently, brighter and clearer lidar images of specific aerosol objects and background. The results about the optimum wavelengths obtained under different atmospheric-turbidity conditions (clear or hazy atmosphere), in the presence of cirrus clouds, are proved by statistical modeling and processing of realistic (noisy) lidar profiles and recovering the atmospheric extinction profiles along the LOS. It is shown that up to certain characteristic altitudes (that are lower at higher turbidity) the UV wavelengths are advantageous in the above sense. Above the mentioned altitudes, successively, first the VIS and then the NIR wavelengths become more efficient compared to the UV wavelengths.

###### Acknowledgements:

This research is funded by the Bulgarian National Science Fund under contract КP-06-N28/10.2018 and by the Bulgarian Ministry of Education and Science under grant D01-151/28.08.2018.

#### Simulation of motion of satellites after fixing the values of their accelerations

Kamil Mazitov1 , Mikhail Yushkov2

1St. Petersburg State University, St. Petersburg, Russian Federation
2St. Petersburg State University, Russia, Mathematic and Mekhanic, Russian Federation

###### Abstract

At the Department of Theoretical and Applied Mechanics of the Faculty of Mathematics and Mechanics of St. Petersburg State University [1] the theory of motion of nonholonomic systems with linear nonholonomic constraints of high order n>2 was created. The high-order constraints are considered as program and ideal ones, and their reaction force is considered as the required control force. A compatible system of differential equations with respect to unknown generalized coordinates and Lagrange multipliers is constructed to solve the problem. The report examines the motion of Soviet satellites of the systems “Cosmos”, “Molniya”, “Tundra” after fixing the values of their accelerations in apogees. This corresponds to imposing the nonlinear second-order nonholonomic constraints on the further motion of satellites [2, 3]. The equations of constraints are differentiated in time and presented as linear third-order constraints to make it possible to apply the above theory. The motions of satellites are studied in polar coordinates, the origin of this system coinciding with the center of the Earth. It turns out that after fixing the acceleration values in the apogees, the satellites begin to rotate between two concentric circles, alternately touching each of them.

###### Acknowledgements:

References 1. Soltakhanov, Sh.Kh., Yushkov, M.P.,Zegzhda S.A. Mechanics of non-holonomic systems. A New Class of control systems. Berlin Heidelberg: Springer-Verlag. 2009. 329 p. 2. Soltakhanov, Sh.Kh.,Yushkov, M.P. The use of the generalized Gauss principle for constructing the equations of motion for systems with non-holonomic third-order constraints // Vestnik Leningradskogo Universiteta. 1990. Ser. 1. Issue.3. No. 15. Pp. 77-83 (in Russian) 3. Soltakhanov, Sh.Kh.,Yushkov, M.P. The equations of motion of a certain nonholonomic system in the presence of second-order constraints // Vestnik Leningradskogo Universiteta. 1991. Ser. 1. Issue.4. No. 22. Pp. 26-29 (in Russian)

#### EDUCATIONAL ROBOTICS AS A TEACHING TOOL IN HIGHER EDUCATION INSTITUTIONS: A BIBLIOGRAPHICAL ANALYSIS

Jesús González1 , Henry Sánchez2 , Liliana Martínez3

###### Abstract

The incorporation of robotics as an educational tool in higher education institutions has represented in recent years an innovative mechanism towards improving the teaching of mathematics, physics and development of control software. This work shows our research about the use of efficient robotics in educational processes in higher education institutions and their perspectives of new innovations towards teaching in engineering, health sciences, biology, chemistry, physics, etc. Bibliometric tools were used to analyze the evolution of educational robotics as an element that contributes to the improvement of teaching and involvement in teaching methods used by teachers.

###### Acknowledgements:

This work was financed by the Universidad del Magdalena (Fonciencias)

#### Viscoelastic metamaterial design for wave propagation with a low-frequency passband

Zheng Li1

1Peking University, Mechanics and engineering science, China

###### Abstract

Wave propagation in heterogeneous or inhomogeneous media is of great importance in scientific and technological research. Especially, artificially designed sub-wavelength materials with exceptional effective properties, termed as metamaterials, have dedicated to manipulating waves in unimaginable ways. In order to design the viscoelastic metamaterial with a low-frequency passband, we present a theoretical study and experimental realization of a dissipative elastic metamaterial that functions as a bandpass filter with a low-frequency passband. The mechanism of dissipation in this structure is well described by a mass-spring-damper model that reveals that the imaginary part of the wavenumber is non-zero, even in the passband of dissipative metamaterials. By using the Kelvin-Voigt mechanical analog, the effects of using viscoelastic materials is investigated. A prototype for this viscoelastic metamaterial model is fabricated by 3D printing techniques using soft and hard acrylics as constituent materials. Results show that the passband becomes narrower with the increase of the damping coefficients and also with increasing the length of the metamaterial. The transmittance of the printed metamaterial is measured and shows good agreement with theoretical predictions, demonstrating its potential in the design of compact waveguides, filters and other advanced devices for controlling mechanical waves.

###### Acknowledgements:

National Natural Science Foundation of China under grant No. 11672004

#### A multi-temperature kinetic Ising model and its applications to partisanship dynamics in the US Senate

Irina Mazilu1 , Anthony Lorson2 , Sho Gibbs3 , Will Hanstedt4 , Dan Mazilu5

1Washington and Lee University, Department of Physics and Engineering, United States
2Washington and Lee University, Physics and Engineering, United States
3Washington and Lee University, Physics and Engineering, United States
4Washington and Lee University, Physics and Engineering Department, United States
5Washington and Lee University, Department of Physics and Engineering, United States

###### Abstract

As the political landscape becomes increasingly complex, the classic paradigms used in political science have failed to remain relevant and other methods of study are needed. We use a multi-temperature kinetic Ising model to analyze the partisanship dynamics of the US Senate. We use Monte Carlo simulations, mean field theory and numerical analysis of the master equation of a system of 100 senators (agents) separated into various categories based on their political leanings and interactions with each other. Results show an interesting development of partisanship between the agents after a short time. The model can be extended to other cooperative stochastic systems in physics and social sciences.

#### Modeling of the process of treatment of polluted washing water in circulating water systems

Andrei Melekhin1

1National Research Moscow State University of Civil Engineering, Heat and gas supply and ventilation, Russian Federation

###### Abstract

The modeling of the process of cleaning polluted washing water in circulating water use systems and solutions to the problems of optimizing the process parameters.

#### Simulation of mechanical behaviour of the proximal femur as a poroelastic solid using particles

Alexey Smolin1 , Galina Eremina2 , Andrey Dimaki3 , Evgeny Shilko4

1Institute of Strength Physics and Materials Science of Siberian Branch of Russian Academy of Sciences, Laboratory of Computer-Aided Design of Materials, Russian Federation
2Institute of Strength Physics and Materials Science of SB RAS, Laboratory of computer-aided design of materials, Russian Federation
3Institute of Strength Physics and Materials Science of SB RAS, Laboratory of computer-aided design of materials, Russian Federation
4Institute of Strength Physics and Materials Science SB RAS, Laboratory of computer-aided design of materials, Russian Federation

###### Abstract

Full understanding of the mechanical behaviour of living bone is the key to solving many important problems of modern orthopaedics and arthroplasty. An important role in the study of the mechanical behaviour of living bone belongs to the development and use of comprehensive numerical models. In this work, we model the mechanical behaviour of the proximal femur as a 3D poroelastic solid consisting of the interior cancellous part and the outer cortical part. For simplicity, both parts are assumed to be isotopic linear poroelastic material. But they have different values of porosity, fluid content and elastic properties, which are taken from literature. For computer simulation, we used the so-called movable cellular automaton method, which is a representative of simply deformed discrete elements i.e. computational particle mechanics. The method allows simulating dynamics of the elastic skeleton deformation and viscous fluid flow in the skeleton pores according to Biot’s theory of linear poroelasticity. Using the model developed we study the mechanical behaviour of the proximal part of the femur in compression with different rate of loading and different boundary conditions. The results obtained for both saturated and drained bones are discussed.

###### Acknowledgements:

The investigation has been carried out at financial support of the grant No. 17-11-01232 of the Russian Science Foundation (the models developed and the simulations) and framework of the Russian Fundamental Research Program of the State Academies of Sciences for 2013–2020 (Priority direction III.23, the modifications of the MCA software for importing CAD models and modelling pore structure).

#### Robust stability of a class of differential systems with state after-effect dynamics

Manuel De la Sen1

1University of the Basque Country, Elwctricity and Electronics, Spain

###### Abstract

This paper is concerned with the investigation of the global stability and global asymptotic stability of the error with respect to its nominal version of a non-linear time-varying perturbed functional differential system which is influenced by point, finite-distributed and Volterra-type distributed delayed dynamics. The boundedness of the error and its asymptotic convergence to the zero equilibrium are investigated and some formal “ ad- hoc” results are proved.

#### Mesoscopic model for nano-channel confined DNA

Marco Zoli1

1University of Camerino, School of Science & Technology, Italy

###### Abstract

The stability properties of ds-DNA are important in a number of molecular biology techniques (e.g., polymerase chain reaction) and nanotechnological devices (e.g., DNA-based sensors) in which short fragments of synthetic DNA are used as a recognition element by virtue of the peculiar Watson-Crick base pairing, allowing for selective hybridization with a target sequence. The helix stability properties are also key to single molecule denaturation mapping experiments, recently used combined with nanochannel arrays, which confine and stretch the DNA molecule to be analyzed. These techniques are based on the fact that AT rich regions melt at lower temperatures than GC rich regions; staining the molecule with a fluorescent dye that binds only to ds regions one obtains an optical barcode unique to the sequence of the specific molecule. The DNA properties are also strongly affected in confined conditions as those which occur in vivo in the crowded environments of cells where macro-molecules \textit{i)} reduce the free volume for base pair fluctuations thus suppressing the melting entropy, \textit{ii)} interfere with the dynamics of DNA looping thus affecting the speed of gene activation or repression. While considerable amount of experimental work has been carried out over the last decades to investigate the relation among macro-molecular crowding, DNA dynamics and its biological functioning, much less theoretical studies have been produced so far on DNA in crowded conditions. Here I focus on the interplay between DNA structure and confining environment analyzing how a crowders distribution around a single DNA chain may concur to shape the helical conformation and the overall size of the molecule itself. The study assumes a coarse grained Hamiltonian model which describes the helical molecule at the level of the base pair. The equilibrium statistics of the system is obtained by a computational method based on a finite temperature path integral method which I have developed over the last years. The method has been widely discussed in conjunction with calculations of some fundamental indicators of DNA flexibility at short length scale such as the cyclization probabilities, the persistence lengths and the single molecule response to stretching perturbations induced by external loads. After reviewing the method and previous researches, I present some recent results regarding the stretching and twisting of short DNA fragments simulating the presence of specific crowders profiles.

#### A heat transfer problem with a free boundary in context of endovenous laser ablation

Alena Astrakhantseva1 , Alexander Chebotarev2 , Andrey Kovtanyuk3

1Far Eastern Federal University, Department of computer science, mathematical and computer modelling, Russian Federation
2Far Eastern Federal University, Institute for Applied Mathematics FEB RAS, , Russian Federation
3Far Eastern Federal University, Institute for Applied Mathematics FEB RAS , , Russian Federation

###### Abstract

Endovenous laser ablation is a very effective minimally invasive therapy to manage leg varicosities. The corresponding mathematical model is based on conversion of absorbed laser energy into heat. To describe the process of endovenous laser ablation, the radiative-conductive heat transfer model with moving source is chosen. The conventional non-stationary normalized $P_1$ approximation of the radiative-conductive heat transfer model is considered in a bounded domain $\Omega \subset \mathbf{R}^3$ which consists of a finite number of disjoint subdomains $\Omega_j$, $j=1,..., p$\,: $$\label{1} a \partial\theta/\partial t - \mathrm{div}\,(k\nabla\theta) - b \varphi = u_1,\; - \mathrm{div}\,(\alpha \nabla \varphi) + \beta \varphi = u_2,\; x\in\Omega,\ t\in (0,T).$$ Here, $\theta$ is the normalized temperature; $\varphi$ is the normalized radiation intensity averaged over all directions; $k$ is the thermal conductivity; $a$, $b$, $\alpha$, and $\beta$ are piece-wise constant functions describing the thermal and radiation properties of the medium (see, e.g., \cite{1}), $a(x)=a_i$, $b(x)=b_i$, $\alpha(x)=\alpha_i$, $\beta(x)=\beta_i$ if $x \in \Omega_i$, $j=1,..., p$. The functions $u_{1,2}=u_{1,2}(x,t)$ describe the intensities of heat and radiation sources. Let $k(x) = k_j$ if $x \in \Omega_j$, $j=2,...,p$\,;\, $k(x) = c(\theta) k_1$ if $x \in \Omega_1$, where $c(\theta) = 1$ if $\theta < \theta_*$, and $c(\theta) = m > 1$ if $\theta \geq \theta_*$\,;\, $k_1, ... k_p, m = Const$. The subdomain $\Omega_1$ corresponds to blood fraction, and the factor $c(\theta)$ simulates the rise of thermal conductivity due to boiling effect. We consider the right-hand sides of equations (1) having the structure $u_{1,2} = P_{1,2}(t)f_\varepsilon(x,r(t))$, $x\in \Omega,\,t\in (0,T)$. The functions $P_{1,2}$ describe the powers of heat and radiation sources, $f_\varepsilon(x,r(t))=1$ if $|x-r(t)|<\varepsilon$, and $f_\varepsilon(x,r(t))=0$ otherwise; $r(t)$ is a given trajectory of a moving source. The following boundary conditions on $\Gamma := \partial \Omega$ and the initial condition at $t=0$ are assumed: $$\label{2} a\partial_n \theta + h(\theta - \theta_b)|_\Gamma = 0,\;\; \alpha\partial_n \varphi + 0.5\varphi|_\Gamma = 0, \quad \theta|_{t=0} = \theta_0.$$ Here, $\partial_n$ denotes the derivative in direction of the outward normal $n$; the boundary functions, $\theta_{b}$, $h$, and the initial function, $\theta_0$, are given. Let $\theta_i(x) = \theta(x)$ and $\varphi_i(x) = \varphi(x)$ if $x \in \Omega_i$, $j=1,..., p$. At the internal boundaries between adjoint subdomains $\Omega_i$ and $\Omega_j$, \, $1 \leq i,j \leq p$,\, $i \neq j$, we set the following conjugation conditions: $$\label{3} \theta_i = \theta_j, \;\; a_i\partial_n \theta_i = a_j\partial_n \theta_j, \;\;\; \varphi_i = \varphi_j, \;\; \alpha_i\partial_n \varphi_i = \alpha_j\partial_n \varphi_j,\;\;\; x \in \overline{\Omega}_i \cap \overline{\Omega}_j.$$ In the current work, a priori estimates of temperature and radiation intensity in the space $L^{\infty}$ ensuring the unique solvability of the problem (1)--(3) are presented. The theoretical analysis is illustrated by numerical examples simulated the process of endovenous laser ablation. \begin{thebibliography}{9} \bibitem{1} G.V.~Grenkin, A.Yu.~Chebotarev, A.E.~Kovtanyuk, N.D.~Botkin, K.-H.~Hoffmann, \textit{J. Math. Anal. Appl.}, \textbf{433}, 1243--1260 (2016). %\bibitem{2} A.E.~Kovtanyuk, A.Yu.~Chebotarev, N.D.~Botkin, K.-H.~Hoffmann, \textit{Commun. Nonlinear Sci. Numer. Simulat.}, \textbf{20}, 776--784 (2015). \end{thebibliography}

#### Nonlinear Finite Element Analysis of Thermal Field Distribution in Cavity Structure of Electronic Packaging

Lingfei Zhang1 , Xinquan Lai2 , Jun Ma3 , Chen Liu4 , Yun Zhang5

1Qinghai Nationalities University , College of Physics and Electronic Information Engineering , China
2Xidian University, The Institute of Electronic CAD, China
3Qinghai Normal University, School of Computer, China
4Xidian University, The Institute of Electronic CAD, China
5Xidian University, The Institute of Electronic CAD, China

###### Abstract

Aiming at the heat dissipation problem of the cavity structure of electronic packaging. Firstly, according to the theory of thermal field analysis and the non-linear finite element formula of thermal field, the thermal field finite element model for the cavity structure of electronic packaging is established. Depend on the cavity structure of electronic packaging, the thermal field distribution in different situations of the electronic packaging cavity structure is simulated, considering the thermal field analysis of the cavity under the influence of gravity field. In addition, under the influence of the heat source of single or multiple heating electronic components and the effect of radiation, convection, conduction of heating electronic components, the thermal field distribution in the package structure and the characteristics of thermal field are analyzed. Finally, the thermal field analysis of the electronic packaging cavity structure under forced air cooling is discussed.

#### Gödel's incompleteness theorem and Universal physical theories

Uri Ben-Ya'acov1

1Kinneret Academic College on the Sea of Galilee, School of Engineering, Israel

###### Abstract

Is it possible to encompass the full extent of the Universe with a finite number of first principles and inference rules ? The belief that it is possible to arrive at a complete theory that fully describes the whole of the physical world – a theory that accounts, via few and simple first principles, for all the phenomena already observed and that will ever be observed – has been, for many-many years and for most researches, a fundamental tenet of the scientific research. However, Gödel's incompleteness theorem implies that any formal structure, based on a finite number of first principles and inference rules, which is rich enough, cannot be at the same time both consistent and complete. Completeness, in terms of physical theories, implies that if the necessary initial data are given then the state of a physical system can be predicted for any time in the future. Does Gödel's theorem apply to physics ? A common argument in favour of applying Gödel's theorem to physics, is, more or less, that "Gödel's theorem applies to arithmetics which is the basis of mathematics, physics uses mathematics, therefore Gödel's theorem applies to physics". However, the counter-argument says that there are mathematical theories to which Gödel's theorem does not apply, e.g. geometry, and that this is the type of mathematics that physics uses, therefore we should not expect that Gödel's theorem applies to physics. The purpose of the talk is to present and put forward another argument, which I believe is the decisive one. Gödel's theorem (whenever it applies) points to incompleteness in the sense that there will always be claims that may be formulated within this formal system but are undecidable – propositions that cannot be either proved or refuted. A close inspection of Gödel's theorem demonstrates that this impossibility arises when the claims are self-referential, or, more precisely, when the system asks to define itself in its own terms. Self-referencing occurs in physics whenever the observer is also part of the observed system. In most physical system this is not the case, therefore the counter argument should apply. However, when it is the whole Universe that is dealt with, then we, the observers, are also part of it, and Gödel's theorem should apply. The talk will discuss self-referencing in Gödel's theorem, its relation with our involvement in the Universe, and consequences thereof.

#### Effective Data Analysis: A Review of Fuzzy Clustering Techniques Using Kernel Functions

Esha Kashyap1 , Kannan Sr2

1Pondicherry University(A Central University of India), Mathematics, India
2Pondicherry University(A Central University of India), Mathematics, India

###### Abstract

This paper reviews the influence of kernel function in unsupervised way of clustering in data analysis. Unsupervised clustering analysis is considered as an explorative data analysis tool that assists in discovering hidden patterns or natural grouping in data, and has been effectively applied in various applications. The implementation of kernel function with the objective functions of unsupervised clustering techniques contribute an effective works for recognizing nonlinear structures of high dimensional databases and the objective functions are robust in clustering the high dimensional databases which contains outliers with heavy noise. This paper mainly discusses the kernels with the objective functions of fuzzy c-means, possiblistic c-means, and intutionistic fuzzy c-means for clustering the non-liner structured databases. Experimental section of the paper supports to understand the effective of kernel in various clustering methods.

###### Acknowledgements:

This work was financially supported by DST India and MOST Israel

#### NUMERICAL SIMULATION OF THE REFLECTION AT A LIQUID-SOLID INTERFACE OF ULTRASONIC WAVES RADIATED BY A PHASED-ARRAY TRANSDUCER

1Higher School of Applied Sciences, Department of Physics, Algeria

###### Abstract

Phased-array transducer are becoming of common use in ultrasound imaging either in medical applications or in the field of non destructive technique. The modelling of the acoustic field emitted by phased-arrays transducers can be realized by different methods developed in the frequency domain or in the time domain. The method proposed here consists in using the Rayleigh integral method where the reflection at the plane interface is taken into account by using the reflection coefficients for harmonic plane waves. The transient field is obtained by an inverse Fourier transform of the harmonic results. The results obtained put in evidence the fact that the ultrasonic waveforms reflected by a liquid-solid interface and detected by the phased-arrays transducer depend strongly on the geometrical and physical parameters of these kind of transducers. The transient representation of these waves have been analysed and discussed by the rays model. . A potential application of this work would be the study of the acoustic signature of materials by using phased-arrays transducer working in pulsed mode. The obtained results have been compared to those obtained by using a finite element method package.

#### Modeling directed self-assembly of nanoparticles under parallel electric fields

Matthew Withers1 , Elise Baker2 , Dan Mazilu3 , Irina Mazilu4

1Washington and Lee University, Department of Physics and Engineering, United States
2Washington and Lee University, Department of Physics and Engineering, United States
3Washington and Lee University, Department of Physics and Engineering, United States
4Washington and Lee University, Department of Physics and Engineering, United States

###### Abstract

We design and model an experiment to study the effect of electric bias on particle-coverage densities produced during ionic nanoparticle self-assembly. The experiment involves the application of a uniform external electric field parallel to a glass substrate during the self-assembly of silica nanoparticles. We refer to this procedure as directed self-assembly of monolayers (DSAM). In our theoretical analysis, we modify existing cooperative sequential adsorption models to account for diffusion under an applied electric field. We use the mean field approximation to solve for particle-coverage densities. To ascertain the validity of this method, we compare our solutions to Monte Carlo simulations of the system.

#### Computational model for the ionic self-assembly of nanoparticles under the influence of external electric fields

Elise Baker1 , Matthew Withers2 , Emma Aldrich3 , Isabel Shaffrey4 , Justin Pusztay5 , Dan Mazilu6 , Irina Mazilu7

1Washington and Lee University, Department of Physics and Engineering, United States
2Washington and Lee University, Department of Physics and Engineering, United States
3Washington and Lee University, Department of Physics and Engineering, United States
4Washington and Lee University, Department of Physics and Engineering, United States
5Washington and Lee University, Department of Physics and Engineering, United States
6Washington and Lee University, Department of Physics and Engineering, United States
7Washington and Lee University, Department of Physics and Engineering, United States

###### Abstract

We present a class of cooperative stochastic models for adsorption and evaporation of monomers on two- and three-dimensional lattices subjected to perpendicular external electric fields. These models are motivated by the fabrication of optical coatings using layer-by-layer self-assembly. We report computational and analytical results for the time-dependent particle density and discuss a particular experimental implementation of an ionic self-assembled monolayer under the influence of a constant electric field.

#### A Monte Carlo study of a cooperative three-state model with adsorption and evaporation and its applications

Dan Mazilu1 , Matthew Withers2 , Will Hanstedt3 , Sho Gibbs4 , Anthony Lorson5 , Irina Mazilu6

1Washington and Lee University, Department of Physics and Engineering, United States
2Washington and Lee University, Department of Physics and Engineering, United States
3Washington and Lee University, Physics and Engineering Department, United States
4Washington and Lee University, Department of Physics and Engineering, United States
5Washington and Lee University, Physics and Engineering, United States
6Washington and Lee University, Department of Physics and Engineering, United States

###### Abstract

We present a versatile cooperative three-state model with adsorption and evaporation defined on different topologies: two- and three-dimensional lattices and Cayley trees. We discuss this model in the context of two main applications: silica and titania self-assembled optical coatings on glass substrates and drug encapsulation of two different types of nanoparticles on tree-like synthetic polymers called dendrimers and described mathematically as Cayley trees. We present analytical and Monte Carlo simulation results for these different topologies and discuss other possible extensions of the model to social sciences.

#### Optimization mathematical models of the peaceful subordinating interactions of two States

Valeriy Zakharov1

1Lomonosov Moscow State University, Mathematical Analysis, Russian Federation

###### Abstract

The paper presents some optimization dynamic mathematical models of the peaceful currency trading subordinating interactions of two States in favor of one of them, constructed on the base of the earlier created by the author optimization dynamic mathematical model of a State. In all the indicated up to date in the world scientific literature models the considered economical subjects are not States. And the models themselves are not optimization. In the previous articles and monographs the author has developed some general mathematical optimization model of a State. There were conducted some successful numerical simulations on its base. A progress in constructing on this base of some general mathematical optimization models of interactions of several States has come in 2018, when peaceful and military subordinating interactions of two States were mathematically formalized by the author. Namely these kinds of interactions became the most noticeable events in the history of 20 and 21 centuries. The aim of either peaceful or military subordinating interactions is one and the same. It is the achievement of the largest divergence of total wealths of interacting States by the end of some time interval in favor of one of them. However, methods of control at these interactions may qualitatively differ from each other. Further in the present article we consider only the peaceful currency trading subordinating interactions of two States with optimal coordinated or not coordinated controls in favor of the subordinate State. The paper is purely conceptual. Neither theoretical nor practical methods of solution of formulated optimization problems are considered in the paper. All customary terms are used in the mathematical sense only.

#### Modeling of mechanical behavior in additive manufacturing at part scale

Qiang CHEN1 , Erwan Beauchesne2 , Françis Arnaudeau3 , Pierre-Richard Dahoo4 , Constantin Meis5

1Laboratoire ATmosphères, Milieux, Observations Spatiales, IMPEC , France
2Altair Engineering, , France
3Altair Engineering, , France
4Laboratoire ATmosphères, Milieux, Observations Spatiales, , France
5Commissariat à l'Energie Atomique et aux Energies Alternatives, , France

###### Abstract

During the last decade the industrial interest in Additive Manufacturing (AM) has increased significantly. This innovative technology, initially developed for preproduction of visualization models for prototyping, is now close to deliver end-use products for direct industrial needs. Among the AM techniques, Laser Beam Melting is actually capable of producing parts with reliable mechanical properties. However, an AM efficient production still remains a challenging process as the difficulties related to distortion or cracking have not been mastered yet due to the large number of various parameters involved in the process. To reach the right first time level, needed for mass production with considerably reduced inherent costs, high quality numerical simulation is required in order to understand the physical mechanisms involved. Consequently, a numerical model is actually under development for understanding the relationship between different process and material parameters with the mechanical state of final parts such as distortion and residual stress. Macroscopic scale is considered in this work. Classical finite element method is used to solve the coupled thermo-mechanical problem on the whole domain defined by the workpiece, the baseplate and the support structures. At this scale, powder packing is neglected as well as the hydrodynamics behavior within the melt pool. Homogeneous equivalent heat source is used and imposed until several layers below the current deposited layer. Elastoplastic constitutive material law with temperature dependent parameters has been developed. This model is also coupled with phase transformation as it has significant influence on the final distortion. The resolution is based on explicit time scheme, requiring less memory resource compared with implicit resolution with the additional benefit to get rid of all inherent nonlinearities due to the thermo-mechanical coupling. At last, specific time step treatments are done to remedy the large difference between the thermal and mechanical time step. Simulations are carried out with the construction of simple wall and the popular cantilever. The results show the performance of the developed model, including computing efficiency and accuracy. By model simplification and acceleration technology, whole part simulation is affordable even with a laptop in a couple of hours. The accuracy of the model is validated by comparing the distortion with experimental results for different materials.

#### Mathematical model of tungsten erosion with generation of microparticles from the front wall of thermonuclear reactors

Galina Lazareva1

1Novosibirsk State University, Mechanics and mathematics faculty, Russian Federation

###### Abstract

On the experimental stand Beam of Electrons for materials Test Applications (BETA) created in the INP SB RAS, the results of heating the tungsten plate by the action of a high-speed electron beam on it were obtained [1]. The work is devoted to the numerical implementation of the tungsten heating, melting and evaporation processes model. Currently, work on the simulation of erosion of fusion reactor wall material under high-power pulsed plasma flow is divided into three stages. The first stage is the calculation of heat sink around cracks formed under pulsed heat load [2]. The extension of the model involves the inclusion of equations of elasticity. The second stage is the calculation of dynamics of the melt formed under pulsed heat load [3]. The third stage is the calculation of gas dynamics above the surface of the plate. The extension of the model involves the inclusion of Maxwell's equations for calculation of electric and magnetic fields. The results of calculations are correlated with experimental data obtained at the experimental stand of BETA in INP SB RAS. 1. L. Vyacheslavov, A. Arakcheev, A. Burdakov, I. Kandaurov, A. Kasatov, V. Kurkuchekov, K. Mekler, V. Popov, A. Shoshin, D. Skovorodin, Y. Trunev, A. Vasilyev. Novel electron beam based test facility for observation of dynamics of tungsten erosion under intense ELM-like heat loads // AIP Conference Proceedings (2016), 1771, 060004. 2. Lazareva G.G., Arakcheev A.S., Kandaurov I.V., Kasatov A.A., Kurkuchekov V.V., Maksimova A.G., Popov V.A., Shoshin A.A., Snytnikov A.V., Trunev Yu.A., Vasilyev A.A., Vyacheslavov L.N. Calculation of heat sink around cracks formed under pulsed heat load // IOP Conf. Series: Journal of Physics: Conf. Series 894 (2017) 012120. 3. A.S. Arakcheev, D.E. Apushkinskaya, I.V. Kandaurov, A.A. Kasatov, V.V. Kurkuchekov, G.G. Lazareva, A.G. Maksimova, V.A. Popov, A.V. Snytnikov, Yu.A. Trunev, A.A. Vasilyev, L.N. Vyacheslavov Two-dimensional numerical simulation of tungsten melting under pulsed electron beam // Fusion Engineering and Design, 2018, vol 132, pp. 13-17.

###### Acknowledgements:

This work is supported in by RFBR (project no. 19-01-00422 A)

#### Investigation of a Family of Dynamic Systems with Reciprocal Polynomial Right Parts in a Poincare Circle

Irina Andreeva1

1Peter the Great St. Petersburg Polytechnic University, Higher Mathematics, Russian Federation

###### Abstract

A family of dynamical systems on a real plane x, y is considered dx/dt = X (x, y), dy/dt = Y (x, y), where X (x, y), Y (x, y) are reciprocal forms of x and y, X is a cubic, and Y is a square form, such as X (0,1) > 0, Y (0, 1) > 0. A problem is formulated to reveal all topologically different phase portraits possible for these systems in a Poincare circle and outline close to coefficient criteria of each one portrait’s appearance. In order to solve this problem we use a method of serial mappings of Jules Henri Poincare: 1) a central mapping of a plane x, y, augmented with a line at infinity, onto a Poincare sphere ∑ with identified diametrically opposite points, 2) an orthogonal mapping of a lower enclosed semi sphere of a sphere ∑ onto a Poincare circle Ω with identified diametrically opposite points of its boundary Г. Several parts of this work are devoted to a solution of an assigned problem for those systems of the abovementioned family, which decompositions of polynomials X (x, y), Y (x, y) into the real forms of lower degrees contain 3 and 2 multipliers correspondingly; 2 and 2 multipliers; another numbers of different multipliers. Due to these differences we split the whole broad family of dynamic systems under consideration to several subfamilies belong to different hierarchical levels. The process of a study of a fixed subfamily contains the following steps. We enlist singular points of systems belong to the given family in a Poincare circle Ω: they apper to be a finite point O(0, 0)∈Ω and some infinitely remote points. For each singular point we introduce notions of bundles N (node) and S (saddle) of semi trajectories of systems of the family, adjacent to this singular point; of the topodynamical type of the singular point (TD – type); and a separatrix of the singular point. Further we study the behavior of separatrices of singular points of systems belonging to a taken family and answer the questions about a) the uniqueness of continuation of each of separatrices from a small neighborhood of a singular point to all its lengths; b) a mutual arrangement of all separatrices in a Poincare circle Ω. We construct phase portraits of systems belonging to a given subfamily in the both forms such as a graphical form and a table form. The close to coefficient criteria of the realization of each phase portrait are also indicated. The result of this work is the follows: for the whole family exist more than 250 topologically different phase portraits. This amount may seem rather large, but it is necessary to remember: the whole number of dynamic systems in the considered family is countless. By the way it was proved that there are no limit cycles for the systems of this broad family. This thorough study demanded developing some new special investigating methods, which may be used in further research of dynamic systems having polynomial right parts as well as for applications.

###### Acknowledgements:

This work was initialized and conducted together with Professor Dr. Alexey F. Andreev, the Honored Professor of the St. Petersburg State University (1923 - 2017).

#### Quantum tunneling through two sequential barriers: A simple derivation

Zuleima Carrasco1 , Richard Pachacama2 , Cristian Vacacela Gomez3 , Noemi Moreta Morocho4

1Escuela Superior Politécnica de Chimborazo, Physics Research Group, Ecuador
2Escuela Superior Politécnica de Chimborazo, Physics Research Group, Ecuador
3Escuela Superior Politécnica de Chimborazo, Physics Research Group, Ecuador
4Escuela Superior Politécnica de Chimborazo, Physics Research Group, Ecuador

###### Abstract

Quantum tunneling theory is widely used for many applications in different areas from the fundamental research to technological applications. In particular, the quantum tunneling appears in scanning tunneling microscope, nuclear physics, quantum computing, tunnel diode, among other. Here, we show a simple mathematical derivation of the one-dimensional quantum transmission considering two particular cases: (i) for comparison purposes, the conventional quantum tunneling with one potential barrier and (ii) the quantum tunneling with two potential barriers considering a small distance between barriers, in which a pseudo-potential is created and the particle is non-free. As known, the quantum transmission in the first case, depends only on the incident particle energy (kinetic energy), the mass of particle, the energy barrier (potential energy) and the barrier length that the particle passes through. However, on the second case, an extra dependency is observed, i.e., the separation distance between barriers (the Harmant effect is cancel). We have corrobarated that the first case evidence the major quantum transmition probability respect to second one. Aditionally, we evidence that transmition probability can be modulate and controlled by changing the separation distance between barriers, which produces a region where the particles can be free or trapped. If this discovery is confirmed by future experiments, such as waveguide experiments, it could enhance the particle manipulation at nanometer scale improving the image resolution.

###### Acknowledgements:

I would thanks Physics Research Group - ESPOCH and Dr. Cristian Vacacela Gomez, Ms. Noemi Moreta, Dennys Colcha and Dr. Richard Pachacama for the opportunity to present this work at the event, which help me to increase my expertise and aptitudes taken from my undergraduate career.

#### The EPR-B Paradox Resolution. Bell inequalities revisited

Jaykov Foukzon1

1Israel Institute of Technology, Department of mathematics, Israel

###### Abstract

One of the Bell's assumptions in the original derivation of his inequalities was the hypothesis of locality, i.e., the absence of the influence of two remote measuring instruments on one another. That is why violations of these inequalities observed in experiments are often interpreted as a manifestation of the nonlocal nature of quantum mechanics, or a refutation of a local realism. It is well known that the Bell's inequality was derived in its traditional form, without resorting to the hypothesis of locality and without the introduction of hidden variables, the only assumption being that the probability distributions are nonnegative. This can therefore be regarded as a rigorous proof that the hypothesis of locality and the hypothesis of existence of the hidden variables not relevant to violations of Bell's inequalities. The physical meaning of the obtained results is examined. Physical nature of the violation of the Bell inequalities is explained under new EPR-B nonlocality postulate.We show that the correlations of the observables involved in the Bohm--Bell type experiments can be expressed as correlations of classical random variables. The revisited Bell type inequality reads |&lt;AB&gt;+&lt;A′B&gt;+&lt;AB′&gt;-&lt;A′B′&gt;|≤6.

#### Pressure - velocity projection method with mixed type approximation for Oseen discrete operator.

Nikolay Evstigneev1 , Oleg Ryabkov2

1Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow, Russia, 81 Macrodynamical systems, Russian Federation
2Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow, Russia, , Russian Federation

###### Abstract

We are considering the problem of divergence - free projection in rectangular domains for the Oseen (stationary Navier-Stokes) operator ($F(\mathbf{u}, p)$): $$F(\mathbf{u}, p) := (\mathbf{u}, \nabla) \mathbf{u}+\nabla p - \nu \Delta \mathbf{u}-\mathbf{h} = \mathbf{0},$$ $$\nabla \cdot \mathbf{u}=0,$$ with zero wall boundary conditions. It uses nodal Finite Element method (space $\mathcal{P}$) to reconstruct pressure and Finite Difference method (space $\mathcal{V}$ for scalar functions and $\mathcal{V}^d$ for vector functions with $d=2,3$) for other parts of the equations. This allows us to use simple finite difference schemes for linear part (compact difference schemes) and WENO-type schemes for the the nonlinear part in the space of discrete velocities. The boundary conditions in $\mathcal{V}$ are formulated in Finite Volume conservative approach. Besides, such approach compies with the LBB condition automatically. We form the projection operator matrix $\mathtt{P}$ as follows: $$\mathtt{P}:=\mathtt{E}_d+\mathtt{G} \mathtt{A}^{-1} \mathtt{I} \mathtt{D},$$ where matrices are identity ($\mathtt{E}_d:\mathcal{V}^d \to \mathcal{V}^d$), gradient ($\mathtt{G}:\mathcal{P} \to \mathcal{V}^d$), regularized inverse Laplace ($\mathtt{A}^{-1}:\mathcal{P} \to \mathcal{P}$), interpolation ($\mathtt{I}:\mathcal{V} \to \mathcal{P}$) and divergence ($\mathtt{D}:\mathcal{V}^d \to \mathcal{V}$), respectively, from left to right. We wish to use the suggested method in the framework of continuation process in bifurcation analysis problem of stationary solutions. In this case we need so solve the problem using Newton's method: $$\mathcal{P} F_{\mathbf{u}^n} \delta \mathbf{u} = - \mathcal{P}F(\mathbf{u}^n),$$ $$\mathbf{u}^{n+1} = \mathbf{u}^{n} + \delta \mathbf{u}, \mathbf{u}^{n} \leftarrow \mathbf{u}^{n+1},$$ where the application of the projector nulls the pressure gradient. The method is applied incrementally, i.e. $\mathbf{f} = -F(\mathbf{u}^n)$, $\mathbf{g} = \mathcal{P}\mathbf{f}$, and use $\mathbf{g}$ in the right hand side of the linear system. We numerically analize the operator $\mathtt{R}$ that acts in the $\mathcal{V}$ space of divergence operator image: $$\mathtt{R}:=\mathtt{E}_1+\mathtt{D} \mathtt{G} \mathtt{A}^{-1} \mathtt{I},$$ where $\mathtt{E}_1: \mathcal{V} \to \mathcal{V}$. It is shown that all eigenvalues of the operator are less than unity for Oseledets-type wall (marked $w$) boundary conditions for velocity, namely: $(\mathbf{n}|_w, \mathbf{u}|_w) = 0, (\mathbf{\tau}|_w, \mathbf{u}|_w) = -\nabla_{\tau} p$ and zero Neumann conditions for the Poisson equation. We illustrate that the convergence rate depends on the smoothness of the projected function and that the projection method allows one to obtain divergence-free solutions with desired tolerance. We show that for smooth functions we obtain 4-th order convergence in divergence. Finally we demonstrate the method by solving some problems for the 2D Oseen operator. The test 2D MATLAB code in square domain for the projection problem is available at the author's GitHub.

###### Acknowledgements:

This work is supported by RFBR grant no. 18-29-10008 mk.

#### STRESSED STATE OF A STEEL CONSTRUCTION WORKING IN HYDROGEN CONTAINING ENVIRONMENT

Igor Emel'yanov1 , Alexey Polyakov2 , Anastasia Hodak3

1Ural Federal University, Institute of Engineering Science, Russian Academy of Sciences (Ural Branch) , , Russian Federation
2Ural Federal University, Institute of Fundamental Education, Russian Federation
3Ural Federal University, Institute of Fundamental Education, Russian Federation

###### Abstract

An approach is proposed to solve the problem of estimating the stress state of a shell structure loaded with a thermomechanical load and in contact with a hydrogen-containing medium. The stress state of the steel housing of the diffusion apparatus for the production of highly pure hydrogen was determined. The object of study is presented in the form of a composite shell of rotation, loaded by internal pressure and operating at elevated temperatures. The purpose of the work is to determine the stress state of the shell at normal and elevated pressure, taking into account changes in the mechanical properties of the combined effect of temperature and hydrogen. In the general case, the task of calculating such a structure under given operating conditions is related. But for processes with different physical times, it can be represented by a sequence of individual problems of heat propagation, hydrogen diffusion, and the calculation of the stress state. In the phenomenological approach, the relationship between thermal diffusion and mechanical problems is manifested in a change in the parameters of the sample deformation diagram with increasing temperature and hydrogen concentration. The integration of differential equations of a boundary value problem for a shell under pressure is performed by the discrete orthogonalization method S.К. Godunov. The solution obtained made it possible to determine the location of the maximum stresses, in which the greatest changes in the mechanical properties of the material should be expected. According to the results of the calculations, a conclusion was given on the bearing capacity of the structure in the working mode and with increasing hydrogen concentration and internal pressure.

#### About one stochastic model of coexistence of various population groups into the urban environment

Dmitrii Kiselyov1 , Igor Inovenkov2 , Vladimir Nefedov3

1Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics, Russian Federation
2Lomonosov Moscow State University, Department of Computational Math & Cybernatics, Russian Federation
3Lomonosov Moscow State University, Department of Computational Math & Cybernatics, Russian Federation

###### Abstract

The problem of the interaction of various population groups in the framework of urban environment is of current interest this time. The population is divided into different strata according to their economic and social characteristics. For example, a population could be classified according to genetic and phenotypic characteristics, belonging to a particular ethnic group and, first of all, according to income level. In a number of countries, the co-existence of population groups belonging to different social strata gives rise to serious problems and therefore has been studied from different points of view, mainly from a sociological. Due to the qualitative analysis of various situations, it becomes possible to predict and prevent possible conflicts and problems. The significance of this problem is obvious, but reasonable proposals for its solution have not been put forward. In this regard, the construction of a qualitative, but fairly general mathematical model of the dynamics of various groups of the population is of particular interest. Such a mathematical model should be built within the framework of the concept of spatial economics. This paper discusses the first version of the model for a situation where there are only two groups of people. The corresponding system of equations includes two nonlinear diffusion equations with terms describing the interaction of the population groups in model. Of course, the basic difficulty is the selection of coefficients, which will provide the picture as close as possible to reality, so it makes sense to add to the model and stochastic terms that will be responsible for random environmental factors. Thus, a two-dimensional stochastic model of the temporal dynamics of the distribution of two population groups in an urban environment was presented and numerically investigated. As a result of the mathematical modeling certain estimates were obtained regarding the feasibility of taking into account stochastic factors in the proposed mathematical model.

#### Simulation of a road network by a discrete-continuum approach

Alexander Chernyshev1 , Leonid Kurochkin2

1Ioffe Institute, Computational Physics Laboratory, Russian Federation
2Peter the Great St.Petersburg Polytechnic University , , Russian Federation

###### Abstract

Simulation of a payload of a road network is important for design or optimization of such networks. Real-time simulations (Pell et. al., 2017) or predictive simulations in specific conditions can help in redistribution of vehicles and help emergency services reaching problematic areas faster. The hybrid discrete-continuum approach is proposed to carry on simulations of complex areas. SUMO model (Krajzewicz et. al., 2012) is used for discrete approach and describes road junctions and crossings which are small-scale parts. Discrete approach becomes quite resource demanding with the increase of vehicles simulated but provides detailed information about the region under the interest. Continuum approach is based on the Navier-Stokes equations (Wagner, 1997) of fluid medium and is capable of resolving large-scale areas (like straight parts of roads). It does not depend on the number of vehicles but lacks details about whole picture. Combination of both of them can provide consistent model for the description of areas of different scale. The present work is focused on the simulation of a complex road network which consists of a set of road junctions and extended roadways. The network is split into small parts each of which is treated either by discrete or continuum model. At a connection of each pair of parts the data is sampled to get time distribution for the discrete model (for the continuum-to-discrete interpolation) or integrated to get averaged car distribution (for the discrete-to-continuum interpolation). Computational process is carried out either till the convergence (for steady-state problems) or for a specific period of time. Traffic flow at the output points of road network is measured and compared with the predictions. The purpose of this study is to develop criteria for the transition between discrete and continuous description in models of transport networks. The resulting criteria will reduce the computational complexity of models of transport networks. The results of the work will allow the simulation of intelligent transport systems using various data transmission tools (including mesh, LTE, DSRC). Future work will be focused on the incorporation of data network simulation. Taken into account that each vehicle can act as an endpoint in the mobile traffic network (either by installed equipment or driver’s mobile devices) traffic jams can also cause a decay in total data network throughput. Simultaneous simulation of both road and data networks is a challenging problem and requires additional modification of the proposed model.

###### Acknowledgements:

The work is supported by the Russian Foundation for Basic Research, grant No. 18-07-00430

#### A Network-based Voting Model for the United States House of Representatives

Daniel Clark1

1Washington and Lee University, Department of Physics and Engineering , United States

###### Abstract

The polarization and intractability of American politics has received increased scrutiny throughout the 21st century. We attempt to model the complex mechanisms of political cooperation in a finite democratic system. Due to the shorter term-limits and subsequently limited external influences, we select the House of Representatives as an ideal setting to examine the interactions between United States politicians, and therefore we utilize the structure and political topology of the 115th House of Representatives for recent, realistic data. Within this model, legislation is first voted on in a small committee before moving to the entire House. Throughout these voting steps certain agents are assigned a maverick state, which holds their initial vote as fixed, while others’ votes vary based on political values and social influences. At each step the votes and transitions of each agent are studied using Monte Carlo Simulations on networks and network theory. We study the dynamics of both committees and the House as a whole, specifically the impact of inflexible voters, political alignments, and party affiliations.

#### AN APPROACH TOWARDS QUANTIZATION OF NON-RELATIVISTIC OPEN STRING THEORY

Santanu Chatterjee1 , Sanjoy Mukherjee2

1RGM International (India) Pvt. Ltd., Civil, India
2Vikram Solar Limited, Innovation, India

###### Abstract

For decades, scientists have worked relentlessly to move forward to see what lies beyond the third dimension and to find out if there is any existence of a unified theory to explain all the workings of the universe from sub-atomic to gigantic inhabitants of cosmos. This insurmountable task has been taken on by many over the last century or so until the emergence of “super string theory” or “string theory” happened showcasing the fact that an answer seemed possible. From the concepts of a “string”, our ideation on this theory started. In this paper we strived to put forward that the concept of a vibrating one-dimensional microscopic object named “string” can be taken as a fundamental ingredient (in place of point particle) for developing non-relativistic quantum mechanics. Unlike point particle, we take a vibrating string as the quantum object & build a perfectly reasonable quantum mechanical description of the microscopic world. Our main objective in this paper to show that complete development of quantum mechanics is possible based on one dimensional open string.

#### Intelligent nonmodel-based fault diagnosis of electric motors using current signature analysis

Ashraf Zaher1 , Detlef Hummes2 , Ghulam Hussain3

1American University of Kuwait, Electrical and Computer Engineering, Kuwait
2American University of Kuwait, College of Engineering and Applied Sciences – Department of Engineerin, Kuwait
3American University of Kuwait, College of Engineering and Applied Sciences – Department of Engineering, Kuwait

###### Abstract

This paper proposes an efficient technique for detecting mechanical faults in three-phase induction motors, without using mechanical sensors. Only measurements of the currents of every phase are used to identify the fault. The proposed system can diagnose two types of faults corresponding to shaft misalignment or imbalance, along with normal operation. The power spectrum of the experimental data is generated, followed by applying a soft-computing mathematical algorithm that will extract the peaks of the fundamental frequencies and their harmonics, while filtering out noise. These peaks will be compiled in a vector form such that it can be used as inputs to train an artificial neural network (ANN) to produce a decision regarding the operating condition of the motor, via applying intelligent pattern recognition techniques. Mathematical details regarding the structure of the ANN, its training, tuning of its synaptic weights, and the testing/validation phase will be investigated. Detailed analysis of the obtained results is provided to highlight the advantages and limitations of the proposed algorithm. In addition, a comparison is made with similar techniques that use mechanical sensors to contrast their differences and highlight the superiority of the proposed system. The obtained results prove the intelligence and robustness of the proposed system and allows for versatile extensions that promote its application in real-time scenarios for many industrial applications.

###### Acknowledgements:

This work was supported by a grant from the American University of Kuwait, during the academic year 2018-19.

#### Integration of electromagnetic methods of intuba-tion of stratified mediums on the basis of direct and alternating currents

Yuriy Dimitrienko1 , Igor Krasnov2 , Kirill Zubarev3

1Bauman Moscow State Techical University, Fundamental sciences, Russian Federation
2Bauman Moscow State Techical University, Fundamental sciences, Russian Federation
3Bauman Moscow State Techical University, Fundamental sciences, Russian Federation

###### Abstract

In this work the integration of two methods of electroinves-tigation is considered. One method represents intubation by a direct current, the second intubation by alternating cur-rent. The integration is carried out for the purpose of in-crease in accuracy of results of the solution of the inverse task, the problem is solved in a twodimensional approxima-tion. The direct task for the first and second method is solved numerically. The received values were compared with the experimental datas. The inverse task is formulated as a problem of minimization with the functional considering the experimental values received by both the first and second method of electroinvestigation. The problem of optimization is solved on a compact (for each parameter are set top and bottom border).

#### Free vibrations of isotropic FG porous annular and elastically restrained plate using DQM

Yajuvindra Kumar 1

1Government Girls Degree College, Behat, Mathematics, India

###### Abstract

In this paper, author studied free vibrations of a functionally graded (FG) annular plate having porosity. The plate is elastically restrained along the boundary. The material properties of the plate are Porosity dependent. An even porosity distribution is taken in the analysis. The mathematical model of the problem is developed using the concept of physical neutral surface of the plate. The physical neutral surface is taken as the reference plane. Out of many, only first three natural frequencies of the plate are reported using differential quadrature method (DQM). A parametric study is conducted to show the effects of porosity and material distribution parameters on the vibration behavior of the plate.

#### Modelling meson clouds using coherent states

Manuel Fiolhais1

1University of Coimbra, Department of Physics, Portugal

###### Abstract

The use of coherent states to describe boson systems goes back to the 1960's in the context of the radiation field. Since the 1970's, they have also been applied to meson clouds, mainly pions, in the context of the description of baryons by means of effective models involving a quark core surrounded by scalar and pseudo-scalar mesons. The use of coherent states allows for an {\em ab-initio} quantum mechanical description of the mesons, therefore going beyond semi-classical approximations. The coherent state e.g. for p-wave pions (with angular momentum and isospin quantum numbers both equal to 1) is given by $|\psi > = {\cal N}(\xi) \exp (\sum_{tm} \xi_{tm} a^\dagger _{tm} ) |B>$ where ${\cal N}$ is a normalization factor, $| B >$ is a bare baryon state and $\xi_{tm}$ are amplitudes to be determined variationally. The $a^\dagger _{tm}$ is the creation operator for a pion state with angular momentum third component, $m$, and isospin third component, $t$. The radial profile of the pion amplitude results from a variational calculation and it is frozen. Hence, only angular momentum and isospin matters to construct the coherent state above. As already mentioned, the idea of mathematically modelling the meson clouds by means of coherent states, having in mind a full quantum mechanical description of baryon systems in the framework of chiral effective models, is not new. Actually, the author, among others, published several papers on the topic, in order to obtain various properties of the nucleon, the delta resonance and other excited states. However, the goal here is to bring together many aspects that are scattered in the literature, focusing on the versatility of the coherent states and stressing their capabilities. In this study, instead of the more realistic chiral effective models of quarks and mesons, we use a toy model whose Hamiltonian is written as $H= \sum_{tm} a^\dagger_{tm} a_{tm} + G \sum _{tm} B_{tm} \left[ a_{tm} + (-1)^{t+m} a_{-t-m}^\dagger \right]\!,$ where $B_{tm}$ is a baryon spin-isospin operator. The model describes a system of non self-interacting pions linearly coupled to a bare baryon core, $G$ being the coupling constant. This model is simple enough for its exact solutions to be worked out in the strong and weak regimes. These accurate solutions are then compared with the variational approximate solutions. Because the multi-particle coherent state, $|\psi>$, cannot directly describe a nucleon, with definite angular momentum and isospin quantum numbers $\left( J={1\over 2}, I={1\over 2} \right)$, the Peiers-Yoccoz angular momentum (and isospin) projection method is used to construct a state, $|\psi_N>$, with the proper nucleon quantum numbers. The variational method consists in minimizing the energy with respect to the amplitudes, i.e. $d< H > / d \xi_{tm}=0$, with the normalization condition $<\psi_N|\psi_N>=1$ dully implemented in the process. We show that the so-called hedgehog configuration for the quark core and for the pion amplitudes minimizes the mean-field energy. On the other hand, we show that the (Peierls-Yoccoz) projected coherent state is an extremely powerful ansatz since it reproduces the accurate solutions of the model both in the strong coupling regime (which is not surprising) but also in the weak coupling regime. We emphasise the use of the variation-after-projection method, for which the variational Hilbert space is larger, therefore with the trial function spanning a larger space than in the simpler variation-before-projection method. The toy model turns out to be a valuable tool to test different approaches which might be used in more realistic models with, for instance, self-interacting mesons.

#### Inverse operator for a regular nonlinear dynamics

Yehuda Roth1

1Oranim college, science, Israel

###### Abstract

It is known that a dissipative environment is well described by the chaotic process while regular dynamics is associated with animate systems. In this paper, we explore the inverse map of some chaotic maps to find that they are always regular. The result that by reversing a chaotic map we obtain a regular process is associated with the birth of animate systems.

#### Solution to the Troesch Problem for Boundary Equations.

Franco Lindstron1

1Universidad Nacional de La Plata, Matemática, Argentina

###### Abstract

This paper shows, for the first time, that the explicit and exact solution to the Troesch nonlinear twopoint boundary value problem may be computed in a direct and straightforward fashion from the general solution obtained by a generalized Sundman transformation for the related differential equation, which appeared to be a special case of a more general equation. As a result, various initial and boundary value problems may be solved explicitly and exactly.

#### The error function in fractional differential equations

Jorge Olivares Funes 1 , Pablo Martin2 , Fernando Maass3 , Elvis Valero4

1Universidad de Antofagasta , Departamento de Matemáticas , Chile
2University of Antofagasta, Physics department, Chile
3University of Antofagasta, Physics department, Chile

###### Abstract

Fractional differential equations have a great importance and application. That is why the relationship between the fractional derivative and the erf (x) function will be shown below. The objective of this work is to solve the fractional differential equation D ^α y (x) =erf (x), and y(0) = 0, where 0<α<1. We will show the type of generalized hypergeometric solutions obtained by defining the fractional derivative of Caputo and the Laplace transform.

#### Quantum Field Theory in fractal space-time with negative dimension.

Jaykov Foukzon1

1Israel Institute of Technology, Department of mathematics, Israel

###### Abstract

We introduce Hausdorff-Colombeau measure in respect with negative fractal dimensions. Axiomatic quantum field theory in spacetime with negative fractal dimensions is proposed.Spacetime is modelled as a multifractal subset of $R^{4}$ with positive and negative fractal dimensions.The cosmological constant problem arises because the magnitude of vacuum energy density predicted by quantum field theory is about 120 orders of magnitude larger than the value implied by cosmological observations of accelerating cosmic expansion. We pointed out that the fractal nature of the quantum space-time with negative Hausdorff-Colombeau dimensions can resolve this tension. The classical Quantum Field Theory is widely believed to break down at some fundamental high-energy cutoff $E$ and therefore the quantum fluctuations in the vacuum can be treated classically seriously only up to this high-energy cutoff. In this paper we argue that Quantum Field Theory in fractal space-time with negative Hausdorff- Colombeau dimensions gives high energy cutoff on natural way. In order to obtain disered physical result we apply the canonical Pauli-Villars regularization up to $E$. It means that there exist the ghost-driven acceleration of the univers hidden in cosmological constant. http://arxiv.org/abs/1004.0451

#### The soft stadium’s classical dynamics

Julio S Espinoza-Ortiz1 , Roberto E Lagos2

1Federal University of Goias, Physics, Brazil
2UNESP, Rio Claro, SP, Departamento de Fı́sica, IGCE, Brazil

###### Abstract

Billiards are physical models employed to probe experiments that measure the conductivity of quantum dots. In this context, the stadium billiard have been adopted as an standard model for realizations. We study the effect of softening this system in the classical mechanics, pursuing for a more realistic model. This classical approach is a first step towards the truly quantum or semiclassical case. We define the soft stadium as a monomial potential with an exponent {$\alpha\in\Re$} as a parameter, such that for {$\alpha=1$} the system is integrable and the {$\alpha\rightarrow\infty$} limit it converges to the hard billiard. Then, and for computational simplicity, we set up the construction of the classical Poincare map in such a way that it only depends on the partial separability of the system which holds for all {$\alpha$}'s. We present numerical results describing the classical transition from the integrable regime towards the chaotic regime.

###### Acknowledgements:

The authors would like to thank the support of the Goi\'as Research Foundation - FAPEG.

#### Numerical investigation of flow-induced forces in the rods bundle

Sabine Upnere1

1Riga Technical University, Institute of Mechanics, Latvia

###### Abstract

The numerical modelling of cross-flow through the rods bundle with triangular arrangement has been done to analyse flow-induced forces on the rod located in the middle of the bundle. Significant problems of rods in the bundle during the operational time of the system can be caused by the cross-flow. At the same time, it is known that the behaviour of the system is strongly related to many parameters such as bundle geometry, flow, rods support and others. Therefore, there is needed to investigate the characteristics of each type of typical bundles. In this paper is analysed flow-induced hydrodynamic forces in closely-packed rods bundle using Computational Fluid Dynamics. Unsteady Reynolds Averaged Navier-Stokes equations are solved using Finite Volume discretization. The impact of the size of the computational domain and the number of rows in it was investigated to find the optimal case for numerical modelling. Obtained results are compared with references from literature and experimental data.

#### Numerical solution of the direct and inverse problem of electrical exploration using the finite element method

Yuriy Dimitrienko1 , Kirill Zubarev2 , Igor Krasnov3

1Bauman Moscow State Techical University, Fundamental sciences, Russian Federation
2Bauman Moscow State Techical University, Fundamental sciences, Russian Federation
3Bauman Moscow State Techical University, Fundamental sciences, Russian Federation

###### Abstract

This article discusses the results of solving the problem of electrical exploration using direct current. The developed methods and algorithms for solving the direct and inverse exploration tasks are tested on several inhomogeneous models of the environment. The task is considered in three-dimensional approximation. To solve using the finite element method. On the basis of the direct problem algorithm, a method for solving the inverse problem was implemented, which consists in finding the minimum of the deviation functional, which in turn leads to the multiple solution of the direct problem. The obtained results were analyzed, the advantages and shortcomings of the developed methods were revealed, the evaluation of the search time for the optimal solution for the inverse problem was carried out, and the dependence of the solution accuracy on the thickening of the grid when solving the problem by the finite element method was discussed.

#### REVERSIBLE INHIBITOR BIOSENSOR SYSTEMS IN DYNAMIC MODE

Vania Rangelova1

1Technical University Sofia - branch Plovdiv, Electrical Engineering, Bulgaria

###### Abstract

The biosensor amperometric transducers can work in the case of three basic types of reversible inhibitor enzyme systems – with competitive inhibition, with non-competitive inhibition and mixed inhibition. Tipicaly they work in static mode. Now they are investigated in dynamic mode. The kinetic in those type biosensors is generally discussed in terms of a simple extension to the Michaelis-Menten reaction scheme. The investigated biosensors are amperometric product sensitive. The parameters for simulations are chosen from some real experiments with biosensors. The models are described in non stationary diffusion conditions. Solving system of non-linear partial differential equations is reseived in three dimensional size and the concentration profiles in active membrane of substrate S(x,t), inhibitor I(x,t) and product P(x,t) are reseived. The systems of non-linear differential partial equations have been solved numerically in MATLAB medium. The influence of starting concentration of substrate, inhibitor and kinetic parameters - reaction constants of biosensors for substrate and for inhibitor over output current have been investigated.

#### Studying the anti-ferromagnetic states in the Hubbard model using the covariant Gaussian approximation

HSIEN-CHUNG KAO1

1National Taiwan Normal University, Physics, Taiwan

###### Abstract

It has been shown in the literature that doped two-dimensional Hubbard model may exhibit strange metallic transport behavior. We use the covariant Gaussian approximation to study charge and spin correlators in the anti-ferromagnetic phase of in the Hubbard model. The results are then compared to those of quantum Monte Carlo calculations to verify whether such phenomenon does occur.

#### Modelling and Sizing of a Y-shaped laminar flow Micro-fluidic fuel cell

Mayken Espinoza-Andaluz1

1ESPOL, Centro de Energías Renovables y Alternativas, Ecuador

###### Abstract

The energy demand to supply micro devices has been increasing during the last years. Considering the power output of the laminar flow microfluidic fuel (LFFC), it appears as a suitable solution to provide the required electrical energy in small devices. Absence of electrolyte and not requirement of platinum as catalytic material are two of the most important advantages of this type of fuel cells. The current study aims to provide a detailed information about the design and characteristics of a LFFC. A complete analysis of the different shape channels has been considered in this study being selected the best option as the Y-shaped channels. The impact of the inclination degree for the inlet channels has been considered to evaluate the average velocity that the flow can acquire into the channel. In addition, the voltage-current behaviour considering the materials, fuel/oxidant and design characteristics has been obtained from a modelling point of view.

###### Acknowledgements:

The authors kindly acknowledge the financial support from FIMCP-CERA-05-2017. In addition, Åforsk project No 17-331 is gratefully acknowledged.

#### Modeling of Real Particles

Zhong-Cheng Liang1

1Nanjing University of Posts and telecommunications, College of Electronic and Optical Engineering , China

###### Abstract

Point-like and wave-like particles are foundations of classical and modern physics. They are so idealized models that lose the physical authenticity. Real particles are three-dimensional body with mass and volume. The spatial intersection of real particles is empty set, thus ensuring limited density of particles. In the centre-of-mass frame of reference, a real particle has three independent modes of motion: vibration, rotation and translation. Three mode energies $(H,L,K)$ constitute a Cartesian space. The energy space is quantized by vibrating quantum $(H_s=Y_s V_s=hv)$, rotating quantum $(L_s=I_s ω_s^2=lz)$ and translating quantum $(K_s=M_s u_s^2=kT)$. The energy space is divided into six phases and three zones. Three zones represent gas, solid and liquid state of object. There are three equilibrium surfaces, each of which has two stable areas and two excited areas. Two types of phase transition are distinguished by two types of phase interface. Complete energy relations and differential equations can be derived through the statistics of particle ensemble. The results show that the order parameters of liquid, solid and gas are the correlative functions of the particle mass $(M)$, the rotary inertia $(I)$ and the elastic modulus $(Y)$, respectively. Thermodynamic laws are the natural inferences of the theoretical results. A physical theory based on the real particle model has simplicity, consistency and universality.

#### Coherent upper conditional expectations defined by Hausdorff outer measures to make prevision in complex systems

Serena Doria1

1University G.d'Annunzio Chieti-Pescara, Department of Engineering and Geology, Italy

###### Acknowledgements:

The work is supported by the Scientific and Technological Research Council of Turkey, TUBITAK.

#### DESIGN OF NARROWBAND MULTIPLIERLESS COMB COMPENSATOR WITH LOW PASSBAND DEVIATION

Gordana Jovanovic Dolecek1

1Institute INAOE, Electronics, Mexico

###### Abstract

Decimation is the process of decreasing sampling rate in a digital domain, by an integer, called the decimation factor. This process introduces replicas of the main spectrum, called aliasing. Aliasing may deteriorate the decimated signal if the signal is not filtered before decimation, by a low pass filter known as a decimation filter. The simplest decimation filter is a comb filter which has all coefficients equal to unity, and consequently does not require multipliers for its implementation. However, comb filter does not have the flat passband characteristic. The passband droop is increased with the increase of the number of cascaded comb filters. The passband droop must be compensated by a filter called comb compensator. Some desirable characteristics of comb compensator are multiplierless design, and a low absolute value of the passband deviation of the compensated comb. The magnitude response of comb compensator has to approximate the inverse comb magnitude characteristic. In that way the cascade of comb and compensator has the passband characteristic approximately equal to 1. In this paper we present novel narrowband multiplierless compensator with a low absolute value of the passband deviation, whis is less than 0.01dB. The compensator has a magnitude response synthesized as sinewave functions. The parameters of design are the amplitudes of sinewave functions, which depend on the order of the comb filter and practically do not depend on the decimation factors

#### Investigation of Power Networks and their Patterns by Mathematical methods in order to Voltage Stability Enhancement

Seyed Morteza Moghimi1 , Ali Bostani2 , Abolfazl Elahimanesh3

1MicrowaveSoft Inc., Research, Iran (Islamic Republic of)
2American University of Kuwait, Department of Electrical and Computer Engineering, Kuwait
3University of Applied Science and Technology (UAST), Department of Electrical Engineering, Iran, Islamic Republic Of

###### Abstract

Authors in the research paper has considered IEEE 14-bus and 34-bus test network for creation generation and load patterns. This paper aims at analysing the potential impacts that distributed generation (DG) might have on voltage stability of electrical power networks. It is expected that increasing amounts of new generation technologies will be connected to electrical power systems in the near future. Most of these technologies are considerably smaller scale than conventional synchronous generators. In this paper, the impact of DG pattern (size and location of DG) on the voltage stability of two test system is investigated. The simulation methodology is discussed as well. It is found that the effects of DG the voltage stability of a power system strongly depend on the size and location of the distributed generators. The results show that install of DG on the weak bus, improve loadability limit and voltage stability and decrease loss of system. By investigating and reviewing the results of similar patterns in these two systems, the different generation and load patterns impact mechanism of DG units over the behaviour of the systems in terms loadability limit and voltage stability is achieved.

#### a

Dimitrios Vlachos1

1University of Peloponnese, Department of Informatics and Telecommunications, Greece

a

#### Exponential variational integrators for the dynamics of multibody systems with holonomic constraints

Odysseas Kosmas1

1University of Manchester, School of Mechanical, Aerospace & Civil Engineering, United Kingdom

###### Abstract

We here explore a geometric integrator scheme that is determined by a discretization of a variational principle using a higher-order Lagrangian that uses exponential type of interpolation functions. The resulting exponential variational integrators are here extended to conservative mechanical systems with constraints. To do so we first present continuous Euler-Lagrangian equations with holonomic constraints and then mimic the process for the discrete case. The resulting schemes are then tested to a typical dynamical multibody system with constraints, i.e the double pendulum showing the good long-time behavior when compared to other traditional methods.

#### Non-Euclidean Geometries and Arts in the beginning of the 20th century: An interdisciplinary Approach for High School students

1Ionideios Model Lyceum of Pireas, Department of Mathematics, Greece
2Ionideios Model Lyceum of Pireas, Department of Humanities, Greece

###### Abstract

The action we are going to describe was carried out in a class of 27 students in the second grade of the High School (16-17 years old) IONIDIOS MODEL LYCEUM OF PIRAEUS, in the school year 2018-2019. The cooperative action of the mathematician and the philologist of the class, resulted from the common finding of a deficiency in the curricula which resulted in the students' inability to approach holistically the changes imposed on society by the inseparable relation between art, science and technology. With this in mind, the action was designed and focused primarily on presenting trends in art and painting from Impressionism to Van Gogh in parallel with the progress and changes in science and society during that time. It was then attempted to link science, art and technology in the early 20th century through an approach of artistic manifestations, principles and theories about mathematics and non-Euclidean geometries as they influenced architecture, sculpture, painting, the Bauhaus movement. The action was accomplished by achieving its objectives, since the artworks of high aesthetics produced by students, effectively incorporated the theory of modern mathematics and artistic avant-garde and highlighted the link between the scientific and artistic achievements of human creation.

#### Analyzing museum exhibition spaces via visitor movement and exploration: The case of Whitworth Art Gallery of Manchester

Melpomeni Liakou1 , Odysseas Kosmas2

1Hellenic Open University, School of Social Sciences, Greece
2University of Manchester, School of Mechanical, Aerospace & Civil Engineering, United Kingdom

###### Abstract

To analyse the movement and exploration of visitors on museum exhibition spaces, agent based models that simulate their behaviour can be a useful tool. Such a model is proposed here, to which we use appropriate defined dynamical and social forces to describe their motions, while the resulting decision making procedure either preserves or creates groups of individuals. That proves to give realistic visitor motions to complex and multi level spaces while resulting the way they bypass obstacles, move to stairs or follow other groups on their way out. Simulation results are then used to analyse the exhibition spaces of the Whitworth Art Gallery throughout the motion flow of the visitors.