## Conference submissions

#### Resolving non-homogeneous linear differential equations using undetermined coefficients and variation of parameters by means of GeoGebra

Jorge Olivares Funes 1 , Elvis Valero2

1Universidad de Antofagasta , Departamento de Matemáticas , Chile

###### Abstract

In this paper, we show how non-homogeneous 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 non-homogeneous linear differential equations, because it facilitates the teaching and learning process.

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

Jaykov Foukzon1

1Israel Institute of Technology, Department of mathematics, Israel

###### Abstract

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

#### The error function in fractional differential equations

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

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

###### Abstract

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

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

Franco Lindstron1

1Universidad Nacional de La Plata, Matemática, Argentina

###### Abstract

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

#### Inverse operator for a regular nonlinear dynamics

yehuda roth1

1Oranim college, science, Israel

###### Abstract

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

#### Modelling meson clouds using coherent states

Manuel Fiolhais1

1University of Coimbra, Department of Physics, Portugal

###### Abstract

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

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

Yajuvindra Kumar 1

1Government Girls Degree College, Behat, Mathematics, India

###### Abstract

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

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

Yuriy Dimitrienko1 , Igor Krasnov2 , Kirill Zubarev3

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

###### Abstract

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

#### The soft stadium’s classical dynamics

Julio S Espinoza-Ortiz1 , Roberto E Lagos2

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

###### Abstract

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

###### Acknowledgements:

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

#### Dynamics of a particle periodically driven in the deformable potentiels: stochastic resonance

1University of Yaounde 1, Department of Physics, Cameroon

###### Abstract

In connection with stochastic resonance (SR), we study the dynamics of a particle in the deformable travelling-wave 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 on-site potential (ASDP) and ii) double well deformable on-site 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 intra-well 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.

#### FILTERING AND PARALLEL DIFFUSIVE FRACTAL CHARACTERIZATION OF 2-DIMENSIONAL IMAGES

Hafedh Zghidi1

1Silesian University of Technology , Institute of Informatics, Poland

###### Abstract

The article presents a complete solution for filtering and diffusive fractal characterization of 2-dimensional 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.

#### Modeling the growth of a neural network consisted of diferent types of neural cells,

Pantea Davoudifar1 , Keihanak Rowshan Tabari2

1Research Institute for Astronomy and Astrophysics of Maragha, Astroparticle Physics, Iran (Islamic Republic of)
2Research Institute for Astronomy and Astrophysics of Maragha, , Iran, Islamic Republic Of

###### Abstract

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.

#### Using the fuzzy sets for estimating the angular velocity of a small spacecraft rotation motion

Andry Sedelnikov1 , Ekaterina Khnyryova2

1Samara National Research University, , Russian Federation
2Samara national research university , Further Mathematics , Russian Federation

###### Abstract

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.

#### Theory and Model of Technological Hype Cycles

Avi Messica1 , Asnat Greenstein-Messica 2

1COMAS, Finance and Quantitative Methods, Israel
2Ben-Gurion University of the Negev, Data Science and Information Systems, Israel

###### Abstract

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 case-studies, 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 two-phase 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 data-driven mathematical model that enables to draw useful insights on the rich dynamics of hype cycles.

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

Serena Doria1

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

###### Acknowledgements:

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

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

Tatiana Oblakova1

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

###### Abstract

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

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

Aigul Manapova1

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

###### Abstract

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

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

Aigul Manapova1

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

###### Abstract

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

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

Alexander Bushuev1 , Mikhail Ivanov2 , Dmitrii Korotaev3 , Georgy Resh4

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

###### Abstract

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

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

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

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

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

Zekeriya Sarı1 , Gizem Kalender2 , Serkan Günel3

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

###### Abstract

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

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

Gregory Ivanov1 , Evgeniy Kogut2 , Aleksey Konyashkin3 , Oleg Ryabushkin4

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

###### Abstract

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

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

Yulia Maslennikova1 , Alexey Abramov2

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

###### Abstract

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

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

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

###### Abstract

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

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

Yu Goncharova1 , Ilya Indrupskiy2

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

###### Abstract

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

###### Acknowledgements:

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

Jan Glasa1 , Lukas Valasek2 , Peter Weisenpacher3

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

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

Ivan Shiryaev1 , Ernest Zakirov2 , Ilya Indrupskiy3

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

###### Abstract

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

###### Acknowledgements:

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

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

Georgii Aloian1 , Denis Mukhankov2 , Nikita Kovalenko3 , Oleg Ryabushkin4

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

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

Nikita Kovalenko1 , Georgii Aloian2 , Denis Mukhankov3 , Oleg Ryabushkin4

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

###### Abstract

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

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

Ayguzel Aglyamova1 , Ilya Indrupskiy2

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

###### Abstract

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

###### Acknowledgements:

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

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

Dod Prenga1

1University of Tirana, Physic, Albania

###### Abstract

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

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

Eraldo Marinho1

###### Abstract

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

###### Acknowledgements:

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

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

1University of Antofagasta, Department of Mathematics, Chile
2University of Antofagasta, Department of Physics, Chile

###### Abstract

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

###### Acknowledgements:

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

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

Igor Bataronov1 , Viktor Dezhin2

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

###### Abstract

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

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

Gulnaz Galeeva1

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

###### Abstract

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

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

Gulnaz Galeeva1

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

###### Abstract

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

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

Ayse Humeyra Bilge1

1Kadir Has University, Industrial Engineering, Turkey

###### Abstract

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

###### Acknowledgements:

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

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

Amin Najafi1

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

###### Abstract

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

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

Jader González1 , Fernando Durán2 , Jesús González3

###### Abstract

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

###### Acknowledgements:

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

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

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

###### Abstract

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

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

Jesús González1 , Liliana Martínez2 , Henry Sánchez3

###### Abstract

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

#### Poincare decomposition theorems and the Lomov regularization method

Vasily Kachalov1

1National Research University ”MPEI”, Department of Higher Mathematics, Russian Federation

###### Abstract

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 right-hand 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 so-called pseudo-analytic solutions were found.