## Conference submissions

#### Flow of tangent hyperbolic nanofluid over a Riga stretching plate with convective boundary condition

FARHAN ALI1

1FUUAST, MATEMATICS, Pakistan

###### Abstract

The effect of Cattaneo-Christov heat flux on tangent hyperbolic flows through a nanoliquid over a stretchable Riga plate along convective boundary condition has been studied. Riga stretchable plate is differentiated as electro-magnetic actuator contains of stable magnets as the span-wise associated collection of irregular electrodes accumulated on a flat sheet. Model of Cattaneo-Christov heat flux has established to investigate a characteristic of thermal time relaxation. The system PDEs are modelled for non-Newtonian nanofluid which is then transmuted into nonlinear ODEs by utilizing appropriate transformation. These transmuted ODE’s are tackled through shooting method. The impact of physical variables on velocity distribution, temperature field and concentration of nanoparticle has been discussed and graphically presented. The results explain that, a velocity field and thermal boundary layer improves due to modified Hartman number, while the temperature and concentration field reveal the opposite nature.

#### $f(T)$ gravity with scalar field viscous fluid

Shynaray Myrzakul1

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

###### Abstract

We focus on a viable teleparallel cosmological model with a scalar field in a flat Friedman-Robertson-Walker universe. The Lagrangian and equations of motion are obtained. The case of an inhomogeneous viscous dark energy is considered and the cosmological parameters associated with the viscosity parameter are determined.

#### Teleparallel gravity with non-minimally coupled f-essence via Noether symmetry approach

Kairat Myrzakulov1 , Duman Kenzhalin2 , Nurgissa Myrzakulov3

1LN Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
2LN Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
3LN Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan

###### Abstract

In this paper, we examine teleparallel gravity with non-minimally coupled with non-canonical fermionic fields (f-essence). Noether symmetry approach can be used to fix the forms of coupling $F(\Psi)$ and the potential $V(\Psi)$ functions of the fermionic fields. In the context of the Friedman-Robertson-Walker metric, we investigate cosmological solutions of the field equations using these forms obtained by the existent of Noether symmetry.

#### Inflation model with viscous fluid

Shynaray Myrzakul1 , Pyotr Tsyba2 , Olga Razina3 , Yerlan Myrzakulov4

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, DEPARTMENT OF GENERAL AND THEORETICAL PHYSICS, Kazakhstan
4L.N.Gumilyov ENU, General & Theoretical Physics, Kazakhstan

###### Abstract

We investigated f (R) gravity with k-essence using the Starobinsky model as an example, given by the expression $f\left(R\right)=R+\alpha R^2$. Using the hybrid function of the scale factor, we found the scalar field function and its potential. For the model under consideration, the parameters of the slow roll-off satisfy the inflationary stage. Our model allows us to obtain an accelerated expansion of the universe during an inflationary period. A non-uniform non-viscous fluid was investigated, and then the viscosity was introduced in the second example. Received fluid equations for the accelerated universe.

#### Numerical study of the effect of stochastic disturbances on the behavior of solutions of some differential equations

Arsenij Firsov 1 , Igor Inovenkov2 , Vasilij Tikhomirov3 , Vladimir Nefedov4

1Lomonosov Moscow State University, Computational math & Cybernatics, Russian Federation
2Lomonosov Moscow State University, Department of Computational Math & Cybernatics, Russian Federation
3Lomonosov Moscow State University, Department of Computational Math & Cybernatics, Russian Federation
4Lomonosov Moscow State University, Department of Computational Math & Cybernatics, Russian Federation

###### Abstract

Nowadays interest of the deterministic differential system of Lorentz equations is still primarily due to the problem of gas and fluid turbulence. Despite a large number of existing systems for calculating turbulent flows, new modifications of already known models are constantly being investigated. In this paper we consider the effect of stochastic additive perturbations on the Lorentz convective turbulence model. To implement this and subsequent interpretation of the results obtained, a numerical simulation of the Lorentz system perturbed by adding a stochastic differential to its right side is carried out using the programming capabilities of the MATLAB programming environment.

#### On obtaining scientific insight from machine-learnt models

Richard Dybowski1

1University of Cambridge, Chemistry, United Kingdom

###### Abstract

There has been an upsurge of interest in applying machine-learning (ML) techniques to the physical sciences, and a number of these applications have achieved impressive predictive accuracies; however, they have done so without providing any insight into what has been learnt from the training data. The interpretation of ML systems (i.e., a statement of what an ML system has learnt from data) is still in its infancy, but interpretation can lead to scientific discovery, and examples of this are given in the area of chemistry. It is proposed that a research programme be designed that systematically compares the various approaches to interpretable ML within a range of physical-science scenarios.

#### Problems of attracting foreign direct investment into the regional economy

1Kazan National Research Technological University, Department of Management and Entrepreneurship, Russian Federation

###### Abstract

The article discusses topical issues of attracting foreign direct investment in the economy of the Republic of Tatarstan. The assessment of the factors affecting the investment attractiveness of Russian regions made it possible to determine the prospects for the implementation of projects with the participation of foreign investors. In conclusion, the authors highlight the successful practices of attracting foreign investment in the region's economy.

#### High energy neutrino and gamma-ray emissions from the jets of M33 X-7 microquasar

Dimitrios Papadopoulos1 , Theodora Papavasileiou2 , Theocharis Kosmas3

1University of Ioannina, Physics, Greece
2University of Western Macedonia, Informatics, Greece
3University of Ioannina, Physics, Greece

###### Abstract

In this work, after testing the reliability of our algorithms through numerical simulations on the well-studied SS 433 Galactic microquasar, we focus on neutrino and $\gamma$-ray emissions from the extragalactic M33 X-7 system. This is a recently discovered X-ray binary system located in the neighbouring galaxy Messier 33 which has not yet been modelled in detail. The neutrino and $\gamma$-ray energy spectra, produced from the magnetized astrophysical jet of M33 X-7, in the context of our method are assumed to originate from the decay (and scattering) processes taking place among the secondary particles produced assuming that, first, hot (relativistic) protons of the jet scatter on thermal ones (p-p interaction mechanism).

###### Acknowledgements:

TSK acknowledges that this research is co-financed by Greece and the European Union (European Social Fund-ESF) through the Operational Programme "Human Resources Development, Education and Lifelong Learning 2014- 2020" in the context of the project MIS-5047635.

#### Astrophysical magnetohydrodynamical outflows in the extragalactic binary system LMC X-1

Theodora Papavasileiou1 , Dimitrios Papadopoulos2 , Theocharis Kosmas3

1University of Western Macedonia, Informatics, Greece
2University of Ioannina, Physics, Greece
3University of Ioannina, Physics, Greece

###### Abstract

In this work, at first we present a model of studying astrophysical flows of binary systems and microquasars based on the laws of relativistic magnetohydrodynamics. Then, by solving the time independent transfer equation, we estimate the primary and secondary particle distributions within the hadronic astrophysical jets as well as the emissivities of high energy neutrinos and $\gamma$-rays. One of our main goals is, by taking into consideration the various energy-losses of particles into the hadronic jets, to determine through the transport equation the respective particle distributions focusing on relativistic hadronic jets of binary systems. As a concrete example we examine the extragalactic binary system LMC X-1 located in the Large Magellanic Cloud, a satellite galaxy of our Milky Way Galaxy.

###### Acknowledgements:

TSK acknowledges that this research is co-financed by Greece and the European Union (European Social Fund-ESF) through the Operational Programme "Human Resources Development, Education and Lifelong Learning 2014- 2020" in the context of the project (MIS5047635).

#### A mathematical model for the description of the electrical conductivity of graphene/polymer nanocomposites

Yahya Öz1

1Turkish Aerospace, Advanced Materials, Processes and Energies Technology Center, Turkey

###### Abstract

The dispersion of nanomaterials such as graphene has a major influence on the electrical conductivity in nanocomposites with a polymer matrix. For the description of this effect a continuum model is presented. Within this model, the percolation threshold is determined. Moreover, a distributional analysis is used for the purpose of taking electron hopping between graphene into account. Hence, interfacial conductivity enhanced by tunneling is also included in this study. Recent measurements of nanocomposites that are used for aerospace applications are compared with the results of the presented model and show good agreement between model and experiment.

###### Acknowledgements:

The author acknowledges financial support by the Scientifi c and Technological Research Council of Turkey within the support program 1515 for research and laboratory developments within the project 5189901. Moreover, the author is grateful to the Bilkent University Institute of Materials Science and Nanotechnology for providing the needed infrastructure.

#### Calculation of a confidence interval of semantic distance estimates obtained using a large diachronic corpus

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

###### Abstract

Several methods for detection changes in words semantics and appearance of new word meanings have been proposed that use different techniques of estimating semantic distance between words. They are based both on neural network vector models and on simpler vector representations that use frequencies of n-grams including the studied words. The paper objective is to calculate the confidence interval for estimating the semantic distances obtained based on the data of the large diachronic corpus. This task is complicated because the question about the law of distribution of frequency fluctuations of words and n-grams, despite a number of studies, remains open. The confidence intervals are calculated by statistic modeling using random permutations of n-gram frequencies.

#### String Topological Robotics

My Ismail Mamouni1

1CRMEF Rabat, Morocco, Mathematics, Morocco

###### Abstract

We aim to link two well known theories; namely the \textit{string topology} (founded by M. Chas and D. Sullivan in 1999) and the \textit{topological robotics} (founded by M. Farber some few years later, in 2003). For our purpose, we consider $G$ a compact Lie group acting on a path connected $n$-manifold $X$.The relevance of the Lie group $G$ will be discussed through the paper. On the set $\MLP(X)$ of the \textit{loop motion planning algorithms}, we define a kind of a string loop motion planning product, which endows the shifted homology $\mathbb H_*(\MLP(X)) := H_{*+2n}(\MLP(X))$, with a structure of a graded commutative and associative algebra structure. We show after that it yields a structures of Gerstenhaber and Batalin-Vilkovisky algebras.

#### On the Estimation of Some Relevant Parameters in the COVID-19 Pandemic

Manuel De la Sen1 , Aitor Garrido2 , Asier Ibeas3

1University of the Basque Country, Institute of Research and Development of Processes, Spain
2University of the Basque Country, Institute of Research and Development of Processes, Spain
3Universitat Autonoma de Barcelona, Department of Telecommunications and Systems Engineering, Spain

###### Abstract

This paper gives simple rules to calculate the transmission rate and some other parameters in COVID- 19 from recorded data on the infection, recovery and death through several SIR-based epidemic models. In particular, it is emphasized how the transmission rate is highly dependent on the quarantine or confinement interventions. The proposed rules estimate the relevant time-derivative of some of the subpopulations of the model by using the standard known discretization rules.

#### Mathematical modeling the process of wire surfacing by the smoothed particle hydrodynamics method

Roman Davlyatshin 1 , Roman Gerasimov2 , Yuri Bayandin3 , Gleb Permyakov4 , Dmitriy Trushnikov5

1Perm National Research Polytechnic University, Mathematical modeling of systems and processes, Russian Federation
2Perm National Research Polytechnic University, , Russian Federation
3Institute of Continuous Media Mechanics UB RAS, , Russian Federation
4Perm National Research Polytechnic University, , Russian Federation
5Perm National Research Polytechnic University, Department of Welding Production, Metrology and Technology of Material, Mechanical Engineering faculty, Russian Federation

###### Abstract

We discuss issues the process of layer-by-layer synthesis of metal products by wire surfacing. A mathematical model of the process has been developed and implemented that allows one to calculate the volumetric distributions of temperatures, melt flow rates, pressures, components of heat fluxes density, the shape and dimensions of the molten bath, the shape of the free surface of the molten metal, the shape and dimensions of the weld bead. For this purpose, the main physical processes that affect the formation of the metal product were considered, namely: melting and crystallization of the metal, surface tension, the Marangoni effect and the heat source features. The smoothed particle method was used to implement this model. A number of numerical experiments were carried out using the developed model. Firstly, the model parameters for steel and titanium were identified and verified. After that, calculations were carried out to verify the model itself using the obtained roller geometry. The numerical solution for the deposition of one layer was compared with the full-scale experiment. The error was no more than 5% in any direction. Thus, the efficiency and correctness of the constructed model is shown.

###### Acknowledgements:

The work is supported by the Ministry of Science and Higher Education of the Russian Federation (state assignment No. FSNM-2020-0028), the Ministry of Education and Science of the Perm Territory (agreement S-26/787 of 12/21/2017) and the Russian Foundation for Basic Research (RFBR project No. 18 -08-01016A)

#### Embedding of lightweight cryptography into microcontroller

Olga Sidorova1

1Joint institute for nuclear research, FLNP, Russian Federation

###### Abstract

In our day-to-day lives, the use of cryptography is everywhere. For example, we use it to securely send passwords over vast networks for online purchases. Bank servers and e-mail clients save your passwords using cryptography as well. Cryptography is used to secure all transmitted information to authenticate people and devices, and devices to other devices. Investigation of lightweight cryptographic algorithms in application to cyber security of novel battery powered equipment is in high demand. Our main efforts are focused in embedding of cryptography algorithms into smallest 8 bit microcontrollers with very low power consumption. In this talk we report embedding of cryptography algorithm PRESENT and lightweight stream encryption algorithm TRIVIUM into PIC12F675 (Microchip) microcontroller. We provide dependence of microcontroller resources on volume of the encrypted message.

#### Neutron Life Time Experiment with IBR2 Pulsed Neutron Source Shakir Zeynalov,*Egor Lychagin, Pave Sedyshev, Valery Shvetsov And Olga Sidorova

Shakir Zeynalov1

1Joint Institute for Nuclear Research, Neutron Physics, Russian Federation

###### Abstract

In thermal nuclear reactors, most of the power is generated by thermal neutron induced fission. Therefore, fission chambers with targets that respond directly to slow neutrons are of great interest for thermal neutron flux measurements due to relatively low sensitivity to gamma radiation. However, the extreme conditions associated with experiments at very low cross section demand highly possible thermal neutron flux, leading often to substantial design changes. In this paper we report design of a fission chamber for wide range (from 10 to 1012 n/cm2sec) measurement of thermal neutron flux. Test experiments were performed at the first beam of IBR-2 pulsed reactor using digital pulse processing (DPP) technique with modern waveform digitizers (WFD). The neutron pulses detected by the fission chamber in each burst (5 Hz repetition rate) of the reactor were digitized and recorded to PC memory for further on-line and off-line analysis. New method is suggested to make link between the pulse counting, the current mode and the Campbell technique.

#### Tsunamis triggered by subaerial landslide ¿how we determine the initial conditions of the tsunami waves?

Andrea Schmessane1

1UCHILE-USACH, Mathematics department-Physics department, Chile

###### Abstract

Tsunamis triggered by subaerial landslides are a feast of fluid dynamics processes, different approaches has been performed trying to understand the whole phenomena and all their steps: landslide development and behaviour, splash zone, tsunami wave propagation in the near and far field, inundation zone and run up. All those steps compose the main structure that describes the phenomenon, and each one could be obey different models. Many times these models are matched to construct the evolution of this phenomena Then, many times to model one event of this tsunami type is like an art. In this work we explore the current models for the splash zone and the initial condition; the initial tsunami wave is emerged by the impact of the landslide with the water body, and the interaction of landslide with the water until to stopped. Currently, we fix the attention in to evaluate what ingredients we need to take into account for to construct a new model. Considering empirical data about the phenomenon, we propose a different model in the step of the splash zone, which one changes the initial condition of the tsunami wave.

#### A VARIATIONAL APPROACH TO DISSIPATIVE OPTICAL SOLITONS

Mário Ferreira1

1University of Aveiro, , Portugal

###### Abstract

The trial function approach is a useful technique to modelling soliton solutions for equations that can not be solved exactly. We use the variational approach to find approximate solutions for the dissipative solitons described by the cubic-quintic complex Ginzburg-Landau equation. We find that the evolution equations for the soliton parameters are similar to those derived using the method of moments.The existence of both stationary and pulsating soliton solutions is indicated by both approaches and confirmed through some numerical examples.

#### Simulation of the Thermal Effects on Corneal Endothelia Cells during Phacoelmulsification

Zeljka Cvejic1 , Nikola Goles2 , Marko Narancic3 , Bojan Pajic4

1Faculty of Sciences, University of Novi Sad, Department of Physics, Serbia
2Faculty of Sciences, University of Novi Sad, Department of Physics, Serbia
3Faculty of Sciences, University of Novi Sad, Department of Physics, Serbia
4Faculty of Sciences, University of Novi Sad, Department of Physics, Serbia

###### Abstract

Corneal endothelial cells are an important non-regenerative corneal innermost layer to maintain corneal transparency processes. The endothelium has both pump and barrier function, which are important for maintenance of corneal clarity. Also, the transparency of the human lens depends on the balance between structural characteristics of the lens proteins and biochemical interaction of the proteins. If this balance is disturbed, the lens will tend to lose transparency. Furthermore, it will lead to the condition known as cataract. Phacoemulsification is the most widely technique for cataract surgery in which the lens with the cataract is broken up by the ultrasound, irrigated and then implemented intraocular lens in the bag. Beside the fact that endothelia cells are especially sensitive to surgical damage, thermal exposure during phacoemulsification can be also potential cause of post operative endothelial cell lost. In this paper, we simulated temperature changes in the eye during phacoemulsification by using COMSOL Multiphysics software and 2D computional model with axisymmetric geometry. We take in consideration the frictional heat generation from the phaco probe, and calculated the maxium temperatures of corneal endhotelial.

#### NUMERICAL STUDIES OF THE SATURATED ABSORPTION RESONANCIES IN А NONLINEAR SPECTROSCOPY OF THE DEGENERATE ATOMIC TRANSITIONS

E. Saprykin1 , Aleksandr Chernenko2

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

###### Abstract

The paper presents results of the development of the theory of nonlinear resonances in the saturated absorption spectroscopy of degenerate atomic transitions based on the numerical solutions of systems of kinetic equations describing the resonant interaction of an atom with two coherent optical fields, and the inclusion of incoherent fields of spontaneous emission of excited atoms induced by them (the SIR effect [1]). This approach allowed 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).

#### "Monte Carlo Entropic sampling algorithm applied to 3D spin crossover nanoparticles: role of the environment on the thermal hysteresis"

Jorge Linares1 , Catherine Cazelles2 , Sara Gaci3 , Pierre Dahoo4 , Kamel Boukheddaden5

1University of Versailles St. Quentin en Yvelines, GEMAC, France
2University of Versailles St. Quentin en Yvelines, IUT de Mantes, France
3University of Versailles St. Quentin en Yvelines, LATMOS, France
4University of Versailles St. Quentin en Yvelines, LATMOS, France
5University of Versailles St. Quentin en Yvelines, GEMAC, France

###### Abstract

Spin crossover (SCO) compounds [1] exhibit a thermal transition between two states: High-spin (HS) and Low-spin (LS) states. The LS to HS transition temperature, Tup, on heating is higher than the the HS to LS transition temperature, Tdown, on cooling. The width ΔT=Tup – Tdown characterizes the thermal hysteresis. In this contribution, we first have developed a 3D Monte Carlo (MC) entropic sampling algorithm [2] to evaluate the density of states of a SCO nanoparticles using three parameters related to the “magnetization”, the “spin-spin correlation” and the number of molecules at the surface; then we analyzed the role of the interaction, characterized by a parameter “L”, between the external environment of the nanoparticle and the molecules on its surface. We show that increasing “L” generates a thermal hysteresis whose width increases with the strength of the “L” and shifts downward the system’s transition temperature. These behaviors are also studied as function of the SCO nanoparticle size. The computational parameters are: Δ/kB = 1300 K, J/kB = 20 K, G/kB = 125 K and ln(g) = 6.01. REFERENCE 1. E. König,. Struct. Bond. 1991, 76, 51-152. 2. I. Shteto, J. Linares, F. Varret, Physical Review E 56 (1997), 5128-5137.

#### Exact Solution for an Elastic Square Plate Loaded with Tangential Stresses

Irina Menshova1 , Alexander Kerzhaev2 , Guangming Yu3 , Xiankun Zeng4

1Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences, Moscow, Laboratory of Geodynamics, Russian Federation
2Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences, Laboratory of Geodynamics, Russian Federation
3Qingdao University of Technology, , China
4Qingdao University of Technology, , China

###### Abstract

This paper provides an exact solution to the boundary value problem of elasticity theory for a square loaded with tangential stresses along all its sides (even-symmetric deformation with respect to the central axes). The solution is represented as series in Papkovich–Fadle eigenfunctions. The coefficients of the series are determined by simple closed formulas.

###### Acknowledgements:

The research was funded by RFBR and NSFC according to the research project No. 20-51-53021, by the Russian Science Foundation under grant No. 19-71-00094, and by the National Natural Science Foundation of China (No. 51674150) and NSFC-RFBR (No. 5191101589).

#### On the Connection Between Deutsch-Jozsa Algorithm and Bent Functions

Eraldo Marinho1

1Universidade Estadual Paulista Julio de Mesquita Filho / UNESP, Statistics, Applied Mathematics and Computing, Brazil

###### Abstract

It is presently shown that the Deutsch-Jozsa algorithm is connected to the concept of bent function. Particularly, it is noticeable that the quantum circuit used to denote the well-known quantum algorithm is by itself the quantum computer that performs the Walsh transform of a Boolean function. Consequently, the output from the Deutsch-Jozsa algorithm, when the hidden function is bent, corresponds to a flat spectrum of quantum states.

#### Spin waves of single-molecule magnet Fe8 with respect to dipolar and quadrupole excitations

Yousef Yousefi1

1Payame Noor University, Physics, Iran, Islamic Republic Of

###### Abstract

In this paper, we have studied the equations describing the proposed experimental Hamiltonian of a single-molecule magnet Fe8. In this research, we used from coherent states in real parameter and Fayman path integral. These nonlinear equations fully described dynamic of this single-molecule magnet in Su (2) and Su (3) groups. The solutions of these equations are magnetic solitons (not calculated in this study). »Linear equations show that for this SMM, the mean square torque ( Quadrupole excitation) is not constant and its dynamic consists of two parts. One part, rotate around the classical spin vector and the other is related to changing the size of the quadrupole torque. The spin wave dispersion equation for dipole and quadruple branches is calculated for small linear excitations from ground state (vacuum). These equations show that, for dipole branch, the spin wave is damping away from the single-molecular magnet and oscillating and not damping for the quadrupole branch.

#### Analytical study of the spin tunneling effect by considering dipole excitations in single-molecular magnet Mn12

Yousef Yousefi1

1Payame Noor University, Physics, Iran, Islamic Republic Of

###### Abstract

Spin tunneling effect in Single Molecule Magnet Mn12 is studied by instanton calculation technique using SU(2) spin coherent state in real parameter as a trial function. For this SMM, tunnel splitting ( steps in hysteresis loop) arises due to the presence of a Berry phase in action, which causes interference between tunneling trajectories (instantons). In the analytical calculation, the assumption of the linearity of the instanton solution in term of applied magnetic field is used. It is observed that the number of quenching points of magnetic tunneling, the number of steps in hysteresis loop, are equal to the number of points obtained from numerical calculation. Of course, the position of the points (the magnitude of the field in which the tunneling amplitude is zero) is different.

#### Numerical simulations of gaseous flames in combustion chamber applications

Cosmin Katona1 , Carmen Safta2 , Florin Frunzulica3 , Marcel Goemans4

1University Politehnica Bucharest, Power Engineering Faculty, Romania
2University Politehnica Bucharest, Power Engineering Faculty, Romania
3University Politehnica Bucharest, Aerospace Engineering Faculty, Romania
4TIALOC Belgium NV, 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.

#### Construction of vertical boreholes for closed loop heat pump systems: Geoexchanger System for Buildings Heating and Cooling

Abdeen Omer1

1UON, Energy Research Institute (ERI), United Kingdom

###### Abstract

Geothermal heat pumps (GSHPs), or direct expansion (DX) ground source heat pumps, are a highly efficient renewable energy technology, which uses the earth, groundwater or surface water as a heat source when operating in heating mode or as a heat sink when operating in a cooling mode. It is receiving increasing interest because of its potential to decrease primary energy consumption and thus reduce emissions of the greenhouse gases (GHGs). The main concept of this technology is that it uses the lower temperature of the ground (approximately <32°C), which remains relatively stable throughout the year, to provide space heating, cooling and domestic hot water inside the building area. The purpose of this study, however, is to examine the means of reducing of energy consumption in buildings, identifying GSHPs as an environmental friendly technology able to provide efficient utilisation of energy in the buildings sector, promoting the use of GSHPs applications as an optimum means of heating and cooling, and presenting typical applications and recent advances of the DX GSHPs. The study highlighted the potential energy saving that could be achieved through the use of ground energy sources. It also focused on the optimisation and improvement of the operation conditions of the heat cycle and performance of the DX GSHP. It is concluded that the direct expansion of the GSHP, combined with the ground heat exchanger in foundation piles and the seasonal thermal energy storage from solar thermal collectors, is extendable to more comprehensive applications.

###### Acknowledgements:

The financial support for this research work from the Energy Research Institute is gratefully acknowledged. I am grateful to my wife Kawthar Abdelhai Ali for standing beside me.

#### "Local mean field approximation applied to a 3D spin crossover nanoparticles configuration: free energy analysis of the relative stability of the stationary states “

Catherine Cazelles1 , Yogendra Singh2 , Jorge Linares3 , Pierre Dahoo4 , Kamel Boukheddaden5

1University of Versailles St. Quentin en Yvelines, IUT de Mantes, France
2University of Versailles St. Quentin en Yvelines, GEMAC, France
3University of Versailles St. Quentin en Yvelines, GEMAC, France
4University of Versailles St. Quentin en Yvelines, LATMOS, France
5University of Versailles St. Quentin en Yvelines, GEMAC, France

###### Abstract

We apply the local mean field approximation [1] to an inhomogeneous 3D spin crossover (SCO) [2] nanoparticle with a specific focus on molecules at the bulk, the corner, edge and at surface positions. Each SCO molecule is described by a two-levels fictitious spin having two eigenvalues s=+1 and s=-1, respectively associated with the high-spin (HS) and low-spin (LS) sates. The expression of the four different partition functions writes Z_α=2 cosh⁡β((∆-k_B Tlng-2Γq_α<σ>-2z_α L)/2 ) Where, α=b,c,e,s (b≡bulk, c≡corner, e≡edge and s≡surface). Here, ∆ (>0) is the energy difference between the HS and LS sates, g = g_HS/g_LS is the degeneracy ratio between HS and LS energy levels, q_α is the lattice coordination number, z_α the number of interactions between surface and edge molecules and their immediate environment, and Γ and L are the interaction terms. The total variational local mean-field free energy is F=F_b+F_c+F_e+F_s. With the computational parameters Δ/kB=3126 K, Γ/kB=150 K, L/kB=650 K and ln(g)=8.45. we have obtained a three states hysteresis loop. The stable, metastable and unstable states are analyzed in terms of the free energy. 1. S.E. Allal, J. Linares, K. Boukheddaden, P. R. Dahoo, F. de Zela, Journal of Physics SC, 936 (2017) 012052, 2. P. Gütlich, Struct. Bond. 1981, 44, 83–195.

#### Electrically Controlled Nanoscale Photonic Grating with Multiferroic Helical Structures

Ramaz Khomeriki1

1Ivane Javakhishvili Tbilisi State University, Physics, Georgia

###### Abstract

Single phase multiferroic with easy plane magnetic anisotropy and Dzyaloshinskii-Moriya type electro-magnetic coupling is considered. Static electric field causes the establishment of helically ordered ground state and it is shown that this structure acts as a periodic potential for light propagation through the multiferroic. The corresponding magnon-photonic band-gap spectrum is calculated and the possibility of light trapping while driving inside the photonic gap is numerically revealed.

###### Acknowledgements:

This work was supported by Shota Rustaveli National Science Foundation of Georgia (SRNSFG) (Grant No. FR-19-4049)

#### Sharing economy as a part of the sustainable development concept

Timur Absalyamov1 , Svetlana Absalyamova2 , Chulpan Mukhametgalieva3 , Rustem Sakhapov4

1Kazan Federal University, Institute of Management Economics and Finance, Russian Federation
2Kazan Federal University, , Russian Federation
3Kazan Federal University, , Russian Federation
4Kazan State University of Architecture and Engineering, Road Construction Machinery, Russian Federation

###### Abstract

The article is devoted to the study of sharing economy as a new economic model. Today, sharing economy or economy of joint consumption, is in serious competition with traditional industries. The paper presents basic approaches to determination of the sharing economy essence. It considers the factors contributing to its formation and growth. Among the main factors, the authors highlight technological, economic, environmental and social factors. The paper studies the development dynamics of individual sectors of the joint consumption economy in Russia, their contribution to the implementation of the Sustainable Development Goals. Moreover, the authors explore new trends, such as the expansion of geography, changes in the demographic composition of participants, and the integration of sharing in ecosystems. The risks of further expansion of the sharing economy are studied as well - the risk of personal data leakage, problems with the state of critical infrastructure, etc.

#### Modeling of mover with anti-skid devices

Rustem Sakhapov1 , Marat Makhmutov2 , Mukhammat Gatiyatullin3 , Regina Nikolaeva4

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

For a mover equipped with anti-skid devices, the process of slipping is being formed due to the factors of soil compression, shift and cut by tire hooks. With a decrease in the number of removable hooks, the period, when the first hook is disengaged and the second has not yet entered into interaction with the soil, increases. At the moment, traction and hitching properties of the wheel are formed only by tire hooks. During the interaction of the removable hook with the soil, the traction ability of the wheel consists of the shear forces of the soil “bricks” sandwiched between the tire hooks and the soil deformation forces by the removable hooks. With increasing height, length and thickness of the hook, the traction forces of РС and РВ increase. However, the hook height parameter, in contrast to the length, is optimized by the diameter of the wheel, the depth of the soil, track and tire deflection. In addition, with an increase in the height of the hook, the resistance to the movement of the wheel increases. The study obtains models of the influence of the hook length lc on the traction and bearing capacity of the hook. With an increase in the slipping process, the ratio of traction forces to implementation increases. Therefore, the functional qualities of anti-skid devices depend not only on the parameters of the hook, but also on the operating modes of the mover. The graphical analysis shows the relationship between the parameters of the removable hook according to the criterion of reliability and performance of the anti-skid system. The influence of the hook parameters on the functional qualities of the removable device, the ability to perform traction propulsion properties is revealed. The paper provides the dependencies for determining the optimal geometric parameters of the removable hook, knowing the dependence of the implementation force on the penetration depth of a unit base area, while taking into account the force on the implementation of the anti-skid device strut.

#### Thermal stresses in an elastic clamped square: Exact solution

Alexander Kerzhaev1

1Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences, Laboratory of Geodynamics, Russian Federation

###### Abstract

This paper presents a method for determining thermal stresses in an elastic clamped square with a given temperature distribution (the plane problem). First, the solution to the temperature problem for an infinite plane is constructed. Then, the solution for a square is added to this solution, with the help of which the boundary conditions on its sides are satisfied. The thermal stresses have been obtained in the form of series in Papkovich–Fadle eigenfunctions, the coefficients of which are determined explicitly. The final formulas are simple and can easily be used in engineering.

###### Acknowledgements:

This work was supported by the Russian Science Foundation, Grant No. 19-71-00094.

#### Investigation of domain structure in ferroelectric thin films using the Ising model

Evgenii Menshikov1 , Olga Maksimova2 , Stepan Osipov3

1Cherepovets State University, Laboratory of Mathematical and Computer Modeling, Russian Federation
2Cherepovets State University (CHSU), , Russian Federation
3Cherepovets State University, Department of Physics, Russian Federation

###### Abstract

We have studied domain structures in thin ferroelectric films in the framework of the Ising model. The configuration energy was calculated taking into account both short-range exchange and long-range dipole-dipole interactions. The classical Ising model is not applicable for this case because it explains well only the behavior of bulk ferroelectrics. However, this model may predict the existence of a critical film thickness at which there is no phase transition. In this paper, the depolarizing field, which is the dominant factor influencing the existence of a phase transition in thin films, is taken into account for the study of size effects. We used the Monte Carlo method with standard Metropolis algorithm to generate configurations on a simple three-dimensional cubic lattice. A study of the domains sizes relatively to the spontaneous polarization direction was performed. Temperature dependences of domain sizes (in the longitudinal and transverse directions to the free surface) are obtained for different values of interaction constants. It is proved that the introduction of a depolarizing field leads to the appearance of a dead layer on the film boundaries e. It is shown that the value of the dead layer increases with increasing temperature. At a certain temperature (not equal to the Curie point), the dead layer is destroyed. The dependence of the dielectric susceptibility of a thin ferroelectric film on the temperature at different thicknesses have been obtained. It is shown that these dependencies have two maxima. The first maximum corresponds to a phase transition, the second one exists only in thin films and corresponds to the destruction of the dead layer.

###### Acknowledgements:

Russian Foundation for Basic Research, Project No. 19-42-350001

#### Distributed order fractional wave equations with irregular coefficients

Ljubica Oparnica1

1Ghent University , Department of Mathematics: Analysis, Logic and Discrete Mathematics, Belgium

###### Abstract

We derive and analyze fractional wave equations describing wave propagation in one-dimension viscoelastic media modeled by distributed-order fractional constitutive stress-strain relation. More precisely, we consider the system of equations: the equation of motion of the one-dimensional deformable-body, the constitutive equation of distributed order fractional type, describing the mechanical properties of the linear viscoelastic body, and the strain for small local deformations. The system is equivalent to the integrodifferential wave-type equation. First, we've proved that the fundamental solution to the generalized Cauchy problem for the distributed order wave equation exists and it is unique, and we have found that the wave propagation speed is related to the material properties. In particular, we discuss the fundamental solutions corresponding to four thermodynamically acceptable classes of linear fractional constitutive models and power-type distributed-order models. This results concerns homogeneous materials and are obtained in S. Konjik, Lj. Oparnica, and D. Zorica, Distributed-order fractional constitutive stress-strain relation in wave propagation modeling. Zeitschrift fu ̈r angewandte Mathematik und Physik 70:51, 2019. Further, we are interested in having similar results in cases when viscoelastic material/media is heterogeneous. so that coefficients in equations become non-smooth functions depending on space (or even time) and could be irregular, such as Dirac delta distribution. We want to apply variational techniques to prove well-posedness results for bounded coefficients and very weak solution concepts to treat strong irregularities in the equations when they appear. Joint talk with Sanja Konjik

#### Dimension reduction of preference profile for aggregation of energy audit data

Sergey Muravyov1 , Maria Borisova2

1Tomsk Polytechnic University, Division of Automation and Robotics, Russian Federation
2Tomsk Polytechnic University, , Russian Federation

###### Abstract

Resource conservation is an important factor in maintaining society sustainability. An effective resource saving is ensured by systematic energy audits. Traditionally, the processing energy audit outcomes is a routine work with a large amount of unstructured data that is difficult to fully take into account. This kind of activity can be avoided using the preference aggregation method based on the treatment of exclusively binary relations of weak order. The main stages of the method are as follows: (1) shaping the set substations A, the standard auxiliary expenses (SAE) of which should be analyzed; (2) forming the preference profile Λ, consisting of m rankings of n substations for each of the components of SAE; (3) finding the consensus ranking for the profile Λ by the Kemeny's preference aggregation rule. When applying the Kemeny rule, it should be taken into account that this combinatorial problem is NP-complete, i.e. is characterized by an exponential growth of the solution time as a function of the dimension n = |A|. At the problem dimension n ≤ 20, suitable for practical application, the Kemeny rule can be successfully applied. Therefore, the paper aims to improve a technique based on preference aggregation, which allows to process a big amount of data from instrumental examinations of energy losses by substations of electrical energy distribution networks. An approach to transformation of the initial preference profile into the hierarchical one is considered. The absence of the influence of such a transformation on the correctness of processing results is shown. The workability of the proposed method is demonstrated on the basis of real energy surveys using the example of the Khakass enterprise of the Backbone Electric Grids (BEGs), being a part of Siberian BEG of the Unified National Electric Network of Russia. The method makes it possible to identify sources of economically inefficient expenditure of energy resources and unjustified energy losses, and also to provide compression of large volumes of energy survey data without diminution of essential information. The proposed method allows obtaining and representing a great am¬ount of data of instrumental survey of substation energy losses in a form of a compact integral estimate in the ordinal scale. It can be an appropriate and promising tool for organizations engaged in energy consulting.

###### Acknowledgements:

This work was supported by the Russian Science Foundation, project # 18-19-00203

#### Predicting the Behaviour of a Vortex Shedding-Based Passive Mechanical Micro Heat Exchanger

Francisco Granados-Ortiz1 , Marina Garcia-Cardosa2 , Joaquin Ortega-Casanova3

1University of Malaga, Mechanical, Thermal and Fluid Engineering, Spain
2University of Malaga, Department of Mechanical, Thermal and Fluid Engineering, Spain
3University of Malaga, Department of Mechanical, Thermal and Fluid Engineering, Spain

###### Abstract

In the recent years, microscale applications are gaining increasing importance. Reduced scale electronic devices, microscale biomedical and biomechanical engineering applications are experiencing important developments. Despite their advances, the technology and resources needed to develop new designs may be a drawback for reduced scale engineering testing. In this work, a computer-based design of a micro heat exchanger is developed by means of mathematical methods. The micro heat exchanger consists of a rectangular pillar confined in a microchannel, with two fluids entering at different temperatures. The mixing between two fluids takes place because of the vortex-shedding physics downstream the pillar. In spite of vortex-shedding is a well-known mechanism in flow physics, it is not possible to know a priori whether a configuration (for a given geometry and flow velocity) may or may not lead to this desired vortex detachment. Therefore, Machine Learning methods are used for prediction, trained with finite-volume numerical simulations of different micro heat exchanger devices. Upon these results, relevant designs or modifications for the micro exchanger can be proposed prior physical construction and experimental testing, saving important resources and efforts.

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#### Movement characteristics of a non-smooth model with a closed curve equilibrium

Judita Buchlovská Nagyová1

1VSB - Technical University of Ostrava, IT4Innovations, Czech Republic

###### Abstract

The main aim of this study is to analyze the dynamical properties of a model with a closed curve equilibrium. The corresponding three-variable model is given as a set of nonlinear ordinary differential equations containing non-smooth functions. The dynamics of the model are studied depending on three parameters. For this purpose, new methods, as the 0-1 test for chaos and approximate entropy, are applied. Using these tools, the dynamics are quantified and qualified. Depending on the system's parameters, it is shown that irregular (chaotic) and regular (periodic) movement character appears.

#### Mathematical model of electrical conductivity of biological tissues based on ion electrodiffusion equations

Nikita Kovalenko1 , Kirill Sovin2 , Nikolay Shamankov3 , Aleksandr Seleznev4 , Oleg Ryabushkin5

1Moscow Institute of Physics and Technology, The School of Electronics, Photonics and Molecular Physics, Russian Federation
2Moscow Institute of Physics and Technology, Phystech School of Electronics, Photonics and Molecular Physics, Russian Federation
3Moscow Institute of Physics and Technology, Department of Photonics, Russian Federation
4Moscow Institute of Physics and Technology (State University), The School of Electronics, Photonics and Molecular Physics, Department of Photonics, Russian Federation
5Fryazino Branch of Kotelnikov Institute of Radio Engineering and Electronics of RAS, , Russian Federation

###### Abstract

The processes of vital activity of biological tissues are closely related to their electrical properties. Electrical conductivity measurements are widely used in studies of animal (bioelectrical impedance analysis, electrical impedance tomography) and plant tissues (determination of wood moisture, control of plant growth). Biological tissues are highly heterogeneous media, which leads to a dispersion of electrical conductivity in the radio frequency spectral range caused by interphase polarization. The effective medium theory with dipole-dipole interaction (EMT-DDI) is the most developed theory for constructing mathematical models of biological cells and tissues. The presented approach is based on dividing the medium into phases with different electrical conductivity and dielectric permittivity and calculating the effective macroscopic electrical properties of the medium. EMT-DDI also allows us to take into account dipole-dipole interactions between separate phase clusters of a heterogeneous medium. Another approach to building a model of biological tissues is to use electrodiffusion equations. These equations operate with the concentrations of charge carriers and their mobility in the medium. This approach is more fundamental, but at the moment it is almost not developed due to the complexity of the equations and described media. This paper presents an original approach to mathematical modeling of electrical properties of biological tissues based on electrodiffusion equations. The approach is based on the division of biological tissue into living cells separated by membranes. Each cell contains as variables: average concentrations of various types of ions, the number of ions accumulated at the cell borders, the electric potential and its first and second spatial derivatives in the center of the cells. The model calculates the time dependencies of the described variables. It is assumed that the potential setting time is much less than the characteristic time of ion redistribution. The time step simulation algorithm can be represented as two stages. At the first stage, the values of electric potentials and their spatial derivatives in the simulated cells are calculated based on the Laplace equation inside the cells, the potential continuity conditions, and the Maxwell conditions at the cell-membrane boundaries. In the second step, ion flows between each pair of interacting cells and from the borders to the center of the cell are calculated based on the electrodiffusion equations. Next, the calculated flows are used to calculate the ion concentrations at the new time step. The presented model allows us to monitor the kinetics of the distribution of the concentration of ions and electrical potentials in biological tissue. The effective electrical conductivities obtained from the model are in good agreement with the results obtained from generally accepted methods. Thus, the paper presents an original approach to modeling the electrical properties of biological tissues based on electrodiffusion equations. This approach has more prospects for the interpretation of experimental data than the widely presented EMT-DDI and can be used to model changes in the electrical properties of tissues at the cellular level.

#### Modeling the integrity of course learning using percolation through intra-subject relations

Tatyana Gnitetskaya1 , Alexey Tsoy2

1Far Eastern Federal University, The School of Natural Sciences, Russian Federation
2Far Eastern Federal University, Department of General and experimental physics, Russian Federation

###### Abstract

This article deals with the problem of modeling the assessment of the level of integrity of the content of the physics course learned by students. The need for such modeling is due to the need to bring education courses to an online format. The degree of integrity of learning is proposed to be managed by modeling the percolation of intra-disciplinary relations of the course structure. The model uses the graph model of intra-disciplinary relations (T. N Gnitetskaya) and the principles of percolation theory (P-theory). The article provides a few practical solutions for the use of P-theory. An algorithm has been developed that allows forming the themes of the physics course into the desired structure.

#### First principles modeling of three-phase interface system of ZrB2-ZrC-ZrSi2

Serzat Safaltin1 , Meltem Bolluk2 , Sebahattin Gürmen3

1Istanbul Technical University, Metallurgical and Materials Engineering, Turkey
2Istanbul Technical University, Metallurgical and Materials Engineering, Turkey
3Istanbul Technical University, Metallurgical and Materials Engineering, Turkey

###### Abstract

Advanced zirconium compound products show superior properties such as high refractory characteristics, abrasion resistance, corrosion resistance, fracture toughness and hardness. These products are useful candidates specifically for high temperature applications. The production is a challenge because of high temperature and/or pressure requirements to give enough densification for applications while most of them depends on different compositions. For example, ZrB2 known for its high refractory properties like good thermal shock resistance, chemical stability to liquid metals, high oxidation resistance and high melting point but requires sintering aid to lower porosity. ZrC has high abrasion resistance and similar thermal properties like ZrB2, but its low resistance to oxidation prevents some features. SiC is the most used C source during composite synthesis of ZrC structures and Si will form Zr-Si structures (ZrSi2 in equilibrium). ZrSi and ZrSi2 show low electrical resistivity and high thermal conductivity compared to ZrB2 and ZrC. It performs well to inhibit oxidation of underlying structures. Therefore, it is rational to use boride, carbide and silicide structures of zirconium together for high performance applications. To explore stable structures as candidates, we modeled crystalline layers of ZrB2, ZrC and ZrSi2 surface models to explore interfacial properties of binary and ternary composites with density functional theory. We studied the energy, bonding lengths and electron densities to describe interfaces and compared ternary models with mono and binary model results.

#### Einstein field equations for Bose-Einstein condensates in cosmology

Alice Roitberg1

1Università degli Studi di Milano Bicocca, Matematica e Applicazioni, Italy

###### Abstract

In this work we consider the Gross-Pitaevskii equation for Bose-Einstein condensates (BECs) in a general Riemannian metric. Given initial conditions dictated by an external potential, we consider the free expansion of the condensate when the external potential is turned off. Focusing on the forces associated with the geometry of the initial configuration, we show how these are related to the Ricci curvature tensor and the Ricci scalar and we find an Einstein field equation governing the steady flow. Some important correlations between the study of defects in BECs and the appearance of cosmological singularities will be addressed, in particular the emergence of an effective Lorentzian spacetime geometry, which is what is needed to obtain Hawking radiation effects.

#### A Polynomial Preconditioner for the LSQR method$\\$ $^1$Somayyeh Ghadamyari and $^1$Maryam Mojarrab$\\$ $^1$Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

Maryam Mojarrab1

1University of Sistan and Baluchestan, Department of mathematics, Iran (Islamic Republic of)

###### Abstract

The LSQR method is an iterative procedure for solving $Ax = b$, where $A$ is a large and sparse matrix. The base of the LSQR method is the bidiagonalization procedure of Golub and Kahan. This method is mathematically equivalent to the standard conjugate gradient method (CG), but there are some differences in their numerical properties. In order to dissolving this problem, a polynomial preconditioner for the LSQR method is proposed which reduces the number of iterations for convergence. Some numerical examples illustrate the potency and efficiency of this preconditioned method.

#### Model of the spectral dependence of changes in the polarization state of laser radiation in magneto-optical crystal in the presence of multiple reflections from its faces

Aleksandr Seleznev1 , Danil Rodionov2 , Nikita Kovalenko3 , Renat Shaidullin4 , Oleg Ryabushkin5

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 (State University), , Russian Federation
3Moscow Institute of Physics and Technology, The School of Electronics, Photonics and Molecular Physics, Russian Federation
4Fryazino Branch of Kotelnikov Institute of Radio Engineering and Electronics of RAS, , Russian Federation
5Fryazino Branch of Kotelnikov Institute of Radio Engineering and Electronics of RAS, , Russian Federation

#### Reliability-centered maintenance and cost optimization for offshore oil and gas components

Anu Hanish Nithin1 , Srinivas Sriramula2 , Terry Ebinum3

1University of Aberdeen, Engineering, United Kingdom
2University of Aberdeen, Engineering, United Kingdom
3Optimal, , United Kingdom

###### Abstract

Reliability-Centered Maintenance (RCM) is widely used for enterprise asset management in the Oil and Gas sector. The traditional RCM process encompasses the development of equipment hierarchy, the determination of the functional failure of the assets, identification of the critical failure modes and the development of suitable maintenance strategies for these failure modes through RCM logic tree analysis. However, the current industry standards and conditions call for greater strides of production availability and reliability of the assets. The aim of the paper is to deliver an enhanced RCM oriented optimization framework for the assets through the implementation of probabilistic and statistical analysis. Probabilistic analysis of the most critical components predicts the failure over time. The mean time to failure, mean time between failure and mean time to repair parameters are determined from the failure history. The best fit probability distribution is determined through maximum likelihood estimation. The parameters of the probability distribution, for instance, the shape and scale parameters of Weibull distribution determines the failure pattern of the particular failure mode over time. The failure modes of a particular component are considered in series or parallel configuration leading to the determination of their overall failure contribution to system reliability. The cost optimization modules allow the analyst to determine the optimum intervals for maintenance or replacement of the maintainable items. The enhanced RCM methodology, therefore, provides a quantitative and cost-effective solutions for asset maintenance and management. A case study of an equipment in the Oil and Gas sector will be presented to illustrate the optimization framework.

#### Estimation of Parameters for Non-Equilibrium Phase Transitions During the Flow of Oil and Gas Mixtures

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

###### Abstract

Problems of unsteady gas-liquid flows in wellbores with phase transitions are common for hydrocarbon production and well drilling. Typically, flow in wellbores is sufficiently fast which requires taking into account the non-equilibrium nature of phase transitions. The set of equations describing conservation of mass for components and momentum conservation for the mixture is supplemented by the relaxation equation for concentration of gas dissolved in the liquid. It is known that the characteristic times of gas evolution from the liquid and gas dissolution in the liquid differ significantly and depend both on fluid properties, thermobaric conditions, and the flow structure. Therefore, obtaining estimates of relaxation times for real flows turns to be a difficult problem. In this study, we propose a method for estimating the characteristic relaxation times for gas evolution and dissolution during the gas-liquid flow in a well. The method combines the solution of the convective diffusion equation for the growth / decay of a vapor bubble in a liquid with the current parameters of the gas-liquid flow. Estimates of the relaxation times for the bubbly flow (small bubbles, gas evolution predominates) and slug flow (large bubbles, dissolution prevails), as functions of time from the beginning of the process, are obtained for the parameters of a real flow in a wellbore. It is shown that the obtained dependencies are consistent with the typical scaling of the diffusion process with respect to the size of bubbles. The results are important for mathematical simulation of gas-liquid flows in wellbores during hydrocarbon production, as well as for calculation of the gas-kick process during well drilling with oil-based muds.

###### Acknowledgements:

The study is a contribution to the research program under the State Research Contract of OGRI RAS (topic АААА-А19-119022090096-5)

#### Estimation of Uncertainty of a Volumetric Reservoir Model and Optimization of Numerical Inversion in Well Log Data Interpretation

Elvira Khismatullina1 , Ilya Indrupskiy2 , K. Kovalenko3 , N. Samokhvalov4

1National University of Oil and Gas «Gubkin University», , Russian Federation
2Oil and Gas Research Institute of the Russian Academy of Sciences (OGRI RAS), , Russian Federation
3National University of Oil and Gas «Gubkin University»,, , Russian Federation
4National University of Oil and Gas «Gubkin University», , Russian Federation

###### Acknowledgements:

The study is a contribution to the research program under the State Research Contract of OGRI RAS (topic АААА-А19-119022090096-5 for I.M. Indrupskiy and topic АААА-А19-119030690047-6 for K.V.Kovalenko)

#### Modelling preferential flow through unsaturated porous media with an extended Richards Equation to capture hysteresis and relaxation behaviour

Warren Roche1 , Kieran Murphy2 , Denis Flynn3

1Waterford Institute of Technology, Science, Ireland
2Waterford Institute of Technology, Department of Computing and Mathematics, Ireland
3Waterford Institute of Technology, Computing and Mathematics, Ireland

###### Abstract

The unsaturated flow of water in soil through unstable wetting fronts has been documented in literature ([1] - [4]). These instabilities can lead to the development of finger-flow profile, whose paths can be "remembered" by a solid matrix of soil during future infiltration even after periods of desaturation. This process has been modelled by an extended Richards equation, a PDE which has been modified to account for hysteresis and the non-equilibrium and dynamic processes required for finger flow ([3],[4]). For this talk, numerical results of current work shall be presented, including how rate-independent hysteresis, via the Preisach operator, can be incorporated in the modified Richards equation. [1] Hill D E and Parlange J-Y 1972 Soil Sci. Soc. Am. Proc. 36 697-702 [2] Flynn, Denis & McNamara, Hugh & Pokrovskii, Alexej. (2006). Application of the Preisach Model to Soil-Moisture Hysteresis. The Science of Hysteresis. 3. 10.1016/B978-012480874-4/50025-7. [3] Sander, G.C., Glidewell, O.J. and Norbury, J., 2008, November. Dynamic capillary pressure, hysteresis and gravity-driven fingering in porous media. In J. Phys. Conf. Ser. 138, 012023. [4] Chapwanya, M. and Stockie, J.M., 2010. Numerical simulations of gravity‐driven fingering in unsaturated porous media using a nonequilibrium model. Water Resources Research, 46(9).

###### Acknowledgements:

Waterford Institute of Technology PhD Scholarship

#### About Identifiability of Oil and Water Relative Permeability Curves and Reservoir Heterogeneity through Integrated Well Test Study

Ernest Zakirov1 , D. Anikeev2 , Ilya Indrupskiy3 , T. Tsagan-Mandzhiev4 , Yu. Alekseeva5

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 the Russian Academy of Sciences (OGRI RAS), , Russian Federation
4Oil and Gas Research Institute of the Russian Academy of Sciences (OGRI RAS), , Russian Federation
5Oil and Gas Research Institute of the Russian Academy of Sciences (OGRI RAS), , Russian Federation

###### Abstract

Relative permeabilities play very important role in petroleum reservoir engineering. Those functions predetermine waterflooding efficiency and oil/water ratio within the production forecast. Traditionally multiphase flow parameters are estimated from special core analysis data. Such measurements suffer from small representative elementary volume (REV) and pointwise characterization of reservoir properties. Its highly uncertain description can often distort the actual flow conditions at the reservoir level in a 3D flow simulation model. Undoubtedly, those functions could be history matched based on production data but such a procedure requires long history of waterflooding. So the idea to apply integrated well test study to estimate the displacement efficiency and/or relative permeability functions at downhole conditions was realized and implemented. Well testing is traditionally applied in reservoir engineering for estimation of basic single-phase flow parameters. Our approach is extended to multi-phase flow and is based on data collection at well bottomholes and its subsequent assimilation in a flow simulation model. In this paper we summarize both peculiarities of mathematical problem statement and identifiability of multiphase flow parameters through inverse problem solution, and also discuss 10+ year experience in interpretation of two-phase well tests with our techniques. To estimate multiphase flow parameters, we have to jointly consider complex data of well logging and dynamic data of well testing. Both data are used in the inverse problem with the least squares data mismatch quality criterion. Depending on the well test type, forward problem corresponds to the 1D, 2D of 3D multiphase fluid flow model in porous media. The latter consists of continuity equations for phases/components coupled with multiphase Darcy equations instead of momentum balances. For data assimilation the modern methods of optimal control theory (adjoint methods) are successfully applied. For all synthetic test cases true reservoir parameters were accurately recovered based on data of forward simulation with true parameters. In order to estimate reservoir heterogeneity, we apply an anisotropic single-phase model to identify the ratio of vertical to horizontal permeability. Data of well self-interference testing were used for vertical permeability estimation. Depending on the amplitude of reservoir pressure perturbation, actual reservoir properties could be properly inferred from observations.

###### Acknowledgements:

The study is a contribution to the research program under the State Research Contract of OGRI RAS (topic АААА-А19-119022090096-5)

#### A compact 3-dB coupler with stubs

Denis Letavin1

1Ural Federal University, , Russian Federation

###### Abstract

High-resistance lines and idle stubs were studied as a miniaturization tool, a directional splitter. Replacement of all λ/4 segments included in the coupler with the proposed artificial transmission lines allowed reducing the area of the device by 76.8% at the operating frequency of 1.9 GHz. The mathematical calculation of the devices was performed in Cadence AWR DE. The manufactured layout has comparable characteristics with the characteristics obtained in the model. The negative side of miniaturization is a reduction in the frequency band of the coupler.

#### A compact 3-dB coupler with microstrip cells

Denis Letavin1 , Ilya Terebov2

1Ural Federal University, , Russian Federation
2UrFU, , Russian Federation

###### Abstract

The article examines the design of a compact coupler with an operating frequency of 1.8 GHz, which can be used in power supply circuits of antenna arrays. The proposed design has small dimensions and characteristics comparable to the traditional design. The reduction of dimensions is achieved by using synthesized microstrip cells installed instead of conventional sections. The coupler was modeled and manufactured, and the measured characteristics matched the calculations well.

#### Design of miniature directional coupler with wide bandwidth

Denis Letavin1

1Ural Federal University, , Russian Federation

###### Abstract

A miniature wide-band coupler consisting of compact structures and curved loops has been developed. The topology of the structures is chosen in such a way as to achieve similar characteristics in the passband with the characteristics of the four-quarter wavelengths. The area of the proposed coupler is 69.8% smaller than the area of the same device as standard. The simulation was carried out in the CADENCE AWR program. It was shown that due to miniaturization of the coupler, there is a deterioration of such characteristics as the operating frequency band, the preservation of the phase difference between the outputs in a wide frequency band and the attenuation of the signal in the band. A mock coupler was made, and this made it possible to confirm experimentally the correctness of calculations in AWR Design Environment.

#### Dystopian Statistics and Predictive Educational Models: Resourcing to Speculative Data to Address Present Educational Issues

Ana S. Moura1 , João Barreiros2 , M. Natália Cordeiro3

1LAQV-REQUIMTE, University of Porto, Department of Chemistry and Biochemistry, Portugal
2Author of Speculative Fiction, , Portugal
3LAQV-REQUIMTE, University of Porto, Department of Chemistry and Biochemistry, Portugal

###### Abstract

Higher Education Student burnout or the use of Ritalin for inducing normative behavior in problematic students are among the Educational-related issues that have been addressed by recent predictive social and educational models. These new models interface graph theory, Quantum Chemistry, speculative data from literary science fiction works, ethics, and sociology. Through the use of these proposed models, this work approaches the quantification for imagination-related productions as useful data to Educational modeling in the areas of students’ mental health and individual rights. It proposes new mathematical tools for predicting and solving problematic educational scenarios, within time and statistics, and providing validation by juxtaposing speculative data versus reality through recent tools such as quantum-based models and Reductio ad dystopia.

#### The Quest for Tracking Patient Zero: Medical Social Networks and Probabilities

Ana S. Moura1 , Patrícia Gonçalves2 , M. Natália Cordeiro3 , Pedro Campos4

1LAQV-REQUIMTE, University of Porto, Department of Chemistry and Biochemistry, Portugal
3LAQV-REQUIMTE, University of Porto, Department of Chemistry and Biochemistry, Portugal
4INESC TEC, Faculdade de Economia, University of Porto, , Portugal

###### Abstract

Covid-19 pandemic has seen the individual right to privacy and the imperious need to track asymptomatic patients collide, through the use of several tracking applications that aim to contain infectious foci. The emergent field of medical social networks presents itself as one of the strong possibilities to address the problem, interfacing ethics, medical data, and dynamic visualization models. This work proposes a state-of-the-art review of the applied statistics and probabilities within such models and the avenues it may provide in the present and future pandemic scenarios.

#### A model for rainfall-runoff with rate-independent hysteresis for modelling a simplified catchment

Denis Flynn1 , Warren Roche2

1Waterford Institute of Technology, Computing and Mathematics, Ireland
2Waterford Institute of Technology, Science, Ireland

###### Abstract

Rate-independent hysteresis is a nonlinear phenomenon where the output depends not only on the current input but also the previous history of inputs to the system. In multiphase porous media such as soils, the hysteresis is in the relationship between the moisture content and the capillary pressure [1]. $\\$ In this work, we develop a simplified hysteretic rainfall-runoff model consisting of the following subsystems that capture much of the physics of flow through a slab of soil:$\\$ $1)$ A slab of soil where rainfall enters and if enough water is present in the soil, it will subsequently drain into the groundwater reservoir. This part of the model is represent by ODE with a Preisach operator [1,2,3].$\\$ $2)$ An overland flow component: If the rainfall exceeds the maximum infiltration rate of the soil, the excess will become surface runoff. This part of the model is represented by a series of two hysteretic reservoirs [4,5] instead of the two linear reservoirs in the literature [5,6,7]. $\\$ $3)$ A ground water storage and outflow subsystem that is also modelled by a hysteretic reservoir.$\\$ Finally, the outputs from the groundwater output and the overland flow are combined to give the total runoff. $\\$ We will examine this model and compare it with non-hysteretic case both qualitatively and quantitively. In addition, we will examine the next steps to include effects of vegetation and evaporation.$\\$ [1] D. Flynn, H. McNamara, P. O'Kane, and A. Pokrovskii, Science of Hysteresis: Application of the Preisach model to Soil-Moisture Hysteresis. Academic Press, 2005, vol. 3, no. ISBN: 0-12-480874- 3, ch. 7, pp. 689-744.$\\$ [2] D. Flynn and O. Rasskazov, "On the integration of an ODE involving the derivative of a Preisach nonlinearity," Journal of Physics: Conference Series, vol. 22, pp. 43-55, 2005. [Online]. Available: http://stacks.iop.org/1742-6596/22/43. $\\$ [3] D. Flynn, J. P. O'Kane, and A. Zhezherun, "Numerical solution of odes involving the derivative of a Preisach operator and with discontinuous RHS," Journal of Physics: Conference Series, vol. 55, pp. 63-73, 2006. [Online]. Available: http://stacks.iop.org/1742-6596/55/63. $\\$ [4] J. P. O'Kane, "The hysteretic linear reservoir - a new preisach model," Physica B: Condensed Matter, vol. 372, no. 1-2, pp. 388-392, February 2006. $\\$ [5] J. P. O'Kane and D. Flynn, "Thresholds, switches and hysteresis in hydrology from the pedon to the catchment scale: a non-linear systems theory," Hydrol. Earth Syst. Sci., vol. 11, no. 1, pp. 443-459, 17 Jan. 2007. $\\$ [6] J. Dooge and J. O'Kane, Deterministic Methods in Systems Hydrology. A.A. Balkema Publishers, Lisse (NL), 2003. $\\$ [7] J.P. O’Kane, "The FEST model-a test bed for hysteresis in hydrology and soil physics," J. Phys.: Conf. Ser. 22 (2005) 148-163.

###### Acknowledgements:

The authors kindly acknowledge the financial support from the WIT PhD Scholarship Programme (WD/2015/06).

#### Simulation of Time-Lapse Resistivity Logging During Two-Phase Well Testing in Petroleum Reservoirs

O. Shishkina1 , Ilya Indrupskiy2 , K. Kovalenko3 , Anastasya Makarova4 , Ernest Zakirov5 , D. Anikeev6 , E. Anikeeva7

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
3National University of Oil and Gas «Gubkin University»,, , Russian Federation
4National University of Oil and Gas «Gubkin University», , Russian Federation
5Oil and Gas Research Institute of the Russian Academy of Sciences (OGRI RAS), , Russian Federation
6Oil and Gas Research Institute of the Russian Academy of Sciences (OGRI RAS), , Russian Federation
7Oil and Gas Research Institute of the Russian Academy of Sciences (OGRI RAS), , Russian Federation

###### Abstract

Well testing methods are widely used in petroleum industry to identify reservoir parameters in-situ, at real reservoir flow conditions. Two-phase tests with water injection extend capabilities of well testing to evaluation of oil-water flow characteristics. Typically, forward problem of two-phase well testing consists in the numerical solution of oil and water flow equations in 1D or 2D with full account for real fluid and reservoir properties. Inverse problem is also solved numerically with the adjoint method. Well bottomhole pressure, phase rates and near-wellbore water saturation are used as measured data. However, water saturation is actually not directly measured on wells. Instead, it is interpreted from time-lapse well logging data, with resistivity logging being one of the options. This means that forward and inverse problems are to be extended to incorporate direct simulations of resistivity logging. In this paper we address the corresponding forward problem. The extended model formulation for reservoir flow includes additional equation for salt mass conservation (salt transport in water phase). Water saturation and salt concentration distributions obtained at the moments of time-lapse resistivity logging are used to compute reservoir resistivity distributions, which serve as heterogeneous coefficients for the 2D elliptical problem for electrical potential. The latter one is solved numerically for different positions of the source electrode to simulate apparent resistivity readings. Different types of logging tools are considered as possible options including through-the-casing resistivity logging for cased wells. Examples are presented to show how time-lapse changes in simulated resistivity logging data reflect the specifics of the two-phase flow with changing water salinity during the well test.

###### Acknowledgements:

The study is a contribution to the research program under the State Research Contract of OGRI RAS (topic АААА-А19-119022090096-5 for O.A. Shishkina, I.M.Indrupskiy, E.S.Zakirov, D.P.Anikeev, and E.S.Anikeeva and topic АААА-А19-119030690047-6 for K.V.Kovalenko)

#### Group analysis of equilibrium equations of nematocholesteric

Igor Klebanov1 , Georgii Sorokin2

1South Ural State University, School of Electronic Engineering and Computer Science, Russian Federation
2South Ural State University, School of Electronic Engineering and Computer Science, Russian Federation

###### Abstract

In this paper, we obtained Lie algebra admitted by the system of equilibrium equations of nematocholesteric, which models the equilibrium configurations of the elastic field in the one-constant approximation of the continuum theory. We found that in the case of a pure nematic, the system admits a ten-dimensional Lie algebra, and in the case of a cholesteric system admits a four-dimensional Lie algebra. In addition, we have received particular analytical solution of a system of model equations.

#### Analysis and modeling of Fano resonances in coupled cantilevers

Hugo Aya Baquero1

1Universidad Distrital Francisco José de Caldas, , Colombia

###### Abstract

The coupled oscillators model has been used for decades to interpret the Fano interference in a variety of systems: optical, plasmonic, and microwave. Hence, Fano resonance can be modeled with a weak or tightly coupled mechanical oscillators system, which provide insight into the interaction dynamics of a radioactive continuum of propagation modes and a discrete state. Therefore, the coupled cantilevers model was implemented in a FEM routine, in order to study and discuss aspects of the Fano resonance. The study of the Fano resonance in coupled cantilevers shows that this model may be applied in the field of micromechanical sensors.

###### 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.

#### Stelios Kotsios Evangelos Melas

Evangelos Melas1

1University of Thessaly, Mathematics, Greece

###### Abstract

The goal of this paper is to present invariants of planar point clouds, that is functions which take the same value before and after a linear transformation of a planar point cloud via a 2 x 2 invertible matrix. In the approach we adopt here, these invariants are functions of two variables derived from the least squares straight line of the planar point cloud under consideration. A linear transformation of a point cloud induces a nonlinear transformation of these variables. The said invariants are solutions to certain Partial Differential Equations, which are obtained by employing Lie theory. We find cloud invariants in the general case of a four-parameter transformation matrix, as well as, cloud invariants of various one-parameter sets of transformations which can be practically implemented. Case studies and simulations which verify our findings are also provided.

#### A general-purpose ionic radii regression model for material informatics

1King Fahd University of Petroleum & Minerals , Electrical Engineering, Saudi Arabia

###### Abstract

Ionic radius of an element plays a vital role in materials science due to its application in the structure-property prediction. It has been an effective tool for assessing crystal structure which is primarily used, along with chemical composition, for predicting material properties. Inspired by the development of computational materials science and material informatics, the present work expands the acclaimed Shannon's table of 492 ions (for typical oxidation states and coordination geometries) to 987 ions. . Accordingly, a rigorous machine learning (ML) approach was employed to extend the ionic radii table using all possible combinations of oxidation states (OS) and coordination numbers (CN) available in material repositories. A general-purpose ionic radii regression model for Shannon’s database was developed as a function of the period number, oxidation state, coordination environment, ionization potential and orbital configuration. By optimizing the hyperparameters of machine learning algorithms, Gaussian Process Regression showed the minimum the root mean square error in ionic radii of 0.0332A with an R-square of 99.3%. These results showed the effective implementation of the model which was then employed for predicting a new set of ionic radii for uncommon OS and CN carefully harvested from the crystallographic database of 7969 crystal structures from the materials project repository. The generated data was then consolidated with the reputable Shannon’s data and has been made available online in an extended database repository (https://cmd-ml.github.io). The consolidated table will assist in accurate prediction of the crystal structure and material properties by employing definite ionic radius values based on the OS and CN.

###### Acknowledgements:

Authors: Ahmer A.B. Baloch 1, Saad Alqahtani 2, Faisal Mumtaz 1, Ali H. Muqaibel 2, Sergey Rashkeev 1, Fahhad H. Alharbi 2,3 1) Qatar Environment and Energy Research Institute, Hamad bin Khalifa University, Qatar. 2) Electrical Engineering Department, King Fahd University of Petroleum and Minerals, Saudi Arabia 3) K.A. CARE Energy Research & Innovation Center, Saudi Arabia

#### Liouvillian solutions to the perturbation equations of the Schwarzschild black hole

Evangelos Melas1

1University of Thessaly, Mathematics, Greece

###### Abstract

It is well known that the equations governing the evolution of scalar, electromagnetic, and gravitational perturbations of the background geometry of a Schwarzschild black hole can be reduced to a single master equation. We use Kovacic’s algorithm to obtain all Liouvillian solutions, i.e., essentially all solutions in terms of quadratures, of this master equation. We show that one of the Liouvillian solutions is a product of elementary functions, one of them being a polynomial solution P to an associated confluent Heun equation. P admits a finite expansion both in terms of truncated confluent hypergeometric functions of the first kind, and also in terms of associated Laguerre polynomials. Remarkably both expansions entail not constant coefficients but appropriate function coefficients instead. We highlight the relation of these results with inspiring new developments. Our results set the stage for deriving similar results in other black hole geometries 4-dim and higher.

#### Numerical modeling of emulsion droplets motion under the influence of non-uniform electric field

Viktor Kireev1 , Bakyt Shalabaeva2 , Nurbolat Jaichibekov3 , Zhanserik Kozhabai4

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
4L.N. Gumilyov Eurasian National University, Faculty of mechanics and mathematics, Kazakhstan

###### Abstract

One of the vital problems in the oil industry is the efficient removal of water from water-in-oil emulsions. In practice, various methods of destruction of water-in-oil emulsions are used - mechanical, thermal, chemical and electrical. In electric dehydrators, water-in-oil emulsions are placed in a constant/alternating electric field or are processed by radio-frequency/microwave electromagnetic field. An important scientific task is a detailed study and modeling of physical processes occurring in individual emulsion droplets and their aggregates under the influence of an electromagnetic field. In the present work, using numerical simulation, the features of emulsion droplets clusters movement under the influence of non-uniform electric field. It is shown that for an emulsion with given physical properties, it is possible to select such parameters of the electric field, at which the most intense convergence and coalescence of emulsion droplets occurs. The obtained results can be used for the design of new electric dehydrators and the selection of their optimal operating mode.

###### Acknowledgements:

The research was supported by the grant of the Committee of Science of the Ministry of Education and Science of the Republic of Kazakhstan (project no. АР05134098)

#### A new approach to mathematical modeling of polydisperse emulsions separation

Airat Musin1 , Elmira Tukhbatova2 , Liana Kovaleva3 , Viktor Kireev4

1Bashkir State University, Applied Physics, Russian Federation
2Bashkir State University, Applied Physics, Russian Federation
3Bashkir State University, Applied Physics, Russian Federation
4Bashkir State University, Applied Physics, Russian Federation

###### Abstract

Emulsions are found both in nature and in many technological processes in various industries. In some circumstances, it is required to obtain stable long-life emulsions. For example, it is necessary in the food industry, construction, and medicine. In other cases, emulsions have to be break and to obtain pure substances making up the emulsion. In particular emulsion separation is a widespread process in the oil industry in order to improve commercial oil quality. At the moment, there are a lot of experimental, theoretical and numerical works, which brought us closer to understanding physical processes occurring in the emulsion. However, the study of the properties of emulsions is still relevant. In reality, emulsion systems are polydisperse, which means that emulsions include droplets of various sizes. Development of adequate mathematical models taking into account droplets of different radii is quite difficult. In this paper, the influence of polydispersity on the emulsion sedimentation rate is considered. A new mathematical model is developed that allows to describe the dynamics of polydisperse system sedimentation. The mathematical model of emulsion separation is built in diffusion approximation and it is based on the convection-diffusion differential equation with additional constitutive relations. The sedimentation rate of the emulsion is calculated using the Hadamard–Rybczynski formula. The crucial role in the mathematical model plays an original empirical formula that describes the dependence between mean droplet radius and emulsion concentration. This formula allows to take into account the polydispersity of the system and its influence on the process of the emulsion sedimentation. Using numerical modeling the effect of the functional dependence of mean droplets radius on their concentration on sedimentation rate of polydisperse emulsion and dispersed phase volumetric content are investigated. It is shown that the volume of the settled liquid over time determined numerically is in a good agreement with experimental data. The paper results can be useful in the numerical study of the properties of disperse systems with inclusions of various diameters.

###### Acknowledgements:

The research was supported by the grant of the Russian Science Foundation (project no. 19-11-00298)

#### Structural characteristics of gluconolactone/gluconic acid aqueous solution used for biofuel cell by molecular dynamics

Shigeki Matsunaga1

1National Institute of Technology, Nagaoka College, General Education, Japan

###### Abstract

In recent years, biofuel cells have been drawing attention. Glucose is one of the promising energy resources used in biofuel cells because it is obtained by degrading cellulose, which is abundant in nature. Biofuel cells are also expected as the next generation portable chemical battery that is safe and can be used by the human body. In a recent report, enzyme fuel cells achieved 10 times the energy storage of lithium-ion batteries [1]. At the anode of a biofuel cell, glucose is oxidized to produce gluconolactone, as, C6H12O6 → C6H10O6 + 2H+ + 2e-. Therefore, the aqueous glucose solution at the anode of a biofuel cell contains many components, including buffer solutions. There are many molecular dynamics (MD) studies on glucose aqueous solution, but few MD studies dealing with multicomponent systems. In recent years, we have systematically carried out MD studies of multicomponent aqueous solutions. [2-5]. In addition, we have conducted research on aqueous solutions of glycolic acid and lactic acid used in biofuel cells [6-8]. In this study, as part of a series of studies, we would like to consider the structural characteristics of glucose-oxidized gluconolactone/gluconic acid aqueous solution as a model for the anode of biofuel cells. First, the components of the solution, such as the structure of gluconolactone and the atomic charge, are optimized using density functional theory (DFT) using Gaussian. References [1] Z. Zhu, T. K. Tam, F. Sun, C. You, and Y.-H. P. Zhang, Nature Comm. 5, 3026 (1-8) (2014) [2] S. Matsunaga, J. Mol. Liq. 226, 90-95 (2017) [3] S. Matsunaga, Int. J. Mol. Sci. 17, 45 (1-18) (2016) [4] S. Matsunaga, Mol. Sim. 41, 913-917 (2015) [5] S. Matsunaga and S. Tamaki, J. Sol. Chem. 43, 1771-1790 (2014) [6] S. Matsunaga, IOP Conf. Ser.: Mater. Sci. and Eng., 369(1) 012014(1-6) (2018) [7] S. Matsunaga, AIP Conf. Proc. 1981 020115(1-4) (2018) [8] S. Matsunaga, Polymer Eng. & Sci. 59(12) 2474-2478 (2019)

#### Optimizing thermo-mechanical processing and material coupling parameters in numerical modeling for additive manufacturing

Antoine Lamanna1 , Erwan Beauchesne2 , Pierre Dahoo3 , Constantin Meis4

1ESTACA, Automotive, France
2Altair Engineering France, Research Development, France
3University of Versailles St. Quentin en Yvelines, LATMOS, France
4CEA - Saclay, , France

###### Abstract

Additive manufacturing (AM) is gaining increasing industrial interest. Initially conceived to facilitate the pre-production, to manufacture efficiently and cheaply unique parts such as prototypes, it is now able to deliver parts that meet industrial production needs. In addition, AM is an effective way to achieve parts designed using topological optimization. Laser beam melting is an AM technique able to produce specific parts with mechanical properties matching industrial expectations. However, efficient production remains complex because of distortion, cracking and other failures linked to the process and to the machine parameters. The prime material being generally expensive and in order to achieve the required manufacturing quality from the very first attempt while reducing the processing time to market necessary for low cost mass production, a high-quality digital simulation is mandatory. We thus study the relation between the process and the material parameters with the final mechanical state of the part using a numerical model which is developed in parallel. This work focuses on the macroscopic scale. In order to carry out the thermo-mechanical study we use a finite element resolution method on the whole domain defined by the part, its supports and the baseplate. At this scale, one can neglect the packing of the powder as well as the hydrodynamic behavior of the melt pool in the laser beam melting process. We consider a Gaussian energy distribution for the heat source, imposed on several layers of powders below the deposited layer. Starting from a previous study [1], which considers the temperature dependence of the Young modulus, we improve, in this work, the model by considering the temperature dependency of other physical parameters pertaining to material properties or to elastoplastic and thermal laws coefficients. The aim is to bridge the macroscopic scale study of AM to the mesoscopic scale from results of this study. In a first step simulations are carried out with simple models like walls, cubes, beams and the popular cantilever used for calibrations. The results show the gain in precision with the contribution of the temperature dependence of various parameters as well as by considering the phase-transition during the printing process. The computing time is compatible with laptops and can iterate the simulations easily. The accuracy of the model is validated by comparing the distortion to the experimental results for different materials.

#### Motions of the human cardiac cell electrophysiology model

1VSB - Technical University of Ostrava, IT4Innovations, Czech Republic

###### Abstract

One of the many processes in the human body on which our lives depend is the proper propagation of the electrical signal in the heart tissue. This propagation is dependent on the work of each heart cell, and even small variations in the synchronous work of these cells can lead to life-threatening conditions. A proper understanding of cardiac electrophysiology is therefore essential to understanding heart function and treating heart disease. In this work, cardiac electrophysiology is investigated using a mathematical model of a human ventricular cell (Bueno-Orovio-Cherry-Fenton model). This model is paced by regular stimulation impulses, and its responses to this stimulation are analyzed in terms of their dynamic properties, and the dependence of its dynamic parameters for the frequency and amplitude of stimulation. For this analysis, classical and modern tools from the field of dynamic systems theory (e.g. entropy measures, recurrence plot, recurrence quantification analysis, the 0-1 test for chaos) are used.

###### Acknowledgements:

This work was supported by The Ministry of Education, Youth and Sports from the National Programme of Sustainability (NPU II) project IT4Innovations excellence in science -- LQ1602; by The Ministry of Education, Youth and Sports from the Large Infrastructures for Research, Experimental Development and Innovations project IT4Innovations National Supercomputing Center -- LM2015070; by SGC grant No. SP2020/137 "Dynamic system theory and its application in engineering", V\v{S}B - Technical University of Ostrava, Czech Republic.

#### Relativistic three-body bound states in a three-dimensional Faddeev scheme

Kamyar Mohseni1 , NA NA2 , Mehdi Radin3

1K. N. Toosi University of Technology, Tehran, Iran., Department of Physics, Iran, Islamic Republic Of
2NA, , United States
3 K. N. Toosi University of Technology, Department of Physics, Iran, Islamic Republic Of

###### Abstract

Einstein's theory of special relativity was formulated over 100 years ago. There are still issues for systems composed of more than two particles since the pair can be influenced by the presence and motion of the other particles. A three-nucleon system is the simplest system for which the role of the force between a pair of nucleons in the presence of the third nucleon can be qualitatively investigated. Since the three-nucleon problem can be numerically solved with controlled errors, it provides an ideal theoretical laboratory for studying special relativity's effects in the few-nucleon environment. % The estimation of relativistic effects on the three-nucleon bound state energy has been extensively studied. There are two basic approaches to a relativistic formulation of the three-nucleon problem. One is a manifestly covariant scheme linked to a field theoretical approach, and the other is based on an exact realization of the symmetry of the Poincar\'e group in three-nucleon quantum mechanics. The latter method shows that the difference between the relativistic and the nonrelativistic dynamics arises from i.) the momentum dependence of the kinetic energy or free propagator, ii.) in the relation of potential operators to the two-body (2B) $t-$matrices, iii.) and in the form of the momentum basis. % We have recently studied the relativistic corrections in three-body (3B) bound states in a 3D scheme. To this aim, we have formulated the relativistic form of Faddeev equations in momentum space as a function of relativistic Jacobi momentum vectors. It leads to three-dimensional Faddeev integral equations with the Fadeev components depending on the magnitude of Jacobi momentum vectors and the angle between them. The inputs for Faddeev integral equations are relativistic two-body $t-$matrices, which are calculated from the boost two-body potential obtained directly from the non-relativistic potential by solving a nonlinear equation. Our exact and detailed numerical study of relativistic effects in 3B bound states indicates that the relativistic effects lead to a roughly 2\% reduction in the three-body binding energy using a spin-independent Malfliet-Tjon potential. We have numerically studied the contribution of different relativistic corrections in the 3B binding energy.

#### Application of induction heating in the FDM/FFF 3D manufacturing

Alexander Oskolkov1 , Dmitriy Trushnikov2 , Igor Bezukladnikov3

1Perm National Research Polytechnic University, Department of Welding Production, Metrology and Technology of Material, Mechanical Engineering faculty, Russian Federation
2Perm National Research Polytechnic University, Department of Welding Production, Metrology and Technology of Material, Mechanical Engineering faculty, Russian Federation
3Perm National Research Polytechnic University, Department of Automation and Telemechanics, Electrical Engineering faculty, Russian Federation

###### Abstract

This article addresses the problem of induction heating in its application to the FDM/FFF 3D manufacturing. One of the major problems of the FDM/FFF is the instability of layer-to-layer adhesion quality, and on the larger scale - maintaining the homogeneity of material inside the whole printed object. Approach for mitigating and/or resolving of those problems, based on the fast and reliable control of the extruded material temperature during the printing process was proposed. Such approach uses specially created testbed system, consists of the ultra-low weight induction heated nozzle and fast temperature controller. This equipment allows to provide rapid heating and cooling of the nozzle at low input power. On the contrary, using of the nozzle with the minimal thermal mass poses the problems of maintaining even heat distribution on the nozzle surface, and therefore inside the heated material. Multiphysics FEM model for the electromagnetic and thermal problem for the proposed nozzle and inductor configuration was formulated, and numerically solved using COMSOL 5.5. Parametric optimization of the inductor form and heating signal frequency was conducted. Series of the experiments with the optimized inductor construction were made using the proposed testbed, showing significant increase of the heating speed and uniform heat distribution on the nozzle surface, and therefore in the final printed object quality. Experimental data for the all stages of conducted research is provided.

###### Acknowledgements:

The work is supported by the Ministry of Education and Science of the Perm Territory (agreement S-26/787 of 12/21/2017) and the Russian Foundation for Basic Research (RFBR project No. 18 -08-01016A)

#### Elementary function solutions to the CEV model

Evangelos Melas1

1University of Thessaly, Mathematics, Greece

###### Abstract

In the equity markets the stock price volatility increases as the stock price declines. The classical Black$-$Scholes$-$Merton (BSM) option pricing model does not reconcile with this association. Cox introduced the constant elasticity of variance (CEV) model in 1975, in order to capture this inverse relationship between the stock price and its volatility. An important parameter in the model is the parameter $\beta$, the elasticity of volatility. The CEV model subsumes some of the previous option pricing models. For $\beta=0$, $\beta=-1/2$, and $\beta=-1$ the CEV model reduces respectively to the BSM model, the square$-$root model of Cox and Ross, and the Bachelier model. Both in the case of the BSM model and in the case of the CEV model it has become traditional to begin a discussion of option pricing by starting with the vanilla European calls and puts. Mathematically, it makes sense to investigate the simpler cases first. In the case of BSM model simpler solutions are the log and power solutions. These contracts, despite the simplicity of their mathematical description, are attracting increasing attention as a trading instrument. Similar simple solutions have not been studied so far in a systematic fashion for the CEV model. We use Kovacic's algorithm to derive, for all half$-$integer values of $\beta$, all solutions in quadratures'' of the CEV ordinary differential equation. These solutions give rise, by separation of variables, to simple solutions to the CEV partial differential equation. In particular, when $\beta=...,-\frac{5}{2},-2,-\frac{3}{2},-1, 1, \frac{3}{2}, 2, \frac{5}{2},...,$ we obtain four classes of of denumerably infinite elementary function solutions, when $\beta=-\frac{1}{2}$ and $\beta=\frac{1}{2}$ we obtain two classes of of denumerably infinite elementary function solutions, whereas, when $\beta=0$ we find two elementary function solutions. In the derived solutions we have also dispensed with the unnecessary assumption made in the the BSM model asserting that the underlying asset pays no dividends during the life of the option.

#### Representation theory of the BMS group in three space-time dimensions

Evangelos Melas1

1University of Thessaly, Mathematics, Greece

###### Abstract

The ordinary Bondi$-$Metzner$-$Sachs (BMS) group $B$ is the common asymptotic symmetry group of all asymptotically flat Lorentzian space$-$times. As such, $B$ is the best candidate for the universal symmetry group of General Relativity (G.R.). Strongly continuous unitary irreducible representations (IRs) of $B(2,1)$, the analogue of $B$ in three space$-$time dimensions, are analysed in the Hilbert topology. %it is proved that All IRs of $B(2,1)$ are induced from IRs of compact little groups', which are the closed subgroups of $SO(2)$. %It follows that some IRS of $B(2,1)$ are controlled %by the IRs of the finite symmetry groups of regular %polygons in ordinary Euclidean 2$-$space. %It is proved that \it All \normalfont IRs of $B(2,1)$ are obtained by Wigner$-$Mackey's inducing construction %semi$-$direct product theory notwithstanding the fact that $B(2,1)$ is not locally compact in the employed Hilbert topology.

#### Differential operators and the symmetric groups

Ibrahim Nonkane1

1Université Ouaga II, Département d’économie et de mathématique appliquée, IUFIC, Burkina Faso

###### Abstract

In this paper, we study the action of The rational quantum Calogero-Moser system on polynomials. In this vein, we study polynomials ring as a module over a ring of invariant differential operators by elaborating its irreducible submodules. We endowed $\mathbb{C} [x_1,\ldots, x_n]$ with a differential structure by using directly the action of the Weyl algebra associated with the ring of symmetric $\mathbb{C} [x_1,\ldots, x_n]^{S_n}$ after a localization. Then we study the polynomials representation of the ring of invariant differential operators under the symmetric group. We use the representation theory of symmetric groups to exhibit the generators of its simple components.

#### Gauge equivalence between the two-component generalization of the (2+1)-dimensional Davey-Stewartson I equation and $\Gamma$-spin system

Nurzhan Serikbayev1 , Gulgassyl Nugmanova2 , Akbota Meirmanova3

1L.N. GUMILYOV EURASIAN NATIONAL UNIVERSITY, Faculty of Physics and Technical Sciences, Kazakhstan
2 L.N.Gumilyov Eurasian National University, Mathematical and Computer Modeling, Kazakhstan
3L.N. GUMILYOV EURASIAN NATIONAL UNIVERSIT, Faculty of Physics and Technical Sciences, Kazakhstan

###### Abstract

In recent years, multidimensional nonlinear evolutionary equations have been actively studied within the framework of the theory of solitons. Their relevance is confirmed by numerous scientific publications. In this work the gauge equivalence between the (2+1)-dimensional integrable two-component Davey-Stewartson I (DSI) equation and the $\Gamma$-spin system is established.

#### Computation of the masses of neutrinos from the Hadron and Boson masses via the Rotating Lepton model of elementary particles

Constantinos Vayenas1

1University of Patras, Chemical Engineering , Greece

###### Abstract

Constantinos Vayenasa,b*, Dionysios Tsousis and Dimitrios Grigoriou aUniversity of Patras, Caratheodory 1 St, GR-26504 Patras, Greece bAcademy of Athens, Panepistimiou 28 Ave., 10679, Athens, Greece Abstract We use the Rotating Lepton Model (RLM) of elementary particles1 to compute analytically the masses of neutrinos from the masses of composite particles, such as hadrons, in the structures of which neutrinos have been recently shown to participate. In this way three distinct neutrino masses are computed which is in good agreement with the values obtained experimentally at Superkamiokande for the three neutrino flavors of the Normal Hierarchy2. References 1. C.G. Vayenas, D. Tsousis and D. Grigoriou, Computation of the masses, energies and internal pressures of hadrons, mesons and bosons via the Rotating Lepton Model. Physica A, 545 123679 (2020). 2. Takaaki Kajita, Discovery of neutrino oscillations. Rep. Prog. Phys. 69, 1607 (2006).

###### Acknowledgements:

This research is co-financed by the State of Greece and the European Union (European Social Fund- ESF) through the Operational Programme «Human Resources Development, Education and Lifelong Learning» in the context of the project “Reinforcement of Postdoctoral Researchers - 2nd Cycle” (MIS-5033021), implemented by the State Scholarships Foundation (ΙΚΥ).

#### Modelling the optical control of electron spin dynamics in a quantum dot near a WS$_2$ layer

Dionisis Stefanatos1 , Vasilios Karanikolas2 , Emmanuel Paspalakis3

1University of Patras, , Greece
2University of Patras, , Greece
3University of Patras, , Greece

###### Abstract

A quantum dot in the Voigt configuration is a basic system with important potential applications in quantum technologies. The spin states of this quantum dot can act as a prototype qubit. By applying laser pulses the dynamics of the quantum dot spin can be controlled and the necessary quantum gates can be achieved. An important problem is the initialization, i.e., the creation of one of the two electron spin states starting from the natural initial state of the system, which is an equal incoherent mixture of the two spin states. The initialization process can be achieved by proper interaction of the quantum dot with laser pulses. Also, it has been realized that the integration of the quantum dot with photonic structures that give preferential Purcell-enhanced decay rate towards the target spin state increases the fidelity of spin initialization. Here, we propose a new coupled quantum dot - nanophotonic structure that may give high initialization fidelity in short times by coupling the quantum dot with a tungsten disulfide (WS$_2$) monolayer. For the modelling of the spin dynamics we combine quantum dynamics calculations with electromagnetic calculations. Specifically, we model the interaction of the quantum dot with the applied laser field with density matrix equations. Also, the spontaneous decay rates that enter in the density matrix equations are obtained by electromagnetic calculations based on the electromagnetic Green's tensor, which is calculated with the scattering superposition method. We first show that the spontaneous decay rates for the quantum dot near a WS$_2$ monolayer are enhanced by the Purcell effect and are anisotropic for quantum dot dipole moments parallel and perpendicular to the layer. We then use the most common method for initialization, optical pumping and show that a preferential Purcell-enhanced decay rate towards the target spin state increases the fidelity of spin initialization in short times, in comparison to the case that the quantum dot is placed in an isotropic photonic environment.

###### Acknowledgements:

Co-financed by Greece and the European Union - European Regional Development Fund via the General Secretariat for Research and Technology bilateral Greek-Russian Science and Technology collaboration project on Quantum Technologies (project code name POLISIMULATOR).

#### CNN with residual learning extensions in neutrino high energy physics

Miroslav Kubu1 , Petr Bour2

1Czech Technical University in PRAGUE, FNSPE, Department of Mathematics, Czech Republic
2Czech Technical University in PRAGUE, FNSPE, Department of Mathematics, Czech Republic

###### Abstract

As many reconstruction steps in neutrino high energy physics (HEP) are similar to image pattern recognition tasks, we explore the potential of Convolutional Neural Networks (CNN) combined with residual machine learning algorithm. Characteristic features from neutrino track image pixelmaps are extracted at different scales and these features are used for classification of the type of neutrino interaction. In this contribution, we sumarize observed performance of the residual neural networks (ResNet) for neutrino charged current (CC) interaction detections using image-like Monte Carlo simulated data for muon and electron neutrinos. The two topologies depicted at the neutrino detectors differ, muon neutrino CC interaction is dominated by a slowly ionizing muon, while electron neutrino CC interaction is usually recorded as a wide shower. For the ResNet performance evaluation, we use area under ROC curve (AUC) as the evaluation metric. We observe an improvement while using residual learning compared to general CNN architecture, which is caused by a more stable training with lesser vulnerability to the vanishing gradient of the ResNets. Moreover, stacking other hidden layers within our ResNet model greatly increased the AUC value on the test neutrino dataset without the signs of unstable training or overfitting.

###### Acknowledgements:

This work was supported by the research grants LTT180001, LM2015068, SGS18/188/OHK4/3T/14, and CAAS EF16 019/0000778 (MEYS/EU).

#### Mathematical modeling of elastic waves radiation during screw dislocation segment oscillations

Viktor Dezhin1

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

###### Abstract

In this paper, we consider elastic waves radiation (acoustic emission) during oscillations of screw dislocation segment under action of external influences. The dislocation oscillations braking by medium was not taken into account. Using results of [1], elements of generalized susceptibility inverse matrix for a screw dislocation segment in nondissipative crystal are written. The energy emitted by the dislocation oscillator has been found. Using numerical calculations of the generalized susceptibility matrix elements for the screw dislocation segment [2], estimate of the radiated energy is obtained. 1. Bataronov I L, Dezhin V V (2016) J. Phys. Conf. Ser. 738 012108. 2. Bataronov I L, Dezhin V V (2017) J. Phys. Conf. Ser. 936 01236.

#### Mathematical modeling of elastic wave radiation during infinite screw dislocation bending vibrations

Viktor Dezhin1

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

###### Abstract

In this paper, we consider elastic waves radiation (acoustic emission) by infinite screw dislocation performing small bending vibrations under action of external influences. Braking of the dislocation vibrations by medium was not taken into account. To solve this problem, inverse generalized susceptibility of an infinite screw dislocation is written down [1]. It is found that condition for the emission of elastic waves by a screw dislocation is satisfied for two ranges of wave vector component values along the dislocation line. For average value of energy emitted per unit time per unit length of the screw dislocation, corresponding expressions are obtained. 1. Bataronov I L, Dezhin V V and Roshchupkin A M (1993) Bull. Russ. Acad. Sciences - Physics 57 1947.

#### Fluid flow structures in an evaporating sessile droplet depending on the droplet size and properties of liquid and substrate

Marianna Turchaninova1 , Ekaterina Melnikova2 , Alexandra Gavrilina3 , Lev Barash4

1National Research University Higher School of Economics, , Russian Federation
2National Research University Higher School of Economics, , Russian Federation
3National Research University Higher School of Economics, , Russian Federation
4Landau Institute for Theoretical Physics, computational physics, Russian Federation

###### Abstract

We investigate numerically quasi-steady internal flows in an axially symmetrical evaporating sessile droplet depending on the ratio of substrate to fluid thermal conductivities, fluid volatility, contact angle and droplet size. Temperature distributions and vortex structures are obtained for droplets of 1-hexanol, 1-butanol and ethanol. To this purpose, the hydrodynamics of an evaporating sessile drop, effects of the thermal conduction in the droplet and substrate and diffusion of vapor in air have been jointly taken into account. The equations have been solved by finite element method using ANSYS Fluent. The phase diagrams demonstrating the number and orientation of the vortices as functions of the contact angle and the ratio of substrate to fluid thermal conductivities, are obtained and analyzed for various values of parameters. In particular, influence of gravity on the droplet shape and the effect of droplet size have been considered. We have found that the phase diagrams of highly volatile droplets do not contain a subregion corresponding to a reversed single vortex, and their single-vortex subregion becomes more complex. The phase diagrams for droplets of larger size do not contian subregions corresponding to a regular single vortex and to three vortices. We demonstrate how the single-vortex subregion disappears with a gradual increase of the droplet size.

###### Acknowledgements:

This work was supported by the Russian Science Foundation project No. 18-71-10061.

#### Cosmological models with two scalar fields

Nurgissa Myrzakulov1

1LN Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan

In this paper

#### A novel general decomposition theorem for modular multiplicative inverse operators

Luis A. Cortés Vega1

1Antofagasta University, Mathematics, Chile

###### Abstract

In this paper, we present a new general decomposition theorem for modular multiplicative inverse operators. We treat the new result in greater detail, in such a way that may be of more use to the general reader. Finally, a comparison with previous results is briefly discussed.

#### On Abrupt Changes of the Approximate and Sample Entropy Values in Supercomputer Power Consumption

Jiří Tomčala1

1VSB - Technical University of Ostrava, IT4Innovations, Czech Republic

###### Abstract

When calculating the Approximate Entropy (ApEn) and the Sample Entropy (SampEn) of a time series, representing the course of supercomputer power consumption, seemingly unexplained abrupt changes sometimes appear. These sudden changes occur when calculating the course of ApEn and SampEn values using a floating time window and can be manifested also in other discrete-valued time series, such as the development of prices on stock exchanges, time series from birth-death models, count-data time series, etc. These abrupt changes are not continuous and it is clear that these sudden jumps do not reflect real changes in the complexity degree of the analyzed time series. This can cause erroneous detection of a change in the degree of complexity of the time series, which can trigger a false alarm that something unusual is happening in the complex system being monitored (human brain, engine gearbox, financial market, supercomputer infrastructure, etc.). This work reveals in detail the mechanism of this phenomenon and also proposes measures to prevent its occurrence.

###### Acknowledgements:

This work was supported by the Ministry of Education, Youth and Sports from the Large Infrastructures for Research, Experimental Development, and Innovations project “e-INFRA CZ-LM2018140” and by SGC Grant No. SP2020/137 “Dynamic system theory and its application in engineering”, VSB-Technical University of Ostrava, Czech Republic.

#### Stochastic thermostats and temperature expressions

Alex Samoletov1 , Bakhti Vasiev2

1University of Liverpool, Mathematical Sciences, United Kingdom
2The University of Liverpool, Mathematical Science, United Kingdom

###### Abstract

Alex Samoletov and Bakhtier Vasiev Department of Mathematical Sciences, University of Liverpool, UK E-mail: A.Samoletov@liverpool.ac.uk E-mail: B.Vasiev@liverpool.ac.uk Abstract. Molecular dynamics (MD) is in the core of fundamental research for a range of disciplines in natural sciences and is known for its applications in the design of new functional materials and the drug discovery. MD simulations are performed under certain thermodynamic conditions, typically at fixed temperature and pressure. The thermodynamic variables in the MD are modeled using equations that are called thermostats. Many different thermostats have been proposed. Recently, we have shown that a range of thermostats can be derived in the framework of a unified approach based on the fundamental principles of statistical physics [1]. This theoretical method has the potential to be applied beyond the MD. As we have shown, dynamic thermostat schemes are based on the concept of temperature expression (in short, θ-expression, where θ = k B T ), as it defined in [1,2]. Only a few specific θ-expressions have been used so far and reported in the literature, i.e., the kinetic, virial, and so-called generalized temperature expression. In this presentation, we are using a wider set of θ-expressions. This set forms a linear space. Also, the mapping of a vector of θ-expressions into a θ-expression is properly defined. We are systematically utilizing this observation which makes it possible to modify known and propose new thermostats with improved ergodicity and computational efficiency. Here, we are specifically focused on the Nosé-Hoover-Langevin (NHL) stochastic scheme [3,4]. Currently, this scheme is implemented in the main software packages and is the standard de facto in MD simulation. We have extended the classic NHL scheme with additional temperature control tools. However, as with the original NHL scheme, a single thermostat variable is used in extended equations. Simultaneous thermostatting of all phase-space variables with minimal extra computational costs is an advantage of the modified NHL scheme presented here. We demonstrate that the NHL thermostat scheme can be significantly improved with minimal computational costs. References 1. A. Samoletov, B. Vasiev, J.Chem.Phys. 147 (2017) 204106. 2. A. Samoletov, B. Vasiev, (2020) (to be published) 3. A. Samoletov, C. Dettmann, M. Chaplain, J.Stat.Phys. 128 (2007) 1321-36. 4. A. Samoletov, C. Dettmann, M. Chaplain, J.Chem.Phys. 132 (2010) 246101. Acknowledgment This work has been supported by the EPSRC grant EP/N014499/1

#### Simulation of magnetic particle capture in the breast

Luz Camargo Casallas1 , Jennifer Pacheco Fandiño2 , Diego Rodriguez Patarroyo3

1Universidad Distrital Francisco José de Caldas, , Colombia
2Universidad Distrital Francisco José de Caldas, Bogotá, Colombia
3Universidad Distrital Francisco José de Caldas, Bogotá, Colombia

###### Abstract

New strategies, such as magnetic guidance of medicines, are used in cancer treatment. This work determined topological characteristics of blood vessels in the breast with cancer. To remove the topology of the blood vessels mammogram imaging of cancer patients, image preprocessing was performed using conventional methods (Canny, Prewitt and Sobel), with neural networks, and with light correction techniques, a 3D model was generated with finite element software to simulate velocity and blood flow, 700 nanoparticles of Magnetite were included, with a magnet of Neodymiun and the number of nanoparticles reaching the tumor was evaluated. The best results were obtained with the light correction method that improved the definition of blood vessels with the topology obtained and more particles were found to reach the magnetic field tumor compared when it is absent.

###### Acknowledgements:

The authors would like to thank Vilma Fandiño during the selection of the images.

#### Application of Convolutional Neural Networks in Neutrino Physics

1Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Department of Mathematics, Czech Republic
2Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Department of Mathematics, Czech Republic

###### Abstract

Convolutional neural networks (CNNs), as a deep learning algorithm, have successfully been used for analyzing visual image data over the past years. As some of the physical experiments can produce image-like data, it is more than fitting to combine the interdisciplinary knowledge between high energy physics and deep learning. Especially in the domain of neutrino physics, the particle classification problem has played an important role and CNNs have shown exceptional results for the image classification. In this paper, results of application of CNN called SE-ResNET on Monte Carlo simulated image data is presented. These visual images are tailored to fit measured data from future Deep Underground Neutrino Experiment. The image classification focuses primarily on neutrino flavor classification, namely on classification of charged current (CC) electron $\nu_{e}$, CC muon $\nu_{\mu}$, CC tauon $\nu_{\tau}$ and neutral current (NC); and secondarily on other characteristics of the image, such as whether the observed particle is neutrino or antineutrino. The results are important for further physical analysis of the neutrino experiment event, e.g. for study of neutrino oscillation.

#### Elasticity index evaluation based on Le Cam divergence and kernel density estimator in PM space

Vaclav Kus1 , Erik Dolejš2

1Czech Technical University in PRAGUE, FNSPE, Department of Mathematics, Czech Republic
2Czech Technical University in PRAGUE, FNSPE , Department of Mathematics, Czech Republic

###### Abstract

This work focuses on the application of Preisach-Mayergoyz (PM) model applied to the evaluation of elastic properties of hysteretic material. In the first part, essential concepts are explained such as material hysteresis, probability density functions of PM space, optimization algorithm used, and phi-divergence measures applied in the PM identification process. Next, two different characterizations of PM space of hysterons based on kernel density estimators are proposed, either for one-dimensional PM space projection or for fully two-dimensional pyramid kernel. Finally, new index of elasticity is built up by means of the squared Le$\,$Cam divergence $$LC^2(P,Q)= \int \bigl( \sqrt p - \sqrt q \bigr)^2 \text{d}\mu,$$ where $p$ and $q$ denote probability densities corresponding to the super-elastic distribution $P$ and the probability distribution $Q$ found by our optimizated PM identification process, respectively. This elasticity index describes ability of the material to absorb mechanical deformation, or alternatively, it gives an evidence about the certain degree of damage of the material. This proposed index of elasticity $I\!E_K$ is evaluated for the case of experimental data measured on the steel dampers used for the protection against earthquakes.

###### Acknowledgements:

These results were supported by the research grants SGS18/188/OHK4/3T/14 (MEYS) and LTT180001 (MEYS).

#### Theoretical and experimental investigation of spatial temperature distribution in active fiber under conditions of laser radiation generation

Aleksandr Kostrov1 , Nikita Kovalenko2 , Renat Shaidullin3 , Oleg Ryabushkin4

1Moscow Institute of Physics and Technology, The School of Electronics, Photonics and Molecular Physics, Russian Federation
2Moscow Institute of Physics and Technology, The School of Electronics, Photonics and Molecular Physics, Russian Federation
3Fryazino Branch of Kotelnikov Institute of Radio Engineering and Electronics of RAS, , Russian Federation
4Fryazino Branch of Kotelnikov Institute of Radio Engineering and Electronics of RAS, , Russian Federation

###### Abstract

High power fiber lasers are widely used in scientific research and different industry applications. Nowadays, the output power of the continuous-wave fiber lasers has reached 20 kW and 500 kW in single-mode and multi-mode regimes, respectively. The future power scaling is mainly limited by active fiber heating, which is generally caused by quantum defect, i.e. the difference between energies of pump and generating photons. Therefore, different theoretical models and experimental techniques are being developed for investigation of heating of active waveguides of fiber lasers. The aim of this work is the theoretical and experimental investigation of the longitudinal and transversal temperature distribution of active GT-wave waveguide, doped with Yb/Er ions, under conditions of laser generation. The temperature distribution in active waveguide was calculated as the composition of two mathematical models: computation of longitudinal pump radiation distribution by solution of rate equations for Yb/Er doped active medium and computation of transversal temperature distribution by solution of heat equation for convectively cooled fiber using FEM method. The theoretical results were in a good agreement with experimental data, measured by the piezoelectric resonators used as temperature sensors, placed on the surface of the fiber. The temperatures of these sensors were determined from the temperature-dependent frequency shift of its piezoelectric resonance. Also special emphasis was given to the input area of pumping radiation, which is the most heated part of active fiber. The pump radiation transferring length in GT-wave waveguide and the location of the most heated fiber area, as well as the maximum temperature value, were calculated using a created model of pump radiation transferring from the multi-mode waveguide to the active core of the single-mode waveguide. The typical heating values varied from 40 K to 5 K along the fiber for 20 W of pump power and the most heated region was 10 cm away from the pump input point.

#### Recent developments in topological field theory

Renzo Ricca1

1U. Milano-Bicocca, Department of Mathematics & Applications, Italy

###### Abstract

In this talk we present and discuss some recent work in topological field theory, starting with a brief review of modern developments and current state of the art. We then address 3 aspects centred on the author’s own contributions, focussing on aspects of vortex knot topology in classical and quantum systems, role of potential and physical surfaces subject to topological change, and recent work on decaying processes involving structural changes and topological cascade.

#### A mathematical model for calculation of the influence of ferromagnetic components in Vertical Displacement Events and stability simulations of tokamak plasmas

Calin Atanasiu1

1National Institute for Laser, Plasma and Radiation Physics, Bucharest, Romania, Plasma Phyics and Nuclear Fusion, Lab. 22, Romania

###### Abstract

Iron core transformer tokamaks have a distinct element, namely the iron core which can affect the plasma stability of the plasma. As a consequence of the high non-linear dependence of the magneto-hydrodynamic solutions on the iron permeability μFe in JET tokamak for example, Vertical Displacement Events (VDEs), equilibrium and stability calculations are more complicated and more time consuming than in air core transformer tokamaks. By considering the ferromagnetic components as a linear, isotropic and homogeneous media on subdomains, it is known that these media can be replaced by a homogeneous one (vacuum) and a surface- current density distribution iFe(l) on the separation surfaces between subdomains, with l the curve taken along the curve separating two different magnetic media. For the case of geometry with rotational symmetry, this surface-current density distribution along a curve, in a meridian plane, is given by a Fredholm integral equation of second kind. Practically, the advantage of this method is more obvious for the inverse formulation of the VDEs and stability problems by moving the non-linear term (due to the iron permeability μFe) from the differential operator to the r.h.s. of the equations. In this paper, we are presenting how the influence of ferromagnetic components in the equations of the surface currents developed in the vessel structures during Wall Touching Kink Modes (WTKMs) can be taken into account and are reviewing the equations to be solved in order to simulate the influence of the ferromagnetic components in VDEs and equilibrium stability calculations. The numerical results of these simulations for a real JET tokamak structure and plasma parameters will be reported in a future paper.

#### Numerical modeling of emulsion separation in a rectangle bath with heated lid

Airat Musin1 , Indira Shaisitdikova2 , Liana Kovaleva3 , Viktor Kireev4

1Bashkir State University, Applied Physics, Russian Federation
2Bashkir State University, Applied Physics, Russian Federation
3Bashkir State University, Applied Physics, Russian Federation
4Bashkir State University, Applied Physics, Russian Federation

###### Abstract

Let's consider a rectangle bath filled with emulsion of water droplets suspended in oil. It is assumed that all water droplets are spheres of the same diameter and there is a structural and mechanical barrier on the droplets surface, which prevents their coalescence and breaking. At initial state droplets are evenly distributed in the bath. The bath lid (the upper boundary) is heated and it has a higher temperature than the bath bottom. Under the action of gravity, water droplets start to move downward and the process of emulsion separation occurs. The aim of the work is to study the features of the gravity separation of a monodisperse emulsion in an inhomogeneous temperature field, taking into account that the continuous phase (oil) viscosity has a significant temperature dependence. The 1D mathematical model of non-isothermal emulsion separation is based on a diffusion one-temperature approximation. The model consists of equations for the mass and energy conservation of the dispersed and continuous phases. Neglecting the macroscopic motion of the emulsion the model ultimately reduce to two differential equations: the diffusion-type equation that includes the forces acting on emulsion droplets and the convective heat equation. The numerical solution of the mathematical model equations was carried out in OpenFoam software. The results of numerical modeling demonstrated that the dynamics of the process of non-isothermal emulsion separation has significant differences from an isothermal one. The dependence of the time of complete emulsion separation on the parameter characterizing the degree of change in the viscosity of the continuous phase on temperature was determined. It is also shown that in the process of emulsion separation, a region with an increased volume fraction of droplets is formed.

###### Acknowledgements:

The research was supported by the grant of the Russian Science Foundation (project no. 19-11-00298)

#### A Comparison of Numerical Solvers for The Delay Eigenvalue Problem of Coupled Oscillators

ABDELRAHMAN S. ABDELRAHMAN1 , Hussain Al-Qahtani2 , Fahhad Alharbi3

1King Fahd University of Petroleum and Minerals , Electrical Engineering, Saudi Arabia
2King Fahd University of Petroleum and Minerals, , Saudi Arabia
3King Fahd University of Petroleum & Minerals , Electrical Engineering, Saudi Arabia

###### Abstract

Probably, coupled harmonic oscillators system is one of the most used simple physical toy models as a building block for a lot of analyses and applications in physics and chemistry. The fruitfulness of the model is unmistakable as it has applications in almost all branches of physics and many other areas. In this work, we investigate the extension of the conventional model by introducing a time constant delay in the coupling and examine its impact on the dynamics of the system. The resulted system of delay differential equations is solved by linearization around the instantaneous case using the Krylov approach. This is valid for small and moderate delays. Then, the model is applied to analyze the dynamics of the optical two-level system with delayed interaction. The delay-free model is based on Frimmer-Novotny work. It is found that the effects of the delay are considerable and can explain some observed phenomena.

###### Acknowledgements:

Authors: Abdelrahman S. Abdelrahman, Hussain Al-Qahtani, Fahhad H. Alharbi.

#### Simulation of Pressure Build-Up in Oil Wells with Non-Equilibrium Gas Dissolution

Ilya Indrupskiy1 , Ksenia Basova2 , T. Tsagan-Mandzhiev3

1Oil and Gas Research Institute of the Russian Academy of Sciences (OGRI RAS), , Russian Federation
2National University of Oil and Gas «Gubkin University», , Russian Federation
3Oil and Gas Research Institute of the Russian Academy of Sciences (OGRI RAS), , Russian Federation

###### Abstract

Multiphase flow models are widely used to simulate fluid dynamics in oil reservoirs. It is assumed traditionally that the phase behavior of the hydrocarbon system (evolution of free gas or its dissolution in oil) can be described with equilibrium models. However, in real oil reservoirs hysteresis is observed in the processes of gas evolution (release from oil) and dissolution. With a decrease in pressure below the saturation point, gas evolution occurs and exhibits equilibrium dynamics, so that the properties of oil can be described as a function of pressure. With a reverse increase in pressure, gas dissolution takes place in a non-equilibrium manner. In this case, deviation of the current oil properties from equilibrium can be described with a relaxation model. Models of unsteady fluid flow in porous medium are used in interpretation of transient oil-well tests data. Pressure build-up dynamics are recorded in most situations. If the bottomhole pressure during well operation falls below the saturation pressure, it is necessary to take into account the release of dissolved gas and its subsequent dissolution. Numerical simulation of the corresponding processes, taking into account the non-equilibrium gas dissolution, can help to assess the influence of the characteristic relaxation time on the pressure build-up dynamics in oil wells, which is important for correct interpretation. In this study, we present a mathematical model and a numerical scheme for solving the direct problem of unsteady two-phase flow of an oil-gas mixture around a well during operation and subsequent pressure build-up. Non-equilibrium gas dissolution and evolution with different characteristic times is taken into account on the basis of relaxation equation for the dissolved gas content in oil (solution gas-oil ratio – sGOR). A fully implicit numerical scheme is used for calculation of pressure and sGOR, with additional iterations to update oil and gas saturations. Test simulations show the effect of the characteristic relaxation time on the shape of the pressure build-up curve and its derivative used in the interpretation of well test data.

###### Acknowledgements:

The study is a contribution to the research program under the State Research Contract of OGRI RAS (topic АААА-А19-119022090096-5)

#### The reachable regions construction for the inelastic anisotropic billiards

Alexey Grushevskii1

1Keldysh Institue of Applied Mathematics - KIAM, Russian Academy of Sciences, Russian Federation

###### Abstract

Modern methods of the ballistic design of space flights (entry of a spacecraft with non-zero aerodynamic quality into the planet's atmosphere, carrying out gravity assist maneuvers around planets) are associated with the need to calculate a lot of trajectories (i.e. of the phase beams). For their effective use and determination of dynamically admissible reachability regions, it is necessary to identify and study the structure of accompanying singularities of the phase parameters and to construct the corresponding adequate and adaptive models. In this sense, the analogy of the motion of these systems with the singular motion of billiard systems turns out to be very fruitful. First of all, we are talking about anisotropic billiards with dissipation taken into account. In this work, we set and studied the model problems about the flat stones skipping on the surface of the water (the ricochets) and an inelastic ball analogue which is bouncing or rolling on an imperfect surface in the presence of a side deviation effect. Methods for the “anisotropic” ricochet processes evaluating using isotropic ones are given. A model description of the 3D ricochet using the three-dimensional indicatrices is introduced. The main indicatrices types classification for the singular reflection from the plane surface is carried out. Methods for evaluating “anisotropic” ricochet processes using isotropic ones are given. Depending on the ratio of the rolling friction and instantaneous friction coefficients, the ricochets exceeded the permanent movements. The lifetime of the rebound depends on Newton's recovery factor æ (and does not depend on the instantaneous friction coefficient). Model problems of the ricocheting pebble on the surface of the water surface and the inelastic ball bouncing or rolling on an imperfect surface in the presence of a side bouncing effect are posed and studied. The estimates of their maximum reachable regions are obtained

#### Space-time breather solution in nonlinear Klein-Gordon equations

Yasuhiro Takei1 , Yoritaka Iwata2

1Mizuho Information & Research Institute, , Japan
2Kansai University, Faculty of Chemistry, Materials and Bioengineering, Japan

###### Abstract

Klein-Gordon equations describe the dynamics of waves/particles in sub-atomic scales. For nonlinear Klein-Gordon equations, their breather solutions are usually known as time periodic solutions with the vanishing spatial-boundary condition. The existence of breather solution is known for the Sine-Gordon equations, while the Sine-Gordon equations are also known as the soliton equation (e.g., for sub-atomic solitons, see [1-3]). The breather solutios is a certain kind of time periodic solutions that are not only play an essential role in the bridging path to the chaotic dynamics, but provide multi-dimensional closed loops inside phase space. In this paper, based on the high-precision numerical scheme [4-5], the appearance of breathing mode is studied for nonlinear Klein-Gordon equations with periodic boundary condition. The spatial periodic boundary condition is imposed, so that the breathing-type solution in our scope is periodic with respect both to time and space. In conclusion, the existence condition of space-time periodic solution is presented, and the compact manifolds inside the infinite-dimensional dynamical system is shown. The space-time breather solutions of Klein-Gordon equations can be a fundamental building block for the sub-atomic nonlinear dynamics.

###### Acknowledgements:

The calculations were carried out by the workstation system at Tokyo Institute of Technology, and Kansai University.

#### Frequency response of a microcantilever inmersed in fluid

Manuel Quiñones1 , Luz Camargo Casallas2 , Hugo Aya Baquero3

1Universidad Distrital Francisco José de Caldas, , Colombia
2Universidad Distrital Francisco José de Caldas, , Colombia
3Universidad Distrital Francisco José de Caldas, , Colombia

###### Abstract

The micromechanical systems include devices and technology such as actuators and electronic elements on a micrometric scale. A key piece in the development of these systems are the micro cantilevers, which mechanical and dynamic features allow to design sensors and actuators, among others. However, the dynamic response of a microcantilever is altered when it is immersed in a ﬂuid, such as water or even air. This work presents the physical models that describe the behavior of the microcantilevers in ﬂuids (water and air) through the analysis of ﬁnite elements. The results show that the density and viscosity of the ﬂuid alter both the oscillation amplitude of the microcantilever and modify the oscillation frequency. Nevertheless, the behavior of the microcantilever in vacuum and air is quite similar.

#### On some fullerenes with Cubic symmetry

Francisco Sanchez Bernabe1

###### Abstract

We consider several fullerenes with cubic symmetry, this means that they have six faces and eight vertex. One of them is $C_24$ with octagonal faces and triangular vertex. Then, fullerene $C_32$ has a more elaborated structure, because is formed by eight squares, and twelve hexagons. The next fullerene that we review is $C_48$ which is formed by six octagons, eight hexagons, and twelve squares. Our following fullerene is $C_80$ with six faces integrated by four heptagons, and one centred square. Then, we present $C_128$ with six faces formed by five hexagons, and two heptagons, with vertex formed by three pentagons, each of them. Furthermore, we consider the classical fullerene $C_152$ with six faces integrated by six hexagons with one centred hexagon.

#### Quasi-singular methods for determining the limiting properties of the spacecraft entry trajectories into the planet's atmosphere

Alexey Grushevskii1

1Keldysh Institue of Applied Mathematics - KIAM, Russian Academy of Sciences, Russian Federation

###### Abstract

The problem of the limiting dynamic properties determining of the spacecraft (SC) trajectories with non-zero aerodynamic quality entered the atmosphere of a planet (Earth, Venus, Mars etc.) often has singularities. First of all, the singularity of the optimal control and of the SC’ dynamic characteristics is appeared after the interplanetary flight or after the SC maneuver in deep space. The target landing point is either the regular landing site on the Earth, or is the selected region with the specified geological characteristics on the surface of the planet (for example, Venus). The bulk and very laborious numerical experiments have shown that the optimal in terms of maximum coverage of the planet's surface by virtual trajectories of the descending spacecraft often presented as the trajectory with non-monotonic altitude changes (up to secondary spacecraft departure from the atmosphere and secondary entrance) and with the compact atmospheric regions of the spacecraft velocity break points. As it turned out, at the same time, the reachability areas on the surface of the planet obtained by optimization methods, have non-trivial geometric details. One of the most interesting nuances is the non-smooth beake-like border of the reverse side of the reachable area. In the certain sense, we can talk about generalized SC ricochets on the planet's atmosphere, which allow us to expand the reachability of the SC (both in terms of range and lateral range). The paper presents a phenomenological semi-analytical model for the phase beams constructing of the quasi-singular SC descent in the planet's atmosphere, which allows us to synthesize the main nuances of the reachability areas, instead the long-time big data optimization. As the result, the time of the preliminary mission ballistic design can be significantly reduced

#### Deformations of the Heisenberg Lie algebra

María Alejandra Alvarez1

1Universidad de Antofagasta, Departamento de Matemáticas, Chile

###### Abstract

In this note we compute all deformations of the 3-dimensional Heisenberg Lie algebra $\mathfrak{h}_3$. This shows that $\mathfrak{h}_3$ deforms to almost all Lie algebras of dimension 3.

###### Acknowledgements:

The author is supported by Fondo Puente de Investigación de Excelencia FPI-18-02 Universidad de Antofagasta.

#### Recent scaling properties of Bitcoin price returns

Tetsuya Takaishi1

1Hiroshima University of Economics, Department of Liberal Arts, Japan

###### Abstract

For most financial markets, the cumulative distribution of returns is known to show a power-law distribution with a tail index 3, which is referred to as the inverse cubic law. On the other hand, it is claimed that the scaling property of the cumulative distribution of Bitcoin returns differs from those of other markets and exhibits a power-law with a tail index around 2, which is called the inverse square law. We investigate scaling properties of Bitcoin returns using recent trade data and find that the tail index of the cumulative return distribution is around three, which is consistent with the values found for other assets. Thus we argue that properties of the Bitcoin market vary over time and the recent Bitcoin market becomes more mature, having similar scaling properties with other financial markets.

#### Uncertainty Quantification and Sensitivity Analysis of Concrete Gravity Dams Using Multi-Linear Regression Technique.

Abdelhamid Hebbouche1

1École Nationale Supérieure d’ Hydraulique, MVRE, Blida, Algeria., , Algeria

###### Abstract

A Hebbouche1, F Belheouane2, A Rassoul3 1. École Nationale Supérieure d’ Hydraulique, MVRE, Blida, Algeria 2. University of Saad Dahlab, Blida, Algeria 3. École Nationale Supérieure d’ Hydraulique, GEE, Blida, Algeria Abstract : The main sources of uncertainties in the dynamic analysis of hydraulic structures usually come from modeling assumptions and resulting errors, or even variability of seismic loading. The seismic risk is an important factor to take into account when we evaluate the security of existing dam in service or designing a new one.Among the new methods used to quantify the risk on a structure subjected to an earthquake; is the multi-linear regression technique widely used in such cases.To study the effect of uncertain parameters on the dynamic response of the gravity dams; a very large number of non-linear time history analyzes were carried out, based on a Latin Hypercube Sampling (LHS) numerical simulation procedure, applied for two types of near and far earthquakes. Then, a sensitivity analysis was realized to show the influence of the uncertain parameters on the structures responses. The main aim of this work is to carry out a sensitivity study of each random variable on the dynamic behavior of the dam and to quantify its risk using the multi-linear regression technique. This methodology is applied on a dam located West of Algiers (Algeria).

#### A refined version of the inverse decomposition theorem for modular multiplicative inverse operators

Luis A. Cortés Vega1

1Antofagasta University, Mathematics, Chile

###### Abstract

The inverse decomposition theorem asserts that a certain class of modular multiplicative inverses operators defined on a Group of units pre-established can be broken down "in a form suitable" into other operators of the same class all defined on Groups of units smaller than the original. The first author [Proyecciones. J. Math., 37 (2018), p.p 265--293] has shown recently this theorem. The purpose of this note is to obtain a refined version of this result. Unlike previous methods, our result requires some additional assumptions. In this sense, our result is sharper.

#### Effect of temperature on the energy gap in a superconductivity model using $U$-centers.

Darya Apushkinskaya1 , Evgeny Apushkinskiy2 , Boris Popov3 , Vladimir Saveliev4 , Vladimir Sobolevskiy5 , Lidia Krukovskaya6

1Saarland University, Mathematics, Germany
2Peter the Great St. Petersburg Polytechnic University, Physics Department, Russian Federation
3Peter the Great St. Petersburg Polytechnic University , Physics, Russian Federation
4Peter the Great St. Petersburg Polytechnic University , Physics, Russian Federation
5Peter the Great St. Petersburg Polytechnic University , Physics, Russian Federation
6Peter the Great St. Petersburg Polytechnic University , Physics, Russian Federation

###### Abstract

According to the theory of $U$-centers [1], a strong electron-lattice interaction can lead to the fact that the binding energy of two electrons at certain temperatures is higher than the energy of their Coulomb repulsion and, therefore, the possibility of the formation of Cooper pairs appears. If these pairs move coherently [2] without falling apart, then superconductivity occurs. In this work using the Hubbard Hamiltonian [3]: $$H^{\text{eff}}=\sum\limits_k\left(\varepsilon_k-U-\mu)c^+_{k\sigma}c_{k\sigma}-\frac{1}{2}\sum\limits_{k,k'}\frac{t^2_{k,k'}}{U_k}c^+_{k\sigma}c^+_{k\bar{\sigma}}c_{k' \bar{\sigma}}c_{k'\sigma}$$ and applying the secondary quantization method, we calculate the temperature dependence of the superconducting gap $\Delta=\Delta (T)$. A temperature dependence of the HTSC resistance in the normal state demonstrates the features of both semiconductor and metallic behavior. It is known that high-temperature superconductors exhibit such properties only in the normal state [4]. In the work presented now, using mathematical calculations, we discuss the presence of four regions of the HTSC phase diagram $T = T (ν)$, where ν is the relative concentration of $U$-centers. The formation mechanisms of negative $U$-centers are not considered here. We only assume that they are present in HTSC. References: 1. Apushkinsky E.G., Astrov M.S., Popov B.P., Sobolevsky V.K., Physica B 385, (2004) 563. 2. Landau L.D., Lifshiz E.M., Statistical Physics. Nauka, Moscow (1980) 568 pp. 3. Popov B.P., Tsendin K.D., Denisov D.V., Supercond. Sci. Technol. 19, (2006) 313-318. 4. Apuchkinski E., Popov B., Tsendin K., Saveliev V., Sobolevski V., Krukovskai L., Conference. ICANS 28 . France. (2019) №1, с. Mo. M.P4.

#### Optimal spacecraft asymptotic velocity for the high inclined orbits formation using gravity assists in the planetary systems

Alexey Grushevskii1

1Keldysh Institue of Applied Mathematics - KIAM, Russian Academy of Sciences, Russian Federation

###### Abstract

The inclination changing of the celestial bodies’ orbits is one of the most energy-consuming procedures. Nevertheless, for a number of promising space projects, leaving the main plane of the planetary or satellite system is fundamentally necessary and demanded. In this case only the possibility of realizing the formation of maximally inclined spacecraft (SC) orbits using gravity assist maneuvers (GAM) is remained. Their use is a modern highly effective trend in the interplanetary flights theory. However, the dynamic possibilities of GAM using are also limited. The maximum possible value of the SC orbital inclination (which gives the extreme point inclination pole - IncPole) depends on the modulus Vinf of the SC asymptotic velocity on the flyby hyperbola and is directly proportional to it (the GAM geometric limitation) However, the magnitude of the change in inclination at one GAM is inversely proportional to Vinf (GAM dynamic limitation – DLim). As a result, a compromise value of Vinf is existing, which varies for each specific case of a planet or a massive planet' satellite, when the GAM is performed near it. Since in order to achieve a significant inclination, due to the DLim, not one GAM, but a whole series of GAMs may be required, in addition, each GAM must ensure the "resonance" of the orbital periods of the planet and spacecraft after the GAM in order to guarantee their new meeting. According the Jacobi integral existing in the restricted three body problem the Vinf is an invariant during in all interplanetary flights using GAMs. An effective theory of constructing a series of "increasing" GAM by authors have been developed in the form of cranking "jumps" along the resonance levels of the asymptotic velocity from the initial inclination to the maximum possible point IncPole. This point may not belong to any isoline of one of the main resonances itself in the general case. This reduces the GAMs effectiveness and necessarily increases the mission time of flight. A heuristic consideration consists in choosing (in the "resonant tuning") the such value of the design value of Vinf, which ensures the localisation of the inclination pole in the vicinity of one of the main resonance curves between the orbital periods of the spacecraft and the planet (resonant V*). Thus, with the help of the GAM, it is possible to get to the IncPole by jumping along the resonance curve thru the minimum amount of GAM. The paper presents the V* calculating formulas and gives its estimates for the Solar system and for the planets satellite systems

#### Divergence decision tree classification with Kolmogorov kernel smoothing in high energy physics

Vaclav Kus1 , Kristina Jaruskova2

1Czech Technical University in PRAGUE, FNSPE, Department of Mathematics, Czech Republic
2Czech Technical University in PRAGUE, FNSPE, Department of Mathematics, Czech Republic

###### Abstract

The binary classification of a given dataset is a task of assigning one of the two possible classes to each observation. This can be achieved by many machine learning techniques, e.g. logistic regression, decision trees, neural networks. The supervised divergence decision tree (SDDT) is our own binary classification algorithm in favour of the R\'enyi divergence, which incorporates multi-dimensional kernel density estimates (KDEs) as the main part of the splitting process in its tree nodes. However, the KDE needs an efficient smoothing in order to obtain quite satisfactory classification results. In this paper, the D-discrepancy method for selecting the bandwidth was applied. It is based on an evaluation of divergences, or distances, between two estimated distributions. The Kolmogorov metric distance on probability space is used and the performance of such a novel technique is compared to standard smoothing techniques. The final goal is to perform a binary classification and achieve the best possible results with respect to the AUC value (area under ROC curve) on a given high energy physics (HEP) dataset, specifically for d+Au heavy ions decay data. This HEP dataset is described and the main structure of the used SDDT is outlined. Final classification results are presented for KDE under Kolmogorov D-method of smoothing in SDDT algorithm.

###### Acknowledgements:

These results were supported by the research grants CAAS EF16\_019/0000778 , LTT180001 (MEYS), and SGS18/188/OHK4/3T/14.

#### Wind and Temperature Effect on the Performance of a Mobile e-nose platform for Real Time Victim Localization

Spyridon Blionas1

1University of the Peloponnese, Informatics and Telecommunications, Greece

###### Abstract

In this paper it is presented the influence of weather conditions on the performance of the sensors of a mobile e-nose system that measures the atmospheric air, gas components’ concentrations (actually CO₂ and O₂), into a rubble void, where humans are entrapped, after a disastrous event that caused the collapsing of a building/construction. In this case, the entrapped humans in the void, they affect the air composition and temperature into the void. Additionally to the human(s) created CO₂ source(s), O2 sink(s), and heat source(s) (from body temperature), rubble openings (possibly too many), create sources of fresh atmospheric air and sinks for letting the air from the inside of the cavity to go out of it and vice-versa. The existence of the aforementioned sources/sinks constantly affect the air composition and temperature into the void and makes gas components’ concentrations dynamic rather than static. There will be studied the fresh atmospheric air sources into a cavity taking into account also the outside weather conditions. The final goal is to estimate the concentrations of CO₂ and O2 into the cavity as a function of time, having as parameters, the external weather conditions, the openings of the void and the number of entrapped humans. Estimating the concentrations it will enable the operator of a mobile e-nose system with sensors of a specific sensitivity and specificity, to determine the possibilities of detecting the presence of humans in a rubble void.

###### Acknowledgements:

This work was supported by the European Commission under INACHUS, a collaborative project part for research, technological development and demonstration (Grant Agreement NO 607522).

#### Expected Performance of a Mobile e-nose platform for Real Time Victim Localization

Spyridon Blionas1

1University of the Peloponnese, Informatics and Telecommunications, Greece

###### Abstract

In this paper it is presented an analysis for the performance of the sensors of a mobile e-nose system that measures the atmospheric air, gas components’ concentrations (actually CO₂ and O₂), into a rubble void, where humans are entrapped, after a disastrous event that caused the collapsing of a building/construction. In this case, the entrapped humans in the void, they affect the air composition and temperature into the void. The existence of human(s) creates CO₂ source(s), O2 sink(s), and heat source(s) as well (from body temperature). The existence of the entrapped humans constantly affect the air composition and temperature into the void and makes gas components’ concentrations dynamic. There will be presented the human CO₂ source(s), and O2 sink(s) inside a cavity. The final goal is to estimate the concentrations of CO₂ and O2 into the cavity as a function of time, having as parameters the number of entrapped humans. Estimating the concentrations it will enable the operator of a mobile e-nose system with sensors of a specific sensitivity and specificity, to determine the possibilities of detecting the presence of humans in a rubble void, nevertheless without considering the effect of weather conditions.

###### Acknowledgements:

This work was supported by the European Commission under INACHUS, a collaborative project part for research, technological development and demonstration (Grant Agreement NO 607522).

#### Biophysical parameters affecting lung surfactant function, surface tension and the transition from aerosol to droplet exhalation (in relation to COVID-19 infection)

Wilfried Allaerts1

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

###### Abstract

A considerable number of biophysical and biochemical studies has increased our understanding of the surface activity of surfactant proteins B and C (SP-B, SP-C) in the (mammalian) lung and their importance for a healthy, proper breathing system. For instance, it is well-known that these surfactant proteins are released from the lamellar bodies of type II cells of the lung alveoli (type II pneumocytes), and that at compression, the lipid-protein monolayer of the surfactant is squeezed into three-dimensional (3D) stacks, acting as a surfactant reservoir. For a correct surface function, the production, dimerization, stacking and secretion (in the right order) of the main component SP-B, as well as of the other constituents, is essential. SP-B is a small homodimeric, hydrophobic protein that interacts with phospholipids (palmitoylated and others) and with hydrophobic compounds in general (like cholesterol). Moreover, studies have demonstrated the influence of hydrophobic nanoparticles on lung surfactant model systems, well before the outbreak of the COVID-19 pandemic. The potentially devastating effect of SARS-CoV-2 infection on vital lung function, including pneumonia and Acute respiratory distress syndrome (ARDS), meanwhile has been confirmed worldwide by thousands of fatal cases, although the mechanism of its onset is not completely understood. In theory, any virus carrying palmitoylated spike proteins (like beta-coronaviruses in general) might interfere with the alveolar surface activity, when infecting the deep respiratory system. However, it is clearly established that SARS-CoV-2 uses the Angiotensin converting enzyme 2 receptor (ACE2) for entry in the host, which receptor is expressed on the same type II pneumocytes, and, as a result, the virus may directly interfere with the secretion of surfactant proteins. This study aims at elucidating the main targets for containment of the spread of the SARS-CoV-2 virus via the respiratory system, a better understanding of the role of virus-surfactant interactions, the formation of aerosols and role of the inflammatory components of the immune system, as well as the role of positive pressure ventilation systems on particle exhalation, as being used at ICUs. Finally, suggestions are made for important goals for future biophysics research in infectious disease prevention and containment.

#### Development of the sharing economy in Russia

Gulnaz Galeeva1

1FGBOAU K(P)FU, Institute of Economics and Finance Management, Russian Federation

###### Abstract

The article discusses the main approaches to defining the sharing economy in Russia and abroad. The factors of development of sectors of the sharing economy in Russia are highlighted. The analysis and assessment of the prospects for the development of the sharing economy in Russia is presented.

#### Problems of attracting foreign direct investment into the regional economy

Gulnaz Galeeva1

1FGBOAU K(P)FU, Institute of Economics and Finance Management, Russian Federation

###### Abstract

The article discusses topical issues of attracting foreign direct investment in the economy of the Republic of Tatarstan. The assessment of the factors affecting the investment attractiveness of Russian regions made it possible to determine the prospects for the implementation of projects with the participation of foreign investors. In conclusion, the authors highlight the successful practices of attracting foreign investment in the region's economy.

#### Dynamical and Statistical properties of DNA

George Kalosakas1

1University of Patras, Materials Science, Greece

###### Abstract

Using the coarse-grained Peyrard-Bishop-Dauxois (PBD) model [1], which efficiently describes base pair openings in double stranded DNA, various dynamical and statistical properties will be presented. Following an introduction of the basic assumptions and the successes of the PBD model in reproducing experimental observations regarding the melting transition [1-3], as well as base pair openings of gene promoter sequences[4-6], more recent results will be discussed. These concern the chaotic properties of the model for different temperatures and base pair composition (guanine-cytosine versus adenine-thymine base pairs) [7] and the probability distributions of bubble lengths and bubble lifetimes at physiological temperature [8]. [1] T. Dauxois, M. Peyrard, and, A. R. Bishop, Phys. Rev. E 47, R44 (1993). [2] A. Campa and A. Giansanti, Phys. Rev. E 58, 3585 (1998). [3] D. Cule and T. Hwa, Phys. Rev. Lett. 79, 2375 (1997). [4] C. H. Choi, G. Kalosakas, K. O. Rasmussen, M. Hiromura, A. Bishop, and A. Usheva, Nucleic Acids Res. 32, 1584 (2004). [5] G. Kalosakas, K. O. Rasmussen, A. R. Bishop, C. H. Choi, and A. Usheva, Europhys. Lett. 68, 127 (2004). [6] B. S. Alexandrov, V. Gelev, S. W. Yoo, L. B. Alexandrov, Y. Fukuyo, A. R. Bishop, K. O. Rasmussen, and A. Usheva, Nucleic Acids Res. 38, 1790 (2010). [7] M. Hillebrand, G. Kalosakas, A. Schwellnus, and Ch. Skokos, Phys. Rev. E 99, 022213 (2019). [8] M. Hillebrand, G. Kalosakas, Ch. Skokos, and A.R. Bishop, preprint (2020).

#### Computer modeling of the dynamics of several population groups within the framework of the spatial economy model

Sergei Gerasimov1 , Igor Inovenkov2

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

###### Abstract

Nowadays, the topic of urban studies is becoming increasingly relevant. Planning and building a “city of the future” is becoming one of the main challenges for many countries. It is foolish to deny the tendency in the modern world to overpopulate and mix different groups of the population; this happens not only at the national level, but also in many other respects. In this paper, the dynamics of four different population groups in an urban environment will be considered. Systems of parabolic partial differential equations will be used.

#### A variational method for studying the stability of one nonlinear dynamical system

1Lomonosov Moscow State University, Department of Computational Math & Cybernatics, Russian Federation
2Lomonosov Moscow State University, Department of Computational Math & Cybernatics, Russian Federation

###### Abstract

In this work using the variational method the stability of the equilibrium states of a nonlinear dynamic system was studied: $$\frac{dx_{1}}{dt}=x_{1}(\mu_{1}-(x_{1}^{2}+2x_{2}^{2})),$$ $$\frac{dx_{2}}{dt}=x_{2}(\mu_{2}-(2x_{1}^{2}+x_{2}^{2})),$$ where $\mu_{1} ,\; \mu_{2} >0$ - fixed parameters. This system is, of course, nonlinear and more perspective from the point of view of its analysis than the well-known mathematical model `the brusselator'' considered in many works. The variational method is particularly effective when the Lyapunov's method does not give the desired result or creates insurmountable difficulties or causes inaccuracies in its application. The proposed method is simple to implement and allows you to serve as an incentive for further research in this direction. proposed nonlinear dynamic system has five stationary points (equilibrium positions): $(0,0)$, $(a,0)$ and $(0,b)$, where $a=\pm \sqrt{\mu_{1}}$, $b=\pm \sqrt{\mu_{2}}$. For the zero (trivial) equilibrium position $(0,0)$ just prove that the perturbed solution is stable only if $\mu_{1}=\mu_{2}=0$. For the equilibrium position $(a,0)$ it is proved that the necessary stability conditions for the perturbed solution are valid if the inequality $0<\mu_{2} <2\mu_{1}$. For the equilibrium position $(0,b)$ it is established that the necessary stability conditions for the perturbed solution are valid if it is satisfied that $0<\mu_{1}<2\mu_{2}$.

#### Modeling the influence of the Earth rotation axis position on the global climate variations

Valeriy Parkhomenko1

1The Federal Research Center "Computer Science And Control" of The Russian Academy Of Sciences, Bauman Moscow State Technical University, Dorodnicyn Computing Centre, Russian Federation

###### Abstract

This study presents the results of numerical experiments to determine the Earth’s climate when its rotation axis is displaced without changing the axis tilt to the ecliptic plane. There is some evidence of the possibility of this shift in the past. The calculations were carried out using a hydrodynamic three-dimensional global climate model, including blocks of atmosphere, thermohaline large-scale ocean circulation and sea ice. Numerical experiments demonstrate a significant temperature changes throughout the world. A large area of Antarctica warmed up to temperatures above 15 ° C. This is reason of intense melting of glaciers for a long time. Significant warming of the Arctic Ocean will lead to sea ice melting in the Arctic. Strong changes in temperature and ice cover lead to significant changes in horizontal ocean circulation. A procedure is proposed for calculating wind speed in atmosphere energy - moisture balance model. It is based on the geostrophic approach, taking into account the thermal component of the wind, and introducing the mechanism of friction on the underlying surface. A technique has been developed for the formation of the necessary maps and the relationships between them when turning the Earth rotation axis or using new cartographic data.

#### Multi-physics simulation of shedding of in-flight ice

Andrea Rausa1 , Alberto Guardone2

1Politecnico di Milano, Department of Aerospace Science and Technology, Italy
2Politecnico di Milano, Department of Aerospace Science & Technology, Italy

###### Abstract

In-flight ice accretion may possibly jeopardise the safety of fixed- and rotary-wing aircraft. Icing can possibly occur if supercooled water droplets in clouds impinge on the aircraft surfaces and freeze upon impact. It may result in instrument failures and degradation of the aerodynamic performances. A major problem related to ice accretion is the possibility of ice shedding from the main body and impacting other parts of the aircraft or being ingested by the engines. In fixed-wing aircraft, shedding is caused by the action of the aerodynamic forces or the activation of an Ice Protection System. In the present work, a multi-physics framework is presented to simulate ice accretion and shedding from wings and engine nacelles. The aerodynamics is computed using the open-source tool-kit SU2. Cloud droplet trajectories are computed using the arbitrary-precision Lagrangian in-house solver PoliDrop. Then, the in-house ice accretion tool-kit PoliMIce is used to determine the ice layer. A FEM structural analysis is performed on the accreted ice shape by means of the open-source code MoFEM. Internal stresses within the ice geometry due to aerodynamic forces are computed. The possibility of the occurrence of cracks in the ice layer is assessed and its propagation is determined numerically. Two-dimensional ice accretion simulations are performed to check the validity of the present approach and compare fairly well with available results.

#### Dynamic model of ultrasonic micro-scale impact processing by two coaxial longitudinal waveguides

Ildar vagapov1

1Kazan Federal University , Naberezhnye Chelny Institute, Russian Federation

###### Abstract

A dynamic model of the ultrasonic vibro-impact processing using an oscillation system with two longitudinal coaxial waveguides mounted with a gap between their working ends is considered. One waveguide is connected with an ultrasonic transducer and the other serves as a passive resonant anvil. Waveguides are described as of visco-elastic rods with close natural frequencies. The material being deformed in the gap between the vibrating ends of waveguides is approximated by a rigid-plastic rheology. Vibro-impact processing is presented as the forced oscillations of two coupled resonant subsystems, where the workpiece is assumed both as the processing load and the nonlinear coupling link. The amplitude and phase responses of the longitudinal oscillations of the two-rod system are calculated, the ranges of oscillatory stability are determined. The difference in the natural frequencies of the waveguides is taken into account. Two cases of the relation between the natural frequencies of interchangeable waveguides are considered: the natural frequency of the forced waveguide is higher or lower than that of the passive waveguide. It is shown that in the first case resonance of the anti-phase oscillations of waveguides take place. In the second case the oscillation system resonates on the in-phase eigen-mode. The anti-phase oscillations are preferable for vibro-impact processing because the working ends of waveguides move toward each other at the impact moment. Application of ultrasonic micro-forging to cutting edge sharpening is exemplified. The threshold value of the impact force, which is necessary to overcome the resistance to plastic flow, is derived analytically. The maximum achievable degree of plastic deformation is estimated. It is shown that the anti-resonant mode of operation of the oscillatory system is most effective. Recommendations for design parameters and resonance tuning of ultrasonic equipment are given.

#### Geesthacht Coupled Coastal Model System (GCOAST)

Joanna Staneva1

1HZG, Hydrodynamics and Data Assimilation, Germany

###### Abstract

The GCOAST (Geesthacht Coupled cOAstal model SysTem) is built upon a flexible and comprehensive coupled model system, integrating most important key components of the regional and coastal systems, that enable to include information from observations. It encompasses: (i) atmosphere-ocean-waves interactions, (ii) the dynamics and fluxes in the land-sea transition, (iii) the coupling of the marine hydrosphere and biosphere. Triggered by the need for novel modelling capacity, GCOAST system is designed to handle cross compartment fluxes of water and energy between the atmosphere and ocean thought the dynamic wave interface, dynamics and biogeochemistry in the land-ocean transition and marine ecosystems and benthic-pelagic coupling, transport and transformation of environmental pollutants. Coupling of different models is a commonly used approach when addressing the complex interactions between different components of the earth system. We focus on the nonlinear feedback between strong tidal currents and wind -waves, which can no longer be ignored, in particular in the coastal zone where its role seems to be dominant. In NEMO stand-alone model, the momentum flux from the atmosphere, which is related to the wind speed, is passed directly to the ocean and this is controlled by the drag coefficient. However, in the real ocean, the waves also play the role of a reservoir for momentum and energy because different amounts of the momentum flux from the atmosphere is taken up by the waves. In the coupled model system the momentum transferred into the ocean model is estimated as the fraction of the total flux that goes directly to the currents plus the momentum lost from wave dissipation. Additionally, we demonstrate that the wave-induced Stokes Coriolis force leads to a deflection of the current. During extreme events, the Stokes velocity is comparable in magnitude to the current velocity. The resulting wave-induced drift is crucial for the transport of particles in the upper ocean. The performance of the coupled modelling system also illustrated for the cases of several extreme events and assessment of coupled model versus newly available data (e.g. Sentinel) is performed. The comparisons with in-situ and satellite data showed that the implementation of wave model component into the coupled systems reduces the errors, especially under severe storm conditions.

###### Acknowledgements:

This work is supported by the Initiative and Networking Fund of the Helmholtz Association through the project “Advanced Earth System Modelling Capacity (ESM)” and Cluster of Excellence “Climate, Climatic Change, and Society” (CLICCS) .

#### General mathematical model for energetic and informatic evaluated over natively producing surrounded systems

Valeriy Zakharov1

1Lomonosov Moscow State University, Mathematical Analysis, Russian Federation

###### Abstract

Informatics reached extraordinary heights in its development. However, a satisfactory solid theoretical foundation for this science has not been established until now. The reason is the absence of satisfactory general definitions of the notions of information and information system. The distinguished peculiarity is inherent not to Informatics only. In Physics despite of its longer existence the situation with the solid theoretical foundation gets on in the same way: there are no satisfactory general definitions of the notions of energy and energy system. In 1964 the outstanding American physicist Richard Feynman in his famous lectures [Feynman R.F., Leighton R.S., Sands M. The Feynman Lectures on Physics. V. 1: Mainly Mechanics, Radiation, and Heat. − United States of America: Addison Wesley Publishing Company, 1964. − 270 p.] in §1 of Chapter 4 has written: «It is important to realize that in physics today, we have no knowledge of what energy is. We do not have a picture that energy comes in little blobs of a definite amount. It is not that way. However, there are formulas for calculating some numerical quantity, …». The following conclusion may be done from this apparently not random coincidence: the cause of the described situation is founded not in Informatics itself and not in Physics itself, but in the absence of satisfactory general solid theoretical conception of the world and its being, in which the notions of information and energy might appear in some natural deductive way. Some joint (synthetic) closed in itself idea about the world and its being is expounded in the report, which gives the opportunity to invent the parallel definitions of the energy and the information not exceeding the bounds of the united world. This allows us to introduce some sufficiently general notion of the produciпg (conservatively-dynamic surrounded stream) system, described by the proper system of evolutional equations. In the capacity of important partial cases of such systems the proper notions of the energetic producing system and the informatic producing system are introduced. The explicitly analyzed examples of the heating stove (as the energetic producing system) and the personal computer (as the informatic producing system) expose the applicability of proposed idea to a generalized and formalized description of some wide class of systems really existing.

#### Simple math model for calculation about possibility to disclose Stealth

Oleksandr Denisov1

1Harbin Institute of Technology, Department of Microwave Engineering, China

###### Abstract

. Stealth coating is the antidote against of the radar. But it can be disclosed by the microwave radiometer because their job based on the measuring the radio-brightness contrast between Stealth object and the background of the environments (sky is cold, Earth is warm). This short report presents some math model for the simplest calculation of the possible disclosing distance till the Stealth object.

###### Acknowledgements:

Authors wishing to acknowledge assistance from colleagues in Harbin Institute of Technology.

#### Several Classes of Plain Dynamic Systems Qualitative Investigation

Irina Andreeva1

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

###### Abstract

Dynamic systems in applications are useful as mathematical models of those processes and phenomena, where statistical events, or fluctuations, may be disregarded. Dynamic systems may be divided into the two main categories - the systems with continuous time (the flows), and systems with discrete time (the cascades). During the investigations of, first of all, flows, normal autonomous systems of ordinary differential equations are used. The present work is devoted to the original rigorous research of some important family of dynamic systems having reciprocal polynomial right parts, which are the forms of their phase variables. The whole wide family under consideration is being split into numeric subfamilies belonging to different hierarchical levels, and is subjected to the first and the second Poincare transformations, or mappings. As a result, the full qualitative pattern of trajectories is constructed - using the Poincare sphere - in the Poincare disk. A series of new special investigation methods was developed, useful for further investigations of similar dynamic systems’ classes. References. 1. Andreeva,Irina, Andreev, Alexey. Investigation of a Family of Cubic Dynamic Systems. //Vibroengineering Procedia. Vol.15. Dec.2017. Pp.88-93. 2. Andreeva I.A., Andreev A.F. Phase Portraits of One Family of Cubic Systems in a Poincare Circle. I.//Vestnic RAEN. 2017. Vol.17. №4. Pp.8–18. 3. Andreeva I.A., Andreev A.F. Phase Portraits of a Family of Cubic Systems in a Poincare Circle.I I.//Vestnic RAEN. 2018. Vol.18. №4. Pp.11–15. 4. Andreev A.F., Andreeva I.A. Phase Portraits of Some Family of Cubic Dynamic Systems in a Poincare Circle. III.//Vestnic RAEN. 2019. Vol.19. №2. Pp.20–24. 5. Andreev A.F., Andreeva I.A. On a Behavior of Trajectories of a Certain Family of Cubic Dynamic Systems in a Poincare Circle. // IOP Journal of Physics, Conference Series, 2018, 1141. 6. Andreeva I.A., Efimova T.O. Phase Portraits of a Special Class of Dynamic Systems in a Poincare Circle.//IOP Journal of Physics, Conference Series, 2019, 1236.

###### Acknowledgements:

Prof. Dr. Alexey F. Andreev, St.Petersburg State University, Russia

#### To the optimized approach to get the fundamental property of the gravity assists maneuvers from the Jacobi integral

Alexey Grushevskii1

1Keldysh Institue of Applied Mathematics - KIAM, Russian Academy of Sciences, Russian Federation

###### Abstract

The design of interplanetary trajectories using a series of gravity assists maneuvers begins with the ballistic mission design. It is reasonable to construct the corresponding initial approximation using the patched conics method within the model of the circular restricted three-body problem. Such a construction requires the calculation of the “transfer parameter” Vinf - the asymptotic velocity of the spacecraft relative the target planet, when switching from heliocentric arcs to planetocentric segments and vice versa. In the circular restricted three-body problem model, can be calculated using the Jacobi integral J (or using it's analogue - the Tisserand parameter Ti ) and the basic property of the Jacobi integral for the gravity assists maneuvers within the framework of the circular restricted three body problem: J=3 - Vinf*Vinf . According to this property, the J value does not change during the multiple gravity assists maneuvers that preserve the Jacobi integral constant are performed. This fact is known in astrodynamics but it is classically derived in a rather cumbersome method. In this study, a shorter method for it’s obtaining is proposed. The modifications of the representation of the Jacobi integral in the circular restricted three-body problem for the various configurations of three bodies and the table of transformations of the Jacobi integral and the Tisserand parameter are presented for all cases.

#### On dark stars, galactic rotation curves and fast radio bursts

Igor Nikitin1

1Fraunhofer Institute for Algorithms and Scientific Computing, SCAI, Germany

###### Abstract

This paper is a continuation of our recent work on Radial Dark Matter stars (RDM-stars), black holes, coupled with radial flows of dark matter. As a galaxy model, it produces flat rotation curves, approximately valid for many galaxies far from the center. In this paper, more detailed modeling is carried out, including the vicinity of the galactic center. Assuming that the distribution of stellar black holes repeats the distribution of luminous matter, we get a perfect match between the model rotation curves and the observed ones. Further, using numerical integration, we examine the gravitational field of an individual RDM-star. The computation shows the event horizon being erased and rapidly increasing mass density arising instead (mass inflation). In this regime, we apply the previously constructed Planck star model, where at high densities a repulsive force occurs (quantum bounce). In our stationary model, the evolution of a Planck star has stopped under the pressure of dark matter flows. This system is considered as a possible source of Fast Radio Bursts (FRBs). In a scenario involving an asteroid falling onto an RDM-star, the model reproduces the correct frequency range of FRBs. Their total energy, coherence and short duration are explained as well.

#### Mathematical modeling and visualization of topologically non-trivial solutions in general relativity

Igor Nikitin1

1Fraunhofer Institute for Algorithms and Scientific Computing, SCAI, Germany

###### Abstract

In general relativity, there is a class of solutions that currently do not have observed analogues, but on which the theory is shaped, giving an understanding what is fundamentally possible within its framework. Such solutions include wormholes, tunnels that connect distant regions in spacetime. Although not a single wormhole has yet been discovered, there is a large number of works devoted to their study, thanks to which wormholes as a class of solutions become firmly established in modern science. In this paper, we consider two topologically nontrivial types of solutions related to wormholes. First: wormholes that can open and close. In this relation, we will discuss topological censorship theorems, which under certain conditions prohibit changing topology. We will also discuss known ways to circumvent these theorems. Using analytical and numerical methods, as well as visualization, we will construct an example of an opening and closing wormhole with the dimensions of the central black hole in the Milky Way galaxy. Our construction continues the work by Kardashev, Novikov and Shatskiy, in which a static wormhole with the same parameters was considered. The second type is a modification of Visser's dihedral wormhole solution for a dynamic case.

#### Fatigue tests simulation of materials with a random endurance limit

1Perm National Research Polytechnic University , Department of Applied Mathematics, Russian Federation
2Perm National Research Polytechnic University , Department of Applied Mathematics, Russian Federation

###### Abstract

Abstract. Fatigue tests of materials are characterized by long duration and high cost. In this regard, it is relevant to develop methods for modeling test results in the widest possible range of loads. Fatigue curve mathematical model includes the equation of the relationship between the amplitude of the stress and the durability of the samples, considering the random nature of the values of durability and the limit of unbounded endurance. At the first stage, the values of the model parameters are determined using the maximum likelihood function using real test data in a limited range of stress amplitudes. At the second stage, the problem solution is found considering the random value of the limit of unbounded endurance. Moreover, the mean estimate is obtained from the solution of the first part of the problem. The estimate of the unbounded endurance limit variance is obtained by calculation from the variance balance conditions. The results of modeling fatigue tests for aluminum alloy samples in a wide range of stress amplitude values are presented. Simulation results for determining the values of the fatigue curve left tolerance are considered.

#### Explanation of Light Deflection, Precession of Mercury’s Perihelion, Gravitational Red Shift and Rotation Curves in Galaxies, by using General Relativity or equivalent Generalized Scalar Gravitational Potential, according to Special Relativity and Newtonian Physics

Spyridon Vossos1 , Elias Vossos2 , Christos Massouros3

1National and Kapodistrian University of Athens, Core Department, Greece
2National and Kapodistrian University of Athens, Core Department, Greece
3National and Kapodistrian University of Athens, Core Department, Greece

###### Abstract

The development of Geometric theories of gravitation and the application of the Dynamics of General Relativity (GR) is the mainstream approach of gravitational field. Besides, the Generalized Special Relativity (GSR) contains the fundamental parameter (ξI) of Theories of Physics (TPs). Thus, it expresses at the same time Newtonian Physics (NPs) for ξI→0 and Einstein Relativity Theory (ERT) for ξI=1. Moreover, the weak Equivalence Principle (EP) in the context of GSR, has the interpretation: mG=m (1), where mG and m are the gravitational mass and the inertial rest mass, respectively. In this paper, we bridges GR with GSR. This is achieved, by using a GSR-Lagrangian, which contains the proper time of the corresponding GR-Lagrangian. Thus, we obtain a new generalized central scalar GSR-gravitational potential V=V(k,l,r,r_dot,φ_dot), where k=k(ξI), l=l(ξI), r is the distance from the center of gravity and r_dot, φ_dot are the radial and angular velocity, respectively. We demand that ‘this new GSR-gravitational field in accordance with EP (1), gives the same equation of orbit as Schwarzschild Metric (SM) does’ and we obtain k=1 and l=ξI^2. Thus, it emerges that both the NPs and Einsteinian Special Relativity (SR) have the horizon at one Schwarzschild radius (rS). The procedure described in this paper can be applied to any other spacetime metric of GR, in order to find out the corresponding GSR-gravitational potential. We modify the aforementioned central scalar GSR-gravitational potential as V=V(h,k,l,r_dot,φ_dot), where h=h(r). The combination of the above with MOND interpolating functions, or distributions of Dark Matter (DM) in galaxies, provides the functions h=h(r). Thus, we obtain a new central GSR-Gravitational field strength g=g(h,k,l,r_dot,φ_dot), which not only explains the Precession of Mercury’s perihelion, Deflection of Light, Gravitational Red Shift and Rotation Curves in Galaxies, eliminating Dark Matter, but also gives a possible explanation to the Dark Energy problem, by using parameter ξI that depends on cosmic time. .................. COMMENTS: ..................... It is considered that Special Relativity (SR) cannot explain the Gravitational phenomena and only General Relativity (GR) can do this (by using curved spacetime) [1] (pp. 90, 111, 116), [2] (pp. 34, 109), [3] (p. 249). In this paper, we prove that there exist suitable generalized gravitational potentials, according to SR or Newtonian Physics (NPs) that can produce exactly the same results as GR. This is achieved by using the GR-time dilation and the Lagrangian of Generalized Special Relativity (GSR). The procedure is analytically developed in case of Schwarzschild metric, but can also be applied to any kind of metrics. ................ [1] Einstein, A 1920 Relativity: The Special and General Theory; (Holt, New York, USA). Translated by Robert W. Lawson. https://ibiblio.org/ebooks/Einstein/Einstein_Relativity.pdf [2] Rindler W 2006 Relativity: Special, General and Cosmological (New York: Oxford University Press). [ISBN: 978-0-19-856732-5]. [3] Tsamparlis M 2010 Special relativity: An introduction with 200 problems and solutions (Berlin Heidelberg: Springer-Verlag) [ISBN: 978-3-642-03836-5, e-ISBN: 978-3-642-03837-2]

#### Space-time chaos in the nonlinear Schrödinger equation

Nikolai Magnitskii1

1Federal Research Center "Computer Science and Control", Laboratory of Chaotic Dynamics, Russian Federation

###### Abstract

The paper provides an analytical and numerical analysis of the transition to space-time chaos in the generalized nonlinear Schrödinger equation $$i ∂ψ/∂t+c_1 (∂^2 ψ)/(∂y^2 )+c_2 ψ+c_3 |ψ|^2 ψ=0 (1)$$ with complex, in the general case, parameters. Equation (1) describes, in particular, the wave amplitude of a surface plasmon polariton propagating over the contact surface of a metal with a dielectric [1]. It is proved that equation (1) has an infinite number of different stable wave solutions running along the spatial axis with arbitrary velocities, as well as an infinite number of different modes of space-time chaos in full accordance with the universal Feigenbaum-Sharkovsky-Magnitskii bifurcation theory [2-4]. In this case, the bifurcation parameter is the value of the speed of propagation of traveling waves along the spatial axis, which is clearly not included in the original equation. 1. Burov D.A., Evstigneev N. M., Magnitskii N. A. On the chaotic dynamics in two coupled partial differential equations for evolution of surface plasmon polaritons. Comm. Nonlin. Sci. Numer. Simul., ELSEVIER, 2017,v.46, p. 26-36. 2. Magnitskii N.A. Universality of Transition to Chaos in All Kinds of Nonlinear Differential Equations. Chapter in monograph Nonlinearity, Bifurcation and Chaos - Theory and Applications, Chapter 6, INTECH, 2012, p. 133-174. 3. Magnitskii N.A. Bifurcation Theory of Dynamical Chaos. Chapter in monograph Chaos Theory, Chapter 11, INTECH, 2018, p.197-215. 4. Magnitskii N.A. Traveling Waves and Space-Time Chaos in the Kuramoto–Sivashinsky Equation. Differential Equations, 2018, Vol. 54, No. 9, pp. 1266–1270.

#### Gravitation in the theory of compressible oscillating ether

Nikolai Magnitskii1

1Federal Research Center "Computer Science and Control", Laboratory of Chaotic Dynamics, Russian Federation

###### Abstract

Previously, the basic laws and equations of electrodynamics, atomic physics, and elementary particles theory were derived from the theory and equations of compressible oscillating ether [1-3]. In this work, the ethereal theory of gravitation is constructed, the similarities and differences between gravitational and electrostatic fields are explained. It is shown that in gravitation there are no attractive forces, but there are pressing forces, and that the gravitational constant is not really constant, but weakly depends on the chemical composition of interacting bodies. Gravitational interactions between bodies do not propagate from one body to another at a certain speed, and at any moment, the stationary gravitational fields of any bodies exist with and around the bodies, and therefore neither gravitational waves nor gravitons exist in nature. The values of all parameters of the ether, including the density of its unperturbed state, are found. 1. Magnitskii N.A. Theory of compressible oscillating ether. Results in Physics, 12 (2019), p.1436–1445. 2. Magnitskii N.A. Fundamentals of the theory of compressible oscillating ether. IOP Conf. Series: Journal of Physics: Conf. Series 1141 (2018) 012052. 3. Magnitskii N.A. Structure and properties of atomic nuclei in the theory of compressible oscillating ether. IOP Conf. Series: Journal of Physics: Conf. Series 1391 (2019) 012084.

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

Antonio Sornoza1 , Jonathan Yepez2 , Mayken Espinoza-Andaluz3 , Martin Andersson4

1Escuela Superior Politecnica del Litoral, ESPOL, , Ecuador
2Escuela Superior Politecnica del Litoral, ESPOL, , Ecuador
3Escuela Superior Politecnica del Litoral, ESPOL, Facultad de Ingenieria Mecanica y Ciencias de la Produccion, FIMP. Centro de Energias Renovables y Alternativas, CERA, Ecuador
4Lund University, Department of Energy Sciences, Sweden

###### 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.

#### Remastering the imperfect home-made CT projections data for further reconstruction

1al-Farabi Kazakh National University, Physics and Technology, Kazakhstan
2al-Farabi Kazakh National University, Physics and Technology, Kazakhstan

###### Abstract

We have investigated the extent of applicability of the software tools to treat the faulty, shifted, off-axis sequence of images for the home-made computed tomography. Homography and other related image transformation tools from the open-source and non-free OpenCV libraries have been tested. The developed set of methods could be used as a standalone library for the other CT software packages.

###### Acknowledgements:

This research was originally commissioned and funded by the ADANI Company, producing and manufacturing medical, security, spectroscopy and inspection X-ray systems in Minsk, Republic of Belarus. Experimental data were taken at and original data processing software was developed for the ADANI Company. Publication efforts and further development of the method and software package, were supported from the "Fundamental and applied research in related felds of physics of terrestrial, near-earth and atmospheric processes and their practical application" project #BR05236494, administered by the Ministry of Science and Education, at Kazakh National University, Almaty, Republic of Kazakhstan.

#### Disconnected stationary solutions for 2D Kolmogorov flow problem in periodic domain

Nikolay Evstigneev1

1Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, 81 Dynamics of Macrosystems, Russian Federation

###### Abstract

The classical A.N. Kolmogorov's flow problem for the stationary 2D Navier-Stokes equations on a stretched torus for velocity vector function $\mathbf{u}:\mathbb{T}(\alpha)^2 \to \mathbb{R}^2$ and pressure scalar function $p:\mathbb{T}(\alpha)^2 \to \mathbb{R}$ is considered as: $$(\mathbf{u}, \nabla) \mathbf{u} + \nabla p - \frac{1}{R}\bigtriangleup \mathbf{u} - (\sin(\beta y);0)^\mathrm{T} = 0,$$ $$\nabla \cdot \mathbf{u} = 0,$$ where $R$ is the Reynolds number (bifurcation parameter), $\alpha$ is the stretch factor for the domain $\mathbb{T}(\alpha)^2:=[0;2\pi/\alpha] \times [0;2\pi]$ and $\bigtriangleup$ is the Laplace operator. The force vector field depends only on the second spatial variable $y$ and coefficient $\beta$ is an integer. We designate that $\mathbf{u} = (u,v)^\mathrm{T}$, the problem has a trivial solution $u=\frac{R}{\beta^2} \sin(\beta y), v = 0$. An equivalent infinite dimensional system of equations can be obtained in the Fourier space using Galerkin method as: $$\sum_{\{l,m\} \in \mathbb{Z}^2 }\left[ \mathrm{i} \alpha (j-l)\left(1 - \frac{\alpha^2 l^2 + \alpha l m}{\alpha^2 l^2 + m^2} \right) \hat{u}_{l,m}\hat{u}_{j-l,k-m} + \mathrm{i} (k-m)\left(1 - \frac{\alpha l m + m^2}{\alpha^2 l^2 + m^2} \right) \hat{v}_{l,m}\hat{u}_{j-l,k-m} \right] +$$ $$+ \frac{1}{R} (\alpha^2 j^2 + k^2) \hat{u}_{j,k} - \frac{\beta}{2}\delta_{\beta}^{|k|} = 0,$$ $$\sum_{\{l,m\} \in \mathbb{Z}^2 }\left[ \mathrm{i} \alpha (j-l)\left(1 - \frac{\alpha^2 l^2 + \alpha l m}{\alpha^2 l^2 + m^2} \right) \hat{u}_{l,m}\hat{v}_{j-l,k-m} + \mathrm{i} (k-m)\left(1 - \frac{\alpha l m + m^2}{\alpha^2 l^2 + m^2} \right) \hat{v}_{l,m}\hat{v}_{j-l,k-m} \right] +$$ $$+ \frac{1}{R} (\alpha^2 j^2 + k^2) \hat{v}_{j,k} = 0, \forall {j,k} \in \mathbb{Z}^2,$$ where the pressure is eliminated from the system by the projection operator $\mathbb{P}:=(id - \nabla \bigtriangleup^{-1} \nabla \cdot)$ applied to the nonlinear term and the system is obtained by the following ansatz: $f(\mathbf{x}) = \sum_{ \{j,k\} \in \mathbb{Z}^2} \hat{f}_{j,k} e^{\mathrm{i}(\alpha j+k)}$, $\hat{f}_{0,0} = 0$ and $\hat{f}_{j,-k} = \left( \hat{f}_{j,k} \right)^*$, $\hat{f}_{-j,0} = \left(\hat{f}_{j,0} \right)^*$ due to reality condition. \par Many papers are dedicated to the problem at hand. First, early results of Meshalkin and Senai demonstrated that the system is asymptotically stable for any $\alpha&gt;1$. Further researches were conducted by many authors that shown complex system behaviour, infinite number of pitchfork bifurcations as $\alpha \to 0$, existence of recurrent flows for high Reynolds numbers, complex nonlinear dynamics involving cascades of limited cycles and invariant tori of period three as well as chaotic behaviour was found. \par This paper is focusing on the numerical investigation of the finite dimensional Fourier-Galerkin system (using $(512/\alpha) \times (512)$ Fourier harmonics), construction of the solution curves in the parameter-phase space and analysis of disconnected solutions. The system of equations is transformed to the problem $F(\hat{\mathbf{u}}, R) = \mathbf{0}$ for the fixed values of $\alpha$ and $\beta = 2$, where $\hat{\mathbf{u}} = (\hat{u}, \hat{v})^{\mathrm{T}}$ and $R \in [1;20]$. The nontrivial solution curve $\hat{\mathbf{u}}(R)$ that bifurcated from the trivial solution $\hat{\mathbf{u}}_0(R)$ at point $R_0$ is called connected solution curve and $\hat{\mathbf{u}}(R_0) = \hat{\mathbf{u}}_0(R_0)$ at the bifurcation curve. All other curves that bifurcated from the connected curve are also called connected solution curves. Note, that the stability of these solutions is irrelevant meaning that connected curves are applicable to both subcritical and supercritical bifurcations. The disconnected solution curve $\hat{\mathbf{u}}_d(R)$ is such a solution curve that $\hat{\mathbf{u}}_d,R \neq \hat{\mathbf{u}},R$ for any admissible value of $R$, where $\hat{\mathbf{u}}$ is a connected curve. The paper presents bifurcation diagrams for $\alpha = \{1,2,3,4\}$ and shows the location of such disconnected curves. These curves can be responsible for the multistability in chaotic regimes.

###### Acknowledgements:

This work was supported by the Russian Foundation for Basic Research, grants: 18-29-10008mk and 20-07-00066.

#### Bifurcation diagram of stationary solutions of the 2D Kuramoto-Sivashinsky equation in periodic domains

Nikolay Evstigneev1 , Oleg Ryabkov2

1Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, 81 Dynamics of Macrosystems, Russian Federation
2Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, 81 Dynamics of Macrosystems, Russian Federation

###### Abstract

Stationary 2D Kuramoto-Sivashinsky equation for scalar function $u:\mathbb{T}(L)^2 \to \mathbb{R}$ is considered: $$\lambda \left( 2 uu_x + 2 uu_y + \bigtriangleup u \right) + 4 \bigtriangleup^2 u=0,$$ $$u \in \mathbb{T}(L)^2: \mathbf{x} \in [0, L\pi] \times [0, \pi],$$ where $L$ is the integer stretch factor, $\lambda$ is the bifurcation parameter, $()_{j}$ is the derivative in the $j$-direction and $\bigtriangleup$ is the Laplace operator. The constants used in the equations are widely used in other papers and the zero mean is assumed. This equation is physically relevant in terms of model equations for turbulence as well as chaotic dynamical systems. These equations can also describe the behaviour of the thin film hydrodynamics. The equation in question was analyzed by many authors, including very detail numerical analysis of time dependent solutions by A. Kalogirou, E. E. Keaveny and D. T. Papageorgiou as well as analytical analysis of stationary solutions by Cao, Titi; Foias, Titi; Nicolaenko; Ambrose, Azzucato; Temam. A closely related paper by Changpin and Zhonghua discusses the bifurcation of the nontrivial solution from the stationary one at particular points. This paper is dealing with analytical as well as numerical analysis of bifurcations of stationary including the search for dislocated solution curves. For periodic domain the equation is transfered to the Fourier domain with the ansatz $u(\mathbf{x}) = \sum_{ \{j,k\} \in \mathbb{Z}^2} \hat{u}_{j,k} e^{\mathrm{i}(j/L+k)}$, $\hat{u}_{0,0} = 0$ and $\hat{u}_{j,-k} = \left( \hat{u}_{j,k} \right)^*$, $\hat{u}_{-j,0} = \left(\hat{u}_{j,0} \right)^*$ due to reality condition that results in the following discrete infinite dimensional operator: $$F(\hat{u}, \lambda):=\lambda \left[ 2 \sum_{\{l,m\} \in \mathbb{Z}^2 } \left( \frac{\mathrm{i}l}{L} \hat{u}_{l,m} \hat{u}_{l-j,m-k} + \mathrm{i} m \hat{u}_{l,m} \hat{u}_{l-j,m-k} \right) - \left( \frac{1}{L^2} j^2 + k^2 \right) \hat{u}_{j,k} \right] +$$ $$+ 4 \left( \frac{1}{L^4} j^4 + \frac{2}{L^2} j^2 k^2 + k^4 \right)\hat{u}_{j,k} = 0, \forall \{j,k\} \in \mathbb{Z}^2,$$ with $\hat{u0} = \hat{u}_{j,k} = 0$ as a trivial solution.\\ One can immediately observe, that the linear operator $F_u(\hat{u0})$ has eigenvalues $\lambda_{j,k} = \lambda(j^2/L^2 + k^2) - 4(j^4/L^4+2j^2/L^2k^2+k^2)$. Hence the possible bifurcation points of the trivial solution are those points, where $\lambda_{j,k} = 0$. This paper reveals the complexity of the bifurcation structure and analyzes the points of possible bifurcations and linear operator kernel dimensions, which is high. Next, the problem is reduced to finite dimensional grid of $2048 \times 2048$ Fourier harmonics that is solved numerically using deflated pseudo-arclength continuation method. The paper describes heuristics that are used to pass high order degenerate points, where $\text{dim}(\text{ker}(F_u))&gt;1$. The analysis is done for $\lambda \in [0; 30]$, where high order bifurcations as well as dislocated curves of solutions are found.

###### Acknowledgements:

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

#### Optimal control and stability analysis of nonlinear control-affine systems

Armen Bagdasaryan1

1American University of the Middle East, Department of Mathematics, Kuwait

###### Abstract

In this talk we will discuss the problems of optimal control and stabilization for nonlinear control-affine systems of the form $$\dot{x} = A(x)+B(x)u$$ where $$x=x(t), \; x\in\mathbb{R}^n, \; u\in \mathbb{R}^1, \; |u|\leq 1$$ and the vector functions $A(x), B(x)$ are assumed to be smooth in the domain $D\subset \mathbb{R}^n$, $0\in D$, $A(0)=0$. We assume that the system is small-time locally controllable (STLC) at $x = 0$, that is, if $x = 0$ is locally continuously reachable in small time with small control. We give an in-depth analysis of optimal control techniques for the above systems and then consider the problem of synthesis of continuous control $u=u(x)$, $u(0)=0$, that stabilizes the system at the equilibrium point $(x,u)=(0,0)$. The solution to the problem is based on the transformation of the system to the canonical form, and on the usage of nonlinear stabilization.

#### Visual reasoning and the perception of forms

Sara Vesely1 , Alessandro Vesely2 , Caterina Alessandra Dolci3 , Sibilla Renata Dolci4

1CNR, ITB, Italy
2TANA, , Italy
3University of Milan, , Italy
4University of Milan, VESPA, , Italy

###### Abstract

Whenever a new device enables our senses to access an uncharted sensible world, our experience needs to be widened to be able to embrace it. Many animals don't recognize themselves in mirrors. Therefore, mirrors found in ancient Egyptian tombs bear witness to a device that involved a widening of human experience. While by then reflectors were commonly believed to hold the spirit of their beholder, they also provided the motivating force for use of geometry as a logical framework, rather than the form of the outer world. Euclid of Alexandria conceived of geometric constructions and their rules as the connecting link between visual world and hypothetical-deductive reasoning. Yet, he didn't have a clue about receivers. In our opinion the problem of linking received information in an image format to a mathematical space cannot be solved once and for all, but rather needs to be posed and understood afresh once in a while. All the more so in an information and telecommunication era, when the techniques of acquisition and rendering of visual information have been extended well beyond the domain of optical instruments, and the language of mathematics has advanced to a different level of proficiency.

#### Performance of two redundant quantum channels for single qubits under indefinite causal order

1Tecnologico de Monterrey, Physics and Mathematics, Mexico
2Tecnologico de Monterrey, Physics and Mathematics, Mexico

###### Abstract

Indefinite causal order has introduced novel procedures to improve the quality of quantum communication. This procedure introduces the superposition of paths on a set of consecutive quantum channels. It has demonstrated enhancement in communication on well characterized quantum channels as depolarizing, dephasing-noise and teleportation ones. This work modelling a generic quantum channel for single qubits in terms of Kraus operators for the channels in the form of Pauli operators. An output quantum state for a single qubit states going through a certain imperfect quantum communication channel can be obtained analytically. Then, the quality of such outputs are analysed using the quantum fidelity measure.

#### Predicting entanglement and coherent times in FMO complex using the HEOM method

Francisco Delgado1 , Alan Anaya-Morales2 , Bruno Gonzalez-Soria3

1Tecnologico de Monterrey, Physics and Mathematics, Mexico
2Tecnologico de Monterrey, Physics and Mathematics, Mexico
3Tecnologico de Monterrey, Physics and Mathematics, Mexico

###### Abstract

Advances in ultrafast-spectorscopy techniques have revealed long time quantum coherences between electronic states in Fenna-Matthews-Olson (FMO) bacteriochlorophylls, molecules responsible of the energy transfer in the photosynthetic process of green sulfur bacteria. Several methods have been explored to model this quantum phenomenon, mainly using quantum open systems theory. Most of these methods studied do not take into account the memory effects of the surrounding, commonly approximated as a phonon bath on thermal equilibrium. This article applies the Hierarchical Equations of Motion method (HEOM), a non Markovian approach, for the modelling of the system evolution to perform predictions about the coherence times scales together with the global or semi-local entanglement measures involved during the quantum excitation process analysed in terms of some relevant parameters in such system. This analysis suggests a possible roadmap to track or to fit genetic modifications improving the photosynthetic performance.

###### Acknowledgements:

Bruno Gonzalez-Soria, Francisco Delgado, Alan Anaya-Morales

#### An invisible DWT watermarking algorithm using noise removal with application to dermoscopic images

Simona Moldovanu1 , Michiș (Damian) Felicia Anișoara2 , Luminita Moraru3

1Dunarea de Jos University, Department of Computer Science and Information Technology Faculty of Automatic Control, Computers, Electrical Engineering and Electronics, Romania
2Dunarea de Jos University of Galati, Faculty of Sciences and Environment, Department of Chemistry, Physics& Environment, Romania
3Dunarea de Jos University, Faculty of Sciences and Environment, Department of Chemistry, Physics& Environment, Romania

###### Abstract

A new approach for the digital watermarking process is proposed to be part of the pre-processing stage of a computer-aided diagnosis system. We propose to embed a denoised image acting as watermark image in the original host image with the final goal of improving the quality of demoscopic images for further image processing operation related to CAD. The proposed algorithm uses Discrete Wavelet Transform (DWT) corroborated with some basic properties of Human Visual System such as Contrast Sensitive Function (CSF) and Noise Visibility Function (NVF) with the goal of correlating the texture properties and noise. This approach hides the watermark (i.e. denoised version of the host image) in high-pass subbands that are focused on image features. The main concern is to evaluate the distortion produced to the host image by watermarking and an objective quality measure function, i.e. Weighted Peak Signal-to-Noise Ratio (WPSNR), is used to evaluate the existing differences between the original and watermarked images. The proposed approach is tested using the available skin lesion images from the digital image archive of the Department of Dermatology of the University Medical Center Groningen. The experiment results show the improved performance of the proposed scheme against a 3 3 median filtering attack in comparison with the a 5 5 median filtering attack.

#### Algorithm for solutions of nonlinear equations of strongly monotone type and applications to convex minimization and variational inequality problems

Mathew Aibinu1

1Durban University of Technology, Institute for Systems science & KZN e-Skills CoLab, South Africa

###### Abstract

Real life problems are governed by equations which are nonlinear in nature. Nonlinear equations occur in modeling problems, such as minimizing costs in industries and minimizing risks in businesses. A technique which does not involve the assumption of existence of a real constant whose calculation is unclear is used to obtain a strong convergence result for nonlinear equations of (p, η)-strongly monotone type, where η > 0, p > 1. As a consequence of the main result, the solutions of convex minimization and variational inequality problems are obtained. This solution has applications in other fields such as engineering, Physics, Biology, Chemistry, Economics and game theory.

#### First-order linear partial differential equations using the GeoGebra and GeoGebra 3D graphical calculator

Jorge Olivares Funes1 , Pablo Martin2 , Elvis Valero3

1University of Antofagasta, Department of Mathematics, Chile
2University of Antofagasta, physics department, Chile

###### Abstract

Consider $$A∂z/∂y+B∂z/∂x=0$$, Where A, B 𝜖 R. We will solve these types of linear partial differential equations using the GeoGebra Graphical Calculator and their solutions will be seen by GeoGebra 3D. The use of GeoGebra in the study of PDE is a subject that is still being studied and developed with great potential.

#### Anisotropy of glancing angle deposited films: results of atomistic simulation

Fedor Grigoriev1 , Sulimov Vladimir2 , Alexander Tikhonravov3

1M.V. Lomonosov MSU, Russian Federation, RCC, Russian Federation
2M.V. Lomonosov Moscow State University, Research Computing Center, Russian Federation
3M.V. Lomonosov Moscow State University, Research Computing Center, Russian Federation

###### Abstract

Glancing angle deposition (GLAD) is one of the technique for the fabrication of the anisotropic thin films with high porosity and low refractive index. In this technique the incoming flux of the deposited atoms is directed almost parallel to the substrate surface. Due to density fluctuation in the deposited atoms flow and shadow effect, it results in formation of the different separate nanostructures - tree-like column, slanted column, chevron-like structures and so on – on the substrate. GLAD films are widely used in the optical coating due to low reflectance and anisotropy properties. The structural and optical properties of GLAD-films essentially depend on their fabrication conditions. Experimental investigation of these dependencies is still challenge for the existing experimental techniques. On the other hand due to the progress in high performance computing, now it is possible to study thin films deposition process using the atomistic simulation. In the present work the anisotropy of the GLAD SiO2 films is investigated using the classical atomistic simulation and anisotropic Bruggeman effective medium theory. The depolarizing factors defining the difference of the refractive index components are calculated based on the geometry parameters of the pores between the slanted columns forming the large-scale GLAD structure. Averaged shape parameters of these ellipsoids are defined using the density gradient tensor. It is revealed that the values of difference of main components of refractive index tensor are equal 0,03 and 0,05 for deposition angles 60 grad and 80 grad, if the free volume fraction is calculated using the dependence of film density on the deposition angle. The obtained values coincide with experimental results for silicon dioxide films. Simulation is carried out using the equipment of the shared research facilities of HPC computing resources at Lomonosov Moscow State University.

###### Acknowledgements:

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

#### The modified bessel functions I_3 / 4 (x) and I_-3/4 (x) in certain fractional differential equations

Jorge Olivares Funes1 , Pablo Martin2 , Elvis Valero3

1University of Antofagasta, Department of Mathematics, Chile
2University of Antofagasta, physics department, Chile

###### Abstract

The fractional derivative of Caputo, has huge and important applications in various areas of science and engineering. In this case, through the definition of the Caputo derivative and the Laplace transform and its inverse, we propose to show the solutions that can be obtained for each specific value of alpha of the following fractional differential equations $$\frac{d^\alpha y}{{dx}^\alpha}= I_3/4(x)$$ , $$\frac{d^\alpha y}{{dx}^\alpha}= I_-3/4(x)$$ , with $$m-1<α\le m$$ , $$m\ \in N$$. Where the non-homogeneous parts I_3 / 4 (x) and I_-3/4 (x) are the modified Bessel functions of the first species.

#### A study on hidden dimensions, winding number & selected topics of Algebraic Topology in String Theory

SANTANU CHATTERJEE1 , Sanjoy Mukherjee2

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

###### Abstract

String theory provides an encouraging way to unify all force fields in our universe into a single framework. Different vibrational patterns of a single string resemble different particles. Bosonic strings require 26 spatial dimensions in order to produce particles in a similar fashion as 10 spatial dimensions are required to produce Fermions states. These extra dimensions (beyond 3 spatial & 1-time dimension) are compactified into very small scale and thus in today’s scale of probing energy it is not possible to detect them experimentally. This idea of extra dimensions, hidden from our perception is tempting & worth in-depth theoretical work. Certain topological features and its application on String theory will also be discussed in this paper. We will try to fathom these small plank scale compactified dimensions & will try to throw some light on the various topological aspects of quantum geometry offered by this remarkable theory.

#### Novel explanation of the Active Galactic Nuclei.The Power Source of Quasars as a result of vacuum polarization by the gravitational singularities on BHs horizon.

Jaykov Foukzon1

1 Israel Institute of Technology , Center for Mathematical Sciences, Technion - Israel Institute of Technology. , Israel

###### Abstract

Novel explanation of the Active Galactic Nuclei.The Power Source of Quasars as a result of vacuum polarization by the gravitational singularities on BHs horizon. J.Foukzon¹, E.Menkova² A.Potapov³ ¹Department of mathematics, Israel Institute of Technology, Haifa, Israel ²All-Russian Research Institute for Optical and Physical Measurements, Moscow,Russia ³Kotel'nikov Institute of Radioengineering and Electronics of the Russian Academy of Sciences, Moscow, Russia In this paper we argue that the current paradigm for AGN and quasars essentially incomplete and rivision is needed. Remind that the current paradigm for AGN and quasars is that their radio emission is explained by synchrotron radiation from relativistic electrons that are Doppler boosted through bulk motion. In this model, the intrinsic brightness temperatures cannot exceed 10¹¹ to 10¹² K. Typical Doppler boosting is expected to be able to raise this temperature by a factor of 10.The observed brightness temperature of the most compact structures in BL Lac, constrained by baselines longer than 5.3Gλ, must indeed exceed 2×10¹³K and can reach as high as ~ 3×10¹⁴K. As well known, these visibilities correspond to the structural scales of 30-40 μas oriented along position angles of 25°-30°.These values are indeed close to the width of the inner jet and the normal to its direction.The observed, T_{b,obs}, and intrinsic, $$T_{b,int}$$, brightness temperatures are related by Eq.1: $$T_{b,obs}=δ(1+z)⁻¹T_{b,int}$$ with δ=7.2.The estimeted by Eq.1 a lower limit of the intrinsic brightness temperature in the core component of our Radio Astron observations of $$T_{b,int}>2.910¹² K$$. It is commonly considered that inverse Compton losses limit the intrinsic brightness temperature for incoherent synchrotron sources, such as AGN, to about 10¹²K [1].In case of a strong flare, the "Compton catastrophe" is calculated to take about one day to drive the brightness temperature below 10¹²K [1]. The estimated lower limit for the intrinsic brightness temperature of the core in the Radio Astron image of $$T_{b,int}>2.910¹²K$$ is therefore more than an order of magnitude larger than the equipartition brightness temperature limit established in [1] and at least several times larger than the limit established by inverse Compton cooling. Remark 1.Note that if the estimate of the maximum brightness temperature given in [1], is closer to actual values, it would imply $$T_{b;int}=5×10¹³K$$. This is difficult to reconcile with current incoherent synchrotron emission models from relativistic electrons, requiring alternative models such as emission from relativistic protons. Remark 2. However the proton, as we know, is 1836 times heavier than an electron and absolutely huge energy is required to accelerated it to sublight speed. We argue that these alternative models such as emission from relativistic protons can be suported by semiclassical gravity effect finds its roots in the singular behavior of quantum fields on curved distributional spacetimes presented by rotating gravitational singularities [2]. [1] J. L. Gómez, A. P. Lobanov, G. Bruni, Y. Y. Kovalev,Probing the innermost regions of AGN jets and their magnetic fields with Radio Astron.I.Imaging BL Lacertae at 21 microarcsecond resolution. Astrophysical journal 817 (2016) 96, DOI:10.3847/0004-637X/817/2/96 arXiv:1512.04690 [astro-ph.HE] [2] J.Foukzon,E.Menkova,A.Potapov, Colombeau Solutions to Einstein Field Equations in General Relativity: Gravitational Singularities, Distributional SAdS BH Spacetime-Induced Vacuum Dominance.110 pp. Published November 14, 2019 ISBN-13 (15) 978-93-89562-22-4 https://doi.org/10.9734/bpi/mono/978-93-89562-22-4

#### Exploring the exact differential equations with GeoGebra software

Jorge Olivares Funes1 , Elvis Valero2

1University of Antofagasta, Department of Mathematics, Chile

###### Abstract

In this paper, we will show the solutions of certain exact differential equations that are obtained through the interactive GeoGebra software. GeoGebra software has been of great motivational support in the processes of teaching and modeling in mathematics in various universities and colleges, especially in the engineering careers of the University of Antofagasta in the courses of differential equations and calculation of several variables.

#### Multi-criteria optimization of wind power plant parameters

Andrei Melekhin1

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

###### Abstract

The use of renewable energy sources to generate electricity is a hot topic. The author has developed a mathematical model of the aerodynamic process of a wind power plant with the solution of a multi-criteria optimization problem. The optimal range of controlled parameters affecting the aerodynamic process with a minimum amount of blown surface and maximum electrical energy production is determined. Regularities of aerodynamic process are established. The convergence of the results of the study in the calculation on the basis of theoretical dependencies and the solution of the mathematical model is determined. To find the optimal controlled parameters of the aerodynamic installation, a complex research method developed by the author is applied, based on multi-criteria optimization of parameters with the introduction of empirically obtained data.The preliminary procedure of IOSO NM 3.8 consists in the formation of an initial plan of the experiment, which can be implemented both in a passive way (using information about various parameters, optimization criteria and constraints obtained earlier) and in an active way, when too much is generated in the initial search area in accordance with a given distribution law. For each vector of variable parameters, the values of optimization criteria and constraints are determined by direct reference to the mathematical model of the object under study. The number of points that make up the initial plan of the experiment depends on the dimension of the problem and the chosen approximation functions. The solution results in a Pareto (optimal) set of solutions.

#### Effects of quantum interference on tunneling magnetoresistance through a single aromatic molecule

1University of Sistan and Baluchestan, physics, Iran (Islamic Republic of)

###### Abstract

The spin-dependent transport properties through a single aromatic molecule sandwiched between two ferromagnetic (FM) electrodes is investigated theoretically. The transmission probability, current–voltage characteristic and tunnel magnetoresistance (TMR) are analyzed by the tight-binding Hamiltonian model and the nonequilibrium Green’s function technique. It is shown that all these characteristics are sensitive to the quantum interference effects originated from the molecule-to-electrode coupling. The spin-dependent transport properties are characterized by several significant factors. One of the important factors in the spin-dependent transport properties of single molecules is the effect of quantum interference that has recently attracted much attention in recent years [1-2]. The effect of quantum interference associated with the molecule-to-electrode interface geometry. In other words, such effects occur when the electronic wavefunctions propagating along the various pathways through ferromagnetic junction. [1] Guimarães M H D, Zomer P J, Vera-Marun I J, van Wees B J 2014 Nano Lett. 14 2952 [2] Stadler R 2009 Phys. Rev. B 80 125401

#### Simulator development of a rotary magneto-caloric refrigerator by stepwise regenerator modeling approach

Julio Tedesco1 , L. Diógenes T. Câmara2

1Polytecnique Institute of UERJ, IPRJ/DEMEC, Brazil
2Polytecnique Institute of UERJ, Department of Mechanical Engineering and Energy, Brazil

###### Abstract

Magnetic refrigeration is a new promising technology based on the magneto-caloric effect of solid materials like gadolinium that offers smaller global environmental impact if compared to conventional refrigeration vapor compression processes which utilizes in general the ozone depletion chlorofluorocarbons refrigerants. The rotary refrigerators presents a new challenge in terms of complexity if compared to reciprocating ones which is compensated by refrigeration capacity, steady process operation, performance etc. The modeling and simulation of magneto-caloric refrigerator processes can provide important data in the development and optimization of the experimental units which are in general the only research step carried out by the researchers. A novel full process simulator of a magneto-caloric refrigerator was implemented to simulate the process performance over different conditions of rotating frequency, pump flow rate, room temperature etc. A stepwise modeling approach of the clockwise regenerator movement was implemented which simplifies the phenomena of heat transfers in the regenerators leading to ordinary differential equations which are solved more easily if compared to the partial differential equations in general applied to such complex process. The magneto-caloric bed material utilized in the rotating clockwise wheel was gadolinium with an anticlockwise closed flow loop of water which percolates the six gadolinium porous beds and also the hot and cold heat exchanger. The simulator was able to represent the transient aspects as well as the steady state conditions of the magneto-caloric refrigerator processes in terms of both low time performance and numerical stability. The inversion in heat transfer profiles along the process can be used as a limit in the calculation of the maximum heat transfer absorption in the refrigerator cold exchanger according to the operating conditions assumed.

#### The open unsymmetrical stadium billiard

Julio Espinoza-Ortiz1 , Roberto E. Lagos-Monaco2

1Federal University of Goias-Catalão, Physics, Brazil

###### Abstract

In open billiards a particle can escape from the cavity through a leak. This type of systems have received special attention because of their applications to a wide variety of physical phenomena ranging from hydrodynamics to quantum chaos and astronomy. Chaotic leaked billiards are characterized by a so called transient behavior, i.e. by the presence of chaotic motion with a finite life time impossible to be studied just through the analysis of its asymptotic behavior. Under this scenario, we consider the quarter stadium billiard and study the influence of its leaking marginal unstable periodic orbits on the survival trajectories. A rigorous statistical analysis of the survival probability is presented. To pursue this objectives, we set up the classical trajectories' solution in such a way that the system only depends on its partial separability and then from it we pass to construct the Birkhoff map. The possibility of more than one leak into a billiard is also considered.

#### Research of the plasma characteristics in the magnetooperated hollow arc cathode

Mikhail Dokukin1

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

###### Abstract

Need of a research of processes for the heavy current discharge with the refractory hollow cathode when pumping through it inert working gas is dictated by the requirements of technologies of welding and melting of the chemically active metals in a vacuum. In the offered work the experimental and theoretical research of the magnetooperated hollow cathode for the purpose of determination of the intra cathodic plasma parameters and the influence of the last on the power characteristics of the external discharge is conducted. Good compliance of the settlement quantities of this plasma with the results of experiments on the model device is obtained. Recommendations for improvement of the operational characteristics of the used arc vacuum technological devices are made.

#### Quantum Implementation for Comparing Sets of Data

yehuda Roth1

###### Abstract

Based on entangled states, quantum computers have the advantage of simultaneously implementing a large number of processes. The coherence of entanglement enables a single operator (logical gate) to be activated simultaneously on all of the states in the superposition Consequently, to implement a quantum computer, a quantum algorithm has to be implemented. In this paper, we propose a different quantum approach that can simultaneously analyze a large amount of data. Although our process allows many processes to work simultaneously, it is not within the conventional frame of quantum computers.

#### On instability of three-dimensional dynamic equilibrium states of self-gravitating Vlasov-Poisson gas

Yuriy Gubarev1 , Shuang Sun2

1Lavrentyev Institute for Hydrodynamics, Laboratory for Fluid and Gas Vortex Motions, Russian Federation
2Novosibirsk National Research State University, Department for Differential Equations, Russian Federation

###### Abstract

The Vlasov-Poisson model of boundless collisionless gas of neutral particles in a self-consistent gravitational field continues to be one of the basic models of modern astrophysics. This is due to simplicity, clarity, and obvious effectiveness of the model in describing large-scale processes in the Universe. Despite the fact that this model has been intensively studied for a long time, from the point of view of the mathematical stability theory, it was possible to establish, by and large, only sufficient conditions for the theoretical stability (at semi-infinite time intervals) of a number of dynamic equilibrium states with respect to both small and finite perturbations, but from incomplete unclosed subclasses. In this work, we consider the spatial motions of the boundless collisionless self-gravitating Vlasov-Poisson gas of neutral particles in a three-dimensional Cartesian coordinate system: $$\frac{\partial f}{\partial t} + v_i\frac{\partial f}{\partial x_i} - \frac{\partial \varphi }{\partial x_i}\frac{\partial f}{\partial v_i} = 0, \frac{\partial ^2\varphi }{\partial x^2_i} = 4\pi \int \limits _{\mathbb{R}^3}f({\bf x}, {\bf v}, t)d{\bf v} \ (1)$$ $$i = 1, 2, 3; f = f({\bf x}, {\bf v}, t) \geq 0; f({\bf x}, {\bf v}, 0) = f_0({\bf x}, {\bf v})$$ Here $f$ denotes the distribution function of neutral particles (for reasons of convenience, their masses are assumed to be the same and equal to unity); $t$ is time; ${\bf x} = (x_1, x_2, x_3)$ and ${\bf v} = (v_1, v_2, v_3)$ denote coordinates and velocities of neutral particles; $\varphi ({\bf x}, t)$ is the potential of a self-consistent gravitational field; $f_0({\bf x}, {\bf v})$ denotes the initial data for the function $f$. We suppose that the distribution function $f$ asymptotically approaches zero as $|{\bf v}| \rightarrow \infty$, and this function along with the potential $\varphi$ are periodic in argument ${\bf x}$ or asymptotically approach zero as $|{\bf x}| \rightarrow \infty$ too. Summation is performed on repeating lower index $i$ throughout the work. It is assumed that the mixed problem (1) has the following exact stationary solutions: $$f = f^0({\bf x}, {\bf v}) \geq 0, \varphi = \varphi ^0({\bf x}) \ (2)$$ $$v_i\frac{\partial f^0}{\partial x_i} = \frac{\partial \varphi ^0}{\partial x_i}\frac{\partial f^0}{\partial v_i}, \frac{\partial ^2\varphi ^0}{\partial x^2_i} = 4\pi \int \limits _{\mathbb{R}^3}f^0({\bf x}, {\bf v})d{\bf v}$$ The aim of this work is to prove the absolute linear instability for the spatial states of dynamic equilibrium (2) of the boundless collisionless self-gravitating Vlasov-Poisson gas with respect to small three-dimensional perturbations $f^\prime ({\bf x}, {\bf v}, t)$ and $\varphi ^\prime ({\bf x}, t)$: $$\frac{\partial f^\prime }{\partial t} + v_i\frac{\partial f^\prime }{\partial x_i} - \frac{\partial \varphi ^\prime }{\partial x_i}\frac{\partial f^0}{\partial v_i} - \frac{\partial \varphi ^0}{\partial x_i}\frac{\partial f^\prime }{\partial v_i} = 0 \ (3)$$ $$\frac{\partial ^2\varphi ^\prime }{\partial x^2_i} = 4\pi \int \limits _{\mathbb{R}^3}f^\prime ({\bf x}, {\bf v}, t)d{\bf v}; f^\prime ({\bf x}, {\bf v}, 0) = f_0^\prime ({\bf x}, {\bf v})$$ where $f_0^\prime ({\bf x}, {\bf v})$ denotes the initial data for the function $f^\prime$. In the work, a transition from kinetic equations (1) which describe the motion of the gas under study to an infinite system of relations similar to the equations of isentropic flow of a compressible fluid medium in the “vortex shallow water” and Boussinesq approximations was carried out. In the course of the instability proof, the well-known sufficient Newcomb-Gardner-Rosenbluth condition for stability of dynamic equilibrium states (2) with respect to one incomplete unclosed subclass of small spatial perturbations was conversed. Also, a linear ordinary differential second-order inequality with constant coefficients was obtained. An a priori exponential lower estimate for the growth of small three-dimensional perturbations (3) follows from this inequality when the sufficient conditions for linear practical instability of the considered dynamic equilibrium states found in this work are satisfied. Since the obtained estimate was deduced without any additional restrictions on the equilibrium states under study, then the absolute linear instability of the spatial states (2) of the dynamic equilibrium of the Vlasov-Poisson gas with respect to small three-dimensional perturbations (3) was thereby proved. The results of the work are fully consistent with the classical Earnshaw instability theorem. This theorem states that any equilibrium configuration of point electric charges is unstable if, besides its own Coulomb forces of attraction and repulsion, no other forces act on them. Now the area of applicability for the Earnshaw theorem is expanded from electrostatics to kinetics, namely, to the boundless collisionless self-gravitating Vlasov-Poisson gas of neutral particles. Constructiveness is inherent in the sufficient conditions for linear practical instability established here, which allows them to be used as a testing and control mechanism for conducting physical experiments and performing numerical calculations.

#### Getting and regularizing a hexagonal irregular grid

Sergei V Ryzhkov1 , Victor Kuzenov2 , Sanya Dobrynina3 , V. Shumaev4 , Andrey Starostin5

1Bauman Moscow State Technical University, Thermal Physics Department, Russian Federation
2Dukhov VNIAA, , Russian Federation
3BMSTU, , Russian Federation
4BMSTU, Thermal Physics Department, Russian Federation
5BMSTU, , Russian Federation

###### Abstract

A method is proposed for the transition from a tetrahedral to a hexagonal irregular computational grid. A variant of the elliptic “regularizer” of the grid is developed, which is based on the “mechanical analogy” and is based on the solution of linear equations of the theory of elasticity. The paper presents the initial results of the reconstruction and “regularization” of the computational grid, as well as the distribution of the “angular” criterion for assessing its quality. The hexagonal “regularized” computational grid is shown, as well as the distribution of the “angular” criterion for assessing its quality for the geometric model of a hypersonic aircraft. From the calculation results it follows that the “regularized” grid fills almost the entire volume of the computational domain, and the criterion for assessing the quality of the hexagonal “regularized” computational grid is more than 0.7. Moreover, to achieve this result, ~20 iterations were required only.

#### Mathematical modelling of flows around the slider body with cavity

Duong Ngoc Hai1 , Nguyen Quang Thai2

1Vietnam Academy of Science and Technology (VAST), Graduate University of Science and Technology, Viet Nam
2Vietnam Academy of Science and Technology (VAST), Institute of Mechanics, Vietnam

###### Abstract

While an object at ambient temperature moving within a fluid, if the relative speed between the object and fluid is large enough, due to evaporation the natural vapour cavities can be appeared on the object’s surface. The mixture flows of such fluids and cavities are called as the natural cavitating flows or cavitating flows. The mathematical modelling for this kind of flows are usually complex because of the transient of laminar to turbulent region in flow near body wall, and moreover the existence of phase transition and vapour cavity with changed shapes. In this case, the mathematical models will contain pairs of models, such as flow pattern model for turbulent transient flows and cavitation model for cavitating flows to achieve the correct calculation results. In this paper, the typical mathematical models of cavitating flow around a slider body in water based on the combining of two possible turbulent flow models (LES – Large Eddy Simulation and RAS – Reynolds Averaged Simulation) and, to a pair, three cavitation models (Kunz, Schnerr-Sauer and Merkle models) are presented. Based on those the numerical simulations for cavitating flow around the two different shape bodies (hemisphere head body and sphere shape bodies) at same flow condition (cavitation number σ = 0.2) are performed by using each above mathematical model. The comparisons of numerical results with published experimental measurement results are performed to evaluate the effect of body shapes (existence of the cylinder body) and the accuracy of numerical results. The paper results might be helpful for investigation of cavitation phenomena

###### Acknowledgements:

This work was supported partly by Grant of the NCVCC42.02/20-20 from the Vietnam Academy of Science and Technology (VAST).

#### Finite Elements and Finite Differences in some differential equations of second linear order with GeoGebra

Jorge Olivares Funes1 , Elvis Valero2

1University of Antofagasta, Department of Mathematics, Chile

###### Abstract

Let's consider the differential equations of the shape $$-\ \frac{d}{\ dx}(p (x)\frac{dy}{dx\ })\ + q(x)y = f(x)$$, $$y(0)=y(a)=0, a>0.$$ Using GeoGebra software and the numerical methods of finite elements and finite differences, We will display the various numerical approximations they get for each value of "a" along with their absolute and relative error in various applets and examples.

#### M. Rostami and V. Zeitlin "Understanding evolution, propagation, and landfall of tropical cyclones with moist-convective rotating shallow-water model"

1Ecole Normale Superieure, Geosciences, France

###### Abstract

We show how some essential features of tropical cyclones (TC), and their evolution and trajectories, can be captured by, and understood with the so-called moist-convective shallow-water model, which incorporates moist convection, crucial in TC dynamics, in a simple albeit self-consistent way. The TC are represented in the model by intense localised vortices with profiles of horizontal velocity and relative vorticity close to the observed ones. The vortex trajectories and their interactions with idealised topography, in a form of zonal and meridional ridges and elliptic islands, and the dynamical role of moist convection in these processes are then analysed with the help of numerical simulations with a state-of-the-art finite-volume scheme.

#### Multiphysic Simulation of molten pool transients for electron beam welding and additive manufacturing processes investigation

Alexey Shcherbakov1 , Daria Gaponova2 , Andrey Sliva3 , Regina Rodyakina4 , Alexey Goncharov5 , Alexander Gudenko6 , Viktor Kostin7 , Viktor Dragunov8

1National Research Untiversity "Moscow Power Engineering Institute" (MPEI), Dept. of Electric Power Supply of Industrial Enterprises and Electrotechnologies, Dept. of Metal Technology, Russian Federation
2National Research Untiversity "Moscow Power Engineering Institute" (MPEI), Dept. of Electric Power Supply of Industrial Enterprises and Electrotechnologies, Dept. of Metal Technology, Russian Federation
3National Research Untiversity "Moscow Power Engineering Institute" (MPEI), Dept. of Metal Technology, Russian Federation
4National Research Untiversity "Moscow Power Engineering Institute" (MPEI), Dept. of Metal Technology, Russian Federation
5National Research Untiversity "Moscow Power Engineering Institute" (MPEI), Dept. of Metal Technology, Russian Federation
6National Research Untiversity "Moscow Power Engineering Institute" (MPEI), Dept. of Metal Technology, Russian Federation
7National Research Untiversity "Moscow Power Engineering Institute" (MPEI), Dept. of Electric Power Supply of Industrial Enterprises and Electrotechnologies, Russian Federation
8National Research Untiversity "Moscow Power Engineering Institute" (MPEI), Dept. of Metal Technology, Russian Federation

###### Abstract

Molten pool free surface shape calculation and its evaluation in time for analysis of electron beam melting and welding processes is a very important problem. This is because experimental methods can provide only a part of the necessary information. Electron beam heating creates the conditions for intense metal transfer, and pool surface shape affects on the energy absorption efficiency. This paper reports the method which combines the Monte-Carlo simulation for spatial and energy parameters of heating source calculating with the Volume of Fluid algorithm for liquid free-surface numerical evaluation. The velocity and pressure field technique calculation in a molten pool with the action of surface tension forces and vapor recoil pressure, is described. It is shown that the proposed simulation method allows to study heat and mass transfer transient processes, including deep penetration channel formation. Model validation was carried out. It is shown that the simulation results are consistent with experimental data obtained using a high-speed camera.

###### Acknowledgements:

This work was carried out at the National Research University «Moscow Power Engineering Institute» with the financial support of the Russian Science Foundation (project code No. 18-19-00652.)

#### Molecular Dynamics Simulations of Polyethylene Bilayers

Nikolaos Romanos1 , GRIGORIOS MEGARIOTIS2 , Doros Theodorou3

1NTUA, Chemical Engineering, Greece
2NATIONAL TECHNICAL UNIVERSITY OF ATHENS, SCHOOL OF CHEMICAL ENGINEERING, Greece
3National Technical University of Athens, School of Chemical Engineering, Greece

###### Abstract

Molecular Dynamics Simulations of PE bilayers Nikolaos Romanos, Grigorios Megariotis,* and Doros N. Theodorou* School of Chemical Engineering, National Technical University of Athens (NTUA), 9 Heroon Polytechniou Street, Zografou Campus, Athens GR-15780, Greece Abstract By conducting Molecular Dynamics (MD) simulations of Polyethylene (PE) polymer melts consisting of two different films, each comprised of chains of different molar mass, in molecular contact with each other, we compare the structural and dynamical properties between these subsystems. Joining layers of the same chemical constitution but different molecular weights is explored as a route towards packaging materials that combine good mechanical and barrier properties with recyclability and therefore provide more sustainable solutions for contemporary industrial needs. Initially, we construct two independent PE thin films characterized by periodic boundary conditions in two directions, but of finite thickness in the third direction. An “amorphous builder” is used for this purpose, which builds the chains bead by bead (united atom), using the TraPPE force field. A slab is made by joining the two films in the nonperiodic direction. The slab is energy minimized and then subjected to NPT molecular dynamics (MD) simulation at 350K and 1 bar will be conducted, over times longer than the longest relaxation times of both films. Both structural and dynamical properties of the films are calculated, including the self-diffusion coefficient for the centers and the interdiffusion coefficient across the interface. To whom any correspondence should be addressed: gregm@mail.ntua.gr, doros@central.ntua.gr

###### Acknowledgements:

This research work was supported by the Hellenic Foundation for Research and Innovation (H.F.R.I.) under the “First Call for H.F.R.I. Research Projects to support Faculty members and Researchers and the procurement of high-cost research equipment grant” (Project Number: 1263). Also, this work was supported by computational time granted from the Greek Research and Technology Network (GRNET) in the National HPC facility –ARIS– under project ID pr008038_thin (MuSiTABOS).

#### Modeling shape and volume transitions in liquid crystal elastomers

Vladislav Egorov1 , Olga Maksimova2 , Masahiko Okumura3 , Shuta Noro4 , Hiroshi Koibuchi5

1Cherepovets State University (CHSU), , Russian Federation
2Cherepovets State University (CHSU), , Russian Federation
3National Institute of Technology (KOSEN), Sendai College, , Japan
4National Institute of Technology (KOSEN), Sendai College, Genaral Engineering, Japan
5National Institute of Technology (KOSEN), Sendai College, General Engineering, Japan

###### Abstract

A liquid crystal elastomer (LCE) is a composite material of liquid crystal and polymers, which exhibit novel properties that are not inherent in liquid crystals and polymers individually. One of the properties specific to this material immersed in a solvent is the volume and shape transitions [K. Urayama, Macromolecules 40.7 (2007): 2277-2288]. These transitions were studied in [A. Matsuyama and T. Kato, The Journal of chemical physics 116.18 (2002) pp.8175-8182]) and predicted to have a discontinuous change in the shape anisotropy with varying temperature. In this study, we apply Finsler geometry (FG) model of LCE to study these two different transitions. Up to now, the FG model is successful to describe of the shape deformation of LCE under electric field [E. Proutorov, N. Matsuyama and H. Koibuchi, Journal of Physics: Condensed Matter 30.40 (2018) 405101]. Here, we further extend the model by including an Ising-like variable to incorporate swollen and non-swollen states of LCE in addition to the variable corresponding to the directional degrees of freedom of liquid crystals. Tentative results of Monte Carlo simulation are consistent with the experimentally observed fact that the volume transition is discontinuous and the shape transition is smooth. Moreover, numerically obtained maximal value of shape anisotropy is close to experimentally observed one.

#### Langevin simulations of protoplasmic streaming in non-Euclidean geometry

Shuta Noro1 , Masahiko Okumura2 , Satoshi Hongo3 , Shinichiro Nagahiro4 , Hisatoshi Ikai5 , Madoka Nakayama6 , Hiroshi Koibuchi7

1National Institute of Technology (KOSEN), Sendai College, Genaral Engineering, Japan
2National Institute of Technology (KOSEN), Sendai College, , Japan
3National Institute of Technology (KOSEN), Sendai College,, , Japan
4National Institute of Technology (KOSEN), Sendai College, , Japan
5National Institute of Technology (KOSEN), Sendai College, , Japan
6National Institute of Technology (KOSEN), Sendai College, , Japan
7National Institute of Technology (KOSEN), Sendai College, General Engineering, Japan

###### Abstract

The role of protoplasmic streaming in plant cell is a transportation of biological materials, and the streaming is driven by the myosin molecule, which is called the molecular motor. This circular flow, activated by the molecular motor, was experimentally observed via laser Doppler velocimetry, and it was reported that there are two distinct peaks in the velocity distribution [R. Mustacich and B. Ware, Phys. Rev. Lett. 33, 617-620 (1974)]. Recently, these peaks are numerically reproduced by stochastic Navier-Stokes (NS) simulation technique, however, interaction of fluids and biological materials is neglected [arXiv:2006.12067]. Here in this report, we show that this complex interaction can be implemented in the NS equation via Finsler geometry (FG) modeling technique by including an internal directional degrees of freedom σ (∈S^1:circle) corresponding to the small biological materials. We show that the interaction effectively makes the viscosity coefficient small (large) when the variable σ is randomly (uniformly) aligned. This implies that the complex interaction between fluids and biological materials is effectively implemented by FG modeling technique.

###### Acknowledgements:

This work is supported in part by the Collaborative Research Project of the National Institute of Technology (KOSEN), Sendai College.

#### Finsler geometry modeling of complex fluids: reduction in viscous resistance

Masahiko Okumura1 , Ippei Homma2 , Shuta Noro3 , Hiroshi Koibuchi4

1National Institute of Technology (KOSEN), Sendai College, , Japan
2National Institute of Technology (KOSEN), Sendai College, General Engineering, Japan
3National Institute of Technology (KOSEN), Sendai College, Genaral Engineering, Japan
4National Institute of Technology (KOSEN), Sendai College, General Engineering, Japan

###### Abstract

Complex fluids refer to a broad range of materials that have two different phases such as solid-liquid, fluid-gas, etc. Non-Newtonian fluid, in which viscosity resistance is not always proportional to velocity, is a complex fluid with macromolecules such as liquid crystals. Interestingly, the viscosity resistance varies depending on whether macromolecules are included or not. This change in the macroscopic property is expected to come from an interaction between fluids and macromolecules. In this study, we apply Finsler geometry (FG) modelling technique to implement this complex interaction and to clarify the mechanism behind the reduction of viscosity resistance. In the FG modelling, new dynamical variable corresponding to the directional degrees of freedom of macromolecules is introduced in the case of Couette flow. This variable is numerically updated by Monte Carlo simulation technique during the iterations of stochastic Navier-Stokes equation. Tentative results indicate that the distribution of viscosity force and its position dependence are considerably different from those in standard Newtonian fluids.

###### Acknowledgements:

This work is supported in part by the Collaborative Research Project of the National Institute of Technology (KOSEN), Sendai College.

#### Finsler geometry modeling of anisotropic diffusion in Turing patterns

Hiroshi Koibuchi1 , Masahiko Okumura2 , Shuta Noro3

1National Institute of Technology (KOSEN), Sendai College, General Engineering, Japan
2National Institute of Technology (KOSEN), Sendai College, , Japan
3National Institute of Technology (KOSEN), Sendai College, Genaral Engineering, Japan

###### Abstract

Turing patterns, such as those observed in zebra, are well known to be described by differential equations called diffusion-reaction (DR) equations. These equations are composed of diffusion and reaction terms, in which the diffusion term is defined by Laplace operator. Laplace operator is always used to describe nearest neighbor interactions, which are generally isotropic because of the isotropic differentials in the symmetric Euclidean space. For this reason, to describe anisotropies in the zebra patterns, the diffusion constants are assumed to be direction dependent in the reaction-diffusion equations. However, the origin of those direction dependent constants is unclear. In this presentation, we study this problem by Finsler geometry modeling technique [Physica A393, pp.37-50 (2014)]. In the FG modeling, differential operators naturally become direction dependent because of the direction dependent distance. To define such anisotropy, we introduce internal degrees of freedom, which are treated dynamically in the model, which is a hybrid version of a statistical mechanical model and the DR equation model. The statistical mechanical model is defined by Hamiltonian corresponding to the DR equations. Hybrid simulation technique is also introduced, and the simulation data show that the FG modeling is effective to study Turing patterns because direction-dependent diffusion constants are not necessary and automatically generated.

#### Time Dependent Stabilization of a Hamiltonian System

Asher Yahalom1 , Natalia Puzanov2

1Ariel University, Electrical & Electronic Engineering, Israel
2Ariel University, Department of Physics, Israel

###### Abstract

In this paper we consider the unstable chaotic attractor of a Hamiltonian system with Toda lattice potential and stabilize it by an integral form control. In order to obtain stability results, we use a control function in an integral form: u(t) = 􏰇0t k(t, s)X(s)ds, in which all the back story of the process X(t) is taken into consideration. Using the exponential kernel k(t, s) = e−β(t−s), we replace the study of integro-differential system of order 4 with an analysis of 5th order system of ordinary differential equations (without integrals). Numerical solution of the resulting system leads to the asymptotically stabilization of the unstable fixed point.

#### Equilibrium configurations of a whisker touching a wall

Geoff Goss1

1London South Bank University, Engineering, United Kingdom

###### Abstract

A whisker serves to mechanically transmit the forces exerted at the point(s) of contact with an external object to fixed base where they can be measured. We model the whisker as a thin elastic rod which is intrinsically curved. We assume that the rod is isotropic and homogeneous. We study 2D equilibrium configurations of the whisker when it touches a plane wall. Two parameters characterize the set of solutions: the distance from the whisker base point to the wall and the angle between the wall direction and the tangent to whisker at the base point. The contact to the wall is assumed frictionless. There exist three types of contacts: the whisker may touch the wall either at a point along its shaft or at its tip or at both points simultaneously. We formulate a boundary value problem which includes the system of ODEs governing the whisker equilibria and the boundary conditions. The latter may have three different forms depending on the particular contact type. The equations are integrable so that their general solution can be expressed in terms of Jacobi elliptic functions. In all three cases, we solve the BVP by integrating the ODEs numerically or by using analytical solutions. We compute a series of bifurcation diagrams representing dependence of the whisker configurations, the type of contact, and the force and moment at the base, on the geometric parameters of the problem. The results may be helpful for design of artificial whisker sensors and for studies of the functioning of mammalian vibrissae.

#### On morphological skeletonization of natural whiskers.

Eugene Starostin1

1London South Bank University, School of Engineering, United Kingdom

###### Abstract

We first discuss the medial axis transform of a slender 2D object introduced by H.Blum. We show that neither the medial axis nor the associated symmetric chord axis is well suited to the purpose of a mechanical model construction. We present an alternative complete shape descriptor that involves reduction to the centreline equipped with a thickness function of the orthogonal cross-section. We apply the proposed method to animal whiskers that are generically curved and tapered. The contours of the whisker shape are extracted from 2D greyscale scans. The centreline is approximated as a curve with linear curvature (the Euler spiral) and the thickness function that models the taper is chosen linear. The coefficients of those linear functions are computed by fitting the model edges to the whisker contour points. We conclude with a discussion of various generalisations of the model.

#### Alog periodic approach in analyzing local critical behavior for Covid -19 spread in Albania

Elmira Kushta1 , Dode Prenga2

1University of Vlora “I.Qemali”, Faculty of Technical Science, Mathamatics, Albania
2University of Tirana, Faculty of Natural Sciences, Physics, Condensed Matter Group, Albania

###### Abstract

Log-periodic functions of general type =y_0+A(t-t_c )^m (1+Bcos⁡(ω*log⁡(t-t_c )+φ_1 ) ) and its alternative forms have been demonstrated as successful in the analysis of systems with discrete scale of invariance (DSI) structure. The majority of its application belongs to the financial index dynamics, energy release in earthquake or avalanches and similar processes. In a more general view the DSI structure would be temporarily present whenever self-organization behavior would occur, so the log-periodic function can ascribe the time dynamics sufficiently well for broader system group. Particularly, if for a given system the self-organization behavior is under way and some opposing or imitating activities are imposed in system, multilevel DSI structure could been developed and the response would depart from the log-periodic shape. If such effects would have been not sufficiently strong as to affect the critical time occurrence, their net outcome could produce changes that anticipate or postpone the old process values. Based on those arguments we proposed to use a new LPP function of the form y=y_0+A(t-t_c )^m+〖B(t-t_c )〗^m cos⁡(ω*log⁡(t-t_c )+φ_1)+Ccos(⁡(ω-ω_1 )log⁡(t-t_c )+φ_2)+D(t-t_c )^m cos⁡((ω+ω_1)log⁡(t-t_c )+φ_3). In the case of the historical exchange rates of national Albanian currency versus Euro or USD, the continuous Central Bank intervention is supposed to opposes the dangerous price move and therefore a multiple DSI structure is generated in the system. Or the daily new positive tests records of the COVID-19 infection spread in the country which initially embodied the findings of the state laboratories, by the time would be affected from the pressure for more tests exerted by the anxious individuals, resulting henceforth in a herding-like behavior. The reactive behavior aiming to oppose undesired occurrence is supposed to generate additional LPP sub-processes that has been trapped by the herein proposed LPP function. In particular, the LPP fit to the Covid-19 new cases data series, has challenged the ODE models for this process, their estimates and their statistical predictions. So, in this case, the LPP has predicated the multiphase waving behavior giving two peak dynamics, each of them predicted weeks before its recurrence, series respectively at 28 April and 10-12 June that have been confirmed later at the time of real occurrence within 2 days uncertainty. As the conditions changes, the self-organization process could be transformed significantly making other critical time to appear. In this sense the critical time would assign a local specific behavior. If we acknowledge the critical time as the moment when the number of new cases occurred and the new case diagnosed would become significantly monotony correlated, whereas theoretically it represent the moment where the regime change is most likely to occur. An extended time approach produce a global peak located near the middle of July etc. We believe that this approach could be effective in the prediction of the local critical behavior for a wide-ranging type of the process.

#### Magnetic winding – a key to unlocking topological complexity in flux emergence

David MacTaggart1

1University of Glasgow, School of Mathematics and Statistics, United Kingdom

###### Abstract

The solar atmosphere is composed of highly complex magnetic field structures. It has long been appreciated that the topological complexity of these magnetic fields is fundamental to the dynamics of the solar atmosphere, e.g. the formation and initiation of eruptions. Magnetic helicity, an invariant of ideal magnetohydrodynamics that combines information on magnetic flux with the underlying field line topology, is the main quantity that is currently used to study topological complexity in the solar atmosphere. Remarkably, the input of this topological quantity can be estimated in the solar atmosphere. However, since helicity is biased by a magnetic flux weighting, the interpretation of magnetic helicity in observations is complicated. In this talk, we introduce a measure of topological complexity, the magnetic winding, which is based purely on the field topology and is not biased by the magnetic flux. We show that, in conjunction with the helicity, the magnetic winding can reveal much more information about the underlying topology of a magnetic field. In particular, it can identify localized regions of complex field line topology clearly which the helicity cannot. We present examples related to solar flux emergence and discuss the potential of magnetic winding in the forecasting of solar eruptions.

###### Acknowledgements:

This work is in collaboration with Chris Prior (University of Durham).

#### Influence of M-cells on the generation of re-entry in Short QT Syndrome

Ponnuraj Kirthi Priya1 , Srinivasan Jayaraman2

1Tata Consultancy Services, , India
2Tata Consultancy Services, , United States

###### Abstract

The distribution of M-cells have always been vital in creating intrinsic spatial heterogeneity thereby acting as a substrate for the development and maintenance of re-entry. Here, a 2D anisotropic transmural tissue made up of endocardial (endo), midmyocardial (mid) and epicardial (epi) layers was constructed by using the ventricular cell model developed by Ten Tusscher et al. Two configurations, the entire column of mid layer and an island within the mid layer of the tissue were considered as M cells. In the latter configuration, slight alterations were introduced in the slow delayed rectifying potassium current and the outward transient current so that the APD is highest in the M-cells followed by the endo, mid and epi cells. The likelihood of reentry generation under conditions of KCNQ1-linked Short QT syndrome type 2 (SQTS2) was then analysed in these two types of tissue configurations. Simulation results show that on including SQTS2 conditions and on pacing the tissue with premature beats in between normal beats, re-entrant waves were generated in the tissue containing a column of M- cells whereas in the tissue including the M-cell island, re-entry was not generated. This study is not in line with those reported earlier due to the variations in the size of the chosen M-cell island as well as the cellular electrophysiological properties. From this investigation, the need for further analysis on the size, location as well as the ionic properties of the M-cells in relation to the neighboring cells has been emphasized.

#### Optimal robot control

Abbes LOUNIS1

1University of Tizi Ouzou (UMMTO), Department of Mathematics, Algeria

###### Abstract

This paper presents a problem of optimal control of a robot, the problem is to determine a command that allows to reach the final state from the initial state in record time.This problem will be solved by applying The Pontryagin’s Maximum Principle (PMP) combined with Picard’s successive approximation method and shooting method.

.

#### Twist effects on quantum vortex defects

Matteo Foresti1

1University of Milano Bicocca, Mathematics, Italy

###### Abstract

We demonstrate that on a quantum vortex in Bose-Einstein condensates can form a new, central phase singularity. We define the twist phase for isophase surfaces and show that if the injection of a twist phase is global this phenomenon is given by an analog of the Aharonov- Bohm effect. We show analytically that the injection of a twist phase makes the filament unstable, that is the GP equation is modified by a new term that makes the Hamiltonian non-Hermitian. Using Kleinert’s theory for multi-valued fields we show that this instability is compensated by the creation of the second vortex, possibly linked with the first one.

#### A Block preconditioner for the Gl-LSMR algorithm$\\$ $^1$Afsaneh Hasanpour and $^1$Maryam Mojarrab$\\$ $^1$Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

Maryam Mojarrab1

1University of Sistan and Baluchestan, Department of mathematics, Iran (Islamic Republic of)

###### Abstract

The global LSMR (Least Squares Minimal Residual) method is an absorbing solver for linear systems with multiple right-hand sides‎. Sometimes, it may convergence slowly such as the other methods‎. ‎To prevent this event, we have proposed‎ ‎a block preconditioner for the global LSMR method which could solve linear systems with a block partitioned coefficient matrix and multiple right-hand sides‎. Numerical examples and comparing the preconditioned Gl-LSMR method with the Gl-LSMR method validate the effectiveness of the preconditioner‎. Numerical results confirm that the BPGLSMR (Block Preconditioned Gl-LSMR) method has a better performance in reducing the number of iterations and CPU time rather than Gl-LSMR‎.

#### Numerical Modelling of the Draft Rate in a Mechanically Ventilated Climatic Chamber

Radostina Angelova1 , Sergey Mijorski2 , Detelin Markov3 , Peter Stankov4 , Rositsa Velichkova5 , Iskra Simova6

1Technical University of Sofia, Centre for Research and Design in Human Comfort, Energy and Environment (CERDECEN), Bulgaria
2SoftSim Consult Ltd, Sofia, Bulgaria
3Technical University of Sofia, Centre for Research and Design in Human Comfort, Energy and Environment (CERDECEN), Bulgaria
4Technical University of Sofia, Centre for Research and Design in Human Comfort, Energy and Environment (CERDECEN), Bulgaria
5Technical University of Sofia, Centre for Research and Design in Human Comfort, Energy and Environment (CERDECEN), Bulgaria
6Technical University of Sofia, Centre for Research and Design in Human Comfort, Energy and Environment (CERDECEN), Bulgaria

###### Abstract

The thermal environment in an indoor space is determined by the thermal state of the human body, and the local thermal discomfort. The draught rate (DR) is one of the indices for thermal discomfort. The achievement of air distribution without draught is one of the goals of the ventilation methods. It is especially important in the design of climatic chambers, where the volume is small, and the research studies may require prolonged occupant’s exposure. Our study shows results from CFD simulation of a mechanically ventilated climatic chamber, performed in the design stage of the chamber. Velocity profiles distribution, temperature distribution and DR are used to assess the thermal comfort of the person in the chamber. The results obtained allowed designing of proper indoor environment with desired characteristics for air distribution and human exposure.

###### Acknowledgements:

The paper is supported by the project № DN17 /12/12.12.2017, funded by Bulgarian Science Fund with the Ministry of Education and Science.

#### Quantum-chemical and docking analysis on the binding potential of phenolic acids from Graptopetalum paraguayense E. Walther to HSV thymidine kinase active site

Miroslav Rangelov1 , Nadezhda Todorova2 , Petia Genova-Kalou3 , Nina Stoyanova4 , Nadezhda Markova5

1Bulgarian Academy of Sciences, Institute of Organic Chemistry with Centre of Phytochemistry, Bulgaria
2Bulgarian Academy of Sciences, Institute of Biodiversity and Ecosystem Research, Bulgaria
3National Centre of Infectious and Parasitic Diseases, National Reference Laboratory “Rickettsia and tissue cultures”, Bulgaria
4Bulgarian Academy of Sciences, Institute of General and Inorganic Chemistry, Bulgaria
5Bulgarian Academy of Sciences, Institute of Organic Chemistry with Centre of Phytochemistry, Bulgaria

###### Abstract

Herpes simplex virus types 1 and 2 (HSV-1 and HSV-2) are members of the Herpesviridae family and are among the most common human pathogens, infecting about 90% of the world population. HSV thymidine kinase (TK) catalyzes the transfer of the gamma-phosphate group of ATP to thymidine to generate dTMP in the salvage pathway of pyrimidine synthesis. The dTMP serves as a substrate for DNA polymerase during viral DNA replication. TK allows the virus to be reactivated and to grow in non-proliferative cells lacking a high concentration of phosphorylated nucleic acid precursors. Thus, TKs are the main targets in anti-herpes virus treatments and potential therapeutic targets in antitumor gene therapy strategies. Recently we found that the total methanol extract from the succulent plant Graptopetalum paraguayense E. Walther (GP) demonstrates/has a significant inhibitory effect on HSV-1 as well as the GP phenolic fraction. Since TK appears to be a key feature in the replication of large DNA viruses such as HSV, we present theoretical investigations on the binding expedient of phenolic acids from this fraction to viral TK amino acids. Twelve different phenolic acids such as gallic acid, trans-ferulic acid, syringic acid, and others were found by GS/MS analyses. MOE 2016 software package was used to dock selected structures in the active site defined in published XRD (X-ray diffraction) structures of the Herpes Simplex Virus 1 thymidine kinase. The structure was protonated according to implemented Protonate3D algorithm and was scored according to implemented GBVI/WSA dG scoring function. The interaction energies of ligands (phenolic acids) in the pockets based on the GBVI/WSA dG scoring function were sorted and four best ligands according to ligand-pocket interactions were selected: trans-ferulic, gallic, syringic and gentisic acids have optimal interactions with the receptor. From the results based on the molecular docking methods, different types of hydrogen-bonded complexes of phenolic acids with amino acids, protonated amines, mineral acids and water molecules were modelled. The data received from our quantum-chemical calculations suggest that all twelve phenolic acids could form stable complexes with amino acids from the TK active site. The complexes formed are stable and trans-ferulic and gallic acids demonstrate great binding affinity to the active site of TK where they can exhibit their inhibitory properties. The calculations were performed at B3LYP/6-31+G(d,p) level of theory using GAUSSIAN 09 software package.

###### Acknowledgements:

This work was supported by the Bulgarian National Science Fund under Grant DN19/16/2017.

#### The influence of isoenergy surface anisotropy and surface scattering kinetics on the conductivity of a thin metal layer

Oleg Savenko1 , Dmitry Romanov2 , Irina Kuznetsova3

1P.G. Demidov Yaroslavl State University, Microelectronics and General Physics, Russian Federation
2P. G. Demidov Yaroslavl State University, Department of microelectronics and general physics, Russian Federation
3P.G. Demidov Yaroslavl State University, Microelectronics and General Physics, Russian Federation

###### Abstract

A kinetic theory of the conductivity of a thin metal layer in a longitudinal alternative electric field is constructed. We assume the layer thickness is much greater than the electron de Broglie wavelength and less than the skin layer depth. Therefore the skin effect and electron energy spectrum quantization are neglected. The Soffer model is used as the boundary conditions for the Boltzmann equation. We suppose the roughness parameters of the upper and lower layer surface have different values. The Fermi surface is an ellipsoid of revolution, the main axis of which lies in the layer plane. The dependences of conductivity tensor components on the layer thickness, electric field frequency, Fermi surface anisotropy parameter, and surface roughness parameters are analyzed. The results are compared with the ones performed earlier within the framework of diffuse-mirror boundary conditions and with experimental data.

###### Acknowledgements:

The reported study was funded by RFBR, project number 19-32-90008.

#### Computer simulation in proton therapy

Eugenia Echkina1 , Natalia Guzminova2

1Moscow State University, Computational Mathematics and Cybernetics, Russian Federation
2A.I. Yevdokimov Moscow State University of Medicine and Dentistry, , United Kingdom

###### Abstract

The ionising radiation as a method of cancer treatment has a long history. Any types of radiation have been employed to achieve control of tumour viability such as a 'low' linear energy transfer (LET) beam of photons, two 'high' LET unmodified and spread-out Bragg peak (SOBP) beams of protons. Per the end of 2018, about 190036 patients have been treated with protons (1), 93 facilities in clinical operation worldwide in April 2020 (2). The unattainable goal so far is the creation and implementation of such a treatment plan in which the target volume receives 100% of the prescribed dose and healthy surrounding tissue 0%. The goal of modern science to find ways to "optimised" treatment plan especially in childhood cancer, where the preservation of healthy tissue surrounding the tumour is especially important. In our work we presented the results of a calculated experiment of the interaction of a laser impulse with various targets and showed the dependence of energy distribution from the target types.

#### On regular and irregular movement of cylinder colliding with a moving belt

Marek Lampart1

1VSB-Technical University of Ostrava, Czech Republic, IT4Innovations, Czech Republic

###### Abstract

The main aim of this paper is to introduce a new mechanical system modeled by a non-autonomous system of ordinary differential equations and to detect its movement character using a combination of the 0-1 test for chaos and approximate entropy instead of the standard Lyapunov exponent treatment. The investigated system consists of a cylinder hanging on a flexible rope, and a moving belt. Such a system with impacts and dry friction is illustrative of many industrial applications, such as stones falling on a moving conveyor belt. The mathematical model of the system has three degrees of freedom, from which two correspond to the position of the cylinder centre and the last one to its angular rotation. The studied system was excited by a slider moving in the vertical direction, and by impacts between the cylinder and the belt. Consequently, the cylinder exhibits movement with both regular (periodic) and irregular (chaotic) patterns depending on the excitation amplitude and frequency. The goal of the research was to qualify and quantify the movement character. For this purpose, the 0-1 test for chaos together with approximate entropy was applied to find regions of parameters for which chaos or regularity was observed.

#### The influence of the load’s geometrical characteristics on the generation of the electro-thermo-mechanical instability in a single wire Z-pinch

Evaggelos Kaselouris1 , Giorgos Tamiolakis2 , V Dimitriou3 , M Tatarakis4

1Hellenic Mediterranean University, Institute of Plasma Physics & Lasers - IPPL, Greece
2hellenic mediterranean university, Department of Electronic Engineering, Greece
3Hellenic Mediterranean University, Department of Music Technology & Acoustics, Greece
4Hellenic Mediterranean University, Institute of Plasma Physics & Lasers - IPPL, Greece

###### Abstract

The Z-pinch plasma device is a type of plasma confinement system that uses electrical current to generate a magnetic field which compresses a current-carrying wire [1,2]. In a previous proof-of-principle study, we demonstrated that in the interaction of a single wire with a pulsed current, the generated Electro-Thermo-Mechanical (ETM) instability in the solid phase acts as a seeding mechanism for the later developed instabilities observed in the plasma phase [3]. In this study, the influence of the geometrical characteristics, such as length and thickness of the load-wire, on the generation of the ETM instability are investigated. Finite element multiphysics-multiphase simulations starting from the solid state are coupled with Magneto-Hydro-Dynamics (MHD) simulations to study the solid to plasma phase transition and the matter’s dynamics. The numerical results of the wire expansion dynamics prior to plasma formation are validated by experimental results from a modified Fraunhofer diffraction diagnostic, while in the plasma phase the simulated plasma dynamics is validated by shadowgraphic and interferometric experimental results. The numerical and experimental results demonstrate a satisfactory agreement for the wire expansion dynamics and the growth rate of the developed instabilities, for varying wire thickness and length. [1] M. G. Haines, A review of the dense Z-pinch, Plasma Phys. Control. Fusion 53, 093001 (2011). [2] M. Tatarakis, R. Aliaga-Rossel, A. E. Dangor, and M. G. Haines, Optical probing of fiber z-pinch plasmas, Phys. Plasmas 5, 682–691 (1998). [3] E. Kaselouris, V. Dimitriou, I. Fitilis, A. Skoulakis, G. Koundourakis, E. L. Clark, Μ. Bakarezos, I. K. Nikolos, N. A. Papadogiannis &amp;amp;amp;amp;amp;amp; M. Tatarakis, The influence of the solid to plasma phase transition on the generation of plasma instabilities, Nature Commun. 8, 1713 (2017).

###### Acknowledgements:

This research is co-financed by Greece and the European Union (European Social Fund-ESF) through the Operational Programme «Human Resources Development, Education and Lifelong Learning 2014-2020» in the context of the project “Mitigation study of plasma instabilities in Z-pinch device using dielectric coatings (MIS 5048186). This work was supported by computational time granted from the Greek Research & Technology Network (GRNET) in the National HPC facility ARIS under project ID pr007020 LaMIPlaS- II.

#### On scientific insight from machine-learning models

Richard Dybowski1

1University of Cambridge, Chemistry, United Kingdom

###### Abstract

There has been an upsurge of interest in applying machine-learning (ML) techniques to chemistry, and a number of these applications have achieved impressive predictive accuracies; however, they have done so without providing any insight into what has been learnt from the training data. The interpretation of ML systems (i.e., a statement of what an ML system has learnt from data) is still in its infancy, but interpretation can lead to scientific discovery, and examples of this are given in the areas of drug discovery and quantum chemistry. It is proposed that a research programme be designed that systematically compares the various model-agnostic and model-specific approaches to interpretable ML within a range of chemical scenarios.

#### Multi-fidelity sparse polynomial chaos expansion based on Gaussian process regression and least angle regression

Dong XIAO1 , Michele FERLAUTO2 , Liming SONG3 , Jun LI4

1Xi'an Jiaotong University, Department of Thermodynamic Engineering, China
2Politecnico di Torino, Department of Mechanical and Aerospace Engineering, Italy
3Xi'an Jiaotong University, Department of Thermodynamic Engineering, China
4Xi'an Jiaotong University, Department of Thermodynamic Engineering, China

###### Abstract

Polynomial chaos (PC) expansion meta-model has been wildly employed and investigated in the field of uncertainty quantification (UQ) and sensitivity analysis (SA). However, the majority of the multi-fidelity polynomial chaos expansion (MF-PC) models in the literature are still focused on using high-fidelity (HF) PC model to correct low fidelity (LH) model directly, without cross-correlation between PC models of different fidelities. To address this shortcoming, a multi-fidelity sparse polynomial chaos expansion (MF-sPC) model is proposed based on least angle regression (LAR) and recursive Gaussian process regression (GPR) in this paper. From low to high degree of fidelity, the autoregressive scheme in MF GPR is employed to construct MF-sPC model, in which the sparse polynomial chaos (sPC) model of each fidelity is built iteratively coupling with GPR, LAR and cross validation (CV), as gradually expanding the design of experiment (DoE) to reach a given CV error. This recursive scheme finally yields a MF-sPC model with highest fidelity which takes advantage of all sPC models of the lower fidelities. And the proposed MF-sPC model is validated by a test example in detail, and the results reveal that this MF meta-model performs outstanding both in convergence speed and model accuracy.

###### Acknowledgements:

This work is done by the author during his visiting to Politecnico di Torino and sponsored by his Alma Mater Xi'an Jiaotong University, under the supervision of professor Michele Ferlauto and Liming Song. I have to express my sincere gratitude and reverence to my two mentors, and also to those two universities and two countries, China and Italy.

#### Knots in Proteins

Kenneth Millett1

1University of California, Santa Barbara, Mathematics, United States

###### Abstract

Since 2000, knots in proteins have attracted the attention of biologists and mathematicians. Following a brief historical inventory, we will describe the application of algebraic and topological methods to identify and quantify the presence of knotting, we will describe new methods and describe recent discoveries of instances of knots in proteins, their mathematical character, and reflect on what they tell us about their biological and functional consequences.

#### Topological climate change with permafrost feedback

William Langford1 , Allan Willms2 , Kolja Kypke3 , Nathaniel Nethercott4

1University of Guelph, Department of Mathematics and Statistics, Canada
2University of Guelph, Department of Mathematics and Statistics , Canada
3University of Guelph, Department of Mathematics and Statistics , Canada
4University of Guelph, Department of Mathematics and Statistics , Canada

###### Abstract

Climate models predict that the climate of the Earth is warming and will continue to warm in coming centuries, if there is no mitigation. A recent model [Kypke et al., Anthropocene climate bifurcation, Nonlin. Process. Geophys., accepted 2020] forecasts that, if the current rate of increase of carbon dioxide in the atmosphere continues unabated, then in the next century the climate of the Earth will not only get warmer, but will transition abruptly via a bifurcation, to a warm, equable climate unlike any climate seen on Earth since the Pliocene. This transition to a new climate state is a topological change. That model includes the effects of water vapour feedback and ice albedo feedback, as well as ocean and atmospheric heat transport. This paper adds to that model the amplifying effect of permafrost feedback. That is, as the Arctic warms, permafrost will thaw, releasing large amounts of the greenhouse gases carbon dioxide and methane, which cause further warming. Since knowledge of permafrost stores and release rates is limited, a range of permafrost carbon release sensitivities $(Q_{10})$ is considered. The model predicts that permafrost feedback accelerates the timing and increases the amplitude of a topological climate change in the Arctic, and reinforces the view that permafrost feedback should not be ignored in Anthropocene climate models.

###### Acknowledgements:

This work was supported by the Natural Sciences and Engineering Research Council of Canada.

#### Cauchy problem for non-line equation of peridynamics

Asal Yuldasheva1

1Moscow state university Tashkent branch, Applied mathematics and informatics, Uzbekistan

###### Abstract

In the classical theory of solid mechanics, the behavior of solids is described by partial diﬀerential equations (PDE) through Newtons second law of motion. However, when spontaneous cracks and fractures exist, such PDE models are inadequate to characterize the discontinuities of physical quantities such as the displacement ﬁeld. Recently, a peridynamic continuum model was proposed which only involves the integration over the diﬀerences of the displacement ﬁeld. The peridynamic equation of motion is considered for a large class of nonlinear pairwise force functions modeling isotropic microelastic material. In this paper, we study the well-posedness and regularity of a peridynamic model. We convert the model to an operator valued Volterra integral equation. Then the existence and regularity of the solution of the peridynamics problem are established through the study of the Volterra integral equation.

###### Acknowledgements:

This work was supported by Academy of Sciences Republic of Uzbekistan OT-F4-(88) and OT-F4- (36/32).

#### Photo-voltaic power 24-hour statistical predictions using PDE models of stepwise evolved Polynomial networks with the sum PDE partition and L-transform substitution

1VŠB-Technical University of Ostrava, Faculty of Electrical Engineering and Computer Science, Czech Republic
2VŠB-Technical University of Ostrava, Faculty of Electrical Engineering and Computer Science, Czech Republic

###### Abstract

Computational methods based on Artificial Intelligence (AI) can convert or post-process data produced by Numerical Weather Prediction (NWP) systems to pre-dict Photo-Voltaic (PV) power in consideration of a plant specific situation. Their statistical models, developed with historical data series, are more precise if rely on the latest weather observations and PV measurements as NWP models are usual-ly run every 6 hours with a delay of a few hours. Moreover, their forecasts accu-racy is mostly inadequate for PV plant actual operation. Differential Polynomial Neural Network (D-PNN) is a novel biologically inspired neuro-computing tech-nique which can model complex patterns without reducing significantly the data dimensionality as standard regression or soft-computing does. D-PNN combines appropriate 2-inputs to decompose the n-variable Partial Differential Equation (PDE), being able to describe the atmospheric dynamics, into a set of particular sub-PDEs in its nodes. The 2-variable PDEs are converted using adapted proce-dures of Operational Calculus (OC) to obtain the Laplace images of unknown node functions, which are inverse L-transformed to obtain the originals. D-PNN produces applicable sum PDE components in its nodes to extend step by step its composite models towards the optima. The compared PDE and AI models are developed with spatial historical data from the estimated optimal daily training pe-riods to process the last day input data series and predict Clear Sky Index (CSI) at the corresponding 24-hour horizon.

###### Acknowledgements:

This work was supported from European Regional Development Fund (ERDF) “A Research Platform focused on Industry 4.0 and Robotics in Ostrava”, under Grant No. CZ.02.1.01/0.0/0.0/17 049/0008425.

#### Bifurcations in Nonisothermal Gas Absorption with Simultaneous Reactions

Abdullah Shaikh1

1King Fahd University of Petroleum & Minerals, Chemical Engineering Department, Saudi Arabia

###### Abstract

Nonisothermal reactive gas absorption (RGA) processes are defined as processes involving gas absorption with simultaneous chemical reaction(s). An accurate estimation of the rate of gas absorption taking into consideration transport-reaction interactions as well as thermodynamic and mixing effects in such systems is required for rational design and optimum operation of gas-liquid reactors. In this work we extend and generalize our recent work [Chem. Eng. Commun., 294(3), 310-320 (2017)] on nonisothermal reactive absorption by developing a rigorous two-film model to include, general-order, reversible gas-liquid reactions. The model is subsequently used to analyze the dynamic features of nonisothermal RGA including the possible occurrence of static bifurcations. In this contribution we also consider the development of a priori criteria to assess the significance of intraphase and interphase thermal gradients in the case of exothermic gas-liquid reactions. Validation of the criteria is done by application to a number of experimental RGA systems.

#### Obtaining the predicted number of cycles of femoral prosthesis manufactured with ASTM F138 and ASTM F75 aloys, applying the method of finite element

Wilson Carlos da Silva Junior1 , Caique Movio Pereira de Souza2 , Fabio da Silva Bortoli3 , CARLOS FRAJUCA4 , Renato Chaves Souza5

1IFSP, MECHANICS, Brazil
2Instituto Federal de São Paulo – IFSP, , Brazil
3IFSP, MECHANICS, Brazil
4IFSP, MECHANICS, Brazil
5Instituto Federal de São Paulo – IFSP, , Brazil

###### Abstract

A hip prosthesis is typically subjected to cyclic loads proportional to the patient´s weight in response to each step and hence requires a cyclic compression stress approach. Austenitic stainless steels have been used in surgical applications over many years due to low cost, good mechanical properties and resistance to corrosion. This study aims to calculate the predictive number of cycles applied to femoral prosthesis made with ASTM F138 and ASTM F75 alloys.

#### Using Particle Swarm Optimization for design comb compensator with magnitude response synthetized as sine function

Sergio Salguero1 , Gordana Jovanovic Dolecek2 , Antonio Fernandez de Lara Sosa3

1Instituto Nacional de Astrofísica, Óptica y Electrónica, Departamento de Electrónica, Mexico
2Institute INAOE, Electronics, Mexico
3Institute INAOE, , Mexico

###### Abstract

Using Particle Swarm Optimization for design comb compensator with magnitude response synthetized as sine function Sergio Salguero, Gordana Jovanovic Dolecek and Antonio Fernandez de Lara Sosa Department of Electronics, Institute INAOE, Puebla, Mexico gordana@ieee.org Comb compensator improves the passband characteristic of comb filter, i.e. decreases the comb passband droop. This paper presents one method for design comb compensator with the magnitude response synthetized as sine function. The parameter of design is the amplitude of sine function denoted as A. The goal is to find the amplitude of sine function A for each value of comb parameter, K, K=1,…,5, where K is the number of the cascaded comb filters. First the optimum values of the amplitude of sinusoidal function A, for each value of K, K=1,…5 are obtained using Particle Swarm Optimization (PSO). It is demonstrated that the obtained values A practically do not depend on the decimation factor M, for M&amp;gt;10. In next step the obtained values of the parameter A are presented in form of sum of powers of two (SPT) to get a multiplierless design. The method is illustrated with one example and compared with the methods from literature.

#### Modeling a calibrator for laser interferometer gravitational wave detectors

CARLOS FRAJUCA1 , Fabio da Silva Bortoli2 , Andre Rogerio Prado3 , Nadja Magalhaes4 , Wilson Carlos da Silva Junior5 , Renato Chaves Souza6

1IFSP, MECHANICS, Brazil
2IFSP, MECHANICS, Brazil
3Instituto Federal de São Paulo – IFSP, , Brazil
4Unifesp, Physics, Brazil
5IFSP, MECHANICS, Brazil
6Instituto Federal de São Paulo – IFSP, , Brazil

###### Abstract

LiGO is the detector of gravitational waves, as this detector has more than 160 active attenuator system, the normal methods for calibration seems to not work properly. This work aims to model a calibrator for this detector in the form of a resonant-mass Nb gravitational detector thar has the same sensitivity of LIGO detector bur operating in a narrow band. This detector will detect the same gravitational wave and uses this signal to calibrate LIGO. A simulation in a lumped model is made and it shoes that the calibration is achievable.

###### Acknowledgements:

FAPESP, CNPQ and Capes

#### Spatiotemporal localizations of light in quadratically nonlinear media with transversal inhomogeneity

Ivan Chuprikov1 , Alexey Kalinovich2 , Maria Komissarova3 , Sergey Sazonov4 , Irina Zakharova5

1Lomonosov Moscow State University, Photonics and Microwave Physics, Russian Federation
2Lomonosov Moscow State University, , Russian Federation
3Lomonosov Moscow State University, , Russian Federation
4National Research Centre “Kurchatov Institute”, , Russian Federation
5Lomonosov Moscow State University, Faculty of Physics, Russian Federation

###### Acknowledgements:

The investigation was made using support of the Russian Science Foundation (Grant 17-11- 01157).

#### Modeling a broadband detector for an experiment that measures the speed of gravity over short distances

CARLOS FRAJUCA1 , Fabio da Silva Bortoli2 , Nadja Magalhaes3 , Wilson Carlos da Silva Junior4 , Renato Chaves Souza5

1IFSP, MECHANICS, Brazil
2IFSP, MECHANICS, Brazil
3Unifesp, Physics, Brazil
4IFSP, MECHANICS, Brazil
5Instituto Federal de São Paulo – IFSP, , 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 2 sapphire device that works as a detector suspended in vacuum 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. As sapphire has a very high mechanical Q the detection band should be quite small lowering the detection sensitivity. In this work a new shape for the detector device is show allowing a band detection of several hundred Hertz. The detector is modeled in a FInite Element Program to obtain its normal mode frequencies.

###### Acknowledgements:

FAPESP, CNPq and Capes

#### Computer modeling of the resonant systems of the Ku-range magnetron

1Harbin Institute of Technology, Microwave Engineering Department, China

###### Abstract

Magnetron is one of the most widely known and used vacuum microwave sources of electromagnetic radiation. Despite the fact that the magnetron has a relatively simple design, the simulation of electron-wave interaction in this device is a complex problem that requires significant computer time and resources of the hardware used. In consequence, searching the new approaches, directed towards speeding up the simulation process provided conservation of a common self-consistent setting up a problem is a topical and complicated challenge. This paper presents the results of computer modelling frequency spectrum of oscillation modes excited in the interaction space of cold resonant systems as well as the azimuthal distributions of the longitudinal components of a RF field for each of excited mode. As an example, there were consider the resonant systems of the magnetron in the form of anode blocks having the resonators of different shape: a “rising sun” anode block and a “hole-and-slot” anode block. In addition, the anode blocks consist of two resonant systems, one comprising the small cavities and the other the large cavities. The action of the geometry dimensions of the small and large cavities on frequency of excited modes and their separation is shown. The obtained results allowed to clarify shaping a total RF field in the interaction space of the anode blocks of magnetrons. It is shown, that the mechanism of shaping the total RF field connects with interference of RF fields excited severally in the resonant systems consisting of the small and large cavities. The azimuthal distribution of a total RF field was used in the 3-D mathematical model of the KU-range magnetron for computer modelling its output characteristics. By using such approach there were studied dependence of the output parameters (output power) on the distance between a cathode and an anode of the anode block. For computer modelling the electrodynamic characteristics of the anode blocks of the magnetron we used the CST code and for simulation of electron-wave interaction in the magnetron there was used the SICM-3D v.4 code.

#### Determination of the tensile strength of metal materials when taking into account the effects of hydrogen

Igor Emel’yanov1 , Anastasia Hodak2

1Ural Federal University, Institute of Fundamental Education, Department of Structural Mechanics, Russian Federation
2Ural Federal University, Institute of Fundamental Education, Department of Structural Mechanics, Russian Federation

###### Abstract

Various metal constructions often are operated in contact with aggressive environment. For example, pipelines designed to transport hydrogen-containing environment. The negative influence of an aggressive environment on the mechanical properties of various materials during the operation of structures is one of the important factors that must be taken into account. The occurring degradation processes in the metal of structural elements will affect the residual life of the structures. A mathematical model based on experimental research, determining the tensile strength of metallic materials, taking into account the influence of an aggressive hydrogen-containing environment, is proposed. For this, experimental researches of samples of steel and titanium materials after the process of their hydrogenation were carried out. It is known that the processes of heat conduction and diffusion of hydrogen into a metal have different physical times, but are described by identical differential equations in structure. Therefore, the developed mathematical apparatus for solving heat conduction problems, based on the finite element method, is used in the work to solve the problem of hydrogen diffusion into metal. The results of numerical simulation of hydrogen penetration into the sample allow us to obtain an equation describing the change in the tensile strength of the material under study, depending on the hydrogen concentration.

#### Systematic Regional Optical Model Potential for α–Nucleus Elastic Scattering at low Energies

Kassem Behairy1 , Zakaria Mahmoud2

1Aswan university, Physics , Egypt
2A New Vally University, Physics , Egypt

###### Abstract

The elastic scattering of α – particle from 39Y, 42MO, 48Cd, 50Sn and 62Sm nuclei (Z=39-62) at energies around the coulomb barrier is reanalyzed. The aim is to obtain a regional optical model potential (OMP) for this range of target mass number with a systematic model-parameters. For this purpose, we used the folding model with two different effective nucleon – nucleon (NN) interaction. These effective NN interactions are the density– and energy–dependent JLM and the DDM3Y1 with finite range exchange term, respectively. The derived potentials are used to reanalyze twenty-one sets of data for the considered systems. The OMPs are constructed first using real folded potentials based on JLM and DDM3Y1 effective NN interactions supplied with the conventional Wood–Saxon (WS) imaginary part. These two OMPs potentials are denoted as JLM-R and DDM3Y1-FR, respectively, in addition, the full complex folded OMP based on the complex JLM effective NN is used, which is denoted as JLM-RI. The semi-microscopic JLM-R and DDM3Y1-FR potentials are reproduced the experimental data over the full angular range very well compared to microscopic JLM-RI potential.

#### MODELLING AN EXPERIMENT TO MEASURE THE SPEED OF GRAVITY IN SHORT DISTANCES USING ROTATING MASSES

Carlos Fabricio Junior1 , Eduardo Sanchez2 , CARLOS FRAJUCA3 , Fabio da Silva Bortoli4 , Nadja Magalhaes5 , Wilson Carlos da Silva Junior6 , Renato Chaves Souza7

1IFSP, MECHANICS, Brazil
2IFSP, MECHANICS, Brazil
3IFSP, MECHANICS, Brazil
4IFSP, MECHANICS, Brazil
5Unifesp, Physics, Brazil
6IFSP, MECHANICS, Brazil
7Instituto Federal de São Paulo – IFSP, , Brazil

###### Abstract

An experiment to measure the speed of gravitational signals using rotating masses in short distances is been developed with the intention to study its behaviour when medium different from air is allocated between the emitter and the detecton and check if the speed of the interaction changes. The experiment is composed of two masses rotating at incredible rotation (the goal is rotate the masses at rotation speed higher than 600,000 RPM, that excites a saphire bar called the detector. The amplitudes of the central device (detector) is monitored by an ultralow phase noise microwave signal using resonance in the whispering gallery modes and coled down at 4.2 K. Between the rotating masses and the detector, a different medium will be placed, and then the speed is measured and compared with the case where the medium is pure air. The modelling of the experiment is made assuming the detector as a spring-mass system. The results show that the detection is achievable.

###### Acknowledgements:

FAPESP, CNPq and CApe

#### STOCHASTIC SIMULATION TO PROJECT SUPPLY OF THE KAZAKHSTAN GENERAL PRACTICE WORKFORCE TO 2030

Berik Koichubekov1 , Azamat Kharin2 , Marina Sorokina3 , Ilya Korshukov4 , Bauyrzhan Omarkulov5 , Temirlan Ukubayev6

1Karaganda Medical University, Department of Informatics and biostatistics, Kazakhstan
2Karaganda Medical University, Department of Informatics and Biostatistics, Kazakhstan
3Karaganda Medical University, Department of Informatics and Biostatistics, Kazakhstan
4Karaganda Medical University, Department of Informatics and Biostatistics, Kazakhstan
5Karaganda Medical University, Department of Informatics and Biostatistics, Kazakhstan
6Karaganda Medical University, Department of Informatics and Biostatistics, Kazakhstan

###### Abstract

Our aim was to explore the effect of the uncertainty of some parameters on total General Practitioner (GP) supply in Kazakhstan to 2030. System dynamics simulation was used to develop model for General Practitioner workforce forecasting. Sensitivity analysis (Monte Carlo method) was performed to account for changes in the number of GP as each and set of model parameters is varied. Three key input parameters were explored: retirement rate, attrition rate, recruitment rate. For each parameter relative sensitivity was calculated. Created model is the least sensitive to the parameter of the retirement rate, but is very sensitive to attrition rate. Staff turnover is one of the main problems of primary health care. The attrition rate parameter has great potential for controlling the flow of labor. The level of recruitment (other than new GPs) is another factor that has a significant impact on forecasting GPs. The sensitivity to this parameter is comparable to the sensitivity to the rate of depletion. We believe that measures taken to reduce dropouts will simultaneously increase recruitment. We also evaluated the effect of all three parameters simultaneously. If the most likely scenario is realized, then the proposal of a General Practitioner will almost completely cover the needs with a small deficit of 68 to 305 doctors. If the high limit or low limit scenarios in the labor market are implemented, Healthcare Ministry will face serious problems.

#### Modeling militantism and partisanship spreading in the chain and square lattice opinion structures by using q-XY opinion model

Dode Prenga1 , Elmira Kushta2 , Margarita Ifti3

1University of Tirana, Faculty of Natural Sciences, Physics, Condensed Matter Group, Albania
2University of Vlora “I.Qemali”, Faculty of Technical Science, Mathamatics, Albania
3University of Tirana, Faculty of Natural Sciences, Physics, Albania

###### Abstract

Abstract: In this work we have considered the spreading of militantism in 1D and 2D square lattice by operating the q-XY opinion utility optimization as control mechanism for the update process. The average utility and opinion are calculated in the framework of standard statistical mechanics using the opinion utility in the pair as U=-J/2 (O ⃗^2-2)-F ⃗O ⃗+q(J/2 (O ⃗^2-2)*F ⃗O ⃗ ). The average opinion and other thermodynamic quantities for opinion pair are calculated from the partition function calculated Z=8πe^(-β) ∫_0^2▒〖e^((JβO^2)/2) I_0 (βFO(1-qJ/2 (O^2-2))) 〗 1/√(4-O^2 ) dO and the agreement of the all community is modeled as one by one talk between the militant and opinion nodes. So, starting form a random configuration, an opinion node is updated at a given time step if its opinion values is greater than the q-opinion calculated for given conditions (q, F, T). The respective new value is chosen randomly in the interval [old value, q*-opinion value] where q* correspond to the q-opinion with one constituent (the militant) aligned to the exterior field. At the same time the q parameter is changed by a given portion toward better values, to count interior changes in a pair after long discussion and persuasion. All new values are accepted with a Metropolis like probability calculated by employing q-utilities of the nodes under updating process. For the quasi stationary regime where interaction type is preserved that is 1-q J/2 (O ⃗^2-2)&gt;0 given 0≤O≤1 ) it resulted that our systems accept a militant offer only partially. The bounded chain opinion structures will embrace the militant opinion up to 0.9 but lower agreement level is mostly common. It supports the fact that no idea can be full dominant in a community whatever the condition would be. There are always peoples that contradict it. For square opinion lattices we obtained that the militant attitude would never cover all the community and it progresses slowly. In both cases the final level of the agreement depends strongly on the intensity of the field F. If dropping the type preservation conditions, the dynamics become more sensitive toward the exterior field and q value itself. By increasing the exterior field value we observed the alternation of the agreement level as function of the interaction parameter J and coupling parameter q. For large communities the number of epochs to reach the highest agreement level becomes abnormally large and we refer it as the impossibility for the existences of the militant societies on this point of view.

#### Deliberative architecture for smart sensors in the filtering operation of a water purification plant.

EDUARDO MENDOZA MERCHAN1 , Joselyne Andramuño2 , Israel Benitez3 , Jose Nuñez4

3Universidad de Oriente, Automatics Department, Cuba
4Universidad de la Costa, Energy Department , Colombia

###### Abstract

The increase of applications for industrial smart sensors is booming, mainly due to the use of distributed automation architectures, industrial evolution and recent technological advances, which guide the industry to a greater degree of automation, integration and globalization. In this research work, an architecture for deliberative-type intelligent industrial sensors is proposed, based on the BDI (Belief Desire Intentions) model, adaptable to the measurement of different variables of the filtering process of a water purification plant. An intelligent sensor with functions of signal digitalization, self-calibration, alarm generation, communication with PLC, user interface for parameter adjustment, and analysis with data extrapolation have been arranged. For decision making, the use of fuzzy logic techniques has been considered, which allows imprecise parameters to be appropriately represented, simplifying decision problem solving in the industrial environment, generating stable and fast systems with low processing requirements. The proposed architecture has been modeled, simulated and validated using UML language in conjunction with Petri nets, which facilitate the representation of discrete system events, presenting them clearly and precisely. In the implementation and testing of the prototype, C / C ++ language has been used in an 8-bit microcontroller, experimentally corroborating the operation of the device, which allowed evaluating the behavior of a pseudo-intelligent agent based on the requirements of the water treatment plant, and also through comparisons with similar works developed by other researchers.

#### Short DNA properties in a cylindrical channel

Marco Zoli1

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

###### Abstract

The intrinsic flexibility of the DNA molecule and the predictability of the Watson-Crick base pairing are key to the self-assembly of 2D and 3D structures in functional materials with biomedical applications. The stretching properties of single fragments have been extensively investigated over the last decades by micro-manipulation techniques sampling the DNA extension as a response to external loads or to proteins which deform the helical structure upon binding. The relation between helical twist and stretching also appears in the confinement of single molecules through a crowders distribution [1,2] and in a nano-channel which provides a new tool for accurate genome sequencing and mapping. Here I extend a well-established three dimensional mesoscopic model for the double helix [3,4,5] incorporating in the system Hamiltonian a hard-wall repulsive potential which simulates the cylindrical channel. Using statistical mechanics methods based on path integral techniques, I compute the macroscopic helical parameters performing the averages over the ensemble of microscopic base pair fluctuations. The average molecule elongation, measured by the end-to-end distance, is derived as a function of the channel potential parameters both for a homogeneous and a heterogeneous chain. The overall results yield consistent quantitative estimates for the stretching and twisting of short chains supporting the choice of the channel potential term [6]. Some new results regarding the choice of the DNA model parameters are discussed. [1] M. Zoli, Journal of Physics: Conf. Ser. vol. 1391, 012004 (2019). [2] M. Zoli, Physical Chemistry Chemical Physics vol. 21, 12566-12575 (2019). [3] M. Zoli, The Journal of Chemical Physics vol. 141, 174112 (2014). [4] M. Zoli, The Journal of Chemical Physics vol. 144, 214104 (2016). [5] M. Zoli, The Journal of Chemical Physics vol. 148, 214902 (2018). [6] M. Zoli, EPL (Europhysics Letters) vol. 130, 28002 (2020).

#### On transient heat analysis of a two-step convective reactive cylinder

Ramoshweu Lebelo1

1Vaal University of Technology, Education, South Africa

###### Abstract

This article looks at the analysis of heat transfer due to combustion of reactive materials in a stockpile modelled in a cylindrical domain. The transient heat analysis is studied through the investigation of effects kinetic parameters, embedded on the differential equation governing the problem, have on the temperature of the system. The temperature patterns due to the parameters effect, are depicted in graphs generated through Maple software. The complicated nonlinear partial differential equation is solved numerically using Finite difference method (FDM). The results show that parameters such as the order of reaction slow down the exothermic chemical reaction, while parameters like the reaction rate enhance the combustion process.

#### Design of Comb-Based Decimation Filter with Low Power Consumption, Increased Alias Rejection and Decreased Passband Droop

Antonio Fernandez de Lara Sosa1 , Gordana Jovanovic Dolecek2 , Sergio Salguero Luna3

1Institute INAOE, , Mexico
2Institute INAOE, Electronics, Mexico
3Institute INAOE, , Mexico

###### Abstract

This paper presents design of a low power comb-based decimation filter for decimation of 100. The proposed structure is composed of two stages. The first and second stages are decimated by 4 and 25, respectively. The first stage is a nonrecursive structure composed of two cosine filters each decimated by 2. The second stage is a Cascaded-Integrator-Comb (CIC) structure, decimated by 25. Since CIC structure is moved to lower rate we get a low power structure. The alias rejection is improved increasing the number of cascaded filters by 1 or 2, at second stage. The passband droop is decreased by introducing the compensator at lower rate, i.e. after downsampling by 100. The parameters of compensator are obtained using method of intervals.

#### Determining the optimal solution of the Kuper-Shmidt equation by implementing Jacobi and Airfoil bases expansion methods

Ali Rafiee1

1 Islamic Azad University, Department of Mathematics, Iran, Islamic Republic Of

###### Abstract

In this paper, Kuper-schmidt equation is solved by using collocation method with the Jacobi and the Airfoil polynomials. This equation PDE is one of the most important equations in physics and chemistry. This nonlinear equation in mechanical engineering appears as a wave phenomenon, and in plasma physics discusses systems that are composed of positive and negative charged particles and can move freely. Comparison of the level of hot electron production and its level causes the harmonic emission of some source signals and heat electrons in the plasma, are radiated spherically. The Kuper-schmidt equation plays an important role in spherical nonlinear scattering, plasma waves, solitary waves are propagated in nonlinear scattering of media. These waves maintain a stable shape. Due to the dynamic equilibrium and nonlinearity of this equation, an approximate solution has been proposed in many papers. In this paper, by applying numerical methods to the equation, nonlinear devices can be solved by nonlinear solution methods such as Newton's iterative method. The existence, uniqueness of the solution, and the convergence of the methods are proved, and we will show in an example that with a low repetition of the stopping criterion |u_(n+1)-u_n | . It can be reached and this indicates the accuracy of the solution to this methods.

#### Analysis of The Structural Behavior Of Minarets With Different Building Materials Under Horizontal Loads By Finite Element Approach And Comparison of The Materials Used With Construction Cost Analysis

PINAR USTA1

1Isparta University of Applied Sciences, Civil Engineering, Turkey

###### Abstract

Many masonry constructions were damaged by seismic loads. In this study one minaret is selected. In contrast to the classical structures, minarets are tall, thin and masonry structures. Each year Turkey has also built many mosques and minarets. Unfortunately, it was seen that, there were no Turkish standard and specification causally related to analysis and design of minarets. So Usually these structures are built without any control and skillful skill. Therefore, they are highly sensitive under the effects of strong wind and earthquake. Therefore, this study was conducted to determine which material could be more reliable, suitable, and economical for minaret structures. In this study Four Different types of construction materials are chosen for the minaret and seismic load analysis are conducted. Since the structural behavior of historical minarets were represented with mathematical models, three dimensional (solid) models were implemented by using the finite element technique and by SAP2000 V21 program. As a result of the analyzes, the demand and capacity curves arising from the seismic loads of the minaret to be constructed using different building materials and the damage status of the buildings were also investigated and compared in terms of their economic dimensions.

#### New open computational resource for plasma processes modelling

Aleksandr Zhilkin1 , Dmitry Sychugov2 , Lev Vysotsky3 , Ihor Zotov4 , Sergey Soloviev5 , Anuar Sadykov6

1Moscow State University, Computational Mathematics and Cybernetics, Russian Federation
2Moscow State University, Computational Mathematics and Cybernetics, Russian Federation
3Moscow State University, , Russian Federation
4Moscow State University, , Russian Federation
5Lomonosov Moscow State University, Calculate mathematics, Russian Federation
6IAE NNC RK, Of thermonuclear reasearches, Kazakhstan

###### Abstract

The authors created a new open resource, currently located at URL nfusion.cs.msu.ru. The resource includes remotely accessible versions of Tokameq (TOKAMak EQuilibrium) - code for calculation of MHD equilibria in tokamak, Tokscen (TOKamak SCENario) - code for calculation of plasma evolution in tokamak, RPB (Reconstruction of Plasma Boundary) - code for reconstruction of plasma boundary from magnetic measurements, and mesher - code for fast tetrahedral mesh generation. The system is designed for simultaneous access of multiple users and has informational support in English and Russian languages. This work was supported by the Fund N 20-07-00391 of Russian Foundation for Basic Research

#### Intelligent distributed module for local control of lighting and electrical outlets in a home

Joselyne Andramuño1 , EDUARDO MENDOZA MERCHAN2 , Jose Nuñez3

3Universidad de la Costa, Energy Department , Colombia

###### Abstract

This article proposes a control of lighting and electrical loads, suitable for smart homes, using embedded systems with low-cost wireless communication modules. The system is based on a distributed intelligent home automation architecture, to work autonomously or interconnect wirelessly to a larger system. It has a set of sensors that allow you to ration the use of electricity through automatic switching off the lights or electrical devices, allowing the lighting to be regulated. It has several modules that communicate to a central node wirelessly, and an interface based on a mobile application. UML and Petri Nets were used for the projection, modeling and validation of the system, its implementation was developed in C / C ++ language for 32-bit microcontrollers. Tests of the prototype showed stable behavior, fast communications and sufficient coverage for a single-family house, whose performance is higher to other similar works found in the scientific community.

#### Influence of clustering round magnetic nano-dots on magnetization reversal

Tomasz Blachowicz1 , Andrea Ehrmann2

1Silesian University of Technology, Institute of Physics - Center for Science and Education, Poland
2Bielefeld University of Applied Sciences, Faculty of Engineering and Mathematics, Germany

###### Abstract

Square and round magnetic nano-dots of varying dimensions exhibit a large amount of possible magnetization reversal processes, from domain wall nucleation and propagation to multi-vortex states [1,2]. Clustering such single nano-dots, however, may strongly modify these magnetization reversal processes due to the interactions between neighboring particles [3]. Here we thus investigate the difference between magnetization reversal processes in clusters of hexagonally arranged round nano-dots under different orientations of the external magnetic field in comparison with single particle behavior. [1] A. Ehrmann, T. Blachowicz, Vortex and double-vortex nucleation during magnetization reversal in Fe nanodots of different dimensions, J. Magn. Magn Mater. 475, 727-733 (2019) [2] A. Ehrmann, T. Blachowicz, Systematic study of magnetization reversal in square Fe nanodots of varying dimensions in different orientations, Hyperfine Interactions 239, 8 (2018) [3] A. Ehrmann, T. Blachowicz, Influence of the distance between nanoparticles in clusters on the magnetization reversal process, Journal of Nanomaterials 2017, 5046076 (2017)

#### Numerical analysis of a vibro-impact system with ideal and non-ideal excitation

Dzanko Hajradinovic1 , Miodrag Zukovic2 , Ivana Kovacic3

1Faculty of Mechanical engineering Sarajevo, Mechanics, Bosnia and Herzegowina
2University of Novi Sad, Faculty of Technical Sciences, Serbia
3University of Novi Sad, Faculty of Technical Sciences, Serbia

###### Abstract

This study is concerned with modelling and analyses of a vibro-impact system consisting of a crank-slider mechanism and one oscillator attached to it, where the system can be exposed to ideal or non-ideal excitation. The impact occurs during the motion of the oscillator when it hits a base, and the excitation of the driving source is affected by this behaviour. The aim is to determine the interaction between a driving torque and the motion of the oscillator. To achieve this aim in a methodologically sound manner, both vibro-impact systems with ideal and non-ideal excitation are analysed. For these system differential equations are formed and the impact model is provided in the paper. The impact causes a strong nonlinearity in the system. The mathematical model of the vibro-impact system with ideal excitation is presented as a second order differential equation where the vibro-impact system with non-ideal excitation is given as a coupled system of nonlinear second order differential equations. Numerical simulations are carried out for the two systems and the results obtained are shown in terms of frequency-response diagrams as well as in terms of time-displacement diagrams. The results found for different systems are compared mutually, and the differences between them are pointed out. Impact solutions for different regions of the excitation frequency are shown. For a specific value of the excitation frequency in the frequency response diagram where multiple solutions are found, basin of attractor diagrams are formed. Average value of the excitation frequency is used for the vibro-impact system with non-ideal excitation.

###### Acknowledgements:

The first author acknowledges the support of the Ministry of Education and Science of the Kanton Sarajevo. The second and the third author acknowledge support of the Ministry of Education and Science of the Republic of Serbia.

#### Fast diffetentiation of noisy data: Application to algorithmic trading

Dimitrios Vlachos1

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

###### Abstract

The problem of differentiating a function which is specified by a noisy data set, has many scientific applications although finite-difference approximations loose the hidden trends in data by amplifying any noise present. A modified total-variation regularisation, which allows for discontinuous solutions is considered here. The method has an analytical solution which in turn performs very fast and can accept constraints. The method is applied to forex tick values in order to isolate hidden trends in price movements.

#### A new linear scaling algorithm for density functional theory Based on Daubechies wavelet

Ang-Yang Yu1

1Changchun University of Science and Technology, , China

###### Abstract

Density functional theory calculations were traditionally suffered from an inherent cubic scaling with respect to the size of the system. Thus, a linear scaling algorithm is needed in order to make the computational time increases linearly with system size. In this work, a new linear scaling algorithm, which makes use of Daubechies wavelets to construct a minimal set of localized adaptively contracted basis functions, was designed and developed. This extraordinary algorithm ensures that the Kohn-Sham orbitals can be represented with an ultrahigh and controllable precision. Furthermore, this approach can be combined with sparse matrix algebra to obtain a linear scaling with respect to the number of electrons in an investigated system. Due to reduced complexity of density functional theory calculations, this algorithm will have wide applications in many numerical experiments in the near future.

#### Light-front approach to relativistic electrodynamics

Gaetano Fiore1

1INFN, Sezione di Napoli, Italy

###### Abstract

I will illustrate how our recent light-front approach simplifies the study of the relativistic dynamics of charged particles subject to an electromagnetic (EM) field Fμν that is the sum of a (even very intense) plane travelling wave F μν (ct − z) and a t static part Fμν(x,y,z); it adopts the light-like coordinate ξ = ct−z instead of time s t as an independent variable. This can be applied in several phenomena of extreme acceleration, both in vacuum and in a cold diluted pasma hit by a very short and intense laser pulse (LWF acceleration, slingshot effect, etc.)

#### How many shades of grey? On the proximity of density functional approximation to ab initio method via calculations of electric multipole moments

Demetrios Xenides1

1University of Patras, Chemistry, Greece

###### Abstract

The wide spreading of the application of Density Functional Approximation via its represtnatives, i.e. the Density Functionals (DFs), in almost all the fields of computational chemistry is globally witnessed. Therefore, it is believed that an evaluation of their performance in tedious calculations will offer useful insights to both users and developers. As such calculations we chose the prediction of electric multipole moments of first to fourth order, namely dipole (μα/ea0), quadrupole (Θαβ/ea20), octupole (Ωαβγ/ea30) and hexadecapole (Φαβγδ/ea40). Values at both ab initio up to the highly accurate couple cluster with singles and doubles (reference values) as well as different flavors of DFs: hybrid, GGA, double hybrid , long range corrected, including dispersion correction, both hybrid and long range corrected and some from the Minessota family. The target set is a group of 10 molecules of C2v symmetry. The results were further analyzed with the root mean square deviation (RMSD) method as to find the method that is the most proximal to reference CCSD. The functionals PBE1PBE, CAM-B3LYP and B2PLYP seem to survive the proximity test, whereas B97D, M05, M06 and M08 provide results that are the least proximal to CCSD ones.

#### Class of (n,m)-power-D-quasi-hyponormal operators in hilbert space

1Université chlef Algérie, Mathematics, Algeria

###### Abstract

In this paper, we introduce a new classes of operators acting on a complexe hilbert space H , denoted by [(n, m)DQH ], called (n, m)-power-D-quasi-hyponormal associated with a Drazin inversible operator usingits Drazin inverse. Somme propri- eties of (n, m)-power-D-quasi-hyponormal, are investigated and somme exemples. Keywords. Hilbert space, (n, m)-power-D-quasi-hyponormal operators, D-idempotent, power-D-quasi-hyponormal operators, (2, 2)-power-D-quasi-normal operators, Drazin inversible operator.

#### Test paper

Jack Taylor1

1University of London, Department of Informatics, United Kingdom

###### Abstract

Abstract goes here...

#### On the stability of exponential variational integrators for multibody systems with holonomic constraints

Odysseas Kosmas1

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

###### Abstract

In the present we test the stability of the high order exponential variational integrators when applied to mechanical systems with holonomic constraints. Those geometric integrator schemes are determined by a discretization of a variational principle for a discrete Lagrangian. That expression, which is defined using exponential expressions of interpolation functions, is then applied on the discrete Euler-Lagrangian equations with constraints. The resulting schemes are then tested on a typical dynamical multibody system with constraints, i.e the double pendulum, and show good long-time behavior when compared to other traditional methods.

#### Exploiting Dirac equations solution for exact integral calculations in processes of muonic atoms

P. Giannaka1 , Odysseas Kosmas2 , I. Tsoulos3 , Theocharis Kosmas4

1University of Ioannina, , Greece
2University of Manchester, School of Mechanical, Aerospace & Civil Engineering, United Kingdom
3University of Ioannina, , Afghanistan
4University of Ioannina, Physics, Greece

###### Abstract

Precise muon wave functions are calculated by solving the Dirac equations within a method based on modern neural networks and stochastic optimization techniques. The reduced radial wave functions (up and bottom) of a bound muon in muonic atoms are then given as linear combinations of the well behaved sigmoid functions. As concrete applications, the known muon- nucleus overlap integrals, which determine the structure and evolution of muonic atoms (two- body quantum systems bound together due to the fundamental electromagnetic interactions), may accurately be calculated. In this work, the muon-nucleus integrals for a set of nuclei including the 28Si and 64Zn entering the ordinary muon capture rates are exactly obtained through numerical integrations using Gauss integration algorithms.