Jorge Olivares Funes ^{1}
^{1}Universidad de Antofagasta , Departamento de Matemáticas , Chile
In this paper, we show how nonhomogeneous linear differential equations, especially those of the second order, are solved by means of GeoGebra applets by indeterminate coefficient methods and variation of parameters, for the course of differential equations of engineering students. and pedagogy in mathematics from the University of Antofagasta in Chile. The free software GeoGebra has caused that it is increasingly used in the teaching of mathematics, especially in nonhomogeneous linear differential equations, because it facilitates the teaching and learning process.
Jaykov Foukzon^{1}
^{1}Israel Institute of Technology, Department of mathematics, Israel
We introduce HausdorffColombeau measure in respect with negative fractal dimensions. Axiomatic quantum field theory in spacetime with negative fractal dimensions is proposed.Spacetime is modelled as a multifractal subset of $R^{4}$ with positive and negative fractal dimensions.The cosmological constant problem arises because the magnitude of vacuum energy density predicted by quantum field theory is about 120 orders of magnitude larger than the value implied by cosmological observations of accelerating cosmic expansion. We pointed out that the fractal nature of the quantum spacetime with negative HausdorffColombeau dimensions can resolve this tension. The classical Quantum Field Theory is widely believed to break down at some fundamental highenergy cutoff $E$ and therefore the quantum fluctuations in the vacuum can be treated classically seriously only up to this highenergy cutoff. In this paper we argue that Quantum Field Theory in fractal spacetime with negative Hausdorff Colombeau dimensions gives high energy cutoff on natural way. In order to obtain disered physical result we apply the canonical PauliVillars regularization up to $E$. It means that there exist the ghostdriven acceleration of the univers hidden in cosmological constant. http://arxiv.org/abs/1004.0451
Jorge Olivares Funes ^{1} , Pablo Martin^{2} , Fernando Maass^{3} , Elvis Valero^{4}
^{1}Universidad de Antofagasta , Departamento de Matemáticas , Chile
^{2}University of Antofagasta, Physics department, Chile
^{3}University of Antofagasta, Physics department, Chile
^{4}Universidad de Tarapacá, matemáticas, Chile
Fractional differential equations have a great importance and application. That is why the relationship between the fractional derivative and the erf (x) function will be shown below. The objective of this work is to solve the fractional differential equation D ^α y (x) =erf (x), and y(0) = 0, where 0<α<1. We will show the type of generalized hypergeometric solutions obtained by defining the fractional derivative of Caputo and the Laplace transform.
Pablo Martin^{1} , Jorge Olivares^{2} , Adrian Sotomayor^{3}
^{1}Universidad de Antofagasta, Física, Chile
^{2}Universidad de Antofagasta, Matemáticas, Chile
^{3}Universidad de Antofagasta, Matemáticas, Chile
New and more accurate approximation to the modified Bessel function I1 has been found by improving the multipoint quasi rational approximation method, MPQA. The approximation obtained in previous work (1) , has been improved by using the hyperbolic function sinh, instead of cosh. This change also the structure of the approximation , but there is not change in the structure of the approximation , and the number of parameters is also equal.Three terms of the power series and one term of the asymptotic expansion are also used to obtain the parameters of the approximation. In this way there is a decreasing of the relative error from 0.011 to 0.007 . A detail explication of the new procedure is carry on in this presentation. Ref. P. Martin, J. Olivares and A. Sotomayor, “ Precise Analytic Approximation for the Modified Bessel Function I1”, Rev. Mex. Física 63 (2017) 130 133 .
Jaykov Foukzon^{1}
^{1}Israel Institute of Technology, Department of mathematics, Israel
A new approach, which is proposed in this paper allows one to construct the Bellman function V(t,x) and optimal control u(t) directly,i.e.,without any reference to the Bellman equation, by way of using strong large deviations principle for the solutions ColombeauIto's SDE.
Franco Lindstron^{1}
^{1}Universidad Nacional de La Plata, Matemática, Argentina
This paper shows, for the first time, that the explicit and exact solution to the Troesch nonlinear twopoint boundary value problem may be computed in a direct and straightforward fashion from the general solution obtained by a generalized Sundman transformation for the related differential equation, which appeared to be a special case of a more general equation. As a result, various initial and boundary value problems may be solved explicitly and exactly.
yehuda roth^{1}
^{1}Oranim college, science, Israel
It is known that a dissipative environment is well described by the chaotic process while regular dynamics is associated with animate systems. In this paper, we explore the inverse map of some chaotic maps to find that they are always regular. The result that by reversing a chaotic map we obtain a regular process is associated with the birth of animate systems.
Manuel Fiolhais^{1}
^{1}University of Coimbra, Department of Physics, Portugal
The use of coherent states to describe boson systems goes back to the 1960's in the context of the radiation field. Since the 1970's, they have also been applied to meson clouds, mainly pions, in the context of the description of baryons by means of effective models involving a quark core surrounded by scalar and pseudoscalar mesons. The use of coherent states allows for an {\em abinitio} quantum mechanical description of the mesons, therefore going beyond semiclassical approximations. The coherent state e.g. for pwave pions (with angular momentum and isospin quantum numbers both equal to 1) is given by $\psi > = {\cal N}(\xi) \exp (\sum_{tm} \xi_{tm} a^\dagger _{tm} ) B> $ where ${\cal N}$ is a normalization factor, $  B > $ is a bare baryon state and $\xi_{tm}$ are amplitudes to be determined variationally. The $a^\dagger _{tm}$ is the creation operator for a pion state with angular momentum third component, $m$, and isospin third component, $t$. The radial profile of the pion amplitude results from a variational calculation and it is frozen. Hence, only angular momentum and isospin matters to construct the coherent state above. As already mentioned, the idea of mathematically modelling the meson clouds by means of coherent states, having in mind a full quantum mechanical description of baryon systems in the framework of chiral effective models, is not new. Actually, the author, among others, published several papers on the topic, in order to obtain various properties of the nucleon, the delta resonance and other excited states. However, the goal here is to bring together many aspects that are scattered in the literature, focusing on the versatility of the coherent states and stressing their capabilities. In this study, instead of the more realistic chiral effective models of quarks and mesons, we use a toy model whose Hamiltonian is written as $ H= \sum_{tm} a^\dagger_{tm} a_{tm} + G \sum _{tm} B_{tm} \left[ a_{tm} + (1)^{t+m} a_{tm}^\dagger \right]\!, $ where $B_{tm}$ is a baryon spinisospin operator. The model describes a system of non selfinteracting pions linearly coupled to a bare baryon core, $G$ being the coupling constant. This model is simple enough for its exact solutions to be worked out in the strong and weak regimes. These accurate solutions are then compared with the variational approximate solutions. Because the multiparticle coherent state, $\psi>$, cannot directly describe a nucleon, with definite angular momentum and isospin quantum numbers $\left( J={1\over 2}, I={1\over 2} \right)$, the PeiersYoccoz angular momentum (and isospin) projection method is used to construct a state, $\psi_N>$, with the proper nucleon quantum numbers. The variational method consists in minimizing the energy with respect to the amplitudes, i.e. $ d< H > / d \xi_{tm}=0 $, with the normalization condition $<\psi_N\psi_N>=1$ dully implemented in the process. We show that the socalled hedgehog configuration for the quark core and for the pion amplitudes minimizes the meanfield energy. On the other hand, we show that the (PeierlsYoccoz) projected coherent state is an extremely powerful ansatz since it reproduces the accurate solutions of the model both in the strong coupling regime (which is not surprising) but also in the weak coupling regime. We emphasise the use of the variationafterprojection method, for which the variational Hilbert space is larger, therefore with the trial function spanning a larger space than in the simpler variationbeforeprojection method. The toy model turns out to be a valuable tool to test different approaches which might be used in more realistic models with, for instance, selfinteracting mesons.
Yajuvindra Kumar ^{1}
^{1}Government Girls Degree College, Behat, Mathematics, India
In this paper, author studied free vibrations of a functionally graded (FG) annular plate having porosity. The plate is elastically restrained along the boundary. The material properties of the plate are Porosity dependent. An even porosity distribution is taken in the analysis. The mathematical model of the problem is developed using the concept of physical neutral surface of the plate. The physical neutral surface is taken as the reference plane. Out of many, only first three natural frequencies of the plate are reported using differential quadrature method (DQM). A parametric study is conducted to show the effects of porosity and material distribution parameters on the vibration behavior of the plate.
Yuriy Dimitrienko^{1} , Igor Krasnov^{2} , Kirill Zubarev^{3}
^{1}Bauman Moscow State Techical University, Fundamental sciences, Russian Federation
^{2}Bauman Moscow State Techical University, Fundamental sciences, Russian Federation
^{3}Bauman Moscow State Techical University, Fundamental sciences, Russian Federation
In this work the integration of two methods of electroinvestigation is considered. One method represents intubation by a direct current, the second intubation by alternating current. The integration is carried out for the purpose of increase in accuracy of results of the solution of the inverse task, the problem is solved in a twodimensional approximation. The direct task for the first and second method is solved numerically. The received values were compared with the experimental datas. The inverse task is formulated as a problem of minimization with the functional considering the experimental values received by both the first and second method of electroinvestigation. The problem of optimization is solved on a compact (for each parameter are set top and bottom border).
Julio S EspinozaOrtiz^{1} , Roberto E Lagos^{2}
^{1}Federal University of Goias, Physics, Brazil
^{2}UNESP, Rio Claro, SP, Departamento de Fı́sica, IGCE, Brazil
Billiards are physical models employed to probe experiments that measure the conductivity of quantum dots. In this context, the stadium billiard have been adopted as an standard model for realizations. We study the effect of softening this system in the classical mechanics, pursuing for a more realistic model. This classical approach is a first step towards the truly quantum or semiclassical case. We define the soft stadium as a monomial potential with an exponent {$\alpha\in\Re$} as a parameter, such that for {$\alpha=1$} the system is integrable and the {$\alpha\rightarrow\infty$} limit it converges to the hard billiard. Then, and for computational simplicity, we set up the construction of the classical Poincare map in such a way that it only depends on the partial separability of the system which holds for all {$\alpha$}'s. We present numerical results describing the classical transition from the integrable regime towards the chaotic regime.
The authors would like to thank the support of the Goi\'as Research Foundation  FAPEG.
Yannick Joel Wadop Ngouongo^{1}
^{1}University of Yaounde 1, Department of Physics, Cameroon
In connection with stochastic resonance (SR), we study the dynamics of a particle in the deformable travellingwave potentials in the presence of the external excitation force and the thermal fluctuations force. We model the deformation of the systems by the i) asymmetric deformable onsite potential (ASDP) and ii) double well deformable onsite potential (DWDP). The phenomenon of SR is known to take place in sinusoidal and nonsinusoidal systems. However, the question of the appeareance of SR in the ASDP as well as DWDP systems has not been resolved. The cooperative effect of noise and external force does show up in these systems. This numerical work presents the characterization of SR through an investigation of the input energy lost by the system to the environment per period of the external force which is also equivalent to the hysteresis loop area or average input energy. SR is characterized by the presence of a peak when the temperature increases. A double SR is observed in the ASDP case, first peak occurring at weak temperature has nothing to do with usual mechanical resonance. But it just associated to intrawell dynamics. However, second peak arising at higher temperature, relates to a classical SR phenomenon. In the DWDP case, only one resonance peak is observed. In both the systems the average input energy of occurrence of SR nonmonotonically depends of the shape parameter. We show that at low temperature the input energy depends very strongly on the initial positions of the particle. For each of the two models, this input energy is confined to two narrow bands in some range of the shape parameter. The input energy distribution of these is also explored. As function of the shape parameter, it can be unimodal or bimodal. Using the DWDP system, we investigated the presence of Chaos in the system in the goal to show that the disappearance of SR in the system can be due to Chaos.
Hafedh Zghidi^{1}
^{1}Silesian University of Technology , Institute of Informatics, Poland
The article presents a complete solution for filtering and diffusive fractal characterization of 2dimensional images. This includes preparing the sample by subtracting background, application of random walk procedure and its parallelization using two different approaches. For each technique the processing time is measured to compare speedups with regard to a sequential implementation. To prove the correctness of the results, a black square is used as the reference sample, for which diffusive fractal dimension is known and equls 2. Finally the results for a complex image are elaborated.
Pantea Davoudifar^{1} , Keihanak Rowshan Tabari^{2}
^{1}Research Institute for Astronomy and Astrophysics of Maragha, Astroparticle Physics, Iran (Islamic Republic of)
^{2}Research Institute for Astronomy and Astrophysics of Maragha, , Iran, Islamic Republic Of
In space physics the use of living organisms is not always possible. To study the environment condition, here a method were developed to create a network of given neurons. Different geometrical structures of the neurons were built using biological constraint. The fluence dose due to cosmic radiation were studied for the resulted structures. A factor of survival were defined and the structures were studied under short and long term radiation dosimetry. The effect of solar cycles and solar events were studied on radiation environment.
Andry Sedelnikov^{1} , Ekaterina Khnyryova^{2}
^{1}Samara National Research University, , Russian Federation
^{2}Samara national research university , Further Mathematics , Russian Federation
To know and understand the conditions of carrying out technological processes it is necessary to estimate the rotational motion parameters of the spacecraft. The parameters of the AIST small spacecraft rotational motion around its center of mass were estimated using measurement data of current from solar panels. At the same time, there is a problem in interpretation the telemetry data from small spacecraft: sometimes the significant current was recorded on two opposite solar panels. The paper shows a way to solve this problem using the fuzzy sets. As a membership function it is offered to use the normality condition of the direction cosines. The processing of telemetry data is given for AIST small spacecraft prototype. The offered approach can significantly increase the accuracy of angular velocity estimating using measurements of current from solar battery.
Avi Messica^{1} , Asnat GreensteinMessica ^{2}
^{1}COMAS, Finance and Quantitative Methods, Israel
^{2}BenGurion University of the Negev, Data Science and Information Systems, Israel
A new emerging technology, viewed as disruptive, occasionally generates a surge of public expectations over its potential application. This collective excitation (and decay) is generated and diffuses in a complex array of large random networks (e.g. social, media) that are difficult to model via small world models. Former studies of this phenomenon – termed as hype cycle  have focused mainly on descriptive, few casestudies, analysis using a corpus of newspaper articles and explained specific dynamics in a specific context. Motivated by the lack of a mathematical model, we studied a simple twophase mean field model that is able to explain the dynamics, as well as various patterns, of correlated expectations. Our contribution is as follows, we used an online query data (via Google Trends) as a proxy for public expectations to study more than one hundred technologies. We extended the classification of the diffusion pattern with three new categories to better reflect different observed dynamics. Lastly, we present a datadriven mathematical model that enables to draw useful insights on the rich dynamics of hype cycles.
Serena Doria^{1}
^{1}University G.d'Annunzio ChietiPescara, Department of Engineering and Geology, Italy
A new mathematical model of coherent upper conditional expectations based on Hausdorff outer measures is proposed in a metric space $(\Omega,d)$ to make prevision when the conditioning events are fractal sets, i.e. sets with noninteger Hausdorff dimension. The necessity to propose a new tool to define coherent upper conditional expectations arises because they cannot be obtained as extensions of linear conditional expectations defined, by the RadonNikodym derivative, in the axiomatic approach (Billingsley, 1986); it occurs because one of the defining properties of the RadonNikodym derivative, that is to be measurable with respect to the $\sigma$field of the conditioning events, contradicts a necessary condition for the coherence. Given a partition $\textbf{B}$ of $\Omega$ for every $B \in \textbf{B}$ denote by $s$ the Hausdorff dimension of $B$ and let $h^{s}$ be the Hausdorff $s$dimensional Hausdorff outer measure associated to the coherent upper conditional expectation $. For every bounded random variable $X$ a coherent upper conditional expectation $\overline{P}(XB)$ is defined by the Choquet integral with respect to its associated Hausdorff outer measure if the conditioning event has positive and finite Hausdorff outer measure in its Hausdorff dimension. Otherwise if the conditioning event has Hausdorff outer measure in its Hausdorff dimension equal to zero or infinity it is defined by a 01 valued finitely, but not countably, additive probability.
ZhongCheng Liang^{1}
^{1}Nanjing University of Posts and telecommunications, College of Electronic and Optical Engineering , China
Pointlike and wavelike particles are foundations of classical and modern physics. They are so idealized models that lose the physical authenticity. Real particles are threedimensional body with mass and volume. The spatial intersection of real particles is empty set, thus ensuring limited density of particles. In the centreofmass frame of reference, a real particle has three independent modes of motion: vibration, rotation and translation. Three mode energies $(H,L,K)$ constitute a Cartesian space. The energy space is quantized by vibrating quantum $(H_s=Y_s V_s=hv)$, rotating quantum $(L_s=I_s ω_s^2=lz)$ and translating quantum $(K_s=M_s u_s^2=kT)$. The energy space is divided into six phases and three zones. Three zones represent gas, solid and liquid state of object. There are three equilibrium surfaces, each of which has two stable areas and two excited areas. Two types of phase transition are distinguished by two types of phase interface. Complete energy relations and differential equations can be derived through the statistics of particle ensemble. The results show that the order parameters of liquid, solid and gas are the correlative functions of the particle mass $(M)$, the rotary inertia $(I)$ and the elastic modulus $(Y)$, respectively. Thermodynamic laws are the natural inferences of the theoretical results. A physical theory based on the real particle model has simplicity, consistency and universality.
Mayken EspinozaAndaluz^{1}
^{1}ESPOL, Centro de Energías Renovables y Alternativas, Ecuador
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 Yshaped 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 voltagecurrent behaviour considering the materials, fuel/oxidant and design characteristics has been obtained from a modelling point of view.
The authors kindly acknowledge the financial support from FIMCPCERA052017. In addition, Åforsk project No 17331 is gratefully acknowledged.
HSIENCHUNG KAO^{1}
^{1}National Taiwan Normal University, Physics, Taiwan
It has been shown in the literature that doped twodimensional Hubbard model may exhibit strange metallic transport behavior. We use the covariant Gaussian approximation to study charge and spin correlators in the antiferromagnetic phase of in the Hubbard model. The results are then compared to those of quantum Monte Carlo calculations to verify whether such phenomenon does occur.
Vania Rangelova^{1}
^{1}Technical University Sofia  branch Plovdiv, Electrical Engineering, Bulgaria
The biosensor amperometric transducers can work in the case of three basic types of reversible inhibitor enzyme systems – with competitive inhibition, with noncompetitive inhibition and mixed inhibition. Tipicaly they work in static mode. Now they are investigated in dynamic mode. The kinetic in those type biosensors is generally discussed in terms of a simple extension to the MichaelisMenten reaction scheme. The investigated biosensors are amperometric product sensitive. The parameters for simulations are chosen from some real experiments with biosensors. The models are described in non stationary diffusion conditions. Solving system of nonlinear partial differential equations is reseived in three dimensional size and the concentration profiles in active membrane of substrate S(x,t), inhibitor I(x,t) and product P(x,t) are reseived. The systems of nonlinear differential partial equations have been solved numerically in MATLAB medium. The influence of starting concentration of substrate, inhibitor and kinetic parameters  reaction constants of biosensors for substrate and for inhibitor over output current have been investigated.
Yuriy Dimitrienko^{1} , Kirill Zubarev^{2} , Igor Krasnov^{3}
^{1}Bauman Moscow State Techical University, Fundamental sciences, Russian Federation
^{2}Bauman Moscow State Techical University, Fundamental sciences, Russian Federation
^{3}Bauman Moscow State Techical University, Fundamental sciences, Russian Federation
This article discusses the results of solving the problem of electrical exploration using direct current. The developed methods and algorithms for solving the direct and inverse exploration tasks are tested on several inhomogeneous models of the environment. The task is considered in threedimensional approximation. To solve using the finite element method. On the basis of the direct problem algorithm, a method for solving the inverse problem was implemented, which consists in finding the minimum of the deviation functional, which in turn leads to the multiple solution of the direct problem. The obtained results were analyzed, the advantages and shortcomings of the developed methods were revealed, the evaluation of the search time for the optimal solution for the inverse problem was carried out, and the dependence of the solution accuracy on the thickening of the grid when solving the problem by the finite element method was discussed.
Sabine Upnere^{1}
^{1}Riga Technical University, Institute of Mechanics, Latvia
The numerical modelling of crossflow through the rods bundle with triangular arrangement has been done to analyse flowinduced forces on the rod located in the middle of the bundle. Significant problems of rods in the bundle during the operational time of the system can be caused by the crossflow. At the same time, it is known that the behaviour of the system is strongly related to many parameters such as bundle geometry, flow, rods support and others. Therefore, there is needed to investigate the characteristics of each type of typical bundles. In this paper is analysed flowinduced hydrodynamic forces in closelypacked rods bundle using Computational Fluid Dynamics. Unsteady Reynolds Averaged NavierStokes equations are solved using Finite Volume discretization. The impact of the size of the computational domain and the number of rows in it was investigated to find the optimal case for numerical modelling. Obtained results are compared with references from literature and experimental data.
Ashraf Zaher^{1}
^{1}American University of Kuwait, Electrical and Computer Engineering, Kuwait
This paper proposes an efficient technique for detecting mechanical faults in threephase induction motors, without using mechanical sensors. Only measurements of the currents of every phase are used to identify the fault. The proposed system can diagnose two types of faults corresponding to shaft misalignment or imbalance, along with normal operation. The power spectrum of the experimental data is generated, followed by applying a softcomputing mathematical algorithm that will extract the peaks of the fundamental frequencies and their harmonics, while filtering out noise. These peaks will be compiled in a vector form such that it can be used as inputs to train an artificial neural network (ANN) to produce a decision regarding the operating condition of the motor, via applying intelligent pattern recognition techniques. Mathematical details regarding the structure of the ANN, its training, tuning of its synaptic weights, and the testing/validation phase will be investigated. Detailed analysis of the obtained results is provided to highlight the advantages and limitations of the proposed algorithm. In addition, a comparison is made with similar techniques that use mechanical sensors to contrast their differences and highlight the superiority of the proposed system. The obtained results prove the intelligence and robustness of the proposed system and allows for versatile extensions that promote its application in realtime scenarios for many industrial applications.
This work was supported by a grant from the American University of Kuwait, during the academic year 201819.
Santanu Chatterjee^{1} , Sanjoy Mukherjee^{2}
^{1}RGM International (India) Pvt. Ltd., Civil, India
^{2}KEC International Limited, Engineering Services, India
For decades, scientists have worked relentlessly to move forward to see what lies beyond the third dimension and to find out if there is any existence of a unified theory to explain all the workings of the universe from subatomic to gigantic inhabitants of cosmos. This insurmountable task has been taken on by many over the last century or so until the emergence of “super string theory” or “string theory” happened showcasing the fact that an answer seemed possible. From the concepts of a “string”, our ideation on this theory started. In this paper we strived to put forward that the concept of a vibrating onedimensional microscopic object named “string” can be taken as a fundamental ingredient (in place of point particle) for developing nonrelativistic quantum mechanics. Unlike point particle, we take a vibrating string as the quantum object & build a perfectly reasonable quantum mechanical description of the microscopic world. Our main objective in this paper to show that complete development of quantum mechanics is possible based on one dimensional open string.
Santanu Chatterjee^{1} , Sanjoy Mukherjee^{2}
^{1}RGM International (India) Pvt. Ltd., Civil, India
^{2}KEC International Limited, Engineering Services, India
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 indepth 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.
Nadir MAGHLAOUI^{1}
^{1}Higher School of Applied Sciences, Physics, Algeria
Phasedarray transducer are becoming of common use in ultrasound imaging either in medical applications or in the field of non destructive technique. The modelling of the acoustic field emitted by phasedarrays transducers can be realized by different methods developed in the frequency domain or in the time domain. The method proposed here consists in using the Rayleigh integral method where the reflection at the plane interface is taken into account by using the reflection coefficients for harmonic plane waves. The transient field is obtained by an inverse Fourier transform of the harmonic results. The results obtained put in evidence the fact that the ultrasonic waveforms reflected by a liquidsolid interface and detected by the phasedarrays transducer depend strongly on the geometrical and physical parameters of these kind of transducers. The transient representation of these waves have been analysed and discussed by the rays model. . A potential application of this work would be the study of the acoustic signature of materials by using phasedarrays transducer working in pulsed mode. The obtained results have been compared to those obtained by using a finite element method package.
Esha Kashyap^{1} , Kannan Sr^{2}
^{1}Pondicherry University(A Central University of India), Mathematics, India
^{2}Pondicherry University(A Central University of India), Mathematics, India
This paper reviews the influence of kernel function in unsupervised way of clustering in data analysis. Unsupervised clustering analysis is considered as an explorative data analysis tool that assists in discovering hidden patterns or natural grouping in data, and has been effectively applied in various applications. The implementation of kernel function with the objective functions of unsupervised clustering techniques contribute an effective works for recognizing nonlinear structures of high dimensional databases and the objective functions are robust in clustering the high dimensional databases which contains outliers with heavy noise. This paper mainly discusses the kernels with the objective functions of fuzzy cmeans, possiblistic cmeans, and intutionistic fuzzy cmeans for clustering the nonliner structured databases. Experimental section of the paper supports to understand the effective of kernel in various clustering methods.
This work was financially supported by DST India and MOST Israel
Uri BenYa'acov^{1}
^{1}Kinneret Academic College on the Sea of Galilee, School of Engineering, Israel
Is it possible to encompass the full extent of the Universe with a finite number of first principles and inference rules ? The belief that it is possible to arrive at a complete theory that fully describes the whole of the physical world – a theory that accounts, via few and simple first principles, for all the phenomena already observed and that will ever be observed – has been, for manymany years and for most researches, a fundamental tenet of the scientific research. However, Gödel's incompleteness theorem implies that any formal structure, based on a finite number of first principles and inference rules, which is rich enough, cannot be at the same time both consistent and complete. Completeness, in terms of physical theories, implies that if the necessary initial data are given then the state of a physical system can be predicted for any time in the future. Does Gödel's theorem apply to physics ? A common argument in favour of applying Gödel's theorem to physics, is, more or less, that "Gödel's theorem applies to arithmetics which is the basis of mathematics, physics uses mathematics, therefore Gödel's theorem applies to physics". However, the counterargument says that there are mathematical theories to which Gödel's theorem does not apply, e.g. geometry, and that this is the type of mathematics that physics uses, therefore we should not expect that Gödel's theorem applies to physics. The purpose of the talk is to present and put forward another argument, which I believe is the decisive one. Gödel's theorem (whenever it applies) points to incompleteness in the sense that there will always be claims that may be formulated within this formal system but are undecidable – propositions that cannot be either proved or refuted. A close inspection of Gödel's theorem demonstrates that this impossibility arises when the claims are selfreferential, or, more precisely, when the system asks to define itself in its own terms. Selfreferencing occurs in physics whenever the observer is also part of the observed system. In most physical system this is not the case, therefore the counter argument should apply. However, when it is the whole Universe that is dealt with, then we, the observers, are also part of it, and Gödel's theorem should apply. The talk will discuss selfreferencing in Gödel's theorem, its relation with our involvement in the Universe, and consequences thereof.
Lingfei Zhang^{1} , Xinquan Lai^{2} , Jun Ma^{3} , Chen Liu^{4} , Yun Zhang^{5}
^{1}Qinghai Nationalities University , College of Physics and Electronic Information Engineering , China
^{2}Xidian University, The Institute of Electronic CAD, China
^{3}Qinghai Normal University, School of Computer, China
^{4}Xidian University, The Institute of Electronic CAD, China
^{5}Xidian University, The Institute of Electronic CAD, China
Aiming at the heat dissipation problem of the cavity structure of electronic packaging. Firstly, according to the theory of thermal field analysis and the nonlinear finite element formula of thermal field, the thermal field finite element model for the cavity structure of electronic packaging is established. Depend on the cavity structure of electronic packaging, the thermal field distribution in different situations of the electronic packaging cavity structure is simulated, considering the thermal field analysis of the cavity under the influence of gravity field. In addition, under the influence of the heat source of single or multiple heating electronic components and the effect of radiation, convection, conduction of heating electronic components, the thermal field distribution in the package structure and the characteristics of thermal field are analyzed. Finally, the thermal field analysis of the electronic packaging cavity structure under forced air cooling is discussed.
Alena Astrakhantseva^{1} , Alexander Chebotarev^{2} , Andrey Kovtanyuk^{3}
^{1}Far Eastern Federal University, Department of computer science, mathematical and computer modelling, Russian Federation
^{2}Far Eastern Federal University, Institute for Applied Mathematics FEB RAS, , Russian Federation
^{3}Far Eastern Federal University, Institute for Applied Mathematics FEB RAS , , Russian Federation
Endovenous laser ablation is a very effective minimally invasive therapy to manage leg varicosities. The corresponding mathematical model is based on conversion of absorbed laser energy into heat. To describe the process of endovenous laser ablation, the radiativeconductive heat transfer model with moving source is chosen. The conventional nonstationary normalized $P_1$ approximation of the radiativeconductive heat transfer model is considered in a bounded domain $\Omega \subset \mathbf{R}^3$ which consists of a finite number of disjoint subdomains $\Omega_j$, $j=1,..., p$\,: \begin{equation}\label{1} a \partial\theta/\partial t  \mathrm{div}\,(k\nabla\theta)  b \varphi = u_1,\;  \mathrm{div}\,(\alpha \nabla \varphi) + \beta \varphi = u_2,\; x\in\Omega,\ t\in (0,T). \end{equation} Here, $\theta$ is the normalized temperature; $\varphi$ is the normalized radiation intensity averaged over all directions; $k$ is the thermal conductivity; $a$, $b$, $\alpha$, and $\beta$ are piecewise constant functions describing the thermal and radiation properties of the medium (see, e.g., \cite{1}), $a(x)=a_i$, $b(x)=b_i$, $\alpha(x)=\alpha_i$, $\beta(x)=\beta_i$ if $x \in \Omega_i$, $j=1,..., p$. The functions $u_{1,2}=u_{1,2}(x,t)$ describe the intensities of heat and radiation sources. Let $k(x) = k_j$ if $x \in \Omega_j$, $j=2,...,p$\,;\, $k(x) = c(\theta) k_1$ if $x \in \Omega_1$, where $c(\theta) = 1$ if $\theta < \theta_*$, and $c(\theta) = m > 1$ if $\theta \geq \theta_*$\,;\, $k_1, ... k_p, m = Const$. The subdomain $\Omega_1$ corresponds to blood fraction, and the factor $c(\theta)$ simulates the rise of thermal conductivity due to boiling effect. We consider the righthand sides of equations (1) having the structure $u_{1,2} = P_{1,2}(t)f_\varepsilon(x,r(t))$, $x\in \Omega,\,t\in (0,T)$. The functions $P_{1,2}$ describe the powers of heat and radiation sources, $f_\varepsilon(x,r(t))=1$ if $xr(t)<\varepsilon$, and $f_\varepsilon(x,r(t))=0$ otherwise; $r(t)$ is a given trajectory of a moving source. The following boundary conditions on $\Gamma := \partial \Omega$ and the initial condition at $t=0$ are assumed: \begin{equation}\label{2} a\partial_n \theta + h(\theta  \theta_b)_\Gamma = 0,\;\; \alpha\partial_n \varphi + 0.5\varphi_\Gamma = 0, \quad \theta_{t=0} = \theta_0. \end{equation} Here, $\partial_n$ denotes the derivative in direction of the outward normal $n$; the boundary functions, $\theta_{b}$, $h$, and the initial function, $\theta_0$, are given. Let $\theta_i(x) = \theta(x)$ and $\varphi_i(x) = \varphi(x)$ if $x \in \Omega_i$, $j=1,..., p$. At the internal boundaries between adjoint subdomains $\Omega_i$ and $\Omega_j$, \, $1 \leq i,j \leq p$,\, $i \neq j$, we set the following conjugation conditions: \begin{equation}\label{3} \theta_i = \theta_j, \;\; a_i\partial_n \theta_i = a_j\partial_n \theta_j, \;\;\; \varphi_i = \varphi_j, \;\; \alpha_i\partial_n \varphi_i = \alpha_j\partial_n \varphi_j,\;\;\; x \in \overline{\Omega}_i \cap \overline{\Omega}_j. \end{equation} In the current work, a priori estimates of temperature and radiation intensity in the space $L^{\infty}$ ensuring the unique solvability of the problem (1)(3) are presented. The theoretical analysis is illustrated by numerical examples simulated the process of endovenous laser ablation. \begin{thebibliography}{9} \bibitem{1} G.V.~Grenkin, A.Yu.~Chebotarev, A.E.~Kovtanyuk, N.D.~Botkin, K.H.~Hoffmann, \textit{J. Math. Anal. Appl.}, \textbf{433}, 12431260 (2016). %\bibitem{2} A.E.~Kovtanyuk, A.Yu.~Chebotarev, N.D.~Botkin, K.H.~Hoffmann, \textit{Commun. Nonlinear Sci. Numer. Simulat.}, \textbf{20}, 776784 (2015). \end{thebibliography}
Marco Zoli^{1}
^{1}University of Camerino, School of Science & Technology, Italy
The stability properties of dsDNA are important in a number of molecular biology techniques (e.g., polymerase chain reaction) and nanotechnological devices (e.g., DNAbased sensors) in which short fragments of synthetic DNA are used as a recognition element by virtue of the peculiar WatsonCrick base pairing, allowing for selective hybridization with a target sequence. The helix stability properties are also key to single molecule denaturation mapping experiments, recently used combined with nanochannel arrays, which confine and stretch the DNA molecule to be analyzed. These techniques are based on the fact that AT rich regions melt at lower temperatures than GC rich regions; staining the molecule with a fluorescent dye that binds only to ds regions one obtains an optical barcode unique to the sequence of the specific molecule. The DNA properties are also strongly affected in confined conditions as those which occur in vivo in the crowded environments of cells where macromolecules \textit{i)} reduce the free volume for base pair fluctuations thus suppressing the melting entropy, \textit{ii)} interfere with the dynamics of DNA looping thus affecting the speed of gene activation or repression. While considerable amount of experimental work has been carried out over the last decades to investigate the relation among macromolecular crowding, DNA dynamics and its biological functioning, much less theoretical studies have been produced so far on DNA in crowded conditions. Here I focus on the interplay between DNA structure and confining environment analyzing how a crowders distribution around a single DNA chain may concur to shape the helical conformation and the overall size of the molecule itself. The study assumes a coarse grained Hamiltonian model which describes the helical molecule at the level of the base pair. The equilibrium statistics of the system is obtained by a computational method based on a finite temperature path integral method which I have developed over the last years. The method has been widely discussed in conjunction with calculations of some fundamental indicators of DNA flexibility at short length scale such as the cyclization probabilities, the persistence lengths and the single molecule response to stretching perturbations induced by external loads. After reviewing the method and previous researches, I present some recent results regarding the stretching and twisting of short DNA fragments simulating the presence of specific crowders profiles.
Manuel De la Sen^{1}
^{1}University of the Basque Country, Elwctricity and Electronics, Spain
This paper is concerned with the investigation of the global stability and global asymptotic stability of the error with respect to its nominal version of a nonlinear timevarying perturbed functional differential system which is influenced by point, finitedistributed and Volterratype distributed delayed dynamics. The boundedness of the error and its asymptotic convergence to the zero equilibrium are investigated and some formal “ ad hoc” results are proved.
Alexey Smolin^{1}
^{1}Institute of Strength Physics and Materials Science of Siberian Branch of Russian Academy of Sciences, Laboratory of ComputerAided Design of Materials, Russian Federation
Full understanding of the mechanical behaviour of living bone is the key to solving many important problems of modern orthopaedics and arthroplasty. An important role in the study of the mechanical behaviour of living bone belongs to the development and use of comprehensive numerical models. In this work, we model the mechanical behaviour of the proximal femur as a 3D poroelastic solid consisting of the interior cancellous part and the outer cortical part. For simplicity, both parts are assumed to be isotopic linear poroelastic material. But they have different values of porosity, fluid content and elastic properties, which are taken from literature. For computer simulation, we used the socalled movable cellular automaton method, which is a representative of simply deformed discrete elements i.e. computational particle mechanics. The method allows simulating dynamics of the elastic skeleton deformation and viscous fluid flow in the skeleton pores according to Biot’s theory of linear poroelasticity. Using the model developed we study the mechanical behaviour of the proximal part of the femur in compression with different rate of loading and different boundary conditions. The results obtained for both saturated and drained bones are discussed.
The investigation has been carried out at financial support of the grant No. 171101232 of the Russian Science Foundation (the models developed and the simulations) and framework of the Russian Fundamental Research Program of the State Academies of Sciences for 2013–2020 (Priority direction III.23, the modifications of the MCA software for importing CAD models and modelling pore structure).
Andrei Melekhin^{1}
^{1}National Research Moscow State University of Civil Engineering, Heat and gas supply and ventilation, Russian Federation
The modeling of the process of cleaning polluted washing water in circulating water use systems and solutions to the problems of optimizing the process parameters.
Irina Mazilu^{1} , Anthony Lorson^{2} , Sho Gibbs^{3} , Will Hanstedt^{4} , Dan Mazilu^{5}
^{1}Washington and Lee University, Department of Physics and Engineering, United States
^{2}Washington and Lee University, Physics and Engineering, United States
^{3}Washington and Lee University, Physics and Engineering, United States
^{4}Washington and Lee University, Physics and Engineering Department, United States
^{5}Washington and Lee University, Department of Physics and Engineering, United States
As the political landscape becomes increasingly complex, the classic paradigms used in political science have failed to remain relevant and other methods of study are needed. We use a multitemperature kinetic Ising model to analyze the partisanship dynamics of the US Senate. We use Monte Carlo simulations, mean field theory and numerical analysis of the master equation of a system of 100 senators (agents) separated into various categories based on their political leanings and interactions with each other. Results show an interesting development of partisanship between the agents after a short time. The model can be extended to other cooperative stochastic systems in physics and social sciences.
Matthew Withers^{1} , Elise Baker^{2} , Dan Mazilu^{3} , Irina Mazilu^{4}
^{1}Washington and Lee University, Department of Physics and Engineering, United States
^{2}Washington and Lee University, Department of Physics and Engineering, United States
^{3}Washington and Lee University, Department of Physics and Engineering, United States
^{4}Washington and Lee University, Department of Physics and Engineering, United States
We design and model an experiment to study the effect of electric bias on particlecoverage densities produced during ionic nanoparticle selfassembly. The experiment involves the application of a uniform external electric field parallel to a glass substrate during the selfassembly of silica nanoparticles. We refer to this procedure as directed selfassembly of monolayers (DSAM). In our theoretical analysis, we modify existing cooperative sequential adsorption models to account for diffusion under an applied electric field. We use the mean field approximation to solve for particlecoverage densities. To ascertain the validity of this method, we compare our solutions to Monte Carlo simulations of the system.
Elise Baker^{1} , Matthew Withers^{2} , Emma Aldrich^{3} , Isabel Shaffrey^{4} , Justin Pusztay^{5} , Dan Mazilu^{6} , Irina Mazilu^{7}
^{1}Washington and Lee University, Department of Physics and Engineering, United States
^{2}Washington and Lee University, Department of Physics and Engineering, United States
^{3}Washington and Lee University, Department of Physics and Engineering, United States
^{4}Washington and Lee University, Department of Physics and Engineering, United States
^{5}Washington and Lee University, Department of Physics and Engineering, United States
^{6}Washington and Lee University, Department of Physics and Engineering, United States
^{7}Washington and Lee University, Department of Physics and Engineering, United States
We present a class of cooperative stochastic models for adsorption and evaporation of monomers on two and threedimensional lattices subjected to perpendicular external electric fields. These models are motivated by the fabrication of optical coatings using layerbylayer selfassembly. We report computational and analytical results for the timedependent particle density and discuss a particular experimental implementation of an ionic selfassembled monolayer under the influence of a constant electric field.
Dan Mazilu^{1} , Matthew Withers^{2} , Will Hanstedt^{3} , Sho Gibbs^{4} , Anthony Lorson^{5} , Irina Mazilu^{6}
^{1}Washington and Lee University, Department of Physics and Engineering, United States
^{2}Washington and Lee University, Department of Physics and Engineering, United States
^{3}Washington and Lee University, Physics and Engineering Department, United States
^{4}Washington and Lee University, Department of Physics and Engineering, United States
^{5}Washington and Lee University, Physics and Engineering, United States
^{6}Washington and Lee University, Department of Physics and Engineering, United States
We present a versatile cooperative threestate model with adsorption and evaporation defined on different topologies: two and threedimensional lattices and Cayley trees. We discuss this model in the context of two main applications: silica and titania selfassembled optical coatings on glass substrates and drug encapsulation of two different types of nanoparticles on treelike synthetic polymers called dendrimers and described mathematically as Cayley trees. We present analytical and Monte Carlo simulation results for these different topologies and discuss other possible extensions of the model to social sciences.
Daniel Clark^{1}
^{1}Washington and Lee University, Department of Physics and Engineering , United States
The polarization and intractability of American politics has received increased scrutiny throughout the 21st century. We attempt to model the complex mechanisms of political cooperation in a finite democratic system. Due to the shorter termlimits and subsequently limited external influences, we select the House of Representatives as an ideal setting to examine the interactions between United States politicians, and therefore we utilize the structure and political topology of the 115th House of Representatives for recent, realistic data. Within this model, legislation is first voted on in a small committee before moving to the entire House. Throughout these voting steps certain agents are assigned a maverick state, which holds their initial vote as fixed, while others’ votes vary based on political values and social influences. At each step the votes and transitions of each agent are studied using Monte Carlo Simulations on networks and network theory. We study the dynamics of both committees and the House as a whole, specifically the impact of inflexible voters, political alignments, and party affiliations.
Alexander Chernyshev^{1} , Leonid Kurochkin^{2}
^{1}Ioffe Institute, Computational Physics Laboratory, Russian Federation
^{2}Peter the Great St.Petersburg Polytechnic University , , Russian Federation
Simulation of a payload of a road network is important for design or optimization of such networks. Realtime simulations (Pell et. al., 2017) or predictive simulations in specific conditions can help in redistribution of vehicles and help emergency services reaching problematic areas faster. The hybrid discretecontinuum approach is proposed to carry on simulations of complex areas. SUMO model (Krajzewicz et. al., 2012) is used for discrete approach and describes road junctions and crossings which are smallscale parts. Discrete approach becomes quite resource demanding with the increase of vehicles simulated but provides detailed information about the region under the interest. Continuum approach is based on the NavierStokes equations (Wagner, 1997) of fluid medium and is capable of resolving largescale areas (like straight parts of roads). It does not depend on the number of vehicles but lacks details about whole picture. Combination of both of them can provide consistent model for the description of areas of different scale. The present work is focused on the simulation of a complex road network which consists of a set of road junctions and extended roadways. The network is split into small parts each of which is treated either by discrete or continuum model. At a connection of each pair of parts the data is sampled to get time distribution for the discrete model (for the continuumtodiscrete interpolation) or integrated to get averaged car distribution (for the discretetocontinuum interpolation). Computational process is carried out either till the convergence (for steadystate problems) or for a specific period of time. Traffic flow at the output points of road network is measured and compared with the predictions. The purpose of this study is to develop criteria for the transition between discrete and continuous description in models of transport networks. The resulting criteria will reduce the computational complexity of models of transport networks. The results of the work will allow the simulation of intelligent transport systems using various data transmission tools (including mesh, LTE, DSRC). Future work will be focused on the incorporation of data network simulation. Taken into account that each vehicle can act as an endpoint in the mobile traffic network (either by installed equipment or driver’s mobile devices) traffic jams can also cause a decay in total data network throughput. Simultaneous simulation of both road and data networks is a challenging problem and requires additional modification of the proposed model.
The work is supported by the Russian Foundation for Basic Research, grant No. 180700430
Dmitrii Kiselyov^{1} , Igor Inovenkov^{2} , Vladimir Nefedov^{3}
^{1}Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics, Russian Federation
^{2}Lomonosov Moscow State University, Department of Computational Math & Cybernatics, Russian Federation
^{3}Lomonosov Moscow State University, Department of Computational Math & Cybernatics, Russian Federation
The problem of the interaction of various population groups in the framework of urban environment is of current interest this time. The population is divided into different strata according to their economic and social characteristics. For example, a population could be classified according to genetic and phenotypic characteristics, belonging to a particular ethnic group and, first of all, according to income level. In a number of countries, the coexistence of population groups belonging to different social strata gives rise to serious problems and therefore has been studied from different points of view, mainly from a sociological. Due to the qualitative analysis of various situations, it becomes possible to predict and prevent possible conflicts and problems. The significance of this problem is obvious, but reasonable proposals for its solution have not been put forward. In this regard, the construction of a qualitative, but fairly general mathematical model of the dynamics of various groups of the population is of particular interest. Such a mathematical model should be built within the framework of the concept of spatial economics. This paper discusses the first version of the model for a situation where there are only two groups of people. The corresponding system of equations includes two nonlinear diffusion equations with terms describing the interaction of the population groups in model. Of course, the basic difficulty is the selection of coefficients, which will provide the picture as close as possible to reality, so it makes sense to add to the model and stochastic terms that will be responsible for random environmental factors. Thus, a twodimensional stochastic model of the temporal dynamics of the distribution of two population groups in an urban environment was presented and numerically investigated. As a result of the mathematical modeling certain estimates were obtained regarding the feasibility of taking into account stochastic factors in the proposed mathematical model.
Igor Emel'yanov^{1} , Alexey Polyakov^{2} , Anastasia Hodak^{3}
^{1}Ural Federal University, Institute of Engineering Science, Russian Academy of Sciences (Ural Branch) , , Russian Federation
^{2}Ural Federal University, Institute of Fundamental Education, Russian Federation
^{3}Ural Federal University, Institute of Fundamental Education, Russian Federation
An approach is proposed to solve the problem of estimating the stress state of a shell structure loaded with a thermomechanical load and in contact with a hydrogencontaining medium. The stress state of the steel housing of the diffusion apparatus for the production of highly pure hydrogen was determined. The object of study is presented in the form of a composite shell of rotation, loaded by internal pressure and operating at elevated temperatures. The purpose of the work is to determine the stress state of the shell at normal and elevated pressure, taking into account changes in the mechanical properties of the combined effect of temperature and hydrogen. In the general case, the task of calculating such a structure under given operating conditions is related. But for processes with different physical times, it can be represented by a sequence of individual problems of heat propagation, hydrogen diffusion, and the calculation of the stress state. In the phenomenological approach, the relationship between thermal diffusion and mechanical problems is manifested in a change in the parameters of the sample deformation diagram with increasing temperature and hydrogen concentration. The integration of differential equations of a boundary value problem for a shell under pressure is performed by the discrete orthogonalization method S.К. Godunov. The solution obtained made it possible to determine the location of the maximum stresses, in which the greatest changes in the mechanical properties of the material should be expected. According to the results of the calculations, a conclusion was given on the bearing capacity of the structure in the working mode and with increasing hydrogen concentration and internal pressure.
Nikolay Evstigneev^{1} , Oleg Ryabkov^{2}
^{1}Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow, Russia, 81 Macrodynamical systems, Russian Federation
^{2}Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow, Russia, , Russian Federation
We are considering the problem of divergence  free projection in rectangular domains for the Oseen (stationary NavierStokes) operator ($F(\mathbf{u}, p)$): $$F(\mathbf{u}, p) := (\mathbf{u}, \nabla) \mathbf{u}+\nabla p  \nu \Delta \mathbf{u}\mathbf{h} = \mathbf{0},$$ $$\nabla \cdot \mathbf{u}=0,$$ with zero wall boundary conditions. It uses nodal Finite Element method (space $\mathcal{P}$) to reconstruct pressure and Finite Difference method (space $\mathcal{V}$ for scalar functions and $\mathcal{V}^d$ for vector functions with $d=2,3$) for other parts of the equations. This allows us to use simple finite difference schemes for linear part (compact difference schemes) and WENOtype schemes for the the nonlinear part in the space of discrete velocities. The boundary conditions in $\mathcal{V}$ are formulated in Finite Volume conservative approach. Besides, such approach compies with the LBB condition automatically. We form the projection operator matrix $\mathtt{P}$ as follows: $$\mathtt{P}:=\mathtt{E}_d+\mathtt{G} \mathtt{A}^{1} \mathtt{I} \mathtt{D},$$ where matrices are identity ($\mathtt{E}_d:\mathcal{V}^d \to \mathcal{V}^d$), gradient ($\mathtt{G}:\mathcal{P} \to \mathcal{V}^d$), regularized inverse Laplace ($\mathtt{A}^{1}:\mathcal{P} \to \mathcal{P}$), interpolation ($\mathtt{I}:\mathcal{V} \to \mathcal{P}$) and divergence ($\mathtt{D}:\mathcal{V}^d \to \mathcal{V}$), respectively, from left to right. We wish to use the suggested method in the framework of continuation process in bifurcation analysis problem of stationary solutions. In this case we need so solve the problem using Newton's method: $$\mathcal{P} F_{\mathbf{u}^n} \delta \mathbf{u} =  \mathcal{P}F(\mathbf{u}^n),$$ $$\mathbf{u}^{n+1} = \mathbf{u}^{n} + \delta \mathbf{u}, \mathbf{u}^{n} \leftarrow \mathbf{u}^{n+1},$$ where the application of the projector nulls the pressure gradient. The method is applied incrementally, i.e. $\mathbf{f} = F(\mathbf{u}^n)$, $\mathbf{g} = \mathcal{P}\mathbf{f}$, and use $\mathbf{g}$ in the right hand side of the linear system. We numerically analize the operator $\mathtt{R}$ that acts in the $\mathcal{V}$ space of divergence operator image: $$\mathtt{R}:=\mathtt{E}_1+\mathtt{D} \mathtt{G} \mathtt{A}^{1} \mathtt{I},$$ where $\mathtt{E}_1: \mathcal{V} \to \mathcal{V}$. It is shown that all eigenvalues of the operator are less than unity for Oseledetstype wall (marked $w$) boundary conditions for velocity, namely: $(\mathbf{n}_w, \mathbf{u}_w) = 0, (\mathbf{\tau}_w, \mathbf{u}_w) = \nabla_{\tau} p$ and zero Neumann conditions for the Poisson equation. We illustrate that the convergence rate depends on the smoothness of the projected function and that the projection method allows one to obtain divergencefree solutions with desired tolerance. We show that for smooth functions we obtain 4th order convergence in divergence. Finally we demonstrate the method by solving some problems for the 2D Oseen operator. The test 2D MATLAB code in square domain for the projection problem is available at the author's GitHub.
This work is supported by RFBR grant no. 182910008 mk.
Jaykov Foukzon^{1}
^{1}Israel Institute of Technology, Department of mathematics, Israel
One of the Bell's assumptions in the original derivation of his inequalities was the hypothesis of locality, i.e., the absence of the influence of two remote measuring instruments on one another. That is why violations of these inequalities observed in experiments are often interpreted as a manifestation of the nonlocal nature of quantum mechanics, or a refutation of a local realism. It is well known that the Bell's inequality was derived in its traditional form, without resorting to the hypothesis of locality and without the introduction of hidden variables, the only assumption being that the probability distributions are nonnegative. This can therefore be regarded as a rigorous proof that the hypothesis of locality and the hypothesis of existence of the hidden variables not relevant to violations of Bell's inequalities. The physical meaning of the obtained results is examined. Physical nature of the violation of the Bell inequalities is explained under new EPRB nonlocality postulate.We show that the correlations of the observables involved in the BohmBell type experiments can be expressed as correlations of classical random variables. The revisited Bell type inequality reads

Zuleima Carrasco^{1}
^{1}Escuela Superior Politecnica de Chimborazo, Physics Research Group  ESPOCH, Ecuador
Quantum tunneling theory is widely used for many applications in different areas from the fundamental research to technological applications. In particular, the quantum tunneling appears in scanning tunneling microscope, nuclear physics, quantum computing, tunnel diode, among other. Here, we show a simple mathematical derivation of the onedimensional quantum transmission considering two particular cases: (i) for comparison purposes, the conventional quantum tunneling with one potential barrier and (ii) the quantum tunneling with two potential barriers considering a small distance between barriers, in which a pseudopotential is created and the particle is nonfree. As known, the quantum transmission in the first case, depends only on the incident particle energy (kinetic energy), the mass of particle, the energy barrier (potential energy) and the barrier length that the particle passes through. However, on the second case, an extra dependency is observed, i.e., the separation distance between barriers (the Harmant effect is cancel). We have corrobarated that the first case evidence the major quantum transmition probability respect to second one. Aditionally, we evidence that transmition probability can be modulate and controlled by changing the separation distance between barriers, which produces a region where the particles can be free or trapped. If this discovery is confirmed by future experiments, such as waveguide experiments, it could enhance the particle manipulation at nanometer scale improving the image resolution.
I would thanks Physics Research Group  ESPOCH and Dr. Cristian Vacacela Gomez, Ms. Noemi Moreta, Dennys Colcha and Dr. Richard Pachacama for the opportunity to present this work at the event, which help me to increase my expertise and aptitudes taken from my undergraduate career.
Irina Andreeva^{1}
^{1}Peter the Great St. Petersburg Polytechnic University, Higher Mathematics, Russian Federation
A family of dynamical systems on a real plane x, y is considered dx/dt = X (x, y), dy/dt = Y (x, y), where X (x, y), Y (x, y) are reciprocal forms of x and y, X is a cubic, and Y is a square form, such as X (0,1) > 0, Y (0, 1) > 0. A problem is formulated to reveal all topologically different phase portraits possible for these systems in a Poincare circle and outline close to coefficient criteria of each one portrait’s appearance. In order to solve this problem we use a method of serial mappings of Jules Henri Poincare: 1) a central mapping of a plane x, y, augmented with a line at infinity, onto a Poincare sphere ∑ with identified diametrically opposite points, 2) an orthogonal mapping of a lower enclosed semi sphere of a sphere ∑ onto a Poincare circle Ω with identified diametrically opposite points of its boundary Г. Several parts of this work are devoted to a solution of an assigned problem for those systems of the abovementioned family, which decompositions of polynomials X (x, y), Y (x, y) into the real forms of lower degrees contain 3 and 2 multipliers correspondingly; 2 and 2 multipliers; another numbers of different multipliers. Due to these differences we split the whole broad family of dynamic systems under consideration to several subfamilies belong to different hierarchical levels. The process of a study of a fixed subfamily contains the following steps. We enlist singular points of systems belong to the given family in a Poincare circle Ω: they apper to be a finite point O(0, 0)∈Ω and some infinitely remote points. For each singular point we introduce notions of bundles N (node) and S (saddle) of semi trajectories of systems of the family, adjacent to this singular point; of the topodynamical type of the singular point (TD – type); and a separatrix of the singular point. Further we study the behavior of separatrices of singular points of systems belonging to a taken family and answer the questions about a) the uniqueness of continuation of each of separatrices from a small neighborhood of a singular point to all its lengths; b) a mutual arrangement of all separatrices in a Poincare circle Ω. We construct phase portraits of systems belonging to a given subfamily in the both forms such as a graphical form and a table form. The close to coefficient criteria of the realization of each phase portrait are also indicated. The result of this work is the follows: for the whole family exist more than 250 topologically different phase portraits. This amount may seem rather large, but it is necessary to remember: the whole number of dynamic systems in the considered family is countless. By the way it was proved that there are no limit cycles for the systems of this broad family. This thorough study demanded developing some new special investigating methods, which may be used in further research of dynamic systems having polynomial right parts as well as for applications.
This work was initialized and conducted together with Professor Dr. Alexey F. Andreev, the Honored Professor of the St. Petersburg State University (1923  2017).
Galina Lazareva^{1}
^{1}Novosibirsk State University, Mechanics and mathematics faculty, Russian Federation
On the experimental stand Beam of Electrons for materials Test Applications (BETA) created in the INP SB RAS, the results of heating the tungsten plate by the action of a highspeed electron beam on it were obtained [1]. The work is devoted to the numerical implementation of the tungsten heating, melting and evaporation processes model. Currently, work on the simulation of erosion of fusion reactor wall material under highpower pulsed plasma flow is divided into three stages. The first stage is the calculation of heat sink around cracks formed under pulsed heat load [2]. The extension of the model involves the inclusion of equations of elasticity. The second stage is the calculation of dynamics of the melt formed under pulsed heat load [3]. The third stage is the calculation of gas dynamics above the surface of the plate. The extension of the model involves the inclusion of Maxwell's equations for calculation of electric and magnetic fields. The results of calculations are correlated with experimental data obtained at the experimental stand of BETA in INP SB RAS. 1. L. Vyacheslavov, A. Arakcheev, A. Burdakov, I. Kandaurov, A. Kasatov, V. Kurkuchekov, K. Mekler, V. Popov, A. Shoshin, D. Skovorodin, Y. Trunev, A. Vasilyev. Novel electron beam based test facility for observation of dynamics of tungsten erosion under intense ELMlike heat loads // AIP Conference Proceedings (2016), 1771, 060004. 2. Lazareva G.G., Arakcheev A.S., Kandaurov I.V., Kasatov A.A., Kurkuchekov V.V., Maksimova A.G., Popov V.A., Shoshin A.A., Snytnikov A.V., Trunev Yu.A., Vasilyev A.A., Vyacheslavov L.N. Calculation of heat sink around cracks formed under pulsed heat load // IOP Conf. Series: Journal of Physics: Conf. Series 894 (2017) 012120. 3. A.S. Arakcheev, D.E. Apushkinskaya, I.V. Kandaurov, A.A. Kasatov, V.V. Kurkuchekov, G.G. Lazareva, A.G. Maksimova, V.A. Popov, A.V. Snytnikov, Yu.A. Trunev, A.A. Vasilyev, L.N. Vyacheslavov Twodimensional numerical simulation of tungsten melting under pulsed electron beam // Fusion Engineering and Design, 2018, vol 132, pp. 1317.
This work is supported in by RFBR (project no. 190100422 A)
Qiang CHEN^{1} , Erwan Beauchesne^{2} , Françis Arnaudeau^{3} , PierreRichard Dahoo^{4} , Constantin Meis^{5}
^{1}Laboratoire ATmosphères, Milieux, Observations Spatiales, IMPEC , France
^{2}Altair Engineering, , France
^{3}Altair Engineering, , France
^{4}Laboratoire ATmosphères, Milieux, Observations Spatiales, , France
^{5}Commissariat à l'Energie Atomique et aux Energies Alternatives, , France
During the last decade the industrial interest in Additive Manufacturing (AM) has increased significantly. This innovative technology, initially developed for preproduction of visualization models for prototyping, is now close to deliver enduse products for direct industrial needs. Among the AM techniques, Laser Beam Melting is actually capable of producing parts with reliable mechanical properties. However, an AM efficient production still remains a challenging process as the difficulties related to distortion or cracking have not been mastered yet due to the large number of various parameters involved in the process. To reach the right first time level, needed for mass production with considerably reduced inherent costs, high quality numerical simulation is required in order to understand the physical mechanisms involved. Consequently, a numerical model is actually under development for understanding the relationship between different process and material parameters with the mechanical state of final parts such as distortion and residual stress. Macroscopic scale is considered in this work. Classical finite element method is used to solve the coupled thermomechanical problem on the whole domain defined by the workpiece, the baseplate and the support structures. At this scale, powder packing is neglected as well as the hydrodynamics behavior within the melt pool. Homogeneous equivalent heat source is used and imposed until several layers below the current deposited layer. Elastoplastic constitutive material law with temperature dependent parameters has been developed. This model is also coupled with phase transformation as it has significant influence on the final distortion. The resolution is based on explicit time scheme, requiring less memory resource compared with implicit resolution with the additional benefit to get rid of all inherent nonlinearities due to the thermomechanical coupling. At last, specific time step treatments are done to remedy the large difference between the thermal and mechanical time step. Simulations are carried out with the construction of simple wall and the popular cantilever. The results show the performance of the developed model, including computing efficiency and accuracy. By model simplification and acceleration technology, whole part simulation is affordable even with a laptop in a couple of hours. The accuracy of the model is validated by comparing the distortion with experimental results for different materials.
Valeriy Zakharov^{1}
^{1}Lomonosov Moscow State University, Mathematical Analysis, Russian Federation
The paper presents some optimization dynamic mathematical models of the peaceful currency trading subordinating interactions of two States in favor of one of them, constructed on the base of the earlier created by the author optimization dynamic mathematical model of a State. In all the indicated up to date in the world scientific literature models the considered economical subjects are not States. And the models themselves are not optimization. In the previous articles and monographs the author has developed some general mathematical optimization model of a State. There were conducted some successful numerical simulations on its base. A progress in constructing on this base of some general mathematical optimization models of interactions of several States has come in 2018, when peaceful and military subordinating interactions of two States were mathematically formalized by the author. Namely these kinds of interactions became the most noticeable events in the history of 20 and 21 centuries. The aim of either peaceful or military subordinating interactions is one and the same. It is the achievement of the largest divergence of total wealths of interacting States by the end of some time interval in favor of one of them. However, methods of control at these interactions may qualitatively differ from each other. Further in the present article we consider only the peaceful currency trading subordinating interactions of two States with optimal coordinated or not coordinated controls in favor of the subordinate State. The paper is purely conceptual. Neither theoretical nor practical methods of solution of formulated optimization problems are considered in the paper. All customary terms are used in the mathematical sense only.
Zheng Li^{1}
^{1}Peking University, Mechanics and engineering science, China
Wave propagation in heterogeneous or inhomogeneous media is of great importance in scientific and technological research. Especially, artificially designed subwavelength materials with exceptional effective properties, termed as metamaterials, have dedicated to manipulating waves in unimaginable ways. In order to design the viscoelastic metamaterial with a lowfrequency passband, we present a theoretical study and experimental realization of a dissipative elastic metamaterial that functions as a bandpass filter with a lowfrequency passband. The mechanism of dissipation in this structure is well described by a massspringdamper model that reveals that the imaginary part of the wavenumber is nonzero, even in the passband of dissipative metamaterials. By using the KelvinVoigt mechanical analog, the effects of using viscoelastic materials is investigated. A prototype for this viscoelastic metamaterial model is fabricated by 3D printing techniques using soft and hard acrylics as constituent materials. Results show that the passband becomes narrower with the increase of the damping coefficients and also with increasing the length of the metamaterial. The transmittance of the printed metamaterial is measured and shows good agreement with theoretical predictions, demonstrating its potential in the design of compact waveguides, filters and other advanced devices for controlling mechanical waves.
National Natural Science Foundation of China under grant No. 11672004
Vladimir Vaskevich^{1} , Shvab Irina^{2}
^{1}Novosibirsk State University, Department of Mathematics and Mechanics, Russian Federation
^{2}Novosibirsk State University, Department of Mathematics and Mechanics, Russian Federation
Equations under study have the form in which the time derivative of an unknown function $u(t,k)$ is expressed by the linear combination of the function $u(t,k)$ and a double integral over the space variables from the weighted quadratic expression of same function $u(t,k)$: $$ \frac{du}{dt}(t, k) + b(t,k)u (t, k)=\iint\limits_{P (k)} W (k, k_1, k_2) u (t, k_1) u (t, k_2) dk_1 dk_2. $$ Here the function $b(t,k)$ is continuous, and the domain $P (k)$ is unbounded. Moreover $P (k)$ does not depend on time, but depends on the spatial variable $k$. We introduce special functional classes associated with the equation under study and consider the Cauchy problem with initial data on the positive semiaxis $k>0$. In application to the Cauchy problem, we consider the method of successive approximations. We found the estimation of the successive approximation quality, which depends on the number of the iterated solution.
The authors were partially supported by the Russian Foundation for Basic Research (project no.~190100422).
Shvab Irina^{1}
^{1}Novosibirsk State University, Department of Mathematics and Mechanics, Russian Federation
In the paper we discuss a biomechanical model of microcirculation and transcapillary metabolism and present a mathematical model of metabolic processes occurring in microcirculation level. We conside the following interrelated processes: the flow of blood (a nonNewtonian fluid) in capillaries; filtration and reabsorption of fluid through the wall of the arterial capillary into the surrounding tissue and from this one back to the venous capillary; the movement of fluid in the interstices, the exchange of substances between the interstitial fluid and tissue cells, drainage into the lymphatic capillaries. Biological tissue is modeled as a porous, resilient, isotropic matrix or frame saturated with a fluid of the same type. It is believed that the liquid is contained in the pores of the matrix. The study of microcirculation allows you to better understand the complex interlinked processes of metabolism in the body, identify the causes of pathologies and suggest possible treatment interstitium.
supported by the Russian Foundation for Basic Research (project no.~190100422)
Boris Kryzhanovsky^{1} , Leonid Litinskii^{2}
^{1}Scientific Research Institute for System Analysis Russian Academy of Sciences, Center of Optical Neural Technologies, Russian Federation
^{2}Scientific Research Institute for System Analysis Russian Academy of Sciences, Center of Optical Neural Technologies, Russian Federation
We used a Monte Carlo method to analyze a planar Ising model taking into account a ferromagnetic interaction with next neighbors. We found that independent of the value of the additional interaction, the character of singularity of the heat capacity did not change. Namely, at the critical point the heat capacity has a logarithmic singularity. We obtained a phenomenological formula relating the value of the critical temperature with the value of the additional ferromagnetic interaction.
The work financially supported by State Program of SRISA RAS No. 006520190003 (AAAA191190115900902).
Marcin Lawnik^{1}
^{1}Silesian University of Technology, NIP: 6310200736, , Poland
Logistic map is one of the simplest, and at the same time the most commonly used dynamic system, which is characterized by chaos. The article presents approximations of the logistic map through its extension into the Fourier series. Obtained in such way dynamical systems were analyzed, among others for the Lyapunov exponent and bifurcation diagrams. Furthermore the issue of the density of the iterated variable and some applications in chaos based cryptography were commented.
Mikhail Ivanov^{1} , Georgy Resh^{2}
^{1}JSC Military Industrial Corporation NPO Mashinostroyenia, Bauman Moscow State Technical University, Computational Mathematics and Mathematical Physics Department, Russian Federation
^{2}JSC Military Industrial Corporation NPO Mashinostroyenia, Bauman Moscow State Technical University, Aerospace Systems Department, Russian Federation
This paper deals with the dynamic process of interaction of a thinwalled compliant (adaptive) spatial structure made of a permeable microporous capillary phase separator with a lyophilic homogeneous liquid mixture flowing through. It is shown that a comprehensive compression force occurs during an intake of a liquid medium from a vessel with a spatial structure placed in it. The force is applied to the portion of the phase separator that is located in the gas phase region above the moving gasliquid interface. The existence of the comprehensive force impact is determined by a complex of phenomena of various physical nature: GalileoTorricelli principle, surface interactions, natural and/or artificial gravity. The detected effect can be used to maintain the current characteristic linear dimension of the spatial structure below a certain limiting value determined by a known formula of the theory of rigid capillary liquid intake devices used by F.T. Dodge, V.M. Polyaev and other researchers when studying operating conditions of such units. This allows increasing the time of liquid production and reducing its residues in the vessel, while maintaining the specified capillary retention capacity of the phase separator. It also allows expanding the field of practical application of capillary phase separators.
Nikolay Evstigneev^{1}
^{1}Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow, Russia, 81 Macrodynamical systems, Russian Federation
This paper outlines the problem of applying multigrid methods for the stationary advecitondiffusion operator: $$F(\mathbf{u}):=(\mathbf{a},\nabla) \mathbf{u}\mu \Delta \mathbf{u}\mathbf{f} = \mathbf{0},$$ in bounded domain $\Omega \subset \mathbb{R}^d$ with piecewise Lipschitzcontinuous boundary $\partial \Omega$ and $\mathbf{u}:\Omega \to \mathbb{R}^d, d=\{2,3\}$. Here $\mathbf{a}$ is a given vector field, $\mu$ is a parameter, $\mathbf{f}$ is a source term. We assume that all functions are smooth enough to be represented by discretization methods. Two main discretizations are considered: finite difference method for Dirichlet boundary conditions and pseudospectral method for the periodic boundary. We test the following smoothers for multigrid methods: Jacobi smoother, GaussSeidel smoother, Krylovtype smoother (GMRES, BiCGStab, BiCGStab(L) with and without preconditioners). The analysis is performed in the space formed by the cross product of discretization parameters, $\mu$ values, given advection filed $\mathbf{a}$, multigrid levels and smoothers. We demonstrate that the most efficient strategy depends on parameter value and given velocity field. Best variants include GaussSeidel smoothers which is optimal for advectiondominated problem while multigrid method is used as a preconditioner for a Krylov method. We also suggest different prolongation and restriction operators in Fourier space. Such operators can construct an efficient multigrid method for spectral or pseudospectral methods where explicit dense matrix storage is impossible. All 2D tests are available as MATLAB codes at the author's GitHub.
This work is supported by RFBR grant no. 182910008 mk.
Vasilij Tikhomirov^{1} , Vladimir Nefedov^{2}
^{1}Lomonosov Moscow State University, Department of Computational Math & Cybernatics, Russian Federation
^{2}Lomonosov Moscow State University, Department of Computational Math & Cybernatics, Russian Federation
It is known that the generalized system of relativistic electrodynamics equations can be obtained by the principle of minimal action when solving a variational extremal problem of maximizing a certain special functional. The possibility of using the homotopy (deformation) method for studying the invariance of extremals for the generalized system of equations of relativistic electrodynamics is considered in this paper. This method makes it possible to investigate the stability of extremals of the action functional. An analysis of the Lyapunov’s stability of solutions of this system is carried out by a deformation (homotopy) method for Hamiltonian systems.
Anastasia Pomortseva^{1}
^{1}Saint Petersburg Mining University, Geological, Russian Federation
The paper examines the historical behaviour of such unique natural phenomena as the sheets of aufeis in the North East of Russia. They are studied using statistical methods for analyzing dendrochronological data. Dendrochronology is a scientific method based on comparing quantitative indicators of tree ring growth and the dynamics of aufeis formation in the past. Tree ring growth is an integral indicator which reflects the diversity of conditions in which trees grow and interact with the environment. Time series were obtained for the UlakhanTaryn and Buluus aufeis deposits located in the Middle Lena basin in Central Yakutia. Regression models were created using dendrochronological data, with the majority of the models being nonlinear. The sample mean, sample variance, and sample correlation coefficient were calculated for the time series. The regression model of the time series under study was represented as a combination of a nonrandom component, including the age trend and a climatic component, and a random component with zero expectation, which is the sum of factors unaccounted for, including autocorrelation. Depending on the locations where data were collected, both strong and moderate and weak dependencies of pine growth on aufeis influence were revealed. If there was strong or moderate aufeis influence, humidity had a minor impact on tree growth. If aufeis influence was weak, tree growth was moderately influenced by precipitation. There is a moderate dependence of tree growth on air temperature in all cases.
Sanjay Puri^{1}
^{1}Jawaharlal Nehru University, School of Physical Sciences, India
Consider a disordered system which is rendered thermodynamically unstable by a sudden change of parameters, e.g., temperature, pressure. The subsequent farfromequilibrium evolution of the system is characterized by the emergence and growth of domains of the preferred phases. This subject of domain growth has attracted great attention in the literature. In pure and isotropic systems, the domains typically show a powerlaw growth in time. The presence of quenched disorder, which is present in most experimental systems, leads to the trapping of domain boundaries at disordered sites. Then, growth can only proceed by thermally activated hopping over disorder barriers. This results in a crossover from a powerlaw growth regime to a logarithmic growth regime. This talk will review our understanding of these problems.
Fabricio Forgerini^{1} , Leonardo Oliveira^{2} , Anderson Rodrigues^{3}
^{1}Federal University of Southern Bahia, Institute of Humanities, Arts and Science, Brazil
^{2}Federal University of Southern Bahia, , Brazil
^{3}Federal University of Southern Bahia, , Brazil
We study the Majority Rule (MR) model, a sociophysics model developed to describe how a group of agents with initial different opinions can reach consensus. At each instant of time, a group is selected at random and discuss among each other. After the discussion, all members of this discussion group follow the majority opinion. The number of agents in the discussion group is not fixed and it is selected each instant of time from a Gaussian distribution. The system dynamics stops when only one opinion survive. In this work we introduced in the MR model a 'reputation' for each agent, a weight to be considered in the system dynamics. Our results show that the introduction of reputation leads the system to a steady state in which not every agent on the system have exactly the same status, but a majority of them sharing the same opinion. In addition, our model with the inclusion of reputation do not show the critical point usually observed. Instead we have obtained the critical point $p_c = 1$, in contrast with the standard Majority Rule model.
Sinem Arslan^{1} , Münevver TezerSezgin^{2}
^{1}Middle East Technical University, Department of Mathematics, Turkey
^{2}Middle East Technical University, Department of Mathematics, Turkey
We present the magnetohydrodynamic (MHD) flow of an electrically conducting, incompressible fluid in a long channel of rectangular crosssection (duct) which is driven by a pressure gradient. An external magnetic field is applied vertically to the duct (perpendicular to the channelaxis). The steady, laminar, fullydeveloped MHD flow equations are given in terms of the velocity $V(x,y)$ and the induced magnetic field $B(x,y)$ in the duct region. The top and bottom walls of the duct are noslip walls and electrically insulated whereas the side walls admit both the slip velocity and partly insulated partly conducting parts. The finite difference method (FDM) is used to solve the governing coupled MHD equations as a whole. Numerical results are depicted in terms of equavelocity and current lines to show the physical effects of the slip and the wall conductivities on the behavior of the fluid velocity and the induced magnetic field. It is found that, as the slip increases the velocity magnitude also increases for all values of Hartmann number. Parabolic boundary layers on the side walls are observed emanating from the points where the conductivity changes.
The work is supported by the Scientific and Technological Research Council of Turkey, TUBITAK.
Jianxiang Wang^{1}
^{1}Peking University, Mechanics and Engineering Science, China
In the last decades, modelling of heat conduction in microstructured systems such as microelectronic devices, heterogeneous materials, and biological tissues has attracted much attention due to its potential applications. However, experimental results show that the Fourier’s law may break down with the decreasing feature sizes, and whether it is valid for heterogeneous materials under high temperature gradients is yet to be explored. Some approaches beyond the Fourier’s law have been proposed from the nanoscale to the macroscale, and most of them are in the form of differential equations, which need highorder gradients. In this paper, first, we derive a governing equation of heat conduction for heterogeneous media. Different from the previous work, we show that although the constituents obey the conventional Fourier’s law, the overall governing equation of the heterogeneous media is in a spatiotemporal nonlocal form. Under certain conditions, it can reduce to the DualPhaseLag (DPL) model. Thus, second, we present a nonFourier heat conduction model in the framework of generalized statebased nonlocal peridynamic (PD) theory by introducing the concept of DPL into the peridynamic framework, which can be easily applied to problems with discontinuities. Its relations with other models are discussed, and numerical procedures are developed for solving the resulted equation. The results for examples are in good agreement with available experimental data.
Valeriy Parkhomenko^{1}
^{1}Moscow State Technical University by N.E. Bauman (BMSTU), FRC "Computer Science and Control" of the Russian Academy of Sciences , Department of Continuum Mechanics, Russian Federation
The aim of the study is to show an important role of the solar radiation flux in positive feedback “temperature  surface albedo” during the transition to glaciation regimes observed in the history of the Earth. The study is based on a threedimensional hydrodynamic global climate coupled model, including ocean model with real depths and continents configuration, sea ice evolution model and energy  moisture balance atmosphere model. A series of numerical experiments were carried out to assess the impact of changes in solar radiation flux on the global climate. It is assumed that the solar constant gradually decreases discretely compared to the current value and in each case is determined the steady climatic mode. Simulation period is about 2000 years. Gradual increase in the sea ice area and a catastrophic increase at the end of stage 3, when the oceans are completely covered with ice (so called “snow ball Earth”) are get. These results are naturally explained by the presence of the “temperature decrease  glaciation” positive feedback. The stage 3 maximum surface air temperature is 30 ° C, the minimum 85 °C. Strong temperature and ice cover changes lead to significant changes in the horizontal and vertical thermohaline ocean circulation. The vertical thermohaline circulation has the weakened horizontal velocities in the north direction in the ocean upper layers and increased in the direction of the equator in the deep layers (in contrast to the present situation).
Vasilii Volodin^{1} , Andrei Tolokonskii^{2}
^{1}National Research Nuclear University MEPhI, Institute of Nuclear Physics and Engineering, Russian Federation
^{2}National Research Nuclear University MEPhI, Institute of Nuclear Physics and Engineering, Russian Federation
Math modelling is used as the modeloriented design basis on all system lifecycle stages in field of technical systems design. Math modelling in nuclear energetics is used for probabilistic safety analysis of nuclear power plant (NPP) and for operating staff training (there are set of simulators for each NPP unit). Open Joint Stock Company “AllRussian Research Institute for Nuclear Power Plants Operation” (OJSC VNIIAES) and The Nuclear Safety Institute of the Russian Academy of Sciences (IBRAE) developed “Virtual digital NPP” project based on full sized math models of NPP using in NPP simulators together with numerical code of severe accidents. The State Atomic Energy Corporation ROSATOM is considering advantages of virtual digital NPP usage for project “Proryv” (reactor BRESTOD300), which is realizing in Seversk. However, we can use math models of NPP simulators or virtual digital NPP another way, not only for technical project verification/validation – we can use them as a digital twin of NPP unit. Therefore, these models, which we must modify for receiving data directly from NPP unit, will be observers as for certain automatic control circuit and for digital NPP I&C system in general. This concept allows estimating technical equipment condition, realizing optimal control etc. We can realize these functions with traditional control theory and probabilistic analysis or with “intelligent” methods such as fuzzy logic or neural networks. Authors analyzed aforementioned concept, his possible limitations and implementation with advantages and disadvantages. Differences between NPP simulators, virtual digital NPP and NPP digital twin are given.
Sachiyo Aburatani^{1} , Yosuke Shida^{2} , Wataru Ogasawara^{3} , Harutake Yamazaki^{4} , Hiroaki Takaku^{5}
^{1}National Institute of Advanced Industrial Science and Technology, Computational BioBig Data Open Innovation Lab., Japan
^{2}Nagaoka University of Technology, Department of Bioengineering, Japan
^{3}Nagaoka University of Technology, Department of Bioengineering, Japan
^{4}Niigata University of Pharmacy and Applied Life Sciences, Department of Applied Life Sciences, Japan
^{5}Niigata University of Pharmacy and Applied Life Sciences, Department of Applied Life Sciences, Japan
Recently, we developed a new statistical method for revealing the regulatory systems in living cells. Our method based on Structural Equation Modelling combined with Cross Correlation. In generally, Structural Equation Modelling is utilized to detect the model adaptability with the measured data, such as large scale questionnaire data and so on. In this study, we developed a new iteration algorithm to infer the causalities between variables as a regulatory network from limited numerical data. To display the regulatory system in living cells as a network graph, genes which are arranged as variables in network model should be selected. In this study, we improved our gene selection method based on cross correlation to summarize the time preceding information from gene expression profiles which were systematic measured in 8 time points. Cross correlation is usually utilized as a measure of similarity between two waves in signal processing by a timelag application, and we defined the values of lags ranged from −4 to +2. By this improved method, we selected 14 genes as regulatory factors for the specific system in oleaginous yeast. In the inferred model, only 6 genes among the selected 14 genes were considered to affect the volume of oil accumulation, and this system is controlled in closed and specific system. Our developed method will be useful to artificial control of cell system in bioproduction and biotechnology field.
Nikolai Magnitskii^{1}
^{1}Federal Research Center "Computer Scienc e and Control", Laboratory of Chaotic Dynamics, Russian Federation
In the work, based on the equations of the compressible oscillating ether, derived from the laws of classical mechanics [1,2], ether mathematical models of the nuclei of atoms of chemical elements were constructed. It is shown that the nucleus of any atom is a superposition of perturbation waves of ether density in several protons and several neutrons, having a common center and propagating around a common axis in one direction or in opposite directions, that is, having unidirectional or opposite spins. Formulas for the values of internal energies, masses, magnetic moments, and binding energies of atomic nuclei are derived, with an accuracy of fractions of a percent coinciding with their experimental values. Formulas for calculating the radii of atomic nuclei are obtained. Answers are given to many topical questions about the structure of atomic nuclei that modern atomic physics is not capable of answering, for example: why there are no nuclei consisting only of protons or only of neutrons; what is the nature of the nuclear forces holding together protons and neutrons in the nucleus; why the sizes of atomic nuclei practically do not depend on the atomic number of the chemical element; why the Coulomb barrier of the nucleus selectively works; why the fragments of the decomposition of transuranium elements into two nuclides are asymmetric; why there is no stable nucleus Be8 ; what is the reason for the different percentage in nature of different isotopes of the same chemical element? 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.
Sergei Gerasimov^{1} , Igor Inovenkov^{2} , Vladimir Nefedov^{3}
^{1}Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics, Russian Federation
^{2}Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics, Russian Federation
^{3}Lomonosov Moscow State University, Department of Computational Math & Cybernatics, Russian Federation
The system of parabolic partial differential equations is considered, which describes the dynamics of various population groups in an urban environment. The model takes into account both the interaction between different groups in the process of their cohabitation and the diffusion processes of the development of urban infrastructure. Various examples of world megacities are considered and some general principles of urban development are formulated.
Orest Malyk^{1} , Stepan Syrotyuk^{2}
^{1}Lviv Polytechnic National University, Semiconductor Electronics Department, Ukraine
^{2}Lviv Polytechnic National University, Semiconductor Electronics Department, Ukraine
At present the main method for increasing the efficiency of solar cells based on cadmium telluride is the using an additional absorbent layer created on the base of triple compounds of cadmium chalcogenides, in particular the solid solution CdSexTe1x. Therefore, the study of the quality of these absorbing layers is an actual application problem. In the present paper the estimation of the quality of the absorbing layer is carried out by analyzing of its kinetic properties. The description of the transport phenomena is carried out by combining two approaches: 1 – using of wave function and selfconsistent potential which were determined from the first principles on the base of projector augmented waves (PAW), as implemented in the ABINIT code [1]; 2 – using the shortrange principle to consider the charge carrier interaction with different types of crystal defects [25]. The PAW basis functions have been generated by means of the AtomPAW [6] code for the following valence states: {5s25p04d10 } for Cd, {4s25s24p25p4 } for Te and {4s24p4 } for Se, respectively. On the base of obtained wave function and selfconsistent potential for for solid solution CdSexTe1x (x=0.25) in the framework of shortrange scattering models the calculation of transition probabilities for electron interaction with polar and nonpolar optical phonons, piezoelectric, acoustic phonons, static starin center, neutral and ionized impurities are presented. The transition matrix elements were obtained by integration over the unit cell using threedimensional Bspline interpolation. The conductivity tensor components were obtained from the exact solution of the stationary Boltzmann equation [7]. For crystals with impurity concentration 5.6x1015 5x1018 cm3 the temperature dependences of electron mobility and Hall factor in the range 15 ÷ 1200 K are calculated. The influence of different scattering mechanisms on the charge carrier mobility is considered. The theoretical curves obtained in the shortrange approach differ qualitatively and quantitatively from those obtained within the longrange models in relaxation time approximation. [1] X. Gonze et al. Computer Phys. Comm. 205, 106 (2016). [2] O.P. Malyk, Mater. Sci. Eng. В. 129, 161 (2006). [3] O.P. Malyk, Phys.Status Solidi C. 6, S86 (2009). [4] O.P. Malyk, S.V. Syrotyuk. Comput. Mater. Sci. 139, 387 (2017). [5] O.P. Malyk, S.V. Syrotyuk. J. Electron. Mater. 47, 4212 (2018). [6] A.R. Tackett et al. Comput. Phys. Commun. 135, 348 (2001). [7] O.P. Malyk. J. Alloys Compd. 371, 146 (2004).
Nobutoshi Ikeda^{1}
^{1}Tohoku Seikatsu Bunka Junior College, Living and culture, Japan
Numerous empirical studies of networked systems have revealed structural similarities in different networks including social networks, world wide web, and biological networks. The existence of hub nodes (the scalefree property) is a typical property of such common structures in real networks. There are several mechanisms to support the scalefree property in growing networks. However, how the powerlaw form of degree distribution of networks can survive in an equilibrium state of number of nodes is an open question, because the deletion of nodes necessary to achieve the equilibrium state has a serious effect on the degree distribution. In this paper, we introduce a mechanism of network evolution based on a random walk which regulates replacements of nodes in the network. We assumed that a roundabout path via a new vertex and a shortcut are formed corresponding to one step of the walker’s movement with a probability $p_v$ and $p_e$, respectively. In addition, we assumed that the lifetime of nodes would be lengthened by walker's visit, and the node would be removed if the walker does not visit beyond a certain time interval. Numerical results showed that this mechanism sustains the powerlaw form of degree distribution, and the same powerlaw form is found in the distribution of the maximum degrees that each node experiences in its life. We showed additionally that when $p_v$ is small, the graph shrinks to a nearly complete graph, which is supported by the extension of the lifetime of fewer nodes. In this model, the visit frequency and recurrence property of the walker to a node determines the degree and lifetime of the node. This is a simple and novel mechanism that supports the scalefree property of a graph where the replacement of nodes achieves an equilibrium state of number of nodes.
Arman Kussainov^{1} , Nurzhan Saduev^{2}
^{1}alFarabi Kazakh National University, Physics and Technology Department, Kazakhstan
^{2}alFarabi Kazakh National University, Physics and Technology Department, Kazakhstan
Computer tomography simulation code was designed to accept an arbitrary set of projections from other simulation software or from the real computer tomography setup. This part of the package's feature was modified and used to reconstruct the structure of the real complex phantom encoded in Xray projections. The phantom was built to test the performance of the hardware intended for later use in security scanners and explore the effectiveness of such a homemade CT scanner and different recording geometries.
This research was originally commissioned and funded by the ADANI Company, producing and manufacturing Medical, Security, Spectroscopy and Inspection Xray Systems in Minsk, Republic of Belarus. Publication efforts, and further development of phantom tracing and multithreading, were supported by ``Fundamental and applied research in related fields of physics of terrestrial, nearearth and atmospheric processes and their practical application'' project #BR05236494, administered by the Ministry of Science and Education, Republic of Kazakhstan.
Eugen Anitas^{1}
^{1}Joint Institute for Nuclear Research, BLTP, Russian Federation
Analytic expressions for form factors of several simple deterministic fractals have been derived in the last years, including mass, surface, fat and multifractals. These expressions are then used to extract the sought structural parameters such as the fractal dimension, lower and upper limits of the fractal, iteration number or the scaling factor. However, for more complex structures, where the fractal symmetry can not be exploited, analytic expressions are not available and we have to resort to other methods. To partially overcome this issue, here we show how Monte Carlo simulation can be used to calculate the corresponding pair distribution function, that is the Fourier transform of smallangle scattering (SAS) intensity and discuss it limitations. In order to illustrate the applicability of this numerical approach we investigate the structural properties of two 2D surface fractals, one with known analytic expression of scattering intensity.
Koji Ishiya^{1} , Shintaroh Ueda^{2}
^{1}National Institute of Advanced Industrial Science and Technology (AIST), Comptational Bio BigData Open Innovation Laboratory, Japan
^{2}The University of Tokyo, Department of Biological Sciences, Japan
DNA molecules are degraded after the biological death of an organism. However, the degree and rate of DNA degradation enormously vary depending on environmental conditions, such as temperature or humidity, which greatly affect DNA preservation. Most samples excavated in warm, humid, or dry areas are often poorlypreserved samples with rather <0.1%–1% endogenous DNA. In these degraded samples, the contamination by exogenous DNA remains a potential challenge, no matter how much effort is made to prevent it. For an accurate DNA sequence analysis, quality control must be thoroughly performed using the mitochondrial DNA as an indicator of exogenous DNA contamination. Here, we propose a practical approach for detecting exogenous human mitochondrial macro haplogroups and discuss the effectiveness of this approach using simulated data. Our approach is based on the Bayes classification, which is a supervised machine learning algorithm, and it can detect a contaminating macro haplogroup in highthroughput sequencing data. This approach can help us to validate the quality of highthroughput sequencing data from possible contaminated or degraded human samples.
Discussions with our lab members greatly contributed to improving this study. This work was supported in part by a GrantinAid for JSPS Fellows 15J08490 (to K.I.), JSPS KAKENHI Grant Number 19K16246 (to K.I.), and JSPS KAKENHI Grant Number 25291104 (to S.U.).
Olga Maksimova^{1} , Oleg Piskunov^{2} , Andrey Maksimov^{3} , Vladislav Egorov^{4} , Aleksandr Baidganov^{5}
^{1}Cherepovets State University, Laboratory of mathematical and computer modelling of nanostructures, Russian Federation
^{2}Cherepovets State University, , Russian Federation
^{3}Cherepovets State University, , Russian Federation
^{4}Cherepovets State University, Laboratory of Mathematical and Computer Modelling of Nanostructures, Russian Federation
^{5}Cherepovets State University, , Russian Federation
A model of the polymer system for computer simulation of deformation processes is presented. The model is a synthesis of analytical calculations (polymer chain in a tube [M. Doi, S. Edwards, The theory of Polymer Dynamics (Clarendon Press), 406 (1988)]) and a computer experiment (simulation of the orientational ordering of polar groups by the Monte Carlo method). Due to analytical calculations, this model makes it possible to analyze relatively large systems compared to other models using the same CPU time. The calculations showed that the dependence of the free energy on the interchain distance in our model has two minima. The first minimum is characterized by the orientational ordering of the polar groups, the second one by their disordered state. The depth and positions of the minima depend on the temperature, the bending stiffness of chain, the modulus of the dipole moment of the polar groups and the depth of the potential well in the LennardJones potential. The results of tensile simulation (stressstrain curves) of a thin polymer film for various values of chain stiffness are presented. The obtained curves have a characteristic yield drop, the size and the position of which depend on the chain stiffness, the temperature and intermolecular interaction constants.
The study was supported by the Russian Foundation For Basic Research, Project № 1942350001
Giorgia Marcelli^{1}
^{1}Sapienza University of Rome/Joint Institute of Nuclear Physics, Theoretical Physics, Italy
This report attempts to exploit structural properties of deterministic multifractal structures through the analysis of multifractal spectra and SmallAngle Scattering (SAS) intensities performed on a two scaling factors fractal model, known as 2D Vicseklike fractal. Hence, we show the box counting dimension $D_0$ in the multifractal spectra coincides with the fractal dimension determined through the evaluation of the scattering exponent in the fractal region of the SAS form factor.
Hossein Ghaffarnejad^{1}
^{1}Semnan university, Physics, Iran (Islamic Republic of)
We applied a generalized scalarvectortensor Brans Dicke gravity model to study canonical quantization of an anisotropic Bianchi I cosmological model. Regarding an anisotropic Harmonic Oscillator potential we show that the corresponding Wheeler de Witt wave functional of the system is described by Hermit polynomials. We obtained a quantization condition on the ADM mass of the cosmological system which raises versus the quantum numbers of the Hermit polynomials. Our calculations show that the inflationary expansion of the universe can be originate from the big bang with no naked singularity due to the uncertainty principle.
Gordana Jovanovic Dolecek^{1}
^{1}Institute INAOE, Electronics, Mexico
Decimation is the process of decreasing sampling rate in a digital domain, by an integer, called the decimation factor. This process introduces replicas of the main spectrum, called aliasing. Aliasing may deteriorate the decimated signal if the signal is not filtered before decimation, by a low pass filter known as a decimation filter. The simplest decimation filter is a comb filter which has all coefficients equal to unity, and consequently does not require multipliers for its implementation. However, comb filter does not have the flat passband characteristic. The passband droop is increased with the increase of the number of cascaded comb filters. The passband droop must be compensated by a filter called comb compensator. Some desirable characteristics of comb compensator are multiplierless design, and a low absolute value of the passband deviation of the compensated comb. The magnitude response of comb compensator has to approximate the inverse comb magnitude characteristic. In that way the cascade of comb and compensator has the passband characteristic approximately equal to 1. In this paper we present novel narrowband multiplierless compensator with a low absolute value of the passband deviation, whis is less than 0.01dB. The compensator has a magnitude response synthesized as sinewave functions. The parameters of design are the amplitudes of sinewave functions, which depend on the order of the comb filter and practically do not depend on the decimation factors
Gordana Jovanovic Dolecek^{1} , Sergio Salguero Luna^{2}
^{1}Institute INAOE, Electronics, Mexico
^{2}Institute INAOE, Electronics, Mexico
Minimum phase (MP) filters have all zeros inside of the unit circle. MP filters have a minimum group delay and a minimum energy delay properties, especially useful in communication systems. The special class of MP filters has all zeros inside and on the unit circle. This paper presents a novel method for design of this class of MP FIR (Finite Impulse Response) digital filters. The method is based on palindromic polynomials and sharpening technique. The coefficients of palindromic polynomials are presented as a sum of powers of two, and consequently can be implemented by using only adders and shifts, resulting in a multiplierless design. Two classes of palindromic polynomials, having all zeros on the unit circle, are considered. Next, the sharpening technique was applied to simultaneously improve the passband and stopband of the designed filter. The choice of the design parameters is also elaborated. All zeros of the designed MP filters are inside or on the unit circle. Method is illustrated with various examples.
Hiroshi Koibuchi^{1}
^{1}National Institute of Technology (KOSEN), Sendai College, General Engineering, Japan
In this presentation, we show that an anisotropic shape change of skyrmion under uniaxial stresses can be explained by Finsler geometry (FG) modeling and its Monte Carlo simulation. This anisotropic shape change was the one experimentally observed in [K. Sibata, et al. , Nature Nano., 10.1038 (2015)], where the reason for this shape change was also explained such that the DzyaloshinskyMoriya (DM) interaction coefficient D becomes directiondependent $D\to (D_x,D_y), D_x\not= D_y$. This is called “straininduced anisotropy” (SIA) of the DM interaction in Ref. [T. Koretsune, et.al., Sci. Rep. 5:13302 (2015)], where a possible origin for this SIA is studied by a firstprinciple quantum mechanical calculation. In the FG modeling technique, the coefficients $(D_x,D_y)$ are automatically determined depending on the internal stressfield, which is also determined by the applied external force. The results are consistent with the reported ones.
This work is supported in part JSPS KAKENHI Grant Number JP17K05149.
Varsha Banerjee^{1}
^{1}Indian Institute of Technology, Delhi, Physics, India
We study the kinetics of phase transitions in disordered dipolar magnets. Using comprehensive Monte Carlo simulations, we perform deep temperature quenches into the ordered phase to understand the effects of quenched disorder and longrange dipolar interactions on domain growth. We observe rough interfaces, anisotropic growth laws and logarithmic slowing down. Our results are useful to interpret pattern formation in a wide range of magnetic and dielectric solids.
Aidana Meirambay^{1} , Koblandy Yerzhanov^{2}
^{1}L.N.Gumilyov Eurasian National University, Department of General and Theoretical Physics, Kazakhstan
^{2}L.N.Gumilyov Eurasian National University, Department of general and theoretical physics, Kazakhstan
The YangMills supersymmetry is considered using the YangBaxter equations as deformations of AdS5 × S5 in which they are substituted as a twist of the conformal Drinfeld algebra. The operators here are represented as Killing vectors. The solution of this problem is represented as Θ  the matrix for which the deformation ϕ was found, which is a super gravitational solution.
Vladislav Egorov^{1}
^{1}Cherepovets State University, Laboratory of Mathematical and Computer Modelling of Nanostructures, Russian Federation
Polyvinylidene difluoride (PVDF) and its copolymers are the most perspective ferroelectric materials for developing actuators, which convert electric energy to mechanical energy. Compared with lowmolecular ferroelectrics, PVDF has better mechanical strength, shock resistance, and flexibility. However, PVDF has an unusual shrinking behavior along the direction of the external field, of which the mechanism is not yet completely understood [I. Katsouras, et al. Nature materials 15.1, 78 (2016)]. Furthermore, the shapechange of material caused by the electric field is typically very complex and difficult to simulate. In recent works [H. Koibuchi et.al., Journal of Physics: Conf. Series 1141 (2018) 012018, Y. Takano and H. Koibuchi, Phys. Rev. E 95, 042411 (2017)], it was shown that the Finsler geometry (FG) technique can be applied for modeling mechanical behavior of rubbers and soft biological materials. In the present study, the FG model is extended for describing the reverse piezoelectric effect in ferroelectric polymers. The Finsler metric is defined by the variable σ, which represents the directional degree of freedom in polymerchain segment or its dipole moment. The results of Monte Carlo simulations indicate that FG modeling is suitable for reproducing experimental strainelectric field (SE) curves of PVDFbased polymers in both longitudinal and transverse directions. In addition, the influence of the sample thickness on the SE curves is studied and analyzed.
This work is supported in part by the Collaborative Research Project of the Institute of Fluid Science, Tohoku University, and JSPS KAKENHI Grant Number JP17K05149.
Eugenia Echkina^{1} , Natalia Guzminova^{2}
^{1}Moscow State University, Computational Mathematics and Cybernetics, Russian Federation
^{2}Moscow state university of medicine and dentistry , Medical department , Russian Federation
In this paper, we discuss using laser plasma as a source of highenergy ions for the purposes of hadron (proton) therapy. Hadron therapy (HT) is a modern, highprecision form of radiation therapy that uses protons to irradiate diseased tissue. HT has received the greatest use for the fight against cancer. The high accuracy of cancer cell damage, together with the gentlest impact on healthy organs and normal tissues, the absence or mild side effects, make proton therapy indispensable where the tumour is located next to the vital organs, in paediatrics, where the anatomical location of the tumour makes it impossible to surgical removal and use of photon therapy will place the patient at an unacceptable risk. In our work we present the results of mathematical modeling of laser pulse with substance. Сomputer modeling gives the chance of selection of parameters of a laser pulse and target, for more exact focusing of an pulse and obtaining the set energy of ions.
Nurzhan Serikbayev^{1} , Gulgassyl Nugmanova^{2} , Ratbay Myrzakulov^{3}
^{1}L.N.Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
^{2}L.N. Gumilyov Eurasian National University, Mathematical and computer modeling, Kazakhstan
^{3}L.N. Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
The geometricgauge equivalent of the famous Ishimori spin equation is the (2 + 1)dimensional DaveyStewartson equation, which in turn is one of the (2 + 1)dimensional generalizations of the nonlinear Schrödinger equation. Multicomponent generalization of nonlinear integrable equations attract considerable interest from both physical and mathematical points of view. In this paper, the twocomponent integrable generalization of the (2 + 1)dimensional DaveyStewartson I equation is obtained based on its onecomponent representation, and the corresponding Lax representation is also obtained.
Ioan Bica^{1}
^{1}West University of Timisoara, Faculty of Physics, Romania
An electrical device (ED) based on magnetorheological gel (MG) consisting of silicone rubber and Fe microparticles is fabricated. An experimental setup is built and described for measuring the electrical resistance R and capacitance C of ED in a static and in a periodic timevarying magnetic field (PTVMF). The results show that both R and C are significantly influenced by increasing the magnetic flux density, and the PTVMF induces transient processes in ED. We also show that electrical and rheological characteristics of MG are changed as a result of the rearrangement of Fe microparticles , with direct effects on R and C of ED.
Oded Shor^{1} , Ayelet Shauer^{2} , Nataly Kucherenko^{3} , Yair Elitzur^{4} , David Luria^{5} , Yulia Einav^{6}
^{1}Hadassah Medical Center, , Israel
^{2}Hadassah Medical Center, , Israel
^{3}Holon Institute of Technology, , Israel
^{4}Hadassah Medical Center, , Israel
^{5}Hadassah Medical Center, , Israel
^{6}Holon Institute of Technology, Faculty of Engineering, Israel
The cardiac ryanodine receptor RyR2 is a calcium release channel present in the cardiac muscle cells, which plays a major role in the regulation of Ca2+ homeostasis in the heart. We discovered a novel RyR2 missense mutation, G3118R, in a large family presenting with cardiac arrest phenotype. Interestingly, and unlike the other clinically relevant mutations in this gene, which are dominantly inherited, G3118R mutation is clearly recessive. Moreover, the mechanism by which this mutation determines this unusual clinical phenotype is unknown. We performed functional studies of the mutant RyR2 channel, including measurements of changes in intracellular Ca2+ levels and the monitoring of the endoplasmic reticulum Ca2+ dynamics. G3118R causes suppression of function of the channel, which is by far less described mechanism caused by most RyR2 mutations. Next, we used a Normal Mode Analysis to study the changes in the stability and the flexibility of RyR2 protein. G3118R is located in a peripheral region, whose function is unknown, but it affects allosterically the distant pore region by the means of changing the vibrational entropy and the potential energy values. The calculated entropy for the channel bearing the mutation in 0, 1, 2, 3 or 4 monomers are graduately increasing, indicating a cumulative effect of the mutation on the protein instability. Moreover, modeling other known mutations and normal variations in RyR2 reveals that dominant mutations mostly affect all 4 monomers, whether physiologically normal variations mostly affect 0 or 1 monomer only, suggesting a novel mode of structural impact, which has not been previously described.
Sachiyo Aburatani^{1} , Yuichi Kokabu^{2} , Ryota Teshima^{3} , Teppei Ogawa^{4} , Michihiro Araki^{5} , Tomokazu Shirai^{6}
^{1}National Institute of Advanced Industrial Science and Technology, Computational BioBig Data Open Innovation Lab., Japan
^{2}MITSUI KNOWLEDGE INDUSTRY CO., LTD., Bioscience Department , Japan
^{3}MITSUI KNOWLEDGE INDUSTRY CO., LTD., Bioscience Department, Japan
^{4}MITSUI KNOWLEDGE INDUSTRY CO., LTD., Bioscience Department, Japan
^{5}Kyoto University, Graduate School of Medicine, Japan
^{6}RIKEN, CSRS, Japan
Huge types of chemical reactions are usually occurred in living cells for surviving and adapting to various conditions. By those chemical reactions, the reactants and products are known to be sequentially modified through the metabolic pathways. Recently, synthetic biology field is shed light on to utilize and control these living cell abilities for construction of new/useful chemical compound. Actually, several types of computational algorithms have been developed to estimate the efficient metabolic pathways for biosynthesizing new chemical compounds. In this study, we defined a new feature to evaluate the possibility of those inferred metabolic pathways. We focused on the main chain structure of chemical compound as nondirection graph, and developed a method to define the similarity of these main chain structure graphs. In this study, we defined four features; 1) the number of nodes of main chain graph, 2) the graphical density of main chain graph, 3) the chemical density of main chain and 4) the graph centrality of reaction group in main chain graph. At first, we defined the main chain structures of all chemical compounds in living cells, about 10,000 compounds. After that, we calculated the values of the four features by defined equations in each compound. Finally, we calculated the correlation coefficients between all chemical compounds pairs from defined four feature values. By the comparison of similarities of main chain graphs between known chemical reactions in living cells, we had some insights for evaluation of chemical relation in living cells. In this presentation, we’ll present the details of our methods to evaluate the possibility of chemical reaction in living cells from new feature.
Anna Wawrzyńczak^{1} , Monika Monika BerendtMarchel^{2}
^{1}Siedlce University, Science Faculty, Poland
^{2}Siedlce University, , Poland
Release of hazardous materials in chemical industries is a significant threat to surrounding areas. This thread can be answered by the reconstruction system capable of localizing the source of airborne contamination solely based on substance concentrations recorded by the sensors network. However, such systems require multiple runs of the selected atmospheric contaminant transport model. The complexity of the contaminated terrain involves the application of the complicated and computationally expensive dispersion models. We examine the possibility of training an artificial neural network (ANN) so that it could effectively simulate the atmospheric toxin transport. The use of a fast neural network in place of costly computational dispersion models in systems localizing the source of contamination might significantly improve their efficiency (speed). In this paper, we train the ANN with the use of the training dataset covering the contamination source term parameters and point output concentrations generated by the Gaussian dispersion model. We test various ANN structures, i.e., numbers of ANN layers, neurons, and activation functions to achieve the ANN capable of estimating the contaminant concentration. The performed tests confirm that trained ANN has the potential to replace the dispersion model in the contaminant source localization systems.
Kuniyoshi Abe^{1} , Soichiro Ikuno^{2}
^{1}Gifu Shotoku University, Faculty of Economics and Information, Japan
^{2}Tokyo University of Technology, School of Computer Science, Japan
The hybrid BiConjugate Gradient (BiCG) methods such as BiCG stabilized (BiCGSTAB), Generalized Producttype based BiCG (GPBiCG), and BiCGstab($\ell$) are wellknown for efficiently solving linear equations. GPBiCG and BiCGstab($\ell$) is more effective and robust than BiCGSTAB. In the cases of the convergence behavior with a long stagnation phase, it is important to have BiCG coefficients that are as accurate as possible, and the stabilization strategy, which stabilizes the computation of the BiCG coefficients, has been developed. It may avoid stagnation and lead to faster computation. On present petascale highperformance computing hardware, the scalability of Krylov subspace methods has recently become increasingly prominent. The main bottleneck for efficient parallelization is the inner products which require a global reduction. The parallel variants of BiCGSTAB reducing the number of global communication phases and hiding the communication latency have been proposed. However, it has been reported that the convergence speed of the parallel variants of BiCGSTAB may become slower than that of the standard BiCGSTAB, and they may not be as robust as the standard. In this paper, therefore, we design parallel variants of GPBiCG, which is more robust than BiCGSTAB. Then we compare the convergence speed between the standard BiCGSTAB and GPBiCG methods and the parallel variants by numerical experiments. Moreover, we examine whether the stabilization strategy is effective.
This research was partly supported by JSPS KAKENHI Grant Number 19K12008.
Eugenia Echkina^{1} , Igor Inovenkov^{2}
^{1}Moscow State University, Computational Mathematics and Cybernetics, Russian Federation
^{2}Lomonosov Moscow State University, Department of Computational Math & Cybernatics, Russian Federation
Mathematical modeling of processes in hightemperature plasma is an important element of studying of behavior of laboratory and space plasma. Threedimensional nonlinear magnetohydrodynamic models allow to describe adequately such thin and interesting phenomena as formation of magnetic islands in tokamak plasma, emergence of current layers and "locks". In our paper we present the results of computer simulation of process of the magnetic reconnection in 3D magnetic configuration using the parallel algorithm.
Spyridon Vossos^{1} , Elias Vossos^{2} , Christos Massouros^{3}
^{1}NKUA, E. C., Greece
^{2}NKUA, E. C., Greece
^{3}National and Kapodistrian University of Athens, Euripus Campus, Greece
The mainstream approach of gravitational field is the development of Geometric theories of gravitation and the application of the Dynamics of General Relativity (GR) [12]. Besides, the Generalized Special Relativity (GSR) contains the fundamental parameter (ξ) of Theories of Physics (TPs). Thus, it expresses at the same time Newtonian Physics (NPs) for ξ→0 and Einstein Relativity Theory (ERT) for ξ=1 [3]. Moreover, the Equivalence Principle (EP) in the context of GSR, has two possible interpretations [46]: mG=m (1), or mG=γ(ξ,β) m (2), where β=υ/c and mG, m, γ are the gravitational mass, inertial rest mass and Lorentz γfactor, respectively. In this paper we initially present a new central scalar potential V=V(k,r), where k=k(ξ) and r is the distance from the center of gravity. We demand that this new GSR gravitational field in accordance with EP (1), gives the same precession of Mercury’s orbit as Schwarzschild Metric (SM) does [2] and we obtain k=6ξ^2. This emerges Einsteinian SRhorizon at r=5 rS, while NPs extends the horizon at six Schwarzschild radius (6 rS). We also can explain the Gravitational Red Shift (GRS), if only the proposed GSR Gravitational field strength g=g(k,r) is combined with EP (2). We modify the aforementioned Gravitational field as g=g(a,k,r), where a=a(ξ,r). The combination of the above with MOND interpolating functions [711] or the distributions of Dark Matter (DM) in galaxies [2,1216], provides six different functions a=a(ξ,r). Thus we obtain a new GSR central scalar potential V=V(a,k,r), which not only explains the Precession of Mercury’s Perihelion, but also the Rotation Curves in Galaxies [716], eliminating Dark Matter.
Dimitrios Vlachos^{1}
^{1}University of Peloponnese, Department of Informatics and Telecommunications, Greece
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Armen Bagdasaryan^{1} , Dubravka Gavric^{2}
^{1}American University of the Middle East, Mathematics, Kuwait
^{2}American University of the Middle East, Mathematics, Kuwait
In this work we consider the theoretical foundations of building fuzzy models of system dynamics, analysis of situations, their development, and control in complex weaklystructured systems based on knowledge modeling and expert preferences. The proposed fuzzy models can serve as mathematical tool for analyzing the behavior of a system in various situations, as well as to serve as the basis of specialized computer simulation systems of decision support in unstructured fuzzy situations. As is known, decision making problems under uncertainty can be divided into two groups: decision making in static situations and decision making in dynamic situations. For decision making in static situations, the methods and models of decision support based on the theory of choice are developed. The meaning of these methods is to order the set of possible solutions to the problem (alternatives) and then select the best alternative using the subjective utility function of the expert. The construction of the utility function is based on the extraction of an individual system of preferences, assessments and knowledge of the expert. For decisionmaking in dynamic situations, the dynamic models, including those based on expert knowledge, are used. To build a dynamic model of a situation, the expert knowledge about physical, economic, or social processes occurring in a system, which are represented as a cognitive map, is employed. The decision making in this case is to predict the development of situations and to find a strategy for steering the situation from the current state to the desired target state. The decisionmaking process includes the following steps: (1) analysis of the situation, (2) generation of solutions  alternatives, (3) evaluation of alternatives, (4) selection of the best alternative. The methods discussed above provide decision support at different stages of the decision process: models of analysis of static situations are focused on evaluation and ordering of alternatives, and models of analysis of dynamic situations are focused on generating of strategies (alternatives) to achieve the targets of control, that is, the desired target state of the situation. Obviously, these models complement each other. Thus, one of the aims of this paper is to develop mathematical methods for constructing integrated decision support models based on fuzzy models of hierarchical estimation, control, and fuzzy cognitive modeling.
Vladimir TertychnyDauri^{1}
^{1}ITMO University (Saint Petersburg National Research University of Information Technologies, Mechanics and Optics), Department of Physics and Engineering, Russian Federation
This work is devoted to solution of some problems connected with kinetic equations of reproduction for charged particles and charged splinters of the fission inside of nuclear toroidal electromagnetic generator (nuclegen). There are discussed questions of solutions behaviour for charged equations. Special attention is paid to charge kinetics of the nuclegen under the influence of small random disturbances and stimulated by this influence to analysis of stochastic motion properties for the ionite gas.
Eduardo Sanchez^{1} , Davinson Silva^{2} , Carlos Alberto Junior^{3} , Carlos Frajuca^{4} , Fabio Bortoli^{5}
^{1}IFSP, , Brazil
^{2}FATEC, , Brazil
^{3}IFSP, , Brazil
^{4}IFSP, Mechanics, Brazil
^{5}Instituto Federal de Educação, Ciência e Tecnologia de São Paulo  Campus São Paulo, Department of Mechanics, Brazil
Variable Reluctance Motors (VRM) have great advantages for applications in the most diverse areas of the industry and equipment, due to its versatility, robustness, stability and the possibility of precise control of rotation, power and torque. In view of these advantages, it was decided to develop and simulate this type of motor for the onscreen prototype, which is intended for the calibration of gravimeters, intended for the detection of gravitational waves through the effect of these waves on rotating objects in ultrahigh rotations of the order of 500,000 rpm. The proposed device requires a 1: 10,000 rpm error control, which will be possible due to the stability characteristics of the MRV. Due to the extremely low permissible vibration, the system uses magnetic bearings of the Lenz type in the rotor, with neodymium magnets interacting with the aluminum shaft, ensuring low friction and vibration. All of these aspects can be simulated using Matlab / Simulink, allowing a MRV performance perspective on the prototype.
The authos acknowledges CNPq and FAPESP.
Evgenii Krushinevskii^{1} , Sergei Andrianov^{2}
^{1}SaintPetersburg State University, Faculty of Applied Mathematics and Control Processes , Russian Federation
^{2}SaintPetersburg State University, Faculty of Applied Mathematics and Control Processes , Russian Federation
The article explores the methods of mathematical and computer modeling of the nonlinear dynamics of particle beams in cyclic accelerators in terms of the matrix formalism using both numerical and symbolic representations of the corresponding nonlinear differential equations. This paper shows how the matrix formalism approach allows the use of modern computational algorithms and artificial intelligence methods for more efficient and flexible modeling of particle beam dynamics in accelerators. Also, the article proposes a method of representing control elements using LEGO objects, which makes it possible to increase the efficiency of using control elements from a computational point of view and to facilitate the process of modeling particle dynamics.
Andrei Maksimov^{1} , Olga Baruzdina^{2} , Olga Maksimova^{3} , Vladislav Egorov^{4} , Aleksandr Baidganov^{5}
^{1}Cherepovets State University, Physics, Russian Federation
^{2}Cherepovets State University, Physics, Russian Federation
^{3}Cherepovets State University, Laboratory of mathematical and computer modelling of nanostructures, Russian Federation
^{4}Cherepovets State University, Laboratory of Mathematical and Computer Modelling of Nanostructures, Russian Federation
^{5}Cherepovets State University, , Russian Federation
To study the switching in thin ferroelectric films, we used a modified threedimensional Ising model. It is taken into account that under the influence of an internal electric field caused by spontaneous polarization, free particles move to the outer surfaces of the film and create an additional depolarizing field which depends on the value of the longrange orientation order in the film. The polarization was calculated by the Monte Carlo method. The hysteresis curves were calculated as a function of the frequency and the amplitude of the field, the temperature and the film thickness. The influence of the depolarizing field on the hysteresis curves for thin ferroelectric films has been investigated. To study this effect, the dependences of the area of the hysteresis curves for different values of film were also calculated. The effect of the depolarizing field weakens with increasing thickness of the film. This effect has a negligible influence for the film thickness of greater than 10 unit cells.
The study was supported by the Russian Foundation For Basic Research, Project № 193250032
Artur Aleksanyan^{1}
^{1}IPR NASA, Theoretical laboratory, Armenia
We have studied modification of the fluorescence spectra of a roomtemperature atomic rubidium vapor in the region of $^{85}Rb$ and $^{87}Rb$ $D_{2}$ line while changing the temporal rate of linear (triangular) scanning of laser radiation frequency. Increase of the ramping speed over certain value ($≈10^6$ MHz/s) results in essential modification of magnitudes of individual atomic transitions, different on rising and falling slopes, which characterize transition from a steadystate interaction regime to a transient one. Our experimental results are well consistent with the developed theoretical model. The obtained results can be used for determination of atomic system parameters such as relaxation rates. Possible followup actions on addressed control of atomic levels population is discussed.
Dubravka Gavric^{1} , Armen Bagdasaryan^{2}
^{1}American University of the Middle East, Mathematics, Kuwait
^{2}American University of the Middle East, Mathematics, Kuwait
Constant and rapid increase of social media users implies the increase of spread of misinformation in social media networks. One of the leading networks Twitter is becoming significant source of information and news for online users. This research proposes a new approach to the problem of combating misinformation in social media network Twitter. The approach is based on the SI (Epidemic) Fuzzy Model to combat the spread of misinformation on Twitter. The mathematical model is given by a system of differential equations including fuzzy parameters and factors that describe various characteristics of misinformation spread in complex network. We also reflect on current challenges in combating misinformation in social media with the goal to stimulate future research in that domain by pointing out important factors that need to be taken into account while developing a model for combating misinformation.
Alan Anaya^{1} , Francisco Delgado^{2}
^{1}Tecnologico de Monterrey, Escuela de Ingenieria y Ciencias, Mexico
^{2}Tecnologico de Monterrey, Escuela de Ingenieria y Ciencias, Mexico
Elucidating the conformational structure of proteins is one of the most significant challenges in the area of biophysics and bioinformatics. One of the simplest models for predicting native protein structure are the HydrophobicPolar and the MiyazawaJernigan approaches where the energy function is reduced by proper interactions among constitutive amino acids on a discrete lattice according to the quantum adiabatic theorem. Even though its simplicity, it has been proved its NPcompleteness for two and three dimensions. Quantum Adiabatic Computation allow us to construct a time dependent Hamiltonian where the lowest energy eigenstate conducts to the most probable protein conformation in a finite time of simmering. Still, for the most simple cases, evolution involves a lot of quantum states in superposition. As instance, for an $8$ amino acid peptide in $3D$, the associated state contains trillions of terms showing the potential of quantum processing. In this paper, we simulated (by using quantum adiabatic algorithms on a classical computer), the evolution carriedout with such Hamiltonians on a $3D$ grid for peptides with an achievable number of amino acids, thus comparing the performances of several techniques and tools.
Medine Demir^{1} , Songül Kaya^{2} , Aytekin Çıbık^{3}
^{1}METU, MATHEMATICS, Turkey
^{2}METU, MATHEMATICS, Turkey
^{3}Gazi University, MATHEMATICS, Turkey
This paper investigates approximate solutions for the DarcyBrinkman equations with doublediffusive convection. Double diffusive convection drives a flow which occurs due to buoyancy arising from the combination of temperature and concentration gradients. It holds very importance in various numbers of natural processes and engineering applications such as oceanography, geology, metallurgy, contaminant transport etc.. It is well known that, like all multiphysics problems, simulation of the doublediffusive system can be very expensive and thus practitioners need efficient methods to approximate solutions. In this study, we propose an accurate and efficient numerical model for a family of second order time stepping methods for the DarcyBrinkman system. The method uses the idea of curvature stabilization in which the discrete curvature of the solutions is added together with the linearized advective term at each time step. We prove unconditional stability result and also validate the theoretical findings with several numerical experiments. The numerical results demonstrate that the proposed method is remarkably successful, effective and accurate numerical technique for solving the DarcyBrinkman equations in doublediffusive convection.
Dingwei Huang^{1}
^{1}Chung Yuan Christian University, Department of Physics, Taiwan
We study the fluctuation and evolution of global research interests from 1985 to 2016. We consider 252 research areas in Web of Science and analyze the temporal variation of their rankings. The rank of a subject category reflects the number of annual publications in related scholarly journals, which also reflects the size of a community with shared research interests. The collections in Web of Science database are known to be dominated by science (SCI). This study reveals that, in the high ranks of the narrow categorization, science (SCI) also dominates over social sciences (SSCI) and humanities (A&HCI). In the last three decades, the general ranking of subject categories in SCI continues to rise. In contrast, a decline is observed in both SSCI and A&HCI. Especially a widening gap is noted between SCI and A&HCI. It seems that the arts and humanities have been marginalized in the database. The shift of research interests can also be observed in the continuing change of similarity between two distributions from different years. However, this study shows that the Lorenz curve remains stationary in the last thirty years. For specific subject categories, the rankings change from year to year. Yet the top 20% of categories always consist of 60% of annual publications; the bottom 60% of categories always consist of 20% of annual publications. This implies a 70/30 rule, ie, 70% of annual publications are in the hot 30% research areas. In many complex systems, the 80/20 rule or the Pareto principle can be applied. For example, 80% of wealth is in the hands of 20% richest people. In comparison, the distribution is more even in the academic publications. A delicate balance between exploitation and exploration is important in the process of knowledge accumulation. When the intensification is emphasized, one would expect the hot research areas to attract more attentions to make a significant progress. When the diversification is emphasized, however, one would desire a more even distribution to cover more research areas. This study also illustrated that the dynamics within a broad discipline is ready to be revealed by the narrow categorization in Web of Science. For example, in the last three decades, temporal variation in the subfields is much stronger in (Physics) than in (Psychology).
Bayan Kutum^{1} , Kuralay Yesmakhanova^{2} , Gaukhar Shaikhova^{3}
^{1}L.N.Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
^{2}L. N. Gumilyov Eurasian National University, Department of Mathematical and Computer Modeling, Kazakhstan
^{3}L. N. Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
In this paper, qdifference twodimensional Toda lattice is studied. Hirota’s bilinear technique is applied to it. Soliton solutions are constructed through the resulting bilinear form for qdifference twodimensional Toda equation. Interactions between soliton solitons are displayed with different choices of variable coefficients.
Nurzhan Serikbayev^{1} , Kuralay Yesmakhanova^{2} , Gaukhar Shaikhova^{3}
^{1}L.N.Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
^{2}L. N. Gumilyov Eurasian National University, Department of Mathematical and Computer Modeling, Kazakhstan
^{3}L. N. Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
In this present work, the extended tanh method is used to construct wave solutions of the Davey–Stewartson equations. The extended tanh method is a powerful solution method for obtaining different kind solutions of nonlinear evolution equations. This method can be applied to nonintegrable equations as well as to integrable ones.
Yurii Pepelyshev^{1} , Alexandr Popov^{2} , Sumkhuu Davaasuren^{3}
^{1}Joint Institute for Nuclear Physics, Frank Laboratory of Neutron Physics, Russian Federation
^{2}Joint Institute for Nuclear Research, Frank laboratory of Neutron Physics, Russian Federation
^{3}Joint Institute for Nuclear Research, Frank Laboratory of Neutron Physics, Russian Federation
IBR2M is a pulsed fast reactor of periodic operation. Its main difference from other reactors consists in mechanical reactivity modulation by a movable reflector. In the IBR2M pulsed reactor of periodic operation reactivity pulses are produced by the reactivity modulator which rotating close to the reactor core. When the two reflectors pass the core simultaneously, a reactivity pulse develops and for a short time (450 $\mu$ s) the reactor shuts down being in a supercritical state with prompt neutrons. As the reflectors move away from the reactor core, the reactor becomes deeply subcritical. As a result, the reactor generates powerful neutron pulses (power pulse) with a frequency of 5 Hz and an amplitude of 1830 MW [1]. The operation of the pulsed reactor has a specific feature, in which the knowledge of transient processes is extremely important for the safe and reliable operation of the reactor. For example, the reactor is equipped with an emergency protection system (EPS), including the deviation of peak power of +100 and $$50$\%$ and an average power of $\pm$20$\%$ from the set values. Due to the high sensitivity of the pulsed reactor towards reactivity fluctuations, random changes in the peak power are sufficiently large and reach $\pm$25$\%$ of the average level (for comparison: in a stationary reactor with uranium fuel, the power fluctuations are 14 times smaller). This means that the power perturbation margin before the EPS activation is small. In addition, the dynamic parameters of the reactor are varying during its operation. The operation of the IBR2 pulsed reactor (19872006) has shown that the power reactivity coefficient decreases during the operation of the reactor, therefore each reactor cycle meets its own transfer coefficient [2] and stability margin. In this regard, the study of dynamics of the IBR2M reactor (the modernized version of the IBR2, since 2011) is extremely important. The results of experimental and calculation studies of the IBR2M dynamics gained for its reliable and safe operation in the current paper are presented. The model is constructed on a modular structure using discrete transfer functions of the kinetics unit, the power feedback (PFB) unit conditioned by the heating of the reactor, and the automatic regulator (AR) unit based on nonlinear dependencies [3, 4]. For a confident prediction of the behavior of the reactor at rated power, it is important to imagine in what way the reactor parameters change in the process of burnup. However, the experiments required for this purpose have been carried out not at a nominal but reduced reactor power. For this purpose, the dynamics model of the IBR2M has been developed, which includes experimental data on reactor feedback parameters for the period 20152017 at an average power of 0.5 MW. The analysis of the IBR2M reactor dynamics at an average power of 0.5 MW and at a nominal flow of coolant of 100 m$^3$/h has shown that during the IBR2M operation for the period 20152017 with energyproduction up to 1200MW$\times$day considerable changes in the reactor dynamics and stability margins have not occurred. As transient processes at an average power of 0.5 MW and 2 MW are different in nature [5], it is planned to carry out a similar analysis at a nominal power of 2 MW as well. The present work is a continuation of the operation cycle on dynamics of the only pulsed reactor on fast neutrons of periodic operation.
The authors are thankful to the chief engineer A.V. Vinogradov for supporting our research work and to the colleagues of the IBR2M reactor for assistance in carrying out experiments during the period 20152017.
Marco Souza^{1} , Daniel Coppedé^{2} , Carlos Frajuca^{3} , Fabio Bortoli^{4} , Givanildo Santos^{5} , Francisco Nakamoto^{6}
^{1}Instituto Federal de Educação, Ciência e Tecnologia de São Paulo  Campus São Paulo, Department of Mechanics, Brazil
^{2}Instituto Federal de Educação, Ciência e Tecnologia de São Paulo  Campus São Paulo, Department of Mechanics, Brazil
^{3}Instituto Federal de Educação, Ciência e Tecnologia de São Paulo  Campus São Paulo, Department of Mechanics, Brazil
^{4}Instituto Federal de Educação, Ciência e Tecnologia de São Paulo  Campus São Paulo, Department of Mechanics, Brazil
^{5}Instituto Federal de Educação, Ciência e Tecnologia de São Paulo  Campus São Paulo, Department of Mechanics, Brazil
^{6}Instituto Federal de Educação, Ciência e Tecnologia de São Paulo  Campus São Paulo, Department of Mechanics, Brazil
This work shows the latest improvements in the geometry of the quadrupole mass of a gravitational signal generator device, which should be used in an experiment to measure the speed of gravity. This device must generate a tidal gravitational signal with a frequency of 3200 Hz. The gravitational wave detector Mario Schenberg, developed in Brazil, is the first option as the detector of the signal. The previous steps of the project are briefly discussed, and the new FEM (finite element modeling) simulation for the quadrupole mass is shown. An analysis of the mechanical stresses produced at highspeed rotation is presented. The new FEM simulation yields a favorable geometry for the inclusion of the magnetic suspension of the quadrupole mass. The results indicate the feasibility for the continuation of the project and subsequent construction of the real device.
Radka Keslerova^{1} , Hynek Reznicek^{2} , Tomas Padelek^{3}
^{1}CTU in Prague, Department of Technical Mathematics, Czech Republic
^{2}Czech Technical Uni. in Prague, Faculty of mechanical engineering, Czech Republic
^{3}CTU in Prague, Department of Transport Systems, Czech Republic
This work presents the numerical solution of generalized Newtonian fluids in the bypass geometry. The considered geometry consists of the narrowed host tube and the bypass graft with 30, 45, 60 degrees angle of the connection. Two values of the Reynolds number, 100, 200, are tested. The numerical results of nonNewtonian fluids are compared to the reults of Newtonian fluids. The governing system of equations is based on the system of balance laws for mass and momentum. Generalized Newtonian fluids flow in the bypass tube is numerically simulated by using SIMPLE algorithm included in OpenFOAM.
Hynek Reznicek^{1}
^{1}Czech Technical Uni. in Prague, Faculty of mechanical engineering, Czech Republic
The numerical simulation of dust spreading inside the Atmospheric boundary layer are usually modelled by commercial or inhouse CFD software. This contribution deals with the similar problem by using free OpenFOAM CFD toolbox. The buoyantBoussinesqSimpleFoam solver is modified to achieve reasonable results. A newly implemented wall function suitable for ABL preserving turbulent profiles through all domain is tested and verified. Also the effects of vegetative barriers for the dust concentration were studied. The numerical scheme is based on the finite volume method and SIMPLE method. For the convective terms the upwind scheme is used. Second order accuracy is achieved via the piecewise linear reconstruction, where gradients are calculated using least squares approach. To prevent artificial overshooting, minmod limiter is utilized.
The work is supported by CTU in Prague, the grant number is SGS19/154/OHK2/3T/12.
Dmitry Shulgin^{1}
^{1}Urals Federal University, Innovations and Intellectual Property, Russian Federation
A research purpose is to modify the model of patent landscape on an algorithm for the complex construction of technological landscape, taking into account the ecological and economic features of the region. Technological landscape as management tool for determining the points of innovation and technological development involves three basic stages. The first stage is to analyze the ecological and resource conditions in the region. The second is to build the model of wellknown patent landscape. In third stage, identification of the chosen direction, affect investment and development opportunities are presented to support the innovation and technological development of the region. Technological landscape opportunities in the direction of iron metallurgy are constructed for the Sverdlovsk region. The methodology of building technological landscapes over time may be useful in the construction and analysis of the technological trend of the studied direction.
Dmitry Shulgin^{1}
^{1}Urals Federal University, Innovations and Intellectual Property, Russian Federation
The research deals with phenomena occurring in the technical direction lifecycle when a new basic technology begins to prevail over an old one. The aim is to analyze peculiarities of technical direction development near the change point by means of patent data drawn from open sources. Besides discovered patterns, there are also proposed tools for mathematical description of observed transition process and classification for basic technologies. It is shown that identified regularities have the high reliability therefore it could be used in modeling technology lifecycle and technology development forecasting.
Meruyert Zhassybayeva^{1} , Kuralay Yesmakhanova^{2} , Ratbay Myrzakulov^{3}
^{1}L.N. Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
^{2}L. N. Gumilyov Eurasian National University, Department of Mathematical and Computer Modeling, Kazakhstan
^{3}L.N. Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
Nonlinear dispersionless equations can be obtained as dispersionless limits (quasiclassical limits) of integrable hierarchies of equations or by constructing a system of hydrodynamic type. In this paper, the dispersionless limit of the (1+1)dimensional FokasLenells equation is found. We present Lax pair for this dispersionless equation. As well known, the FokasLenells equation characterizes the propagation of ultrashort nonlinear light pulses in optical fibers. Exact solutions of the dispersionless version of the FokasLenells equation describe nonlinear shock waves in optical fiber systems. By using the obtained results, one can find “shock” wave solutions of the dispersionless equation, which have different physical applications.
Zamzagul Shanina^{1} , Ratbay Myrzakulov^{2}
^{1}L.N.Gumilyov Eurasian National University, Department of General & Theoretical Physics , Kazakhstan
^{2}L.N. Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
The coupled integrable dispersionless equations have a significant interest because of structure, integrability, and the possibility of obtaining a soliton solution. In this paper, we construct soliton surfaces for integrable dispersionless equation with selfconsistent sources in Riemann space. The surfaces, arising from MXXXII equation and their reduction in R^3, are studied. We obtain Gaussian and mean curvatures and also evaluate the area of surface parametrically defined with the Riemannian metric. Using the scale transformation and transformation of dependent and independent variables of the coupled dispersionless equations we obtain the equation that describes a currentfed string interacting with an external magnetic field in threedimensional Euclidean space.
Aliya Zhadyranova^{1} , Zhanbota Myrzakul^{2}
^{1}L.N.Gumilyov Eurasian National University, General and Teoretical Physics, Kazakhstan
^{2}Nazarbayev University, Mathematics, Kazakhstan
This paper describes the soliton surfaces approach. We constructed the surface associated with the WittenDijkgraafE.VerlindeH.Verlinde (WDVV) equations using SymTafel formula, which gives a connec tion between the classical geometry of manifolds immersed in R_m and the theory of solitons. The socalled SymTafel formula simplifies the explicit reconstruction of the surface from the knowledge of its fundamen tal forms, unifies various integrable nonlinearities and enables one to apply powerful methods of the soliton theory to geometrical problems. The soliton surfaces approach is very useful in construction of the socalled integrable geometries. Indeed, any class of soliton surfaces is integrable. We consider the geometry of sur faces immersed in Euclidean spaces. Such soliton surfaces for the WDVV equation for n = 3 case with an antidiagonal metric η_11 = 0 are considered, and first and second fundamental forms of soliton surfaces are found for this case. Also, we study an area of surfaces for the WDVV equation for n = 3 case with an antidiagonal metric η_11 = 0.
Piotr Kopka^{1}
^{1}National Centre for Nuclear Research (NCBJ) , Laboratory for Nuclear Energy and Environmental Analyses, Poland
We present the Bayesian framework able to identify the source of the airborne contaminant. We compare the effectiveness of framework utilizing the three popular Monte Carlo algorithms with the use of data from the fullscale field experiment  Copenhagen Tracer Experiments. The input data ta are the online arriving concentrations of released substance registered by sensors, while the output are the posterior probabilities of four parameters characterizing the contamination source, i.e.: contamination source position (x,y,z) and release rate (q). As the forward model to predict the concentrations at the sensors locations, we use fast response Secondorder Closure Integrated Puff model. The performer study present that among the Markov Chain Monte Carlo (MCMC), Sequential Monte Carlo (SMC) and Sequential Monte Carlo Approximate Bayesian Computation (SMC ABC) the last algorithm performed the best in the proposed framework localizing the airborne contaminant source parameters.
Zhanna Sagidullayeva^{1} , Gulgassyl Nugmanova^{2} , Ratbay Myrzakulov^{3}
^{1}L.N. Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
^{2}L.N. Gumilyov Eurasian National University, Mathematical and computer modeling, Kazakhstan
^{3}L.N. Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
In this paper, we present the dispersionless limit (quasiclassical limit) of the generalized LandauLifshitz equation with a selfconsistent vector potential. Using the scale transformation we also obtained the Lax representation, the compatibility condition of which give us the considering system. The results can be used to describe spin waves in magnets and ferromagnets in the absence of dispersive properties of the medium.
Agnieszka Siluszyk^{1} , Agnieszka Gil^{2} , Renata Modzelewska^{3} , Szczepan Moskwa^{4} , Marek Siluszyk^{5} , Anna Wawrzyńczak^{6}
^{1}Siedlce University of Natural Sciences and Humanities, Faculty of Sciences, Poland
^{2}Siedlce University, , Poland
^{3}Siedlce University, , Portugal
^{4}AGH University of Science and Technology in Krakow, , Poland
^{5}Siedlce University, , Poland
^{6}Siedlce University, Science Faculty, Poland
Abstract. The space weather and space climate problem is wellknown, in specially, for all which deal with investigations of disturbances of satellites operation, failures in groundbased electrical and electronic systems caused by geomagnetic storms. In spite of many studies on the changeable Sun and the uctuations in the interplanetary space triggered by solardriven disturbances, the question, which of the components of magnetic storms in uences the strongest the electrical and electronic systems is still open. Here, we consider this matter for the data of electrical grids breakdowns having unidentied reasons, as well as failures connected to the aging of the infrastructure elements and breakdowns of electronic devices, which occurred during the periods of an increased geomagnetic activity. Mathematical and statistical methods, among them neural net clustering, demonstrate that there exist connections between the groups of the coecients characterizing the state of Earths vicinity during magnetic storms and the number of failures in electrical network in southern Poland.
Nurgul Suikimbayeva^{1} , Pyotr Tsyba^{2} , Olga Razina^{3}
^{1}L.N.Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
^{2}L N Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
^{3}L N Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
We consider the XXZ model of a magnet with spin1/2. Depending on the configuration of the system for a finite number of spins N in the chain we obtained possible values of energy and momentum.
Tolkyn Kassenova^{1} , Pyotr Tsyba^{2} , Olga Razina^{3}
^{1}L.N.Gumilyov Eurasian National University, Department of General and Theoretical Physics, Kazakhstan
^{2}L N Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
^{3}L N Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
An eightvertex model is investigated over a Grassmann algebra. The constant solutions of the Yang – Baxter equation are used, the calculations of the supertrace and the superdeterminants in a nonstandard basis are given, using a block matrix. The constant solutions of the Yang – Baxter equation are used in quantization of the knot theory. The solution of the quantum Yang – Baxter equation is the R  matrix, which corresponds to the transfer – matrix of the eightvertex model of statistical mechanics.
Duman Kenzhalin^{1} , Kairat Myrzakulov^{2}
^{1}L.N. Gumilyov Eurasian National University, Kazakhstan, Department of General & Theoretical Physics, Kazakhstan
^{2}Eurasian National University, Department of General & Theoretical Physics, Kazakhstan
A cosmological model where a fermion field is nonminimally coupled with the gravitational field in Bianchi type I spacetime is studied. By applying Noether symmetry the possible functions for the coupling and for the potential density of the fermion field are determined. Cosmological solutions are found showing that the nonminimally coupled fermion field behaves as an dark energy describing an accelerated expansion scenario.
Gulnur Bauyrzhan^{1}
^{1}L.N.Gumilyov Eurasian National University, Department of general and theoretical physics, Kazakhstan
In mathematics and physics, one of the main tasks is to relate differential geometry and nonlinear differential equations, it means that the study of particular cases of subvarieties, curves, and surfaces are of great importance. Soliton surfaces associated with integrable systems to play an essential role in many problems with the physical application. In this paper, we study the complex modified Korteweg–de Vries (cmKdV) equation. It is well known that the cmKdV equation is a very important integrable equation. We present the relationship between an integrable system and soliton surfaces and namely Lax representation of the cmKdV equation was used to obtain the first and second fundamental forms.
Carlos Frajuca^{1} , Fabio Bortoli^{2}
^{1}IFSP, Mechanics, Brazil
^{2}Instituto Federal de Educação, Ciência e Tecnologia de São Paulo  Campus São Paulo, Department of Mechanics, Brazil
An experiment to measure the speed of gravitational signals in short distances is been developed with the goal to study its behavior as traveling through a medium. The experiment is composed of 3 sapphire devices suspended in vacuum and cooled down to 4.2 Kelvin. The amplitudes of the central device (detector) is monitored by an ultralow phase noise microwave signal using resonance in the whispering gallery modes. The other two sapphire devices are excited by piezoelectric crystals which make the two devices vibrate at the same frequency and phase. Between the two vibrating devices and the detector, a different medium will placed, then the speed is measured and compared with the case where the medium is pure air. The modeling of the experiment is made assuming the detector as a springmass system. The results shows that the detection is possible.
The authos acknowledge CNPq and FAPESP.
Denis letavin^{1}
^{1}UrFU, Radio telecommunication, Russian Federation
This paper presents the topology of the directional coupler that carries out the power division of 1 to 3. The area of the proposed device was reduced by 72.5% due to the use of artificial cells, whose characteristics are equivalent to quarterwave segments, with smaller dimensions. Using the NIAWR Environment 14 program, the topology of the proposed device was developed, with an operating frequency of 1 GHz and on the FR4 material. Then, using a photolithography, a prototype of the coupler was made and its characteristics were measured using a R&S vector network analyser.
Author are grateful for the simulation software NIAWR Design Environment provided by the National Instruments Company. The research was executed by the grant of the Ministry of education and science of the Russian Federation (project № 8.2538.2017/4.6). The research was performed on equipment of the Urals Federal University common use center.
Denis letavin^{1}
^{1}UrFU, Radio telecommunication, Russian Federation
This paper analyzes the new compact design of couplers based on the use of microstrip lowpass filters. The proposed design achieves significant reduction in coupler size while obtaining the same characteristics as of the conventional coupler. Prototype of the coupler with the central frequency of 1 GHz was produced on the substrate with dielectric permittivity of 4.4. The experimental results showed good agreement with numerical simulations. The size of the ratrace coupler was reduced by 83.7%.
Vladimir Bochkarev^{1} , Valery Solovyev^{2}
^{1}Kazan Federal University, Institute of Physics, Russian Federation
^{2}Kazan Federal University, Institute of Philology and Intercultural Communication, Russian Federation
It was previously shown that the WordNet thesaurus has a smallworld structure. We obtained a similar result for RuWordNet, a recently created thesaurus of the Russian language, and determined the main characteristics of the network of semantic relations in the Russian language. They are the average length of the path between the vertices, the maximum path length between the vertices, the cluster coefficient and the assortativity coefficient. The distribution of the vertices degrees was also considered. We compared the values of the structural parameters of the networks for WordNet and RuWordNet. A significant difference between RuWordNet and WordNet is that RuWordNet has many semantic relations of the 'POSsynonymy' type (synonymy between words of different parts of speech) that are hardly found in WordNet. The values of structural constants were determined for RuWordNet both regarding this type of relations and without taking into account these relations, which allows one to estimate the influence of relations between parts of speech on the structure of the words network.
Igor Bataronov^{1} , Viktor Dezhin^{2}
^{1}Voronezh State Technical University, Higher mathematics and physical and mathematical modeling, Russian Federation
^{2}Voronezh State Technical University, Higher mathematics and physical and mathematical modeling, Russian Federation
The vibration spectra of the edge, mixed and screw dislocations, depending on the dislocation segment length, are considered. The value of Poisson's ratio 1/3 is assumed. The normalized values of the eigenfrequencies and damping coefficients for different frequency numbers by equating the inverse matrix of dislocation oscillators generalized susceptibilities [1] to zero were found. It is seen from the dependences obtained that in the case of a screw dislocation the transformation of the dislocation oscillators generalized susceptibility poles occurs. For edge and mixed dislocations the transformation of the poles was not observed. This agrees with the results of the vibration spectrum orientation dependence study. The authors suggest that these differences are due to the presence of a screw dislocation quasilocal vibration branches [2]. 1. Bataronov I.L. and Dezhin V.V. J. Phys.: Conf. Ser. V. 738. 012108. (2016). 2. Bataronov I.L. and Dezhin V.V. J. Phys.: Conf. Ser. V. 936. 012035. (2017).
Carlos Alberto Junior^{1} , Carlos Frajuca^{2} , Davinson Silva^{3} , Eduardo Sanchez^{4} , Fabio Bortoli^{5}
^{1}IFSP, , Brazil
^{2}IFSP, Mechanics, Brazil
^{3}FATEC, , Brazil
^{4}IFSP, , Brazil
^{5}Instituto Federal de Educação, Ciência e Tecnologia de São Paulo  Campus São Paulo, Department of Mechanics, Brazil
Brushless DC motors (BLDCM) are recognized for their high efficiency and low maintenance cost and are continuously subject to change in applications without motion control. The BLDCM can be used as an option to traditional switched reluctance motors. For the control of the speed of permanent magnet motors the more common is an integral proportional control (PI). The PI drivers are widely used because of a simple, easytoimplement control structure, but they are presented as control complexities, such as nonlinearity, parametric load perturbations and protection. The use of this method of pulse control (PWM) using a SIMULINK / MATLAB simulation to obtain the values necessary to control the speed of the brushless motor used in the gravitational wave calibrator prototype. SIMULINK / MATLAB is used to become a reliable and flexible simulation. The command will be used for precision accuracy of a ten thousand version of the calibrator.
The authors thanks CNPq and FAPESP.
Vladimir Bochkarev^{1} , Anna Shevlyakova^{2}
^{1}Kazan Federal University, Institute of Physics, Russian Federation
^{2}Kazan Federal University, Institute of International Relations, Russian Federation
Knowledge of probability distribution of frequency of words and phrases is important in solving many practical problems such as estimation of semantic similarity between words, detection of semantic changes and others. It is assumed by many researchers that frequencies of words obey the Poisson law. However, there is much evidence that the Poisson distribution describes empirical data unsatisfactory. The analysis of the probability law in this case is greatly complicated by the fact that series of frequencies in most cases are nonstationary. This paper discusses the distribution law of time series of word frequencies based on the Google Books Ngram corpus data. It is shown that the correlation between the first moments of the frequencies differs from that expected in the assumption of the Poisson distribution. In particular, anomalously high values of frequency dispersion are observed for words with high frequency. To check the significance of deviations from the Poisson law, statistical modeling of frequency series was performed. Alternative assumptions about the probability distribution of word frequencies are also considered.
Viktor Dezhin^{1} , Vladimir Nechaev^{2}
^{1}Voronezh State Technical University, Higher mathematics and physical and mathematical modeling, Russian Federation
^{2}Voronezh State Technical University, Higher mathematics and physical and mathematical modeling, Russian Federation
Bending vibrations of a mixed dislocation in a uniaxial ferroelectrics are considered, the dislocation line is located along the ferroelectric axis. Based on the complete system of equations describing the vibrations of a ferroelectric crystal with a dislocation, system of equations for the mixed dislocation dynamics in a linear approximation in the dislocation displacement is written. An expression for the Peach–Koehler force acting on the dislocation is obtained, and the linear response function of the mixed dislocation is found.
Jose Tadeu Lunardi^{1}
^{1}State University of Ponta Grossa, Mathematics & Statistics, Brazil
The quantum tunneling phenomenon is one of the most counterintuitive features of quantum mechanics, and the problem of determining the time a particle takes to cross a classically forbidden region has been a very controversial subject since the early days of the theory. Recently, advances in ultrafast physics opened the possibility to measure times of ionization of atoms, induced by the application of a strong laser field, at the scale of attoseconds. However, the intrinsic experimental difficulties associated both with the measurements and the interpretation of the results have, so far, prevented an elucidation of the problem and, in fact, contradictory results still persist, with some experiments obtaining a finite nonzero result and others being compatible with instantaneous tunneling. In this work we consider a simple model for the strong field ionization of an electron that, at $t=0$, is in the bound state of a Dirac delta potential well; immediately after $t=0$ the potential is deformed by the application of a strong linear laser field. We use this model to obtain a probability distribution, recently proposed by the authors, for some times associated to the ionization process, including barrier exit times and tunneling times. Although simple, our model shares qualitative features with real attoclock experiments, and we explore these similarities to discuss the possibility of interpreting the time measurements in those experiments as being tunneling times.
Armen Bagdasaryan^{1}
^{1}American University of the Middle East, Mathematics, Kuwait
The problem of synthesis of optimal control of complex nonlinear and multidimensional systems oriented on the building of integrated control systems with the adaptation and selforganization properties is of much current interest. The further development of optimization methods employed in control problems demonstrated their effectiveness and has led to the construction of algorithms of approximate solution of optimization problems that significantly extends the class of control problems that can be set. In this work we consider a synthesis of optimal control for affine nonlinear system, in which a special emphasis is placed on the degenerate problems of optimal control. Our approach is based on the extension of the method of minimization of generalized work function by properly transforming the initial nondegenerate problem of optimal control into degenerate problem of optimal control synthesis. The search for the solution is based on the suboptimal strategy that includes the construction of minimizing sequences that converge intervalwise to the optimal solution of the initial problem. We obtain some optimality conditions as well as the necessary and sufficient conditions of existence of optimal solution.
Ana Lúcia Pereira^{1}
^{1}State University of Ponta Grossa, Department of Mathematics and Statistics, Brazil
Social representations were introduced in the social psychology by Moskovici in 1961, and consists in a framework of ideas, concepts, beliefs or feelings shared by individuals in a given group, regarding some social object. Since then, social representations theory evolved both in its conceptual aspects and in the development of methodological tools to analyse data. In the last decades a great effort was made in the development of quantitative tools, as complementary to the most usual qualitative analysis. For instance, graphs of similarity, several techniques of clustering and statistical analysis of frequency and evocation order are often used to analyse the structure of a social representation. In this work we propose to use the technique of Hodge ranking to rank the vertices in a graph as a complementary quantitative tool to reveal the structure of a social representation. This technique provides an ordering of the data elements (ideas, concepts, feelings, etc.), based on the relative importance individuals associate to them, and has the advantage of working fine with imbalanced data, that is often the case in social representations in which individuals evoque ideas spontaneously, sometimes inconsistently. Another advantage of this technique is that it provides measures of the global inconsistencies in the ranking results.
Hugo Aya Baquero^{1}
^{1}Universidad Distrital Francisco José de Caldas, Facultad de Ingeniería, Colombia
Terminal current in a device increases when energetic carriers create additional carriers by impact ionization. Okuto and Crowell suggested an empirical model for describe this phenomenon. In this paper, Monte Carlo techniques were used to observe the effect of variability in the impact ionization coefficients on the results obtained from a computational model for electrons and holes transport. The model was implemented in FEM simulation tool, in order to study avalanche current in a MOSFET including uncertainty of the impact ionization coefficients of material.
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.
Nurbolat Jaichibekov^{1}
^{1}L.N.Gumilyov Eurasian National University, Faculty of mechanics and mathematics, Kazakhstan
Oscillatory chemical reactions, in which the concentrations of reacting substances change periodically, have been the subject of study by scientists of various specialties for more than one hundred years: chemists, physicists, biologists, geologists, physicians, mathematicians [1]. The bestknown examples of oscillatory chemicals reactions are BrayLiebhafsky reaction (1921), BelousovZhabotinsky reaction (1958) and BriggsRauscher reaction (1972). Liesegang rings (or layers), representing spatial periodic structures, were first discovered by the German chemist Raphael Edward Liesegang in 1896, but a theory has not yet been created that can explain all the mechanisms underlying this periodic reaction [23]. Further theoretical and experimental study of the patterns of formation of Liezegang structures can, in particular, contribute to a deeper understanding of the characteristics of sedimentation in various technological processes in petrochemical production. In the present paper the formation of Liezegang structures, i.e. the process of periodic deposition with the mutual diffusion of two reacting chemicals in the presence of an external constant electric field, is studied using numerical modeling. The mathematical model of the process consists of three differential equations of diffusionreaction for the concentrations of the initial components and the resulting precipitate. The kinetics of sedimentation is described in accordance with the Ostwald’s supersaturation theory. The equations of the mathematical model in onedimensional and twodimensional statements were solved numerically using the control volume method using computer code written by the authors in the C ++ language. As a result of numerical simulation in the absence of an electric field, periodic structures were obtained formed of the precipitate , which qualitatively correspond to the patterns observed in the experiments. It is shown that numerically obtained Liesegang rings satisfy the wellknown laws: the ratio of the distances to neighboring rings remains constant and there is a power dependence between the distances to the rings and the time of their formation. The influence of the ratio of the concentration of the starting substances and the electric field strength on the nature of the structures formed is investigated. It also has been shown that an increase in the electric field strength leads to a decrease in the number of structures formed.
2010 Mathematics Subject Classification: 37N10, 65N08, 80A32
Svetlana Absalyamova^{1} , Liliya Zulfakarova^{2} , Natalya Ivanova^{3} , Chulpan Mukhametgalieva^{4}
^{1}Kazan Federal University, Institute of Management, Economics and Finance, Russian Federation
^{2}Kazan Federal University, Institute of Management, Economics and Finance, Russian Federation
^{3}Kazan Federal University, Institute of Management, Economics and Finance, Russian Federation
^{4}Kazan Federal University, Institute of Management, Economics and Finance, Russian Federation
The article is devoted to the study of modern trends in energy resources megamarket. The results of the study reveal a system of factors affecting the production and consumption of energy resources in the global economy. The authors make a forecast of the development of traditional and alternative energy in the coming decades. The paper assess the degree of influence of the changing conjuncture of the world energy market on the Russian economy. The study shows the presence of high closeness of communication on the Chaddock scale and the direct linear dependence of Russia's GDP at current prices on the volume of oil and gas revenues of the consolidated budget of the Russian Federation, confirmed by calculating the Pearson correlation coefficient. The article proposes a set of measures that reduce the dependence of the Russian budget on the world energy market.
Yuriy Dimitrienko^{1} , Elena Gubareva^{2}
^{1}Bauman Moscow State Technical University, Computational Mathematics and Mathematical Physics, Russian Federation
^{2}Bauman Moscow State Technical University, Computational Mathematics and Mathematical Physics, Russian Federation
The problem of the deformation of thin twolayer plates, in which the slip condition is given at the interface between the layers, instead of the classical case of ideal contact, is considered. The method of asymptotic analysis of the 3dimensional elasticity theory equations is applied to solve this problem when exposed to lateral pressure, longitudinal and shear forces on the end surfaces. Asymptotic analysis is performed on a small geometrical parameter representing the ratio of the thickness to the characteristic length of the plate. Recurrent formulations of local quasionedimensional problems of the theory of elasticity with slippage are obtained. An explicit analytical solutions are obtained for these tasks. The averaged equations of elastic equilibrium of a twolayer plate with slipping layers are derived. It is shown that due to slippage, the order of averaged equations of the theory of plates rises to 5 orders of magnitude, in contrast to the classical 4th order, which takes place in the theory of KirchhoffLove plates. Additional boundary conditions for this system of order 5 are formulated and its analytical solution is obtained for the case of a rectangular plate under the action of uniform pressure. A numerical analysis of the solution of the averaged problem is carried out. It is shown that the presence of slippage of layers significantly increases the plate deflection compared with the conditions of ideal contact of layers
The reported study was funded by Ministry of Education and Science of the RF according to the research project (Goszadanie) No. 9.3602.2017/ПЧ
Yuriy Dimitrienko^{1} , Olga Dimitrienko^{2} , Alexandra Dobrynina^{3}
^{1}Bauman Moscow State Technical University, Computational Mathematics and Mathematical Physics, Russian Federation
^{2}Bauman Moscow State Technical University, , Russian Federation
^{3}Bauman Moscow State Technical University, Computational Mathematics and Mathematical Physics, Russian Federation
The problem of identifying individual buyers in a supermarket based on a large amount of data on cashier's checks in a supermarket over a long period of time is considered. A complex of mathematical models for solving this problem using automated numerical data analysis is proposed. A special product space has been built, the concept of the trajectory of the movement of customers in the product space has been introduced A computational algorithm has been developed for solving the problem of identifying individual customers using panel data of cash vouchers. The algorithm is universal because it does not use any personal data. As an example of specific input data, commodity checks from the supermarket chain were used for a certain period of time.
Identifying of individual buyers, analysis of large panel data
Evgeny Shilko^{1}
^{1}Institute of Strength Physics and Materials Science SB RAS, Laboratory of computeraided design of materials, Russian Federation
The regularities of the nonlinear behavior of viscoelastic materials and the related nonstationarity of mechanical characteristics (namely, their dependence on the loading rate) are the issues in a wide range of analytical and computational studies as these features determine the peculiarities of functioning of critical elements of various technical and natural structures including biological ones. A broad subgroup of materials of this class comprises materials with the high contrast of local mechanical properties that contain viscous soft matter phases as structural constituents. Wellknown examples are porous fluidsaturated materials, such as rocks, bone and soft tissues, other natural and synthesized biomedical and engineering materials. Interstitial fluid can change the behavior of a material dramatically. In particular, the mechanical interaction of solidphase and liquidphase components can determine a strongly pronounced nonlinear dependence of the mechanical behavior and effective mechanical characteristics of the material on the loading rate even in a quasistatic region in which the substance of the solidphase skeleton is insensitive to strain rate. Moreover, at higher loading rates the material response is determined by the ratio of the relaxation times of the skeleton and the characteristic time of redistribution of interstitial fluid in the pore space. The above said determines the relevance of conducting theoretical studies of crucial aspects of nonlinear dynamic behavior (including fracture) of fluidsaturated viscoelastic materials under complex loading conditions. A useful tool for carrying out these studies is computer modeling using the discrete element method (DEM). A key advantage of this particlebased numerical method is the ability to explicitly model fracture processes (including multiple fractures) on various scales from micro to macroscopic. This makes DEM attractive, in particular, for studying contact interaction, friction and wear in viscoelastic contact pairs of different nature, including articular joints. In this work, we developed a DEMbased model, which allows describing the mechanical behavior of porous fluidsaturated materials with a viscoelastic skeleton. To build the model we used an implementation of DEM, which is called the method of movable cellular automata (MCA). The main feature of this implementation is the use of a generalized manybody formulation of relations for the forces of elementelement interaction. Within this formalism, we developed threedimensional models of permeable fluidsaturated materials with solid skeleton characterized by viscoelastic rheological properties (including Kelvin and Maxwell models and the standard model of elastomers). The influence of the pore fluid on the stress state of the skeleton is taken into account based on the Biot model of poroelasticity. Fluid transport in the pore space is modeled using the finitevolume implementation of the classical equation of fluid mass transfer. Using computer modeling, we obtained the generalized relations, which describe the dependences of uniaxial compressive strength and effective Young's modulus of some kinds of viscoelastic fluidsaturated materials on the strain rate, the relaxation times of the skeleton and the characteristic time of redistribution of fluid in the pore space. We showed for the first time that these dependences are logistic and can be described by common sigmoid “master” functions of the special dimensionless parameter. The relevance of the simulation results is determined by the possibility of their application for assessing and predicting the mechanical response of fluidsaturated viscoelastic technical and natural materials (including bone tissue) under dynamic loading.
This research was supported by the Russian Science Foundation (grant No. 171101232).
Lazzat Sansyzbay^{1} , Batyrbay Orazbayev^{2}
^{1}L.N.Gumilyov Eurasian National University, Faculty of Information Technology, Kazakhstan
^{2}L.N.Gumilyov Eurasian National University, Faculty of Information Technology, Kazakhstan
Background. People spend a long period in premises during their life. The parameters of the microclimate, established in the room, directly affect the health of the person and his performance. Therefore, when designing modern buildings, there are increased requirements for creating and providing comfortable conditions for human life and activity. Maintaining the microclimate at a given level is carried out using various automated control systems necessary to regulate specific parameter (temperature, humidity, carbon dioxide concentration). Most of the currently existing microclimate control systems operate on the basis of traditional P, PI, PID controllers. But the work of such systems is effective only in a narrow operating range. With significant fluctuations in environment, it is required to reconfigure the parameters of these regulators each time. In such cases, maintaining comfortable conditions in the room is recommended by using intelligent control technologies, socalled fuzzy control systems, operating in terms of fuzzy logic. Objective. The aim of the paper is to research the possibility of implementation of intelligent control systems to maintain the comfortable microclimate in the premises and checking the adequacy of the system through simulation. Methods. The climate control system is based on fuzzy inference and provides forming the base of fuzzy production rules, fuzzification of input values, aggregation of truth of sub conditions of each rule, activation of conclusions and defuzzification process that generates an output signal to control the smart home functional devices. Procedures of the fuzzy inference and simulation are implemented in the Matlab programming environment using the Fuzzy Logic Toolbox and Simulink packages. Conclusions. The results of the paper showed that the developed intelligent microclimate control system for premises based on fuzzy logic provides a flexible selftuning of the engineering equipment and maintaining the microclimate parameters at the required level.
Rustem Sakhapov^{1} , Muhammat Gatiyatullin^{2} , Regina Nikolaeva^{3} , Marat Makhmutov^{4}
^{1}Kazan State University of Architecture and Engineering, ROAD CONSTRUCTION MACHINERY, Russian Federation
^{2}Kazan State University of Architecture and Engineering, Road construction machinery, Russian Federation
^{3}Kazan State University of Architecture and Engineering , Road construction machinery, Russian Federation
^{4}Kazan State University of Architecture and Engineering , Road construction machinery, Russian Federation
This article investigates the increase of tractioncoupling properties of propellers, patency of machinetractor units and decrease of soil compaction. For a propulsor equipped with antiskid devices, the slippage process is formed due to factors of soil compression by the soiltread and shear of the soil by tire hooks. With the decrease in the number of detachable hooks, the period when the first hook disengaged and the second has not yet entered in interaction with the ground, increases. At the moment, traction and coupling properties of the wheel are formed only due to the tire hooks. When the detachable hook engages with the soil, the traction capacity of the wheel is made up of the forces of shear of soil "bricks" sandwiched between tire hooks and the forces of soil deformation by detachable hooks. As a result of integrating the dependence of the shear stress and deformation of the soil, a formula was obtained to determine the tangential traction force of the tractor. If the skidding of the wheel assembly depends on the pulling force, then the drag force from the antiskid device. Using the known dependencies of the slippage of wheeled propellers, dependences are obtained to determine the slippage of the propulsion unit with the antiskid device. With the increase in the number of antiskid devices on the wheel, slippage is reduced, however, according to the research, the time required for the assembly and disassembly of the device reduces the interchangeability of the wheel assembly. We calculated he number of antiskid devices at which the maximum exchange capacity will be reached. The penetration depths at which the maximum efficiency of the wheel assembly running system will be reached are obtained and the results are tabulated.
Alexey Kislov^{1}
^{1}Ural Federal University, Institute of Physics and Technology, Russian Federation
The effect of trivalent Eu ion on the atomic structure and the vibrational spectrum of cubic Gd2O3 is investigated. This study was performed by means of computer modeling within the framework of a shell model. The equilibrium structures and the phonon symmetrized local densities of states have been calculated. In addition, frequencies of localized vibrations induced by Eu impurity have been determined. These frequencies are compared with the available experimental data in literature.
The work was supported partially by the Ministry of Education and Science of the Russian Federation (Government Task No. 3.1485.2017/4.6) and by Act 211 of Government of the Russian Federation, contract № 02.A03.21.0006
Dmitry Conyuh^{1}
^{1}Ioffe PhysicalTechnical Institute of the Russian Academy of Sciences, , Russian Federation
In this work, we apply the random matrix theory to the study of vibrational properties of disordered systems with a big number of degrees of freedom, such as amorphous solids. The random matrix theory is applied in many fields, for example, in theoretical neuroscience, computer, and social networks. Different random matrix ensembles are used to identify properties of complex systems with different intrinsic symmetries. Mechanical stability of amorphous solids implies the Wishart ensemble with the positive definite dynamical matrix of the form $\hat{M} = \hat{B}\hat{B}^T$. The translational invariance in amorphous solids leads to the sum rule $\sum_i B_{ij} = 0$, which means nonzero correlations of the matrix elements $B_{ij}$. The proposed correlated Wishart ensemble has many universal properties of amorphous solids. One of these properties is the boson peak in the reduced vibrational density of states $g(\omega)/\omega^2$. The boson peak has been observed in many experiments on amorphous solids, but its nature was not clear so far. We show that the boson peak naturally occurs in the proposed model and find its analytical form.
This work is supported by the Russian Federation President Grant no. MK3052.2019.2.
Yerbol Ospanov^{1}
^{1}Shakarim University, cathedra “Automation and Computer Engineering“, Kazakhstan
This paper proposes a method for development of model systems based on various information considering example of technological system of benzene production and researching problems of combined model construction, i.e. sets of mathematical models that enable to extensively describe work of complex chemicaltechnological systems (CTS). Mathematical models are built for fractionating and benzene columns, CTS primary units on benzene production of Atyrau refinery. On the basis of proposed method, it has been established that it is optimum to design combined models for these units, i.e. volumes of target products at the exit are defined using regression models, whereas quality indicators of product are determined using fuzzy models. Influence of aromatic hydrocarbons in reformatte on average octane number of benzene is determined based on logical rules of conditional proof and linguistic models according to knowledge base.
Oleg Rabinovich^{1}
^{1}NUST MISIS, Semiconductor devices, Russian Federation
In this paper we present pin GaAs & perovskite PV cells comparison of inseries or inparallel connection. It is made based on the two tandems types with a nonmonolithic connection and experimental subcells. The results based on tandems simulation are discussed. It is shown that the inparallel connection is preferable than inseries even when the subcell photocurrents are not balanced and the open circuit voltages (Voc) are close to each other. Inparallel connection cell efficiency more than 22 % is demonstrated for the GaAs shading effect by MAPbI3 film, with an achieved shortcircuit current density (Jsc)  39 mA/cm2.
The work was carried out with the financial support of the Ministry of Education and Science of the Russian Federation within the framework of the state task to the university № 3.2794.2017/4.6
Oleg Rabinovich^{1}
^{1}NUST MISIS, Semiconductor devices, Russian Federation
Changing LED performance characteristics, depending on Indium atoms concentration and at different temperatures were simulated. It was suggested that a heterostructure having pn junction area S0 can be considered as a sum of “SmallLED” electrically connected in parallel. Good correlation in simulation and experimental results has been obtained. It was determined that the best AlGaP heterostructure contains 5 wide QW (width 10 nm each) in active region. The main thing is that in central ones there is maximum radiation and at the both ends of active region are “barriers” which help to concentrate electrons/holes in active region and additionally “protect” QW from different defects.

Anatoly Zatsepin^{1}
^{1}Ural Federal University, Institute of Physics and Technology, Russian Federation
The effect of trivalent Eu ion on the atomic structure and the vibrational spectrum of cubic Gd2O3 is investigated. This study was performed by means of computer modeling within the framework of a shell model. The equilibrium structures and the phonon symmetrized local densities of states have been calculated. In addition, frequencies of localized vibrations induced by Eu impurity have been determined. These frequencies are compared with the available experimental data in literature.
The work was supported partially by the Ministry of Education and Science of the Russian Federation (Government Task No. 3.1485.2017/4.6) and by Act 211 of Government of the Russian Federation, contract № 02.A03.21.0006
Wilfried Allaerts^{1}
^{1}Biological Publishing A&O and Erasmus MC, Rotterdam, Immunology, Netherlands
The main global threats of the biosphere on our planet, such as a global biodiversity impairment, global health issues in the developing countries, associated with an environmental decay, unnoticed in previous eras, the rise of greenhouse gasses and global warming, urge for a new evaluation of the applicability of mathematical modelling in the physical sciences and its benefits for society. In this paper, we embark on a historical review of the mathematical models developed in the previous century, that were devoted to the study of the geographical spread of biological infections. The basic notions of connectivity, continuity and distance norm as applied by successive biomathematicians, starting with the names of Volterra, Turing and Kendall, are highlighted in order to demonstrate their usefulness in several new areas of biomathematical research. These new areas include the wellknown fields of community ecology and epidemiology, but also the less wellknown field of multicellular pathway prediction. The biological interpretation of these abstract mathematical notions, as well as the methodological criteria for these interpretative schemes and their corroboration with empirical evidence are discussed. In particular, we will focus on the boundedness norm in polynomial Lyapunov functions and its application in Markovian models for community assembly and in models for cellular pathways in multicellular systems. Finally, the usefulness of hybrid mathematical modelling in miscellaneous biological, environmental and public health issues will be discussed.
Seyed Morteza Moghimi^{1}
^{1}MicrowaveSoft Inc., Research, Canada
One of the most efficient solutions to reduce problems in energy area is the demand response. The choice of a proper demand response program is a critical matter in this subject. In this study, we demonstrate the contribution of demand response (DR) program to the development of a distribution network. The paper’s aim is to design and present a suitable demand response program in a distribution network, which include numbers of distributed generation (DG) resources and some electric vehicles (EV) appropriate. The programs is designed for a common distribution system. Then, a multi objective function for an optimization problem is defined. In the paper, there are two scenarios to perform the demand response programs, provided for emergency situation in a scenario of the load response programs and their based reward price is higher in the condition. The other scenario has considered the programs as some DGs source, cooperating in the optimization problem within hours. Optimization problem result prove the energy management performance in the network. Simulation studies are conducted using Genetic algorithm.
Seyed Morteza Moghimi^{1}
^{1}MicrowaveSoft Inc., Research, Canada
Various electricity reforms have been adopted by a number of countries within the last two decades. Iran, as one of those countries, has restructured its electricity market and intensively privatized the distribution companies. This paper discusses the problems of restructuring the electric power sectors and its defects in Iran distribution companies. Furthermore, this paper investigates the threats facing the privatization of electricity distribution companies. These threats include all security, social and economic threats. For this purpose, mismanagement results in distribution companies and the government having to explain its threats so that sovereignty could eliminate the threats or reduce their effects. If done properly and efficiently, it would fulfil its duties, and the rule requires the establishment of necessities that need to be followed and cared for. These requirements are discussed in the paper, the most important of which is nonmonopoly on electricity distribution companies managed by the private sector. The threat of monopolization is also analyzed in a separate section.
FABIO RIZZO^{1}
^{1}G. D'ANNUNZIO UNIVERSITY, ENGINEERING AND GEOLOGY, Italy
Since some years ago in Abruzzo, a region located in the middle part of Italy, the Environment Protection Regional Agency (ARTA), within a national program framework, has been carrying out studies aimed to assess the geographic hazard distribution of indoor radon concentrations and to estimate the possible existence of high concentrations areas (radon prone areas). Radon in buildings can reach relatively high concentrations, depending on a number of factors (ground and housing characteristics, ventilation rates and so on). Through a number of monitoring campaigns a set of more than 1900 measures has been acquired. Thus, on the basis of these public experimental data, different statistical approaches, aimed to estimate the probability to exceed the level of 200 Bq/m3 (lower than 300 Bq/m3, threshold value currently recommended by the Euratom commission for indoor radon risk acceptability), taken just as a working reference value, have been selected and discussed in this paper. Essentially, ‘Monte Carlo Empirical Bayesian approach’, ‘Bootstrap’ and ‘Gibbs samplers’ methods have been applied and the results have been partially compared. Moreover, some insights on the minimum number of samples, needed to assess the probability distribution as reasonable as possible, are provided.
Victor Kireev^{1} , Bakyt Shalabayeva^{2} , Nurbolat Jaichibekov^{3} , Adelina Nizamova^{4} , Zhanserik Kozhabay^{5}
^{1}Bashkir State University, Applied Physics, Russian Federation
^{2}L.N. Gumilyov Eurasian National University, Faculty of mechanics and mathematics, Kazakhstan
^{3}L.N.Gumilyov Eurasian National University, Faculty of mechanics and mathematics, Kazakhstan
^{4}Mavlutov Institute of Mechanics, Mechanics of Multiphase Systems, Russian Federation
^{5}L.N.Gumilyov ENU , Kazakstan, Faculty Mechaniks and mathematics , Kazakhstan
In the present paper the formation of Liesegang structures, i.e. the process of periodic deposition with the mutual diffusion of two reacting chemicals in the presence of an external constant electric field, is studied using numerical modeling. The mathematical model of the process consists of three differential equations of diffusionreaction for the concentrations of the initial components and the resulting precipitate. The kinetics of sedimentation is described in accordance with the Ostwald’s supersaturation theory. The equations of the mathematical model in onedimensional and twodimensional statements were solved numerically using the control volume method using computer code written by the authors in the C ++ language. As a result of numerical simulation in the absence of an electric field, periodic structures were obtained formed of the precipitate, which qualitatively corresponds to the patterns observed in the experiments. It is shown that numerically obtained Liesegang rings satisfy the wellknown laws: the ratio of the distances to neighbouring rings remains constant and there is a power dependence between the distances to the rings and the time of their formation. The influence of the ratio of the concentration of the starting substances and the electric field strength on the nature of the structures formed is investigated. It also has been shown that an increase in the electric field strength leads to anincrease in the number of structures formed.
The research was executed by the grant of the Ministry of education and science of the Republic Kazakhstan: The authors were supported by the grant AP05134098 of SC of the MES of RK.
Bakyt Shalabayeva^{1} , Nurbolat Jaichibekov^{2} , Zarina Kutpanova^{3} , Altynbek Toleu^{4}
^{1}L.N. Gumilyov Eurasian National University, Faculty of mechanics and mathematics, Kazakhstan
^{2}L.N.Gumilyov Eurasian National University, Faculty of mechanics and mathematics, Kazakhstan
^{3}L.N.Gumilyov Eurasian National University, FACULTY OF INFORMATION TECHNOLOGY, Kazakhstan
^{4}L.N.Gumilyov Eurasian National University, Faculty of Information Technology, Kazakhstan
A mathematical model of turbulent motion of a nonhomogeneous flow is constructed. Based on the pulsation energy balance method, a closed system of equations is obtained for calculating the average velocity and turbidity of a nonuniform flow. The calculation of the pulsation characteristics of the flow with a transverse shift is carried out and the analysis of the effect of the impurity on the pulsation structure of the turbulent flow and its effect on the motion of an unmanned aircraft is carried out. Since the safety assessment and service lifetime of an unmanned aerial vehicle cannot exclude the influence of disturbances in the atmosphere when calculating characteristics.
Dionisis Stefanatos^{1}
^{1}University of Patras, Materials Science, Greece
In this work we derive novel ultrafast shortcuts for adiabatic rapid passage for a qubit where the only control variable is the longitudinal $z$field, while the transverse $x$field remains constant. This restrictive framework is pertinent to some important tasks in quantum information processing, for example the design of a high fidelity controlledphase gate can be mapped to the adiabatic quantum control of such a qubit. We study this problem in the adiabatic reference frame and with appropriately rescaled time, using as control input the derivative of the total field polar angle (with respect to rescaled time). We first show that a constant pulse can achieve perfect adiabatic rapid passage at only specific times, corresponding to resonant shortcuts to adiabaticity. We next show that, by using ``onoff" pulsesequences with appropriate characteristics (amplitude, timing, and number of pulses), a perfect fidelity can be obtained for every duration larger than the limit $\pi/\Omega$, where $\Omega$ is the constant transverse $x$field. The proposed methodology exploits the advantages of composite pulses in the rescaled time, while the corresponding control $z$field varies continuously and monotonically in the original time.
The research is implemented through the Operational Program ``Human Resources Development, Education and Lifelong Learning'' and is cofinanced by the European Union (European Social Fund) and Greek national funds (project E$\Delta$BM34, code MIS 5005825).
Nurzhan Saduev^{1} , Vladimir Oskomov^{2} , Sergey Shaulov^{3} , Orazaly Kalikulov^{4} , Askhat Zhumabayev^{5} , Yerzhan Mukhamejanov^{6} , Inesh Kenzhina^{7} , Nurzhan Yerezep^{8} , Shinbolat Utey^{9} , Aleksander Sedov^{10}
^{1}alFarabi Kazakh National University, Physics and Technology Department, Kazakhstan
^{2}KazNU, , Kazakhstan
^{3}Lebedev Physical Institute, , Russian Federation
^{4}KazNU, , Kazakhstan
^{5}KazNU, PhysTech, Kazakhstan
^{6}KazNU, , Kazakhstan
^{7}KazNU, , Kazakhstan
^{8}KazNU, , Kazakhstan
^{9}KazNU, , Kazakhstan
^{10}KazNU, , Kazakhstan
It is planned to expand the existing installation for the registration of extensive air showers (EAS) at the TianShan mountain cosmic rays station located near Almaty, Kazakhstan at altitude of 3340 meters above sea level, in collaboration between Lebedev Physical Institute of the Russian Academy of Sciences (Moscow, Russia), Kazakh National University (Almaty, Kazakhstan), Institute of Physics and Technology (Almaty, Kazakhstan), Institute of Ionosphere (Almaty, Kazakhstan). At present, the system for registration of electromagnetic shower component consists of ∼ 100 detector points built on the basis of plastic scintillator plates with the sensitive area of 0.25m2 and 1 m2, spread equidistantly over ∼104 m2 space. The extension of the installation is planned by adding ionization chambers, 3000x70x130 mm in size. The purpose of adding ionization chambers is to register the hadron component of the shower, in order to determine the lateral distribution of the of EAS cores. Ionization chambers are assembled into a section of two mutually perpendicular layers of 25 ionization chambers in each layer. Such an arrangement of ionization chambers allows us to estimate the size of the EAS core. At the preliminary stage, the aforementioned section of the ionization chambers was modeled on GEANT4. Based on the obtained simulation results, the installation is planned to be created.
This work was supported by the MES RK PTF program “Fundamental and applied studies in related fields of physics of terrestrial, nearearth and atmospheric processes and their practical application” (IRN: #BR05236494).
Bayan Kutum^{1} , Kuralay Yesmakhanova^{2} , Gaukhar Shaikhova^{3}
^{1}L.N.Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
^{2}L. N. Gumilyov Eurasian National University, Department of Mathematical and Computer Modeling, Kazakhstan
^{3}L. N. Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
In this paper, the differentialqdifference 2D Toda lattice is studied. Hirota’s bilinear technique is applied to it. Soliton solutions are constructed through the resulting bilinear form for the differentialqdifference 2D Toda equation. Interactions between soliton solitons are displayed with different choices of variable coefficients.
Nurzhan Serikbayev^{1} , Kuralay Yesmakhanova^{2} , Gaukhar Shaikhova^{3}
^{1}L.N.Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
^{2}L. N. Gumilyov Eurasian National University, Department of Mathematical and Computer Modeling, Kazakhstan
^{3}L. N. Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
In this present work, the extended tanh method is used to construct traveling wave solutions to the generalized nonlinear Schrodinger equation. The extended tanh method is a powerful solution method for obtaining different kind solutions of nonlinear evolution equations. This method can be applied to nonintegrable equations as well as to integrable ones.
Calin Atanasiu^{1}
^{1}National Institute for Laser, Plasma and Radiation Physics, Bucharest, Romania, Plasma Phyics and Nuclear Fusion, Lab. 22, Romania
C.V. Atanasiu$^1$, L.E. Zakharov$^{2,3}$ $^1$National Institute for Laser, Plasma and Radiation Physics, Atomistilor 409, MG36, 077125 MagureleBucharest, Romania $^2$LiWFusion, Princeton, NJ 08543, USA, $^3$Department of Physics, University of Helsinki, Finland The key basis for tokamak plasma disruption modeling is to understand how currents flow to the plasma facing surfaces during plasma disruption events [1]. Disruptions on JET were capable of melting the plasma facing beryllium tiles. Similar wall damage in ITER should be assessed. Accordingly, this paper will address two important disruption effects in both mitigated and nonmitigated disruptions in JET and ITER: (a) excitation of vertical disruption during the current quench (i.e., abnormal plasma current ramp down) and (b) calculation of the wetting zone of plasma and plasma facing surfaces and of potential leading edge effect in power deposition to the invessel tiles during disruptions. Our work is based on the theory of current sharing between plasma and the wall, revealing Hiro currents as the main leading inductive effect in disruptions [2] and the new mathematical model, called Tokamak MHD (TMHD) [3] specially formulated for disruptions simulation as a replacement of conventional MHD. TMHD considers disruption as fast equilibrium evolution by emphasizing the force balance when the plasma inertia plays no role, while conventional MHD uses the plasma inertia (which is 89 orders lower than electromagnetic forces in JET VDEs) as a driver of time evolution causing numerical instabilities. We have found that the most important element of the power deposition is the geometry of the wetting zone and together with 3D equilibrium can be calculated based on TMHD model. [1] L.E. Zakharov, C.V. Atanasiu, K. Lackner, M. Hoelzl, and E. Strumberger, J. Plasma Phys., 81 515810610 (2015). [2] L.E. Zakharov, Phys. of Plasmas, 15 062507 (2008). [3] L.E. Zakharov, X. Li, Phys. Plasmas 22, 6, 062511, (2015).
Tina Vakhitova^{1} , Landish Gadelshina^{2} , Liliya Zulfakarova^{3} , Liliya Garifova^{4} , Sergei Mokichev^{5}
^{1}Kazan Federal University, Institute of Management, Economics and Finance, Russian Federation
^{2}Kazan Federal University, Institute of Management, Economics and Finance, Russian Federation
^{3}Kazan Federal University, Institute of Management, Economics and Finance, Russian Federation
^{4}Kazan Federal University, Institute of Management, Economics and Finance , Russian Federation
^{5}Kazan Federal University, Institute of Management, Economics and Finance, Russian Federation
Now, when the Russian economy entered a positive phase of the cycle in 20172018, with minimal losses to adapt to external shocks arising in previous years. Against the background of improving quantitative indicators in Russia and its individual regions, there is a deterioration in the structural parameters that characterize the quality of economic growth. There are certain methodological and organizational bases of regulation of investment activity in the region, making possible to research the investment efficiency evaluation, considering the time lag on the example of the food industry of the Republic of Tatarstan. The article discusses various mathematical approaches and methods of managing the selection of investment projects, macroeconomic factors that are forming the investing appeal of regions and industries.
JeanClaude Ndogmo^{1}
^{1}University of Venda, Mathematics, South Africa
The lie group classification of second order linear evolution equations is performed and the results are compared with those of the ordinary differential equation counterpart. An emphasis in this comparison is placed on the number of equivalence classes and their canonical forms, the transformation reducing equations in a given equivalence class to the canonical form, and the iterative properties of the equations.
Yuichi Itto^{1}
^{1}Aichi Institute of Technology, Science Division, Center for General Education, Japan
A recent experimental study has elucidated, for RNAprotein particles exhibiting anomalous diffusion in cytoplasm of a living cell, that the distribution of diffusivity fluctuations (i.e., fluctuating diffusion coefficient) obeys an exponential law. There, it has been pointed out that this exponential distribution is the maximal entropy distribution. Here, time evolution of entropy associated with diffusivity fluctuations is discussed. The entropy production rate under the diffusing diffusivity equation, which offers a description of the dynamical behavior of the fluctuations, is explicitly shown to be positive. The timedependent solution of the equation makes it possible to see how the entropy approaches its maximum value. Thus, the exponential law of the fluctuations is dynamically realized as the maximum entropy distribution. The lower bound on a rate that suppresses the entropy production is also presented.
Václav Kůs^{1}
^{1}Czech Technical University in Prague, Department of Mathematics, Czech Republic
In this contribution the statistical inference based on score functions is developed with the aim of future utilization throughout different fields of physics, for example in detector collision data processing or neutrino prongs matching. New score functions are defined by $$ M_\rho (P,P_n)=\sum_{A\in\mathcal{D}_n} P_n(A) \, \rho\left(\frac{P_n(A)P(A)}{P(A)}\right), $$ where $\mathcal{D}_n$ is a sequence of finite or countable partitions, $P$ and $P_n$ are theoretical and empirical probability measures, while the {\em score kernel} $\rho(\cdot)$ is any function with $\rho(0)=0$, nonincreasing on $(1,0)$ and nondecreasing on $(0,\infty)$. The corresponding minimum score estimators are also presented. We find that consistency of different estimators in various score functions leads to the wellknown consistency in commonly used statistical distances or disparity measures between probability distributions. Conditions under which a specific score function pass to $\phi$divergence of theoretical and empirical distribution are formulated. Conversely, each $\phi$divergence is a score function. Furthermore, the minimization of arbitrary divergence score function leads to the classical histogram density estimator and thus can be used to alternative interpretation of histogram based calculations in (high energy) physics. From the score function setup, the KolmogorovSmirnov testing statistics can be achieved through absolute score function under the class of mutually complement interval partitioning of the real line. It means that the most popular statistical methods, such as histogram estimation and Kolmogorov goodness of fit testing used in physics, can be covered by one unifying score based statistical approach. Also, these methods were previously successfully applied to data sets originated from the particular material elasticity testing (nondestructive defectoscopy) within PreisachMayergoyz space modeling.
These results were supported by the research grants SGS18/188/OHK4/3T/14 (MEYS), LTT180001 (MEYS), and GA1609848S (GACR held at Department of Adaptive Systems, UTIA AV CR).
Alexander Herega^{1}
^{1}Odessa Research and Production Center, Research Department , Ukraine
It was proposed the imitation computer model of percolation clusters, which are selforganized in the process of genesis. It is investigated two and threedimensional cluster systems constructed by the Monte Carlo method. Authors studied how properties of model clusters depend on the interaction parameters and the history of it creation. It is shown how a property of clusters depends on the number of acts of particle interaction, aggregation distance, and on system generation speed. It was obtained the analytical dependences of a number of parameters of the cluster system on the level of selforganization, the characteristic values of the correlation length, and the generation rate of the system.
Faycal Ben Adda^{1}
^{1}Community College of Qatar, Department of Maths and Sciences, Qatar
In this paper a case study of an homogeneous and isotropic expanding spacetime that expand via expansion of its basic element raises a fundamental distinction between recession movement of matter and space expansion. We prove that observing matter recession at an accelerating rate is not an indication for the acceleration of the universe expansion. More precisely, we show that the observed acceleration in the recession movement of galaxies is naturally due to the spacetime deceleration. The case study provides us with a possible spacetime with independent movement that might produce the observed behavior of galaxies registered for the redshift $z<0.5$ as well as for the redshift $z>0.5$. This case study calls into question the recent interpretation of the accelerating recession movement of galaxies as indication for the universe acceleration.
DIPALI GHOSH^{1}
^{1}MICHAEL MADHUSUDAN MEMORIAL COLLEGE, DURGAPUR, BURDWAN, WESTBENGAL, INDIA, PHYSICS, India
As an impact of enhanced advancement of the experimental techniques for the study of Positronium (Ps) impact collisional processes, interest has been created among theoreticians to revise the understanding of fundamental particle antiparticle matter interactions. In the present study, sodium atom and ortho positronium (Ps) have been considered as the target and projectile respectively. From the theoretical point of view, the quasione electron models of the loosely bound outermost electron and a stationary effective potential due to frozen inner shell electrons are the appealing features of sodium atom where as the neutral Ps atom by virtue of its light mass provides an advantage over charged particles and heavy projectiles. The present calculations have been done with Distorted Eikonal Approximation [1] and in the frame work of model potential formalism [2, 3]. Since this complete breakup process becomes a four body problem, from the theoretical perspective, it is a bit difficult task. The complexity mainly arises due to the internal degrees of freedom of the projectile Ps which must be taken into account. Furthermore, the present study of simultaneous target and projectile ionization in Ps Sodium system is different from the complete fragmentation of Ps  H system, as the effective model potential of sodium has been considered. The present triple differential cross sections (TDCS) additionally carries the information about the influence of the Ps on the target electron distributions in a static screened potential. Cross sections for positronium impact simultaneous ionization of isolated Na and Ps for the equal energy sharing and the velocity matching between the ejected electrons and the positron, shows that the kinematics depend on both incident energy and collision geometry. References: [1] S. Roy , D. Ghosh and C. Sinha , J. Phys.B, J. Phys. B 38 2145 (2005) [2] G.A. Hart, and P.L. Goodfriend. J. Chem. Phys, 53 448 (1970) [3]. M K Pandey, YC Lin and Y K Ho, J. Phys.B, 49 034007 (2016)
Eduardo Martinez^{1}
^{1}Universidad de Monterrey, Industrial Design, Mexico
Geneva mechanisms have been used to obtain an output intermittent circular motion by the means of a continuous circular motion. It offers the option of having a rest time with between motions in the output link. This paper is intended to provide the geometric resolution of this mechanisms via number of steps and diameter of output link.
Alexey Grushevskii^{1}
^{1}Keldysh Institute of Applied Mathematics of Russian Academy os Sciences, Department of Space flight mechanics and motion control, Russian Federation
Design of lowenergy space missions using gravity assist maneuvers is a key and pressing research field in modern astrodynamics. By their complexity and popularity, the problems addressing the flights to Jovian moons and other outer planets of the Solar system using gravity maneuvers are of particular interest. The reduction of the spacecraft’s asymptotic velocity and the radiation hazard are really main problems for lowcost Delta V  tours for the Galilean moons exploration. In this work multibody flow adaptive synthesis algorithms to overcome ballistic determinism expressed by exist of the Jacobi integral in the restricted three body problem are developed. It is shown that the diversity of the gravity of the ensemble in the Jovian system, not only complicates the accurate ballistic mission analysis, but, when its multibody effective use, allowing you to tailor flowed algorithms for the constructing scenarios of gravity assist maneuvers for interplanetary missions design, including circumvention of dangerous radiation areas, as well as landing at selected Galilean moon at a reasonable cost, resources and time.
Donlawat Sudsom^{1} , Christoph Döpke^{2} , Tomasz Blachowicz^{3} , Andrea Ehrmann^{4}
^{1}Bielefeld University of Applied Sciences, , Germany
^{2}Bielefeld University of Applied Sciences, , Germany
^{3}Silesian University of Technology, , Poland
^{4}Bielefeld University of Applied Sciences, Faculty of Engineering and Mathematics, Germany
Micromagnetic simulations were used to investigate magnetization reversal processes in elongated ferromagnetic nanodots, prepared by combining two halfcircles with a rectangle. The micromagnetic simulation program OOMMF is based on dynamically solving the LandauLifshitzGilbert equation of motion. Material parameters were chosen as typical for Fe (iron). Lateral dimensions were in most simulations chosen as 730 nm x 133 nm, while the dot height was varied between 3 nm and 54 nm. For different inplane angles of the external magnetic field, varying magnetization reversal processes were found with changing dot thickness, offering a possibility to tailor magnetic states by modifying the thickness of the nanodot.
Jesús González^{1} , José Escobar^{2} , Laury García^{3}
^{1}Universidad del Magdalena, Facultad de Ingeniería, Colombia
^{2}Universidad del Magdalena, Facultad de Ciencias Básicas, Colombia
^{3}Universidad del Magdalena, Facultad de Educación, Colombia
A computational method that contributes to the development of cognitive competences, in students of health sciences and biology of Magdalena University, is based on the use of a novel environment of virtual experiences of physical systems. This article investigates the level of learning achieved through the implementation of virtual laboratories that can be used by the user to work in web environments and mobile devices. Conceptual tests were administered to evaluate students' competences before, during and after instruction. We present some perceptions and comments of the students regarding the virtual laboratories of Newtonian mechanics and we conclude on their effectiveness in the development of cognitive competences.
This work was financed by the Universidad del Magdalena (Fonciencias)
Jesús González^{1} , Jhon De la Hoz^{2} , Laury García^{3}
^{1}Universidad del Magdalena, Facultad de Ingeniería, Colombia
^{2}Universidad del Magdalena, Facultad de Ingeniería, Colombia
^{3}Universidad del Magdalena, Facultad de Educación, Colombia
The influence of virtual tools as didactic means towards the study of electromagnetism phenomena takes greater relevance every day at the Universidad del Magdalena due to the inclusion of a visual and dynamic element beyond the reading of physical text books and even the development of laboratories real electromagnetism. This article shows a very positive perception on the part of the engineering students regarding the advanced virtual laboratories of electromagnetism, influencing the learning of physical concepts and the development of cognitive competences. Students' understanding of the concepts of physics in the domain of electromagnetic physics was evaluated in a pre and posttest design involving 60 participants assigned to four experimental groups and 30 participants assigned to the control group. There were two experimental conditions, namely, experimentation with manipulation of real material, experimentation with virtual manipulation, as well as a condition of control (ie, traditional instruction with no virtual experimentation). Conceptual tests were administered to assess students' comprehension before, during and after the application of the virtual laboratories. The analyzes revealed that even though the two experimental conditions promote the conceptualization and correct interpretations of the students' physical concepts in the domain of electromagnetism better than in the control group as expected; we see that, the use of the virtual tool obtains a greater acceptance as this study shows.
This work was financed by the Universidad del Magdalena (Fonciencias).
Henry Sánchez^{1} , Jesús González^{2} , Jhon De la Hoz^{3}
^{1}Universidad del Magdalena, Facultad de Educación, Colombia
^{2}Universidad del Magdalena, Facultad de Ingeniería, Colombia
^{3}Universidad del Magdalena, Facultad de Ingeniería, Colombia
The teaching of robotics in a properly planned and controlled environment has allowed its incursion into academic stages both in secondary and higher education. So it should be added that the teaching process in this area, motivates and enhances the creativity and cooperative work of the students, connecting it directly with mathematics, physics, computers and electronics, I feel this the foundations that underpin and consolidate as you progress in the teaching process. Therefore, one of the objectives of this tool is to create an interest in science and engineering in students. This study was carried out to answer the question: How do professors and undergraduate students describe the usefulness, effectiveness and efficiency of using a robot as a facetoface education technology for a learning experience? Therefore, one of the objectives of this tool is to create an interest in science and engineering in students. This study was carried out to answer the question: How do professors and undergraduate students describe the usefulness, effectiveness and efficiency of using a robot as a facetoface education technology for a learning experience? For this study, two surveys developed by researchers were conducted to evaluate the perceptions of professors and undergraduates in computer science in a learning experience. The results of this study indicate that the teachers and students of degree in computer of the Universidad del Magdalena, consider the use of robots as a facilitator of teaching processes as a highly motivating tool to undertake new teaching strategies and suggest a greater exploration due to the versatility that Robotics offers today.
This work was financed by the Universidad del Magdalena (Fonciencias).
Jesús González^{1} , Henry Sánchez^{2} , Liliana Martínez^{3}
^{1}Universidad del Magdalena, Facultad de Ingeniería, Colombia
^{2}Universidad del Magdalena, Facultad de Educación, Colombia
^{3}Universidad del Magdalena, Facultad de Educación, Colombia
The incorporation of robotics as an educational tool in higher education institutions has represented in recent years an innovative mechanism towards improving the teaching of mathematics, physics and development of control software. This work shows our research about the use of efficient robotics in educational processes in higher education institutions and their perspectives of new innovations towards teaching in engineering, health sciences, biology, chemistry, physics, etc. Bibliometric tools were used to analyze the evolution of educational robotics as an element that contributes to the improvement of teaching and involvement in teaching methods used by teachers.
This work was financed by the Universidad del Magdalena (Fonciencias)
Angela Romero^{1} , Liliana Martínez^{2} , Jesús González^{3}
^{1}Universidad del Magdalena, Facultad Ciencias de la Salud, Colombia
^{2}Universidad del Magdalena, Facultad de Educación, Colombia
^{3}Universidad del Magdalena, Facultad de Ingeniería, Colombia
Laboratory experimentation using robotics plays an essential role in nursing education. This research to answer the question, How do the use of robots by the nursing students influence the effectiveness, the usefulness, and user friendliness of, their satisfaction with, this kind of education technology for a clinical experience. Furthermore, this technology provide additional benefits such as supporting distance learning, improving lab accessibility to handicapped people, and increasing safety for dangerous experimentation. This paper analyzes the literature on robotics labs in nursing education from its beginnings to 2019, identifying the most influential publications, the most researched topics, and how the interest in those topics has evolved along the way. To do so, bibliographical data gathered from ISI Web of Science, Scopus and MedLine have been examined using two prominent bibliometric approaches: science mapping and performance analysis prominent bibliometric approaches: science mapping and performance analysis.
This work was financed by the Universidad del Magdalena (Fonciencias).
Angela Romero^{1} , Damaris Valderrama^{2} , Jesús González^{3}
^{1}Universidad del Magdalena, Facultad Ciencias de la Salud, Colombia
^{2}Universidad del Magdalena, Facultad Ciencias de la Salud, Colombia
^{3}Universidad del Magdalena, Facultad de Ingeniería, Colombia
Clinical simulation is rapidly becoming an important tool in the training of students who pursue a career in nursing as a viable complement or a substitute for practice with living patients. Although simulation can never replace real clinical practice, it is a useful tool to create realism before performing practical skills during patient care. Robotic simulation can create real scenarios that not only test knowledge, but also provide a safe environment for practicing advanced concepts and difficult patient situations. Members of the nursing faculty often have the challenge of preparing nurses for complex environments and working with interdisciplinary teams. In addition, health care administrators expect a basic competency from new nursing graduates who are prepared to function in the complex work environment independently after orientation. An exploratory and descriptive study was conducted using surveys among the students of the nursing program on the use of a humanoid robot for teaching nursing in the laboratory of practices of the Universidad del Magdalena. The results of this study indicate that, in the program and students are positively motivated about the use of technology as a teaching strategy (especially humanoid robots), which suggests a greater exploration of its use in education Nursing.
This work was financed by the ”Universidad del Magdalena (Fonciencias)”
Luminita Moraru^{1}
^{1}University Dunarea de Jos of Galati, Chemistry, Physics and Environment, Romania
This paper presents the simulation results of the infrasound sound energy transfer through various interfaces and discusses on the acoustic transparency of different media as a function of refraction index. Acoustic transparency is defined as the ratio of acoustic power radiated into the structure to the acoustic power emitted by a wave source. The effect of various surfaces on the transmission of infrasound has been studied by numerical simulation. To examine the transmitted homogeneous and inhomogeneous plane waves at the air  textile interface, we used MATLAB 2016 to calculate and plot the contributions of homogeneous and inhomogeneous plane waves as a function of frequency ranging from 3 to 5 Hz. Textiles (composed of natural or synthetic fibers) such as 100%cotton, 50% cotton – 50% flax, 100% wool (felt), nylon1 and nylon2 and flax showing various wave propagation properties were investigated. We found that almost the entire acoustic power passes through the interface of layered structure in the case of wool, cotton and flax, therefore the reflected power can be neglected. In the case of nylons, an amount of acoustic power ranging from 2% to 25% is reflected into air.
The authors acknowledge funding under the Project MESMERISE 700399 from the European Union’s Horizon 2020 research and innovation programme – the Framework Programme for Research and Innovation (20142020).
Jesús Beltrán^{1} , José Escobar^{2} , Jesús González^{3}
^{1}Universidad del Magdalena, Facultad de Ingeniería, Colombia
^{2}Universidad del Magdalena, Facultad de Ciencias Básicas, Colombia
^{3}Universidad del Magdalena, Facultad de Ingeniería, Colombia
The bound states of two particles such as the EarthMoon system, bounded by the gravitational interaction, the hydrogen atom and the positronelectron system, bounded by the electromagnetic interaction, and the quarkantiquark system (whose union is due to the strong interaction), provide physicists with a natural laboratory for the study of fundamental interactions. The interaction potential of these systems is determined and the results are discussed. We approach the study of the EarthMoon system, reviewing the effects of gravitational interaction and the details of Newton's theory on universal gravity. Also, the Theory of Relativity formulated by Albert Einstein, at the beginning of the 20th century. With regard to the hydrogen atom, the Schrödinger equation is used to calculate the spectrum of energy levels, and Feynman diagrams are used to obtain in detail this interaction potential between a proton and an electron (BreitFermi potential) calculating the energy spectrum again and commenting on the results. Then we apply the same method for positronium (process e e+→e e+), which consists of an electron linked to a positron (antiparticle of the electron), and establish the similarities and differences between these two systems. In the framework of the nonrelativistic quark model (MQNR) the quarksantiquarks (heavy) linked states are studied and using the theory of timeindependent perturbations, the Hamiltonian for this system is obtained in order. This potential is analyzed term by term, to observe its validity in the study of the spectra of the systems, comparing the theoretical results obtained with the experimental ones. Then we apply the same method for positronium (process e e+→e e+), which consists of an electron linked to a positron (antiparticle of the electron), and establish the similarities and differences between these two systems. Within the framework of the nonrelativistic quark model (MQNR) the quarksantiquarks (heavy) linked states are studied and using the theory of timeindependent perturbations, the Hamiltonian is obtained for this system to order . This potential is analyzed term by term, to observe its validity in the study of the spectra of the systems, comparing the theoretical results obtained with the experimental ones.
This work was financed by the Universidad del Magdalena (Fonciencias)
Mikhail Dokukin^{1}
^{1}Bauman Moscow State Technical University, Department of Physics, Russian Federation
Need of a research of processes of hashing of liquid metal fusion for receiving homogeneous alloys is proved in this work. The mathematical model of processes of electromagnetic hashing of the fusions received the arc furnace is given. Statement of a special experiment for check of the offered model is considered. Results of calculations and the made experiments on the smallsized arc furnace are given. In the conclusion good coincidence of the offered theory and an experiment is emphasized and recommendations for improvement of the available processing equipment are made.
Jhon De la Hoz^{1} , Jesús Beltrán^{2} , Jesús González^{3}
^{1}Universidad del Magdalena, Facultad de Ingeniería, Colombia
^{2}Universidad del Magdalena, Facultad de Ingeniería, Colombia
^{3}Universidad del Magdalena, Facultad de Ingeniería, Colombia
This paper presents scientometric analysis of superconductivity research output in South America from 1980 to 2019 and compares it with Global output as reported in Web of Science. The study shows that superconductivity research in South America had a steep growth between 1980 and 2000, particularly an abrupt hike in 2005 is noticeable followed by a more or less steady pattern thereafter up to 2019. South America superconductivity papers are analysed bibliometrically to indicate the authorship, collaboration pattern, to identify the major institutions and most relevant journals; apart from identifying the research field or application area of research in superconductivity.
This work was financed by the Universidad del Magdalena (Fonciencias)
Aitzhan Adilbayev^{1}
^{1}L.N.Gumilev Eurasian National University, mathematical and computer modeling, Kazakhstan
This work is aimed at the study of mathematical algorithms of digital signal processing. Digital signal processing is a set of methods of signal processing based on numerical methods using digital computers and software. Any continuous (analogue) signal s (t) can be sampled in time and frequencydigitized, i.e. represented in digital form. The frequencytime transformations are definitely determined through mathematical Fourier transforms. Fourier transform is a transformation that allows decomposing the signal spectrum into harmonic wave functions. They describe the phase or amplitude of each sine wave corresponding to a particular frequency. The phase is the starting point of the curve and the amplitude is its height. Nowadays processing of discrete signals is carried out in frequency area, which considerably reduce the size of the digital equipment and time of processing. The fast Fourier transform algorithm allows reducing the number of operations to calculate the coefficients of the harmonic terms of the signals for a smaller number of operations. In this work, the main aim is to calculate the phase component of analog signals.
Anna Salnikova^{1}
^{1}BMSTU, FN11, Russian Federation
The proposed work is devoted to the study of a defect in a rectangular plate with a cavity, based on the analysis of thermal fields.
The work was carried out with support of state task of Ministry for Science and Education № 9.5387.2017/БЧ
ChenWu Wu^{1}
^{1}Chinese Academy of Sciences, Institute of Mechanics, China
The technology of Laser power beaming is conceptualized to supply power for an aerostat, for which the interactions between monochromatic light (Laser) and atmosphere as well as semiconductor device are modeled. Firstly, an empirical mathematic model is developed on the atmospheric attenuation of Laser and numerical examples presented for typical situations. Then on, a transient coupled mathematic model is established to analyze the thermomechanical effects on lightelectricity conversion in the photovoltaic cell. Finally, the overall energy efficiency is estimated based on the model for such system of Laser power beaming.
This work was supported by the National Natural Science Foundation of China (Grant No. 11572327 and No. 11332011) and the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDA17030100).
Salah Haggag^{1}
^{1}The Egyptian Russian University, Department of Basic Sciences, Egypt
It is shown that some problems of Einstein's field equations of General Relativity can be modeled as optimal control problems. The advantages of adopting such an approach are explained. Some examples are given for problems in relativistic astrophysics and cosmology. Extension to other problems is explored, and difficulties in the formulation of optimal control problems in General Relativity are indicated.
Seyed Morteza Moghimi^{1}
^{1}MicrowaveSoft Inc., Research, Canada
Network structure and active power generation pattern are effective factors on static loadability limit and buses and voltage stability. This paper has been considered IEEE 14bus and 34bus test network in order to create generation and load patterns. Creating generation and load patterns in these two test networks like almost uniform distribution of generation, generation dispersion, the allocate value from the sharing of centralized generation to distributed generations (DGs) and change generation values on the buses, especially putting generation on buses of weak network is investigated. The conducted analyzes on the obtained results from the desired generation patterns, the authors have realized that the generation uniform distribution between buses or change of generations centralized location or allocate percent from generations centralized sharing to distributed generations and putting these generations on load bus, in the event that with accurate and comprehensive investigation is associated improved voltage stability and loadability limit. By analyzing the different modes and review the results of similar patterns in these two systems, the different generation and load patterns effect mechanism of distributed generation units over the behavior of the system in terms loadability limit and voltage stability is achieved.
Faisal Mumtaz^{1} , Fahhad Alharbi^{2}
^{1}Hamad Bin Khalifa University, College of Science and Engineering, Qatar
^{2}Hamad Bin Khalifa University, , Qatar
The treatment of the problems involving unbounded domains (UDs) with vanishing boundary conditions is always challenging. For spectral methods, in particular, very limited basis sets are commonly used for such domains, in which the ranges of the decay rates with acceptable computational efficiency, are very small. Furthermore, maintaining high level of analyticity becomes burdensome. Developing efficient mapped basis tailored for such problem is one of the main strategies to overcome these difficulties. In this work, we present a technique to generate efficient basis sets for UDs. This approach allows using basis sets defined for bounded domains (BDs) for problems in UDs, and hence, providing more freedom to choose from a variety of basis sets. To ensure computational efficiency, the designed transformations cover a wide range of decay rates and allow solving integrals analytically. The method is applied to solve many differential equations encountered frequently in many physics related problems. The results illustrate the efficiency of the developed technique and mapped basis sets.
This work is supported by Qatar National Research Fund (QNRF) under project NPRP X1071027.
Faisal Mumtaz^{1} , Fahhad Alharbi^{2}
^{1}Hamad Bin Khalifa University, College of Science and Engineering, Qatar
^{2}Hamad Bin Khalifa University, , Qatar
A cusp singularity (CS), is a point at which the slope of a continuous curve changes abruptly in sign and magnitude. A particular type of CS, which is the focus of this paper, is where only the sign of the slope is altered while the magnitude of the slope is unchanged. This type of CSs occur in many natural phenomena such as Kato's cusp and particular plasmonics. Solving such problems numerically can be challenging because of the discontinuity in the derivatives. In this paper, we present an efficient spectral method incorporated with transformation (mapping) to handle the cusp problem. The transformation is based on functions that are locally odd around all the cusp points. The idea is to transform functions from C$^0$ continuity to C$^{\text{N}}$ continuity ($\text{N}>1$), and then implement a spectral method to solve the mapped problem without any domain decomposition. The final solution is obtained with inverse mapping.
This work is supported by Qatar National Research Fund (QNRF) under project NPRP X1071027.
joompon bamrungwong^{1}
^{1}KING MONGKUT'S UNIVERSITY OF TECHNOLOGY NORTH BANGKOK, Faculty of Applied Science, Thailand
The swaging process is commonly used in head stack assembly, which is a process that is undertaken to either reduce or increase the diameter of tubes or rods. In the head stack assembly process, a swage boss engages with an arm hole of EBlock. Current hard disk drives have very small tolerances, requiring the swage effect of new hard disk drives to be reduced to as little as possible. In this study, finite element analysis (FEA) was used to reduce the swage effect. At present, FEA and investigative tests indicate that a significant portion of gram changing through swaging is caused by Eblock tip deformation due to swaging. Deformation of the Eblock tip is the result of unbalanced swage forces between the tension and compression suspension. Achieving optimization concepts leads to a new swage plate design to reduce the gramload change of the target and to equalize the swage forces. The FEA results found that gramload change of the target decreased by 35% on the tension side, and by 65% on the compression side through swage by boss tower. The HGA torque out was not different. The suspension flange was also studied. Subsequently, suspension manufacturing is able to bias the suspension as incoming HGA. The flange deformation might be closer to zero after the swaging process.
I would like to thank the Department of Industrial Physics and Medical Instrumentation, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, as well as Seagate Technology (Thailand) Co., Ltd. for supporting this research.
Vasily Kachalov^{1}
^{1}National Research University ”MPEI”, Department of Higher Mathematics, Russian Federation
An important stage in the development of the differential equations analytic theory was the Poincare decomposition theorems. They assert the existence and uniqueness of solutions of initial problems for normal systems of differential equations, which are analytically dependent on a small parameter, provided that the righthand sides are functions analytic in this parameter. If the Cauchy problem is singularly perturbed, then, in the general case, the solution will not be analytic in a small parameter. Nevertheless, within the concept of the regularization method of S. A. Lomov, the conditions for the existence of socalled pseudoanalytic solutions were found.